Finite Group Databasebeta

← #47986143

Subgroups — #47986143

Order 35456.

928 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22579850C211yesmaximal, characteristic
2C2×#22579842C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊D277C211yesmaximal, characteristic, complemented
4C22×#17984540C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D277C211yesmaximal, characteristic, complemented
6#31799903C211yesmaximal, characteristic, complemented
7#31799892C211yesmaximal, characteristic, complemented
8#31799891C211yesmaximal, characteristic, complemented
9#31799880C211yesmaximal, characteristic, complemented
10#31799880C211yesmaximal, characteristic, complemented
11#31799879C211yesmaximal, characteristic, complemented
12#31799873C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic277C211yesmaximal, characteristic, complemented
14#31799849C211yesmaximal, characteristic, complemented
15#385×C277C211yesmaximal, characteristic, complemented
16C24×D277C2211yescharacteristic
17C22×D1108C2211yescharacteristic
18C22×D1108C2211yescharacteristic
19C22×C22⋊D277C2211yescharacteristic
20C23×Dic277C2211yescharacteristic
21C22×C4×D277C2211yescharacteristic
22C22×C4×D277C2211yescharacteristic
23C22×C4×D277C2211yescharacteristic, complemented
24#22579850C418yescomplemented
25#22579842—24no—
26C4×C22⋊D277—24no—
27C2×#17984542C2211yescharacteristic, complemented
28C2×C22⋊Dic277C2211yescharacteristic
29C2×#17984540—24no—
30C2×#17984540C2211yescharacteristic
31C2×#17984540C2211yescharacteristic
32C2×#17984540C2211yescharacteristic
33C2×#17984540C2211yescharacteristic
34C2×#17984540C2211yescharacteristic
35C2×#17984540C2211yescharacteristic
36C2×#17984540C2211yescharacteristic
37C2×#17984540C2211yescharacteristic
38C2×#17984540C2211yescharacteristic, complemented
39C2×#17984540C2211yescharacteristic, complemented
40C2×#17984540C2211yescharacteristic, complemented
41C22⋊C4×D277—24no—
42C2×C4×Dic277C2211yescharacteristic, complemented
43C2×C4×Dic277C2211yescharacteristic, complemented
44C2×C4×Dic277C2211yescharacteristic, complemented
45#22579787C2211yescharacteristic, complemented
46#22579787C2211yescharacteristic, complemented
47#22579787C2211yescharacteristic, complemented
48#22579787C2211yescharacteristic, complemented
49C23×C4×C277C2211yescharacteristic
50C2×C4⋊C4×C277C2211yescharacteristic, complemented
51C2×C4⋊C4×C277C2211yescharacteristic, complemented
52C2×C22⋊C4×C277C2211yescharacteristic
53C2×C22⋊C4×C277C2211yescharacteristic
54#95×C277C2211yescharacteristic, complemented
55#95×C277C2211yescharacteristic, complemented
56C23×D277—22no—
57C23×D277—22no—
58C23×D277—22no—
59C23×D277—22no—
60C23×D277—41no—
61C23×D277—41no—
62C23×D277C2×C414yescomplemented
63C23×D277C2311yescharacteristic
64C23×D277C2311yescharacteristic
65C23×D277C2311yescharacteristic
66C2×D1108—22no—
67C2×D1108—22no—
68C2×D1108—41no—
69C2×D1108—41no—
70C2×D1108C2×C414yescomplemented
71C2×D1108C2×C414yescomplemented
72C2×C22⋊D277—22no—
73C2×C22⋊D277—22no—
74C2×C22⋊D277C2×C414yescomplemented
75C22×Dic277—22no—
76C22×Dic277—22no—
77C22×Dic277—41no—
78C22×Dic277C2311yescharacteristic
79C22×Dic277C2311yescharacteristic
80C22×Dic277C2311yescharacteristic
81C22×Dic277C2311yescharacteristic
82C22×Dic277C2311yescharacteristic
83C2×C4×D277—22no—
84C2×C4×D277—22no—
85C2×C4×D277—22no—
86C2×C4×D277—22no—
87C2×C4×D277—22no—
88C2×C4×D277—22no—
89C2×C4×D277—41no—
90C2×C4×D277—41no—
91C2×C4×D277—41no—
92#17984542—22no—
93C22⋊Dic277D414yescomplemented
94#17984540—22no—
95#17984540—22no—
96#17984540—22no—
97#17984540—22no—
98#17984540—22no—
99#17984540—22no—
100#17984540—22no—
101#17984540—41no—
102#17984540C2×C414yescomplemented
103#17984540C2×C414yescomplemented
104#17984540D414yescomplemented
105C4×Dic277—22no—
106C4×Dic277—22no—
107C4×Dic277—41no—
108C24×C277C2311yescharacteristic
109C22×C4×C277—22no—
110C22×C4×C277—22no—
111C22×C4×C277—41no—
112C22×C4×C277C2311yescharacteristic
113C22×C4×C277C2311yescharacteristic
114C22×C4×C277C2311yescharacteristic
115C22×C4×C277C2311yescharacteristic
116C22×C4×C277C2311yescharacteristic
117C22×C4×C277C2311yescharacteristic
118C4⋊C4×C277—22no—
119C4⋊C4×C277—41no—
120C22⋊C4×C277—22no—
121C22⋊C4×C277C2×C414yescomplemented
122C22×D277—21no—
123C22×D277—21no—
124C22×D277—21no—
125C22×D277—21no—
126C22×D277—28no—
127C22×D277—21no—
128C22×D277—21no—
129C22×D277—21no—
130C22×D277—21no—
131C22×D277—21no—
132C22×D277—21no—
133C22×D277—21no—
134C22×D277—21no—
135C22×D277—21no—
136C22×D277—21no—
137C22×D277—21no—
138C22×D277—21no—
139C22×D277—28no—
140C22×D277—44no—
141C22×D277—44no—
142C22×D277—44no—
143C22×D277—44no—
144C22×D277—44no—
145C22×D277C22×C412yes—
146C22×D277C22×C412yes—
147C22×D277C22×C412yes—
148C22×D277C2×D412yes—
149C22×D277#4112yes—
150D1108—28no—
151D1108—44no—
152C22⋊D277—28no—
153C2×Dic277—21no—
154C2×Dic277—21no—
155C2×Dic277—21no—
156C2×Dic277—21no—
157C2×Dic277—21no—
158C2×Dic277—21no—
159C2×Dic277—21no—
160C2×Dic277—21no—
161C2×Dic277—21no—
162C2×Dic277—21no—
163C2×Dic277—21no—
164C2×Dic277—44no—
165C2×Dic277C22×C412yes—
166C2×Dic277C2×D412yes—
167C2×Dic277C2×D412yes—
168C2×Dic277C2×D412yes—
169C4×D277—44no—
170C4×D277—44no—
171C4×D277—44no—
172C23×C277—21no—
173C23×C277—21no—
174C23×C277—21no—
175C23×C277—21no—
176C23×C277C22×C412yes—
177C23×C277C2×D412yes—
178C23×C277#4112yes—
179C23×C277C2411yescharacteristic
180C2×C4×C277—21no—
181C2×C4×C277—21no—
182C2×C4×C277—21no—
183C2×C4×C277—21no—
184C2×C4×C277—21no—
185C2×C4×C277—21no—
186C2×C4×C277—21no—
187C2×C4×C277—21no—
188C2×C4×C277—21no—
189C2×C4×C277—21no—
190C2×C4×C277—21no—
191C2×C4×C277—21no—
192C2×C4×C277—21no—
193C2×C4×C277—21no—
194C2×C4×C277—21no—
195C2×C4×C277—44no—
196C2×C4×C277C22×C412yes—
197C2×C4×C277C22×C412yes—
198C2×C4×C277C2×D412yes—
199C22×C277—22no—
200C22×C277—22no—
201C22×C277—22no—
202C22×C277—22no—
203C22×C277—22no—
204C22×C277—22no—
205C22×C277C4×D414yescomplemented
206C22×C277C23×C411yescharacteristic
207C22×C277C22×D411yescharacteristic
208C22×C277C22×D411yescharacteristic
209C22×C277C2×#4111yescharacteristic
210C22×C277C2×#4111yescharacteristic
211C22×C277H(5,𝔽2)11yescharacteristic
212C22×C277H(5,𝔽2)11yescharacteristic
213C2×D277—22no—
214C2×D277—22no—
215C2×D277—22no—
216C2×D277—22no—
217C2×D277—22no—
218C2×D277—22no—
219C2×D277—22no—
220C2×D277—22no—
221C2×D277—22no—
222C2×D277—22no—
223C2×D277—22no—
224C2×D277—22no—
225C2×D277—416no—
226C2×D277—41no—
227C2×D277—41no—
228C2×D277—41no—
229C2×D277—41no—
230C2×D277—41no—
231C2×D277—41no—
232C2×D277—41no—
233C2×D277—41no—
234C2×D277C4×D414yescomplemented
235C4×C277—22no—
236C4×C277—22no—
237C4×C277—22no—
238C4×C277—41no—
239C4×C277—41no—
240C4×C277—41no—
241Dic277—22no—
242Dic277—22no—
243Dic277—22no—
244Dic277—22no—
245Dic277—41no—
246C2×C277—24no—
247C2×C277C2×C4×D411yescharacteristic
248C2×C277C2×C4×D411yescharacteristic
249C2×C277#51811yescharacteristic
250C2×C277D4211yescharacteristic
251C2×C277#54611yescharacteristic
252C2×C277#54611yescharacteristic
253C2×C277#55111yescharacteristic
254D277—24no—
255D277—42no—
256D277—42no—
257C277#235811yescharacteristic, complemented, Sylow
258#2358—2771nomaximal, Sylow
259C2×#120—2771no—
260C2×C4×D4—2771no—
261C2×C4×D4—2771no—
262C22×C22⋊C4—2771no—
263C22×C22⋊C4—2771no—
264#390—2771no—
265#388—2771no—
266#388—2771no—
267#386—2771no—
268#386—2771no—
269#386—2771no—
270#385—2771no—
271#385D27711yescharacteristic, complemented
272C4×C22⋊C4—2771no—
273C4×C22⋊C4—2771no—
274C25—2771no—
275C22×D4—2771no—
276C22×D4—2771no—
277C22×D4—2771no—
278C23×C4—2771no—
279C23×C4—2771no—
280C23×C4—2771no—
281C23×C4—2771no—
282C23×C4C2×D27711yescharacteristic
283#120—2778no—
284C4×D4—5544no—
285C4×D4—5544no—
286C2×C4⋊C4—2771no—
287C2×C4⋊C4C2×D27711yescharacteristic, complemented
288C2×C4⋊C4C2×D27711yescharacteristic, complemented
289C2×C22⋊C4—2771no—
290C2×C22⋊C4—2771no—
291C2×C22⋊C4—2771no—
292C2×C22⋊C4—2771no—
293C2×C22⋊C4—2771no—
294C2×C22⋊C4—2771no—
295C2×C22⋊C4—2771no—
296C2×C22⋊C4—2771no—
297C2×C22⋊C4—2771no—
298C2×C22⋊C4—2771no—
299C2×C22⋊C4—2771no—
300C2×C22⋊C4—2771no—
301C2×C22⋊C4—5544no—
302C2×C22⋊C4—5544no—
303C2×C22⋊C4C2×D27711yescharacteristic
304C2×C22⋊C4C2×D27711yescharacteristic
305C2×C42—2771no—
306C2×C42—2771no—
307C2×C42—2771no—
308#95—2771no—
309#95—2771no—
310#95—2771no—
311#95—2771no—
312#95C2×D27711yescharacteristic, complemented
313#95C2×D27711yescharacteristic, complemented
314C24—2771no—
315C24—2771no—
316C24—2771no—
317C24—2774no—
318C24—5542no—
319C24—5542no—
320C24—5542no—
321C24—5542no—
322C24—11081no—
323C24—11081no—
324C24C22×D27711yescharacteristic
325C2×D4—2774no—
326C2×D4—2774no—
327C2×D4—2774no—
328C2×D4—5542no—
329C2×D4—5542no—
330C2×D4—5542no—
331C2×D4—5542no—
332C2×D4—11081no—
333C2×D4—11081no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—41no—
337C22×C4—2771no—
338C22×C4—2771no—
339C22×C4—2771no—
340C22×C4—2771no—
341C22×C4—2771no—
342C22×C4—5542no—
343C22×C4—5542no—
344C22×C4—5542no—
345C22×C4—5542no—
346C22×C4—5542no—
347C22×C4—5542no—
348C22×C4—5542no—
349C22×C4—5542no—
350C22×C4—11081no—
351C22×C4—11081no—
352C22×C4—11081no—
353C22×C4—11081no—
354C22×C4C22×D27711yescharacteristic
355C22×C4C22×D27711yescharacteristic
356C22×C4C22×D27711yescharacteristic
357C22×C4C22×D27711yescharacteristic
358C22×C4C22×D27711yescharacteristic
359C22×C4C22×D27711yescharacteristic
360C4⋊C4—22no—
361C4⋊C4—41no—
362C4⋊C4—5542no—
363C22⋊C4—22no—
364C22⋊C4—2774no—
365C22⋊C4—2774no—
366C22⋊C4—2774no—
367C22⋊C4—2774no—
368C22⋊C4—5542no—
369C22⋊C4—5542no—
370C22⋊C4—5542no—
371C22⋊C4—5542no—
372C22⋊C4—5542no—
373C22⋊C4—5542no—
374C22⋊C4—5542no—
375C22⋊C4—11081no—
376C22⋊C4C4×D27714yescomplemented
377C42—5542no—
378C42—5542no—
379C42—11081no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—2772no—
385C23—2772no—
386C23—2772no—
387C23—2772no—
388C23—2772no—
389C23—5548no—
390C23—5541no—
391C23—5541no—
392C23—5541no—
393C23—5541no—
394C23—5548no—
395C23—5541no—
396C23—5541no—
397C23—5541no—
398C23—5541no—
399C23—5541no—
400C23—5541no—
401C23—5541no—
402C23—5541no—
403C23—5541no—
404C23—5541no—
405C23—5541no—
406C23—5541no—
407C23—11084no—
408C23—11084no—
409C23—11084no—
410C23—11084no—
411C23—11084no—
412C23C2×C4×D27712yes—
413C23D4×D27712yes—
414C23#1798456412yes—
415C23C23×D27711yescharacteristic
416D4—5548no—
417D4—5548no—
418D4—11084no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—44no—
435C2×C4—2772no—
436C2×C4—2772no—
437C2×C4—2772no—
438C2×C4—2772no—
439C2×C4—5541no—
440C2×C4—5541no—
441C2×C4—5541no—
442C2×C4—5541no—
443C2×C4—5541no—
444C2×C4—5541no—
445C2×C4—5541no—
446C2×C4—5541no—
447C2×C4—5541no—
448C2×C4—5541no—
449C2×C4—5541no—
450C2×C4—11084no—
451C2×C4—11084no—
452C2×C4—11084no—
453C2×C4—11084no—
454C2×C4C2×C4×D27712yes—
455C2×C4C2×C4×D27712yes—
456C2×C4D4×D27712yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—2774no—
464C22—5542no—
465C22—5542no—
466C22—5542no—
467C22—5542no—
468C22—5542no—
469C22—5542no—
470C22—5542no—
471C22—5542no—
472C22—5542no—
473C22—5542no—
474C22—5542no—
475C22—5542no—
476C22—110816no—
477C22—11081no—
478C22—11081no—
479C22—11081no—
480C22—11081no—
481C22—11081no—
482C22—11081no—
483C22—11081no—
484C22—11081no—
485C22#2257984214yescomplemented
486C22C22×C4×D27711yescharacteristic
487C22C2×D4×D27711yescharacteristic
488C22C2×D4×D27711yescharacteristic
489C22#41×D27711yescharacteristic
490C22C2×#1798456411yescharacteristic
491C22#2257992511yescharacteristic
492C22#2257992611yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—41no—
497C4—41no—
498C4—41no—
499C4—5542no—
500C4—5542no—
501C4—5542no—
502C4—5542no—
503C4—11081no—
504C2—24no—
505C2—5544no—
506C2—11082no—
507C2—11082no—
508C2C4×D4×D27711yescharacteristic
509C2C2×#2257984211yescharacteristic
510C2#3180047411yescharacteristic
511C2#3180063411yescharacteristic
512C2#3180064311yescharacteristic
513C2#3180064411yescharacteristic
514C2#3180067911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D277
commutatorC22×C277C23×C4
Fitting#385×C277C2
socle, cosocleC23×C277C24
prime radicalC2×#22579850C2
hypercenter#385D277
hypocenterC277#2358
LCSG ▷ C22×C277 ▷ C277
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×#22579842C2semidirect
3. C2×C4×C22⋊D277C2semidirect
4. C22×#17984540C2semidirect
5. C2×C22⋊C4×D277C2semidirect
6. #31799903C2semidirect
7. #31799892C2semidirect
8. #31799891C2semidirect
9. #31799880C2semidirect
10. #31799880C2semidirect
11. #31799879C2semidirect
12. #31799873C2semidirect
13. C22⋊C4×Dic277C2semidirect
14. #31799849C2semidirect
15. #385×C277C2semidirect
23. C22×C4×D277C22semidirect
24. #22579850C4semidirect
27. C2×#17984542C22semidirect
38. C2×#17984540C22semidirect
39. C2×#17984540C22semidirect
40. C2×#17984540C22semidirect
42. C2×C4×Dic277C22semidirect
43. C2×C4×Dic277C22semidirect
44. C2×C4×Dic277C22semidirect
45. #22579787C22semidirect
46. #22579787C22semidirect
47. #22579787C22semidirect
48. #22579787C22semidirect
50. C2×C4⋊C4×C277C22semidirect
51. C2×C4⋊C4×C277C22semidirect
54. #95×C277C22semidirect
55. #95×C277C22semidirect
62. C23×D277C2×C4semidirect
70. C2×D1108C2×C4semidirect
71. C2×D1108C2×C4semidirect
74. C2×C22⋊D277C2×C4semidirect
93. C22⋊Dic277D4semidirect
102. #17984540C2×C4semidirect
103. #17984540C2×C4semidirect
104. #17984540D4semidirect
121. C22⋊C4×C277C2×C4semidirect
205. C22×C277C4×D4semidirect
234. C2×D277C4×D4semidirect
257. C277#2358semidirect
271. #385D277semidirect
287. C2×C4⋊C4C2×D277semidirect
288. C2×C4⋊C4C2×D277semidirect
312. #95C2×D277semidirect
313. #95C2×D277semidirect
376. C22⋊C4C4×D277semidirect
485. C22#22579842semidirect

Maximal subgroups

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

subgroupindex
C2×#225798502
C2×#225798422
C2×C4×C22⋊D2772
C22×#179845402
C2×C22⋊C4×D2772
#317999032
#317998922
#317998912
#317998802
#317998792
#317998732
C22⋊C4×Dic2772
#317998492
#385×C2772
#2358277