Finite Group Databasebeta

← #14542970

Subgroups — #14542970

Order 2176.

1166 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11763556C211yesmaximal, characteristic, complemented
2#11763553C211yesmaximal, characteristic, complemented
3#11763547C211yesmaximal, characteristic, complemented
4#11763547C211yesmaximal, characteristic, complemented
5#11763511C211yesmaximal, characteristic, complemented
6#11763505C211yesmaximal, characteristic, complemented
7#11763486C211yesmaximal, characteristic, complemented
8#11763485C211yesmaximal, characteristic, complemented
9#11763454C211yesmaximal, characteristic, complemented
10#11763451C211yesmaximal, characteristic, complemented
11#11763449C211yesmaximal, characteristic, complemented
12#11763447C211yesmaximal, characteristic, complemented
13#11763446C211yesmaximal, characteristic, complemented
14D4×C22⋊D17C211yesmaximal, characteristic, complemented
15#11763441C211yesmaximal, characteristic, complemented
16#11763412C211yesmaximal, characteristic, complemented
17#11763411C211yesmaximal, characteristic, complemented
18#11763408C211yesmaximal, characteristic, complemented
19#11763403C211yesmaximal, characteristic, complemented
20#11763401C211yesmaximal, characteristic, complemented
21#11763396C211yesmaximal, characteristic, complemented
22#11763393C211yesmaximal, characteristic, complemented
23#11763392C211yesmaximal, characteristic, complemented
24#11763387C211yesmaximal, characteristic, complemented
25#11763371C211yesmaximal, characteristic, complemented
26#11763369C211yesmaximal, characteristic, complemented
27#11763367C211yesmaximal, characteristic, complemented
28#11763315C211yesmaximal, characteristic, complemented
29C2×#10587572C211yesmaximal, characteristic, complemented
30C2×#10587625C211yesmaximal, characteristic, complemented
31C17×#546C211yesmaximal, characteristic, complemented
32C2×#41×C17C2211yescharacteristic, complemented
33C22×D4×C17C2211yescharacteristic, complemented
34C22×C22⋊D17C2211yescharacteristic
35C22×C22⋊D17C2211yescharacteristic, complemented
36C22×C22⋊D17C2211yescharacteristic, complemented
37C22×C22⋊D17C2211yescharacteristic, complemented
38C23×Dic17C2211yescharacteristic, complemented
39C2×#63254C2211yescharacteristic, complemented
40C2×D4×D17C2211yescharacteristic, complemented
41C2×D4×D17C2211yescharacteristic, complemented
42C2×D4×D17C2211yescharacteristic, complemented
43C2×#63252C2211yescharacteristic, complemented
44C17×#124C2211yescharacteristic, complemented
45C17×#123C2211yescharacteristic, complemented
46C17×#123C2211yescharacteristic, complemented
47C17×C22⋊Q8C2211yescharacteristic, complemented
48C17×#121C2211yescharacteristic, complemented
49C17×#121C2211yescharacteristic, complemented
50C17×#121C2211yescharacteristic, complemented
51C17×#120C2211yescharacteristic, complemented
52C17×#120C2211yescharacteristic, complemented
53C4×D4×C17C2211yescharacteristic, complemented
54C4×D4×C17C2211yescharacteristic, complemented
55C2×C22⋊C4×C17C2211yescharacteristic, complemented
56C2×C22⋊C4×C17C2211yescharacteristic, complemented
57#10587639C2211yescharacteristic
58#10587639C2211yescharacteristic, complemented
59C2×C22⋊Dic17C2211yescharacteristic, complemented
60#10587633C2211yescharacteristic, complemented
61#10587632C2211yescharacteristic, complemented
62#10587632C2211yescharacteristic, complemented
63#10587632C2211yescharacteristic, complemented
64#10587626C2211yescharacteristic, complemented
65#10587626C2211yescharacteristic, complemented
66#10587625C2211yescharacteristic
67#10587625C2211yescharacteristic
68#10587625C2211yescharacteristic, complemented
69#10587625C2211yescharacteristic, complemented
70#10587625C2211yescharacteristic, complemented
71#10587625C2211yescharacteristic, complemented
72#10587625C2211yescharacteristic, complemented
73#10587625C2211yescharacteristic, complemented
74#10587625C2211yescharacteristic, complemented
75#10587625C2211yescharacteristic, complemented
76#10587625C2211yescharacteristic, complemented
77#10587625C2211yescharacteristic, complemented
78#10587625C2211yescharacteristic, complemented
79#10587625C2211yescharacteristic, complemented
80#10587625C2211yescharacteristic, complemented
81#10587624C2211yescharacteristic, complemented
82#10587624C2211yescharacteristic, complemented
83#10587624C2211yescharacteristic, complemented
84#10587624C2211yescharacteristic, complemented
85#10587623C2211yescharacteristic, complemented
86#10587623C2211yescharacteristic, complemented
87#10587623C2211yescharacteristic, complemented
88#10587623C2211yescharacteristic, complemented
89#10587623C2211yescharacteristic, complemented
90#10587623C2211yescharacteristic, complemented
91#10587621C2211yescharacteristic, complemented
92D4×Dic17C2211yescharacteristic, complemented
93D4×Dic17C2211yescharacteristic, complemented
94D4×Dic17C2211yescharacteristic, complemented
95D4×Dic17C2211yescharacteristic, complemented
96#10587616C2211yescharacteristic
97#10587616C2211yescharacteristic, complemented
98#10587616C2211yescharacteristic, complemented
99#10587616C2211yescharacteristic, complemented
100#10587616C2211yescharacteristic, complemented
101#10587616C2211yescharacteristic, complemented
102#10587616C2211yescharacteristic, complemented
103#10587615C2211yescharacteristic, complemented
104#10587615C2211yescharacteristic, complemented
105#10587615C2211yescharacteristic, complemented
106C4×C22⋊D17C2211yescharacteristic, complemented
107C4×C22⋊D17C2211yescharacteristic, complemented
108C4×C22⋊D17C2211yescharacteristic, complemented
109C2×#63227C2211yescharacteristic, complemented
110C2×#63227C2211yescharacteristic, complemented
111C2×#63227C2211yescharacteristic, complemented
112C2×#63227C2211yescharacteristic, complemented
113#10587612C2211yescharacteristic, complemented
114C2×C4⋊Dic17C2211yescharacteristic, complemented
115C2×C4⋊Dic17C2211yescharacteristic, complemented
116#10587610C2211yescharacteristic, complemented
117#10587610C2211yescharacteristic, complemented
118C2×#63225C2211yescharacteristic, complemented
119#10587584C2211yescharacteristic, complemented
120#10587584C2211yescharacteristic, complemented
121#10587584C2211yescharacteristic, complemented
122#10587584C2211yescharacteristic, complemented
123#10587583C2211yescharacteristic, complemented
124#10587582C2211yescharacteristic, complemented
125#10587581C2211yescharacteristic, complemented
126#10587580C2211yescharacteristic, complemented
127#10587580C2211yescharacteristic, complemented
128#10587580C2211yescharacteristic, complemented
129#10587580C2211yescharacteristic, complemented
130#10587579C2211yescharacteristic, complemented
131#10587578C2211yescharacteristic, complemented
132#10587576C2211yescharacteristic, complemented
133#10587576C2211yescharacteristic, complemented
134#10587575C2211yescharacteristic, complemented
135#10587572C2211yescharacteristic, complemented
136#10587572C2211yescharacteristic, complemented
137#10587572C2211yescharacteristic, complemented
138#10587572C2211yescharacteristic, complemented
139#10587572C2211yescharacteristic, complemented
140#10587572C2211yescharacteristic, complemented
141#10587572C2211yescharacteristic, complemented
142#10587572C2211yescharacteristic, complemented
143#10587572C2211yescharacteristic, complemented
144#10587572C2211yescharacteristic, complemented
145#10587572C2211yescharacteristic, complemented
146#10587572C2211yescharacteristic, complemented
147#10587571C2211yescharacteristic, complemented
148#10587571C2211yescharacteristic, complemented
149#10587571C2211yescharacteristic, complemented
150#10587570C2211yescharacteristic, complemented
151#10587570C2211yescharacteristic, complemented
152#10587570C2211yescharacteristic, complemented
153#10587570C2211yescharacteristic, complemented
154#10587570C2211yescharacteristic, complemented
155#10587570C2211yescharacteristic, complemented
156#10587569C2211yescharacteristic, complemented
157#10587569C2211yescharacteristic, complemented
158#10587569C2211yescharacteristic, complemented
159#10587569C2211yescharacteristic, complemented
160#10587569C2211yescharacteristic, complemented
161#10587569C2211yescharacteristic, complemented
162#10587568C2211yescharacteristic
163#10587568C2211yescharacteristic, complemented
164#10587568C2211yescharacteristic, complemented
165#10587568C2211yescharacteristic, complemented
166#10587568C2211yescharacteristic, complemented
167#10587568C2211yescharacteristic, complemented
168#10587567C2211yescharacteristic, complemented
169#10587567C2211yescharacteristic, complemented
170#10587567C2211yescharacteristic, complemented
171#10587567C2211yescharacteristic, complemented
172#10587567C2211yescharacteristic, complemented
173C22⋊C4×D17C2211yescharacteristic, complemented
174C22⋊C4×D17C2211yescharacteristic, complemented
175#10587565C2211yescharacteristic, complemented
176#10587565C2211yescharacteristic, complemented
177#10587565C2211yescharacteristic, complemented
178#10587564C2211yescharacteristic, complemented
179#10587564C2211yescharacteristic, complemented
180#10587564C2211yescharacteristic, complemented
181#10587564C2211yescharacteristic, complemented
182#10587563C2211yescharacteristic, complemented
183#10587562C2211yescharacteristic, complemented
184#10587561C2211yescharacteristic, complemented
185C4×D68C2211yescharacteristic, complemented
186#10587556C2211yescharacteristic, complemented
187C24×C17C2311yescharacteristic
188C24×C17C2311yescharacteristic
189C23×D17C2311yescharacteristic
190C23×D17C2311yescharacteristic
191C23×D17C2311yescharacteristic
192C23×D17C2311yescharacteristic
193#41×C17—42no—
194C2×Q8×C17C2311yescharacteristic
195C2×D4×C17—42no—
196C2×D4×C17C2311yescharacteristic
197C2×D4×C17C2311yescharacteristic
198C2×D4×C17C2311yescharacteristic
199C2×D4×C17C2311yescharacteristic
200C2×D4×C17C2311yescharacteristic
201C2×D4×C17C2311yescharacteristic
202C2×D4×C17C2311yescharacteristic
203C2×D4×C17C2311yescharacteristic
204C2×D4×C17C2311yescharacteristic
205C22×C4×C17C2311yescharacteristic
206C22×C4×C17C2311yescharacteristic
207C22×C4×C17C2311yescharacteristic
208C22×C4×C17C2311yescharacteristic
209C22×C4×C17C2311yescharacteristic
210C22×C4×C17C2311yescharacteristic
211C2×C22⋊D17—42no—
212C2×C22⋊D17—42no—
213C2×C22⋊D17—42no—
214C2×C22⋊D17—42no—
215C2×C22⋊D17C2311yescharacteristic
216C2×C22⋊D17C2311yescharacteristic
217C2×C22⋊D17C2311yescharacteristic
218C2×C22⋊D17C2311yescharacteristic
219C2×C22⋊D17C2311yescharacteristic
220C2×C22⋊D17C2311yescharacteristic
221C2×C22⋊D17C2311yescharacteristic
222C2×C22⋊D17C2311yescharacteristic
223C2×C22⋊D17C2311yescharacteristic
224C2×C22⋊D17C2311yescharacteristic
225C2×C22⋊D17C2311yescharacteristic
226C2×C22⋊D17C2311yescharacteristic
227C2×C22⋊D17C2311yescharacteristic
228C2×C22⋊D17C2311yescharacteristic
229C2×C22⋊D17C2311yescharacteristic
230C2×C22⋊D17C2311yescharacteristic
231C2×C22⋊D17C2311yescharacteristic
232C2×C22⋊D17C2311yescharacteristic
233C2×C22⋊D17C2311yescharacteristic
234C2×C22⋊D17C2311yescharacteristic
235C2×C22⋊D17C2311yescharacteristic
236C2×C22⋊D17C2311yescharacteristic
237C22×Dic17—42no—
238C22×Dic17C2311yescharacteristic
239C22×Dic17C2311yescharacteristic
240C22×Dic17C2311yescharacteristic
241C22×Dic17C2311yescharacteristic
242C22×Dic17C2311yescharacteristic
243C22×Dic17C2311yescharacteristic
244C22×Dic17C2311yescharacteristic
245C22×Dic17C2311yescharacteristic
246C22×Dic17C2311yescharacteristic
247C22×Dic17C2311yescharacteristic
248#63254—42no—
249D4×D17—42no—
250D4×D17—42no—
251D4×D17—42no—
252#63252—42no—
253C2×D68C2311yescharacteristic
254C2×D68C2311yescharacteristic
255C2×D68C2311yescharacteristic
256C2×D68C2311yescharacteristic
257C2×D68C2311yescharacteristic
258C2×D68C2311yescharacteristic
259C2×C4×D17C2311yescharacteristic
260C2×C4×D17C2311yescharacteristic
261C2×C4×D17C2311yescharacteristic
262C2×C4×D17C2311yescharacteristic
263C2×C4×D17C2311yescharacteristic
264C2×C4×D17C2311yescharacteristic
265C2×C4×D17C2311yescharacteristic
266C2×Dic34C2311yescharacteristic
267C2×Dic34C2311yescharacteristic
268C4⋊C4×C17C2311yescharacteristic
269C4⋊C4×C17C2311yescharacteristic
270C4⋊C4×C17C2311yescharacteristic
271C4⋊C4×C17C2311yescharacteristic
272C22⋊C4×C17C2311yescharacteristic
273C22⋊C4×C17C2311yescharacteristic
274C22⋊C4×C17C2311yescharacteristic
275C22⋊C4×C17C2311yescharacteristic
276C22⋊C4×C17C2311yescharacteristic
277C22⋊C4×C17C2311yescharacteristic
278C22⋊C4×C17C2311yescharacteristic
279C22⋊C4×C17C2311yescharacteristic
280C22⋊C4×C17C2311yescharacteristic
281C22⋊C4×C17C2311yescharacteristic
282C22⋊C4×C17C2311yescharacteristic
283C22⋊C4×C17C2311yescharacteristic
284C42×C17C2311yescharacteristic
285C22⋊Dic17C2311yescharacteristic
286C22⋊Dic17C2311yescharacteristic
287C22⋊Dic17C2311yescharacteristic
288C22⋊Dic17C2311yescharacteristic
289C22⋊Dic17C2311yescharacteristic
290C22⋊Dic17C2311yescharacteristic
291C22⋊Dic17C2311yescharacteristic
292C22⋊Dic17C2311yescharacteristic
293C22⋊Dic17C2311yescharacteristic
294C22⋊Dic17C2311yescharacteristic
295C22⋊Dic17C2311yescharacteristic
296C22⋊Dic17C2311yescharacteristic
297#63227C2311yescharacteristic
298#63227C2311yescharacteristic
299#63227C2311yescharacteristic
300#63227C2311yescharacteristic
301#63227C2311yescharacteristic
302#63227C2311yescharacteristic
303#63227C2311yescharacteristic
304#63227C2311yescharacteristic
305#63227C2311yescharacteristic
306#63227C2311yescharacteristic
307#63227C2311yescharacteristic
308#63227C2311yescharacteristic
309#63227C2311yescharacteristic
310#63227C2311yescharacteristic
311#63227C2311yescharacteristic
312#63227C2311yescharacteristic
313#63227C2311yescharacteristic
314#63227C2311yescharacteristic
315#63227C2311yescharacteristic
316#63227C2311yescharacteristic
317#63227C2311yescharacteristic
318#63227C2311yescharacteristic
319#63227C2311yescharacteristic
320#63227C2311yescharacteristic
321#63227C2311yescharacteristic
322#63227C2311yescharacteristic
323C4⋊Dic17C2311yescharacteristic
324C4⋊Dic17C2311yescharacteristic
325C4⋊Dic17C2311yescharacteristic
326C4⋊Dic17C2311yescharacteristic
327C4⋊Dic17C2311yescharacteristic
328C4⋊Dic17C2311yescharacteristic
329C4⋊Dic17C2311yescharacteristic
330C4⋊Dic17C2311yescharacteristic
331C4⋊Dic17C2311yescharacteristic
332C4⋊Dic17C2311yescharacteristic
333C4⋊Dic17C2311yescharacteristic
334C4⋊Dic17C2311yescharacteristic
335#63225C2311yescharacteristic
336#63225C2311yescharacteristic
337#63225C2311yescharacteristic
338#63225C2311yescharacteristic
339#63225C2311yescharacteristic
340#63225C2311yescharacteristic
341#63225C2311yescharacteristic
342#63225C2311yescharacteristic
343#63225C2311yescharacteristic
344#63225C2311yescharacteristic
345#63225C2311yescharacteristic
346#63225C2311yescharacteristic
347#63225C2311yescharacteristic
348#63225C2311yescharacteristic
349C4×Dic17C2311yescharacteristic
350C4×Dic17C2311yescharacteristic
351C4×Dic17C2311yescharacteristic
352C4×Dic17C2311yescharacteristic
353C4×Dic17C2311yescharacteristic
354C23×C17—22no—
355C23×C17—22no—
356C23×C17—22no—
357C23×C17—41no—
358C23×C17—41no—
359C23×C17—41no—
360C23×C17C2411yescharacteristic
361C23×C17C2411yescharacteristic
362C23×C17C2411yescharacteristic
363C23×C17C2411yescharacteristic
364C23×C17C2411yescharacteristic
365C23×C17C2411yescharacteristic
366C22×D17—22no—
367C22×D17—22no—
368C22×D17—41no—
369C22×D17—41no—
370C22×D17—41no—
371C22×D17—41no—
372C22×D17—41no—
373C22×D17—41no—
374C22×D17—41no—
375C22×D17—41no—
376C22×D17—41no—
377C22×D17—41no—
378C22×D17C2411yescharacteristic
379C22×D17C2411yescharacteristic
380C22×D17C2411yescharacteristic
381C22×D17C2411yescharacteristic
382C22×D17C2411yescharacteristic
383Q8×C17—41no—
384D4×C17—22no—
385D4×C17—22no—
386D4×C17—22no—
387D4×C17—22no—
388D4×C17—41no—
389D4×C17—41no—
390D4×C17—41no—
391D4×C17—41no—
392D4×C17—41no—
393C2×C4×C17—22no—
394C2×C4×C17—41no—
395C2×C4×C17—41no—
396C2×C4×C17—41no—
397C2×C4×C17—41no—
398C2×C4×C17—41no—
399C2×C4×C17C2411yescharacteristic
400C2×C4×C17C2411yescharacteristic
401C2×C4×C17C2411yescharacteristic
402C2×C4×C17C2411yescharacteristic
403C2×C4×C17C2411yescharacteristic
404C2×C4×C17C2411yescharacteristic
405C2×C4×C17C2411yescharacteristic
406C2×C4×C17C2411yescharacteristic
407C2×C4×C17C2411yescharacteristic
408C22⋊D17—22no—
409C22⋊D17—22no—
410C22⋊D17—22no—
411C22⋊D17—22no—
412C22⋊D17—22no—
413C22⋊D17—22no—
414C22⋊D17—41no—
415C22⋊D17—41no—
416C22⋊D17—41no—
417C22⋊D17—41no—
418C22⋊D17—41no—
419C22⋊D17—41no—
420C22⋊D17—41no—
421C22⋊D17—41no—
422C22⋊D17—41no—
423C22⋊D17—41no—
424C22⋊D17—41no—
425C22⋊D17—41no—
426C22⋊D17—41no—
427C22⋊D17—41no—
428C22⋊D17—41no—
429C22⋊D17—41no—
430C2×Dic17—22no—
431C2×Dic17—22no—
432C2×Dic17—41no—
433C2×Dic17—41no—
434C2×Dic17—41no—
435C2×Dic17—41no—
436C2×Dic17—41no—
437C2×Dic17—41no—
438C2×Dic17—41no—
439C2×Dic17—41no—
440C2×Dic17C2411yescharacteristic
441C2×Dic17C2411yescharacteristic
442C2×Dic17C2411yescharacteristic
443C2×Dic17C2411yescharacteristic
444C2×Dic17C2411yescharacteristic
445C2×Dic17C2411yescharacteristic
446C2×Dic17C2411yescharacteristic
447C2×Dic17C2411yescharacteristic
448C2×Dic17C2411yescharacteristic
449C2×Dic17C2411yescharacteristic
450C2×Dic17C2411yescharacteristic
451D68—41no—
452D68—41no—
453D68—41no—
454D68—41no—
455D68—41no—
456D68—41no—
457C4×D17—41no—
458C4×D17—41no—
459C4×D17—41no—
460C4×D17—41no—
461C4×D17—41no—
462C4×D17—41no—
463C4×D17—41no—
464Dic34—41no—
465Dic34—41no—
466#3534—171nomaximal, Sylow
467C22×C17—21no—
468C22×C17—21no—
469C22×C17—21no—
470C22×C17—21no—
471C22×C17—21no—
472C22×C17—21no—
473C22×C17—21no—
474C22×C17—21no—
475C22×C17—21no—
476C22×C17—21no—
477C22×C17—21no—
478C22×C17—21no—
479C22×C17—21no—
480C22×C17—21no—
481C22×C17—21no—
482C22×C17—21no—
483C22×C17—44no—
484C22×C17—82no—
485C22×C17H(5,𝔽2)12yes—
486C22×C17H(5,𝔽2)12yes—
487C22×C17C2511yescharacteristic
488C2×D17—21no—
489C2×D17—21no—
490C2×D17—21no—
491C2×D17—21no—
492C2×D17—21no—
493C2×D17—21no—
494C2×D17—21no—
495C2×D17—21no—
496C2×D17—21no—
497C2×D17—21no—
498C2×D17—21no—
499C2×D17—21no—
500C2×D17—21no—
501C2×D17—21no—
502C2×D17—21no—
503C2×D17—82no—
504C2×D17—82no—
505C2×D17—82no—
506C2×D17—82no—
507C4×C17—21no—
508C4×C17—21no—
509C4×C17—21no—
510C4×C17—21no—
511C4×C17—21no—
512C4×C17—21no—
513C4×C17—21no—
514C4×C17—21no—
515C4×C17—21no—
516Dic17—21no—
517Dic17—21no—
518Dic17—21no—
519Dic17—21no—
520Dic17—21no—
521Dic17—21no—
522Dic17—21no—
523Dic17—21no—
524Dic17—21no—
525Dic17—21no—
526Dic17—21no—
527#562—171no—
528#562—171no—
529#560—171no—
530#560—171no—
531#553—171no—
532#553—171no—
533#551—171no—
534#551—171no—
535#546—171no—
536#546—171no—
537#546—171no—
538#546—171no—
539#546—171no—
540#546D1711yescharacteristic, complemented
541D42—171no—
542D42—171no—
543#540—171no—
544#540—171no—
545#539—171no—
546#539—171no—
547#539—171no—
548#538—171no—
549#538—171no—
550#538—171no—
551#537—171no—
552#534—171no—
553#534—171no—
554#534—171no—
555#525—171no—
556C2×#123—171no—
557C2×#121—171no—
558C2×C17—22no—
559C2×C17—22no—
560C2×C17—41no—
561C2×C17—41no—
562C2×C17—41no—
563C2×C17—41no—
564C2×C17C2×H(5,𝔽2)11yescharacteristic
565C2×C17C2×H(5,𝔽2)11yescharacteristic
566C2×C17#58511yescharacteristic
567D17—41no—
568D17—41no—
569D17—41no—
570D17—41no—
571D17—41no—
572C2×#41—171no—
573C2×#41—171no—
574C2×#41C2×D1711yescharacteristic, complemented
575C22×D4—171no—
576C22×D4—171no—
577C22×D4—171no—
578C22×D4—171no—
579C22×D4—171no—
580C22×D4—171no—
581C22×D4—171no—
582C22×D4C2×D1711yescharacteristic, complemented
583C23×C4—171no—
584#127—171no—
585#127—171no—
586#126—171no—
587#126—171no—
588#126—171no—
589#126—171no—
590#126—171no—
591#126—171no—
592#126—171no—
593#126—171no—
594#125—171no—
595#125—171no—
596#125—171no—
597#125—171no—
598#124—171no—
599#124—171no—
600#124—171no—
601#124—171no—
602#124—171no—
603#124C2×D1711yescharacteristic, complemented
604#123—171no—
605#123—171no—
606#123—171no—
607#123—171no—
608#123—171no—
609#123—171no—
610#123—171no—
611#123—171no—
612#123—171no—
613#123—171no—
614#123—171no—
615#123—171no—
616#123—171no—
617#123—171no—
618#123—171no—
619#123—171no—
620#123—171no—
621#123—171no—
622#123—171no—
623#123—171no—
624#123—171no—
625#123—171no—
626#123—171no—
627#123—171no—
628#123—171no—
629#123—171no—
630#123C2×D1711yescharacteristic, complemented
631#123C2×D1711yescharacteristic, complemented
632C22⋊Q8—171no—
633C22⋊Q8—171no—
634C22⋊Q8—171no—
635C22⋊Q8—171no—
636C22⋊Q8—171no—
637C22⋊Q8—171no—
638C22⋊Q8—171no—
639C22⋊Q8—171no—
640C22⋊Q8—171no—
641C22⋊Q8—171no—
642C22⋊Q8—171no—
643C22⋊Q8C2×D1711yescharacteristic, complemented
644#121—171no—
645#121—171no—
646#121—171no—
647#121—171no—
648#121—171no—
649#121—171no—
650#121—171no—
651#121—171no—
652#121—171no—
653#121—171no—
654#121—171no—
655#121—171no—
656#121—171no—
657#121—171no—
658#121—171no—
659#121—171no—
660#121—171no—
661#121—171no—
662#121—171no—
663#121—171no—
664#121—171no—
665#121—171no—
666#121—171no—
667#121—171no—
668#121—171no—
669#121—171no—
670#121—171no—
671#121—171no—
672#121—171no—
673#121—171no—
674#121—171no—
675#121—171no—
676#121—171no—
677#121C2×D1711yescharacteristic, complemented
678#121C2×D1711yescharacteristic, complemented
679#121C2×D1711yescharacteristic, complemented
680#120—171no—
681#120—171no—
682#120—171no—
683#120—171no—
684#120—171no—
685#120—171no—
686#120—171no—
687#120—171no—
688#120—171no—
689#120—171no—
690#120—171no—
691#120—171no—
692#120—171no—
693#120—171no—
694#120C2×D1711yescharacteristic, complemented
695#120C2×D1711yescharacteristic, complemented
696C4×D4—171no—
697C4×D4—171no—
698C4×D4—171no—
699C4×D4—171no—
700C4×D4—171no—
701C4×D4—171no—
702C4×D4—171no—
703C4×D4—171no—
704C4×D4—171no—
705C4×D4—171no—
706C4×D4—171no—
707C4×D4—171no—
708C4×D4—171no—
709C4×D4—171no—
710C4×D4C2×D1711yescharacteristic, complemented
711C4×D4C2×D1711yescharacteristic, complemented
712#117—171no—
713#117—171no—
714#117—171no—
715C2×C4⋊C4—171no—
716C2×C4⋊C4—171no—
717C2×C4⋊C4—171no—
718C2×C22⋊C4—171no—
719C2×C22⋊C4—171no—
720C2×C22⋊C4—171no—
721C2×C22⋊C4—171no—
722C2×C22⋊C4—171no—
723C2×C22⋊C4—171no—
724C2×C22⋊C4—171no—
725C2×C22⋊C4C2×D1711yescharacteristic, complemented
726C2×C22⋊C4C2×D1711yescharacteristic, complemented
727C17#353411yescharacteristic, complemented, Sylow
728C24—171no—
729C24—171no—
730C24—171no—
731C24—171no—
732C24C22×D1711yescharacteristic
733C24C22×D1711yescharacteristic
734#41—42no—
735#41—682no—
736#41—682no—
737C2×Q8—171no—
738C2×Q8—171no—
739C2×Q8C22×D1711yescharacteristic
740C2×D4—42no—
741C2×D4—171no—
742C2×D4—171no—
743C2×D4—171no—
744C2×D4—171no—
745C2×D4—171no—
746C2×D4—171no—
747C2×D4—171no—
748C2×D4—171no—
749C2×D4—171no—
750C2×D4—171no—
751C2×D4—171no—
752C2×D4—171no—
753C2×D4—171no—
754C2×D4—171no—
755C2×D4—171no—
756C2×D4—171no—
757C2×D4—171no—
758C2×D4—171no—
759C2×D4—171no—
760C2×D4—171no—
761C2×D4—171no—
762C2×D4—171no—
763C2×D4—171no—
764C2×D4—171no—
765C2×D4—171no—
766C2×D4—171no—
767C2×D4—171no—
768C2×D4—171no—
769C2×D4—682no—
770C2×D4—682no—
771C2×D4—682no—
772C2×D4—682no—
773C2×D4—682no—
774C2×D4—682no—
775C2×D4—682no—
776C2×D4C22×D1711yescharacteristic
777C2×D4C22×D1711yescharacteristic
778C2×D4C22×D1711yescharacteristic
779C2×D4C22×D1711yescharacteristic
780C2×D4C22×D1711yescharacteristic
781C2×D4C22×D1711yescharacteristic
782C2×D4C22×D1711yescharacteristic
783C2×D4C22×D1711yescharacteristic
784C2×D4C22×D1711yescharacteristic
785C22×C4—171no—
786C22×C4—171no—
787C22×C4—171no—
788C22×C4—171no—
789C22×C4—171no—
790C22×C4—171no—
791C22×C4—171no—
792C22×C4—171no—
793C22×C4—171no—
794C22×C4—171no—
795C22×C4—171no—
796C22×C4—171no—
797C22×C4—171no—
798C22×C4—171no—
799C22×C4—171no—
800C22×C4—171no—
801C22×C4—171no—
802C22×C4—682no—
803C22×C4C22×D1711yescharacteristic
804C22×C4C22×D1711yescharacteristic
805C22×C4C22×D1711yescharacteristic
806C22×C4C22×D1711yescharacteristic
807C22×C4C22×D1711yescharacteristic
808C22×C4C22×D1711yescharacteristic
809C4⋊C4—171no—
810C4⋊C4—171no—
811C4⋊C4—171no—
812C4⋊C4—171no—
813C4⋊C4—171no—
814C4⋊C4—171no—
815C4⋊C4—171no—
816C4⋊C4—171no—
817C4⋊C4—171no—
818C4⋊C4—171no—
819C4⋊C4—171no—
820C4⋊C4—171no—
821C4⋊C4—171no—
822C4⋊C4—171no—
823C4⋊C4—171no—
824C4⋊C4—171no—
825C4⋊C4—171no—
826C4⋊C4—171no—
827C4⋊C4—171no—
828C4⋊C4—171no—
829C4⋊C4—171no—
830C4⋊C4—171no—
831C4⋊C4—171no—
832C4⋊C4—171no—
833C4⋊C4—171no—
834C4⋊C4—171no—
835C4⋊C4C22×D1711yescharacteristic
836C4⋊C4C22×D1711yescharacteristic
837C4⋊C4C22×D1711yescharacteristic
838C4⋊C4C22×D1711yescharacteristic
839C22⋊C4—171no—
840C22⋊C4—171no—
841C22⋊C4—171no—
842C22⋊C4—171no—
843C22⋊C4—171no—
844C22⋊C4—171no—
845C22⋊C4—171no—
846C22⋊C4—171no—
847C22⋊C4—171no—
848C22⋊C4—171no—
849C22⋊C4—171no—
850C22⋊C4—171no—
851C22⋊C4—171no—
852C22⋊C4—171no—
853C22⋊C4—171no—
854C22⋊C4—171no—
855C22⋊C4—171no—
856C22⋊C4—171no—
857C22⋊C4—171no—
858C22⋊C4—171no—
859C22⋊C4—171no—
860C22⋊C4—171no—
861C22⋊C4—171no—
862C22⋊C4—171no—
863C22⋊C4—171no—
864C22⋊C4—171no—
865C22⋊C4—171no—
866C22⋊C4—171no—
867C22⋊C4—171no—
868C22⋊C4—171no—
869C22⋊C4—171no—
870C22⋊C4—171no—
871C22⋊C4—171no—
872C22⋊C4—171no—
873C22⋊C4—171no—
874C22⋊C4—171no—
875C22⋊C4—171no—
876C22⋊C4—171no—
877C22⋊C4C22×D1711yescharacteristic
878C22⋊C4C22×D1711yescharacteristic
879C22⋊C4C22×D1711yescharacteristic
880C22⋊C4C22×D1711yescharacteristic
881C22⋊C4C22×D1711yescharacteristic
882C22⋊C4C22×D1711yescharacteristic
883C22⋊C4C22×D1711yescharacteristic
884C22⋊C4C22×D1711yescharacteristic
885C22⋊C4C22×D1711yescharacteristic
886C22⋊C4C22×D1711yescharacteristic
887C22⋊C4C22×D1711yescharacteristic
888C22⋊C4C22×D1711yescharacteristic
889C42—171no—
890C42—171no—
891C42—171no—
892C42—171no—
893C42—171no—
894C42C22×D1711yescharacteristic
895C23—22no—
896C23—22no—
897C23—22no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—171no—
902C23—171no—
903C23—171no—
904C23—171no—
905C23—171no—
906C23—342no—
907C23—342no—
908C23—681no—
909C23—681no—
910C23—681no—
911C23—681no—
912C23—681no—
913C23—681no—
914C23—681no—
915C23—681no—
916C23—681no—
917C23—681no—
918C23C23×D1711yescharacteristic
919C23C23×D1711yescharacteristic
920C23C23×D1711yescharacteristic
921C23C23×D1711yescharacteristic
922C23C23×D1711yescharacteristic
923C23C23×D1711yescharacteristic
924Q8—41no—
925Q8—681no—
926Q8—681no—
927D4—22no—
928D4—22no—
929D4—22no—
930D4—22no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—342no—
937D4—342no—
938D4—342no—
939D4—342no—
940D4—342no—
941D4—342no—
942D4—681no—
943D4—681no—
944D4—681no—
945D4—681no—
946D4—681no—
947D4—681no—
948D4—681no—
949D4—681no—
950D4—681no—
951D4—681no—
952D4—681no—
953D4—681no—
954D4—681no—
955D4—681no—
956D4—681no—
957D4—681no—
958D4—681no—
959D4—681no—
960D4—681no—
961D4—681no—
962D4—681no—
963D4—681no—
964C2×C4—22no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—171no—
971C2×C4—171no—
972C2×C4—171no—
973C2×C4—171no—
974C2×C4—171no—
975C2×C4—171no—
976C2×C4—171no—
977C2×C4—171no—
978C2×C4—171no—
979C2×C4—171no—
980C2×C4—171no—
981C2×C4—342no—
982C2×C4—342no—
983C2×C4—681no—
984C2×C4—681no—
985C2×C4—681no—
986C2×C4—681no—
987C2×C4—681no—
988C2×C4—681no—
989C2×C4—681no—
990C2×C4—681no—
991C2×C4—681no—
992C2×C4—681no—
993C2×C4—681no—
994C2×C4—681no—
995C2×C4—681no—
996C2×C4—681no—
997C2×C4—681no—
998C2×C4C23×D1711yescharacteristic
999C2×C4C23×D1711yescharacteristic
1000C2×C4C23×D1711yescharacteristic
1001C2×C4C23×D1711yescharacteristic
1002C2×C4C23×D1711yescharacteristic
1003C2×C4C23×D1711yescharacteristic
1004C2×C4C23×D1711yescharacteristic
1005C2×C4C23×D1711yescharacteristic
1006C2×C4C23×D1711yescharacteristic
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—21no—
1017C22—21no—
1018C22—21no—
1019C22—21no—
1020C22—21no—
1021C22—21no—
1022C22—21no—
1023C22—44no—
1024C22—82no—
1025C22—341no—
1026C22—341no—
1027C22—341no—
1028C22—341no—
1029C22—341no—
1030C22—341no—
1031C22—341no—
1032C22—341no—
1033C22—341no—
1034C22—341no—
1035C22—341no—
1036C22—341no—
1037C22—341no—
1038C22—341no—
1039C22—341no—
1040C22—1362no—
1041C22—1362no—
1042C22—1362no—
1043C22—1362no—
1044C22#1058769112yes—
1045C22#1058769612yes—
1046C22C24×D1711yescharacteristic
1047C4—21no—
1048C4—21no—
1049C4—21no—
1050C4—21no—
1051C4—21no—
1052C4—21no—
1053C4—21no—
1054C4—21no—
1055C4—21no—
1056C4—341no—
1057C4—341no—
1058C4—341no—
1059C4—341no—
1060C4—341no—
1061C4—341no—
1062C4—341no—
1063C4—341no—
1064C4—341no—
1065C4—341no—
1066C4—341no—
1067C2—22no—
1068C2—22no—
1069C2—41no—
1070C2—41no—
1071C2—41no—
1072C2—41no—
1073C2—681no—
1074C2—681no—
1075C2—681no—
1076C2—681no—
1077C2—681no—
1078C2C2×#1058769111yescharacteristic
1079C2C2×#1058769611yescharacteristic
1080C2#1176364411yescharacteristic
subgroupG/H
center, FrattiniC22C24×D17
commutator, socle, cosocleC22×C17C25
FittingC17×#546C2
hypercenter#546D17
hypocenterC17#3534
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #11763556C2semidirect
2. #11763553C2semidirect
3. #11763547C2semidirect
4. #11763547C2semidirect
5. #11763511C2semidirect
6. #11763505C2semidirect
7. #11763486C2semidirect
8. #11763485C2semidirect
9. #11763454C2semidirect
10. #11763451C2semidirect
11. #11763449C2semidirect
12. #11763447C2semidirect
13. #11763446C2semidirect
14. D4×C22⋊D17C2semidirect
15. #11763441C2semidirect
16. #11763412C2semidirect
17. #11763411C2semidirect
18. #11763408C2semidirect
19. #11763403C2semidirect
20. #11763401C2semidirect
21. #11763396C2semidirect
22. #11763393C2semidirect
23. #11763392C2semidirect
24. #11763387C2semidirect
25. #11763371C2semidirect
26. #11763369C2semidirect
27. #11763367C2semidirect
28. #11763315C2semidirect
29. C2×#10587572C2semidirect
30. C2×#10587625C2semidirect
31. C17×#546C2semidirect
32. C2×#41×C17C22semidirect
33. C22×D4×C17C22semidirect
35. C22×C22⋊D17C22semidirect
36. C22×C22⋊D17C22semidirect
37. C22×C22⋊D17C22semidirect
38. C23×Dic17C22semidirect
39. C2×#63254C22semidirect
40. C2×D4×D17C22semidirect
41. C2×D4×D17C22semidirect
42. C2×D4×D17C22semidirect
43. C2×#63252C22semidirect
44. C17×#124C22semidirect
45. C17×#123C22semidirect
46. C17×#123C22semidirect
47. C17×C22⋊Q8C22semidirect
48. C17×#121C22semidirect
49. C17×#121C22semidirect
50. C17×#121C22semidirect
51. C17×#120C22semidirect
52. C17×#120C22semidirect
53. C4×D4×C17C22semidirect
54. C4×D4×C17C22semidirect
55. C2×C22⋊C4×C17C22semidirect
56. C2×C22⋊C4×C17C22semidirect
58. #10587639C22semidirect
59. C2×C22⋊Dic17C22semidirect
60. #10587633C22semidirect
61. #10587632C22semidirect
62. #10587632C22semidirect
63. #10587632C22semidirect
64. #10587626C22semidirect
65. #10587626C22semidirect
68. #10587625C22semidirect
69. #10587625C22semidirect
70. #10587625C22semidirect
71. #10587625C22semidirect
72. #10587625C22semidirect
73. #10587625C22semidirect
74. #10587625C22semidirect
75. #10587625C22semidirect
76. #10587625C22semidirect
77. #10587625C22semidirect
78. #10587625C22semidirect
79. #10587625C22semidirect
80. #10587625C22semidirect
81. #10587624C22semidirect
82. #10587624C22semidirect
83. #10587624C22semidirect
84. #10587624C22semidirect
85. #10587623C22semidirect
86. #10587623C22semidirect
87. #10587623C22semidirect
88. #10587623C22semidirect
89. #10587623C22semidirect
90. #10587623C22semidirect
91. #10587621C22semidirect
92. D4×Dic17C22semidirect
93. D4×Dic17C22semidirect
94. D4×Dic17C22semidirect
95. D4×Dic17C22semidirect
97. #10587616C22semidirect
98. #10587616C22semidirect
99. #10587616C22semidirect
100. #10587616C22semidirect
101. #10587616C22semidirect
102. #10587616C22semidirect
103. #10587615C22semidirect
104. #10587615C22semidirect
105. #10587615C22semidirect
106. C4×C22⋊D17C22semidirect
107. C4×C22⋊D17C22semidirect
108. C4×C22⋊D17C22semidirect
109. C2×#63227C22semidirect
110. C2×#63227C22semidirect
111. C2×#63227C22semidirect
112. C2×#63227C22semidirect
113. #10587612C22semidirect
114. C2×C4⋊Dic17C22semidirect
115. C2×C4⋊Dic17C22semidirect
116. #10587610C22semidirect
117. #10587610C22semidirect
118. C2×#63225C22semidirect
119. #10587584C22semidirect
120. #10587584C22semidirect
121. #10587584C22semidirect
122. #10587584C22semidirect
123. #10587583C22semidirect
124. #10587582C22semidirect
125. #10587581C22semidirect
126. #10587580C22semidirect
127. #10587580C22semidirect
128. #10587580C22semidirect
129. #10587580C22semidirect
130. #10587579C22semidirect
131. #10587578C22semidirect
132. #10587576C22semidirect
133. #10587576C22semidirect
134. #10587575C22semidirect
135. #10587572C22semidirect
136. #10587572C22semidirect
137. #10587572C22semidirect
138. #10587572C22semidirect
139. #10587572C22semidirect
140. #10587572C22semidirect
141. #10587572C22semidirect
142. #10587572C22semidirect
143. #10587572C22semidirect
144. #10587572C22semidirect
145. #10587572C22semidirect
146. #10587572C22semidirect
147. #10587571C22semidirect
148. #10587571C22semidirect
149. #10587571C22semidirect
150. #10587570C22semidirect
151. #10587570C22semidirect
152. #10587570C22semidirect
153. #10587570C22semidirect
154. #10587570C22semidirect
155. #10587570C22semidirect
156. #10587569C22semidirect
157. #10587569C22semidirect
158. #10587569C22semidirect
159. #10587569C22semidirect
160. #10587569C22semidirect
161. #10587569C22semidirect
163. #10587568C22semidirect
164. #10587568C22semidirect
165. #10587568C22semidirect
166. #10587568C22semidirect
167. #10587568C22semidirect
168. #10587567C22semidirect
169. #10587567C22semidirect
170. #10587567C22semidirect
171. #10587567C22semidirect
172. #10587567C22semidirect
173. C22⋊C4×D17C22semidirect
174. C22⋊C4×D17C22semidirect
175. #10587565C22semidirect
176. #10587565C22semidirect
177. #10587565C22semidirect
178. #10587564C22semidirect
179. #10587564C22semidirect
180. #10587564C22semidirect
181. #10587564C22semidirect
182. #10587563C22semidirect
183. #10587562C22semidirect
184. #10587561C22semidirect
185. C4×D68C22semidirect
186. #10587556C22semidirect
540. #546D17semidirect
574. C2×#41C2×D17semidirect
582. C22×D4C2×D17semidirect
603. #124C2×D17semidirect
630. #123C2×D17semidirect
631. #123C2×D17semidirect
643. C22⋊Q8C2×D17semidirect
677. #121C2×D17semidirect
678. #121C2×D17semidirect
679. #121C2×D17semidirect
694. #120C2×D17semidirect
695. #120C2×D17semidirect
710. C4×D4C2×D17semidirect
711. C4×D4C2×D17semidirect
725. C2×C22⋊C4C2×D17semidirect
726. C2×C22⋊C4C2×D17semidirect
727. C17#3534semidirect

Maximal subgroups

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

subgroupindex
#117635562
#117635532
#117635472
#117635112
#117635052
#117634862
#117634852
#117634542
#117634512
#117634492
#117634472
#117634462
D4×C22⋊D172
#117634412
#117634122
#117634112
#117634082
#117634032
#117634012
#117633962
#117633932
#117633922
#117633872
#117633712
#117633692
#117633672
#117633152
C2×#105875722
C2×#105876252
C17×#5462
#353417