Finite Group Databasebeta

← C2×#31827170 #49134790

Subgroups — C2×#31827170 #49134790

Order 36224.

1200 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827170C2116yesmaximal, direct product factor
2C2×#22583609C211yesmaximal, characteristic, complemented
3C2×#22583600C212yesmaximal, complemented
4C2×#22583590C211yesmaximal, characteristic, complemented
5C2×#22583589C211yesmaximal, characteristic, complemented
6C2×#22583589C212yesmaximal, complemented
7C2×#22583588C212yesmaximal, complemented
8C2×#22583575C211yesmaximal, characteristic, complemented
9C2×C4×C22⋊D283C212yesmaximal
10C2×C4×C22⋊D283C211yesmaximal, characteristic
11C2×C4⋊C4×D283C211yesmaximal, characteristic, complemented
12C22×C4⋊C4×C283C211yesmaximal, characteristic, complemented
13C22×Dic566C2211yescharacteristic
14C22×Dic566C2212yes—
15C22×C22⋊D283C2211yescharacteristic
16C22×C4×D283C2211yescharacteristic
17C22×C4×D283C2212yes—
18#22583609C2218yescomplemented
19#22583600C22116yescomplemented
20#22583590C2218yescomplemented
21#22583589C2218yescomplemented
22#22583589C22116yescomplemented
23#22583588C22116yescomplemented
24#22583575C2218yescomplemented
25C4×C22⋊D283C2218yes—
26C4×C22⋊D283C22116yes—
27C2×C4⋊Dic283C2212yes—
28C2×C4⋊Dic283C2211yescharacteristic
29C2×Dic283⋊C4C2212yes—
30C2×Dic283⋊C4C2212yes—
31C2×Dic283⋊C4C2212yes—
32C2×Dic283⋊C4C2211yescharacteristic
33C2×Dic283⋊C4C2212yes—
34C4⋊C4×D283C2218yescomplemented
35C2×C22⋊Dic283C2212yes—
36C2×C22⋊Dic283C2211yescharacteristic
37C2×(C2×D283)⋊C4C2211yescharacteristic
38C2×(C2×D283)⋊C4C2212yes—
39C2×C4×Dic283C2212yes—
40C2×C4×Dic283C2211yescharacteristic
41C23×C4×C283C2211yescharacteristic
42C23×C4×C283C2212yes—
43C2×C4⋊C4×C283C2212yes—
44C2×C4⋊C4×C283C2211yescharacteristic
45C2×C4⋊C4×C283C2211yescharacteristic
46C2×C4⋊C4×C283C2218yescomplemented
47C23×D283C2311yescharacteristic
48C2×Dic566—24no—
49C2×Dic566—44no—
50C2×Dic566C2314yes—
51C2×Dic566C2318yes—
52C2×C22⋊D283Q818yescomplemented
53C2×C22⋊D283C2314yes—
54C22×Dic283C2312yes—
55C22×Dic283C2311yescharacteristic
56C22×Dic283C2311yescharacteristic
57C22×Dic283C2312yes—
58C22×Dic283C2311yescharacteristic
59C2×C4×D283—24no—
60C2×C4×D283—44no—
61C2×C4×D283C2314yes—
62C2×C4×D283C2318yes—
63C4⋊Dic283C2314yes—
64C4⋊Dic283C2318yes—
65Dic283⋊C4C2318yes—
66Dic283⋊C4C2314yes—
67Dic283⋊C4C2318yes—
68Dic283⋊C4C2318yes—
69Dic283⋊C4C2318yes—
70C22⋊Dic283C2318yes—
71C22⋊Dic283C2314yes—
72(C2×D283)⋊C4C2314yes—
73(C2×D283)⋊C4C2318yes—
74C4×Dic283C2318yes—
75C4×Dic283C2314yes—
76C24×C283C2311yescharacteristic
77C22×C4×C283—24no—
78C22×C4×C283—44no—
79C22×C4×C283C2312yes—
80C22×C4×C283C2311yescharacteristic
81C22×C4×C283C2312yes—
82C22×C4×C283C2314yes—
83C22×C4×C283C2318yes—
84C22×C4×C283C2311yescharacteristic
85C4⋊C4×C283C2314yes—
86C4⋊C4×C283C2318yes—
87C4⋊C4×C283C2314yes—
88C22×D283—22no—
89C22×D283—22no—
90C22×D283C2×Q814yes—
91C22×D283C2412yes—
92Dic566—28no—
93Dic566—48no—
94C22⋊D283C2×Q8116yescomplemented
95C2×Dic283—22no—
96C2×Dic283—24no—
97C2×Dic283—24no—
98C2×Dic283—22no—
99C2×Dic283C2×Q814yes—
100C2×Dic283C2414yes—
101C2×Dic283C2412yes—
102C2×Dic283C2412yes—
103C2×Dic283C2414yes—
104C2×Dic283C2412yes—
105C4×D283—28no—
106C4×D283—48no—
107C23×C283—22no—
108C23×C283—22no—
109C23×C283C2×Q814yes—
110C23×C283C2412yes—
111C23×C283C2411yescharacteristic
112C2×C4×C283—22no—
113C2×C4×C283—24no—
114C2×C4×C283—24no—
115C2×C4×C283—28no—
116C2×C4×C283—48no—
117C2×C4×C283#4114yes—
118C2×C4×C283C2414yes—
119C2×C4×C283C2412yes—
120C2×C4×C283C2414yes—
121C2×C4×C283C2412yes—
122C22×C283—28no—
123C22×C283—22no—
124C22×C283—22no—
125C22×C283C22×Q814yes—
126C22×C283C22×Q812yes—
127C22×C283C2×#4112yes—
128C22×C283H(5,𝔽2)12yes—
129C22×C283C2511yescharacteristic
130C2×D283—28no—
131C2×D283—22no—
132C2×D283—22no—
133C2×D283C22×Q814yes—
134C4×C283—22no—
135C4×C283—24no—
136C4×C283—24no—
137C4×C283C2×#4114yes—
138Dic283—22no—
139Dic283—24no—
140Dic283—24no—
141Dic283—22no—
142Dic283C22×Q814yes—
143C2×C283—24no—
144C2×C283#55414yescomplemented
145C2×C283C23×Q811yescharacteristic
146C2×C283C22×#4111yescharacteristic
147C2×C283C2×H(5,𝔽2)11yescharacteristic
148D283—24no—
149C283C2×#55411yescharacteristic, complemented, Sylow
150C2×#554—2831nomaximal, Sylow
151#554—28316no—
152C2×C4⋊Q8—2831no—
153C2×#125—2832no—
154C2×C22⋊Q8—2832no—
155C2×C22⋊Q8—2831no—
156C2×C22⋊Q8—2832no—
157C2×C22⋊Q8—2831no—
158C2×C4×Q8—2831no—
159C2×C4×D4—2832no—
160C2×C4×D4—2831no—
161C22×C4⋊C4—2831no—
162C22×C4⋊C4D28311yescharacteristic, complemented
163C22×Q8—2831no—
164C22×Q8—2832no—
165C22×D4—2831no—
166C23×C4—2831no—
167C23×C4—2832no—
168C23×C4C2×D28311yescharacteristic
169C23×C4C2×D28312yes—
170C4⋊Q8—2838no—
171#125—28316no—
172C22⋊Q8—28316no—
173C22⋊Q8—2838no—
174C22⋊Q8—28316no—
175C22⋊Q8—2838no—
176C4×Q8—2838no—
177C4×D4—28316no—
178C4×D4—2838no—
179C2×C4⋊C4—2832no—
180C2×C4⋊C4—2831no—
181C2×C4⋊C4—2831no—
182C2×C4⋊C4—2832no—
183C2×C4⋊C4—2832no—
184C2×C4⋊C4—2832no—
185C2×C4⋊C4—2832no—
186C2×C4⋊C4—2838no—
187C2×C4⋊C4C2×D28311yescharacteristic
188C2×C4⋊C4C2×D28312yes—
189C2×C4⋊C4C2×D28311yescharacteristic
190C2×C4⋊C4C2×D28318yescomplemented
191C2×C22⋊C4—2832no—
192C2×C22⋊C4—2831no—
193C2×C22⋊C4—2832no—
194C2×C22⋊C4—2831no—
195C2×C42—2832no—
196C2×C42—2831no—
197C24—2831no—
198C24C22×D28311yescharacteristic
199C2×Q8—2834no—
200C2×Q8—2838no—
201C2×Q8—5664no—
202C2×Q8—11324no—
203C2×D4—2838no—
204C2×D4—2834no—
205C22×C4—24no—
206C22×C4—44no—
207C22×C4—2831no—
208C22×C4—2832no—
209C22×C4—2831no—
210C22×C4—2831no—
211C22×C4—2832no—
212C22×C4—2834no—
213C22×C4—2838no—
214C22×C4—5664no—
215C22×C4—11324no—
216C22×C4C22×D28314yes—
217C22×C4C22×D28312yes—
218C22×C4C22×D28311yescharacteristic
219C22×C4C22×D28312yes—
220C22×C4C22×D28318yes—
221C22×C4C22×D28311yescharacteristic
222C4⋊C4—2838no—
223C4⋊C4—2834no—
224C4⋊C4—2838no—
225C4⋊C4—2838no—
226C4⋊C4—2838no—
227C4⋊C4—2834no—
228C4⋊C4—2838no—
229C4⋊C4C22×D28314yes—
230C4⋊C4C22×D28318yes—
231C4⋊C4C22×D28314yes—
232C22⋊C4—2838no—
233C22⋊C4—2834no—
234C22⋊C4—2838no—
235C22⋊C4—2834no—
236C42—2838no—
237C42—2834no—
238C23—22no—
239C23—22no—
240C23—2834no—
241C23—2832no—
242C23—5662no—
243C23—5662no—
244C23Q8×D28314yes—
245C23C23×D28312yes—
246C23C23×D28311yescharacteristic
247Q8—5668no—
248Q8—11328no—
249D4—28316no—
250C2×C4—22no—
251C2×C4—24no—
252C2×C4—24no—
253C2×C4—28no—
254C2×C4—48no—
255C2×C4—2834no—
256C2×C4—2832no—
257C2×C4—2834no—
258C2×C4—2832no—
259C2×C4—2832no—
260C2×C4—2834no—
261C2×C4—5662no—
262C2×C4—5664no—
263C2×C4—5664no—
264C2×C4—5662no—
265C2×C4—5668no—
266C2×C4—11328no—
267C2×C4#1798539214yes—
268C2×C4C23×D28314yes—
269C2×C4C23×D28312yes—
270C2×C4C23×D28314yes—
271C2×C4C23×D28312yes—
272C22—22no—
273C22—22no—
274C22—28no—
275C22—2834no—
276C22—5662no—
277C22—5662no—
278C22—5668no—
279C22C2×Q8×D28314yes—
280C22C2×Q8×D28312yes—
281C22C2×#1798539212yes—
282C22#2258365512yes—
283C22C24×D28311yescharacteristic
284C4—22no—
285C4—24no—
286C4—24no—
287C4—2834no—
288C4—5662no—
289C4—5664no—
290C4—5664no—
291C4—5662no—
292C4C2×#1798539214yes—
293C2—24no—
294C2—5664no—
295C2#3182717014yesdirect product factor
296C2C22×Q8×D28311yescharacteristic
297C2C22×#1798539211yescharacteristic
298C2C2×#2258365511yescharacteristic
subgroupG/H
centerC23C23×D283
commutator, cosocleC22×C283C25
FrattiniC22C24×D283
FittingC22×C4⋊C4×C283C2
socleC23×C283C24
prime radicalC22×C22⋊D283C22
hypercenterC22×C4⋊C4D283
hypocenterC283C2×#554
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #31827170C2direct (N × H)
2. C2×#22583609C2semidirect
3. C2×#22583600C2semidirect
4. C2×#22583590C2semidirect
5. C2×#22583589C2semidirect
6. C2×#22583589C2semidirect
7. C2×#22583588C2semidirect
8. C2×#22583575C2semidirect
11. C2×C4⋊C4×D283C2semidirect
12. C22×C4⋊C4×C283C2semidirect
18. #22583609C22semidirect
19. #22583600C22semidirect
20. #22583590C22semidirect
21. #22583589C22semidirect
22. #22583589C22semidirect
23. #22583588C22semidirect
24. #22583575C22semidirect
34. C4⋊C4×D283C22semidirect
46. C2×C4⋊C4×C283C22semidirect
52. C2×C22⋊D283Q8semidirect
94. C22⋊D283C2×Q8semidirect
144. C2×C283#554semidirect
149. C283C2×#554semidirect
162. C22×C4⋊C4D283semidirect
190. C2×C4⋊C4C2×D283semidirect
295. C2#31827170direct (N × H)

Maximal subgroups

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

subgroupindex
#318271702
C2×#225836092
C2×#225836002
C2×#225835902
C2×#225835892
C2×#225835882
C2×#225835752
C2×C4×C22⋊D2832
C2×C4⋊C4×D2832
C22×C4⋊C4×C2832
C2×#554283