Finite Group Databasebeta

← #17204513

Subgroups — #17204513

Order 4352.

2804 conjugacy classes of subgroups.

The subgroup lattice has 1708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763336C211yesmaximal, characteristic, complemented
2C2×#11763319C211yesmaximal, characteristic, complemented
3#14533923C211yesmaximal, characteristic, complemented
4#14533908C211yesmaximal, characteristic, complemented
5#14533893C211yesmaximal, characteristic, complemented
6#14533878C211yesmaximal, characteristic, complemented
7#14533865C211yesmaximal, characteristic, complemented
8#14533856C211yesmaximal, characteristic, complemented
9#14533843C211yesmaximal, characteristic, complemented
10#14533828C211yesmaximal, characteristic, complemented
11#14533797C211yesmaximal, characteristic, complemented
12#14533742C211yesmaximal, characteristic, complemented
13#14533714C211yesmaximal, characteristic, complemented
14#14533673C211yesmaximal, characteristic, complemented
15#14533110C211yesmaximal, characteristic, complemented
16#14532912C211yesmaximal, characteristic, complemented
17#14532314C211yesmaximal, characteristic, complemented
18#14532061C211yesmaximal, characteristic, complemented
19#14532042C211yesmaximal, characteristic, complemented
20#14532029C211yesmaximal, characteristic, complemented
21#14531998C211yesmaximal, characteristic, complemented
22#14531325C211yesmaximal, characteristic, complemented
23#123×Dic17C211yesmaximal, characteristic, complemented
24#14531294C211yesmaximal, characteristic, complemented
25#14531290C211yesmaximal, characteristic, complemented
26#14531285C211yesmaximal, characteristic, complemented
27#14531269C211yesmaximal, characteristic, complemented
28#14531242C211yesmaximal, characteristic, complemented
29C4×D4×Dic17C211yesmaximal, characteristic, complemented
30C2×#11762656C211yesmaximal, characteristic, complemented
31C17×#2425C211yesmaximal, characteristic, complemented
32C22×#63254C2211yescharacteristic
33C23×C4×D17C2211yescharacteristic
34#11763336—28no—
35C2×#10587584C2211yescharacteristic, complemented
36C2×#10587565C2211yescharacteristic, complemented
37C2×#10587575C2211yescharacteristic, complemented
38C2×#10587571C2211yescharacteristic
39C2×#10587571C2211yescharacteristic, complemented
40#11763319—28no—
41C2×#10587615C2211yescharacteristic
42C2×#10587569C2211yescharacteristic
43C2×#10587569C2211yescharacteristic
44C2×#10587583C2211yescharacteristic
45C2×#10587610C2211yescharacteristic
46C2×#10587564C2211yescharacteristic
47C2×#10587616C2211yescharacteristic
48C2×#10587625C2211yescharacteristic
49C2×#10587625C2211yescharacteristic
50C2×#10587624C2211yescharacteristic
51C2×#10587568C2211yescharacteristic
52C2×#10587623C2211yescharacteristic
53C2×#10587623C2211yescharacteristic
54C2×#10587573C2211yescharacteristic, complemented
55C2×D4×Dic17C2211yescharacteristic
56C2×D4×Dic17C2211yescharacteristic
57C2×D4×Dic17C2211yescharacteristic
58C2×#10587579C2211yescharacteristic
59C2×#10587579C2211yescharacteristic
60C2×#10587567C2211yescharacteristic
61C2×#10587567C2211yescharacteristic
62C2×#10587567C2211yescharacteristic
63C2×#10587567C2211yescharacteristic, complemented
64C2×#10587567C2211yescharacteristic, complemented
65C2×#10587578C2211yescharacteristic
66C2×#10587578C2211yescharacteristic, complemented
67C2×#10587563C2211yescharacteristic, complemented
68C22×#63227C2211yescharacteristic
69C22×#63227C2211yescharacteristic
70C22×C4×Dic17C2211yescharacteristic
71C22×C4×Dic17C2211yescharacteristic
72C22×C4×Dic17C2211yescharacteristic, complemented
73#11762751C2211yescharacteristic, complemented
74#11762750C2211yescharacteristic, complemented
75#11762744C2211yescharacteristic
76#11762744C2211yescharacteristic
77#11762743C2211yescharacteristic, complemented
78#11762742C2211yescharacteristic, complemented
79#11762742C2211yescharacteristic, complemented
80#11762738C2211yescharacteristic
81#11762738C2211yescharacteristic, complemented
82#11762737C2211yescharacteristic, complemented
83#11762731C2211yescharacteristic
84#11762731C2211yescharacteristic
85#11762731C2211yescharacteristic
86#11762730C2211yescharacteristic, complemented
87#11762729C2211yescharacteristic, complemented
88#11762726C2211yescharacteristic
89#11762725C2211yescharacteristic
90#11762725C2211yescharacteristic
91#11762725C2211yescharacteristic, complemented
92#11762724C2211yescharacteristic
93#11762724C2211yescharacteristic
94#11762724C2211yescharacteristic
95#11762722C2211yescharacteristic
96#11762722C2211yescharacteristic, complemented
97#11762718C2211yescharacteristic
98#11762718C2211yescharacteristic
99#11762718C2211yescharacteristic
100#11762717C2211yescharacteristic, complemented
101#11762713C2211yescharacteristic, complemented
102#11762713C2211yescharacteristic, complemented
103#11762713C2211yescharacteristic, complemented
104#11762711C2211yescharacteristic
105#11762710C2211yescharacteristic
106#11762710C2211yescharacteristic
107#11762709C2211yescharacteristic
108#11762709C2211yescharacteristic
109#11762709C2211yescharacteristic
110#11762709C2211yescharacteristic, complemented
111#11762708C2211yescharacteristic, complemented
112#11762706C2211yescharacteristic, complemented
113#11762705C2211yescharacteristic, complemented
114#11762703C2211yescharacteristic, complemented
115#11762702C2211yescharacteristic, complemented
116#11762702C2211yescharacteristic, complemented
117#11762701C2211yescharacteristic
118#11762701C2211yescharacteristic, complemented
119#11762701C2211yescharacteristic, complemented
120#11762700C2211yescharacteristic
121#11762699C2211yescharacteristic
122#11762699C2211yescharacteristic
123#11762699C2211yescharacteristic, complemented
124#11762698C2211yescharacteristic
125#11762698C2211yescharacteristic, complemented
126#11762697C2211yescharacteristic, complemented
127#11762695C2211yescharacteristic, complemented
128#11762695C2211yescharacteristic, complemented
129#11762689C2211yescharacteristic
130#11762689C2211yescharacteristic, complemented
131#11762688C2211yescharacteristic
132#11762688C2211yescharacteristic
133#11762688C2211yescharacteristic
134#11762687C2211yescharacteristic
135#11762687C2211yescharacteristic
136#11762686C2211yescharacteristic
137#11762686C2211yescharacteristic
138#11762686C2211yescharacteristic, complemented
139#11762684C2211yescharacteristic
140#11762680C2211yescharacteristic
141#11762680C2211yescharacteristic
142#11762673C2211yescharacteristic, complemented
143#11762672C2211yescharacteristic
144#11762667C2211yescharacteristic
145#11762664C2211yescharacteristic
146C4⋊C4×Dic17C2211yescharacteristic, complemented
147C4⋊C4×Dic17C2211yescharacteristic, complemented
148C4⋊C4×Dic17C2211yescharacteristic, complemented
149C4⋊C4×Dic17C2211yescharacteristic, complemented
150C4×C4⋊Dic17C2211yescharacteristic, complemented
151#11762660C2211yescharacteristic, complemented
152C22⋊C4×Dic17C2211yescharacteristic
153C22⋊C4×Dic17C2211yescharacteristic
154C22⋊C4×Dic17C2211yescharacteristic, complemented
155C22⋊C4×Dic17C2211yescharacteristic, complemented
156C22⋊C4×Dic17C2211yescharacteristic, complemented
157C22⋊C4×Dic17C2211yescharacteristic, complemented
158C22⋊C4×Dic17C2211yescharacteristic, complemented
159C4×C22⋊Dic17C2211yescharacteristic
160C4×C22⋊Dic17C2211yescharacteristic, complemented
161#11762656C2211yescharacteristic
162#11762656C2211yescharacteristic
163#11762656C2211yescharacteristic
164#11762656C2211yescharacteristic
165#11762656C2211yescharacteristic
166#11762656C2211yescharacteristic
167#11762656C2211yescharacteristic
168#11762656C2211yescharacteristic
169#11762656C2211yescharacteristic
170#11762656C2211yescharacteristic
171#11762656C2211yescharacteristic, complemented
172C2×#10587502C2211yescharacteristic
173C42×Dic17C2211yescharacteristic, complemented
174C2×C17×#123C2211yescharacteristic
175C2×C17×#123C2211yescharacteristic
176C2×C17×#121C2211yescharacteristic
177C2×C4×D4×C17C2211yescharacteristic
178C17×#398C2211yescharacteristic, complemented
179C17×#397C2211yescharacteristic, complemented
180C17×#396C2211yescharacteristic, complemented
181C17×#394C2211yescharacteristic, complemented
182C17×#389C2211yescharacteristic, complemented
183C17×#388C2211yescharacteristic, complemented
184C17×#386C2211yescharacteristic
185C17×#386C2211yescharacteristic, complemented
186C17×#385C2211yescharacteristic
187C17×#380C2211yescharacteristic, complemented
188C2×C17×#95C2211yescharacteristic
189C24×D17C2311yescharacteristic
190C22×D4×C17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C22×D4×C17C2311yescharacteristic
193C23×C4×C17C2311yescharacteristic
194C23×C4×C17C2311yescharacteristic
195C23×C4×C17C2311yescharacteristic
196C23×C4×C17C2311yescharacteristic
197C22×C22⋊D17C2311yescharacteristic
198C22×C22⋊D17C2311yescharacteristic
199C22×C22⋊D17C2311yescharacteristic
200C22×C22⋊D17C2311yescharacteristic
201C22×C22⋊D17C2311yescharacteristic
202C22×C22⋊D17C2311yescharacteristic
203C22×C22⋊D17C2311yescharacteristic
204C23×Dic17C2311yescharacteristic
205C23×Dic17C2311yescharacteristic
206C23×Dic17C2311yescharacteristic
207C23×Dic17C2311yescharacteristic
208C23×Dic17C2311yescharacteristic
209C23×Dic17C2311yescharacteristic
210C2×#63254—24no—
211C2×#63254—24no—
212C2×#63254—42no—
213C22×D68C2311yescharacteristic
214C22×D68C2311yescharacteristic
215C22×C4×D17—24no—
216C22×C4×D17—24no—
217C22×C4×D17—42no—
218C22×C4×D17C2311yescharacteristic
219C22×C4×D17C2311yescharacteristic
220C22×C4×D17C2311yescharacteristic
221C22×C4×D17C2311yescharacteristic
222C22×C4×D17C2311yescharacteristic
223C22×Dic34C2311yescharacteristic
224C22×Dic34C2311yescharacteristic
225C17×#123—24no—
226C17×#123—24no—
227C17×#121—24no—
228C4×D4×C17—24no—
229C2×C4⋊C4×C17C2311yescharacteristic
230C2×C4⋊C4×C17C2311yescharacteristic
231C2×C4⋊C4×C17C2311yescharacteristic
232C2×C4⋊C4×C17C2311yescharacteristic
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×C42×C17C2311yescharacteristic
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
259#10587625—24no—
260#10587625—24no—
261#10587624—24no—
262#10587623—24no—
263#10587623—24no—
264D4×Dic17—24no—
265D4×Dic17—24no—
266D4×Dic17D418yescomplemented
267#10587616—24no—
268#10587615—24no—
269C2×#63227—24no—
270C2×#63227—24no—
271C2×#63227C2311yescharacteristic
272C2×#63227C2311yescharacteristic
273C2×#63227C2311yescharacteristic
274C2×#63227C2311yescharacteristic
275C2×#63227C2311yescharacteristic
276C2×#63227C2311yescharacteristic
277C2×#63227C2311yescharacteristic
278C2×#63227C2311yescharacteristic
279C2×#63227C2311yescharacteristic
280C2×#63227C2311yescharacteristic
281C2×#63227C2311yescharacteristic
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×C4⋊Dic17C2311yescharacteristic
299C2×C4⋊Dic17C2311yescharacteristic
300C2×C4⋊Dic17C2311yescharacteristic
301C2×C4⋊Dic17C2311yescharacteristic
302C2×C4⋊Dic17C2311yescharacteristic
303C2×C4⋊Dic17C2311yescharacteristic
304C2×C4⋊Dic17C2311yescharacteristic
305#10587610—24no—
306C2×#63225C2311yescharacteristic
307C2×#63225C2311yescharacteristic
308C2×#63225C2311yescharacteristic
309C2×#63225C2311yescharacteristic
310C2×#63225C2311yescharacteristic
311C2×#63225C2311yescharacteristic
312C2×#63225C2311yescharacteristic
313C2×#63225C2311yescharacteristic
314C2×#63225C2311yescharacteristic
315C2×#63225C2311yescharacteristic
316C2×#63225C2311yescharacteristic
317C2×C4×Dic17—24no—
318C2×C4×Dic17—42no—
319C2×C4×Dic17—42no—
320C2×C4×Dic17C2311yescharacteristic
321C2×C4×Dic17C2311yescharacteristic
322C2×C4×Dic17C2311yescharacteristic
323C2×C4×Dic17C2311yescharacteristic
324C2×C4×Dic17C2311yescharacteristic
325C2×C4×Dic17C2311yescharacteristic
326C2×C4×Dic17C2311yescharacteristic
327C2×C4×Dic17C2311yescharacteristic
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
338#10587584—24no—
339#10587583—24no—
340#10587579—24no—
341#10587579—42no—
342#10587578—24no—
343#10587578—24no—
344#10587575—24no—
345#10587573—24no—
346#10587571—24no—
347#10587571—24no—
348#10587569—24no—
349#10587569—24no—
350#10587568—24no—
351#10587567—24no—
352#10587567—24no—
353#10587567—24no—
354#10587567—24no—
355#10587567—42no—
356#10587565—24no—
357#10587564—24no—
358#10587563—24no—
359C17×#95C2311yescharacteristic
360C17×#95C2311yescharacteristic
361C17×#95C2311yescharacteristic
362C17×#95C2311yescharacteristic
363C17×#95C2311yescharacteristic
364C17×#95C2311yescharacteristic
365C17×#95C2311yescharacteristic
366C17×#95C2311yescharacteristic
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
394C23×D17—22no—
395C23×D17—22no—
396C23×D17—22no—
397C23×D17—22no—
398C23×D17—22no—
399C23×D17—41no—
400C23×D17—41no—
401C23×D17C2411yescharacteristic
402C23×D17C2411yescharacteristic
403C23×D17C2411yescharacteristic
404C2×D4×C17—22no—
405C2×D4×C17—22no—
406C2×D4×C17—22no—
407C2×D4×C17—22no—
408C2×D4×C17—22no—
409C2×D4×C17—22no—
410C2×D4×C17—22no—
411C2×D4×C17—41no—
412C2×D4×C17C2×D414yes—
413C22×C4×C17—22no—
414C22×C4×C17—22no—
415C22×C4×C17—22no—
416C22×C4×C17—22no—
417C22×C4×C17—22no—
418C22×C4×C17—22no—
419C22×C4×C17—22no—
420C22×C4×C17—22no—
421C22×C4×C17—22no—
422C22×C4×C17—41no—
423C22×C4×C17—41no—
424C22×C4×C17—41no—
425C22×C4×C17C2411yescharacteristic
426C22×C4×C17C2411yescharacteristic
427C22×C4×C17C2411yescharacteristic
428C22×C4×C17C2411yescharacteristic
429C22×C4×C17C2411yescharacteristic
430C22×C4×C17C2411yescharacteristic
431C22×C4×C17C2411yescharacteristic
432C22×C4×C17C2411yescharacteristic
433C22×C4×C17C2411yescharacteristic
434C22×C4×C17C2411yescharacteristic
435C22×C4×C17C2411yescharacteristic
436C22×C4×C17C2411yescharacteristic
437C2×C22⋊D17—22no—
438C2×C22⋊D17—22no—
439C2×C22⋊D17—22no—
440C2×C22⋊D17—22no—
441C2×C22⋊D17—22no—
442C2×C22⋊D17—22no—
443C2×C22⋊D17—22no—
444C2×C22⋊D17—22no—
445C2×C22⋊D17—22no—
446C2×C22⋊D17—22no—
447C2×C22⋊D17—22no—
448C2×C22⋊D17—22no—
449C2×C22⋊D17—22no—
450C2×C22⋊D17—22no—
451C2×C22⋊D17—41no—
452C2×C22⋊D17—41no—
453C2×C22⋊D17—41no—
454C2×C22⋊D17—41no—
455C2×C22⋊D17—41no—
456C2×C22⋊D17—41no—
457C2×C22⋊D17—41no—
458C22×Dic17—22no—
459C22×Dic17—22no—
460C22×Dic17—22no—
461C22×Dic17—22no—
462C22×Dic17—22no—
463C22×Dic17—22no—
464C22×Dic17—22no—
465C22×Dic17—22no—
466C22×Dic17—22no—
467C22×Dic17—22no—
468C22×Dic17—41no—
469C22×Dic17—41no—
470C22×Dic17—41no—
471C22×Dic17—41no—
472C22×Dic17—41no—
473C22×Dic17C2×D414yes—
474C22×Dic17C2×D414yes—
475C22×Dic17#4114yescomplemented
476C22×Dic17C2411yescharacteristic
477C22×Dic17C2411yescharacteristic
478C22×Dic17C2411yescharacteristic
479C22×Dic17C2411yescharacteristic
480C22×Dic17C2411yescharacteristic
481C22×Dic17C2411yescharacteristic
482C22×Dic17C2411yescharacteristic
483C22×Dic17C2411yescharacteristic
484C22×Dic17C2411yescharacteristic
485C22×Dic17C2411yescharacteristic
486C22×Dic17C2411yescharacteristic
487C22×Dic17C2411yescharacteristic
488C22×Dic17C2411yescharacteristic
489#63254—416no—
490C2×D68—22no—
491C2×D68—22no—
492C2×D68—22no—
493C2×D68—22no—
494C2×D68—41no—
495C2×D68—41no—
496C2×C4×D17—22no—
497C2×C4×D17—22no—
498C2×C4×D17—22no—
499C2×C4×D17—22no—
500C2×C4×D17—22no—
501C2×C4×D17—22no—
502C2×C4×D17—22no—
503C2×C4×D17—22no—
504C2×C4×D17—22no—
505C2×C4×D17—22no—
506C2×C4×D17—22no—
507C2×C4×D17—22no—
508C2×C4×D17—416no—
509C2×C4×D17—41no—
510C2×C4×D17—41no—
511C2×C4×D17#4114yes—
512C2×Dic34—22no—
513C2×Dic34—22no—
514C2×Dic34—22no—
515C2×Dic34—22no—
516C2×Dic34—41no—
517C2×Dic34—41no—
518C4⋊C4×C17—22no—
519C4⋊C4×C17—22no—
520C4⋊C4×C17—22no—
521C4⋊C4×C17—22no—
522C4⋊C4×C17—22no—
523C4⋊C4×C17—22no—
524C4⋊C4×C17—22no—
525C4⋊C4×C17—41no—
526C22⋊C4×C17—22no—
527C22⋊C4×C17—22no—
528C22⋊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—41no—
536C22⋊C4×C17#4114yescomplemented
537C42×C17—22no—
538C22⋊Dic17—22no—
539C22⋊Dic17—22no—
540C22⋊Dic17—22no—
541C22⋊Dic17—22no—
542C22⋊Dic17—22no—
543C22⋊Dic17—22no—
544C22⋊Dic17—22no—
545C22⋊Dic17—41no—
546C22⋊Dic17C2×D414yes—
547C22⋊Dic17C2×D414yes—
548#63227—22no—
549#63227—22no—
550#63227—22no—
551#63227—22no—
552#63227—22no—
553#63227—22no—
554#63227—22no—
555#63227—22no—
556#63227—22no—
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—41no—
571#63227—41no—
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—41no—
581C4⋊Dic17C2×D414yes—
582#63225—22no—
583#63225—22no—
584#63225—22no—
585#63225—22no—
586#63225—22no—
587#63225—22no—
588#63225—22no—
589#63225—22no—
590#63225—22no—
591#63225—41no—
592#63225—41no—
593C4×Dic17—22no—
594C4×Dic17—22no—
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—41no—
606C4×Dic17—41no—
607C4×Dic17—41no—
608C4×Dic17—41no—
609C4×Dic17—41no—
610C4×Dic17C2×D414yes—
611#34829—171nomaximal, Sylow
612C23×C17—21no—
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×C17C22×D412yes—
630C23×C17C22×D412yes—
631C23×C17C2×#4112yes—
632C23×C17C2×#4112yes—
633C23×C17C2511yescharacteristic
634C22×D17—28no—
635C22×D17—21no—
636C22×D17—21no—
637C22×D17—21no—
638C22×D17—21no—
639C22×D17—21no—
640C22×D17—21no—
641C22×D17—21no—
642C22×D17—21no—
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—44no—
655C22×D17—44no—
656C22×D17—44no—
657C22×D17—44no—
658C22×D17—44no—
659C22×D17—44no—
660C22×D17C2×#4112yes—
661C22×D17C2×#4112yes—
662D4×C17—28no—
663D4×C17—44no—
664D4×C17—44no—
665C2×C4×C17—21no—
666C2×C4×C17—21no—
667C2×C4×C17—21no—
668C2×C4×C17—21no—
669C2×C4×C17—21no—
670C2×C4×C17—21no—
671C2×C4×C17—21no—
672C2×C4×C17—21no—
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—44no—
697C2×C4×C17—44no—
698C2×C4×C17—44no—
699C2×C4×C17—44no—
700C2×C4×C17C22×D412yes—
701C2×C4×C17C2×#4112yes—
702C2×C4×C17C2×#4112yes—
703C2×C4×C17C2×#4112yes—
704C2×C4×C17C2×#4112yes—
705C22⋊D17—44no—
706C22⋊D17—44no—
707C22⋊D17—44no—
708C22⋊D17—44no—
709C22⋊D17—44no—
710C22⋊D17—44no—
711C22⋊D17—44no—
712C2×Dic17—21no—
713C2×Dic17—21no—
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—21no—
723C2×Dic17—21no—
724C2×Dic17—28no—
725C2×Dic17—28no—
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—44no—
745C2×Dic17—44no—
746C2×Dic17—44no—
747C2×Dic17—44no—
748C2×Dic17C22×D412yes—
749C2×Dic17C22×D412yes—
750C2×Dic17C22×D412yes—
751C2×Dic17C22×D412yes—
752C2×Dic17C2×#4112yes—
753C2×Dic17C2×#4112yes—
754C2×Dic17C2×#4112yes—
755C2×Dic17C2×#4112yes—
756C2×Dic17H(5,𝔽2)12yes—
757D68—44no—
758D68—44no—
759C4×D17—28no—
760C4×D17—44no—
761C4×D17—44no—
762C4×D17—44no—
763C4×D17—44no—
764Dic34—44no—
765Dic34—44no—
766C2×#529—171no—
767C2×#525—171no—
768#2560—171no—
769#2559—171no—
770#2558—171no—
771#2557—171no—
772#2556—171no—
773#2555—171no—
774#2554—171no—
775#2553—171no—
776#2549—171no—
777#2543—171no—
778#2539—171no—
779#2534—171no—
780#2488—171no—
781#2472—171no—
782#2425D1711yescharacteristic, complemented
783#2424—171no—
784#2396—171no—
785#2395—171no—
786#2392—171no—
787#2388—171no—
788C4×#124—171no—
789C4×#123—171no—
790C4×#121—171no—
791C4×#121—171no—
792C4×#120—171no—
793#2297—171no—
794#2293—171no—
795C42×D4—171no—
796C2×C4×C22⋊C4—171no—
797C22×C17—22no—
798C22×C17—22no—
799C22×C17—22no—
800C22×C17—22no—
801C22×C17—22no—
802C22×C17—22no—
803C22×C17—22no—
804C22×C17—22no—
805C22×C17—22no—
806C22×C17—41no—
807C22×C17—41no—
808C22×C17—41no—
809C22×C17—41no—
810C22×C17—41no—
811C22×C17—41no—
812C22×C17—41no—
813C22×C17—41no—
814C22×C17—41no—
815C22×C17—41no—
816C22×C17—41no—
817C22×C17#53214yes—
818C22×C17C23×D411yescharacteristic
819C22×C17C22×#4111yescharacteristic
820C22×C17C22×#4111yescharacteristic
821C22×C17C22×#4111yescharacteristic
822C22×C17C22×#4111yescharacteristic
823C22×C17C2×H(5,𝔽2)11yescharacteristic
824C22×C17#58511yescharacteristic
825C2×D17—22no—
826C2×D17—22no—
827C2×D17—22no—
828C2×D17—22no—
829C2×D17—22no—
830C2×D17—22no—
831C2×D17—416no—
832C2×D17—41no—
833C2×D17—41no—
834C2×D17—41no—
835C2×D17—41no—
836C2×D17—41no—
837C2×D17—41no—
838C2×D17—41no—
839C2×D17—41no—
840C2×D17—41no—
841C2×D17—41no—
842C2×D17—41no—
843C2×D17—41no—
844C2×D17—41no—
845C2×D17—41no—
846C2×D17—41no—
847C4×C17—22no—
848C4×C17—22no—
849C4×C17—22no—
850C4×C17—22no—
851C4×C17—22no—
852C4×C17—41no—
853C4×C17—41no—
854C4×C17—41no—
855C4×C17—41no—
856C4×C17—41no—
857C4×C17—41no—
858C4×C17—41no—
859Dic17—22no—
860Dic17—22no—
861Dic17—22no—
862Dic17—22no—
863Dic17—22no—
864Dic17—22no—
865Dic17—41no—
866Dic17—41no—
867Dic17—41no—
868Dic17—41no—
869Dic17—41no—
870Dic17—41no—
871Dic17#54614yes—
872C22×#41—171no—
873C24×C4—171no—
874#529—348no—
875C2×#126—171no—
876C2×#126—171no—
877C2×#125—171no—
878C2×#124—171no—
879C2×#124—171no—
880#525—348no—
881C2×#123—171no—
882C2×#123—171no—
883C2×#123—171no—
884C2×#123C2×D1711yescharacteristic
885C2×#123C2×D1711yescharacteristic
886C2×C22⋊Q8—171no—
887C2×C22⋊Q8—171no—
888C2×C22⋊Q8—171no—
889C2×#121—171no—
890C2×#121—171no—
891C2×#121—171no—
892C2×#121—171no—
893C2×#121C2×D1711yescharacteristic
894C2×#120—171no—
895C2×#120—171no—
896C2×#120—171no—
897C2×C4×Q8—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×C4×D4—171no—
908C2×C4×D4C2×D1711yescharacteristic
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—
917#400—171no—
918#400—171no—
919#399—171no—
920#399—171no—
921#398—171no—
922#398—171no—
923#398—171no—
924#398C2×D1711yescharacteristic, complemented
925#397—171no—
926#397—171no—
927#397—171no—
928#397C2×D1711yescharacteristic, complemented
929#396—171no—
930#396—171no—
931#396—171no—
932#396C2×D1711yescharacteristic, complemented
933#395—171no—
934#395—171no—
935#394—171no—
936#394—171no—
937#394—171no—
938#394—171no—
939#394—171no—
940#394—171no—
941#394—171no—
942#394C2×D1711yescharacteristic, complemented
943#393—171no—
944#393—171no—
945#392—171no—
946#392—171no—
947#392—171no—
948#392—171no—
949#391—171no—
950#391—171no—
951#391—171no—
952#390—171no—
953#390—171no—
954#390—171no—
955#390—171no—
956#390—171no—
957#390—171no—
958#390—171no—
959#389—171no—
960#389—171no—
961#389—171no—
962#389C2×D1711yescharacteristic, complemented
963#388—171no—
964#388—171no—
965#388—171no—
966#388—171no—
967#388—171no—
968#388—171no—
969#388—171no—
970#388—171no—
971#388—171no—
972#388—171no—
973#388—171no—
974#388—171no—
975#388—171no—
976#388C2×D1711yescharacteristic, complemented
977#387—171no—
978#387—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#386C2×D1711yescharacteristic
990#386C2×D1711yescharacteristic, complemented
991#385—171no—
992#385—171no—
993#385—171no—
994#385C2×D1711yescharacteristic
995#382—171no—
996#381—171no—
997#380—171no—
998#380C2×D1711yescharacteristic, complemented
999#379—171no—
1000C4×C4⋊C4—171no—
1001C4×C4⋊C4—171no—
1002C4×C4⋊C4—171no—
1003C4×C4⋊C4—171no—
1004C4×C4⋊C4—171no—
1005C4×C4⋊C4—171no—
1006C4×C22⋊C4—171no—
1007C4×C22⋊C4—171no—
1008C4×C22⋊C4—171no—
1009C4×C22⋊C4—171no—
1010C4×C22⋊C4—171no—
1011C4×C22⋊C4—171no—
1012C4×C22⋊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—
1026C2×#95—171no—
1027C2×#95C2×D1711yescharacteristic
1028C43—171no—
1029C2×C17—24no—
1030C2×C17—42no—
1031C2×C17—81no—
1032C2×C17C2×#53211yescharacteristic
1033C2×C17#344411yescharacteristic
1034C2×C17#345911yescharacteristic
1035C2×C17C2×#54611yescharacteristic
1036C2×C17D4×#4111yescharacteristic
1037C2×C17#347511yescharacteristic
1038C2×C17#348111yescharacteristic
1039D17—42no—
1040D17—42no—
1041D17—81no—
1042C25—171no—
1043C2×#41—344no—
1044C2×#41—344no—
1045C2×#41—682no—
1046C22×Q8—171no—
1047C22×Q8—171no—
1048C22×D4—171no—
1049C22×D4—171no—
1050C22×D4—171no—
1051C22×D4—171no—
1052C22×D4—171no—
1053C22×D4—171no—
1054C22×D4—171no—
1055C22×D4—171no—
1056C22×D4—171no—
1057C22×D4C22×D1711yescharacteristic
1058C22×D4C22×D1711yescharacteristic
1059C22×D4C22×D1711yescharacteristic
1060C23×C4—171no—
1061C23×C4—171no—
1062C23×C4—171no—
1063C23×C4—171no—
1064C23×C4—171no—
1065C23×C4—171no—
1066C23×C4—171no—
1067C23×C4—171no—
1068C23×C4—171no—
1069C23×C4—171no—
1070C23×C4—171no—
1071C23×C4—344no—
1072C23×C4—344no—
1073C23×C4—682no—
1074C23×C4C22×D1711yescharacteristic
1075C23×C4C22×D1711yescharacteristic
1076C23×C4C22×D1711yescharacteristic
1077C23×C4C22×D1711yescharacteristic
1078#126—344no—
1079#126—344no—
1080#125—344no—
1081#124—344no—
1082#124—344no—
1083#123—24no—
1084#123—24no—
1085#123—344no—
1086#123—344no—
1087#123—344no—
1088C22⋊Q8—344no—
1089C22⋊Q8—344no—
1090C22⋊Q8—344no—
1091#121—24no—
1092#121—344no—
1093#121—344no—
1094#121—344no—
1095#121—344no—
1096#120—344no—
1097#120—344no—
1098#120—344no—
1099C4×Q8—344no—
1100C4×D4—24no—
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—682no—
1110C4×D4—682no—
1111#117—344no—
1112#117—344no—
1113#117—344no—
1114C2×C4⋊C4—171no—
1115C2×C4⋊C4—171no—
1116C2×C4⋊C4—171no—
1117C2×C4⋊C4—171no—
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⋊C4C22×D1711yescharacteristic
1133C2×C4⋊C4C22×D1711yescharacteristic
1134C2×C4⋊C4C22×D1711yescharacteristic
1135C2×C4⋊C4C22×D1711yescharacteristic
1136C2×C4⋊C4C22×D1711yescharacteristic
1137C2×C4⋊C4C22×D1711yescharacteristic
1138C2×C4⋊C4C22×D1711yescharacteristic
1139C2×C4⋊C4C22×D1711yescharacteristic
1140C2×C22⋊C4—171no—
1141C2×C22⋊C4—171no—
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—171no—
1208C2×C42—344no—
1209C2×C42—682no—
1210C2×C42—682no—
1211C2×C42C22×D1711yescharacteristic
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#95C22×D1711yescharacteristic
1237#95C22×D1711yescharacteristic
1238#95C22×D1711yescharacteristic
1239#95C22×D1711yescharacteristic
1240#95C22×D1711yescharacteristic
1241#95C22×D1711yescharacteristic
1242#95C22×D1711yescharacteristic
1243#95C22×D1711yescharacteristic
1244C17#3482911yescharacteristic, complemented, Sylow
1245C24—171no—
1246C24—171no—
1247C24—171no—
1248C24—342no—
1249C24—342no—
1250C24—342no—
1251C24—342no—
1252C24—342no—
1253C24—681no—
1254C24—681no—
1255C24C23×D1711yescharacteristic
1256C24C23×D1711yescharacteristic
1257C24C23×D1711yescharacteristic
1258#41—6816no—
1259C2×Q8—342no—
1260C2×Q8—342no—
1261C2×Q8—342no—
1262C2×Q8—342no—
1263C2×Q8—681no—
1264C2×Q8—681no—
1265C2×D4—22no—
1266C2×D4—22no—
1267C2×D4—22no—
1268C2×D4—22no—
1269C2×D4—22no—
1270C2×D4—22no—
1271C2×D4—22no—
1272C2×D4—41no—
1273C2×D4—342no—
1274C2×D4—342no—
1275C2×D4—342no—
1276C2×D4—342no—
1277C2×D4—342no—
1278C2×D4—342no—
1279C2×D4—342no—
1280C2×D4—342no—
1281C2×D4—342no—
1282C2×D4—342no—
1283C2×D4—342no—
1284C2×D4—342no—
1285C2×D4—342no—
1286C2×D4—342no—
1287C2×D4—342no—
1288C2×D4—342no—
1289C2×D4—342no—
1290C2×D4—342no—
1291C2×D4—681no—
1292C2×D4—681no—
1293C2×D4—681no—
1294C2×D4—681no—
1295C2×D4—681no—
1296C2×D4—681no—
1297C2×D4—681no—
1298C2×D4—681no—
1299C2×D4—681no—
1300C2×D4D4×D1714yes—
1301C22×C4—22no—
1302C22×C4—22no—
1303C22×C4—22no—
1304C22×C4—22no—
1305C22×C4—22no—
1306C22×C4—22no—
1307C22×C4—22no—
1308C22×C4—22no—
1309C22×C4—22no—
1310C22×C4—41no—
1311C22×C4—41no—
1312C22×C4—41no—
1313C22×C4—171no—
1314C22×C4—174no—
1315C22×C4—174no—
1316C22×C4—171no—
1317C22×C4—171no—
1318C22×C4—171no—
1319C22×C4—171no—
1320C22×C4—171no—
1321C22×C4—171no—
1322C22×C4—174no—
1323C22×C4—174no—
1324C22×C4—171no—
1325C22×C4—171no—
1326C22×C4—171no—
1327C22×C4—171no—
1328C22×C4—171no—
1329C22×C4—171no—
1330C22×C4—342no—
1331C22×C4—342no—
1332C22×C4—342no—
1333C22×C4—342no—
1334C22×C4—342no—
1335C22×C4—342no—
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—681no—
1353C22×C4—681no—
1354C22×C4—6816no—
1355C22×C4—681no—
1356C22×C4—681no—
1357C22×C4—681no—
1358C22×C4—681no—
1359C22×C4—681no—
1360C22×C4C23×D1711yescharacteristic
1361C22×C4C23×D1711yescharacteristic
1362C22×C4C23×D1711yescharacteristic
1363C22×C4C23×D1711yescharacteristic
1364C22×C4C23×D1711yescharacteristic
1365C22×C4C23×D1711yescharacteristic
1366C22×C4C23×D1711yescharacteristic
1367C22×C4C23×D1711yescharacteristic
1368C22×C4C23×D1711yescharacteristic
1369C22×C4C23×D1711yescharacteristic
1370C22×C4C23×D1711yescharacteristic
1371C22×C4C23×D1711yescharacteristic
1372C4⋊C4—22no—
1373C4⋊C4—22no—
1374C4⋊C4—22no—
1375C4⋊C4—22no—
1376C4⋊C4—22no—
1377C4⋊C4—22no—
1378C4⋊C4—22no—
1379C4⋊C4—41no—
1380C4⋊C4—174no—
1381C4⋊C4—342no—
1382C4⋊C4—342no—
1383C4⋊C4—342no—
1384C4⋊C4—342no—
1385C4⋊C4—342no—
1386C4⋊C4—342no—
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—681no—
1396C4⋊C4—681no—
1397C4⋊C4—681no—
1398C22⋊C4—22no—
1399C22⋊C4—22no—
1400C22⋊C4—22no—
1401C22⋊C4—22no—
1402C22⋊C4—22no—
1403C22⋊C4—22no—
1404C22⋊C4—22no—
1405C22⋊C4—22no—
1406C22⋊C4—22no—
1407C22⋊C4—41no—
1408C22⋊C4—174no—
1409C22⋊C4—174no—
1410C22⋊C4—174no—
1411C22⋊C4—342no—
1412C22⋊C4—342no—
1413C22⋊C4—342no—
1414C22⋊C4—342no—
1415C22⋊C4—342no—
1416C22⋊C4—342no—
1417C22⋊C4—342no—
1418C22⋊C4—342no—
1419C22⋊C4—342no—
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—681no—
1441C22⋊C4—681no—
1442C22⋊C4—681no—
1443C22⋊C4—681no—
1444C22⋊C4—681no—
1445C22⋊C4#6325414yescomplemented
1446C42—22no—
1447C42—174no—
1448C42—342no—
1449C42—342no—
1450C42—342no—
1451C42—342no—
1452C42—342no—
1453C42—342no—
1454C42—342no—
1455C42—342no—
1456C42—342no—
1457C42—342no—
1458C42—342no—
1459C42—342no—
1460C42—681no—
1461C42—681no—
1462C42—681no—
1463C42—681no—
1464C42—681no—
1465C23—21no—
1466C23—21no—
1467C23—21no—
1468C23—21no—
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—172no—
1483C23—172no—
1484C23—348no—
1485C23—341no—
1486C23—341no—
1487C23—341no—
1488C23—341no—
1489C23—341no—
1490C23—341no—
1491C23—341no—
1492C23—341no—
1493C23—341no—
1494C23—341no—
1495C23—341no—
1496C23—341no—
1497C23—341no—
1498C23—341no—
1499C23—341no—
1500C23—341no—
1501C23—341no—
1502C23—341no—
1503C23—341no—
1504C23—684no—
1505C23—684no—
1506C23—684no—
1507C23—684no—
1508C23—684no—
1509C23—684no—
1510C23C2×D4×D1712yes—
1511C23C2×D4×D1712yes—
1512C23C2×#6325412yes—
1513C23#41×D1712yes—
1514C23C24×D1711yescharacteristic
1515Q8—684no—
1516Q8—684no—
1517D4—28no—
1518D4—44no—
1519D4—44no—
1520D4—684no—
1521D4—684no—
1522D4—684no—
1523D4—684no—
1524D4—684no—
1525D4—684no—
1526D4—684no—
1527D4—684no—
1528D4—684no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—21no—
1533C2×C4—21no—
1534C2×C4—21no—
1535C2×C4—21no—
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—44no—
1561C2×C4—44no—
1562C2×C4—44no—
1563C2×C4—44no—
1564C2×C4—172no—
1565C2×C4—172no—
1566C2×C4—172no—
1567C2×C4—172no—
1568C2×C4—172no—
1569C2×C4—172no—
1570C2×C4—172no—
1571C2×C4—172no—
1572C2×C4—172no—
1573C2×C4—348no—
1574C2×C4—348no—
1575C2×C4—348no—
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—684no—
1607C2×C4—684no—
1608C2×C4—684no—
1609C2×C4—684no—
1610C2×C4—684no—
1611C2×C4—684no—
1612C2×C4—684no—
1613C2×C4—684no—
1614C2×C4C2×D4×D1712yes—
1615C2×C4C2×#6325412yes—
1616C2×C4C2×#6325412yes—
1617C2×C4#41×D1712yes—
1618C2×C4#41×D1712yes—
1619C22—22no—
1620C22—22no—
1621C22—22no—
1622C22—22no—
1623C22—22no—
1624C22—22no—
1625C22—22no—
1626C22—22no—
1627C22—22no—
1628C22—41no—
1629C22—41no—
1630C22—41no—
1631C22—41no—
1632C22—41no—
1633C22—41no—
1634C22—41no—
1635C22—41no—
1636C22—41no—
1637C22—41no—
1638C22—41no—
1639C22—342no—
1640C22—342no—
1641C22—342no—
1642C22—342no—
1643C22—342no—
1644C22—342no—
1645C22—6816no—
1646C22—681no—
1647C22—681no—
1648C22—681no—
1649C22—681no—
1650C22—681no—
1651C22—681no—
1652C22—681no—
1653C22—681no—
1654C22—681no—
1655C22—681no—
1656C22—681no—
1657C22—681no—
1658C22—681no—
1659C22—681no—
1660C22—681no—
1661C22#1176335414yes—
1662C22C22×D4×D1711yescharacteristic
1663C22C2×#41×D1711yescharacteristic
1664C22C2×#41×D1711yescharacteristic
1665C22C2×#41×D1711yescharacteristic
1666C22C22×#6325411yescharacteristic
1667C22H(5,𝔽2)×D1711yescharacteristic
1668C22#1176364611yescharacteristic
1669C4—22no—
1670C4—22no—
1671C4—22no—
1672C4—22no—
1673C4—22no—
1674C4—41no—
1675C4—41no—
1676C4—41no—
1677C4—41no—
1678C4—41no—
1679C4—41no—
1680C4—41no—
1681C4—174no—
1682C4—342no—
1683C4—342no—
1684C4—342no—
1685C4—342no—
1686C4—342no—
1687C4—342no—
1688C4—681no—
1689C4—681no—
1690C4—681no—
1691C4—681no—
1692C4—681no—
1693C4—681no—
1694C2—24no—
1695C2—42no—
1696C2—81no—
1697C2—682no—
1698C2—682no—
1699C2—1361no—
1700C2C2×#1176335411yescharacteristic
1701C2#1454207811yescharacteristic
1702C2#1454219211yescharacteristic
1703C2D17×#54611yescharacteristic
1704C2#1454227111yescharacteristic
1705C2#1454234711yescharacteristic
1706C2#1454238911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2425C2
hypercenter#2425D17
hypocenterC17#34829
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2425

Complements

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

NH ≅ G/Ntype
1. C2×#11763336C2semidirect
2. C2×#11763319C2semidirect
3. #14533923C2semidirect
4. #14533908C2semidirect
5. #14533893C2semidirect
6. #14533878C2semidirect
7. #14533865C2semidirect
8. #14533856C2semidirect
9. #14533843C2semidirect
10. #14533828C2semidirect
11. #14533797C2semidirect
12. #14533742C2semidirect
13. #14533714C2semidirect
14. #14533673C2semidirect
15. #14533110C2semidirect
16. #14532912C2semidirect
17. #14532314C2semidirect
18. #14532061C2semidirect
19. #14532042C2semidirect
20. #14532029C2semidirect
21. #14531998C2semidirect
22. #14531325C2semidirect
23. #123×Dic17C2semidirect
24. #14531294C2semidirect
25. #14531290C2semidirect
26. #14531285C2semidirect
27. #14531269C2semidirect
28. #14531242C2semidirect
29. C4×D4×Dic17C2semidirect
30. C2×#11762656C2semidirect
31. C17×#2425C2semidirect
35. C2×#10587584C22semidirect
36. C2×#10587565C22semidirect
37. C2×#10587575C22semidirect
39. C2×#10587571C22semidirect
54. C2×#10587573C22semidirect
63. C2×#10587567C22semidirect
64. C2×#10587567C22semidirect
66. C2×#10587578C22semidirect
67. C2×#10587563C22semidirect
72. C22×C4×Dic17C22semidirect
73. #11762751C22semidirect
74. #11762750C22semidirect
77. #11762743C22semidirect
78. #11762742C22semidirect
79. #11762742C22semidirect
81. #11762738C22semidirect
82. #11762737C22semidirect
86. #11762730C22semidirect
87. #11762729C22semidirect
91. #11762725C22semidirect
96. #11762722C22semidirect
100. #11762717C22semidirect
101. #11762713C22semidirect
102. #11762713C22semidirect
103. #11762713C22semidirect
110. #11762709C22semidirect
111. #11762708C22semidirect
112. #11762706C22semidirect
113. #11762705C22semidirect
114. #11762703C22semidirect
115. #11762702C22semidirect
116. #11762702C22semidirect
118. #11762701C22semidirect
119. #11762701C22semidirect
123. #11762699C22semidirect
125. #11762698C22semidirect
126. #11762697C22semidirect
127. #11762695C22semidirect
128. #11762695C22semidirect
130. #11762689C22semidirect
138. #11762686C22semidirect
142. #11762673C22semidirect
146. C4⋊C4×Dic17C22semidirect
147. C4⋊C4×Dic17C22semidirect
148. C4⋊C4×Dic17C22semidirect
149. C4⋊C4×Dic17C22semidirect
150. C4×C4⋊Dic17C22semidirect
151. #11762660C22semidirect
154. C22⋊C4×Dic17C22semidirect
155. C22⋊C4×Dic17C22semidirect
156. C22⋊C4×Dic17C22semidirect
157. C22⋊C4×Dic17C22semidirect
158. C22⋊C4×Dic17C22semidirect
160. C4×C22⋊Dic17C22semidirect
171. #11762656C22semidirect
173. C42×Dic17C22semidirect
178. C17×#398C22semidirect
179. C17×#397C22semidirect
180. C17×#396C22semidirect
181. C17×#394C22semidirect
182. C17×#389C22semidirect
183. C17×#388C22semidirect
185. C17×#386C22semidirect
187. C17×#380C22semidirect
266. D4×Dic17D4semidirect
475. C22×Dic17#41semidirect
536. C22⋊C4×C17#41semidirect
574. #63227#41semidirect
782. #2425D17semidirect
924. #398C2×D17semidirect
928. #397C2×D17semidirect
932. #396C2×D17semidirect
942. #394C2×D17semidirect
962. #389C2×D17semidirect
976. #388C2×D17semidirect
990. #386C2×D17semidirect
998. #380C2×D17semidirect
1244. C17#34829semidirect
1445. C22⋊C4#63254semidirect

Maximal subgroups

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

subgroupindex
C2×#117633362
C2×#117633192
#145339232
#145339082
#145338932
#145338782
#145338652
#145338562
#145338432
#145338282
#145337972
#145337422
#145337142
#145336732
#145331102
#145329122
#145323142
#145320612
#145320422
#145320292
#145319982
#145313252
#123×Dic172
#145312942
#145312902
#145312852
#145312692
#145312422
C4×D4×Dic172
C2×#117626562
C17×#24252
#3482917