Finite Group Databasebeta

← #34110115

Subgroups — #34110115

Order 20096.

398 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757853C211yesmaximal, characteristic
2#23757754C211yesmaximal, characteristic, complemented
3#23757612C211yesmaximal, characteristic, complemented
4#23757611C211yesmaximal, characteristic, complemented
5#23757607C211yesmaximal, characteristic, complemented
6#23757600C211yesmaximal, characteristic, complemented
7#23757598C211yesmaximal, characteristic, complemented
8#23757588C211yesmaximal, characteristic, complemented
9#23757586C211yesmaximal, characteristic, complemented
10#23757314C211yesmaximal, characteristic, complemented
11#107×D157C211yesmaximal, characteristic, complemented
12#23757273C211yesmaximal, characteristic, complemented
13#23757268C211yesmaximal, characteristic, complemented
14#23757238C211yesmaximal, characteristic, complemented
15#484×C157C211yesmaximal, characteristic, complemented
16C2×#14578955C2211yescharacteristic
17C2×#14578954C2211yescharacteristic
18C2×#14578937C2211yescharacteristic
19C2×C8×D157C2211yescharacteristic
20#19097749—21no—
21#19097747C2211yescharacteristic
22#19097746—21no—
23#19097746C2211yescharacteristic
24#19097745C2211yescharacteristic
25#19097744—21no—
26#19097744—21no—
27#19097736—21no—
28#19097733—21no—
29C4×C22⋊D157—21no—
30C4×C22⋊D157—21no—
31#19097730C2211yescharacteristic
32#19097729C2211yescharacteristic
33#19097729C2211yescharacteristic
34C4⋊C4×D157C2211yescharacteristic
35C4⋊C4×D157C2211yescharacteristic
36C4⋊C4×D157C2211yescharacteristic
37#19097705C2211yescharacteristic
38#19097704C2211yescharacteristic
39#19097704C2211yescharacteristic
40#19097704C2211yescharacteristic
41#19097703C2211yescharacteristic
42#19097702C2211yescharacteristic
43#19097695C2211yescharacteristic
44#19097695C2211yescharacteristic
45#19097693C2211yescharacteristic
46#19097693C2211yescharacteristic
47#19097691C2211yescharacteristic
48#19097691C2211yescharacteristic
49C22⋊#11929434C2211yescharacteristic
50#19097683C2211yescharacteristic
51#19097683C2211yescharacteristic
52C22⋊Q8×C157C2211yescharacteristic
53C2×C4⋊C4×C157C2211yescharacteristic
54#107×C157C2211yescharacteristic
55#107×C157C2211yescharacteristic
56#103×C157C2211yescharacteristic
57#103×C157C2211yescharacteristic
58C22⋊C8×C157C2211yescharacteristic
59#14578955—22no—
60#14578955—22no—
61#14578954—22no—
62#14578954—22no—
63C2×Dic314D411yescharacteristic
64C2×D628—21no—
65C2×D628—21no—
66C2×D628D411yescharacteristic
67C2×D628C2311yescharacteristic
68C2×C22⋊D157—21no—
69C2×C22⋊D157D411yescharacteristic
70C2×C22⋊D157D411yescharacteristic
71C2×C4×D157—21no—
72C2×C4×D157—21no—
73C2×C4×D157—21no—
74C2×C4×D157—21no—
75C2×C4×D157C2311yescharacteristic
76C2×C4×D157C2311yescharacteristic
77#14578937—22no—
78C2×#11929434C2311yescharacteristic
79C2×#11929434C2311yescharacteristic
80C8×D157—22no—
81C4⋊Dic157C2311yescharacteristic
82C4⋊Dic157C2311yescharacteristic
83C4⋊Dic157C2311yescharacteristic
84#14578933—21no—
85#14578933—21no—
86#14578933—21no—
87#14578933—21no—
88C22⋊Dic157—21no—
89#14578931—21no—
90#14578931—21no—
91#14578931—21no—
92#14578931—21no—
93#14578931—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×D157—21no—
109C22×D157C2×D411yescharacteristic
110C22×D157C2×D411yescharacteristic
111Dic314—22no—
112D628—22no—
113D628—21no—
114D628—21no—
115D628—42no—
116D628—81no—
117C22⋊D157—22no—
118C22⋊D157—22no—
119C22⋊D157—81no—
120C2×Dic157—21no—
121C2×Dic157—21no—
122C2×Dic157—21no—
123C2×Dic157C2×D411yescharacteristic
124C2×Dic157C2×D411yescharacteristic
125C4×D157—21no—
126C4×D157—21no—
127C4×D157—42no—
128C4×D157—81no—
129C4×D157—81no—
130C4×D157—81no—
131C4×D157#4112yes—
132C4×D157#4112yes—
133#11929434—21no—
134#11929434—21no—
135C23×C157C2×D411yescharacteristic
136Q8×C157—21no—
137Q8×C157—21no—
138C2×C4×C157—21no—
139C2×C4×C157—21no—
140C2×C4×C157—21no—
141C2×C4×C157—21no—
142C2×C4×C157—21no—
143C2×C4×C157—21no—
144C2×C4×C157—81no—
145C2×C4×C157C2×D411yescharacteristic
146C2×C4×C157C2411yescharacteristic
147C8×C157—21no—
148C8×C157—21no—
149C22×C157—21no—
150C22×C157—21no—
151C22×C157—21no—
152C22×C157C22×D411yescharacteristic
153C2×D157—21no—
154C2×D157—21no—
155C2×D157—21no—
156C2×D157—21no—
157C2×D157—21no—
158C2×D157—41no—
159C2×D157—41no—
160C2×D157—41no—
161C2×D157#12312yes—
162C4×C157—21no—
163C4×C157—41no—
164C4×C157—41no—
165C4×C157—41no—
166C4×C157—41no—
167C4×C157C2×#4111yescharacteristic
168C4×C157C2×#4111yescharacteristic
169Dic157—21no—
170Dic157—41no—
171Dic157—41no—
172Dic157—41no—
173Dic157#12312yes—
174C2×C157—41no—
175C2×C157C2×#12311yescharacteristic
176C2×C157#57611yescharacteristic
177C2×C157#57811yescharacteristic
178D157—22no—
179D157—41no—
180D157—81no—
181C157#309811yescharacteristic, complemented, Sylow
182#3098—1571nomaximal, Sylow
183#537—1571no—
184#520—1571no—
185#485—1571no—
186#485—1571no—
187#484—1571no—
188#484D15711yescharacteristic, complemented
189#482—1571no—
190#482—1571no—
191#480—1571no—
192#480—1571no—
193#428—1571no—
194C2×#107—1571no—
195#417—1571no—
196#416—1571no—
197#408—1571no—
198C2×#41—1571no—
199C2×#41—1571no—
200C2×M16—1571no—
201C22×C8—1571no—
202C22⋊Q8—3141no—
203C22⋊Q8—1571no—
204C22⋊Q8C2×D15711yescharacteristic
205#121—3141no—
206#121—3141no—
207#121—3141no—
208#121—1571no—
209#121—1571no—
210C4×Q8—3141no—
211C4×D4—3141no—
212C4×D4—3141no—
213C4×D4—3141no—
214#117—1571no—
215#117—1571no—
216#117—1571no—
217C2×C4⋊C4—1571no—
218C2×C4⋊C4—1571no—
219C2×C4⋊C4—1571no—
220C2×C4⋊C4C2×D15711yescharacteristic
221#107—1571no—
222#107—1571no—
223#107—1571no—
224#107—1571no—
225#107C2×D15711yescharacteristic
226#107C2×D15711yescharacteristic
227#106—1571no—
228#106—1571no—
229#103—1571no—
230#103—1571no—
231#103C2×D15711yescharacteristic
232#103C2×D15711yescharacteristic
233#102—1571no—
234#102—1571no—
235#102—1571no—
236#102—1571no—
237C22⋊C8—1571no—
238C22⋊C8—1571no—
239C22⋊C8—1571no—
240C22⋊C8C2×D15711yescharacteristic
241#41—3142no—
242#41—3142no—
243#41—3142no—
244#41—3142no—
245C2×Q8—1571no—
246C2×Q8C22×D15711yescharacteristic
247C2×D4—3141no—
248C2×D4—3141no—
249C2×D4—3141no—
250C2×D4—1571no—
251C2×D4—1571no—
252C2×D4—1571no—
253C2×D4—1571no—
254C22×C4—21no—
255C22×C4—3141no—
256C22×C4—3141no—
257C22×C4—3141no—
258C22×C4—3141no—
259C22×C4—1571no—
260C22×C4—1571no—
261C22×C4C22×D15711yescharacteristic
262M16—3142no—
263C2×C8—3142no—
264C2×C8—1571no—
265C2×C8—1571no—
266C2×C8C22×D15711yescharacteristic
267C2×C8C22×D15711yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—3141no—
271C4⋊C4—3141no—
272C4⋊C4—3141no—
273C4⋊C4—3141no—
274C4⋊C4—1571no—
275C4⋊C4—1571no—
276C4⋊C4—1571no—
277C4⋊C4C22×D15711yescharacteristic
278C4⋊C4C22×D15711yescharacteristic
279C4⋊C4C22×D15711yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—3141no—
282C22⋊C4—3141no—
283C22⋊C4—3141no—
284C22⋊C4—3141no—
285C22⋊C4—3141no—
286C22⋊C4—3141no—
287C42—3141no—
288C42—3141no—
289C42—3141no—
290C23—3141no—
291C23—1571no—
292C23—1571no—
293C23D4×D15711yescharacteristic
294Q8—21no—
295Q8—21no—
296Q8—3142no—
297D4—3142no—
298D4—3142no—
299D4—3142no—
300D4—3141no—
301D4—3141no—
302D4—6282no—
303D4—12561no—
304D4—12561no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—3141no—
313C2×C4—3141no—
314C2×C4—3141no—
315C2×C4—3141no—
316C2×C4—3141no—
317C2×C4—6282no—
318C2×C4—1571no—
319C2×C4—1571no—
320C2×C4—1572no—
321C2×C4—1572no—
322C2×C4—12561no—
323C2×C4—12561no—
324C2×C4—12561no—
325C2×C4D4×D15711yescharacteristic
326C2×C4C23×D15711yescharacteristic
327C8—21no—
328C8—21no—
329C8—3141no—
330C8—3141no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—3141no—
335C22—3141no—
336C22—3141no—
337C22—3141no—
338C22—3141no—
339C22—6281no—
340C22—6281no—
341C22—6281no—
342C22—1572no—
343C22C2×D4×D15711yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—3141no—
350C4—6281no—
351C4—6281no—
352C4—6281no—
353C4—1572no—
354C4#41×D15711yescharacteristic
355C4#41×D15711yescharacteristic
356C2—41no—
357C2—3142no—
358C2—6281no—
359C2—12561no—
360C2#123×D15711yescharacteristic
361C2#2375807711yescharacteristic
362C2#2375808611yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#484×C157C2
socleC22×C157C22×D4
prime radical#23757853C2
hypercenter#484D157
hypocenterC157#3098
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. #23757754C2semidirect
3. #23757612C2semidirect
4. #23757611C2semidirect
5. #23757607C2semidirect
6. #23757600C2semidirect
7. #23757598C2semidirect
8. #23757588C2semidirect
9. #23757586C2semidirect
10. #23757314C2semidirect
11. #107×D157C2semidirect
12. #23757273C2semidirect
13. #23757268C2semidirect
14. #23757238C2semidirect
15. #484×C157C2semidirect
181. C157#3098semidirect
188. #484D157semidirect

Maximal subgroups

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

subgroupindex
#237578532
#237577542
#237576122
#237576112
#237576072
#237576002
#237575982
#237575882
#237575862
#237573142
#107×D1572
#237572732
#237572682
#237572382
#484×C1572
#3098157