Finite Group Databasebeta

← C2×#31827178 #49134799

Subgroups — C2×#31827178 #49134799

Order 36224.

1240 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827178C2116yesmaximal, direct product factor
2C2×#22583609C211yesmaximal, characteristic, complemented
3C2×#22583598C212yesmaximal, complemented
4C2×#22583596C212yesmaximal, complemented
5C2×#22583585C211yesmaximal, characteristic, complemented
6C2×#22583584C211yesmaximal, characteristic, complemented
7C2×#22583583C212yesmaximal, complemented
8C2×#22583572C211yesmaximal, characteristic, complemented
9C2×C4×C22⋊D283C211yesmaximal, characteristic, complemented
10C2×#22583568C211yesmaximal, characteristic, complemented
11C2×#22583567C212yesmaximal, complemented
12C2×#117×C283C211yesmaximal, characteristic, complemented
13C22×Dic566C2212yes—
14C22×D1132C2211yescharacteristic
15C22×D1132C2212yes—
16C22×C22⋊D283C2211yescharacteristic
17C22×C22⋊D283C2212yes—
18C22×C4×D283C2212yes—
19C22×C4×D283C2211yescharacteristic
20#22583609C2218yescomplemented
21#22583598C22116yescomplemented
22#22583596C22116yescomplemented
23#22583585C2218yescomplemented
24#22583584C2218yescomplemented
25#22583583C22116yescomplemented
26#22583572C2218yescomplemented
27C4×C22⋊D283C2218yescomplemented
28#22583568C2218yescomplemented
29#22583567C22116yescomplemented
30C2×C4⋊Dic283C2211yescharacteristic
31C2×Dic283⋊C4C2212yes—
32C2×Dic283⋊C4C2211yescharacteristic
33C2×C22⋊Dic283C2211yescharacteristic
34C2×(C2×D283)⋊C4C2212yes—
35C2×(C2×D283)⋊C4C2212yes—
36C2×(C2×D283)⋊C4C2212yes—
37C2×(C2×D283)⋊C4C2212yes—
38C2×(C2×D283)⋊C4C2211yescharacteristic
39C2×C4×Dic283C2212yes—
40C2×C4×Dic283C2211yescharacteristic
41C23×C4×C283C2211yescharacteristic
42#117×C283C2218yescomplemented
43C2×C4⋊C4×C283C2211yescharacteristic
44C2×C4⋊C4×C283C2211yescharacteristic
45C2×C22⋊C4×C283C2212yes—
46C2×C42×C283C2212yes—
47C23×D283C2311yescharacteristic
48C23×D283C2312yes—
49C2×Dic566—44no—
50C2×Dic566C2318yes—
51C2×D1132—24no—
52C2×D1132—44no—
53C2×D1132C2314yes—
54C2×D1132C2318yes—
55C2×C22⋊D283—24no—
56C2×C22⋊D283—44no—
57C2×C22⋊D283C2314yes—
58C2×C22⋊D283C2318yes—
59C22×Dic283C2311yescharacteristic
60C22×Dic283C2311yescharacteristic
61C22×Dic283C2312yes—
62C22×Dic283C2311yescharacteristic
63C2×C4×D283—28no—
64C2×C4×D283—24no—
65C2×C4×D283C2318yes—
66C2×C4×D283C2314yes—
67C4⋊Dic283C2314yes—
68Dic283⋊C4C2314yes—
69Dic283⋊C4C2318yes—
70C22⋊Dic283C2314yes—
71(C2×D283)⋊C4C2318yes—
72(C2×D283)⋊C4C2318yes—
73(C2×D283)⋊C4C2318yes—
74(C2×D283)⋊C4C2314yes—
75(C2×D283)⋊C4C2318yes—
76C4×Dic283C2318yes—
77C4×Dic283C2314yes—
78C24×C283C2311yescharacteristic
79C22×C4×C283—24no—
80C22×C4×C283C2312yes—
81C22×C4×C283C2311yescharacteristic
82C22×C4×C283C2312yes—
83C22×C4×C283C2314yes—
84C22×C4×C283C2311yescharacteristic
85C4⋊C4×C283C2314yes—
86C4⋊C4×C283C2314yes—
87C22⋊C4×C283C2318yes—
88C42×C283C2318yes—
89C22×D283—24no—
90C22×D283—22no—
91C22×D283—22no—
92C22×D283—24no—
93C22×D283—24no—
94C22×D283—22no—
95C22×D283C2412yes—
96C22×D283C2414yes—
97Dic566—48no—
98D1132—28no—
99D1132—48no—
100C22⋊D283—28no—
101C22⋊D283—48no—
102C2×Dic283—22no—
103C2×Dic283—24no—
104C2×Dic283—22no—
105C2×Dic283#4114yes—
106C2×Dic283C2412yes—
107C2×Dic283C2412yes—
108C2×Dic283C2414yes—
109C2×Dic283C2412yes—
110C4×D283—28no—
111C4×D283—216no—
112C23×C283—22no—
113C23×C283—22no—
114C23×C283—22no—
115C23×C283C2412yes—
116C23×C283C2411yescharacteristic
117C2×C4×C283—22no—
118C2×C4×C283—24no—
119C2×C4×C283—24no—
120C2×C4×C283—28no—
121C2×C4×C283#4114yes—
122C2×C4×C283C2412yes—
123C2×C4×C283C2414yes—
124C2×C4×C283C2414yes—
125C2×C4×C283C2412yes—
126C22×C283—22no—
127C22×C283—22no—
128C22×C283—22no—
129C22×C283—44no—
130C22×C283C2×#4112yes—
131C22×C283C2×#4112yes—
132C22×C283H(5,𝔽2)12yes—
133C22×C283C2511yescharacteristic
134C2×D283—24no—
135C2×D283—22no—
136C2×D283—22no—
137C2×D283—24no—
138C2×D283—24no—
139C2×D283—22no—
140C2×D283—44no—
141C2×D283—48no—
142C4×C283—22no—
143C4×C283—24no—
144C4×C283—24no—
145C4×C283C2×#4114yes—
146Dic283—22no—
147Dic283—24no—
148Dic283—22no—
149Dic283C2×#4114yes—
150C2×C283—42no—
151C2×C283#55514yescomplemented
152C2×C283C22×#4111yescharacteristic
153C2×C283C22×#4111yescharacteristic
154C2×C283C2×H(5,𝔽2)11yescharacteristic
155D283—42no—
156D283—44no—
157C283C2×#55511yescharacteristic, complemented, Sylow
158C2×#555—2831nomaximal, Sylow
159#555—28316no—
160C2×C4⋊Q8—2831no—
161C2×#124—2832no—
162C2×#124—2832no—
163C2×#121—2831no—
164C2×#121—2831no—
165C2×#121—2832no—
166C2×C4×D4—2831no—
167C2×C4×D4—2831no—
168C2×#117—2831no—
169C2×#117—2832no—
170C2×#117D28311yescharacteristic, complemented
171C22×Q8—2832no—
172C22×D4—2831no—
173C22×D4—2832no—
174C22×D4—2831no—
175C22×D4—2832no—
176C23×C4—2832no—
177C23×C4—2831no—
178C23×C4C2×D28311yescharacteristic
179C4⋊Q8—2838no—
180#124—28316no—
181#124—28316no—
182#121—2838no—
183#121—2838no—
184#121—28316no—
185C4×D4—2838no—
186C4×D4—2838no—
187#117—2838no—
188#117—28316no—
189#117C2×D28318yescomplemented
190C2×C4⋊C4—2831no—
191C2×C4⋊C4—2832no—
192C2×C4⋊C4—2831no—
193C2×C4⋊C4C2×D28311yescharacteristic
194C2×C4⋊C4C2×D28311yescharacteristic
195C2×C22⋊C4—2831no—
196C2×C22⋊C4—2832no—
197C2×C22⋊C4—2832no—
198C2×C22⋊C4—2832no—
199C2×C22⋊C4—2832no—
200C2×C22⋊C4—2831no—
201C2×C22⋊C4C2×D28312yes—
202C2×C42—2832no—
203C2×C42—2831no—
204C2×C42C2×D28312yes—
205C24—2832no—
206C24—2831no—
207C24C22×D28311yescharacteristic
208C2×Q8—2838no—
209C2×Q8—11324no—
210C2×D4—2834no—
211C2×D4—2838no—
212C2×D4—2834no—
213C2×D4—2838no—
214C2×D4—5664no—
215C2×D4—5664no—
216C2×D4—11324no—
217C2×D4—11324no—
218C22×C4—24no—
219C22×C4—2831no—
220C22×C4—2831no—
221C22×C4—2831no—
222C22×C4—2832no—
223C22×C4—2838no—
224C22×C4—2834no—
225C22×C4—5668no—
226C22×C4—5664no—
227C22×C4C22×D28314yes—
228C22×C4C22×D28312yes—
229C22×C4C22×D28311yescharacteristic
230C22×C4C22×D28312yes—
231C22×C4C22×D28311yescharacteristic
232C4⋊C4—2834no—
233C4⋊C4—2838no—
234C4⋊C4—2834no—
235C4⋊C4C22×D28314yes—
236C4⋊C4C22×D28314yes—
237C22⋊C4—2834no—
238C22⋊C4—2838no—
239C22⋊C4—2838no—
240C22⋊C4—2838no—
241C22⋊C4—2838no—
242C22⋊C4—2834no—
243C22⋊C4C22×D28318yes—
244C42—2838no—
245C42—2834no—
246C42C22×D28318yes—
247C23—22no—
248C23—22no—
249C23—22no—
250C23—2834no—
251C23—2832no—
252C23—5664no—
253C23—5662no—
254C23—5662no—
255C23—5664no—
256C23—5662no—
257C23—5664no—
258C23C23×D28312yes—
259C23C23×D28311yescharacteristic
260Q8—11328no—
261D4—5668no—
262D4—5668no—
263D4—11328no—
264D4—11328no—
265C2×C4—24no—
266C2×C4—22no—
267C2×C4—24no—
268C2×C4—28no—
269C2×C4—2834no—
270C2×C4—2832no—
271C2×C4—2832no—
272C2×C4—2832no—
273C2×C4—2834no—
274C2×C4—56616no—
275C2×C4—5662no—
276C2×C4—5664no—
277C2×C4—5662no—
278C2×C4—5668no—
279C2×C4#1798539214yes—
280C2×C4C23×D28314yes—
281C2×C4C23×D28312yes—
282C2×C4C23×D28314yes—
283C2×C4C23×D28312yes—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—44no—
288C22—5664no—
289C22—5662no—
290C22—5662no—
291C22—5664no—
292C22—5662no—
293C22—5664no—
294C22—11328no—
295C22—11324no—
296C22#41×D28312yes—
297C22C2×#1798539212yes—
298C22#2258365612yes—
299C22C24×D28311yescharacteristic
300C4—24no—
301C4—22no—
302C4—24no—
303C4—2834no—
304C4—5662no—
305C4—5664no—
306C4—5662no—
307C4C2×#1798539214yes—
308C2—42no—
309C2—11324no—
310C2—11322no—
311C2#3182717814yesdirect product factor
312C2C2×#41×D28311yescharacteristic
313C2C22×#1798539211yescharacteristic
314C2C2×#2258365611yescharacteristic
subgroupG/H
centerC23C23×D283
commutator, cosocleC22×C283C25
FrattiniC22C24×D283
FittingC2×#117×C283C2
socleC23×C283C24
hypercenterC2×#117D283
hypocenterC283C2×#555
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. #31827178C2direct (N × H)
2. C2×#22583609C2semidirect
3. C2×#22583598C2semidirect
4. C2×#22583596C2semidirect
5. C2×#22583585C2semidirect
6. C2×#22583584C2semidirect
7. C2×#22583583C2semidirect
8. C2×#22583572C2semidirect
9. C2×C4×C22⋊D283C2semidirect
10. C2×#22583568C2semidirect
11. C2×#22583567C2semidirect
12. C2×#117×C283C2semidirect
20. #22583609C22semidirect
21. #22583598C22semidirect
22. #22583596C22semidirect
23. #22583585C22semidirect
24. #22583584C22semidirect
25. #22583583C22semidirect
26. #22583572C22semidirect
27. C4×C22⋊D283C22semidirect
28. #22583568C22semidirect
29. #22583567C22semidirect
42. #117×C283C22semidirect
151. C2×C283#555semidirect
157. C283C2×#555semidirect
170. C2×#117D283semidirect
189. #117C2×D283semidirect
311. C2#31827178direct (N × H)

Maximal subgroups

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

subgroupindex
#318271782
C2×#225836092
C2×#225835982
C2×#225835962
C2×#225835852
C2×#225835842
C2×#225835832
C2×#225835722
C2×C4×C22⋊D2832
C2×#225835682
C2×#225835672
C2×#117×C2832
C2×#555283