Finite Group Databasebeta

← #17202986

Subgroups — #17202986

Order 4352.

2938 conjugacy classes of subgroups.

The subgroup lattice has 1714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763319C211yesmaximal, characteristic, complemented
2C2×#41×Dic17C211yesmaximal, characteristic, complemented
3#14532984C211yesmaximal, characteristic, complemented
4#14532969C211yesmaximal, characteristic, complemented
5#14532894C211yesmaximal, characteristic, complemented
6#14532879C211yesmaximal, characteristic, complemented
7#14532800C211yesmaximal, characteristic, complemented
8#14532785C211yesmaximal, characteristic, complemented
9#14532701C211yesmaximal, characteristic, complemented
10#14532686C211yesmaximal, characteristic, complemented
11#14532612C211yesmaximal, characteristic, complemented
12#14532530C211yesmaximal, characteristic, complemented
13#14532460C211yesmaximal, characteristic, complemented
14#14532326C211yesmaximal, characteristic, complemented
15#14532244C211yesmaximal, characteristic, complemented
16#14532170C211yesmaximal, characteristic, complemented
17#14532099C211yesmaximal, characteristic, complemented
18#14532066C211yesmaximal, characteristic, complemented
19#14532055C211yesmaximal, characteristic, complemented
20#14532027C211yesmaximal, characteristic, complemented
21#14531996C211yesmaximal, characteristic, complemented
22#123×Dic17C211yesmaximal, characteristic, complemented
23#14531303C211yesmaximal, characteristic, complemented
24#121×Dic17C211yesmaximal, characteristic, complemented
25#14531294C211yesmaximal, characteristic, complemented
26#14531289C211yesmaximal, characteristic, complemented
27#14531269C211yesmaximal, characteristic, complemented
28#14531224C211yesmaximal, characteristic, complemented
29#14531220C211yesmaximal, characteristic, complemented
30C2×#11762656C211yesmaximal, characteristic, complemented
31C17×#2430C211yesmaximal, characteristic, complemented
32C22×#63254C2211yescharacteristic
33C23×C4×D17C2211yescharacteristic
34#11763319—28no—
35C2×#10587572C2211yescharacteristic
36C2×#10587569C2211yescharacteristic
37C2×#10587569C2211yescharacteristic
38C2×#10587583C2211yescharacteristic
39C2×#10587610C2211yescharacteristic
40C2×#10587625C2211yescharacteristic
41C2×#10587624C2211yescharacteristic
42C2×#10587623C2211yescharacteristic
43C2×#10587623C2211yescharacteristic
44C2×#10587623C2211yescharacteristic
45#41×Dic17—28no—
46C2×Q8×Dic17C2211yescharacteristic, complemented
47C2×Q8×Dic17C2211yescharacteristic, complemented
48C2×D4×Dic17C2211yescharacteristic
49C2×D4×Dic17C2211yescharacteristic
50C2×D4×Dic17C2211yescharacteristic
51C2×D4×Dic17C2211yescharacteristic
52C2×D4×Dic17C2211yescharacteristic
53C2×D4×Dic17C2211yescharacteristic, complemented
54C2×D4×Dic17C2211yescharacteristic, complemented
55C2×D4×Dic17C2211yescharacteristic, complemented
56C2×#10587567C2211yescharacteristic
57C2×#10587567C2211yescharacteristic
58C2×#10587567C2211yescharacteristic
59C2×#10587567C2211yescharacteristic
60C2×#10587612C2211yescharacteristic
61C2×#10587612C2211yescharacteristic, complemented
62C2×#10587612C2211yescharacteristic, complemented
63C2×#10587578C2211yescharacteristic
64C2×#10587563C2211yescharacteristic, complemented
65C22×#63227C2211yescharacteristic
66C22×#63227C2211yescharacteristic
67C22×C4×Dic17C2211yescharacteristic
68C22×C4×Dic17C2211yescharacteristic
69C22×C4×Dic17C2211yescharacteristic, complemented
70C22×C4×Dic17C2211yescharacteristic, complemented
71#11762751C2211yescharacteristic, complemented
72#11762751C2211yescharacteristic, complemented
73#11762748C2211yescharacteristic, complemented
74#11762746C2211yescharacteristic
75#11762743C2211yescharacteristic, complemented
76#11762741C2211yescharacteristic, complemented
77#11762741C2211yescharacteristic, complemented
78#11762737C2211yescharacteristic, complemented
79#11762736C2211yescharacteristic
80#11762734C2211yescharacteristic, complemented
81#11762732C2211yescharacteristic, complemented
82#11762731C2211yescharacteristic
83#11762731C2211yescharacteristic
84#11762731C2211yescharacteristic
85#11762730C2211yescharacteristic, complemented
86#11762725C2211yescharacteristic
87#11762725C2211yescharacteristic
88#11762725C2211yescharacteristic
89#11762725C2211yescharacteristic
90#11762725C2211yescharacteristic
91#11762724C2211yescharacteristic
92#11762723C2211yescharacteristic, complemented
93#11762721C2211yescharacteristic, complemented
94#11762720C2211yescharacteristic
95#11762720C2211yescharacteristic
96#11762717C2211yescharacteristic
97#11762717C2211yescharacteristic
98#11762717C2211yescharacteristic
99#11762713C2211yescharacteristic, complemented
100#11762713C2211yescharacteristic, complemented
101#11762712C2211yescharacteristic, complemented
102#11762709C2211yescharacteristic
103#11762709C2211yescharacteristic
104#11762709C2211yescharacteristic
105#11762708C2211yescharacteristic, complemented
106#11762706C2211yescharacteristic, complemented
107#11762703C2211yescharacteristic, complemented
108#11762702C2211yescharacteristic, complemented
109#11762702C2211yescharacteristic, complemented
110#11762702C2211yescharacteristic, complemented
111#11762702C2211yescharacteristic, complemented
112#11762701C2211yescharacteristic
113#11762701C2211yescharacteristic
114#11762699C2211yescharacteristic
115#11762699C2211yescharacteristic
116#11762699C2211yescharacteristic
117#11762697C2211yescharacteristic, complemented
118#11762697C2211yescharacteristic, complemented
119#11762696C2211yescharacteristic, complemented
120#11762695C2211yescharacteristic, complemented
121#11762695C2211yescharacteristic, complemented
122#11762694C2211yescharacteristic, complemented
123#11762692C2211yescharacteristic, complemented
124#11762692C2211yescharacteristic, complemented
125#11762692C2211yescharacteristic, complemented
126#11762690C2211yescharacteristic, complemented
127#11762689C2211yescharacteristic
128#11762689C2211yescharacteristic
129#11762689C2211yescharacteristic
130#11762689C2211yescharacteristic
131#11762689C2211yescharacteristic, complemented
132#11762688C2211yescharacteristic
133#11762688C2211yescharacteristic
134#11762688C2211yescharacteristic
135#11762688C2211yescharacteristic
136#11762686C2211yescharacteristic
137#11762686C2211yescharacteristic
138#11762685C2211yescharacteristic
139#11762685C2211yescharacteristic
140#11762684C2211yescharacteristic
141#11762684C2211yescharacteristic, complemented
142#11762683C2211yescharacteristic
143#11762683C2211yescharacteristic
144#11762682C2211yescharacteristic
145#11762682C2211yescharacteristic
146#11762681C2211yescharacteristic
147#11762672C2211yescharacteristic
148#11762670C2211yescharacteristic, complemented
149#11762669C2211yescharacteristic
150#11762667C2211yescharacteristic, complemented
151#11762664C2211yescharacteristic
152C4⋊C4×Dic17C2211yescharacteristic, complemented
153C4⋊C4×Dic17C2211yescharacteristic, complemented
154C4⋊C4×Dic17C2211yescharacteristic, complemented
155#11762660C2211yescharacteristic, complemented
156C22⋊C4×Dic17C2211yescharacteristic
157C22⋊C4×Dic17C2211yescharacteristic, complemented
158C22⋊C4×Dic17C2211yescharacteristic, complemented
159C22⋊C4×Dic17C2211yescharacteristic, complemented
160C22⋊C4×Dic17C2211yescharacteristic, complemented
161C22⋊C4×Dic17C2211yescharacteristic, complemented
162#11762656C2211yescharacteristic
163#11762656C2211yescharacteristic
164#11762656C2211yescharacteristic
165#11762656C2211yescharacteristic
166#11762656C2211yescharacteristic
167#11762656C2211yescharacteristic
168#11762656C2211yescharacteristic
169#11762656C2211yescharacteristic
170#11762656C2211yescharacteristic
171#11762656C2211yescharacteristic
172#11762654C2211yescharacteristic, complemented
173C2×#10587502C2211yescharacteristic
174C22×#41×C17C2211yescharacteristic
175C2×C17×#123C2211yescharacteristic
176C2×C17×#121C2211yescharacteristic
177C2×C17×#121C2211yescharacteristic
178C17×#395C2211yescharacteristic, complemented
179C17×#394C2211yescharacteristic, complemented
180C17×#393C2211yescharacteristic, complemented
181C17×#392C2211yescharacteristic, complemented
182C17×#386C2211yescharacteristic
183C17×#386C2211yescharacteristic
184C17×#386C2211yescharacteristic, complemented
185C17×#386C2211yescharacteristic, complemented
186C17×#385C2211yescharacteristic, complemented
187C17×#385C2211yescharacteristic, complemented
188C2×C17×#95C2211yescharacteristic
189C24×D17C2311yescharacteristic
190C2×#41×C17—24no—
191C2×#41×C17—24no—
192C2×#41×C17—24no—
193C22×Q8×C17C2311yescharacteristic
194C22×D4×C17C2311yescharacteristic
195C22×D4×C17C2311yescharacteristic
196C22×D4×C17C2311yescharacteristic
197C22×D4×C17C2311yescharacteristic
198C22×D4×C17C2311yescharacteristic
199C22×D4×C17C2311yescharacteristic
200C23×C4×C17C2311yescharacteristic
201C23×C4×C17C2311yescharacteristic
202C23×C4×C17C2311yescharacteristic
203C23×C4×C17C2311yescharacteristic
204C23×C4×C17C2311yescharacteristic
205C22×C22⋊D17C2311yescharacteristic
206C22×C22⋊D17C2311yescharacteristic
207C22×C22⋊D17C2311yescharacteristic
208C22×C22⋊D17C2311yescharacteristic
209C22×C22⋊D17C2311yescharacteristic
210C22×C22⋊D17C2311yescharacteristic
211C23×Dic17C2311yescharacteristic
212C23×Dic17C2311yescharacteristic
213C23×Dic17C2311yescharacteristic
214C23×Dic17C2311yescharacteristic
215C23×Dic17C2311yescharacteristic
216C23×Dic17C2311yescharacteristic
217C23×Dic17C2311yescharacteristic
218C23×Dic17C2311yescharacteristic
219C2×#63254—24no—
220C2×#63254—24no—
221C2×#63254—42no—
222C22×C4×D17—24no—
223C22×C4×D17—24no—
224C22×C4×D17—42no—
225C22×C4×D17C2311yescharacteristic
226C22×C4×D17C2311yescharacteristic
227C22×C4×D17C2311yescharacteristic
228C22×C4×D17C2311yescharacteristic
229C22×Dic34C2311yescharacteristic
230C17×#123—24no—
231C17×#121—24no—
232C17×#121—24no—
233C2×C4⋊C4×C17C2311yescharacteristic
234C2×C4⋊C4×C17C2311yescharacteristic
235C2×C4⋊C4×C17C2311yescharacteristic
236C2×C4⋊C4×C17C2311yescharacteristic
237C2×C22⋊C4×C17C2311yescharacteristic
238C2×C22⋊C4×C17C2311yescharacteristic
239C2×C22⋊C4×C17C2311yescharacteristic
240C2×C22⋊C4×C17C2311yescharacteristic
241C2×C22⋊C4×C17C2311yescharacteristic
242C2×C22⋊C4×C17C2311yescharacteristic
243C2×C22⋊C4×C17C2311yescharacteristic
244C2×C22⋊C4×C17C2311yescharacteristic
245C2×C22⋊C4×C17C2311yescharacteristic
246C2×C22⋊C4×C17C2311yescharacteristic
247C2×C22⋊C4×C17C2311yescharacteristic
248C2×C22⋊Dic17C2311yescharacteristic
249C2×C22⋊Dic17C2311yescharacteristic
250C2×C22⋊Dic17C2311yescharacteristic
251C2×C22⋊Dic17C2311yescharacteristic
252C2×C22⋊Dic17C2311yescharacteristic
253C2×C22⋊Dic17C2311yescharacteristic
254C2×C22⋊Dic17C2311yescharacteristic
255C2×C22⋊Dic17C2311yescharacteristic
256C2×C22⋊Dic17C2311yescharacteristic
257C2×C22⋊Dic17C2311yescharacteristic
258C2×C22⋊Dic17C2311yescharacteristic
259C2×C22⋊Dic17C2311yescharacteristic
260C2×C22⋊Dic17C2311yescharacteristic
261C2×C22⋊Dic17C2311yescharacteristic
262C2×C22⋊Dic17C2311yescharacteristic
263C2×C22⋊Dic17C2311yescharacteristic
264C2×C22⋊Dic17C2311yescharacteristic
265Q8×Dic17—24no—
266Q8×Dic17—24no—
267#10587625—24no—
268#10587624—24no—
269#10587623—24no—
270#10587623—24no—
271#10587623—24no—
272D4×Dic17—24no—
273D4×Dic17—24no—
274D4×Dic17—24no—
275D4×Dic17—24no—
276D4×Dic17—24no—
277D4×Dic17—24no—
278D4×Dic17—42no—
279D4×Dic17D418yescomplemented
280C2×#63227—24no—
281C2×#63227—24no—
282C2×#63227C2311yescharacteristic
283C2×#63227C2311yescharacteristic
284C2×#63227C2311yescharacteristic
285C2×#63227C2311yescharacteristic
286C2×#63227C2311yescharacteristic
287C2×#63227C2311yescharacteristic
288C2×#63227C2311yescharacteristic
289C2×#63227C2311yescharacteristic
290C2×#63227C2311yescharacteristic
291C2×#63227C2311yescharacteristic
292C2×#63227C2311yescharacteristic
293C2×#63227C2311yescharacteristic
294C2×#63227C2311yescharacteristic
295C2×#63227C2311yescharacteristic
296C2×#63227C2311yescharacteristic
297C2×#63227C2311yescharacteristic
298C2×#63227C2311yescharacteristic
299C2×#63227C2311yescharacteristic
300#10587612—24no—
301#10587612—24no—
302#10587612—24no—
303C2×C4⋊Dic17C2311yescharacteristic
304C2×C4⋊Dic17C2311yescharacteristic
305C2×C4⋊Dic17C2311yescharacteristic
306C2×C4⋊Dic17C2311yescharacteristic
307C2×C4⋊Dic17C2311yescharacteristic
308C2×C4⋊Dic17C2311yescharacteristic
309C2×C4⋊Dic17C2311yescharacteristic
310C2×C4⋊Dic17C2311yescharacteristic
311C2×C4⋊Dic17C2311yescharacteristic
312C2×C4⋊Dic17C2311yescharacteristic
313C2×C4⋊Dic17C2311yescharacteristic
314C2×C4⋊Dic17C2311yescharacteristic
315#10587610—24no—
316C2×#63225C2311yescharacteristic
317C2×#63225C2311yescharacteristic
318C2×#63225C2311yescharacteristic
319C2×#63225C2311yescharacteristic
320C2×#63225C2311yescharacteristic
321C2×#63225C2311yescharacteristic
322C2×#63225C2311yescharacteristic
323C2×#63225C2311yescharacteristic
324C2×C4×Dic17—24no—
325C2×C4×Dic17—24no—
326C2×C4×Dic17—24no—
327C2×C4×Dic17—42no—
328C2×C4×Dic17C2311yescharacteristic
329C2×C4×Dic17C2311yescharacteristic
330C2×C4×Dic17C2311yescharacteristic
331C2×C4×Dic17C2311yescharacteristic
332C2×C4×Dic17C2311yescharacteristic
333C2×C4×Dic17C2311yescharacteristic
334C2×C4×Dic17C2311yescharacteristic
335C2×C4×Dic17C2311yescharacteristic
336C2×C4×Dic17C2311yescharacteristic
337C2×C4×Dic17C2311yescharacteristic
338C2×C4×Dic17C2311yescharacteristic
339C2×C4×Dic17C2311yescharacteristic
340C2×C4×Dic17C2311yescharacteristic
341C2×C4×Dic17C2311yescharacteristic
342C2×C4×Dic17C2311yescharacteristic
343C2×C4×Dic17C2311yescharacteristic
344C2×C4×Dic17C2311yescharacteristic
345#10587583—24no—
346#10587578—24no—
347#10587572—24no—
348#10587569—24no—
349#10587569—24no—
350#10587567—24no—
351#10587567—24no—
352#10587567—24no—
353#10587567—42no—
354#10587563—42no—
355C17×#95C2311yescharacteristic
356C17×#95C2311yescharacteristic
357C17×#95C2311yescharacteristic
358C17×#95C2311yescharacteristic
359C17×#95C2311yescharacteristic
360C17×#95C2311yescharacteristic
361C17×#95C2311yescharacteristic
362C17×#95C2311yescharacteristic
363#10587502C2311yescharacteristic
364#10587502C2311yescharacteristic
365#10587502C2311yescharacteristic
366#10587502C2311yescharacteristic
367#10587502C2311yescharacteristic
368#10587502C2311yescharacteristic
369#10587502C2311yescharacteristic
370#10587502C2311yescharacteristic
371#10587502C2311yescharacteristic
372#10587502C2311yescharacteristic
373#10587502C2311yescharacteristic
374#10587502C2311yescharacteristic
375#10587502C2311yescharacteristic
376#10587502C2311yescharacteristic
377#10587502C2311yescharacteristic
378#10587502C2311yescharacteristic
379#10587502C2311yescharacteristic
380#10587502C2311yescharacteristic
381#10587502C2311yescharacteristic
382#10587502C2311yescharacteristic
383#10587502C2311yescharacteristic
384#10587502C2311yescharacteristic
385#10587502C2311yescharacteristic
386#10587502C2311yescharacteristic
387#10587502C2311yescharacteristic
388#10587502C2311yescharacteristic
389#10587502C2311yescharacteristic
390#10587502C2311yescharacteristic
391C24×C17C2411yescharacteristic
392C24×C17C2411yescharacteristic
393C24×C17C2411yescharacteristic
394C24×C17C2411yescharacteristic
395C23×D17—22no—
396C23×D17—22no—
397C23×D17—22no—
398C23×D17—22no—
399C23×D17—22no—
400C23×D17—41no—
401C23×D17—41no—
402C23×D17C2411yescharacteristic
403C23×D17C2411yescharacteristic
404#41×C17—232no—
405C2×Q8×C17—22no—
406C2×Q8×C17—22no—
407C2×Q8×C17—22no—
408C2×D4×C17—22no—
409C2×D4×C17—22no—
410C2×D4×C17—22no—
411C2×D4×C17—22no—
412C2×D4×C17—22no—
413C2×D4×C17—22no—
414C2×D4×C17—22no—
415C2×D4×C17—22no—
416C2×D4×C17—22no—
417C2×D4×C17—22no—
418C2×D4×C17—22no—
419C2×D4×C17—22no—
420C2×D4×C17—22no—
421C2×D4×C17—22no—
422C2×D4×C17—41no—
423C2×D4×C17—41no—
424C2×D4×C17C2×D414yes—
425C2×D4×C17#4114yescomplemented
426C22×C4×C17—22no—
427C22×C4×C17—22no—
428C22×C4×C17—22no—
429C22×C4×C17—22no—
430C22×C4×C17—22no—
431C22×C4×C17—22no—
432C22×C4×C17—22no—
433C22×C4×C17—22no—
434C22×C4×C17—22no—
435C22×C4×C17—22no—
436C22×C4×C17—22no—
437C22×C4×C17—22no—
438C22×C4×C17—41no—
439C22×C4×C17—41no—
440C22×C4×C17#4114yescomplemented
441C22×C4×C17C2411yescharacteristic
442C22×C4×C17C2411yescharacteristic
443C22×C4×C17C2411yescharacteristic
444C22×C4×C17C2411yescharacteristic
445C22×C4×C17C2411yescharacteristic
446C22×C4×C17C2411yescharacteristic
447C22×C4×C17C2411yescharacteristic
448C22×C4×C17C2411yescharacteristic
449C22×C4×C17C2411yescharacteristic
450C22×C4×C17C2411yescharacteristic
451C22×C4×C17C2411yescharacteristic
452C2×C22⋊D17—22no—
453C2×C22⋊D17—22no—
454C2×C22⋊D17—22no—
455C2×C22⋊D17—22no—
456C2×C22⋊D17—22no—
457C2×C22⋊D17—22no—
458C2×C22⋊D17—22no—
459C2×C22⋊D17—22no—
460C2×C22⋊D17—22no—
461C2×C22⋊D17—22no—
462C2×C22⋊D17—22no—
463C2×C22⋊D17—22no—
464C2×C22⋊D17—41no—
465C2×C22⋊D17—41no—
466C2×C22⋊D17—41no—
467C2×C22⋊D17—41no—
468C2×C22⋊D17—41no—
469C2×C22⋊D17—41no—
470C22×Dic17—22no—
471C22×Dic17—22no—
472C22×Dic17—22no—
473C22×Dic17—22no—
474C22×Dic17—22no—
475C22×Dic17—22no—
476C22×Dic17—22no—
477C22×Dic17—22no—
478C22×Dic17—22no—
479C22×Dic17—22no—
480C22×Dic17—22no—
481C22×Dic17—22no—
482C22×Dic17—22no—
483C22×Dic17—22no—
484C22×Dic17—22no—
485C22×Dic17—22no—
486C22×Dic17—22no—
487C22×Dic17—41no—
488C22×Dic17—41no—
489C22×Dic17—41no—
490C22×Dic17—41no—
491C22×Dic17—41no—
492C22×Dic17C2×D414yes—
493C22×Dic17C2×D414yes—
494C22×Dic17C2411yescharacteristic
495C22×Dic17C2411yescharacteristic
496C22×Dic17C2411yescharacteristic
497C22×Dic17C2411yescharacteristic
498C22×Dic17C2411yescharacteristic
499C22×Dic17C2411yescharacteristic
500C22×Dic17C2411yescharacteristic
501C22×Dic17C2411yescharacteristic
502C22×Dic17C2411yescharacteristic
503C22×Dic17C2411yescharacteristic
504C22×Dic17C2411yescharacteristic
505C22×Dic17C2411yescharacteristic
506C22×Dic17C2411yescharacteristic
507C22×Dic17C2411yescharacteristic
508#63254—416no—
509C2×C4×D17—22no—
510C2×C4×D17—22no—
511C2×C4×D17—22no—
512C2×C4×D17—22no—
513C2×C4×D17—22no—
514C2×C4×D17—22no—
515C2×C4×D17—22no—
516C2×C4×D17—22no—
517C2×C4×D17—22no—
518C2×C4×D17—416no—
519C2×C4×D17—41no—
520C2×C4×D17—41no—
521C2×C4×D17#4114yescomplemented
522C2×Dic34—22no—
523C2×Dic34—22no—
524C2×Dic34—41no—
525C4⋊C4×C17—22no—
526C4⋊C4×C17—22no—
527C4⋊C4×C17—22no—
528C4⋊C4×C17—22no—
529C22⋊C4×C17—22no—
530C22⋊C4×C17—22no—
531C22⋊C4×C17—22no—
532C22⋊C4×C17—22no—
533C22⋊C4×C17—22no—
534C22⋊C4×C17—22no—
535C22⋊C4×C17—22no—
536C22⋊C4×C17—22no—
537C22⋊C4×C17—22no—
538C22⋊C4×C17—41no—
539C22⋊C4×C17—41no—
540C22⋊Dic17—22no—
541C22⋊Dic17—22no—
542C22⋊Dic17—22no—
543C22⋊Dic17—22no—
544C22⋊Dic17—22no—
545C22⋊Dic17—22no—
546C22⋊Dic17—22no—
547C22⋊Dic17—22no—
548C22⋊Dic17—41no—
549C22⋊Dic17—41no—
550C22⋊Dic17—41no—
551C22⋊Dic17—41no—
552C22⋊Dic17—41no—
553C22⋊Dic17—41no—
554C22⋊Dic17—41no—
555C22⋊Dic17C2×D414yes—
556C22⋊Dic17C2×D414yes—
557#63227—22no—
558#63227—22no—
559#63227—22no—
560#63227—22no—
561#63227—22no—
562#63227—22no—
563#63227—22no—
564#63227—22no—
565#63227—22no—
566#63227—22no—
567#63227—22no—
568#63227—22no—
569#63227—22no—
570#63227—22no—
571#63227—22no—
572#63227—41no—
573#63227—41no—
574#63227#4114yescomplemented
575C4⋊Dic17—22no—
576C4⋊Dic17—22no—
577C4⋊Dic17—22no—
578C4⋊Dic17—22no—
579C4⋊Dic17—22no—
580C4⋊Dic17—22no—
581C4⋊Dic17—22no—
582C4⋊Dic17—22no—
583C4⋊Dic17—22no—
584C4⋊Dic17—41no—
585C4⋊Dic17—41no—
586C4⋊Dic17C2×D414yes—
587#63225—22no—
588#63225—22no—
589#63225—22no—
590#63225—22no—
591#63225—41no—
592#63225—41no—
593#63225—41no—
594#63225—41no—
595C4×Dic17—22no—
596C4×Dic17—22no—
597C4×Dic17—22no—
598C4×Dic17—22no—
599C4×Dic17—22no—
600C4×Dic17—22no—
601C4×Dic17—22no—
602C4×Dic17—22no—
603C4×Dic17—22no—
604C4×Dic17—22no—
605C4×Dic17—22no—
606C4×Dic17—22no—
607C4×Dic17—22no—
608C4×Dic17—22no—
609C4×Dic17—41no—
610C4×Dic17—41no—
611C4×Dic17C2×D414yes—
612#34732—171nomaximal, Sylow
613C23×C17—21no—
614C23×C17—21no—
615C23×C17—21no—
616C23×C17—21no—
617C23×C17—21no—
618C23×C17—21no—
619C23×C17—21no—
620C23×C17—21no—
621C23×C17—21no—
622C23×C17—21no—
623C23×C17—21no—
624C23×C17—21no—
625C23×C17—21no—
626C23×C17—21no—
627C23×C17—21no—
628C23×C17—21no—
629C23×C17—21no—
630C23×C17—21no—
631C23×C17—21no—
632C23×C17—21no—
633C23×C17—21no—
634C23×C17—21no—
635C23×C17—21no—
636C23×C17C22×D412yes—
637C23×C17C22×D412yes—
638C23×C17C2×#4112yes—
639C23×C17C2×#4112yes—
640C23×C17C2×#4112yes—
641C23×C17C2511yescharacteristic
642C22×D17—28no—
643C22×D17—21no—
644C22×D17—21no—
645C22×D17—21no—
646C22×D17—21no—
647C22×D17—21no—
648C22×D17—21no—
649C22×D17—21no—
650C22×D17—21no—
651C22×D17—21no—
652C22×D17—21no—
653C22×D17—21no—
654C22×D17—21no—
655C22×D17—44no—
656C22×D17—44no—
657C22×D17—44no—
658C22×D17—44no—
659C22×D17—44no—
660C22×D17—44no—
661C22×D17C2×#4112yes—
662C22×D17C2×#4112yes—
663Q8×C17—28no—
664D4×C17—28no—
665D4×C17—28no—
666D4×C17—28no—
667D4×C17—44no—
668D4×C17—44no—
669D4×C17—44no—
670C2×C4×C17—28no—
671C2×C4×C17—28no—
672C2×C4×C17—28no—
673C2×C4×C17—21no—
674C2×C4×C17—21no—
675C2×C4×C17—21no—
676C2×C4×C17—21no—
677C2×C4×C17—21no—
678C2×C4×C17—21no—
679C2×C4×C17—21no—
680C2×C4×C17—21no—
681C2×C4×C17—21no—
682C2×C4×C17—21no—
683C2×C4×C17—21no—
684C2×C4×C17—21no—
685C2×C4×C17—21no—
686C2×C4×C17—21no—
687C2×C4×C17—21no—
688C2×C4×C17—21no—
689C2×C4×C17—21no—
690C2×C4×C17—21no—
691C2×C4×C17—21no—
692C2×C4×C17—21no—
693C2×C4×C17—21no—
694C2×C4×C17—21no—
695C2×C4×C17—21no—
696C2×C4×C17—21no—
697C2×C4×C17—21no—
698C2×C4×C17—21no—
699C2×C4×C17—21no—
700C2×C4×C17—44no—
701C2×C4×C17—44no—
702C2×C4×C17C22×D412yes—
703C2×C4×C17C2×#4112yes—
704C2×C4×C17C2×#4112yes—
705C2×C4×C17C2×#4112yes—
706C2×C4×C17C2×#4112yes—
707C2×C4×C17C2×#4112yes—
708C22⋊D17—44no—
709C22⋊D17—44no—
710C22⋊D17—44no—
711C22⋊D17—44no—
712C22⋊D17—44no—
713C22⋊D17—44no—
714C2×Dic17—21no—
715C2×Dic17—21no—
716C2×Dic17—21no—
717C2×Dic17—21no—
718C2×Dic17—21no—
719C2×Dic17—21no—
720C2×Dic17—21no—
721C2×Dic17—21no—
722C2×Dic17—28no—
723C2×Dic17—28no—
724C2×Dic17—21no—
725C2×Dic17—21no—
726C2×Dic17—21no—
727C2×Dic17—21no—
728C2×Dic17—21no—
729C2×Dic17—21no—
730C2×Dic17—21no—
731C2×Dic17—21no—
732C2×Dic17—21no—
733C2×Dic17—21no—
734C2×Dic17—21no—
735C2×Dic17—21no—
736C2×Dic17—21no—
737C2×Dic17—21no—
738C2×Dic17—21no—
739C2×Dic17—21no—
740C2×Dic17—21no—
741C2×Dic17—21no—
742C2×Dic17—21no—
743C2×Dic17—21no—
744C2×Dic17—21no—
745C2×Dic17—21no—
746C2×Dic17—21no—
747C2×Dic17—21no—
748C2×Dic17—21no—
749C2×Dic17—21no—
750C2×Dic17—21no—
751C2×Dic17—44no—
752C2×Dic17—44no—
753C2×Dic17—44no—
754C2×Dic17—44no—
755C2×Dic17—44no—
756C2×Dic17—44no—
757C2×Dic17C22×D412yes—
758C2×Dic17C22×D412yes—
759C2×Dic17C22×D412yes—
760C2×Dic17C22×D412yes—
761C2×Dic17C2×#4112yes—
762C2×Dic17C2×#4112yes—
763C2×Dic17H(5,𝔽2)12yes—
764C4×D17—28no—
765C4×D17—44no—
766C4×D17—44no—
767C4×D17—44no—
768Dic34—44no—
769C2×#525—171no—
770C2×C4×#41—171no—
771#2477—171no—
772#2476—171no—
773#2471—171no—
774#2470—171no—
775#2465—171no—
776#2464—171no—
777#2458—171no—
778#2457—171no—
779#2450—171no—
780#2444—171no—
781#2438—171no—
782#2430D1711yescharacteristic, complemented
783#2424—171no—
784#2418—171no—
785#2411—171no—
786#2404—171no—
787#2398—171no—
788#2396—171no—
789#2392—171no—
790#2388—171no—
791C4×#123—171no—
792C4×#123—171no—
793C4×#121—171no—
794C4×#121—171no—
795C4×#120—171no—
796#2297—171no—
797#2290—171no—
798#2290—171no—
799C2×C4×C22⋊C4—171no—
800C22×C17—22no—
801C22×C17—22no—
802C22×C17—22no—
803C22×C17—22no—
804C22×C17—22no—
805C22×C17—22no—
806C22×C17—22no—
807C22×C17—22no—
808C22×C17—22no—
809C22×C17—22no—
810C22×C17—22no—
811C22×C17—22no—
812C22×C17—41no—
813C22×C17—41no—
814C22×C17—41no—
815C22×C17—41no—
816C22×C17—41no—
817C22×C17—41no—
818C22×C17—41no—
819C22×C17—41no—
820C22×C17—41no—
821C22×C17—41no—
822C22×C17—41no—
823C22×C17—41no—
824C22×C17—41no—
825C22×C17—41no—
826C22×C17—41no—
827C22×C17#52514yes—
828C22×C17C23×D411yescharacteristic
829C22×C17C22×#4111yescharacteristic
830C22×C17C22×#4111yescharacteristic
831C22×C17C22×#4111yescharacteristic
832C22×C17C22×#4111yescharacteristic
833C22×C17C2×H(5,𝔽2)11yescharacteristic
834C22×C17#58511yescharacteristic
835C2×D17—22no—
836C2×D17—22no—
837C2×D17—22no—
838C2×D17—22no—
839C2×D17—22no—
840C2×D17—22no—
841C2×D17—416no—
842C2×D17—41no—
843C2×D17—41no—
844C2×D17—41no—
845C2×D17—41no—
846C2×D17—41no—
847C2×D17—41no—
848C2×D17—41no—
849C2×D17—41no—
850C4×C17—22no—
851C4×C17—22no—
852C4×C17—22no—
853C4×C17—22no—
854C4×C17—22no—
855C4×C17—22no—
856C4×C17—41no—
857C4×C17—41no—
858C4×C17—41no—
859C4×C17—41no—
860C4×C17—41no—
861Dic17—22no—
862Dic17—22no—
863Dic17—22no—
864Dic17—22no—
865Dic17—41no—
866Dic17—41no—
867Dic17—41no—
868Dic17—41no—
869Dic17—41no—
870Dic17—41no—
871Dic17—41no—
872Dic17—41no—
873Dic17—41no—
874Dic17#54614yes—
875C22×#41—171no—
876C22×#41C2×D1711yescharacteristic
877C24×C4—171no—
878#525—348no—
879C2×#123—171no—
880C2×#123—171no—
881C2×#123—171no—
882C2×#123C2×D1711yescharacteristic
883C2×C22⋊Q8—171no—
884C2×C22⋊Q8—171no—
885C2×#121—171no—
886C2×#121—171no—
887C2×#121C2×D1711yescharacteristic
888C2×#121C2×D1711yescharacteristic
889C2×#120—171no—
890C2×#120—171no—
891C2×#120—171no—
892C4×#41—348no—
893C2×C4×Q8—171no—
894C2×C4×Q8—171no—
895C2×C4×D4—171no—
896C2×C4×D4—171no—
897C2×C4×D4—171no—
898C2×C4×D4—171no—
899C2×C4×D4—171no—
900C2×C4×D4—171no—
901C2×C4×D4—171no—
902C2×C4×D4—171no—
903C2×C4×D4—171no—
904C2×C4×D4—171no—
905C2×C4×D4—171no—
906C2×C4×D4—171no—
907C2×#117—171no—
908C2×#117—171no—
909C2×#117—171no—
910C2×#117—171no—
911C2×#117—171no—
912C22×C22⋊C4—171no—
913C22×C22⋊C4—171no—
914C22×C42—171no—
915C22×C42—171no—
916C22×C42—171no—
917C22×C42—171no—
918#400—171no—
919#400—171no—
920#400—171no—
921#399—171no—
922#398—171no—
923#398—171no—
924#398—171no—
925#397—171no—
926#397—171no—
927#397—171no—
928#396—171no—
929#396—171no—
930#396—171no—
931#396—171no—
932#395—171no—
933#395C2×D1711yescharacteristic, complemented
934#394—171no—
935#394—171no—
936#394—171no—
937#394—171no—
938#394—171no—
939#394—171no—
940#394—171no—
941#394C2×D1711yescharacteristic, complemented
942#393—171no—
943#393—171no—
944#393—171no—
945#393C2×D1711yescharacteristic, complemented
946#392—171no—
947#392—171no—
948#392—171no—
949#392C2×D1711yescharacteristic, complemented
950#391—171no—
951#391—171no—
952#390—171no—
953#390—171no—
954#390—171no—
955#390—171no—
956#389—171no—
957#389—171no—
958#388—171no—
959#388—171no—
960#388—171no—
961#388—171no—
962#388—171no—
963#388—171no—
964#388—171no—
965#388—171no—
966#388—171no—
967#388—171no—
968#388—171no—
969#388—171no—
970#387—171no—
971#387—171no—
972#387—171no—
973#387—171no—
974#387—171no—
975#387—171no—
976#387—171no—
977#387—171no—
978#386—171no—
979#386—171no—
980#386—171no—
981#386—171no—
982#386—171no—
983#386—171no—
984#386—171no—
985#386—171no—
986#386—171no—
987#386—171no—
988#386—171no—
989#386—171no—
990#386—171no—
991#386C2×D1711yescharacteristic
992#386C2×D1711yescharacteristic
993#386C2×D1711yescharacteristic, complemented
994#386C2×D1711yescharacteristic, complemented
995#385—171no—
996#385—171no—
997#385—171no—
998#385—171no—
999#385—171no—
1000#385—171no—
1001#385—171no—
1002#385C2×D1711yescharacteristic, complemented
1003#385C2×D1711yescharacteristic, complemented
1004#381—171no—
1005#381—171no—
1006#380—171no—
1007#380—171no—
1008#379—171no—
1009C4×C4⋊C4—171no—
1010C4×C4⋊C4—171no—
1011C4×C4⋊C4—171no—
1012C4×C4⋊C4—171no—
1013C4×C22⋊C4—171no—
1014C4×C22⋊C4—171no—
1015C4×C22⋊C4—171no—
1016C4×C22⋊C4—171no—
1017C4×C22⋊C4—171no—
1018C4×C22⋊C4—171no—
1019C4×C22⋊C4—171no—
1020C4×C22⋊C4—171no—
1021C4×C22⋊C4—171no—
1022C4×C22⋊C4—171no—
1023C4×C22⋊C4—171no—
1024C4×C22⋊C4—171no—
1025C4×C22⋊C4—171no—
1026C4×C22⋊C4—171no—
1027C4×C22⋊C4—171no—
1028C4×C22⋊C4—171no—
1029#376—171no—
1030C2×#95—171no—
1031C2×#95C2×D1711yescharacteristic
1032C2×C17—24no—
1033C2×C17—42no—
1034C2×C17—42no—
1035C2×C17—81no—
1036C2×C17C2×#52511yescharacteristic
1037C2×C17#344411yescharacteristic
1038C2×C17#346011yescharacteristic
1039C2×C17C2×#54611yescharacteristic
1040C2×C17D4×#4111yescharacteristic
1041C2×C17#347511yescharacteristic
1042C2×C17#348111yescharacteristic
1043D17—42no—
1044D17—42no—
1045C25—171no—
1046C2×#41—24no—
1047C2×#41—24no—
1048C2×#41—24no—
1049C2×#41—344no—
1050C2×#41—344no—
1051C2×#41—682no—
1052C22×Q8—171no—
1053C22×Q8C22×D1711yescharacteristic
1054C22×D4—171no—
1055C22×D4—171no—
1056C22×D4—171no—
1057C22×D4—171no—
1058C22×D4—171no—
1059C22×D4—171no—
1060C22×D4C22×D1711yescharacteristic
1061C22×D4C22×D1711yescharacteristic
1062C22×D4C22×D1711yescharacteristic
1063C22×D4C22×D1711yescharacteristic
1064C22×D4C22×D1711yescharacteristic
1065C22×D4C22×D1711yescharacteristic
1066C23×C4—171no—
1067C23×C4—171no—
1068C23×C4—171no—
1069C23×C4—171no—
1070C23×C4—171no—
1071C23×C4—171no—
1072C23×C4—171no—
1073C23×C4—171no—
1074C23×C4—171no—
1075C23×C4—171no—
1076C23×C4—171no—
1077C23×C4—171no—
1078C23×C4—344no—
1079C23×C4—344no—
1080C23×C4—682no—
1081C23×C4C22×D1711yescharacteristic
1082C23×C4C22×D1711yescharacteristic
1083C23×C4C22×D1711yescharacteristic
1084C23×C4C22×D1711yescharacteristic
1085C23×C4C22×D1711yescharacteristic
1086#123—24no—
1087#123—344no—
1088#123—344no—
1089#123—344no—
1090C22⋊Q8—344no—
1091C22⋊Q8—344no—
1092#121—24no—
1093#121—24no—
1094#121—344no—
1095#121—344no—
1096#120—344no—
1097#120—344no—
1098#120—344no—
1099C4×Q8—344no—
1100C4×Q8—344no—
1101C4×D4—178no—
1102C4×D4—344no—
1103C4×D4—344no—
1104C4×D4—344no—
1105C4×D4—344no—
1106C4×D4—344no—
1107C4×D4—344no—
1108C4×D4—344no—
1109C4×D4—344no—
1110C4×D4—344no—
1111C4×D4—682no—
1112C4×D4—682no—
1113#117—344no—
1114#117—344no—
1115#117—344no—
1116#117—344no—
1117#117—682no—
1118C2×C4⋊C4—171no—
1119C2×C4⋊C4—171no—
1120C2×C4⋊C4—171no—
1121C2×C4⋊C4—171no—
1122C2×C4⋊C4—171no—
1123C2×C4⋊C4—171no—
1124C2×C4⋊C4—171no—
1125C2×C4⋊C4—171no—
1126C2×C4⋊C4—171no—
1127C2×C4⋊C4—171no—
1128C2×C4⋊C4—171no—
1129C2×C4⋊C4—171no—
1130C2×C4⋊C4—171no—
1131C2×C4⋊C4—171no—
1132C2×C4⋊C4—171no—
1133C2×C4⋊C4—171no—
1134C2×C4⋊C4—171no—
1135C2×C4⋊C4—171no—
1136C2×C4⋊C4—171no—
1137C2×C4⋊C4—171no—
1138C2×C4⋊C4C22×D1711yescharacteristic
1139C2×C4⋊C4C22×D1711yescharacteristic
1140C2×C4⋊C4C22×D1711yescharacteristic
1141C2×C4⋊C4C22×D1711yescharacteristic
1142C2×C22⋊C4—171no—
1143C2×C22⋊C4—171no—
1144C2×C22⋊C4—171no—
1145C2×C22⋊C4—171no—
1146C2×C22⋊C4—171no—
1147C2×C22⋊C4—171no—
1148C2×C22⋊C4—171no—
1149C2×C22⋊C4—171no—
1150C2×C22⋊C4—171no—
1151C2×C22⋊C4—171no—
1152C2×C22⋊C4—171no—
1153C2×C22⋊C4—171no—
1154C2×C22⋊C4—171no—
1155C2×C22⋊C4—171no—
1156C2×C22⋊C4—171no—
1157C2×C22⋊C4—171no—
1158C2×C22⋊C4—171no—
1159C2×C22⋊C4—171no—
1160C2×C22⋊C4—171no—
1161C2×C22⋊C4—171no—
1162C2×C22⋊C4—171no—
1163C2×C22⋊C4—171no—
1164C2×C22⋊C4—171no—
1165C2×C22⋊C4—171no—
1166C2×C22⋊C4—171no—
1167C2×C22⋊C4—171no—
1168C2×C22⋊C4—171no—
1169C2×C22⋊C4—171no—
1170C2×C22⋊C4—171no—
1171C2×C22⋊C4—171no—
1172C2×C22⋊C4—171no—
1173C2×C22⋊C4—171no—
1174C2×C22⋊C4—171no—
1175C2×C22⋊C4—171no—
1176C2×C22⋊C4—171no—
1177C2×C22⋊C4—344no—
1178C2×C22⋊C4—344no—
1179C2×C22⋊C4C22×D1711yescharacteristic
1180C2×C22⋊C4C22×D1711yescharacteristic
1181C2×C22⋊C4C22×D1711yescharacteristic
1182C2×C22⋊C4C22×D1711yescharacteristic
1183C2×C22⋊C4C22×D1711yescharacteristic
1184C2×C22⋊C4C22×D1711yescharacteristic
1185C2×C22⋊C4C22×D1711yescharacteristic
1186C2×C22⋊C4C22×D1711yescharacteristic
1187C2×C22⋊C4C22×D1711yescharacteristic
1188C2×C22⋊C4C22×D1711yescharacteristic
1189C2×C22⋊C4C22×D1711yescharacteristic
1190C2×C42—171no—
1191C2×C42—171no—
1192C2×C42—171no—
1193C2×C42—171no—
1194C2×C42—171no—
1195C2×C42—171no—
1196C2×C42—171no—
1197C2×C42—171no—
1198C2×C42—171no—
1199C2×C42—171no—
1200C2×C42—171no—
1201C2×C42—171no—
1202C2×C42—171no—
1203C2×C42—171no—
1204C2×C42—171no—
1205C2×C42—171no—
1206C2×C42—171no—
1207C2×C42—344no—
1208C2×C42—344no—
1209C2×C42—344no—
1210C2×C42—682no—
1211#95—171no—
1212#95—171no—
1213#95—171no—
1214#95—171no—
1215#95—171no—
1216#95—171no—
1217#95—171no—
1218#95—171no—
1219#95—171no—
1220#95—171no—
1221#95—171no—
1222#95—171no—
1223#95—171no—
1224#95—171no—
1225#95—171no—
1226#95—171no—
1227#95—171no—
1228#95—171no—
1229#95—171no—
1230#95—171no—
1231#95—171no—
1232#95—171no—
1233#95—171no—
1234#95—171no—
1235#95—171no—
1236#95—171no—
1237#95—171no—
1238#95—171no—
1239#95C22×D1711yescharacteristic
1240#95C22×D1711yescharacteristic
1241#95C22×D1711yescharacteristic
1242#95C22×D1711yescharacteristic
1243#95C22×D1711yescharacteristic
1244#95C22×D1711yescharacteristic
1245#95C22×D1711yescharacteristic
1246#95C22×D1711yescharacteristic
1247C17#3473211yescharacteristic, complemented, Sylow
1248C24—171no—
1249C24—171no—
1250C24—342no—
1251C24—342no—
1252C24—342no—
1253C24—342no—
1254C24—342no—
1255C24—681no—
1256C24—681no—
1257C24C23×D1711yescharacteristic
1258C24C23×D1711yescharacteristic
1259C24C23×D1711yescharacteristic
1260C24C23×D1711yescharacteristic
1261#41—232no—
1262#41—6816no—
1263C2×Q8—22no—
1264C2×Q8—22no—
1265C2×Q8—22no—
1266C2×Q8—342no—
1267C2×Q8—342no—
1268C2×Q8—681no—
1269C2×D4—22no—
1270C2×D4—22no—
1271C2×D4—22no—
1272C2×D4—22no—
1273C2×D4—22no—
1274C2×D4—22no—
1275C2×D4—22no—
1276C2×D4—22no—
1277C2×D4—22no—
1278C2×D4—22no—
1279C2×D4—22no—
1280C2×D4—22no—
1281C2×D4—22no—
1282C2×D4—22no—
1283C2×D4—41no—
1284C2×D4—41no—
1285C2×D4—342no—
1286C2×D4—342no—
1287C2×D4—342no—
1288C2×D4—342no—
1289C2×D4—342no—
1290C2×D4—342no—
1291C2×D4—342no—
1292C2×D4—342no—
1293C2×D4—342no—
1294C2×D4—342no—
1295C2×D4—342no—
1296C2×D4—342no—
1297C2×D4—681no—
1298C2×D4—681no—
1299C2×D4—681no—
1300C2×D4—681no—
1301C2×D4—681no—
1302C2×D4—681no—
1303C2×D4D4×D1714yes—
1304C2×D4#6325414yescomplemented
1305C22×C4—22no—
1306C22×C4—22no—
1307C22×C4—22no—
1308C22×C4—22no—
1309C22×C4—22no—
1310C22×C4—22no—
1311C22×C4—22no—
1312C22×C4—22no—
1313C22×C4—22no—
1314C22×C4—22no—
1315C22×C4—22no—
1316C22×C4—22no—
1317C22×C4—41no—
1318C22×C4—41no—
1319C22×C4—171no—
1320C22×C4—174no—
1321C22×C4—174no—
1322C22×C4—171no—
1323C22×C4—171no—
1324C22×C4—171no—
1325C22×C4—171no—
1326C22×C4—174no—
1327C22×C4—171no—
1328C22×C4—171no—
1329C22×C4—171no—
1330C22×C4—171no—
1331C22×C4—171no—
1332C22×C4—171no—
1333C22×C4—171no—
1334C22×C4—171no—
1335C22×C4—171no—
1336C22×C4—342no—
1337C22×C4—342no—
1338C22×C4—342no—
1339C22×C4—342no—
1340C22×C4—342no—
1341C22×C4—342no—
1342C22×C4—342no—
1343C22×C4—342no—
1344C22×C4—342no—
1345C22×C4—342no—
1346C22×C4—342no—
1347C22×C4—342no—
1348C22×C4—342no—
1349C22×C4—342no—
1350C22×C4—342no—
1351C22×C4—342no—
1352C22×C4—342no—
1353C22×C4—342no—
1354C22×C4—342no—
1355C22×C4—342no—
1356C22×C4—342no—
1357C22×C4—342no—
1358C22×C4—342no—
1359C22×C4—342no—
1360C22×C4—342no—
1361C22×C4—342no—
1362C22×C4—681no—
1363C22×C4—681no—
1364C22×C4—6816no—
1365C22×C4—681no—
1366C22×C4—681no—
1367C22×C4—681no—
1368C22×C4—681no—
1369C22×C4—681no—
1370C22×C4#6325414yescomplemented
1371C22×C4C23×D1711yescharacteristic
1372C22×C4C23×D1711yescharacteristic
1373C22×C4C23×D1711yescharacteristic
1374C22×C4C23×D1711yescharacteristic
1375C22×C4C23×D1711yescharacteristic
1376C22×C4C23×D1711yescharacteristic
1377C22×C4C23×D1711yescharacteristic
1378C22×C4C23×D1711yescharacteristic
1379C22×C4C23×D1711yescharacteristic
1380C22×C4C23×D1711yescharacteristic
1381C22×C4C23×D1711yescharacteristic
1382C4⋊C4—22no—
1383C4⋊C4—22no—
1384C4⋊C4—22no—
1385C4⋊C4—22no—
1386C4⋊C4—174no—
1387C4⋊C4—342no—
1388C4⋊C4—342no—
1389C4⋊C4—342no—
1390C4⋊C4—342no—
1391C4⋊C4—342no—
1392C4⋊C4—342no—
1393C4⋊C4—342no—
1394C4⋊C4—342no—
1395C4⋊C4—342no—
1396C4⋊C4—342no—
1397C4⋊C4—342no—
1398C4⋊C4—342no—
1399C4⋊C4—342no—
1400C4⋊C4—681no—
1401C4⋊C4—681no—
1402C4⋊C4—681no—
1403C4⋊C4—681no—
1404C4⋊C4—681no—
1405C4⋊C4—681no—
1406C22⋊C4—22no—
1407C22⋊C4—22no—
1408C22⋊C4—22no—
1409C22⋊C4—22no—
1410C22⋊C4—22no—
1411C22⋊C4—22no—
1412C22⋊C4—22no—
1413C22⋊C4—22no—
1414C22⋊C4—22no—
1415C22⋊C4—41no—
1416C22⋊C4—41no—
1417C22⋊C4—174no—
1418C22⋊C4—174no—
1419C22⋊C4—174no—
1420C22⋊C4—342no—
1421C22⋊C4—342no—
1422C22⋊C4—342no—
1423C22⋊C4—342no—
1424C22⋊C4—342no—
1425C22⋊C4—342no—
1426C22⋊C4—342no—
1427C22⋊C4—342no—
1428C22⋊C4—342no—
1429C22⋊C4—342no—
1430C22⋊C4—342no—
1431C22⋊C4—342no—
1432C22⋊C4—342no—
1433C22⋊C4—342no—
1434C22⋊C4—342no—
1435C22⋊C4—342no—
1436C22⋊C4—342no—
1437C22⋊C4—342no—
1438C22⋊C4—342no—
1439C22⋊C4—342no—
1440C22⋊C4—342no—
1441C22⋊C4—342no—
1442C22⋊C4—342no—
1443C22⋊C4—681no—
1444C22⋊C4—681no—
1445C22⋊C4—681no—
1446C22⋊C4—681no—
1447C22⋊C4—681no—
1448C22⋊C4—681no—
1449C22⋊C4—681no—
1450C22⋊C4—681no—
1451C22⋊C4—681no—
1452C42—174no—
1453C42—342no—
1454C42—342no—
1455C42—342no—
1456C42—342no—
1457C42—342no—
1458C42—342no—
1459C42—342no—
1460C42—342no—
1461C42—342no—
1462C42—342no—
1463C42—342no—
1464C42—342no—
1465C42—342no—
1466C42—342no—
1467C42—681no—
1468C42—681no—
1469C23—21no—
1470C23—21no—
1471C23—21no—
1472C23—21no—
1473C23—21no—
1474C23—21no—
1475C23—21no—
1476C23—21no—
1477C23—21no—
1478C23—21no—
1479C23—21no—
1480C23—21no—
1481C23—21no—
1482C23—21no—
1483C23—21no—
1484C23—21no—
1485C23—21no—
1486C23—21no—
1487C23—21no—
1488C23—21no—
1489C23—21no—
1490C23—21no—
1491C23—21no—
1492C23—172no—
1493C23—172no—
1494C23—348no—
1495C23—341no—
1496C23—341no—
1497C23—341no—
1498C23—341no—
1499C23—341no—
1500C23—341no—
1501C23—341no—
1502C23—341no—
1503C23—341no—
1504C23—341no—
1505C23—341no—
1506C23—341no—
1507C23—684no—
1508C23—684no—
1509C23—684no—
1510C23—684no—
1511C23—684no—
1512C23—684no—
1513C23C2×D4×D1712yes—
1514C23C2×D4×D1712yes—
1515C23C2×#6325412yes—
1516C23C2×#6325412yes—
1517C23C2×#6325412yes—
1518C23C24×D1711yescharacteristic
1519Q8—28no—
1520Q8—684no—
1521D4—28no—
1522D4—28no—
1523D4—28no—
1524D4—44no—
1525D4—44no—
1526D4—44no—
1527D4—684no—
1528D4—684no—
1529D4—684no—
1530D4—684no—
1531D4—684no—
1532D4—684no—
1533C2×C4—28no—
1534C2×C4—28no—
1535C2×C4—28no—
1536C2×C4—21no—
1537C2×C4—21no—
1538C2×C4—21no—
1539C2×C4—21no—
1540C2×C4—21no—
1541C2×C4—21no—
1542C2×C4—21no—
1543C2×C4—21no—
1544C2×C4—21no—
1545C2×C4—21no—
1546C2×C4—21no—
1547C2×C4—21no—
1548C2×C4—21no—
1549C2×C4—21no—
1550C2×C4—21no—
1551C2×C4—21no—
1552C2×C4—21no—
1553C2×C4—21no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—21no—
1557C2×C4—21no—
1558C2×C4—21no—
1559C2×C4—21no—
1560C2×C4—21no—
1561C2×C4—21no—
1562C2×C4—21no—
1563C2×C4—44no—
1564C2×C4—44no—
1565C2×C4—172no—
1566C2×C4—172no—
1567C2×C4—172no—
1568C2×C4—172no—
1569C2×C4—172no—
1570C2×C4—172no—
1571C2×C4—172no—
1572C2×C4—348no—
1573C2×C4—348no—
1574C2×C4—348no—
1575C2×C4—341no—
1576C2×C4—341no—
1577C2×C4—341no—
1578C2×C4—341no—
1579C2×C4—341no—
1580C2×C4—341no—
1581C2×C4—341no—
1582C2×C4—341no—
1583C2×C4—341no—
1584C2×C4—341no—
1585C2×C4—341no—
1586C2×C4—341no—
1587C2×C4—341no—
1588C2×C4—341no—
1589C2×C4—341no—
1590C2×C4—341no—
1591C2×C4—341no—
1592C2×C4—341no—
1593C2×C4—341no—
1594C2×C4—341no—
1595C2×C4—341no—
1596C2×C4—341no—
1597C2×C4—341no—
1598C2×C4—341no—
1599C2×C4—341no—
1600C2×C4—341no—
1601C2×C4—341no—
1602C2×C4—341no—
1603C2×C4—341no—
1604C2×C4—341no—
1605C2×C4—341no—
1606C2×C4—341no—
1607C2×C4—341no—
1608C2×C4—341no—
1609C2×C4—341no—
1610C2×C4—684no—
1611C2×C4—684no—
1612C2×C4—684no—
1613C2×C4—684no—
1614C2×C4—684no—
1615C2×C4—684no—
1616C2×C4—684no—
1617C2×C4—684no—
1618C2×C4—684no—
1619C2×C4C2×D4×D1712yes—
1620C2×C4C2×#6325412yes—
1621C2×C4C2×#6325412yes—
1622C2×C4C2×#6325412yes—
1623C2×C4#41×D1712yes—
1624C2×C4#41×D1712yes—
1625C22—22no—
1626C22—22no—
1627C22—22no—
1628C22—22no—
1629C22—22no—
1630C22—22no—
1631C22—22no—
1632C22—22no—
1633C22—22no—
1634C22—22no—
1635C22—22no—
1636C22—22no—
1637C22—41no—
1638C22—41no—
1639C22—41no—
1640C22—41no—
1641C22—41no—
1642C22—41no—
1643C22—41no—
1644C22—41no—
1645C22—41no—
1646C22—41no—
1647C22—41no—
1648C22—41no—
1649C22—41no—
1650C22—41no—
1651C22—41no—
1652C22—342no—
1653C22—342no—
1654C22—342no—
1655C22—342no—
1656C22—342no—
1657C22—342no—
1658C22—6816no—
1659C22—681no—
1660C22—681no—
1661C22—681no—
1662C22—681no—
1663C22—681no—
1664C22—681no—
1665C22—681no—
1666C22—681no—
1667C22#1176331514yes—
1668C22C22×D4×D1711yescharacteristic
1669C22C2×#41×D1711yescharacteristic
1670C22C2×#41×D1711yescharacteristic
1671C22C22×#6325411yescharacteristic
1672C22C22×#6325411yescharacteristic
1673C22H(5,𝔽2)×D1711yescharacteristic
1674C22#1176364611yescharacteristic
1675C4—22no—
1676C4—22no—
1677C4—22no—
1678C4—22no—
1679C4—22no—
1680C4—22no—
1681C4—41no—
1682C4—41no—
1683C4—41no—
1684C4—41no—
1685C4—41no—
1686C4—174no—
1687C4—342no—
1688C4—342no—
1689C4—342no—
1690C4—342no—
1691C4—681no—
1692C4—681no—
1693C4—681no—
1694C4—681no—
1695C4—681no—
1696C4—681no—
1697C4—681no—
1698C4—681no—
1699C4—681no—
1700C2—24no—
1701C2—42no—
1702C2—42no—
1703C2—81no—
1704C2—682no—
1705C2—682no—
1706C2C2×#1176331511yescharacteristic
1707C2#1454207911yescharacteristic
1708C2#1454220111yescharacteristic
1709C2D17×#54611yescharacteristic
1710C2#1454227111yescharacteristic
1711C2#1454234711yescharacteristic
1712C2#1454238911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2430C2
hypercenter#2430D17
hypocenterC17#34732
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2430

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#11763319C2semidirect
2. C2×#41×Dic17C2semidirect
3. #14532984C2semidirect
4. #14532969C2semidirect
5. #14532894C2semidirect
6. #14532879C2semidirect
7. #14532800C2semidirect
8. #14532785C2semidirect
9. #14532701C2semidirect
10. #14532686C2semidirect
11. #14532612C2semidirect
12. #14532530C2semidirect
13. #14532460C2semidirect
14. #14532326C2semidirect
15. #14532244C2semidirect
16. #14532170C2semidirect
17. #14532099C2semidirect
18. #14532066C2semidirect
19. #14532055C2semidirect
20. #14532027C2semidirect
21. #14531996C2semidirect
22. #123×Dic17C2semidirect
23. #14531303C2semidirect
24. #121×Dic17C2semidirect
25. #14531294C2semidirect
26. #14531289C2semidirect
27. #14531269C2semidirect
28. #14531224C2semidirect
29. #14531220C2semidirect
30. C2×#11762656C2semidirect
31. C17×#2430C2semidirect
46. C2×Q8×Dic17C22semidirect
47. C2×Q8×Dic17C22semidirect
53. C2×D4×Dic17C22semidirect
54. C2×D4×Dic17C22semidirect
55. C2×D4×Dic17C22semidirect
61. C2×#10587612C22semidirect
62. C2×#10587612C22semidirect
64. C2×#10587563C22semidirect
69. C22×C4×Dic17C22semidirect
70. C22×C4×Dic17C22semidirect
71. #11762751C22semidirect
72. #11762751C22semidirect
73. #11762748C22semidirect
75. #11762743C22semidirect
76. #11762741C22semidirect
77. #11762741C22semidirect
78. #11762737C22semidirect
80. #11762734C22semidirect
81. #11762732C22semidirect
85. #11762730C22semidirect
92. #11762723C22semidirect
93. #11762721C22semidirect
99. #11762713C22semidirect
100. #11762713C22semidirect
101. #11762712C22semidirect
105. #11762708C22semidirect
106. #11762706C22semidirect
107. #11762703C22semidirect
108. #11762702C22semidirect
109. #11762702C22semidirect
110. #11762702C22semidirect
111. #11762702C22semidirect
117. #11762697C22semidirect
118. #11762697C22semidirect
119. #11762696C22semidirect
120. #11762695C22semidirect
121. #11762695C22semidirect
122. #11762694C22semidirect
123. #11762692C22semidirect
124. #11762692C22semidirect
125. #11762692C22semidirect
126. #11762690C22semidirect
131. #11762689C22semidirect
141. #11762684C22semidirect
148. #11762670C22semidirect
150. #11762667C22semidirect
152. C4⋊C4×Dic17C22semidirect
153. C4⋊C4×Dic17C22semidirect
154. C4⋊C4×Dic17C22semidirect
155. #11762660C22semidirect
157. C22⋊C4×Dic17C22semidirect
158. C22⋊C4×Dic17C22semidirect
159. C22⋊C4×Dic17C22semidirect
160. C22⋊C4×Dic17C22semidirect
161. C22⋊C4×Dic17C22semidirect
172. #11762654C22semidirect
178. C17×#395C22semidirect
179. C17×#394C22semidirect
180. C17×#393C22semidirect
181. C17×#392C22semidirect
184. C17×#386C22semidirect
185. C17×#386C22semidirect
186. C17×#385C22semidirect
187. C17×#385C22semidirect
279. D4×Dic17D4semidirect
425. C2×D4×C17#41semidirect
440. C22×C4×C17#41semidirect
521. C2×C4×D17#41semidirect
574. #63227#41semidirect
782. #2430D17semidirect
933. #395C2×D17semidirect
941. #394C2×D17semidirect
945. #393C2×D17semidirect
949. #392C2×D17semidirect
993. #386C2×D17semidirect
994. #386C2×D17semidirect
1002. #385C2×D17semidirect
1003. #385C2×D17semidirect
1247. C17#34732semidirect
1304. C2×D4#63254semidirect
1370. C22×C4#63254semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117633192
C2×#41×Dic172
#145329842
#145329692
#145328942
#145328792
#145328002
#145327852
#145327012
#145326862
#145326122
#145325302
#145324602
#145323262
#145322442
#145321702
#145320992
#145320662
#145320552
#145320272
#145319962
#123×Dic172
#145313032
#121×Dic172
#145312942
#145312892
#145312692
#145312242
#145312202
C2×#117626562
C17×#24302
#3473217