Finite Group Databasebeta

← #34108799

Subgroups — #34108799

Order 20096.

392 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757741C211yesmaximal, characteristic
2#23757334C211yesmaximal, characteristic, complemented
3#23757333C211yesmaximal, characteristic, complemented
4#23757333C211yesmaximal, characteristic, complemented
5#23757328C211yesmaximal, characteristic, complemented
6#23757327C211yesmaximal, characteristic, complemented
7#23757324C211yesmaximal, characteristic, complemented
8#23757323C211yesmaximal, characteristic, complemented
9#23757295C211yesmaximal, characteristic, complemented
10C4⋊C8×D157C211yesmaximal, characteristic, complemented
11#23757238C211yesmaximal, characteristic
12#23757238C211yesmaximal, characteristic
13#23757230C211yesmaximal, characteristic, complemented
14#23757227C211yesmaximal, characteristic, complemented
15#433×C157C211yesmaximal, characteristic, complemented
16C2×#14578954C2211yescharacteristic
17C2×#14578937C2211yescharacteristic
18C2×#14578937C2211yescharacteristic
19C2×C8×D157C2211yescharacteristic
20C2×C8×D157C2211yescharacteristic
21#19097736C411yescharacteristic
22#19097736C411yescharacteristic
23#19097733C411yescharacteristic
24#19097733C411yescharacteristic
25#19097731C411yescharacteristic
26#19097731C411yescharacteristic
27#19097731C411yescharacteristic
28#19097731C411yescharacteristic
29#19097728C2211yescharacteristic
30#19097728C2211yescharacteristic
31C2×C4×Dic157C2211yescharacteristic
32C42×D157C2211yescharacteristic
33C42×D157C2211yescharacteristic
34C4⋊#11929434C2211yescharacteristic
35C4⋊#11929434C2211yescharacteristic
36#19097700C2211yescharacteristic
37#19097700C2211yescharacteristic
38#19097700C2211yescharacteristic
39#19097700C2211yescharacteristic
40C22⋊#11929434C2211yescharacteristic
41C22⋊#11929434C2211yescharacteristic
42#19097683C2211yescharacteristic
43#19097683C2211yescharacteristic
44#19097683C2211yescharacteristic
45#19097683C2211yescharacteristic
46#19097682C2211yescharacteristic
47#19097681C2211yescharacteristic
48#19097681C2211yescharacteristic
49C4×#11929434C2211yescharacteristic
50C8×Dic157C2211yescharacteristic
51C8×Dic157C2211yescharacteristic
52#117×C157C2211yescharacteristic
53C4⋊C8×C157C2211yescharacteristic
54C4⋊C8×C157C2211yescharacteristic
55C22⋊C8×C157C2211yescharacteristic
56C22⋊C8×C157C2211yescharacteristic
57#97×C157C2211yescharacteristic
58C4×C8×C157C2211yescharacteristic
59#14578954—22no—
60#14578954—22no—
61C2×Dic314C2×C411yescharacteristic
62C2×D628C2×C411yescharacteristic
63C2×C22⋊D157C2×C411yescharacteristic
64C2×C22⋊D157C2×C411yescharacteristic
65C22×Dic157C2×C411yescharacteristic
66C22×Dic157C2×C411yescharacteristic
67C2×C4×D157C2×C411yescharacteristic
68C2×C4×D157C2×C411yescharacteristic
69C2×C4×D157C2×C411yescharacteristic
70C2×C4×D157C2×C411yescharacteristic
71C2×C4×D157C2311yescharacteristic
72C2×C4×D157C2311yescharacteristic
73#14578937—22no—
74#14578937—22no—
75C2×#11929434C2311yescharacteristic
76C2×#11929434C2311yescharacteristic
77C2×#11929434C2311yescharacteristic
78C2×#11929434C2311yescharacteristic
79C8×D157—22no—
80C8×D157—22no—
81#14578933C2×C411yescharacteristic
82#14578933C2×C411yescharacteristic
83#14578933C2×C411yescharacteristic
84#14578933C2×C411yescharacteristic
85#14578931C2×C411yescharacteristic
86#14578931C2×C411yescharacteristic
87#14578931C2×C411yescharacteristic
88#14578931C2×C411yescharacteristic
89C4×Dic157C2×C411yescharacteristic
90C4×Dic157C2×C411yescharacteristic
91C4×Dic157C2×C411yescharacteristic
92C4×Dic157C2×C411yescharacteristic
93C4×Dic157C2×C411yescharacteristic
94C4×Dic157C2×C411yescharacteristic
95C4×Dic157C2311yescharacteristic
96C4×Dic157C2311yescharacteristic
97C22×C4×C157C2311yescharacteristic
98C2×C8×C157C2311yescharacteristic
99C2×C8×C157C2311yescharacteristic
100C2×C8×C157C2311yescharacteristic
101C2×C8×C157C2311yescharacteristic
102C4⋊C4×C157C2×C411yescharacteristic
103C4⋊C4×C157C2×C411yescharacteristic
104C22⋊C4×C157C2×C411yescharacteristic
105C22⋊C4×C157C2×C411yescharacteristic
106C42×C157C2311yescharacteristic
107C42×C157C2311yescharacteristic
108C22×D157C22×C411yescharacteristic
109C22×D157C22×C411yescharacteristic
110Dic314—22no—
111D628—22no—
112C22⋊D157—22no—
113C22⋊D157—22no—
114C2×Dic157—22no—
115C2×Dic157—41no—
116C2×Dic157C22×C411yescharacteristic
117C2×Dic157C22×C411yescharacteristic
118C2×Dic157C22×C411yescharacteristic
119C2×Dic157C22×C411yescharacteristic
120C2×Dic157C22×C411yescharacteristic
121C2×Dic157C22×C411yescharacteristic
122C4×D157—21no—
123C4×D157—21no—
124C4×D157—22no—
125C4×D157—22no—
126C4×D157—41no—
127C4×D157—41no—
128C4×D157#4112yes—
129C4×D157#4112yes—
130#11929434—21no—
131#11929434—21no—
132#11929434—21no—
133#11929434—21no—
134C23×C157C22×C411yescharacteristic
135C2×C4×C157—21no—
136C2×C4×C157—21no—
137C2×C4×C157C22×C411yescharacteristic
138C2×C4×C157C22×C411yescharacteristic
139C2×C4×C157C22×C411yescharacteristic
140C2×C4×C157C22×C411yescharacteristic
141C2×C4×C157C22×C411yescharacteristic
142C2×C4×C157C2411yescharacteristic
143C8×C157—21no—
144C8×C157—21no—
145C8×C157—21no—
146C8×C157—21no—
147C22×C157—21no—
148C22×C157—21no—
149C22×C157—21no—
150C22×C157C23×C411yescharacteristic
151C2×D157—21no—
152C2×D157—21no—
153C2×D157—21no—
154C2×D157—21no—
155C2×D157—21no—
156C2×D157#11712yes—
157C4×C157—21no—
158C4×C157—21no—
159C4×C157—21no—
160C4×C157—21no—
161C4×C157—21no—
162C4×C157C2×#4111yescharacteristic
163C4×C157C2×#4111yescharacteristic
164Dic157—21no—
165Dic157—21no—
166Dic157—21no—
167Dic157—21no—
168Dic157#11712yes—
169Dic157#13112yes—
170C2×C157—41no—
171C2×C157C2×#11711yescharacteristic
172C2×C157C2×#13111yescharacteristic
173C2×C157#56811yescharacteristic
174D157—22no—
175D157—41no—
176C157#292511yescharacteristic, complemented, Sylow
177#2925—1571nomaximal, Sylow
178C4×#41—1571no—
179#433—1571no—
180#433—1571no—
181#433—1571no—
182#433D15711yescharacteristic, complemented
183#432—1571no—
184#432—1571no—
185#431—1571no—
186#431—1571no—
187#423—1571no—
188C2×C4⋊C8—1571no—
189#408—1571no—
190#408—1571no—
191#405—1571no—
192#405—1571no—
193C2×#41—1571no—
194C2×M16—1571no—
195C2×M16—1571no—
196C22×C8—1571no—
197C22×C8—1571no—
198C4×Q8—1571no—
199C4×Q8—1571no—
200C4×D4—1571no—
201C4×D4—1571no—
202C4×D4—1571no—
203C4×D4—1571no—
204C4×D4—1571no—
205C4×D4—1571no—
206#117—1571no—
207#117—1571no—
208#117C2×D15711yescharacteristic
209C2×C42—1571no—
210C2×C42—1571no—
211C2×C42—1571no—
212C4⋊C8—1571no—
213C4⋊C8—1571no—
214C4⋊C8—1571no—
215C4⋊C8—1571no—
216C4⋊C8—1571no—
217C4⋊C8—1571no—
218C4⋊C8C2×D15711yescharacteristic
219C4⋊C8C2×D15711yescharacteristic
220C22⋊C8—1571no—
221C22⋊C8—1571no—
222C22⋊C8—1571no—
223C22⋊C8—1571no—
224C22⋊C8—1571no—
225C22⋊C8—1571no—
226C22⋊C8C2×D15711yescharacteristic
227C22⋊C8C2×D15711yescharacteristic
228#97—1571no—
229#97—1571no—
230#97—1571no—
231#97C2×D15711yescharacteristic
232C4×C8—1571no—
233C4×C8—1571no—
234C4×C8—1571no—
235C4×C8C2×D15711yescharacteristic
236#41—3142no—
237#41—3142no—
238C2×Q8—1571no—
239C2×D4—1571no—
240C2×D4—1571no—
241C2×D4—1571no—
242C22×C4—1571no—
243C22×C4—1571no—
244C22×C4—1571no—
245C22×C4—1571no—
246C22×C4—1571no—
247C22×C4—1571no—
248C22×C4—1571no—
249C22×C4—1571no—
250C22×C4C22×D15711yescharacteristic
251M16—3142no—
252M16—3142no—
253C2×C8—3142no—
254C2×C8—3142no—
255C2×C8—1571no—
256C2×C8—1571no—
257C2×C8—1571no—
258C2×C8—1571no—
259C2×C8C22×D15711yescharacteristic
260C2×C8C22×D15711yescharacteristic
261C2×C8C22×D15711yescharacteristic
262C2×C8C22×D15711yescharacteristic
263C4⋊C4—1571no—
264C4⋊C4—1571no—
265C4⋊C4—1571no—
266C4⋊C4—1571no—
267C4⋊C4C4×D15711yescharacteristic
268C4⋊C4C4×D15711yescharacteristic
269C22⋊C4—1571no—
270C22⋊C4—1571no—
271C22⋊C4—1571no—
272C22⋊C4—1571no—
273C22⋊C4C4×D15711yescharacteristic
274C22⋊C4C4×D15711yescharacteristic
275C42—1571no—
276C42—1571no—
277C42—1571no—
278C42—1571no—
279C42—1571no—
280C42—1571no—
281C42—1571no—
282C42—1571no—
283C42C22×D15711yescharacteristic
284C42C22×D15711yescharacteristic
285C23—1571no—
286C23—1571no—
287C23C2×C4×D15711yescharacteristic
288Q8—3142no—
289D4—3142no—
290D4—3142no—
291D4—3142no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—3142no—
295C2×C4—3142no—
296C2×C4—3142no—
297C2×C4—3141no—
298C2×C4—3141no—
299C2×C4—6281no—
300C2×C4—6281no—
301C2×C4—6281no—
302C2×C4—1571no—
303C2×C4—1571no—
304C2×C4—1571no—
305C2×C4—1571no—
306C2×C4—1571no—
307C2×C4—1571no—
308C2×C4—1572no—
309C2×C4—1572no—
310C2×C4C2×C4×D15711yescharacteristic
311C2×C4C2×C4×D15711yescharacteristic
312C2×C4C2×C4×D15711yescharacteristic
313C2×C4C2×C4×D15711yescharacteristic
314C2×C4C2×C4×D15711yescharacteristic
315C2×C4C23×D15711yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8—21no—
320C8—3141no—
321C8—3141no—
322C8—3141no—
323C8—3141no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—3141no—
328C22—3141no—
329C22—3141no—
330C22—3141no—
331C22—3141no—
332C22—1572no—
333C22C22×C4×D15711yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—3141no—
340C4—3141no—
341C4—3141no—
342C4—3141no—
343C4—1572no—
344C4—1572no—
345C4#41×D15711yescharacteristic
346C4#41×D15711yescharacteristic
347C2—41no—
348C2—3142no—
349C2—6281no—
350C2#117×D15711yescharacteristic
351C2#131×D15711yescharacteristic
352C2#2375803811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D157
commutator, socleC22×C157C23×C4
Fitting#433×C157C2
prime radicalC2×#14578954C22
cosocleC2×C4×C157C24
hypercenter#433D157
hypocenterC157#2925
LCSG ▷ C22×C157 ▷ C157
UCSC1 ◁ C2×C4 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #23757334C2semidirect
3. #23757333C2semidirect
4. #23757333C2semidirect
5. #23757328C2semidirect
6. #23757327C2semidirect
7. #23757324C2semidirect
8. #23757323C2semidirect
9. #23757295C2semidirect
10. C4⋊C8×D157C2semidirect
13. #23757230C2semidirect
14. #23757227C2semidirect
15. #433×C157C2semidirect
176. C157#2925semidirect
182. #433D157semidirect

Maximal subgroups

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

subgroupindex
#237577412
#237573342
#237573332
#237573282
#237573272
#237573242
#237573232
#237572952
C4⋊C8×D1572
#237572382
#237572302
#237572272
#433×C1572
#2925157