Finite Group Databasebeta

← #34110098

Subgroups — #34110098

Order 20096.

386 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757846C211yesmaximal, characteristic
2#23757754C211yesmaximal, characteristic
3#23757617C211yesmaximal, characteristic, complemented
4#23757615C211yesmaximal, characteristic, complemented
5#23757612C211yesmaximal, characteristic, complemented
6#23757611C211yesmaximal, characteristic, complemented
7#23757608C211yesmaximal, characteristic, complemented
8#23757607C211yesmaximal, characteristic, complemented
9#23757605C211yesmaximal, characteristic, complemented
10#23757312C211yesmaximal, characteristic, complemented
11#23757308C211yesmaximal, characteristic, complemented
12#23757280C211yesmaximal, characteristic, complemented
13#103×D157C211yesmaximal, characteristic, complemented
14#23757238C211yesmaximal, characteristic
15#483×C157C211yesmaximal, characteristic, complemented
16C2×#14578954C2211yescharacteristic
17C2×Q8×D157C2211yescharacteristic
18C2×#14578937C2211yescharacteristic
19C2×C8×D157C2211yescharacteristic
20#19097770—21no—
21#19097757—21no—
22#19097756—21no—
23#19097753—21no—
24#19097751C2211yescharacteristic
25#19097750C2211yescharacteristic
26#19097747C2211yescharacteristic
27#19097736—21no—
28#19097733—21no—
29C4×C22⋊D157—21no—
30C4×C22⋊D157—21no—
31#19097730C2211yescharacteristic
32#19097729C2211yescharacteristic
33#19097729C2211yescharacteristic
34#19097729C2211yescharacteristic
35C4⋊C4×D157C2211yescharacteristic
36C4⋊C4×D157C2211yescharacteristic
37#19097705C2211yescharacteristic
38#19097704C2211yescharacteristic
39#19097704C2211yescharacteristic
40#19097704C2211yescharacteristic
41#19097703C2211yescharacteristic
42#19097702C2211yescharacteristic
43#19097696C2211yescharacteristic
44#19097696C2211yescharacteristic
45#19097695C2211yescharacteristic
46#19097695C2211yescharacteristic
47#19097694C2211yescharacteristic
48#19097694C2211yescharacteristic
49C22⋊#11929434C2211yescharacteristic
50#19097683C2211yescharacteristic
51#19097683C2211yescharacteristic
52C22⋊Q8×C157C2211yescharacteristic
53C2×C4⋊C4×C157C2211yescharacteristic
54#106×C157C2211yescharacteristic
55#106×C157C2211yescharacteristic
56#103×C157C2211yescharacteristic
57#103×C157C2211yescharacteristic
58C22⋊C8×C157C2211yescharacteristic
59#14578954—22no—
60#14578954—22no—
61C2×Dic314—21no—
62C2×Dic314D411yescharacteristic
63C2×Dic314C2311yescharacteristic
64Q8×D157—22no—
65Q8×D157—22no—
66C2×D628D411yescharacteristic
67C2×C22⋊D157D411yescharacteristic
68C2×C22⋊D157D411yescharacteristic
69C2×C4×D157—21no—
70C2×C4×D157—21no—
71C2×C4×D157—21no—
72C2×C4×D157C2311yescharacteristic
73C2×C4×D157C2311yescharacteristic
74#14578937—22no—
75C2×#11929434C2311yescharacteristic
76C2×#11929434C2311yescharacteristic
77C8×D157—22no—
78C4⋊Dic157—21no—
79C4⋊Dic157C2311yescharacteristic
80C4⋊Dic157C2311yescharacteristic
81C4⋊Dic157C2311yescharacteristic
82#14578933—21no—
83#14578933—21no—
84#14578933—21no—
85#14578933—21no—
86C22⋊Dic157—21no—
87C22⋊Dic157—21no—
88#14578931—21no—
89#14578931—21no—
90#14578931—21no—
91#14578931—21no—
92#14578931—21no—
93C4×Dic157—21no—
94C4×Dic157—21no—
95C4×Dic157—21no—
96C4×Dic157—21no—
97C2×Q8×C157C2311yescharacteristic
98C22×C4×C157—21no—
99C22×C4×C157C2311yescharacteristic
100C2×C8×C157C2311yescharacteristic
101C2×C8×C157C2311yescharacteristic
102C4⋊C4×C157—21no—
103C4⋊C4×C157—21no—
104C4⋊C4×C157C2311yescharacteristic
105C4⋊C4×C157C2311yescharacteristic
106C4⋊C4×C157C2311yescharacteristic
107C22⋊C4×C157—21no—
108C22×D157C2×D411yescharacteristic
109C22×D157C2×D411yescharacteristic
110Dic314—22no—
111Dic314—21no—
112Dic314—21no—
113Dic314—42no—
114D628—22no—
115C22⋊D157—22no—
116C22⋊D157—22no—
117C2×Dic157—21no—
118C2×Dic157—21no—
119C2×Dic157—21no—
120C2×Dic157—21no—
121C2×Dic157C2×D411yescharacteristic
122C2×Dic157C2×D411yescharacteristic
123C4×D157—21no—
124C4×D157—21no—
125C4×D157—42no—
126C4×D157—81no—
127C4×D157—81no—
128C4×D157#4112yes—
129C4×D157#4112yes—
130#11929434—21no—
131#11929434—21no—
132C23×C157C2×D411yescharacteristic
133Q8×C157—21no—
134Q8×C157—21no—
135C2×C4×C157—21no—
136C2×C4×C157—21no—
137C2×C4×C157—21no—
138C2×C4×C157—21no—
139C2×C4×C157—21no—
140C2×C4×C157—21no—
141C2×C4×C157—81no—
142C2×C4×C157C2×D411yescharacteristic
143C2×C4×C157C2411yescharacteristic
144C8×C157—21no—
145C8×C157—21no—
146C22×C157—21no—
147C22×C157—21no—
148C22×C157—21no—
149C22×C157C22×D411yescharacteristic
150C2×D157—21no—
151C2×D157—21no—
152C2×D157—21no—
153C2×D157—21no—
154C2×D157—21no—
155C2×D157#12312yes—
156C4×C157—21no—
157C4×C157—41no—
158C4×C157—41no—
159C4×C157—41no—
160C4×C157—41no—
161C4×C157C2×#4111yescharacteristic
162C4×C157C2×#4111yescharacteristic
163Dic157—21no—
164Dic157—41no—
165Dic157—41no—
166Dic157—41no—
167Dic157—41no—
168Dic157#12312yes—
169C2×C157—41no—
170C2×C157C2×#12311yescharacteristic
171C2×C157#57711yescharacteristic
172C2×C157#57811yescharacteristic
173D157—22no—
174D157—41no—
175C157#309711yescharacteristic, complemented, Sylow
176#3097—1571nomaximal, Sylow
177#536—1571no—
178#520—1571no—
179#485—1571no—
180#485—1571no—
181#485—1571no—
182#485—1571no—
183#484—1571no—
184#484—1571no—
185#483—1571no—
186#483D15711yescharacteristic, complemented
187#428—1571no—
188#427—1571no—
189#419—1571no—
190C2×#103—1571no—
191#408—1571no—
192C2×#41—1571no—
193C22×Q8—1571no—
194C2×M16—1571no—
195C22×C8—1571no—
196C4⋊Q8—3141no—
197#124—3141no—
198#123—3141no—
199#123—3141no—
200C22⋊Q8—1571no—
201C22⋊Q8—1571no—
202C22⋊Q8—1571no—
203C22⋊Q8C2×D15711yescharacteristic
204C4×Q8—3141no—
205C4×D4—3141no—
206C4×D4—3141no—
207C4×D4—3141no—
208#117—1571no—
209#117—1571no—
210#117—1571no—
211#117—1571no—
212C2×C4⋊C4—1571no—
213C2×C4⋊C4—1571no—
214C2×C4⋊C4C2×D15711yescharacteristic
215#107—1571no—
216#107—1571no—
217#107—1571no—
218#107—1571no—
219#106—1571no—
220#106—1571no—
221#106C2×D15711yescharacteristic
222#106C2×D15711yescharacteristic
223#103—1571no—
224#103—1571no—
225#103—1571no—
226#103—1571no—
227#103—1571no—
228#103—1571no—
229#103C2×D15711yescharacteristic
230#103C2×D15711yescharacteristic
231C22⋊C8—1571no—
232C22⋊C8—1571no—
233C22⋊C8—1571no—
234C22⋊C8C2×D15711yescharacteristic
235#41—3142no—
236#41—3142no—
237C2×Q8—3141no—
238C2×Q8—3142no—
239C2×Q8—3142no—
240C2×Q8—1571no—
241C2×Q8—1571no—
242C2×Q8C22×D15711yescharacteristic
243C2×D4—1571no—
244C2×D4—1571no—
245C2×D4—1571no—
246C22×C4—21no—
247C22×C4—3141no—
248C22×C4—3141no—
249C22×C4—3141no—
250C22×C4—1571no—
251C22×C4—1571no—
252C22×C4C22×D15711yescharacteristic
253M16—3142no—
254C2×C8—3142no—
255C2×C8—1571no—
256C2×C8—1571no—
257C2×C8C22×D15711yescharacteristic
258C2×C8C22×D15711yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—3141no—
262C4⋊C4—3141no—
263C4⋊C4—3141no—
264C4⋊C4—3141no—
265C4⋊C4—3141no—
266C4⋊C4—1571no—
267C4⋊C4—1571no—
268C4⋊C4—1571no—
269C4⋊C4C22×D15711yescharacteristic
270C4⋊C4C22×D15711yescharacteristic
271C4⋊C4C22×D15711yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—3141no—
274C22⋊C4—3141no—
275C22⋊C4—3141no—
276C22⋊C4—3141no—
277C22⋊C4—3141no—
278C22⋊C4—3141no—
279C22⋊C4—3141no—
280C42—3141no—
281C42—3141no—
282C42—3141no—
283C42—3141no—
284C23—1571no—
285C23—1571no—
286C23D4×D15711yescharacteristic
287Q8—21no—
288Q8—21no—
289Q8—3142no—
290Q8—3141no—
291Q8—3141no—
292Q8—6282no—
293D4—3142no—
294D4—3142no—
295D4—3142no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—3141no—
304C2×C4—3141no—
305C2×C4—3141no—
306C2×C4—3141no—
307C2×C4—3141no—
308C2×C4—3141no—
309C2×C4—6282no—
310C2×C4—1571no—
311C2×C4—1571no—
312C2×C4—1572no—
313C2×C4—1572no—
314C2×C4—12561no—
315C2×C4—12561no—
316C2×C4D4×D15711yescharacteristic
317C2×C4C23×D15711yescharacteristic
318C8—21no—
319C8—21no—
320C8—3141no—
321C8—3141no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—3141no—
326C22—3141no—
327C22—3141no—
328C22—3141no—
329C22—3141no—
330C22—1572no—
331C22C2×D4×D15711yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—3141no—
338C4—6281no—
339C4—6281no—
340C4—6281no—
341C4—6281no—
342C4—1572no—
343C4#41×D15711yescharacteristic
344C4#41×D15711yescharacteristic
345C2—41no—
346C2—3142no—
347C2—6281no—
348C2#123×D15711yescharacteristic
349C2#2375807911yescharacteristic
350C2#2375808911yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#483×C157C2
socleC22×C157C22×D4
prime radicalC2×#14578954C22
hypercenter#483D157
hypocenterC157#3097
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
3. #23757617C2semidirect
4. #23757615C2semidirect
5. #23757612C2semidirect
6. #23757611C2semidirect
7. #23757608C2semidirect
8. #23757607C2semidirect
9. #23757605C2semidirect
10. #23757312C2semidirect
11. #23757308C2semidirect
12. #23757280C2semidirect
13. #103×D157C2semidirect
15. #483×C157C2semidirect
175. C157#3097semidirect
186. #483D157semidirect

Maximal subgroups

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

subgroupindex
#237578462
#237577542
#237576172
#237576152
#237576122
#237576112
#237576082
#237576072
#237576052
#237573122
#237573082
#237572802
#103×D1572
#237572382
#483×C1572
#3097157