Finite Group Databasebeta

← #17198012

Subgroups — #17198012

Order 4352.

2442 conjugacy classes of subgroups.

The subgroup lattice has 1606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763394C211yesmaximal, characteristic
2#14531954C211yesmaximal, characteristic, complemented
3#14531953C211yesmaximal, characteristic, complemented
4#14531934C211yesmaximal, characteristic, complemented
5#14531933C211yesmaximal, characteristic, complemented
6#14531857C211yesmaximal, characteristic, complemented
7#14531850C211yesmaximal, characteristic, complemented
8#14531782C211yesmaximal, characteristic, complemented
9#14531777C211yesmaximal, characteristic, complemented
10#14531768C211yesmaximal, characteristic, complemented
11#14531763C211yesmaximal, characteristic, complemented
12#14531763C211yesmaximal, characteristic, complemented
13#14531711C211yesmaximal, characteristic, complemented
14#14531707C211yesmaximal, characteristic, complemented
15#14531690C211yesmaximal, characteristic, complemented
16#14531689C211yesmaximal, characteristic, complemented
17#14531561C211yesmaximal, characteristic, complemented
18#14531557C211yesmaximal, characteristic, complemented
19#14531556C211yesmaximal, characteristic, complemented
20#14531554C211yesmaximal, characteristic, complemented
21#14531512C211yesmaximal, characteristic, complemented
22#14531486C211yesmaximal, characteristic, complemented
23#14531485C211yesmaximal, characteristic, complemented
24#14531482C211yesmaximal, characteristic, complemented
25#14531480C211yesmaximal, characteristic, complemented
26#14531474C211yesmaximal, characteristic, complemented
27#14531396C211yesmaximal, characteristic, complemented
28#14531316C211yesmaximal, characteristic, complemented
29C4×#10587625C211yesmaximal, characteristic, complemented
30C2×#11762697C211yesmaximal, characteristic, complemented
31C17×#2358C211yesmaximal, characteristic, complemented
32#11763394C4116yescomplemented
33C2×#10587565C2211yescharacteristic
34C2×#10587565C2211yescharacteristic
35C2×#10587622C2211yescharacteristic
36C2×#10587571C2211yescharacteristic
37C2×#10587569C2211yescharacteristic
38C2×#10587621C2211yescharacteristic
39C2×#10587564C2211yescharacteristic
40C2×#10587625C2211yescharacteristic
41C2×#10587625C2211yescharacteristic
42C2×#10587624C2211yescharacteristic
43C2×#10587639C2211yescharacteristic
44C2×#10587573C2211yescharacteristic, complemented
45C2×D4×Dic17C2211yescharacteristic
46C2×D4×Dic17C2211yescharacteristic
47C2×D4×Dic17C2211yescharacteristic
48C2×C4×C22⋊D17C2211yescharacteristic
49C2×C4×C22⋊D17C2211yescharacteristic
50C2×C4×C22⋊D17C2211yescharacteristic, complemented
51C2×#10587567C2211yescharacteristic
52C2×#10587567C2211yescharacteristic
53C2×#10587567C2211yescharacteristic
54C2×#10587558C2211yescharacteristic, complemented
55C2×#10587563C2211yescharacteristic, complemented
56C22×#63225C2211yescharacteristic
57C22×C22⋊Dic17C2211yescharacteristic
58C22×C22⋊Dic17C2211yescharacteristic
59C22×C22⋊Dic17C2211yescharacteristic
60C22×C4×Dic17C2211yescharacteristic
61#11762715C2211yescharacteristic, complemented
62#11762713C2211yescharacteristic, complemented
63#11762713C2211yescharacteristic, complemented
64#11762712C2211yescharacteristic
65#11762709C2211yescharacteristic
66#11762709C2211yescharacteristic
67#11762709C2211yescharacteristic, complemented
68#11762707C2211yescharacteristic, complemented
69#11762707C2211yescharacteristic, complemented
70#11762706C2211yescharacteristic, complemented
71#11762706C2211yescharacteristic, complemented
72#11762705C2211yescharacteristic, complemented
73#11762704C2211yescharacteristic, complemented
74#11762704C2211yescharacteristic, complemented
75#11762704C2211yescharacteristic, complemented
76#11762703C2211yescharacteristic
77#11762703C2211yescharacteristic
78#11762703C2211yescharacteristic, complemented
79#11762703C2211yescharacteristic, complemented
80#11762703C2211yescharacteristic, complemented
81#11762702C2211yescharacteristic
82#11762702C2211yescharacteristic
83#11762700C2211yescharacteristic, complemented
84#11762699C2211yescharacteristic, complemented
85#11762698C2211yescharacteristic, complemented
86#11762698C2211yescharacteristic, complemented
87#11762697C2211yescharacteristic
88#11762697C2211yescharacteristic
89#11762697C2211yescharacteristic
90#11762697C2211yescharacteristic
91#11762697C2211yescharacteristic
92#11762697C2211yescharacteristic
93#11762697C2211yescharacteristic
94#11762697C2211yescharacteristic
95#11762697C2211yescharacteristic
96#11762697C2211yescharacteristic
97#11762697C2211yescharacteristic, complemented
98#11762696C2211yescharacteristic, complemented
99#11762696C2211yescharacteristic, complemented
100#11762694C2211yescharacteristic, complemented
101#11762694C2211yescharacteristic, complemented
102#11762693C2211yescharacteristic, complemented
103#11762693C2211yescharacteristic, complemented
104#11762693C2211yescharacteristic, complemented
105#11762692C2211yescharacteristic, complemented
106#11762692C2211yescharacteristic, complemented
107#11762691C2211yescharacteristic, complemented
108#11762691C2211yescharacteristic, complemented
109#11762690C2211yescharacteristic, complemented
110#11762689C2211yescharacteristic
111#11762689C2211yescharacteristic
112#11762689C2211yescharacteristic
113#11762688C2211yescharacteristic
114#11762688C2211yescharacteristic
115#11762686C2211yescharacteristic
116#11762686C2211yescharacteristic
117#11762686C2211yescharacteristic, complemented
118#11762685C2211yescharacteristic
119#11762685C2211yescharacteristic
120#11762685C2211yescharacteristic, complemented
121#11762684C2211yescharacteristic
122#11762684C2211yescharacteristic
123#11762683C2211yescharacteristic, complemented
124#11762683C2211yescharacteristic, complemented
125#11762682C2211yescharacteristic
126#11762682C2211yescharacteristic
127#11762682C2211yescharacteristic
128#11762682C2211yescharacteristic
129#11762682C2211yescharacteristic
130#11762682C2211yescharacteristic
131#11762682C2211yescharacteristic, complemented
132#11762681C2211yescharacteristic
133#11762681C2211yescharacteristic
134#11762681C2211yescharacteristic
135#11762681C2211yescharacteristic
136#11762681C2211yescharacteristic
137#11762681C2211yescharacteristic
138#11762681C2211yescharacteristic, complemented
139#11762681C2211yescharacteristic, complemented
140#11762680C2211yescharacteristic, complemented
141#11762674C2211yescharacteristic, complemented
142#11762673C2211yescharacteristic, complemented
143#11762673C2211yescharacteristic, complemented
144#11762673C2211yescharacteristic, complemented
145#11762668C2211yescharacteristic, complemented
146#11762667C2211yescharacteristic
147#11762667C2211yescharacteristic
148#11762667C2211yescharacteristic
149#11762667C2211yescharacteristic
150#11762667C2211yescharacteristic, complemented
151#11762667C2211yescharacteristic, complemented
152#11762666C2211yescharacteristic, complemented
153C4⋊C4×Dic17C2211yescharacteristic, complemented
154C4⋊C4×Dic17C2211yescharacteristic, complemented
155C4×#63225C2211yescharacteristic, complemented
156C4×#63225C2211yescharacteristic, complemented
157C4×#63225C2211yescharacteristic, complemented
158#11762660C2211yescharacteristic, complemented
159#11762660C2211yescharacteristic, complemented
160#11762660C2211yescharacteristic, complemented
161C22⋊C4×Dic17C2211yescharacteristic
162C22⋊C4×Dic17C2211yescharacteristic
163C22⋊C4×Dic17C2211yescharacteristic
164C22⋊C4×Dic17C2211yescharacteristic
165C4×#63227C2211yescharacteristic, complemented
166C4×C22⋊Dic17C2211yescharacteristic
167C4×C22⋊Dic17C2211yescharacteristic
168C4×C22⋊Dic17C2211yescharacteristic, complemented
169C2×#10587502C2211yescharacteristic
170C2×#10587502C2211yescharacteristic
171C2×#10587502C2211yescharacteristic, complemented
172#95×D17C2211yescharacteristic, complemented
173C2×C17×#120C2211yescharacteristic
174C2×C4×D4×C17C2211yescharacteristic
175C2×C4×D4×C17C2211yescharacteristic
176C22×C22⋊C4×C17C2211yescharacteristic
177C22×C22⋊C4×C17C2211yescharacteristic
178C17×#390C2211yescharacteristic
179C17×#388C2211yescharacteristic
180C17×#388C2211yescharacteristic
181C17×#386C2211yescharacteristic
182C17×#386C2211yescharacteristic
183C17×#386C2211yescharacteristic
184C17×#385C2211yescharacteristic
185C17×#385C2211yescharacteristic
186C4×C22⋊C4×C17C2211yescharacteristic
187C4×C22⋊C4×C17C2211yescharacteristic
188C25×C17C2311yescharacteristic
189C22×D4×C17C2311yescharacteristic
190C22×D4×C17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C23×C4×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
201C23×Dic17C2311yescharacteristic
202C23×Dic17C2311yescharacteristic
203C23×Dic17C2311yescharacteristic
204C23×Dic17C2311yescharacteristic
205C23×Dic17C2311yescharacteristic
206C23×Dic17C2311yescharacteristic
207C23×Dic17C2311yescharacteristic
208C23×Dic17C2311yescharacteristic
209C22×C4×D17C2311yescharacteristic
210C22×C4×D17C2311yescharacteristic
211C22×C4×D17C2311yescharacteristic
212C22×Dic34C2311yescharacteristic
213C17×#120C2×C418yescomplemented
214C4×D4×C17—42no—
215C4×D4×C17—42no—
216C2×C4⋊C4×C17C2311yescharacteristic
217C2×C4⋊C4×C17C2311yescharacteristic
218C2×C4⋊C4×C17C2311yescharacteristic
219C2×C22⋊C4×C17—42no—
220C2×C22⋊C4×C17—42no—
221C2×C22⋊C4×C17C2311yescharacteristic
222C2×C22⋊C4×C17C2311yescharacteristic
223C2×C22⋊C4×C17C2311yescharacteristic
224C2×C22⋊C4×C17C2311yescharacteristic
225C2×C22⋊C4×C17C2311yescharacteristic
226C2×C22⋊C4×C17C2311yescharacteristic
227C2×C22⋊C4×C17C2311yescharacteristic
228C2×C22⋊C4×C17C2311yescharacteristic
229C2×C22⋊C4×C17C2311yescharacteristic
230C2×C22⋊C4×C17C2311yescharacteristic
231C2×C22⋊C4×C17C2311yescharacteristic
232C2×C22⋊C4×C17C2311yescharacteristic
233C2×C22⋊C4×C17C2311yescharacteristic
234C2×C22⋊C4×C17C2311yescharacteristic
235C2×C42×C17C2311yescharacteristic
236C2×C42×C17C2311yescharacteristic
237C2×C42×C17C2311yescharacteristic
238#10587639C2×C418yescomplemented
239C2×C22⋊Dic17—42no—
240C2×C22⋊Dic17—42no—
241C2×C22⋊Dic17C2×C418yescomplemented
242C2×C22⋊Dic17C2311yescharacteristic
243C2×C22⋊Dic17C2311yescharacteristic
244C2×C22⋊Dic17C2311yescharacteristic
245C2×C22⋊Dic17C2311yescharacteristic
246C2×C22⋊Dic17C2311yescharacteristic
247C2×C22⋊Dic17C2311yescharacteristic
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
262#10587625C2×C418yescomplemented
263#10587625C2×C418yescomplemented
264#10587624C2×C418yescomplemented
265#10587622C2×C418yescomplemented
266#10587621C2×C418yescomplemented
267D4×Dic17—42no—
268D4×Dic17—42no—
269D4×Dic17C2×C418yescomplemented
270C4×C22⋊D17—42no—
271C4×C22⋊D17—42no—
272C4×C22⋊D17—42no—
273C2×#63227C2311yescharacteristic
274C2×#63227C2311yescharacteristic
275C2×#63227C2311yescharacteristic
276C2×#63227C2311yescharacteristic
277C2×#63227C2311yescharacteristic
278C2×#63227C2311yescharacteristic
279C2×#63227C2311yescharacteristic
280C2×#63227C2311yescharacteristic
281C2×C4⋊Dic17C2311yescharacteristic
282C2×C4⋊Dic17C2311yescharacteristic
283C2×C4⋊Dic17C2311yescharacteristic
284C2×C4⋊Dic17C2311yescharacteristic
285C2×C4⋊Dic17C2311yescharacteristic
286C2×#63225—42no—
287C2×#63225C2311yescharacteristic
288C2×#63225C2311yescharacteristic
289C2×#63225C2311yescharacteristic
290C2×#63225C2311yescharacteristic
291C2×#63225C2311yescharacteristic
292C2×#63225C2311yescharacteristic
293C2×#63225C2311yescharacteristic
294C2×#63225C2311yescharacteristic
295C2×#63225C2311yescharacteristic
296C2×#63225C2311yescharacteristic
297C2×#63225C2311yescharacteristic
298C2×#63225C2311yescharacteristic
299C2×#63225C2311yescharacteristic
300C2×#63225C2311yescharacteristic
301C2×#63225C2311yescharacteristic
302C2×#63225C2311yescharacteristic
303C2×#63225C2311yescharacteristic
304C2×#63225C2311yescharacteristic
305C2×#63225C2311yescharacteristic
306C2×#63225C2311yescharacteristic
307C2×#63225C2311yescharacteristic
308C2×#63225C2311yescharacteristic
309C2×C4×Dic17—42no—
310C2×C4×Dic17C2311yescharacteristic
311C2×C4×Dic17C2311yescharacteristic
312C2×C4×Dic17C2311yescharacteristic
313C2×C4×Dic17C2311yescharacteristic
314C2×C4×Dic17C2311yescharacteristic
315C2×C4×Dic17C2311yescharacteristic
316C2×C4×Dic17C2311yescharacteristic
317C2×C4×Dic17C2311yescharacteristic
318C2×C4×Dic17C2311yescharacteristic
319C2×C4×Dic17C2311yescharacteristic
320C2×C4×Dic17C2311yescharacteristic
321C2×C4×Dic17C2311yescharacteristic
322C2×C4×Dic17C2311yescharacteristic
323C2×C4×Dic17C2311yescharacteristic
324C2×C4×Dic17C2311yescharacteristic
325#10587573—42no—
326#10587571C2×C418yescomplemented
327#10587569C2×C418yescomplemented
328#10587567—42no—
329#10587567—42no—
330#10587567C2×C418yescomplemented
331#10587565C2×C418yescomplemented
332#10587565C2×C418yescomplemented
333#10587564C2×C418yescomplemented
334#10587563—42no—
335#10587558—42no—
336C17×#95C2311yescharacteristic
337C17×#95C2311yescharacteristic
338C17×#95C2311yescharacteristic
339C17×#95C2311yescharacteristic
340C17×#95C2311yescharacteristic
341C17×#95C2311yescharacteristic
342#10587502C2311yescharacteristic
343#10587502C2311yescharacteristic
344#10587502C2311yescharacteristic
345#10587502C2311yescharacteristic
346#10587502C2311yescharacteristic
347#10587502C2311yescharacteristic
348#10587502C2311yescharacteristic
349#10587502C2311yescharacteristic
350#10587502C2311yescharacteristic
351#10587502C2311yescharacteristic
352#10587502C2311yescharacteristic
353#10587502C2311yescharacteristic
354#10587502C2311yescharacteristic
355#10587502C2311yescharacteristic
356#10587502C2311yescharacteristic
357#10587502C2311yescharacteristic
358#10587502C2311yescharacteristic
359#10587502C2311yescharacteristic
360#10587502C2311yescharacteristic
361#10587502C2311yescharacteristic
362#10587502C2311yescharacteristic
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
376C24×C17—22no—
377C24×C17—22no—
378C24×C17—41no—
379C24×C17—41no—
380C24×C17—41no—
381C24×C17—41no—
382C24×C17C22×C414yes—
383C24×C17C2411yescharacteristic
384C24×C17C2411yescharacteristic
385C24×C17C2411yescharacteristic
386C24×C17C2411yescharacteristic
387C23×D17C2411yescharacteristic
388C2×D4×C17—22no—
389C2×D4×C17—22no—
390C2×D4×C17—41no—
391C2×D4×C17—41no—
392C2×D4×C17—41no—
393C2×D4×C17—41no—
394C2×D4×C17C22×C414yes—
395C2×D4×C17C22×C414yes—
396C2×D4×C17C22×C414yes—
397C22×C4×C17—22no—
398C22×C4×C17—22no—
399C22×C4×C17—22no—
400C22×C4×C17—22no—
401C22×C4×C17—41no—
402C22×C4×C17—41no—
403C22×C4×C17—41no—
404C22×C4×C17—41no—
405C22×C4×C17—41no—
406C22×C4×C17—41no—
407C22×C4×C17—41no—
408C22×C4×C17—41no—
409C22×C4×C17—41no—
410C22×C4×C17—41no—
411C22×C4×C17—41no—
412C22×C4×C17C2411yescharacteristic
413C22×C4×C17C2411yescharacteristic
414C22×C4×C17C2411yescharacteristic
415C22×C4×C17C2411yescharacteristic
416C22×C4×C17C2411yescharacteristic
417C22×C4×C17C2411yescharacteristic
418C22×C4×C17C2411yescharacteristic
419C22×C4×C17C2411yescharacteristic
420C22×C4×C17C2411yescharacteristic
421C22×C4×C17C2411yescharacteristic
422C22×C4×C17C2411yescharacteristic
423C2×C22⋊D17—22no—
424C2×C22⋊D17—22no—
425C2×C22⋊D17—41no—
426C2×C22⋊D17—41no—
427C2×C22⋊D17—41no—
428C2×C22⋊D17—41no—
429C2×C22⋊D17—41no—
430C2×C22⋊D17—41no—
431C2×C22⋊D17C22×C414yes—
432C2×C22⋊D17C22×C414yes—
433C2×C22⋊D17C22×C414yes—
434C2×C22⋊D17C22×C414yes—
435C22×Dic17—22no—
436C22×Dic17—22no—
437C22×Dic17—22no—
438C22×Dic17—41no—
439C22×Dic17—41no—
440C22×Dic17—41no—
441C22×Dic17—41no—
442C22×Dic17—41no—
443C22×Dic17—41no—
444C22×Dic17—41no—
445C22×Dic17—41no—
446C22×Dic17—41no—
447C22×Dic17—41no—
448C22×Dic17—41no—
449C22×Dic17—41no—
450C22×Dic17—41no—
451C22×Dic17—41no—
452C22×Dic17—41no—
453C22×Dic17—41no—
454C22×Dic17—41no—
455C22×Dic17—41no—
456C22×Dic17C22×C414yes—
457C22×Dic17C22×C414yes—
458C22×Dic17C22×C414yes—
459C22×Dic17C2411yescharacteristic
460C22×Dic17C2411yescharacteristic
461C22×Dic17C2411yescharacteristic
462C22×Dic17C2411yescharacteristic
463C22×Dic17C2411yescharacteristic
464C22×Dic17C2411yescharacteristic
465C22×Dic17C2411yescharacteristic
466C22×Dic17C2411yescharacteristic
467C22×Dic17C2411yescharacteristic
468C22×Dic17C2411yescharacteristic
469C22×Dic17C2411yescharacteristic
470C22×Dic17C2411yescharacteristic
471C22×Dic17C2411yescharacteristic
472C22×Dic17C2411yescharacteristic
473C22×Dic17C2411yescharacteristic
474C2×C4×D17—22no—
475C2×C4×D17—41no—
476C2×C4×D17—41no—
477C2×C4×D17—41no—
478C2×C4×D17—41no—
479C2×C4×D17—41no—
480C2×C4×D17—41no—
481C2×C4×D17—41no—
482C2×C4×D17C22×C414yes—
483C2×Dic34—41no—
484C2×Dic34—41no—
485C2×Dic34C22×C414yes—
486C4⋊C4×C17—22no—
487C4⋊C4×C17—41no—
488C4⋊C4×C17—41no—
489C22⋊C4×C17—22no—
490C22⋊C4×C17—22no—
491C22⋊C4×C17—22no—
492C22⋊C4×C17—22no—
493C22⋊C4×C17—41no—
494C22⋊C4×C17—41no—
495C22⋊C4×C17—41no—
496C22⋊C4×C17—41no—
497C22⋊C4×C17—41no—
498C22⋊C4×C17—41no—
499C22⋊C4×C17—41no—
500C22⋊C4×C17C22×C414yes—
501C22⋊C4×C17C22×C414yes—
502C22⋊C4×C17C22×C414yes—
503C42×C17—41no—
504C42×C17—41no—
505C42×C17—41no—
506C22⋊Dic17—22no—
507C22⋊Dic17—22no—
508C22⋊Dic17—22no—
509C22⋊Dic17—22no—
510C22⋊Dic17—22no—
511C22⋊Dic17—41no—
512C22⋊Dic17—41no—
513C22⋊Dic17—41no—
514C22⋊Dic17—41no—
515C22⋊Dic17—41no—
516C22⋊Dic17—41no—
517C22⋊Dic17C22×C414yes—
518C22⋊Dic17C22×C414yes—
519C22⋊Dic17C22×C414yes—
520C22⋊Dic17C22×C414yes—
521C22⋊Dic17C22×C414yes—
522C22⋊Dic17C22×C414yes—
523C22⋊Dic17C22×C414yes—
524C22⋊Dic17C22×C414yes—
525C22⋊Dic17C22×C414yes—
526#63227—22no—
527#63227—41no—
528#63227—41no—
529#63227—41no—
530#63227—41no—
531#63227—41no—
532#63227C22×C414yes—
533#63227C22×C414yes—
534C4⋊Dic17—41no—
535C4⋊Dic17—41no—
536C4⋊Dic17—41no—
537C4⋊Dic17C22×C414yes—
538C4⋊Dic17C22×C414yes—
539#63225—22no—
540#63225—22no—
541#63225—22no—
542#63225—41no—
543#63225—41no—
544#63225—41no—
545#63225—41no—
546#63225—41no—
547#63225—41no—
548#63225—41no—
549#63225—41no—
550#63225—41no—
551#63225—41no—
552#63225—41no—
553#63225—41no—
554#63225—41no—
555#63225—41no—
556#63225—41no—
557#63225C22×C414yes—
558#63225C22×C414yes—
559#63225C22×C414yes—
560#63225C22×C414yes—
561C4×Dic17—22no—
562C4×Dic17—22no—
563C4×Dic17—22no—
564C4×Dic17—22no—
565C4×Dic17—41no—
566C4×Dic17—41no—
567C4×Dic17—41no—
568C4×Dic17—41no—
569C4×Dic17—41no—
570C4×Dic17—41no—
571C4×Dic17—41no—
572C4×Dic17—41no—
573C4×Dic17—41no—
574C4×Dic17C22×C414yes—
575C4×Dic17C22×C414yes—
576#34424—171nomaximal, Sylow
577C23×C17—21no—
578C23×C17—21no—
579C23×C17—21no—
580C23×C17—21no—
581C23×C17—21no—
582C23×C17—21no—
583C23×C17—21no—
584C23×C17—21no—
585C23×C17—21no—
586C23×C17—21no—
587C23×C17—21no—
588C23×C17—21no—
589C23×C17—21no—
590C23×C17—21no—
591C23×C17—21no—
592C23×C17—21no—
593C23×C17—21no—
594C23×C17—21no—
595C23×C17—21no—
596C23×C17—21no—
597C23×C17—21no—
598C23×C17—21no—
599C23×C17—28no—
600C23×C17—44no—
601C23×C17—44no—
602C23×C17—82no—
603C23×C17—82no—
604C23×C17—82no—
605C23×C17—82no—
606C23×C17C23×C412yes—
607C23×C17C23×C412yes—
608C23×C17C23×C412yes—
609C23×C17C23×C412yes—
610C23×C17H(5,𝔽2)12yes—
611C23×C172−1+412yes—
612C23×C17C2511yescharacteristic
613C22×D17—21no—
614C22×D17—21no—
615C22×D17—21no—
616C22×D17—21no—
617C22×D17—21no—
618C22×D17—21no—
619C22×D17C23×C412yes—
620D4×C17—28no—
621D4×C17—44no—
622D4×C17—44no—
623C2×C4×C17—21no—
624C2×C4×C17—21no—
625C2×C4×C17—21no—
626C2×C4×C17—21no—
627C2×C4×C17—21no—
628C2×C4×C17—21no—
629C2×C4×C17—21no—
630C2×C4×C17—21no—
631C2×C4×C17—21no—
632C2×C4×C17—21no—
633C2×C4×C17—21no—
634C2×C4×C17—21no—
635C2×C4×C17—21no—
636C2×C4×C17—21no—
637C2×C4×C17—21no—
638C2×C4×C17—21no—
639C2×C4×C17—21no—
640C2×C4×C17—21no—
641C2×C4×C17—21no—
642C2×C4×C17—21no—
643C2×C4×C17—21no—
644C2×C4×C17—21no—
645C2×C4×C17—21no—
646C2×C4×C17—21no—
647C2×C4×C17—21no—
648C2×C4×C17—21no—
649C2×C4×C17—21no—
650C2×C4×C17—21no—
651C2×C4×C17—21no—
652C2×C4×C17—44no—
653C2×C4×C17—82no—
654C2×C4×C17—82no—
655C2×C4×C17—82no—
656C2×C4×C17—82no—
657C2×C4×C17C23×C412yes—
658C2×C4×C17C23×C412yes—
659C2×C4×C17C23×C412yes—
660C2×C4×C17H(5,𝔽2)12yes—
661C22⋊D17—28no—
662C22⋊D17—44no—
663C22⋊D17—44no—
664C22⋊D17—44no—
665C2×Dic17—21no—
666C2×Dic17—21no—
667C2×Dic17—21no—
668C2×Dic17—21no—
669C2×Dic17—21no—
670C2×Dic17—21no—
671C2×Dic17—21no—
672C2×Dic17—21no—
673C2×Dic17—21no—
674C2×Dic17—21no—
675C2×Dic17—21no—
676C2×Dic17—21no—
677C2×Dic17—21no—
678C2×Dic17—21no—
679C2×Dic17—21no—
680C2×Dic17—21no—
681C2×Dic17—21no—
682C2×Dic17—21no—
683C2×Dic17—21no—
684C2×Dic17—21no—
685C2×Dic17—21no—
686C2×Dic17—21no—
687C2×Dic17—21no—
688C2×Dic17—21no—
689C2×Dic17—21no—
690C2×Dic17—21no—
691C2×Dic17—21no—
692C2×Dic17—21no—
693C2×Dic17—21no—
694C2×Dic17—21no—
695C2×Dic17—21no—
696C2×Dic17—21no—
697C2×Dic17—21no—
698C2×Dic17—21no—
699C2×Dic17—21no—
700C2×Dic17—21no—
701C2×Dic17—21no—
702C2×Dic17—44no—
703C2×Dic17—44no—
704C2×Dic17—44no—
705C2×Dic17—44no—
706C2×Dic17—82no—
707C2×Dic17—82no—
708C2×Dic17—82no—
709C2×Dic17—82no—
710C2×Dic17C23×C412yes—
711C2×Dic17C23×C412yes—
712C2×Dic17C23×C412yes—
713C2×Dic17C23×C412yes—
714C2×Dic17C23×C412yes—
715C2×Dic17C23×C412yes—
716C2×Dic17C23×C412yes—
717C2×Dic17H(5,𝔽2)12yes—
718C4×D17—44no—
719C4×D17—82no—
720C4×D17—82no—
721Dic34—44no—
722C2×#538—171no—
723#2379—171no—
724#2379—171no—
725#2376—171no—
726#2376—171no—
727#2367—171no—
728#2367—171no—
729#2359—171no—
730#2359—171no—
731#2358—171no—
732#2358—171no—
733#2358—171no—
734#2358D1711yescharacteristic, complemented
735#2352—171no—
736#2352—171no—
737#2349—171no—
738#2349—171no—
739#2334—171no—
740#2334—171no—
741#2334—171no—
742#2334—171no—
743#2329—171no—
744#2325—171no—
745#2325—171no—
746#2325—171no—
747#2324—171no—
748#2324—171no—
749#2315—171no—
750C4×C22⋊Q8—171no—
751C4×#121—171no—
752C2×#388—171no—
753C22×C17—22no—
754C22×C17—22no—
755C22×C17—22no—
756C22×C17—22no—
757C22×C17—22no—
758C22×C17—22no—
759C22×C17—22no—
760C22×C17—22no—
761C22×C17—22no—
762C22×C17—22no—
763C22×C17—22no—
764C22×C17—22no—
765C22×C17—22no—
766C22×C17—22no—
767C22×C17—22no—
768C22×C17—41no—
769C22×C17—41no—
770C22×C17—41no—
771C22×C17—41no—
772C22×C17—41no—
773C22×C17—41no—
774C22×C17—41no—
775C22×C17—41no—
776C22×C17—41no—
777C22×C17—41no—
778C22×C17—41no—
779C22×C17—41no—
780C22×C17—88no—
781C22×C17#52014yes—
782C22×C17C24×C411yescharacteristic
783C22×C17C2×H(5,𝔽2)11yescharacteristic
784C22×C17C2×H(5,𝔽2)11yescharacteristic
785C22×C17C2×H(5,𝔽2)11yescharacteristic
786C22×C17C2×2−1+411yescharacteristic
787C22×C17#58511yescharacteristic
788C22×C17#58511yescharacteristic
789C2×D17—22no—
790C2×D17—22no—
791C2×D17—22no—
792C2×D17—41no—
793C2×D17—41no—
794C2×D17—41no—
795C2×D17—41no—
796C4×C17—22no—
797C4×C17—22no—
798C4×C17—22no—
799C4×C17—22no—
800C4×C17—41no—
801C4×C17—41no—
802C4×C17—41no—
803C4×C17—41no—
804C4×C17—41no—
805C4×C17—41no—
806C4×C17—41no—
807Dic17—22no—
808Dic17—22no—
809Dic17—22no—
810Dic17—22no—
811Dic17—22no—
812Dic17—22no—
813Dic17—22no—
814Dic17—22no—
815Dic17—41no—
816Dic17—41no—
817Dic17—41no—
818Dic17—41no—
819Dic17—41no—
820Dic17—41no—
821Dic17—41no—
822#538—1716no—
823C2×#126—171no—
824C2×#126—171no—
825C2×#124—171no—
826C2×#124—171no—
827C2×#123—171no—
828C2×#123—171no—
829C2×C22⋊Q8—171no—
830C2×#121—171no—
831C2×#121—171no—
832C2×#121—171no—
833C2×#120—171no—
834C2×#120C2×D1711yescharacteristic
835C2×C4×Q8—171no—
836C2×C4×D4—171no—
837C2×C4×D4—171no—
838C2×C4×D4—171no—
839C2×C4×D4—171no—
840C2×C4×D4—171no—
841C2×C4×D4—171no—
842C2×C4×D4—171no—
843C2×C4×D4—171no—
844C2×C4×D4—171no—
845C2×C4×D4C2×D1711yescharacteristic
846C2×C4×D4C2×D1711yescharacteristic
847C2×#117—171no—
848C2×#117—171no—
849C22×C4⋊C4—171no—
850C22×C22⋊C4—171no—
851C22×C22⋊C4—171no—
852C22×C22⋊C4—171no—
853C22×C22⋊C4C2×D1711yescharacteristic
854C22×C22⋊C4C2×D1711yescharacteristic
855C22×C42—171no—
856#391—171no—
857#391—171no—
858#391—171no—
859#390—171no—
860#390—171no—
861#390—171no—
862#390—171no—
863#390C2×D1711yescharacteristic
864#389—171no—
865#389—171no—
866#389—171no—
867#389—171no—
868#389—171no—
869#389—171no—
870#389—171no—
871#389—171no—
872#388—171no—
873#388—171no—
874#388—171no—
875#388—171no—
876#388—171no—
877#388—171no—
878#388—171no—
879#388—171no—
880#388—171no—
881#388—171no—
882#388—171no—
883#388—171no—
884#388—171no—
885#388—171no—
886#388—171no—
887#388—171no—
888#388—171no—
889#388—171no—
890#388—171no—
891#388—171no—
892#388—171no—
893#388—171no—
894#388C2×D1711yescharacteristic
895#388C2×D1711yescharacteristic
896#387—171no—
897#387—171no—
898#387—171no—
899#387—171no—
900#387—171no—
901#387—171no—
902#387—171no—
903#387—171no—
904#387—171no—
905#387—171no—
906#387—171no—
907#387—171no—
908#386—171no—
909#386—171no—
910#386—171no—
911#386—171no—
912#386—171no—
913#386—171no—
914#386—171no—
915#386—171no—
916#386—171no—
917#386—171no—
918#386—171no—
919#386C2×D1711yescharacteristic
920#386C2×D1711yescharacteristic
921#386C2×D1711yescharacteristic
922#385—171no—
923#385—171no—
924#385—171no—
925#385—171no—
926#385—171no—
927#385—171no—
928#385—171no—
929#385—171no—
930#385—171no—
931#385—171no—
932#385—171no—
933#385—171no—
934#385—171no—
935#385—171no—
936#385—171no—
937#385—171no—
938#385—171no—
939#385—171no—
940#385—171no—
941#385—171no—
942#385C2×D1711yescharacteristic
943#385C2×D1711yescharacteristic
944#382—171no—
945#382—171no—
946#382—171no—
947#382—171no—
948#380—171no—
949#380—171no—
950#380—171no—
951#380—171no—
952#380—171no—
953#380—171no—
954#380—171no—
955#380—171no—
956C4×C4⋊C4—171no—
957C4×C4⋊C4—171no—
958C4×C4⋊C4—171no—
959C4×C4⋊C4—171no—
960C4×C4⋊C4—171no—
961C4×C4⋊C4—171no—
962C4×C4⋊C4—171no—
963C4×C4⋊C4—171no—
964C4×C22⋊C4—171no—
965C4×C22⋊C4—171no—
966C4×C22⋊C4—171no—
967C4×C22⋊C4—171no—
968C4×C22⋊C4—171no—
969C4×C22⋊C4—171no—
970C4×C22⋊C4—171no—
971C4×C22⋊C4—171no—
972C4×C22⋊C4C2×D1711yescharacteristic
973C4×C22⋊C4C2×D1711yescharacteristic
974C2×#95—171no—
975C2×#95—171no—
976C2×#95—171no—
977C2×#95—171no—
978C2×C17—24no—
979C2×C17—42no—
980C2×C17—42no—
981C2×C17—42no—
982C2×C17C2×#52011yescharacteristic
983C2×C17C4×H(5,𝔽2)11yescharacteristic
984C2×C17C4×H(5,𝔽2)11yescharacteristic
985C2×C17#353411yescharacteristic
986C2×C17#353611yescharacteristic
987C2×C17#355811yescharacteristic
988C2×C17#356411yescharacteristic
989D17—42no—
990C25C22×D1711yescharacteristic
991C22×Q8—171no—
992C22×D4—171no—
993C22×D4—171no—
994C22×D4—171no—
995C22×D4—171no—
996C22×D4C22×D1711yescharacteristic
997C22×D4C22×D1711yescharacteristic
998C22×D4C22×D1711yescharacteristic
999C23×C4—171no—
1000C23×C4—171no—
1001C23×C4—171no—
1002C23×C4—171no—
1003C23×C4—171no—
1004C23×C4—171no—
1005C23×C4—171no—
1006C23×C4—171no—
1007C23×C4—171no—
1008C23×C4—171no—
1009C23×C4—171no—
1010C23×C4C22×D1711yescharacteristic
1011C23×C4C22×D1711yescharacteristic
1012C23×C4C22×D1711yescharacteristic
1013C23×C4C22×D1711yescharacteristic
1014C23×C4C22×D1711yescharacteristic
1015#126—178no—
1016#126—178no—
1017#124—178no—
1018#124—178no—
1019#123—178no—
1020#123—178no—
1021C22⋊Q8—178no—
1022#121—178no—
1023#121—178no—
1024#121—178no—
1025#120—178no—
1026#120C4×D1718yescomplemented
1027C4×Q8—682no—
1028C4×D4—42no—
1029C4×D4—42no—
1030C4×D4—178no—
1031C4×D4—178no—
1032C4×D4—682no—
1033C4×D4—682no—
1034C4×D4—682no—
1035C4×D4—682no—
1036C4×D4—682no—
1037C4×D4—682no—
1038C4×D4—682no—
1039#117—682no—
1040#117—682no—
1041C2×C4⋊C4—171no—
1042C2×C4⋊C4—171no—
1043C2×C4⋊C4—171no—
1044C2×C4⋊C4—171no—
1045C2×C4⋊C4—171no—
1046C2×C4⋊C4—171no—
1047C2×C4⋊C4—171no—
1048C2×C4⋊C4—171no—
1049C2×C4⋊C4—171no—
1050C2×C4⋊C4—171no—
1051C2×C4⋊C4—171no—
1052C2×C4⋊C4—171no—
1053C2×C4⋊C4—171no—
1054C2×C4⋊C4—171no—
1055C2×C4⋊C4—171no—
1056C2×C4⋊C4—171no—
1057C2×C4⋊C4—171no—
1058C2×C4⋊C4—171no—
1059C2×C4⋊C4—171no—
1060C2×C4⋊C4—171no—
1061C2×C4⋊C4—171no—
1062C2×C4⋊C4—171no—
1063C2×C4⋊C4—171no—
1064C2×C4⋊C4—171no—
1065C2×C4⋊C4—171no—
1066C2×C4⋊C4—171no—
1067C2×C4⋊C4—171no—
1068C2×C4⋊C4—682no—
1069C2×C4⋊C4C22×D1711yescharacteristic
1070C2×C4⋊C4C22×D1711yescharacteristic
1071C2×C4⋊C4C22×D1711yescharacteristic
1072C2×C22⋊C4—42no—
1073C2×C22⋊C4—42no—
1074C2×C22⋊C4—178no—
1075C2×C22⋊C4—171no—
1076C2×C22⋊C4—171no—
1077C2×C22⋊C4—171no—
1078C2×C22⋊C4—171no—
1079C2×C22⋊C4—171no—
1080C2×C22⋊C4—171no—
1081C2×C22⋊C4—171no—
1082C2×C22⋊C4—171no—
1083C2×C22⋊C4—171no—
1084C2×C22⋊C4—171no—
1085C2×C22⋊C4—171no—
1086C2×C22⋊C4—171no—
1087C2×C22⋊C4—171no—
1088C2×C22⋊C4—171no—
1089C2×C22⋊C4—171no—
1090C2×C22⋊C4—171no—
1091C2×C22⋊C4—171no—
1092C2×C22⋊C4—171no—
1093C2×C22⋊C4—171no—
1094C2×C22⋊C4—171no—
1095C2×C22⋊C4—171no—
1096C2×C22⋊C4—171no—
1097C2×C22⋊C4—171no—
1098C2×C22⋊C4—171no—
1099C2×C22⋊C4—171no—
1100C2×C22⋊C4—171no—
1101C2×C22⋊C4—171no—
1102C2×C22⋊C4—171no—
1103C2×C22⋊C4—682no—
1104C2×C22⋊C4—682no—
1105C2×C22⋊C4C22×D1711yescharacteristic
1106C2×C22⋊C4C22×D1711yescharacteristic
1107C2×C22⋊C4C22×D1711yescharacteristic
1108C2×C22⋊C4C22×D1711yescharacteristic
1109C2×C22⋊C4C22×D1711yescharacteristic
1110C2×C22⋊C4C22×D1711yescharacteristic
1111C2×C22⋊C4C22×D1711yescharacteristic
1112C2×C22⋊C4C22×D1711yescharacteristic
1113C2×C22⋊C4C22×D1711yescharacteristic
1114C2×C22⋊C4C22×D1711yescharacteristic
1115C2×C22⋊C4C22×D1711yescharacteristic
1116C2×C22⋊C4C22×D1711yescharacteristic
1117C2×C22⋊C4C22×D1711yescharacteristic
1118C2×C22⋊C4C22×D1711yescharacteristic
1119C2×C42—171no—
1120C2×C42—171no—
1121C2×C42—171no—
1122C2×C42—171no—
1123C2×C42—171no—
1124C2×C42—171no—
1125C2×C42—171no—
1126C2×C42—171no—
1127C2×C42—171no—
1128C2×C42—171no—
1129C2×C42—171no—
1130C2×C42—171no—
1131C2×C42—171no—
1132C2×C42—171no—
1133C2×C42—171no—
1134C2×C42—682no—
1135C2×C42C22×D1711yescharacteristic
1136C2×C42C22×D1711yescharacteristic
1137C2×C42C22×D1711yescharacteristic
1138#95—171no—
1139#95—171no—
1140#95—171no—
1141#95—171no—
1142#95—171no—
1143#95—171no—
1144#95—171no—
1145#95—171no—
1146#95—171no—
1147#95—171no—
1148#95—171no—
1149#95—171no—
1150#95—171no—
1151#95—171no—
1152#95—171no—
1153#95—171no—
1154#95—171no—
1155#95—171no—
1156#95—171no—
1157#95—171no—
1158#95—171no—
1159#95—171no—
1160#95—171no—
1161#95—171no—
1162#95—171no—
1163#95—171no—
1164#95—171no—
1165#95—171no—
1166#95—171no—
1167#95—171no—
1168#95—171no—
1169#95—171no—
1170#95—171no—
1171#95—171no—
1172#95C22×D1711yescharacteristic
1173#95C22×D1711yescharacteristic
1174#95C22×D1711yescharacteristic
1175#95C22×D1711yescharacteristic
1176#95C22×D1711yescharacteristic
1177#95C22×D1711yescharacteristic
1178C17#3442411yescharacteristic, complemented, Sylow
1179C24—22no—
1180C24—22no—
1181C24—41no—
1182C24—41no—
1183C24—41no—
1184C24—41no—
1185C24—171no—
1186C24C2×C4×D1714yes—
1187C24C23×D1711yescharacteristic
1188C24C23×D1711yescharacteristic
1189C24C23×D1711yescharacteristic
1190C24C23×D1711yescharacteristic
1191C2×Q8—174no—
1192C2×Q8—681no—
1193C2×Q8—681no—
1194C2×D4—22no—
1195C2×D4—22no—
1196C2×D4—41no—
1197C2×D4—41no—
1198C2×D4—41no—
1199C2×D4—41no—
1200C2×D4—174no—
1201C2×D4—174no—
1202C2×D4—174no—
1203C2×D4—174no—
1204C2×D4—342no—
1205C2×D4—342no—
1206C2×D4—681no—
1207C2×D4—681no—
1208C2×D4—681no—
1209C2×D4—681no—
1210C2×D4—681no—
1211C2×D4—681no—
1212C2×D4C2×C4×D1714yes—
1213C2×D4C2×C4×D1714yes—
1214C2×D4C2×C4×D1714yes—
1215C22×C4—22no—
1216C22×C4—22no—
1217C22×C4—22no—
1218C22×C4—22no—
1219C22×C4—41no—
1220C22×C4—41no—
1221C22×C4—41no—
1222C22×C4—41no—
1223C22×C4—41no—
1224C22×C4—41no—
1225C22×C4—41no—
1226C22×C4—41no—
1227C22×C4—41no—
1228C22×C4—41no—
1229C22×C4—41no—
1230C22×C4—171no—
1231C22×C4—171no—
1232C22×C4—171no—
1233C22×C4—171no—
1234C22×C4—171no—
1235C22×C4—171no—
1236C22×C4—171no—
1237C22×C4—171no—
1238C22×C4—174no—
1239C22×C4—174no—
1240C22×C4—174no—
1241C22×C4—174no—
1242C22×C4—171no—
1243C22×C4—171no—
1244C22×C4—171no—
1245C22×C4—171no—
1246C22×C4—171no—
1247C22×C4—171no—
1248C22×C4—171no—
1249C22×C4—342no—
1250C22×C4—342no—
1251C22×C4—342no—
1252C22×C4—342no—
1253C22×C4—681no—
1254C22×C4—681no—
1255C22×C4—681no—
1256C22×C4—681no—
1257C22×C4—681no—
1258C22×C4—681no—
1259C22×C4—681no—
1260C22×C4—681no—
1261C22×C4—681no—
1262C22×C4—681no—
1263C22×C4—681no—
1264C22×C4—681no—
1265C22×C4—681no—
1266C22×C4—681no—
1267C22×C4—681no—
1268C22×C4—681no—
1269C22×C4—681no—
1270C22×C4—681no—
1271C22×C4—681no—
1272C22×C4—681no—
1273C22×C4—681no—
1274C22×C4—681no—
1275C22×C4—681no—
1276C22×C4—681no—
1277C22×C4—681no—
1278C22×C4C23×D1711yescharacteristic
1279C22×C4C23×D1711yescharacteristic
1280C22×C4C23×D1711yescharacteristic
1281C22×C4C23×D1711yescharacteristic
1282C22×C4C23×D1711yescharacteristic
1283C22×C4C23×D1711yescharacteristic
1284C22×C4C23×D1711yescharacteristic
1285C22×C4C23×D1711yescharacteristic
1286C22×C4C23×D1711yescharacteristic
1287C22×C4C23×D1711yescharacteristic
1288C22×C4C23×D1711yescharacteristic
1289C4⋊C4—22no—
1290C4⋊C4—41no—
1291C4⋊C4—41no—
1292C4⋊C4—174no—
1293C4⋊C4—174no—
1294C4⋊C4—174no—
1295C4⋊C4—174no—
1296C4⋊C4—174no—
1297C4⋊C4—174no—
1298C4⋊C4—342no—
1299C4⋊C4—342no—
1300C4⋊C4—342no—
1301C4⋊C4—681no—
1302C4⋊C4—681no—
1303C4⋊C4—681no—
1304C4⋊C4—681no—
1305C4⋊C4—681no—
1306C4⋊C4—681no—
1307C4⋊C4—681no—
1308C4⋊C4—681no—
1309C4⋊C4—681no—
1310C4⋊C4—681no—
1311C4⋊C4—681no—
1312C4⋊C4—681no—
1313C4⋊C4—681no—
1314C4⋊C4—681no—
1315C4⋊C4—681no—
1316C4⋊C4—681no—
1317C4⋊C4—681no—
1318C4⋊C4—681no—
1319C22⋊C4—22no—
1320C22⋊C4—22no—
1321C22⋊C4—22no—
1322C22⋊C4—22no—
1323C22⋊C4—41no—
1324C22⋊C4—41no—
1325C22⋊C4—41no—
1326C22⋊C4—41no—
1327C22⋊C4—41no—
1328C22⋊C4—41no—
1329C22⋊C4—41no—
1330C22⋊C4—174no—
1331C22⋊C4—174no—
1332C22⋊C4—174no—
1333C22⋊C4—174no—
1334C22⋊C4—174no—
1335C22⋊C4—174no—
1336C22⋊C4—174no—
1337C22⋊C4—174no—
1338C22⋊C4—174no—
1339C22⋊C4—174no—
1340C22⋊C4—174no—
1341C22⋊C4—342no—
1342C22⋊C4—342no—
1343C22⋊C4—342no—
1344C22⋊C4—342no—
1345C22⋊C4—342no—
1346C22⋊C4—342no—
1347C22⋊C4—681no—
1348C22⋊C4—681no—
1349C22⋊C4—681no—
1350C22⋊C4—681no—
1351C22⋊C4—681no—
1352C22⋊C4—681no—
1353C22⋊C4—681no—
1354C22⋊C4—681no—
1355C22⋊C4—681no—
1356C22⋊C4—681no—
1357C22⋊C4—681no—
1358C22⋊C4C2×C4×D1714yes—
1359C22⋊C4C2×C4×D1714yes—
1360C22⋊C4C2×C4×D1714yes—
1361C42—41no—
1362C42—41no—
1363C42—41no—
1364C42—174no—
1365C42—174no—
1366C42—342no—
1367C42—342no—
1368C42—342no—
1369C42—342no—
1370C42—681no—
1371C42—681no—
1372C42—681no—
1373C42—681no—
1374C42—681no—
1375C42—681no—
1376C42—681no—
1377C42—681no—
1378C42—681no—
1379C23—21no—
1380C23—21no—
1381C23—21no—
1382C23—21no—
1383C23—21no—
1384C23—21no—
1385C23—21no—
1386C23—21no—
1387C23—21no—
1388C23—21no—
1389C23—21no—
1390C23—21no—
1391C23—21no—
1392C23—21no—
1393C23—21no—
1394C23—21no—
1395C23—21no—
1396C23—21no—
1397C23—21no—
1398C23—21no—
1399C23—21no—
1400C23—21no—
1401C23—28no—
1402C23—44no—
1403C23—44no—
1404C23—82no—
1405C23—82no—
1406C23—82no—
1407C23—82no—
1408C23—172no—
1409C23—341no—
1410C23—341no—
1411C23—341no—
1412C23—341no—
1413C23—341no—
1414C23—341no—
1415C23C22×C4×D1712yes—
1416C23C22×C4×D1712yes—
1417C23C22×C4×D1712yes—
1418C23C22×C4×D1712yes—
1419C23#1058769112yes—
1420C23#1058769712yes—
1421C23C24×D1711yescharacteristic
1422Q8—684no—
1423D4—28no—
1424D4—44no—
1425D4—44no—
1426D4—348no—
1427D4—684no—
1428D4—684no—
1429D4—684no—
1430C2×C4—21no—
1431C2×C4—21no—
1432C2×C4—21no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—21no—
1438C2×C4—21no—
1439C2×C4—21no—
1440C2×C4—21no—
1441C2×C4—21no—
1442C2×C4—21no—
1443C2×C4—21no—
1444C2×C4—21no—
1445C2×C4—21no—
1446C2×C4—21no—
1447C2×C4—21no—
1448C2×C4—21no—
1449C2×C4—21no—
1450C2×C4—21no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—21no—
1457C2×C4—21no—
1458C2×C4—21no—
1459C2×C4—44no—
1460C2×C4—82no—
1461C2×C4—82no—
1462C2×C4—82no—
1463C2×C4—82no—
1464C2×C4—172no—
1465C2×C4—172no—
1466C2×C4—172no—
1467C2×C4—172no—
1468C2×C4—172no—
1469C2×C4—172no—
1470C2×C4—172no—
1471C2×C4—172no—
1472C2×C4—341no—
1473C2×C4—341no—
1474C2×C4—341no—
1475C2×C4—341no—
1476C2×C4—341no—
1477C2×C4—341no—
1478C2×C4—341no—
1479C2×C4—341no—
1480C2×C4—341no—
1481C2×C4—341no—
1482C2×C4—341no—
1483C2×C4—341no—
1484C2×C4—341no—
1485C2×C4—341no—
1486C2×C4—341no—
1487C2×C4—341no—
1488C2×C4—341no—
1489C2×C4—341no—
1490C2×C4—341no—
1491C2×C4—341no—
1492C2×C4—341no—
1493C2×C4—341no—
1494C2×C4—341no—
1495C2×C4—341no—
1496C2×C4—341no—
1497C2×C4—341no—
1498C2×C4—341no—
1499C2×C4—341no—
1500C2×C4—341no—
1501C2×C4—341no—
1502C2×C4—341no—
1503C2×C4—341no—
1504C2×C4—341no—
1505C2×C4—341no—
1506C2×C4—341no—
1507C2×C4—341no—
1508C2×C4—341no—
1509C2×C4—684no—
1510C2×C4—684no—
1511C2×C4—684no—
1512C2×C4—684no—
1513C2×C4—684no—
1514C2×C4—1362no—
1515C2×C4—1362no—
1516C2×C4—1362no—
1517C2×C4—1362no—
1518C2×C4—1362no—
1519C2×C4—1362no—
1520C2×C4C22×C4×D1712yes—
1521C2×C4C22×C4×D1712yes—
1522C2×C4C22×C4×D1712yes—
1523C2×C4#1058769112yes—
1524C22—22no—
1525C22—22no—
1526C22—22no—
1527C22—22no—
1528C22—22no—
1529C22—22no—
1530C22—22no—
1531C22—22no—
1532C22—22no—
1533C22—22no—
1534C22—22no—
1535C22—22no—
1536C22—22no—
1537C22—22no—
1538C22—22no—
1539C22—41no—
1540C22—41no—
1541C22—41no—
1542C22—41no—
1543C22—41no—
1544C22—41no—
1545C22—41no—
1546C22—41no—
1547C22—41no—
1548C22—41no—
1549C22—41no—
1550C22—41no—
1551C22—88no—
1552C22—342no—
1553C22—342no—
1554C22—342no—
1555C22—681no—
1556C22—681no—
1557C22—681no—
1558C22—681no—
1559C22#1176328814yes—
1560C22C23×C4×D1711yescharacteristic
1561C22H(5,𝔽2)×D1711yescharacteristic
1562C22C2×#1058769111yescharacteristic
1563C22C2×#1058769111yescharacteristic
1564C22C2×#1058769711yescharacteristic
1565C22#1176364411yescharacteristic
1566C22#1176364511yescharacteristic
1567C4—22no—
1568C4—22no—
1569C4—22no—
1570C4—22no—
1571C4—41no—
1572C4—41no—
1573C4—41no—
1574C4—41no—
1575C4—41no—
1576C4—41no—
1577C4—41no—
1578C4—342no—
1579C4—342no—
1580C4—342no—
1581C4—342no—
1582C4—342no—
1583C4—342no—
1584C4—342no—
1585C4—342no—
1586C4—681no—
1587C4—681no—
1588C4—681no—
1589C4—681no—
1590C4—681no—
1591C4—681no—
1592C4—681no—
1593C2—24no—
1594C2—42no—
1595C2—42no—
1596C2—42no—
1597C2—682no—
1598C2C2×#1176328811yescharacteristic
1599C2#1454198811yescharacteristic
1600C2C4×#1058769111yescharacteristic
1601C2#1454296211yescharacteristic
1602C2#1454300411yescharacteristic
1603C2#1454329411yescharacteristic
1604C2#1454340011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2358C2
socle, cosocleC23×C17C25
prime radicalC2×#11763394C2
hypercenter#2358D17
hypocenterC17#34424
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2358

Complements

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

NH ≅ G/Ntype
2. #14531954C2semidirect
3. #14531953C2semidirect
4. #14531934C2semidirect
5. #14531933C2semidirect
6. #14531857C2semidirect
7. #14531850C2semidirect
8. #14531782C2semidirect
9. #14531777C2semidirect
10. #14531768C2semidirect
11. #14531763C2semidirect
12. #14531763C2semidirect
13. #14531711C2semidirect
14. #14531707C2semidirect
15. #14531690C2semidirect
16. #14531689C2semidirect
17. #14531561C2semidirect
18. #14531557C2semidirect
19. #14531556C2semidirect
20. #14531554C2semidirect
21. #14531512C2semidirect
22. #14531486C2semidirect
23. #14531485C2semidirect
24. #14531482C2semidirect
25. #14531480C2semidirect
26. #14531474C2semidirect
27. #14531396C2semidirect
28. #14531316C2semidirect
29. C4×#10587625C2semidirect
30. C2×#11762697C2semidirect
31. C17×#2358C2semidirect
32. #11763394C4semidirect
44. C2×#10587573C22semidirect
50. C2×C4×C22⋊D17C22semidirect
54. C2×#10587558C22semidirect
55. C2×#10587563C22semidirect
61. #11762715C22semidirect
62. #11762713C22semidirect
63. #11762713C22semidirect
67. #11762709C22semidirect
68. #11762707C22semidirect
69. #11762707C22semidirect
70. #11762706C22semidirect
71. #11762706C22semidirect
72. #11762705C22semidirect
73. #11762704C22semidirect
74. #11762704C22semidirect
75. #11762704C22semidirect
78. #11762703C22semidirect
79. #11762703C22semidirect
80. #11762703C22semidirect
83. #11762700C22semidirect
84. #11762699C22semidirect
85. #11762698C22semidirect
86. #11762698C22semidirect
97. #11762697C22semidirect
98. #11762696C22semidirect
99. #11762696C22semidirect
100. #11762694C22semidirect
101. #11762694C22semidirect
102. #11762693C22semidirect
103. #11762693C22semidirect
104. #11762693C22semidirect
105. #11762692C22semidirect
106. #11762692C22semidirect
107. #11762691C22semidirect
108. #11762691C22semidirect
109. #11762690C22semidirect
117. #11762686C22semidirect
120. #11762685C22semidirect
123. #11762683C22semidirect
124. #11762683C22semidirect
131. #11762682C22semidirect
138. #11762681C22semidirect
139. #11762681C22semidirect
140. #11762680C22semidirect
141. #11762674C22semidirect
142. #11762673C22semidirect
143. #11762673C22semidirect
144. #11762673C22semidirect
145. #11762668C22semidirect
150. #11762667C22semidirect
151. #11762667C22semidirect
152. #11762666C22semidirect
153. C4⋊C4×Dic17C22semidirect
154. C4⋊C4×Dic17C22semidirect
155. C4×#63225C22semidirect
156. C4×#63225C22semidirect
157. C4×#63225C22semidirect
158. #11762660C22semidirect
159. #11762660C22semidirect
160. #11762660C22semidirect
165. C4×#63227C22semidirect
168. C4×C22⋊Dic17C22semidirect
171. C2×#10587502C22semidirect
172. #95×D17C22semidirect
213. C17×#120C2×C4semidirect
238. #10587639C2×C4semidirect
241. C2×C22⋊Dic17C2×C4semidirect
262. #10587625C2×C4semidirect
263. #10587625C2×C4semidirect
264. #10587624C2×C4semidirect
265. #10587622C2×C4semidirect
266. #10587621C2×C4semidirect
269. D4×Dic17C2×C4semidirect
326. #10587571C2×C4semidirect
327. #10587569C2×C4semidirect
330. #10587567C2×C4semidirect
331. #10587565C2×C4semidirect
332. #10587565C2×C4semidirect
333. #10587564C2×C4semidirect
734. #2358D17semidirect
1026. #120C4×D17semidirect
1178. C17#34424semidirect

Maximal subgroups

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

subgroupindex
C2×#117633942
#145319542
#145319532
#145319342
#145319332
#145318572
#145318502
#145317822
#145317772
#145317682
#145317632
#145317112
#145317072
#145316902
#145316892
#145315612
#145315572
#145315562
#145315542
#145315122
#145314862
#145314852
#145314822
#145314802
#145314742
#145313962
#145313162
C4×#105876252
C2×#117626972
C17×#23582
#3442417