Finite Group Databasebeta

← C2×#20293225 #28349813

Subgroups — C2×#20293225 #28349813

Order 13696.

1144 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293225C2116yesmaximal, direct product factor
2C2×#16812104C211yesmaximal, characteristic, complemented
3C2×#16812103C211yesmaximal, characteristic, complemented
4C2×#16812099C211yesmaximal, characteristic, complemented
5C2×#16812094C211yesmaximal, characteristic, complemented
6C2×#16812094C211yesmaximal, characteristic, complemented
7C2×#16812094C211yesmaximal, characteristic, complemented
8C2×#16812094C211yesmaximal, characteristic, complemented
9C2×#16812089C211yesmaximal, characteristic, complemented
10C2×#16812087C211yesmaximal, characteristic, complemented
11C2×#16812087C211yesmaximal, characteristic, complemented
12C2×#16812084C211yesmaximal, characteristic
13C2×C4×D428C211yesmaximal, characteristic, complemented
14C2×#16812071C211yesmaximal, characteristic, complemented
15C2×C4⋊C4×D107C211yesmaximal, characteristic, complemented
16C2×#125×C107C211yesmaximal, characteristic, complemented
17C22×Dic214C2211yescharacteristic
18C22×D428C2211yescharacteristic
19C22×D428C2211yescharacteristic
20C22×D428C2211yescharacteristic
21C22×C4×D107C2211yescharacteristic
22C22×C4×D107C2211yescharacteristic
23C22×C4×D107C2211yescharacteristic
24C22×C4×D107C2211yescharacteristic
25C22×C4×D107C2211yescharacteristic
26#16812104C2218yescomplemented
27#16812103C2218yescomplemented
28#16812099C2218yescomplemented
29#16812094C2218yescomplemented
30#16812094C2218yescomplemented
31#16812094C2218yescomplemented
32#16812094C2218yescomplemented
33#16812089C2218yescomplemented
34#16812087C2218yescomplemented
35#16812087C2218yescomplemented
36#16812084C2218yes—
37C4×D428C2218yescomplemented
38#16812071C2218yescomplemented
39C2×C4⋊Dic107C2211yescharacteristic
40C2×C4⋊Dic107C2211yescharacteristic
41C2×Dic107⋊C4C2211yescharacteristic
42C2×Dic107⋊C4C2211yescharacteristic
43C2×Dic107⋊C4C2211yescharacteristic
44C2×Dic107⋊C4C2211yescharacteristic
45C2×Dic107⋊C4C2211yescharacteristic
46C2×Dic107⋊C4C2211yescharacteristic
47C4⋊C4×D107C2218yescomplemented
48C2×(C2×D107)⋊C4C2211yescharacteristic
49C2×(C2×D107)⋊C4C2211yescharacteristic
50C2×(C2×D107)⋊C4C2211yescharacteristic
51C2×(C2×D107)⋊C4C2211yescharacteristic
52C2×(C2×D107)⋊C4C2211yescharacteristic
53C2×(C2×D107)⋊C4C2211yescharacteristic
54C2×(C2×D107)⋊C4C2211yescharacteristic
55C2×(C2×D107)⋊C4C2211yescharacteristic
56C2×(C2×D107)⋊C4C2211yescharacteristic
57C2×(C2×D107)⋊C4C2211yescharacteristic
58C2×C4×Dic107C2211yescharacteristic
59#125×C107C2218yescomplemented
60C2×C4⋊C4×C107C2211yescharacteristic
61C2×C4⋊C4×C107C2211yescharacteristic
62C2×C4⋊C4×C107C2211yescharacteristic
63C2×C4⋊C4×C107C2211yescharacteristic
64C2×C4⋊C4×C107C2211yescharacteristic
65C2×C4⋊C4×C107C2211yescharacteristic
66C2×C42×C107C2211yescharacteristic
67C23×D107C2311yescharacteristic
68C23×D107C2311yescharacteristic
69C23×D107C2311yescharacteristic
70C2×Dic214—42no—
71C2×Dic214C2314yes—
72C2×D428—24no—
73C2×D428—24no—
74C2×D428—42no—
75C2×D428C2314yes—
76C2×D428C2314yes—
77C2×D428C2314yes—
78C22×Dic107C2311yescharacteristic
79C22×Dic107C2311yescharacteristic
80C22×Dic107C2311yescharacteristic
81C22×Dic107C2311yescharacteristic
82C22×Dic107C2311yescharacteristic
83C2×C4×D107—24no—
84C2×C4×D107—42no—
85C2×C4×D107—42no—
86C2×C4×D107—42no—
87C2×C4×D107—42no—
88C2×C4×D107C2314yes—
89C2×C4×D107C2314yes—
90C2×C4×D107C2314yes—
91C2×C4×D107C2314yes—
92C2×C4×D107C2314yes—
93C4⋊Dic107C2314yes—
94C4⋊Dic107C2314yes—
95Dic107⋊C4C2314yes—
96Dic107⋊C4C2314yes—
97Dic107⋊C4C2314yes—
98Dic107⋊C4C2314yes—
99Dic107⋊C4C2314yes—
100Dic107⋊C4C2314yes—
101(C2×D107)⋊C4C2314yes—
102(C2×D107)⋊C4C2314yes—
103(C2×D107)⋊C4C2314yes—
104(C2×D107)⋊C4C2314yes—
105(C2×D107)⋊C4C2314yes—
106(C2×D107)⋊C4C2314yes—
107(C2×D107)⋊C4C2314yes—
108(C2×D107)⋊C4C2314yes—
109(C2×D107)⋊C4C2314yes—
110(C2×D107)⋊C4C2314yes—
111C4×Dic107C2314yes—
112C22×C4×C107C2311yescharacteristic
113C22×C4×C107C2311yescharacteristic
114C22×C4×C107C2311yescharacteristic
115C22×C4×C107C2311yescharacteristic
116C22×C4×C107C2311yescharacteristic
117C22×C4×C107C2311yescharacteristic
118C22×C4×C107C2311yescharacteristic
119C4⋊C4×C107C2314yes—
120C4⋊C4×C107C2314yes—
121C4⋊C4×C107C2314yes—
122C4⋊C4×C107C2314yes—
123C4⋊C4×C107C2314yes—
124C4⋊C4×C107C2314yes—
125C42×C107C2314yes—
126C23×C107C2411yescharacteristic
127C22×D107—22no—
128C22×D107—22no—
129C22×D107—22no—
130C22×D107—22no—
131C22×D107—22no—
132C22×D107—22no—
133C22×D107—22no—
134C22×D107—22no—
135C22×D107#4114yes—
136C22×D107C2412yes—
137C22×D107C2412yes—
138C22×D107C2412yes—
139C2×C4×C107—22no—
140C2×C4×C107—22no—
141C2×C4×C107—22no—
142C2×C4×C107—22no—
143C2×C4×C107—22no—
144C2×C4×C107—22no—
145C2×C4×C107—22no—
146C2×C4×C107C2412yes—
147C2×C4×C107C2412yes—
148C2×C4×C107C2412yes—
149C2×C4×C107C2412yes—
150C2×C4×C107C2412yes—
151C2×C4×C107C2412yes—
152C2×C4×C107C2412yes—
153C2×Dic107—22no—
154C2×Dic107—22no—
155C2×Dic107—22no—
156C2×Dic107—22no—
157C2×Dic107—22no—
158C2×Dic107C2412yes—
159C2×Dic107C2412yes—
160C2×Dic107C2412yes—
161C2×Dic107C2412yes—
162C2×Dic107C2412yes—
163D428—28no—
164D428—28no—
165D428—44no—
166C4×D107—28no—
167C4×D107—44no—
168C4×D107—44no—
169C4×D107—44no—
170C4×D107—44no—
171Dic214—44no—
172C22×C107C2×#4112yes—
173C22×C107H(5,𝔽2)12yes—
174C22×C1072−1+412yes—
175C22×C107C2511yescharacteristic
176C2×D107—28no—
177C2×D107—22no—
178C2×D107—22no—
179C2×D107—22no—
180C2×D107—22no—
181C2×D107—22no—
182C2×D107—22no—
183C2×D107—22no—
184C2×D107—22no—
185C2×D107—44no—
186C2×D107—44no—
187C2×D107C2×#4114yes—
188C4×C107—22no—
189C4×C107—22no—
190C4×C107—22no—
191C4×C107—22no—
192C4×C107—22no—
193C4×C107—22no—
194C4×C107—22no—
195Dic107—22no—
196Dic107—22no—
197Dic107—22no—
198Dic107—22no—
199Dic107—22no—
200C2×C107#53914yescomplemented
201C2×C107C22×#4111yescharacteristic
202C2×C107C2×H(5,𝔽2)11yescharacteristic
203C2×C107C2×2−1+411yescharacteristic
204D107—24no—
205D107—42no—
206D107—42no—
207C2×#539—1071nomaximal, Sylow
208C107C2×#53911yescharacteristic, complemented, Sylow
209#539—10716no—
210C2×#126—1071no—
211C2×#126—1071no—
212C2×#125—1071no—
213C2×#125D10711yescharacteristic, complemented
214C2×#123—1071no—
215C2×#123—1071no—
216C2×#123—1071no—
217C2×#123—1071no—
218C2×C22⋊Q8—1071no—
219C2×C22⋊Q8—1071no—
220C2×C22⋊Q8—1071no—
221C2×#121—1071no—
222C2×C4×D4—1071no—
223C2×C4×D4—1071no—
224C22×C4⋊C4—1071no—
225C22×Q8—1071no—
226C22×D4—1071no—
227C22×D4—1071no—
228C22×D4—1071no—
229C23×C4—1071no—
230C23×C4—1071no—
231C23×C4—1071no—
232C23×C4—1071no—
233C23×C4—1071no—
234#126—1078no—
235#126—1078no—
236#125—1078no—
237#125C2×D10718yescomplemented
238#123—1078no—
239#123—1078no—
240#123—1078no—
241#123—1078no—
242C22⋊Q8—1078no—
243C22⋊Q8—1078no—
244C22⋊Q8—1078no—
245#121—1078no—
246C4×D4—1078no—
247C4×D4—1078no—
248C2×C4⋊C4—1071no—
249C2×C4⋊C4—1071no—
250C2×C4⋊C4—1071no—
251C2×C4⋊C4—1071no—
252C2×C4⋊C4—1071no—
253C2×C4⋊C4—1071no—
254C2×C4⋊C4—1071no—
255C2×C4⋊C4—1071no—
256C2×C4⋊C4—1078no—
257C2×C4⋊C4C2×D10711yescharacteristic
258C2×C4⋊C4C2×D10711yescharacteristic
259C2×C4⋊C4C2×D10711yescharacteristic
260C2×C4⋊C4C2×D10711yescharacteristic
261C2×C4⋊C4C2×D10711yescharacteristic
262C2×C4⋊C4C2×D10711yescharacteristic
263C2×C22⋊C4—1071no—
264C2×C22⋊C4—1071no—
265C2×C22⋊C4—1071no—
266C2×C22⋊C4—1071no—
267C2×C22⋊C4—1071no—
268C2×C22⋊C4—1071no—
269C2×C22⋊C4—1071no—
270C2×C22⋊C4—1071no—
271C2×C22⋊C4—1071no—
272C2×C22⋊C4—1071no—
273C2×C42—1071no—
274C2×C42C2×D10711yescharacteristic
275C24—1071no—
276C24—1071no—
277C24—1071no—
278C2×Q8—1074no—
279C2×Q8—4282no—
280C2×D4—1074no—
281C2×D4—1074no—
282C2×D4—1074no—
283C2×D4—4282no—
284C2×D4—2144no—
285C2×D4—2144no—
286C22×C4—1071no—
287C22×C4—1071no—
288C22×C4—1071no—
289C22×C4—1071no—
290C22×C4—1071no—
291C22×C4—1074no—
292C22×C4—1074no—
293C22×C4—1074no—
294C22×C4—1074no—
295C22×C4—1074no—
296C22×C4—4282no—
297C22×C4—4282no—
298C22×C4—4282no—
299C22×C4—4282no—
300C22×C4—2144no—
301C22×C4C22×D10711yescharacteristic
302C22×C4C22×D10711yescharacteristic
303C22×C4C22×D10711yescharacteristic
304C22×C4C22×D10711yescharacteristic
305C22×C4C22×D10711yescharacteristic
306C22×C4C22×D10711yescharacteristic
307C22×C4C22×D10711yescharacteristic
308C4⋊C4—1074no—
309C4⋊C4—1074no—
310C4⋊C4—1074no—
311C4⋊C4—1074no—
312C4⋊C4—1074no—
313C4⋊C4—1074no—
314C4⋊C4—1074no—
315C4⋊C4—1074no—
316C4⋊C4C22×D10714yes—
317C4⋊C4C22×D10714yes—
318C4⋊C4C22×D10714yes—
319C4⋊C4C22×D10714yes—
320C4⋊C4C22×D10714yes—
321C4⋊C4C22×D10714yes—
322C22⋊C4—1074no—
323C22⋊C4—1074no—
324C22⋊C4—1074no—
325C22⋊C4—1074no—
326C22⋊C4—1074no—
327C22⋊C4—1074no—
328C22⋊C4—1074no—
329C22⋊C4—1074no—
330C22⋊C4—1074no—
331C22⋊C4—1074no—
332C42—1074no—
333C42C22×D10714yes—
334C23—1074no—
335C23—1072no—
336C23—1072no—
337C23—1072no—
338C23—2142no—
339C23—2142no—
340C23—2142no—
341C23—2142no—
342C23—2142no—
343C23—2142no—
344C23—2142no—
345C23—2142no—
346C23C23×D10711yescharacteristic
347Q8—4284no—
348D4—4284no—
349D4—2148no—
350D4—2148no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—1072no—
359C2×C4—1072no—
360C2×C4—1072no—
361C2×C4—1072no—
362C2×C4—1072no—
363C2×C4—4284no—
364C2×C4—4284no—
365C2×C4—4284no—
366C2×C4—4284no—
367C2×C4—2148no—
368C2×C4—2142no—
369C2×C4—2142no—
370C2×C4—2142no—
371C2×C4—2142no—
372C2×C4—2142no—
373C2×C4C23×D10712yes—
374C2×C4C23×D10712yes—
375C2×C4C23×D10712yes—
376C2×C4C23×D10712yes—
377C2×C4C23×D10712yes—
378C2×C4C23×D10712yes—
379C2×C4C23×D10712yes—
380C22—1074no—
381C22—4284no—
382C22—4284no—
383C22—2142no—
384C22—2142no—
385C22—2142no—
386C22—2142no—
387C22—2142no—
388C22—2142no—
389C22—2142no—
390C22—2142no—
391C22—2148no—
392C22#41×D10712yes—
393C22#1681215512yes—
394C22#1681215712yes—
395C22C24×D10711yescharacteristic
396C4—22no—
397C4—22no—
398C4—22no—
399C4—22no—
400C4—22no—
401C4—22no—
402C4—22no—
403C4—2142no—
404C4—2142no—
405C4—2142no—
406C4—2142no—
407C4—2142no—
408C2—4282no—
409C2—4282no—
410C2—2144no—
411C2#2029322514yesdirect product factor
412C2C2×#41×D10711yescharacteristic
413C2C2×#1681215511yescharacteristic
414C2C2×#1681215711yescharacteristic
subgroupG/H
centerC23C23×D107
commutator, cosocleC22×C107C25
FrattiniC22C24×D107
FittingC2×#125×C107C2
socleC23×C107C24
prime radicalC2×#16812084C2
hypercenterC2×#125D107
hypocenterC107C2×#539
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. #20293225C2direct (N × H)
2. C2×#16812104C2semidirect
3. C2×#16812103C2semidirect
4. C2×#16812099C2semidirect
5. C2×#16812094C2semidirect
6. C2×#16812094C2semidirect
7. C2×#16812094C2semidirect
8. C2×#16812094C2semidirect
9. C2×#16812089C2semidirect
10. C2×#16812087C2semidirect
11. C2×#16812087C2semidirect
13. C2×C4×D428C2semidirect
14. C2×#16812071C2semidirect
15. C2×C4⋊C4×D107C2semidirect
16. C2×#125×C107C2semidirect
26. #16812104C22semidirect
27. #16812103C22semidirect
28. #16812099C22semidirect
29. #16812094C22semidirect
30. #16812094C22semidirect
31. #16812094C22semidirect
32. #16812094C22semidirect
33. #16812089C22semidirect
34. #16812087C22semidirect
35. #16812087C22semidirect
37. C4×D428C22semidirect
38. #16812071C22semidirect
47. C4⋊C4×D107C22semidirect
59. #125×C107C22semidirect
200. C2×C107#539semidirect
208. C107C2×#539semidirect
213. C2×#125D107semidirect
237. #125C2×D107semidirect
411. C2#20293225direct (N × H)

Maximal subgroups

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

subgroupindex
#202932252
C2×#168121042
C2×#168121032
C2×#168120992
C2×#168120942
C2×#168120892
C2×#168120872
C2×#168120842
C2×C4×D4282
C2×#168120712
C2×C4⋊C4×D1072
C2×#125×C1072
C2×#539107