Finite Group Databasebeta

← C2×#23757959 #34113644

Subgroups — C2×#23757959 #34113644

Order 20096.

1124 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757959C2116yesmaximal, direct product factor
2C2×#19097764C211yesmaximal, characteristic, complemented
3C2×#19097762C211yesmaximal, characteristic, complemented
4C2×#19097761C211yesmaximal, characteristic, complemented
5C2×#19097761C211yesmaximal, characteristic, complemented
6C2×#19097753C211yesmaximal, characteristic
7C2×#19097753C211yesmaximal, characteristic
8C2×#19097749C211yesmaximal, characteristic, complemented
9C2×#19097748C211yesmaximal, characteristic, complemented
10C2×C4×Dic314C211yesmaximal, characteristic, complemented
11C2×#19097731C211yesmaximal, characteristic
12C2×#19097729C211yesmaximal, characteristic, complemented
13C2×#19097728C211yesmaximal, characteristic, complemented
14C2×#19097727C211yesmaximal, characteristic, complemented
15C2×C4⋊C4×D157C211yesmaximal, characteristic, complemented
16C2×#126×C157C211yesmaximal, characteristic, complemented
17C22×Dic314C2211yescharacteristic
18C22×C22⋊D157C2211yescharacteristic
19C23×Dic157C2211yescharacteristic
20C22×C4×D157C2211yescharacteristic
21C22×C4×D157C2211yescharacteristic
22C22×C4×D157C2211yescharacteristic
23#19097764C2218yescomplemented
24#19097762C2218yescomplemented
25#19097761C2218yescomplemented
26#19097761C2218yescomplemented
27#19097753C2218yes—
28#19097753C2218yes—
29#19097749C2218yescomplemented
30#19097748C2218yescomplemented
31C4×Dic314C2218yescomplemented
32#19097731C2218yes—
33#19097729C2218yescomplemented
34#19097728C2218yescomplemented
35#19097727C2218yescomplemented
36C2×C4⋊Dic157C2211yescharacteristic
37C2×C4⋊Dic157C2211yescharacteristic
38C2×C4⋊Dic157C2211yescharacteristic
39C2×C4⋊Dic157C2211yescharacteristic
40C2×#14578933C2211yescharacteristic
41C2×#14578933C2211yescharacteristic
42C2×#14578933C2211yescharacteristic
43C2×#14578933C2211yescharacteristic
44C2×#14578933C2211yescharacteristic
45C2×#14578933C2211yescharacteristic
46C2×#14578933C2211yescharacteristic
47C2×#14578933C2211yescharacteristic
48C2×#14578933C2211yescharacteristic
49C4⋊C4×D157C2218yescomplemented
50C2×C22⋊Dic157C2211yescharacteristic
51C2×C22⋊Dic157C2211yescharacteristic
52C2×#14578931C2211yescharacteristic
53C2×#14578931C2211yescharacteristic
54C2×#14578931C2211yescharacteristic
55C2×C4×Dic157C2211yescharacteristic
56C2×C4×Dic157C2211yescharacteristic
57C2×C4×Dic157C2211yescharacteristic
58C2×C4×Dic157C2211yescharacteristic
59#126×C157C2218yescomplemented
60C2×C4⋊C4×C157C2211yescharacteristic
61C2×C4⋊C4×C157C2211yescharacteristic
62C2×C4⋊C4×C157C2211yescharacteristic
63C2×C22⋊C4×C157C2211yescharacteristic
64C2×C22⋊C4×C157C2211yescharacteristic
65C2×C22⋊C4×C157C2211yescharacteristic
66C2×C42×C157C2211yescharacteristic
67C23×D157C2311yescharacteristic
68C2×Dic314—24no—
69C2×Dic314C2314yes—
70C2×C22⋊D157—24no—
71C2×C22⋊D157C2314yes—
72C22×Dic157—24no—
73C22×Dic157C2311yescharacteristic
74C22×Dic157C2311yescharacteristic
75C22×Dic157C2311yescharacteristic
76C22×Dic157C2311yescharacteristic
77C22×Dic157C2311yescharacteristic
78C22×Dic157C2311yescharacteristic
79C22×Dic157C2314yes—
80C22×Dic157C2311yescharacteristic
81C2×C4×D157—24no—
82C2×C4×D157—24no—
83C2×C4×D157—24no—
84C2×C4×D157C2314yes—
85C2×C4×D157C2314yes—
86C2×C4×D157C2314yes—
87C4⋊Dic157C2314yes—
88C4⋊Dic157C2314yes—
89C4⋊Dic157C2314yes—
90C4⋊Dic157C2314yes—
91#14578933C2314yes—
92#14578933C2314yes—
93#14578933C2314yes—
94#14578933C2314yes—
95#14578933C2314yes—
96#14578933C2314yes—
97#14578933C2314yes—
98#14578933C2314yes—
99#14578933C2314yes—
100C22⋊Dic157C2314yes—
101C22⋊Dic157C2314yes—
102#14578931C2314yes—
103#14578931C2314yes—
104#14578931C2314yes—
105C4×Dic157C2314yes—
106C4×Dic157C2314yes—
107C4×Dic157C2314yes—
108C4×Dic157C2314yes—
109C24×C157C2311yescharacteristic
110C22×C4×C157C2311yescharacteristic
111C22×C4×C157C2311yescharacteristic
112C22×C4×C157C2311yescharacteristic
113C22×C4×C157C2311yescharacteristic
114C22×C4×C157C2311yescharacteristic
115C22×C4×C157C2311yescharacteristic
116C4⋊C4×C157C2314yes—
117C4⋊C4×C157C2314yes—
118C4⋊C4×C157C2314yes—
119C22⋊C4×C157C2314yes—
120C22⋊C4×C157C2314yes—
121C22⋊C4×C157C2314yes—
122C42×C157C2314yes—
123C22×D157—22no—
124C22×D157—22no—
125C22×D157#4114yes—
126C22×D157C2412yes—
127Dic314—28no—
128C22⋊D157—28no—
129C2×Dic157—22no—
130C2×Dic157—22no—
131C2×Dic157—22no—
132C2×Dic157—22no—
133C2×Dic157—22no—
134C2×Dic157—22no—
135C2×Dic157—28no—
136C2×Dic157#4114yes—
137C2×Dic157C2412yes—
138C2×Dic157C2412yes—
139C2×Dic157C2412yes—
140C2×Dic157C2412yes—
141C2×Dic157C2412yes—
142C2×Dic157C2412yes—
143C2×Dic157C2412yes—
144C4×D157—28no—
145C4×D157—28no—
146C4×D157—28no—
147C23×C157—22no—
148C23×C157—22no—
149C23×C157—22no—
150C23×C157C2412yes—
151C23×C157C2411yescharacteristic
152C2×C4×C157—22no—
153C2×C4×C157—22no—
154C2×C4×C157—22no—
155C2×C4×C157—22no—
156C2×C4×C157—22no—
157C2×C4×C157—22no—
158C2×C4×C157C2412yes—
159C2×C4×C157C2412yes—
160C2×C4×C157C2412yes—
161C2×C4×C157C2412yes—
162C2×C4×C157C2412yes—
163C2×C4×C157C2412yes—
164C22×C157—22no—
165C22×C157—22no—
166C22×C157—22no—
167C22×C157—44no—
168C22×C157C2×#4112yes—
169C22×C157C2×#4112yes—
170C22×C1572−1+412yes—
171C22×C157C2511yescharacteristic
172C2×D157—28no—
173C2×D157—22no—
174C2×D157—22no—
175C2×D157C2×#4114yes—
176C4×C157—22no—
177C4×C157—22no—
178C4×C157—22no—
179C4×C157—22no—
180C4×C157—22no—
181C4×C157—22no—
182Dic157—22no—
183Dic157—22no—
184Dic157—22no—
185Dic157—22no—
186Dic157—22no—
187Dic157—22no—
188Dic157C2×#4114yes—
189C2×C157—42no—
190C2×C157#55214yescomplemented
191C2×C157C22×#4111yescharacteristic
192C2×C157C22×#4111yescharacteristic
193C2×C157C2×2−1+411yescharacteristic
194D157—24no—
195C157C2×#55211yescharacteristic, complemented, Sylow
196C2×#552—1571nomaximal, Sylow
197#552—15716no—
198C2×#126—1571no—
199C2×#126D15711yescharacteristic, complemented
200C2×#125—1571no—
201C2×#125—1571no—
202C2×#125—1571no—
203C2×#123—1571no—
204C2×#123—1571no—
205C2×C22⋊Q8—1571no—
206C2×C22⋊Q8—1571no—
207C2×C4×Q8—1571no—
208C2×C4×D4—1571no—
209C2×#117—1571no—
210C2×#117—1571no—
211C2×#117—1571no—
212C22×C4⋊C4—1571no—
213C22×Q8—1571no—
214C22×D4—1571no—
215C23×C4—1571no—
216C23×C4—1571no—
217C23×C4—1571no—
218C23×C4—1571no—
219#126—1578no—
220#126C2×D15718yescomplemented
221#125—1578no—
222#125—1578no—
223#125—1578no—
224#123—1578no—
225#123—1578no—
226C22⋊Q8—1578no—
227C22⋊Q8—1578no—
228C4×Q8—1578no—
229C4×D4—1578no—
230#117—1578no—
231#117—1578no—
232#117—1578no—
233C2×C4⋊C4—1571no—
234C2×C4⋊C4—1571no—
235C2×C4⋊C4—1571no—
236C2×C4⋊C4—1571no—
237C2×C4⋊C4—1571no—
238C2×C4⋊C4—1571no—
239C2×C4⋊C4—1571no—
240C2×C4⋊C4—1571no—
241C2×C4⋊C4—1571no—
242C2×C4⋊C4—1571no—
243C2×C4⋊C4—1571no—
244C2×C4⋊C4—1571no—
245C2×C4⋊C4—1571no—
246C2×C4⋊C4—1578no—
247C2×C4⋊C4C2×D15711yescharacteristic
248C2×C4⋊C4C2×D15711yescharacteristic
249C2×C4⋊C4C2×D15711yescharacteristic
250C2×C22⋊C4—1571no—
251C2×C22⋊C4—1571no—
252C2×C22⋊C4—1571no—
253C2×C22⋊C4—1571no—
254C2×C22⋊C4—1571no—
255C2×C22⋊C4C2×D15711yescharacteristic
256C2×C22⋊C4C2×D15711yescharacteristic
257C2×C22⋊C4C2×D15711yescharacteristic
258C2×C42—1571no—
259C2×C42—1571no—
260C2×C42—1571no—
261C2×C42—1571no—
262C2×C42C2×D15711yescharacteristic
263C24—1571no—
264C24C22×D15711yescharacteristic
265C2×Q8—3144no—
266C2×Q8—1574no—
267C2×D4—3144no—
268C2×D4—1574no—
269C22×C4—3144no—
270C22×C4—3144no—
271C22×C4—3144no—
272C22×C4—3144no—
273C22×C4—1574no—
274C22×C4—1571no—
275C22×C4—1571no—
276C22×C4—1571no—
277C22×C4—1571no—
278C22×C4—1571no—
279C22×C4—1571no—
280C22×C4—1574no—
281C22×C4—1574no—
282C22×C4—1574no—
283C22×C4—1571no—
284C22×C4C22×D15711yescharacteristic
285C22×C4C22×D15711yescharacteristic
286C22×C4C22×D15711yescharacteristic
287C22×C4C22×D15711yescharacteristic
288C22×C4C22×D15711yescharacteristic
289C22×C4C22×D15711yescharacteristic
290C4⋊C4—1574no—
291C4⋊C4—1574no—
292C4⋊C4—1574no—
293C4⋊C4—1574no—
294C4⋊C4—1574no—
295C4⋊C4—1574no—
296C4⋊C4—1574no—
297C4⋊C4—1574no—
298C4⋊C4—1574no—
299C4⋊C4—1574no—
300C4⋊C4—1574no—
301C4⋊C4—1574no—
302C4⋊C4—1574no—
303C4⋊C4C22×D15714yes—
304C4⋊C4C22×D15714yes—
305C4⋊C4C22×D15714yes—
306C22⋊C4—1574no—
307C22⋊C4—1574no—
308C22⋊C4—1574no—
309C22⋊C4—1574no—
310C22⋊C4—1574no—
311C22⋊C4C22×D15714yes—
312C22⋊C4C22×D15714yes—
313C22⋊C4C22×D15714yes—
314C42—1574no—
315C42—1574no—
316C42—1574no—
317C42—1574no—
318C42C22×D15714yes—
319C23—22no—
320C23—22no—
321C23—22no—
322C23—3142no—
323C23—3142no—
324C23—1574no—
325C23—1572no—
326C23C23×D15712yes—
327C23C23×D15711yescharacteristic
328Q8—3148no—
329D4—3148no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—3148no—
337C2×C4—3148no—
338C2×C4—3148no—
339C2×C4—3142no—
340C2×C4—3142no—
341C2×C4—3142no—
342C2×C4—3142no—
343C2×C4—3142no—
344C2×C4—3142no—
345C2×C4—3148no—
346C2×C4—1572no—
347C2×C4—1572no—
348C2×C4—1572no—
349C2×C4—1572no—
350C2×C4—1572no—
351C2×C4—1572no—
352C2×C4—1574no—
353C2×C4—1572no—
354C2×C4C23×D15712yes—
355C2×C4C23×D15712yes—
356C2×C4C23×D15712yes—
357C2×C4C23×D15712yes—
358C2×C4C23×D15712yes—
359C2×C4C23×D15712yes—
360C22—22no—
361C22—22no—
362C22—22no—
363C22—44no—
364C22—3142no—
365C22—3142no—
366C22—3148no—
367C22—1574no—
368C22#41×D15712yes—
369C22#41×D15712yes—
370C22#1909781812yes—
371C22C24×D15711yescharacteristic
372C4—22no—
373C4—22no—
374C4—22no—
375C4—22no—
376C4—22no—
377C4—22no—
378C4—3142no—
379C4—3142no—
380C4—3142no—
381C4—3142no—
382C4—3142no—
383C4—3142no—
384C4—1574no—
385C2—42no—
386C2—3144no—
387C2#2375795914yesdirect product factor
388C2C2×#41×D15711yescharacteristic
389C2C2×#41×D15711yescharacteristic
390C2C2×#1909781811yescharacteristic
subgroupG/H
centerC23C23×D157
commutator, cosocleC22×C157C25
FrattiniC22C24×D157
FittingC2×#126×C157C2
socleC23×C157C24
prime radicalC22×C22⋊D157C22
hypercenterC2×#126D157
hypocenterC157C2×#552
LCSG ▷ C22×C157 ▷ C157
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #23757959C2direct (N × H)
2. C2×#19097764C2semidirect
3. C2×#19097762C2semidirect
4. C2×#19097761C2semidirect
5. C2×#19097761C2semidirect
8. C2×#19097749C2semidirect
9. C2×#19097748C2semidirect
10. C2×C4×Dic314C2semidirect
12. C2×#19097729C2semidirect
13. C2×#19097728C2semidirect
14. C2×#19097727C2semidirect
15. C2×C4⋊C4×D157C2semidirect
16. C2×#126×C157C2semidirect
23. #19097764C22semidirect
24. #19097762C22semidirect
25. #19097761C22semidirect
26. #19097761C22semidirect
29. #19097749C22semidirect
30. #19097748C22semidirect
31. C4×Dic314C22semidirect
33. #19097729C22semidirect
34. #19097728C22semidirect
35. #19097727C22semidirect
49. C4⋊C4×D157C22semidirect
59. #126×C157C22semidirect
190. C2×C157#552semidirect
195. C157C2×#552semidirect
199. C2×#126D157semidirect
220. #126C2×D157semidirect
387. C2#23757959direct (N × H)

Maximal subgroups

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

subgroupindex
#237579592
C2×#190977642
C2×#190977622
C2×#190977612
C2×#190977532
C2×#190977492
C2×#190977482
C2×C4×Dic3142
C2×#190977312
C2×#190977292
C2×#190977282
C2×#190977272
C2×C4⋊C4×D1572
C2×#126×C1572
C2×#552157