Finite Group Databasebeta

← #47986010

Subgroups — #47986010

Order 35456.

792 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22579837C211yesmaximal, characteristic, complemented
2C22×#17984540C211yesmaximal, characteristic
3C2×C22⋊C4×D277C211yesmaximal, characteristic
4#31799893C211yesmaximal, characteristic, complemented
5#31799893C211yesmaximal, characteristic, complemented
6#31799891C211yesmaximal, characteristic, complemented
7#31799891C211yesmaximal, characteristic, complemented
8#31799875C211yesmaximal, characteristic, complemented
9#31799874C211yesmaximal, characteristic, complemented
10#31799864C211yesmaximal, characteristic, complemented
11#31799861C211yesmaximal, characteristic, complemented
12#31799857C211yesmaximal, characteristic
13C22⋊C4×Dic277C211yesmaximal, characteristic, complemented
14C4×#17984540C211yesmaximal, characteristic, complemented
15C4×C22⋊C4×C277C211yesmaximal, characteristic, complemented
16C24×D277C2211yescharacteristic
17C23×Dic277C2211yescharacteristic
18C22×C4×D277C2211yescharacteristic
19C22×C4×D277C2211yescharacteristic
20#22579837—24no—
21C2×#17984542C2211yescharacteristic, complemented
22C2×#17984542C2211yescharacteristic, complemented
23C2×#17984542C2211yescharacteristic, complemented
24C2×#17984542C2211yescharacteristic, complemented
25C2×C22⋊Dic277C2211yescharacteristic
26C2×C22⋊Dic277C2211yescharacteristic
27C2×#17984540—24no—
28C2×#17984540C2211yescharacteristic
29C2×#17984540C2211yescharacteristic
30C2×#17984540C2211yescharacteristic
31C2×#17984540C2211yescharacteristic
32C2×#17984540C2211yescharacteristic
33C2×#17984540C2211yescharacteristic
34C2×#17984540C2211yescharacteristic
35C2×#17984540C2211yescharacteristic
36C2×#17984540C2211yescharacteristic
37C2×#17984540C2211yescharacteristic
38C22⋊C4×D277C418yescomplemented
39C2×C4×Dic277C2211yescharacteristic, complemented
40C2×C4×Dic277C2211yescharacteristic, complemented
41#22579787C2211yescharacteristic, complemented
42#22579787C2211yescharacteristic, complemented
43#22579787C2211yescharacteristic, complemented
44#22579787C2211yescharacteristic, complemented
45#22579787C2211yescharacteristic, complemented
46#22579787C2211yescharacteristic, complemented
47C23×C4×C277C2211yescharacteristic
48C2×C22⋊C4×C277C2211yescharacteristic
49C2×C22⋊C4×C277C2211yescharacteristic
50C2×C42×C277C2211yescharacteristic, complemented
51C2×C42×C277C2211yescharacteristic, complemented
52#95×C277C2211yescharacteristic, complemented
53#95×C277C2211yescharacteristic, complemented
54C23×D277—22no—
55C23×D277—22no—
56C23×D277—22no—
57C23×D277—22no—
58C23×D277—41no—
59C23×D277—41no—
60C23×D277C2×C414yes—
61C23×D277C2311yescharacteristic
62C23×D277C2311yescharacteristic
63C22×Dic277—22no—
64C22×Dic277—22no—
65C22×Dic277—41no—
66C22×Dic277C2311yescharacteristic
67C22×Dic277C2311yescharacteristic
68C22×Dic277C2311yescharacteristic
69C22×Dic277C2311yescharacteristic
70C22×Dic277C2311yescharacteristic
71C22×Dic277C2311yescharacteristic
72C2×C4×D277—22no—
73C2×C4×D277—22no—
74C2×C4×D277—41no—
75C2×C4×D277—41no—
76C2×C4×D277C2×C414yescomplemented
77C2×C4×D277C2×C414yescomplemented
78#17984542—22no—
79#17984542—22no—
80#17984542—41no—
81#17984542—41no—
82C22⋊Dic277—22no—
83C22⋊Dic277C2×C414yes—
84#17984540—22no—
85#17984540—22no—
86#17984540—22no—
87#17984540—22no—
88#17984540—22no—
89#17984540—41no—
90#17984540—41no—
91#17984540C2×C414yescomplemented
92#17984540C2×C414yescomplemented
93#17984540D414yes—
94C4×Dic277—22no—
95C4×Dic277—41no—
96C24×C277C2311yescharacteristic
97C22×C4×C277—22no—
98C22×C4×C277—22no—
99C22×C4×C277—41no—
100C22×C4×C277C2311yescharacteristic
101C22×C4×C277C2311yescharacteristic
102C22×C4×C277C2311yescharacteristic
103C22×C4×C277C2311yescharacteristic
104C22×C4×C277C2311yescharacteristic
105C22×C4×C277C2311yescharacteristic
106C22⋊C4×C277—22no—
107C22⋊C4×C277C2×C414yes—
108C42×C277—22no—
109C42×C277—41no—
110C22×D277—21no—
111C22×D277—21no—
112C22×D277—21no—
113C22×D277—21no—
114C22×D277—28no—
115C22×D277—21no—
116C22×D277—21no—
117C22×D277—21no—
118C22×D277—21no—
119C22×D277—21no—
120C22×D277—21no—
121C22×D277—28no—
122C22×D277—44no—
123C22×D277—44no—
124C22×D277—44no—
125C22×D277—44no—
126C22×D277—44no—
127C22×D277C22×C412yes—
128C22×D277C22×C412yes—
129C22×D277C2×D412yes—
130C22×D277#4112yes—
131C2×Dic277—21no—
132C2×Dic277—21no—
133C2×Dic277—21no—
134C2×Dic277—21no—
135C2×Dic277—21no—
136C2×Dic277—21no—
137C2×Dic277—21no—
138C2×Dic277—21no—
139C2×Dic277—21no—
140C2×Dic277—21no—
141C2×Dic277—21no—
142C2×Dic277—21no—
143C2×Dic277—21no—
144C2×Dic277—21no—
145C2×Dic277—21no—
146C2×Dic277—44no—
147C2×Dic277C22×C412yes—
148C2×Dic277C22×C412yes—
149C2×Dic277C2×D412yes—
150C4×D277—28no—
151C4×D277—44no—
152C23×C277—21no—
153C23×C277—21no—
154C23×C277—21no—
155C23×C277—21no—
156C23×C277C22×C412yes—
157C23×C277#4112yes—
158C23×C277#4112yes—
159C23×C277C2411yescharacteristic
160C2×C4×C277—21no—
161C2×C4×C277—21no—
162C2×C4×C277—21no—
163C2×C4×C277—21no—
164C2×C4×C277—21no—
165C2×C4×C277—21no—
166C2×C4×C277—21no—
167C2×C4×C277—21no—
168C2×C4×C277—21no—
169C2×C4×C277—21no—
170C2×C4×C277—21no—
171C2×C4×C277—21no—
172C2×C4×C277—21no—
173C2×C4×C277—21no—
174C2×C4×C277—21no—
175C2×C4×C277—44no—
176C2×C4×C277C22×C412yes—
177C2×C4×C277C22×C412yes—
178C2×C4×C277C2×D412yes—
179C22×C277—22no—
180C22×C277—22no—
181C22×C277—22no—
182C22×C277—22no—
183C22×C277—22no—
184C22×C277—22no—
185C22×C277#11714yescomplemented
186C22×C277C23×C411yescharacteristic
187C22×C277C22×D411yescharacteristic
188C22×C277C2×#4111yescharacteristic
189C22×C277C2×#4111yescharacteristic
190C22×C277C2×#4111yescharacteristic
191C22×C277H(5,𝔽2)11yescharacteristic
192C22×C277H(5,𝔽2)11yescharacteristic
193C2×D277—22no—
194C2×D277—22no—
195C2×D277—22no—
196C2×D277—22no—
197C2×D277—22no—
198C2×D277—22no—
199C2×D277—22no—
200C2×D277—22no—
201C2×D277—22no—
202C2×D277—416no—
203C2×D277—41no—
204C2×D277—41no—
205C2×D277—41no—
206C2×D277—41no—
207C2×D277C4×D414yes—
208C4×C277—22no—
209C4×C277—22no—
210C4×C277—22no—
211C4×C277—41no—
212C4×C277—41no—
213C4×C277—41no—
214Dic277—22no—
215Dic277—22no—
216Dic277—22no—
217Dic277—41no—
218Dic277—41no—
219Dic277—41no—
220C2×C277—24no—
221C2×C277C2×#11711yescharacteristic
222C2×C277C2×C4×D411yescharacteristic
223C2×C277#51811yescharacteristic
224C2×C277#54611yescharacteristic
225C2×C277#54611yescharacteristic
226C2×C277#55111yescharacteristic
227C2×C277#55111yescharacteristic
228D277—24no—
229D277—42no—
230C277#234211yescharacteristic, complemented, Sylow
231#2342—2771nomaximal, Sylow
232C2×#117—2771no—
233C22×C22⋊C4—2771no—
234C22×C22⋊C4—2771no—
235#388—2771no—
236#388—2771no—
237#388—2771no—
238#388—2771no—
239#385—2771no—
240#385—2771no—
241#381—2771no—
242#380—2771no—
243#379—2771no—
244C4×C22⋊C4—2771no—
245C4×C22⋊C4—2771no—
246C4×C22⋊C4D27711yescharacteristic, complemented
247C25—2771no—
248C23×C4—2771no—
249C23×C4—2771no—
250C23×C4—2771no—
251C23×C4C2×D27711yescharacteristic
252#117—5544no—
253C2×C4⋊C4—2771no—
254C2×C4⋊C4—2771no—
255C2×C4⋊C4—2771no—
256C2×C4⋊C4—2771no—
257C2×C22⋊C4—2771no—
258C2×C22⋊C4—2771no—
259C2×C22⋊C4—2771no—
260C2×C22⋊C4—2771no—
261C2×C22⋊C4—2778no—
262C2×C22⋊C4—2771no—
263C2×C22⋊C4—2771no—
264C2×C22⋊C4—2771no—
265C2×C22⋊C4—2771no—
266C2×C22⋊C4—2771no—
267C2×C22⋊C4—2771no—
268C2×C22⋊C4—2771no—
269C2×C22⋊C4—2771no—
270C2×C22⋊C4—5544no—
271C2×C22⋊C4C2×D27711yescharacteristic
272C2×C22⋊C4C2×D27711yescharacteristic
273C2×C42—2771no—
274C2×C42—2771no—
275C2×C42C2×D27711yescharacteristic, complemented
276C2×C42C2×D27711yescharacteristic, complemented
277#95—2771no—
278#95—2771no—
279#95—2771no—
280#95—2771no—
281#95—2771no—
282#95—2771no—
283#95C2×D27711yescharacteristic, complemented
284#95C2×D27711yescharacteristic, complemented
285C24—2771no—
286C24—2771no—
287C24—2774no—
288C24—5542no—
289C24—5542no—
290C24—5542no—
291C24—5542no—
292C24—11081no—
293C24—11081no—
294C24C22×D27711yescharacteristic
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—41no—
298C22×C4—2771no—
299C22×C4—2771no—
300C22×C4—2771no—
301C22×C4—2774no—
302C22×C4—2774no—
303C22×C4—2771no—
304C22×C4—2771no—
305C22×C4—2771no—
306C22×C4—5542no—
307C22×C4—5542no—
308C22×C4—5542no—
309C22×C4—5542no—
310C22×C4—11081no—
311C22×C4—11081no—
312C22×C4—11081no—
313C22×C4C22×D27711yescharacteristic
314C22×C4C22×D27711yescharacteristic
315C22×C4C22×D27711yescharacteristic
316C22×C4C22×D27711yescharacteristic
317C22×C4C22×D27711yescharacteristic
318C22×C4C22×D27711yescharacteristic
319C4⋊C4—5542no—
320C4⋊C4—5542no—
321C4⋊C4—11081no—
322C4⋊C4—11081no—
323C22⋊C4—22no—
324C22⋊C4—2774no—
325C22⋊C4—2774no—
326C22⋊C4—2774no—
327C22⋊C4—2774no—
328C22⋊C4—5542no—
329C22⋊C4—5542no—
330C22⋊C4—5542no—
331C22⋊C4—5542no—
332C22⋊C4—5542no—
333C22⋊C4—5542no—
334C22⋊C4—11081no—
335C22⋊C4—11081no—
336C22⋊C4C4×D27714yes—
337C42—22no—
338C42—41no—
339C42—5542no—
340C42—11081no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—2772no—
346C23—2772no—
347C23—2772no—
348C23—2772no—
349C23—5548no—
350C23—5541no—
351C23—5541no—
352C23—5541no—
353C23—5541no—
354C23—5548no—
355C23—5541no—
356C23—5541no—
357C23—5541no—
358C23—5541no—
359C23—5541no—
360C23—5541no—
361C23—11084no—
362C23—11084no—
363C23—11084no—
364C23—11084no—
365C23—11084no—
366C23C2×C4×D27712yes—
367C23#1798456312yes—
368C23#1798456312yes—
369C23C23×D27711yescharacteristic
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—44no—
386C2×C4—2772no—
387C2×C4—2772no—
388C2×C4—2772no—
389C2×C4—5548no—
390C2×C4—5541no—
391C2×C4—5541no—
392C2×C4—5541no—
393C2×C4—5541no—
394C2×C4—5541no—
395C2×C4—5541no—
396C2×C4—5541no—
397C2×C4—5541no—
398C2×C4—5541no—
399C2×C4—5541no—
400C2×C4—5541no—
401C2×C4—5541no—
402C2×C4—5541no—
403C2×C4—5541no—
404C2×C4—5541no—
405C2×C4—11084no—
406C2×C4—11084no—
407C2×C4C2×C4×D27712yes—
408C2×C4C2×C4×D27712yes—
409C2×C4D4×D27712yes—
410C22—22no—
411C22—22no—
412C22—22no—
413C22—22no—
414C22—22no—
415C22—22no—
416C22—2774no—
417C22—5542no—
418C22—5542no—
419C22—5542no—
420C22—5542no—
421C22—5542no—
422C22—5542no—
423C22—5542no—
424C22—5542no—
425C22—5542no—
426C22—110816no—
427C22—11081no—
428C22—11081no—
429C22—11081no—
430C22—11081no—
431C22#2257983714yescomplemented
432C22C22×C4×D27711yescharacteristic
433C22C2×D4×D27711yescharacteristic
434C22#41×D27711yescharacteristic
435C22C2×#1798456311yescharacteristic
436C22C2×#1798456311yescharacteristic
437C22#2257992511yescharacteristic
438C22#2257992611yescharacteristic
439C4—22no—
440C4—22no—
441C4—22no—
442C4—41no—
443C4—41no—
444C4—41no—
445C4—5542no—
446C4—5542no—
447C4—5542no—
448C4—11081no—
449C4—11081no—
450C4—11081no—
451C2—24no—
452C2—5544no—
453C2—11082no—
454C2C2×#2257983711yescharacteristic
455C2C4×D4×D27711yescharacteristic
456C2#3180047411yescharacteristic
457C2#3180064211yescharacteristic
458C2#3180064811yescharacteristic
459C2#3180067611yescharacteristic
460C2#3180068111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D277
commutatorC22×C277C23×C4
FittingC4×C22⋊C4×C277C2
socle, cosocleC23×C277C24
prime radicalC24×D277C22
hypercenterC4×C22⋊C4D277
hypocenterC277#2342
LCSG ▷ C22×C277 ▷ C277
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#22579837C2semidirect
4. #31799893C2semidirect
5. #31799893C2semidirect
6. #31799891C2semidirect
7. #31799891C2semidirect
8. #31799875C2semidirect
9. #31799874C2semidirect
10. #31799864C2semidirect
11. #31799861C2semidirect
13. C22⋊C4×Dic277C2semidirect
14. C4×#17984540C2semidirect
15. C4×C22⋊C4×C277C2semidirect
21. C2×#17984542C22semidirect
22. C2×#17984542C22semidirect
23. C2×#17984542C22semidirect
24. C2×#17984542C22semidirect
38. C22⋊C4×D277C4semidirect
39. C2×C4×Dic277C22semidirect
40. C2×C4×Dic277C22semidirect
41. #22579787C22semidirect
42. #22579787C22semidirect
43. #22579787C22semidirect
44. #22579787C22semidirect
45. #22579787C22semidirect
46. #22579787C22semidirect
50. C2×C42×C277C22semidirect
51. C2×C42×C277C22semidirect
52. #95×C277C22semidirect
53. #95×C277C22semidirect
76. C2×C4×D277C2×C4semidirect
77. C2×C4×D277C2×C4semidirect
91. #17984540C2×C4semidirect
92. #17984540C2×C4semidirect
185. C22×C277#117semidirect
230. C277#2342semidirect
246. C4×C22⋊C4D277semidirect
275. C2×C42C2×D277semidirect
276. C2×C42C2×D277semidirect
283. #95C2×D277semidirect
284. #95C2×D277semidirect
431. C22#22579837semidirect

Maximal subgroups

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

subgroupindex
C2×#225798372
C22×#179845402
C2×C22⋊C4×D2772
#317998932
#317998912
#317998752
#317998742
#317998642
#317998612
#317998572
C22⋊C4×Dic2772
C4×#179845402
C4×C22⋊C4×C2772
#2342277