Finite Group Databasebeta

← C2×#23757858 #34113474

Subgroups — C2×#23757858 #34113474

Order 20096.

1336 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757858C2116yesmaximal, direct product factor
2C2×#19097764C211yesmaximal, characteristic, complemented
3C2×#19097764C211yesmaximal, characteristic, complemented
4C2×#19097758C211yesmaximal, characteristic, complemented
5C2×#19097757C211yesmaximal, characteristic, complemented
6C2×#19097753C211yesmaximal, characteristic, complemented
7C2×#19097752C211yesmaximal, characteristic, complemented
8C2×#19097748C211yesmaximal, characteristic, complemented
9C2×#19097743C211yesmaximal, characteristic, complemented
10C2×#19097743C211yesmaximal, characteristic, complemented
11C2×#19097742C211yesmaximal, characteristic, complemented
12C2×#19097740C211yesmaximal, characteristic, complemented
13C2×D4×Dic157C211yesmaximal, characteristic, complemented
14C2×#19097731C211yesmaximal, characteristic, complemented
15C22×C22⋊Dic157C211yesmaximal, characteristic, complemented
16C2×#120×C157C211yesmaximal, characteristic, complemented
17C22×Dic314C2211yescharacteristic, complemented
18C22×C22⋊D157C2211yescharacteristic
19C22×C22⋊D157C2211yescharacteristic
20C22×C22⋊D157C2211yescharacteristic
21C22×C22⋊D157C2211yescharacteristic, complemented
22C23×Dic157C2211yescharacteristic
23C23×Dic157C2211yescharacteristic
24C23×Dic157C2211yescharacteristic, complemented
25C22×C4×D157C2211yescharacteristic, complemented
26#19097764C2218yescomplemented
27#19097764C2218yescomplemented
28#19097758C2218yescomplemented
29#19097757C2218yescomplemented
30#19097753C2218yescomplemented
31#19097752C2218yescomplemented
32#19097748C2218yescomplemented
33#19097743C2218yescomplemented
34#19097743C2218yescomplemented
35#19097742C2218yescomplemented
36#19097740C2218yescomplemented
37D4×Dic157C2218yescomplemented
38#19097731C2218yescomplemented
39C2×C4⋊Dic157C2211yescharacteristic, complemented
40C2×C4⋊Dic157C2211yescharacteristic, complemented
41C2×#14578933C2211yescharacteristic, complemented
42C2×#14578933C2211yescharacteristic, complemented
43C2×#14578933C2211yescharacteristic, complemented
44C2×#14578933C2211yescharacteristic, complemented
45C2×C22⋊Dic157C2211yescharacteristic
46C2×C22⋊Dic157C2211yescharacteristic
47C2×C22⋊Dic157C2211yescharacteristic
48C2×C22⋊Dic157C2211yescharacteristic
49C2×C22⋊Dic157C2211yescharacteristic
50C2×C22⋊Dic157C2211yescharacteristic
51C2×C22⋊Dic157C2211yescharacteristic
52C2×C22⋊Dic157C2218yescomplemented
53C2×C22⋊Dic157C2211yescharacteristic, complemented
54C2×C22⋊Dic157C2211yescharacteristic, complemented
55C2×#14578931C2211yescharacteristic, complemented
56C2×#14578931C2211yescharacteristic, complemented
57C2×C4×Dic157C2211yescharacteristic, complemented
58C2×C4×Dic157C2211yescharacteristic, complemented
59C25×C157C2211yescharacteristic
60C22×D4×C157C2211yescharacteristic
61C22×D4×C157C2211yescharacteristic
62C22×D4×C157C2211yescharacteristic
63#120×C157C2218yescomplemented
64C2×C22⋊C4×C157C2211yescharacteristic
65C2×C22⋊C4×C157C2211yescharacteristic
66C2×C22⋊C4×C157C2211yescharacteristic
67C23×D157C2311yescharacteristic
68C2×Dic314—42no—
69C2×Dic314C2314yescomplemented
70C2×C22⋊D157—24no—
71C2×C22⋊D157—42no—
72C2×C22⋊D157—42no—
73C2×C22⋊D157—42no—
74C2×C22⋊D157C2314yes—
75C2×C22⋊D157C2314yes—
76C2×C22⋊D157C2314yes—
77C2×C22⋊D157C2314yescomplemented
78C22×Dic157—42no—
79C22×Dic157—42no—
80C22×Dic157—42no—
81C22×Dic157C2311yescharacteristic
82C22×Dic157C2311yescharacteristic
83C22×Dic157C2311yescharacteristic
84C22×Dic157C2311yescharacteristic
85C22×Dic157C2311yescharacteristic
86C22×Dic157C2311yescharacteristic
87C22×Dic157C2311yescharacteristic
88C22×Dic157C2314yes—
89C22×Dic157C2314yes—
90C22×Dic157C2314yescomplemented
91C2×C4×D157—42no—
92C2×C4×D157C2314yescomplemented
93C4⋊Dic157C2314yescomplemented
94C4⋊Dic157C2314yescomplemented
95#14578933C2314yescomplemented
96#14578933C2314yescomplemented
97#14578933C2314yescomplemented
98#14578933C2314yescomplemented
99C22⋊Dic157C2314yes—
100C22⋊Dic157C2314yes—
101C22⋊Dic157C2314yes—
102C22⋊Dic157C2314yes—
103C22⋊Dic157C2314yes—
104C22⋊Dic157C2314yes—
105C22⋊Dic157C2314yes—
106C22⋊Dic157C2314yescomplemented
107C22⋊Dic157C2314yescomplemented
108#14578931C2314yescomplemented
109#14578931C2314yescomplemented
110C4×Dic157C2314yescomplemented
111C4×Dic157C2314yescomplemented
112C24×C157—24no—
113C24×C157—42no—
114C24×C157—42no—
115C24×C157C2311yescharacteristic
116C24×C157C2311yescharacteristic
117C24×C157C2311yescharacteristic
118C24×C157C2311yescharacteristic
119C24×C157C2314yes—
120C2×D4×C157—24no—
121C2×D4×C157—42no—
122C2×D4×C157—42no—
123C2×D4×C157C2314yes—
124C2×D4×C157C2314yes—
125C2×D4×C157C2314yes—
126C22×C4×C157C2311yescharacteristic
127C22×C4×C157C2311yescharacteristic
128C22×C4×C157C2311yescharacteristic
129C22⋊C4×C157C2314yes—
130C22⋊C4×C157C2314yes—
131C22⋊C4×C157C2314yes—
132C22×D157—22no—
133C22×D157—22no—
134C22×D157—22no—
135C22×D157C2412yes—
136Dic314—44no—
137C22⋊D157—28no—
138C22⋊D157—44no—
139C22⋊D157—44no—
140C22⋊D157—44no—
141C2×Dic157—22no—
142C2×Dic157—22no—
143C2×Dic157—22no—
144C2×Dic157—22no—
145C2×Dic157—22no—
146C2×Dic157—22no—
147C2×Dic157—22no—
148C2×Dic157—44no—
149C2×Dic157—44no—
150C2×Dic157—44no—
151C2×Dic157C2412yes—
152C2×Dic157C2412yes—
153C2×Dic157C2412yes—
154C2×Dic157C2412yes—
155C2×Dic157C2412yes—
156C2×Dic157C2412yes—
157C2×Dic157C2412yes—
158C4×D157—44no—
159C23×C157—22no—
160C23×C157—22no—
161C23×C157—22no—
162C23×C157—28no—
163C23×C157—22no—
164C23×C157—22no—
165C23×C157—22no—
166C23×C157—22no—
167C23×C157—22no—
168C23×C157—22no—
169C23×C157—22no—
170C23×C157—22no—
171C23×C157—44no—
172C23×C157—44no—
173C23×C157—416no—
174C23×C157#4114yes—
175C23×C157C2412yes—
176C23×C157C2412yes—
177C23×C157C2412yes—
178C23×C157C2412yes—
179C23×C157C2411yescharacteristic
180D4×C157—28no—
181D4×C157—44no—
182D4×C157—44no—
183C2×C4×C157—22no—
184C2×C4×C157—22no—
185C2×C4×C157—22no—
186C2×C4×C157C2412yes—
187C2×C4×C157C2412yes—
188C2×C4×C157C2412yes—
189C22×C157—28no—
190C22×C157—22no—
191C22×C157—22no—
192C22×C157—22no—
193C22×C157—22no—
194C22×C157—22no—
195C22×C157—22no—
196C22×C157—22no—
197C22×C157—22no—
198C22×C157—22no—
199C22×C157—22no—
200C22×C157—22no—
201C22×C157—416no—
202C22×C157—44no—
203C22×C157—44no—
204C22×C157—44no—
205C22×C157C2×#4114yes—
206C22×C157C2×#4112yes—
207C22×C157H(5,𝔽2)12yes—
208C22×C157H(5,𝔽2)12yes—
209C22×C157C2511yescharacteristic
210C2×D157—22no—
211C2×D157—22no—
212C2×D157—22no—
213C2×D157—44no—
214C4×C157—22no—
215C4×C157—22no—
216C4×C157—22no—
217Dic157—22no—
218Dic157—22no—
219Dic157—22no—
220Dic157—22no—
221Dic157—22no—
222Dic157—22no—
223Dic157—22no—
224C2×C157—24no—
225C2×C157—42no—
226C2×C157—42no—
227C2×C157—42no—
228C2×C157#53814yescomplemented
229C2×C157C22×#4111yescharacteristic
230C2×C157C2×H(5,𝔽2)11yescharacteristic
231C2×C157C2×H(5,𝔽2)11yescharacteristic
232D157—42no—
233C157C2×#53811yescharacteristic, complemented, Sylow
234C2×#538—1571nomaximal, Sylow
235#538—15716no—
236C2×#126—1571no—
237C2×#126—1571no—
238C2×#124—1571no—
239C2×#124—1571no—
240C2×#123—1571no—
241C2×#123—1571no—
242C2×C22⋊Q8—1571no—
243C2×#121—1571no—
244C2×#121—1571no—
245C2×#121—1571no—
246C2×#120—1571no—
247C2×#120D15711yescharacteristic, complemented
248C2×C4×D4—1571no—
249C2×C4×D4—1571no—
250C22×C22⋊C4—1571no—
251C25C2×D15711yescharacteristic
252C22×Q8—1571no—
253C22×D4—1571no—
254C22×D4—1571no—
255C22×D4—1571no—
256C22×D4—1571no—
257C22×D4C2×D15711yescharacteristic
258C22×D4C2×D15711yescharacteristic
259C22×D4C2×D15711yescharacteristic
260C23×C4—1571no—
261C23×C4—1571no—
262C23×C4—1571no—
263C23×C4—1571no—
264#126—1578no—
265#126—1578no—
266#124—1578no—
267#124—1578no—
268#123—1578no—
269#123—1578no—
270C22⋊Q8—1578no—
271#121—1578no—
272#121—1578no—
273#121—1578no—
274#120—1578no—
275#120C2×D15718yescomplemented
276C4×D4—1578no—
277C4×D4—1578no—
278C2×C4⋊C4—1571no—
279C2×C4⋊C4—1571no—
280C2×C4⋊C4—1571no—
281C2×C4⋊C4—1571no—
282C2×C4⋊C4—1571no—
283C2×C4⋊C4—1571no—
284C2×C22⋊C4—1571no—
285C2×C22⋊C4—1571no—
286C2×C22⋊C4—1571no—
287C2×C22⋊C4—1571no—
288C2×C22⋊C4—1578no—
289C2×C22⋊C4—1571no—
290C2×C22⋊C4—1571no—
291C2×C22⋊C4—1571no—
292C2×C22⋊C4—1571no—
293C2×C22⋊C4—1571no—
294C2×C22⋊C4—1571no—
295C2×C22⋊C4—1571no—
296C2×C22⋊C4C2×D15711yescharacteristic
297C2×C22⋊C4C2×D15711yescharacteristic
298C2×C22⋊C4C2×D15711yescharacteristic
299C2×C42—1571no—
300C2×C42—1571no—
301C24—24no—
302C24—42no—
303C24—42no—
304C24—1571no—
305C24C22×D15711yescharacteristic
306C24C22×D15711yescharacteristic
307C24C22×D15711yescharacteristic
308C24C22×D15711yescharacteristic
309C24C22×D15714yes—
310C2×Q8—6282no—
311C2×Q8—1574no—
312C2×D4—24no—
313C2×D4—42no—
314C2×D4—42no—
315C2×D4—3144no—
316C2×D4—6282no—
317C2×D4—6282no—
318C2×D4—6282no—
319C2×D4—1574no—
320C2×D4—1574no—
321C2×D4—1574no—
322C2×D4—1574no—
323C2×D4C22×D15714yes—
324C2×D4C22×D15714yes—
325C2×D4C22×D15714yes—
326C22×C4—6282no—
327C22×C4—6282no—
328C22×C4—6282no—
329C22×C4—6282no—
330C22×C4—1571no—
331C22×C4—1571no—
332C22×C4—1571no—
333C22×C4—1571no—
334C22×C4—1571no—
335C22×C4—1571no—
336C22×C4—1571no—
337C22×C4—1574no—
338C22×C4—1574no—
339C22×C4—1574no—
340C22×C4—1574no—
341C22×C4C22×D15711yescharacteristic
342C22×C4C22×D15711yescharacteristic
343C22×C4C22×D15711yescharacteristic
344C4⋊C4—1574no—
345C4⋊C4—1574no—
346C4⋊C4—1574no—
347C4⋊C4—1574no—
348C4⋊C4—1574no—
349C4⋊C4—1574no—
350C22⋊C4—1574no—
351C22⋊C4—1574no—
352C22⋊C4—1574no—
353C22⋊C4—1574no—
354C22⋊C4—1574no—
355C22⋊C4—1574no—
356C22⋊C4—1574no—
357C22⋊C4—1574no—
358C22⋊C4—1574no—
359C22⋊C4—1574no—
360C22⋊C4—1574no—
361C22⋊C4C22×D15714yes—
362C22⋊C4C22×D15714yes—
363C22⋊C4C22×D15714yes—
364C42—1574no—
365C42—1574no—
366C23—22no—
367C23—22no—
368C23—22no—
369C23—28no—
370C23—22no—
371C23—22no—
372C23—22no—
373C23—22no—
374C23—22no—
375C23—22no—
376C23—22no—
377C23—22no—
378C23—44no—
379C23—44no—
380C23—416no—
381C23—3142no—
382C23—3142no—
383C23—3142no—
384C23—1572no—
385C23#1457895314yes—
386C23C23×D15712yes—
387C23C23×D15712yes—
388C23C23×D15712yes—
389C23C23×D15712yes—
390C23C23×D15711yescharacteristic
391Q8—6284no—
392D4—28no—
393D4—44no—
394D4—44no—
395D4—3148no—
396D4—6284no—
397D4—6284no—
398D4—6284no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—3142no—
403C2×C4—3142no—
404C2×C4—3142no—
405C2×C4—3142no—
406C2×C4—3142no—
407C2×C4—3142no—
408C2×C4—3142no—
409C2×C4—6284no—
410C2×C4—6284no—
411C2×C4—6284no—
412C2×C4—6284no—
413C2×C4—1572no—
414C2×C4—1572no—
415C2×C4—1572no—
416C2×C4—1572no—
417C2×C4—1572no—
418C2×C4—1572no—
419C2×C4—1572no—
420C2×C4C23×D15712yes—
421C2×C4C23×D15712yes—
422C2×C4C23×D15712yes—
423C22—22no—
424C22—22no—
425C22—28no—
426C22—22no—
427C22—22no—
428C22—22no—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—22no—
434C22—22no—
435C22—416no—
436C22—44no—
437C22—44no—
438C22—44no—
439C22—3142no—
440C22—3142no—
441C22—3142no—
442C22—6284no—
443C22C2×#1457895314yes—
444C22C2×#1457895312yes—
445C22#1909781612yes—
446C22#1909781612yes—
447C22C24×D15711yescharacteristic
448C4—22no—
449C4—22no—
450C4—22no—
451C4—3142no—
452C4—3142no—
453C4—3142no—
454C4—3142no—
455C4—3142no—
456C4—3142no—
457C4—3142no—
458C2—24no—
459C2—42no—
460C2—42no—
461C2—42no—
462C2—6282no—
463C2#2375785814yesdirect product factor
464C2C22×#1457895311yescharacteristic
465C2C2×#1909781611yescharacteristic
466C2C2×#1909781611yescharacteristic
subgroupG/H
centerC23C23×D157
commutator, cosocleC22×C157C25
FrattiniC22C24×D157
FittingC2×#120×C157C2
socleC23×C157C24
hypercenterC2×#120D157
hypocenterC157C2×#538
LCSG ▷ C22×C157 ▷ C157
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. #23757858C2direct (N × H)
2. C2×#19097764C2semidirect
3. C2×#19097764C2semidirect
4. C2×#19097758C2semidirect
5. C2×#19097757C2semidirect
6. C2×#19097753C2semidirect
7. C2×#19097752C2semidirect
8. C2×#19097748C2semidirect
9. C2×#19097743C2semidirect
10. C2×#19097743C2semidirect
11. C2×#19097742C2semidirect
12. C2×#19097740C2semidirect
13. C2×D4×Dic157C2semidirect
14. C2×#19097731C2semidirect
15. C22×C22⋊Dic157C2semidirect
16. C2×#120×C157C2semidirect
17. C22×Dic314C22semidirect
21. C22×C22⋊D157C22semidirect
24. C23×Dic157C22semidirect
25. C22×C4×D157C22semidirect
26. #19097764C22semidirect
27. #19097764C22semidirect
28. #19097758C22semidirect
29. #19097757C22semidirect
30. #19097753C22semidirect
31. #19097752C22semidirect
32. #19097748C22semidirect
33. #19097743C22semidirect
34. #19097743C22semidirect
35. #19097742C22semidirect
36. #19097740C22semidirect
37. D4×Dic157C22semidirect
38. #19097731C22semidirect
39. C2×C4⋊Dic157C22semidirect
40. C2×C4⋊Dic157C22semidirect
41. C2×#14578933C22semidirect
42. C2×#14578933C22semidirect
43. C2×#14578933C22semidirect
44. C2×#14578933C22semidirect
52. C2×C22⋊Dic157C22semidirect
53. C2×C22⋊Dic157C22semidirect
54. C2×C22⋊Dic157C22semidirect
55. C2×#14578931C22semidirect
56. C2×#14578931C22semidirect
57. C2×C4×Dic157C22semidirect
58. C2×C4×Dic157C22semidirect
63. #120×C157C22semidirect
69. C2×Dic314C23semidirect
77. C2×C22⋊D157C23semidirect
90. C22×Dic157C23semidirect
92. C2×C4×D157C23semidirect
93. C4⋊Dic157C23semidirect
94. C4⋊Dic157C23semidirect
95. #14578933C23semidirect
96. #14578933C23semidirect
97. #14578933C23semidirect
98. #14578933C23semidirect
106. C22⋊Dic157C23semidirect
107. C22⋊Dic157C23semidirect
108. #14578931C23semidirect
109. #14578931C23semidirect
110. C4×Dic157C23semidirect
111. C4×Dic157C23semidirect
228. C2×C157#538semidirect
233. C157C2×#538semidirect
247. C2×#120D157semidirect
275. #120C2×D157semidirect
463. C2#23757858direct (N × H)

Maximal subgroups

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

subgroupindex
#237578582
C2×#190977642
C2×#190977582
C2×#190977572
C2×#190977532
C2×#190977522
C2×#190977482
C2×#190977432
C2×#190977422
C2×#190977402
C2×D4×Dic1572
C2×#190977312
C22×C22⋊Dic1572
C2×#120×C1572
C2×#538157