Finite Group Databasebeta

← #34110239

Subgroups — #34110239

Order 20096.

392 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14578954C211yesmaximal, characteristic, complemented
2#23757611C211yesmaximal, characteristic, complemented
3#23757594C211yesmaximal, characteristic, complemented
4#23757577C211yesmaximal, characteristic, complemented
5#23757570C211yesmaximal, characteristic, complemented
6#23757492C211yesmaximal, characteristic, complemented
7#23757485C211yesmaximal, characteristic, complemented
8#23757433C211yesmaximal, characteristic, complemented
9#23757416C211yesmaximal, characteristic
10#23757383C211yesmaximal, characteristic, complemented
11#23757378C211yesmaximal, characteristic, complemented
12#23757373C211yesmaximal, characteristic, complemented
13#23757371C211yesmaximal, characteristic, complemented
14#23757330C211yesmaximal, characteristic, complemented
15#529×C157C211yesmaximal, characteristic, complemented
16C2×#14578954C2211yescharacteristic
17C2×#14578944C2211yescharacteristic
18C2×#14578942C2211yescharacteristic
19C2×#14578941C2211yescharacteristic
20C2×#14578939C2211yescharacteristic
21C4×Dic314C2211yescharacteristic
22C4×Dic314C2211yescharacteristic
23C4×D628C2211yescharacteristic
24C4×D628C2211yescharacteristic
25C4×C22⋊D157—21no—
26C4×C22⋊D157—21no—
27#19097730C2211yescharacteristic
28#19097728—21no—
29C42×D157—21no—
30#19097704C2211yescharacteristic
31#19097704C2211yescharacteristic
32#19097702C2211yescharacteristic
33#19097702C2211yescharacteristic
34C4⋊#11929434C2211yescharacteristic
35C4⋊#11929434C2211yescharacteristic
36#19097695C2211yescharacteristic
37#19097695C2211yescharacteristic
38#19097694C2211yescharacteristic
39#19097694C2211yescharacteristic
40#19097692C2211yescharacteristic
41#19097692C2211yescharacteristic
42#19097691C2211yescharacteristic
43#19097691C2211yescharacteristic
44C22⋊#11929434C2211yescharacteristic
45C22⋊#11929434C2211yescharacteristic
46#19097682C2211yescharacteristic
47#19097682C2211yescharacteristic
48#126×C157—21no—
49#125×C157C2211yescharacteristic
50#124×C157C2211yescharacteristic
51#123×C157—21no—
52C22⋊Q8×C157C2211yescharacteristic
53#121×C157C2211yescharacteristic
54C4×Q8×C157C2211yescharacteristic
55C4×D4×C157—21no—
56C4×D4×C157C2211yescharacteristic
57#117×C157—21no—
58C2×C42×C157C2211yescharacteristic
59#14578954—22no—
60#14578954—22no—
61C2×Dic314C2311yescharacteristic
62C2×D628C2311yescharacteristic
63C2×C22⋊D157—21no—
64C2×C4×D157—21no—
65C2×C4×D157—21no—
66C2×C4×D157—21no—
67#14578944—22no—
68#14578942—22no—
69#14578941—22no—
70#14578939—22no—
71C2×#11929434C2311yescharacteristic
72C2×#11929434C2311yescharacteristic
73C2×#11929434C2311yescharacteristic
74C2×#11929434C2311yescharacteristic
75C4⋊Dic157C2311yescharacteristic
76C4⋊Dic157C2311yescharacteristic
77#14578933—21no—
78#14578933—21no—
79C22⋊Dic157—21no—
80#14578931—21no—
81#14578931—21no—
82C4×Dic157—21no—
83C4×Dic157—21no—
84C4×Dic157—21no—
85C2×Q8×C157C2311yescharacteristic
86C2×D4×C157—21no—
87C2×D4×C157C2311yescharacteristic
88C22×C4×C157—21no—
89C22×C4×C157D411yescharacteristic
90C22×C4×C157D411yescharacteristic
91C22×C4×C157C2311yescharacteristic
92C4⋊C4×C157—21no—
93C4⋊C4×C157—21no—
94C4⋊C4×C157—21no—
95C4⋊C4×C157—21no—
96C4⋊C4×C157C2311yescharacteristic
97C4⋊C4×C157C2311yescharacteristic
98C22⋊C4×C157—21no—
99C22⋊C4×C157—21no—
100C22⋊C4×C157—21no—
101C22⋊C4×C157—21no—
102C22⋊C4×C157—21no—
103C42×C157—21no—
104C42×C157D411yescharacteristic
105C42×C157D411yescharacteristic
106C42×C157C2311yescharacteristic
107C42×C157C2311yescharacteristic
108C22×D157—21no—
109Dic314—21no—
110Dic314#4112yes—
111D628—21no—
112D628#4112yes—
113C22⋊D157—24no—
114C2×Dic157—21no—
115C2×Dic157—21no—
116C2×Dic157—21no—
117C4×D157—24no—
118C4×D157—42no—
119C4×D157—42no—
120#11929434—21no—
121#11929434—21no—
122#11929434—21no—
123#11929434—21no—
124C23×C157—21no—
125C23×C157C2×D411yescharacteristic
126Q8×C157—21no—
127Q8×C157—21no—
128D4×C157—21no—
129D4×C157—21no—
130D4×C157—42no—
131C2×C4×C157—21no—
132C2×C4×C157—21no—
133C2×C4×C157—21no—
134C2×C4×C157—21no—
135C2×C4×C157—21no—
136C2×C4×C157—41no—
137C2×C4×C157—41no—
138C2×C4×C157—42no—
139C2×C4×C157C2×D411yescharacteristic
140C2×C4×C157C2×D411yescharacteristic
141C2×C4×C157C2×D411yescharacteristic
142C2×C4×C157C2×D411yescharacteristic
143C2×C4×C157C2×D411yescharacteristic
144C2×C4×C157C2411yescharacteristic
145C22×C157—21no—
146C22×C157—21no—
147C22×C157—21no—
148C22×C157—41no—
149C22×C157—41no—
150C22×C157—41no—
151C22×C157C22×D411yescharacteristic
152C2×D157—22no—
153C2×D157—41no—
154C2×D157—41no—
155C4×C157—21no—
156C4×C157—21no—
157C4×C157—21no—
158C4×C157—21no—
159C4×C157—21no—
160C4×C157—41no—
161C4×C157—41no—
162C4×C157—41no—
163C4×C157C2×#4111yescharacteristic
164C4×C157C2×#4111yescharacteristic
165Dic157—22no—
166Dic157—41no—
167Dic157—41no—
168C2×C157—41no—
169C2×C157—81no—
170C2×C157#52511yescharacteristic
171C2×C157#57511yescharacteristic
172C2×C157#57511yescharacteristic
173D157—42no—
174C157#311111yescharacteristic, complemented, Sylow
175#3111—1571nomaximal, Sylow
176#529D15711yescharacteristic, complemented
177C4×#41—1571no—
178#485—1571no—
179#482—1571no—
180#479—1571no—
181#478—1571no—
182#464—1571no—
183#463—1571no—
184#452—1571no—
185#449—1571no—
186#442—1571no—
187#441—1571no—
188#440—1571no—
189#440—1571no—
190#432—1571no—
191C2×#41—1571no—
192C2×Q16—1571no—
193C2×SD16—1571no—
194C2×SD16—1571no—
195C2×D8—1571no—
196#126—21no—
197#125C2×D15711yescharacteristic
198#124C2×D15711yescharacteristic
199#123—21no—
200C22⋊Q8C2×D15711yescharacteristic
201#121C2×D15711yescharacteristic
202C4×Q8—1571no—
203C4×Q8—1571no—
204C4×Q8C2×D15711yescharacteristic
205C4×D4—21no—
206C4×D4—3141no—
207C4×D4—3141no—
208C4×D4—1571no—
209C4×D4—1571no—
210C4×D4C2×D15711yescharacteristic
211#117—21no—
212#117—3141no—
213#117—1571no—
214C2×C42—3141no—
215C2×C42C2×D15711yescharacteristic
216#107—1571no—
217#107—1571no—
218#106—1571no—
219#106—1571no—
220C4⋊C8—1571no—
221C4⋊C8—1571no—
222#103—1571no—
223#103—1571no—
224#103—1571no—
225#103—1571no—
226#102—1571no—
227#102—1571no—
228#102—1571no—
229#102—1571no—
230C22⋊C8—1571no—
231C22⋊C8—1571no—
232#97—1571no—
233#97—1571no—
234#41—3142no—
235#41—3142no—
236C2×Q8—1571no—
237C2×Q8C22×D15711yescharacteristic
238C2×D4—21no—
239C2×D4—3141no—
240C2×D4—1571no—
241C2×D4C22×D15711yescharacteristic
242C22×C4—21no—
243C22×C4—3141no—
244C22×C4—3141no—
245C22×C4—3141no—
246C22×C4C22⋊D15711yescharacteristic
247C22×C4C22⋊D15711yescharacteristic
248C22×C4C22×D15711yescharacteristic
249Q16—3142no—
250SD16—3142no—
251SD16—3142no—
252D8—3142no—
253C2×C8—1571no—
254C2×C8—1571no—
255C2×C8—1571no—
256C2×C8—1571no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—3141no—
262C4⋊C4—3141no—
263C4⋊C4—1571no—
264C4⋊C4—1571no—
265C4⋊C4C22×D15711yescharacteristic
266C4⋊C4C22×D15711yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—3141no—
273C22⋊C4—3141no—
274C22⋊C4—3141no—
275C42—21no—
276C42—3141no—
277C42—3141no—
278C42—3141no—
279C42C22⋊D15711yescharacteristic
280C42C22⋊D15711yescharacteristic
281C42C22×D15711yescharacteristic
282C42C22×D15711yescharacteristic
283C23—21no—
284C23—3141no—
285C23C2×C22⋊D15711yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—3141no—
289Q8—1572no—
290D4—21no—
291D4—21no—
292D4—42no—
293D4—3144no—
294D4—3141no—
295D4—1572no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—3144no—
305C2×C4—3141no—
306C2×C4—3141no—
307C2×C4—3141no—
308C2×C4—6282no—
309C2×C4—6282no—
310C2×C4C2×C22⋊D15711yescharacteristic
311C2×C4C2×C22⋊D15711yescharacteristic
312C2×C4C2×C22⋊D15711yescharacteristic
313C2×C4C2×C22⋊D15711yescharacteristic
314C2×C4C2×C22⋊D15711yescharacteristic
315C2×C4C23×D15711yescharacteristic
316C8—3141no—
317C8—3141no—
318C8—3141no—
319C8—3141no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—3142no—
327C22—6281no—
328C22—6281no—
329C22C22×C22⋊D15711yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—3142no—
339C4—6281no—
340C4—6281no—
341C4#41×D15711yescharacteristic
342C4#41×D15711yescharacteristic
343C2—41no—
344C2—81no—
345C2—6282no—
346C2#2375778011yescharacteristic
347C2#2375807111yescharacteristic
348C2#2375807111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#529×C157C2
socleC22×C157C22×D4
prime radical#23757416C2
hypercenter#529D157
hypocenterC157#3111
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C4×#14578954C2semidirect
2. #23757611C2semidirect
3. #23757594C2semidirect
4. #23757577C2semidirect
5. #23757570C2semidirect
6. #23757492C2semidirect
7. #23757485C2semidirect
8. #23757433C2semidirect
10. #23757383C2semidirect
11. #23757378C2semidirect
12. #23757373C2semidirect
13. #23757371C2semidirect
14. #23757330C2semidirect
15. #529×C157C2semidirect
174. C157#3111semidirect
176. #529D157semidirect

Maximal subgroups

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

subgroupindex
C4×#145789542
#237576112
#237575942
#237575772
#237575702
#237574922
#237574852
#237574332
#237574162
#237573832
#237573782
#237573732
#237573712
#237573302
#529×C1572
#3111157