Finite Group Databasebeta

← #46846190

Subgroups — #46846190

Order 34688.

398 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31774524C211yesmaximal, characteristic, complemented
2#31774369C211yesmaximal, characteristic
3#31774199C211yesmaximal, characteristic, complemented
4#31774198C211yesmaximal, characteristic, complemented
5#31774197C211yesmaximal, characteristic, complemented
6#31774196C211yesmaximal, characteristic, complemented
7#31774186C211yesmaximal, characteristic, complemented
8#31774175C211yesmaximal, characteristic, complemented
9#31774174C211yesmaximal, characteristic, complemented
10#31773936C211yesmaximal, characteristic, complemented
11#31773932C211yesmaximal, characteristic, complemented
12#31773922C211yesmaximal, characteristic, complemented
13#31773900C211yesmaximal, characteristic
14#102×D271C211yesmaximal, characteristic
15#476×C271C211yesmaximal, characteristic, complemented
16C2×D4×D271C2211yescharacteristic
17C2×#16864637C2211yescharacteristic
18C2×C8×D271C2211yescharacteristic
19#22576159C2211yescharacteristic, complemented
20#22576158—21no—
21#22576152C2211yescharacteristic, complemented
22#22576151C2211yescharacteristic, complemented
23#22576150—21no—
24#22576138—21no—
25#22576136—21no—
26C4×D1084C2211yescharacteristic
27D4×Dic271C2211yescharacteristic
28#22576122C2211yescharacteristic
29C4×C22⋊D271—21no—
30(C22⋊D271)⋊C4—21no—
31#22576118C2211yescharacteristic
32#22576118C2211yescharacteristic
33#22576117C2211yescharacteristic
34C4⋊C4×D271C2211yescharacteristic
35C2×(C2×D271)⋊C4—21no—
36C22⋊C4×D271—21no—
37#22576094C2211yescharacteristic, complemented
38#22576093C2211yescharacteristic, complemented
39#22576093C2211yescharacteristic, complemented
40#22576093C2211yescharacteristic, complemented
41#22576092C2211yescharacteristic, complemented
42#22576091C2211yescharacteristic, complemented
43C4⋊(C271⋊C8)C2211yescharacteristic, complemented
44Dic271⋊C8C2211yescharacteristic, complemented
45Dic271⋊C8C2211yescharacteristic, complemented
46#22576082C2211yescharacteristic
47#22576082C2211yescharacteristic
48#22576081C2211yescharacteristic
49#22576081C2211yescharacteristic
50#22576080C2211yescharacteristic
51#22576080C2211yescharacteristic
52C4⋊Q8×C271C2211yescharacteristic, complemented
53C4×D4×C271C2211yescharacteristic
54#106×C271C2211yescharacteristic, complemented
55#106×C271C2211yescharacteristic, complemented
56C4⋊C8×C271C2211yescharacteristic, complemented
57#102×C271C2211yescharacteristic
58#102×C271C2211yescharacteristic
59C23×D271—21no—
60C2×Dic542—21no—
61C2×D1084C2311yescharacteristic
62C2×C22⋊D271—21no—
63D4×D271—22no—
64D4×D271Q814yescomplemented
65C22×Dic271—21no—
66C2×C4×D271—21no—
67C2×C4×D271—21no—
68C2×C4×D271—21no—
69C2×C4×D271C2311yescharacteristic
70#16864637—22no—
71C2×C271⋊C8C2311yescharacteristic
72C2×C271⋊C8C2311yescharacteristic
73C8×D271—22no—
74C4⋊Dic271—21no—
75C4⋊Dic271C2311yescharacteristic
76C4⋊Dic271C2311yescharacteristic
77C4⋊Dic271C2311yescharacteristic
78Dic271⋊C4—21no—
79Dic271⋊C4—21no—
80Dic271⋊C4—21no—
81Dic271⋊C4—21no—
82Dic271⋊C4—21no—
83Dic271⋊C4D411yescharacteristic
84Dic271⋊C4D411yescharacteristic
85C22⋊Dic271—21no—
86(C2×D271)⋊C4—21no—
87(C2×D271)⋊C4—21no—
88(C2×D271)⋊C4—21no—
89(C2×D271)⋊C4—21no—
90(C2×D271)⋊C4D411yescharacteristic
91(C2×D271)⋊C4D411yescharacteristic
92C4×Dic271—21no—
93C4×Dic271—21no—
94C4×Dic271C2311yescharacteristic
95C2×Q8×C271—21no—
96C2×D4×C271C2311yescharacteristic
97C22×C4×C271—21no—
98C2×C8×C271C2311yescharacteristic
99C2×C8×C271C2311yescharacteristic
100C4⋊C4×C271—21no—
101C4⋊C4×C271C2311yescharacteristic
102C4⋊C4×C271C2311yescharacteristic
103C4⋊C4×C271C2311yescharacteristic
104C22⋊C4×C271—21no—
105C42×C271C2311yescharacteristic
106C22×D271—21no—
107C22×D271—24no—
108C22×D271—81no—
109C22×D271—81no—
110C22×D271C2×D411yescharacteristic
111Dic542—81no—
112D1084—21no—
113D1084C2×Q812yes—
114C22⋊D271—24no—
115C2×Dic271—21no—
116C2×Dic271—21no—
117C2×Dic271—21no—
118C2×Dic271—81no—
119C2×Dic271C2×D411yescharacteristic
120C2×Dic271C2×D411yescharacteristic
121C2×Dic271C2×D411yescharacteristic
122C4×D271—81no—
123C4×D271—81no—
124C4×D271—81no—
125C4×D271C2×Q812yes—
126C4×D271#4112yes—
127C271⋊C8—21no—
128C271⋊C8—21no—
129C23×C271—21no—
130Q8×C271—81no—
131D4×C271—21no—
132D4×C271C2×Q812yes—
133C2×C4×C271—21no—
134C2×C4×C271—21no—
135C2×C4×C271—21no—
136C2×C4×C271—81no—
137C2×C4×C271C2×D411yescharacteristic
138C2×C4×C271C2×D411yescharacteristic
139C2×C4×C271C2411yescharacteristic
140C8×C271—21no—
141C8×C271—21no—
142C22×C271—22no—
143C22×C271—41no—
144C22×C271—41no—
145C22×C271C22×D411yescharacteristic
146C2×D271—21no—
147C2×D271—21no—
148C2×D271—22no—
149C2×D271—41no—
150C2×D271—41no—
151C2×D271—84no—
152C2×D271C22⋊Q812yes—
153C4×C271—21no—
154C4×C271—21no—
155C4×C271—41no—
156C4×C271—41no—
157C4×C271—41no—
158C4×C271C22×Q811yescharacteristic
159C4×C271C2×#4111yescharacteristic
160Dic271—21no—
161Dic271—21no—
162Dic271—41no—
163Dic271—41no—
164Dic271—41no—
165Dic271C22⋊Q812yes—
166C2×C271—42no—
167C2×C271C2×C22⋊Q811yescharacteristic
168C2×C271#57611yescharacteristic
169C2×C271#57711yescharacteristic
170D271—22no—
171D271—42no—
172C271#308111yescharacteristic, complemented, Sylow
173#3081—2711nomaximal, Sylow
174#544—2711no—
175#518—2711no—
176#478—2711no—
177#478—2711no—
178#478—2711no—
179#478—2711no—
180#476—2711no—
181#476D27111yescharacteristic, complemented
182#474—2711no—
183#474—2711no—
184#428—2711no—
185#427—2711no—
186#424—2711no—
187#418—2711no—
188C2×#102—2711no—
189C22×D4—2711no—
190C2×M16—2711no—
191C22×C8—2711no—
192C4⋊Q8—2711no—
193C4⋊Q8—5421no—
194C4⋊Q8C2×D27111yescharacteristic, complemented
195#125—2711no—
196#125—2711no—
197#125—5421no—
198C22⋊Q8—5421no—
199C22⋊Q8—5421no—
200C4×D4—2711no—
201C4×D4—2711no—
202C4×D4—2711no—
203C4×D4—5421no—
204C4×D4—5421no—
205C4×D4C2×D27111yescharacteristic
206#117—2711no—
207#117—2711no—
208#117—2711no—
209C2×C4⋊C4—2711no—
210C2×C22⋊C4—5421no—
211C2×C22⋊C4—5421no—
212#107—2711no—
213#107—2711no—
214#107—2711no—
215#107—2711no—
216#106—2711no—
217#106—2711no—
218#106C2×D27111yescharacteristic, complemented
219#106C2×D27111yescharacteristic, complemented
220C4⋊C8—2711no—
221C4⋊C8—2711no—
222C4⋊C8—2711no—
223C4⋊C8C2×D27111yescharacteristic, complemented
224#102—2711no—
225#102—2711no—
226#102—2711no—
227#102—2711no—
228#102—2711no—
229#102—2711no—
230#102C2×D27111yescharacteristic
231#102C2×D27111yescharacteristic
232C24—5421no—
233C2×Q8—21no—
234C2×Q8—5421no—
235C2×D4—2714no—
236C2×D4—2711no—
237C2×D4—5422no—
238C2×D4—5421no—
239C2×D4C22×D27111yescharacteristic
240C22×C4—21no—
241C22×C4—2711no—
242C22×C4—5421no—
243C22×C4—5421no—
244C22×C4—5421no—
245C22×C4—5421no—
246M16—5422no—
247C2×C8—2711no—
248C2×C8—2711no—
249C2×C8—5422no—
250C2×C8C22×D27111yescharacteristic
251C2×C8C22×D27111yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—2711no—
254C4⋊C4—2711no—
255C4⋊C4—2711no—
256C4⋊C4—2711no—
257C4⋊C4—2711no—
258C4⋊C4—5421no—
259C4⋊C4—5421no—
260C4⋊C4—5421no—
261C4⋊C4—5421no—
262C4⋊C4—5421no—
263C4⋊C4—5421no—
264C4⋊C4C22×D27111yescharacteristic
265C4⋊C4C22×D27111yescharacteristic
266C4⋊C4C22×D27111yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—2711no—
269C22⋊C4—2711no—
270C22⋊C4—5421no—
271C22⋊C4—5421no—
272C22⋊C4—5421no—
273C22⋊C4—5421no—
274C22⋊C4—5421no—
275C42—2711no—
276C42—5421no—
277C42—5421no—
278C42C22×D27111yescharacteristic
279C23—21no—
280C23—2711no—
281C23—5424no—
282C23—5421no—
283C23—21681no—
284C23—21681no—
285Q8—81no—
286Q8—21681no—
287D4—21no—
288D4—2712no—
289D4—5424no—
290D4—5421no—
291D4Q8×D27112yes—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—81no—
296C2×C4—2711no—
297C2×C4—2712no—
298C2×C4—2712no—
299C2×C4—2711no—
300C2×C4—2711no—
301C2×C4—5421no—
302C2×C4—5421no—
303C2×C4—5421no—
304C2×C4—21681no—
305C2×C4—21681no—
306C2×C4—21681no—
307C2×C4—21681no—
308C2×C4D4×D27111yescharacteristic
309C2×C4D4×D27111yescharacteristic
310C2×C4C23×D27111yescharacteristic
311C8—21no—
312C8—21no—
313C8—5421no—
314C8—5421no—
315C22—22no—
316C22—41no—
317C22—41no—
318C22—2712no—
319C22—5421no—
320C22—5421no—
321C22—5422no—
322C22—10841no—
323C22—10841no—
324C22—21684no—
325C22C2×D4×D27111yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—2712no—
332C4—5421no—
333C4—5421no—
334C4—10841no—
335C4—10841no—
336C4—10841no—
337C4C2×Q8×D27111yescharacteristic
338C4#41×D27111yescharacteristic
339C2—42no—
340C2—5422no—
341C2—10842no—
342C2C22⋊Q8×D27111yescharacteristic
343C2#3177470111yescharacteristic
344C2#3177470311yescharacteristic
subgroupG/H
centerC22C2×D4×D271
commutator, cosocleC2×C4×C271C24
FrattiniC2×C4C23×D271
Fitting#476×C271C2
socleC22×C271C22×D4
prime radicalC2×D4×D271C22
hypercenter#476D271
hypocenterC271#3081
LCSG ▷ C2×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #31774524C2semidirect
3. #31774199C2semidirect
4. #31774198C2semidirect
5. #31774197C2semidirect
6. #31774196C2semidirect
7. #31774186C2semidirect
8. #31774175C2semidirect
9. #31774174C2semidirect
10. #31773936C2semidirect
11. #31773932C2semidirect
12. #31773922C2semidirect
15. #476×C271C2semidirect
19. #22576159C22semidirect
21. #22576152C22semidirect
22. #22576151C22semidirect
37. #22576094C22semidirect
38. #22576093C22semidirect
39. #22576093C22semidirect
40. #22576093C22semidirect
41. #22576092C22semidirect
42. #22576091C22semidirect
43. C4⋊(C271⋊C8)C22semidirect
44. Dic271⋊C8C22semidirect
45. Dic271⋊C8C22semidirect
52. C4⋊Q8×C271C22semidirect
54. #106×C271C22semidirect
55. #106×C271C22semidirect
56. C4⋊C8×C271C22semidirect
64. D4×D271Q8semidirect
172. C271#3081semidirect
181. #476D271semidirect
194. C4⋊Q8C2×D271semidirect
218. #106C2×D271semidirect
219. #106C2×D271semidirect
223. C4⋊C8C2×D271semidirect

Maximal subgroups

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

subgroupindex
#317745242
#317743692
#317741992
#317741982
#317741972
#317741962
#317741862
#317741752
#317741742
#317739362
#317739322
#317739222
#317739002
#102×D2712
#476×C2712
#3081271