Finite Group Databasebeta

← C2×#31826625 #49130468

Subgroups — C2×#31826625 #49130468

Order 36224.

760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 760 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#17985392C211yesmaximal, characteristic
2C22×#17985382C211yesmaximal, characteristic, complemented
3C22×#17985379C211yesmaximal, characteristic, complemented
4#31826625C218yesmaximal, direct product factor
5C2×#22583533C211yesmaximal, characteristic, complemented
6C2×#22583530C211yesmaximal, characteristic, complemented
7C2×C22⋊(C283⋊C8)C211yesmaximal, characteristic, complemented
8C2×C22⋊Q8×C283C211yesmaximal, characteristic, complemented
9C2×#17985392—24no—
10C2×#17985392—24no—
11C2×#17985392—22no—
12C2×#17985392C2214yes—
13C22×Dic566C2211yescharacteristic
14C22×D1132C2211yescharacteristic
15C22×C22⋊D283—21no—
16C22×C4×D283—21no—
17C2×#17985382—24no—
18C2×#17985382C2214yescomplemented
19C2×#17985379—24no—
20C2×#17985379C2214yescomplemented
21C22×C283⋊C8C2211yescharacteristic
22C22×C283⋊C8C2211yescharacteristic
23#22583533C2214yescomplemented
24#22583530C2214yescomplemented
25C22⋊(C283⋊C8)C2214yescomplemented
26C22×Q8×C283C2211yescharacteristic
27C23×C4×C283C2211yescharacteristic
28C22⋊Q8×C283—22no—
29C22⋊Q8×C283C2214yescomplemented
30C2×C4⋊C4×C283—21no—
31C2×C4⋊C4×C283C2211yescharacteristic
32C2×C22⋊C4×C283—21no—
33C23×D283—21no—
34#17985392—216no—
35#17985392—28no—
36#17985392—28no—
37C2×Dic566—22no—
38C2×Dic566—21no—
39C2×Dic566D414yes—
40C2×Dic566C2312yes—
41C2×D1132—22no—
42C2×D1132—21no—
43C2×D1132D414yes—
44C2×D1132C2312yes—
45C2×C22⋊D283—28no—
46C2×C22⋊D283—24no—
47C22×Dic283—21no—
48C2×C4×D283—28no—
49C2×C4×D283—24no—
50#17985382—28no—
51#17985379—28no—
52C2×C283⋊C8—22no—
53C2×C283⋊C8—22no—
54C2×C283⋊C8C2312yes—
55C2×C283⋊C8C2312yes—
56C24×C283D411yescharacteristic
57C2×Q8×C283—21no—
58C2×Q8×C283—22no—
59C2×Q8×C283—22no—
60C2×Q8×C283C2312yes—
61C22×C4×C283—22no—
62C22×C4×C283—22no—
63C22×C4×C283—21no—
64C22×C4×C283—21no—
65C22×C4×C283D411yescharacteristic
66C22×C4×C283D412yes—
67C22×C4×C283C2312yes—
68C22×C4×C283C2311yescharacteristic
69C4⋊C4×C283—24no—
70C4⋊C4×C283—21no—
71C4⋊C4×C283C2312yes—
72C22⋊C4×C283—24no—
73C22×D283—24no—
74C22×D283—22no—
75C22×D283—42no—
76C22×D283—42no—
77Dic566—24no—
78Dic566—22no—
79Dic566C2×D414yes—
80D1132—24no—
81D1132—22no—
82D1132C2×D414yes—
83C22⋊D283—216no—
84C2×Dic283—24no—
85C2×Dic283—22no—
86C4×D283—216no—
87C283⋊C8—22no—
88C283⋊C8—22no—
89C23×C283—22no—
90C23×C283—22no—
91C23×C283—22no—
92C23×C283C2×D412yes—
93C23×C283C2×D411yescharacteristic
94Q8×C283—22no—
95Q8×C283—22no—
96Q8×C283—42no—
97C2×C4×C283—22no—
98C2×C4×C283—24no—
99C2×C4×C283—22no—
100C2×C4×C283—22no—
101C2×C4×C283—22no—
102C2×C4×C283—22no—
103C2×C4×C283—42no—
104C2×C4×C283—42no—
105C2×C4×C283C2×D412yes—
106C2×C4×C283C2×D412yes—
107C2×C4×C283C2×D412yes—
108C2×C4×C283C2×D411yescharacteristic
109C2×C4×C283C2411yescharacteristic
110C22×C283—22no—
111C22×C283—22no—
112C22×C283—22no—
113C22×C283—44no—
114C22×C283#12012yes—
115C22×C283#13512yes—
116C22×C283#13712yes—
117C22×C283C22×D411yescharacteristic
118C2×D283—24no—
119C2×D283—42no—
120C2×D283—42no—
121C2×D283—48no—
122C4×C283—22no—
123C4×C283—42no—
124C4×C283—42no—
125C4×C283#12012yes—
126C4×C283C22×D411yescharacteristic
127C4×C283C22×D411yescharacteristic
128Dic283—24no—
129C2×C283—42no—
130C2×C283#45214yescomplemented
131C2×C283C2×#12011yescharacteristic
132C2×C283C2×#13511yescharacteristic
133C2×C283C2×#13711yescharacteristic
134D283—44no—
135C283C2×#45211yescharacteristic, complemented, Sylow
136C2×#452—2831nomaximal, Sylow
137C22×#41—2831no—
138C22×Q16—2831no—
139C22×SD16—2831no—
140C2×C22⋊Q8D28311yescharacteristic, complemented
141#452—2838no—
142C2×#103—2831no—
143C2×#102—2831no—
144C2×C22⋊C8—2831no—
145C2×#41—2834no—
146C2×#41—5664no—
147C2×#41—5664no—
148C2×#41—5662no—
149C22×Q8—2831no—
150C22×Q8C2×D28311yescharacteristic
151C22×D4—2831no—
152C22×D4—5661no—
153C23×C4—5661no—
154C23×C4C2×D28311yescharacteristic
155C2×Q16—2834no—
156C2×Q16—5664no—
157C2×SD16—2834no—
158C2×SD16—5664no—
159C22×C8—2831no—
160C22×C8—2831no—
161C22⋊Q8—22no—
162C22⋊Q8C2×D28314yescomplemented
163C2×C4⋊C4—21no—
164C2×C4⋊C4C2×D28311yescharacteristic
165C2×C22⋊C4—21no—
166#103—2834no—
167#102—2834no—
168C22⋊C8—2834no—
169C24—5661no—
170C24C22⋊D28311yescharacteristic
171#41—5668no—
172#41—5668no—
173#41—56616no—
174C2×Q8—21no—
175C2×Q8—22no—
176C2×Q8—22no—
177C2×Q8—2834no—
178C2×Q8—2832no—
179C2×Q8—5662no—
180C2×Q8—5661no—
181C2×Q8C22×D28312yes—
182C2×D4—2834no—
183C2×D4—2832no—
184C2×D4—5668no—
185C2×D4—5664no—
186C2×D4—5662no—
187C2×D4—5661no—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—5668no—
193C22×C4—5661no—
194C22×C4—5664no—
195C22×C4C22⋊D28312yes—
196C22×C4C22⋊D28311yescharacteristic
197C22×C4C22×D28312yes—
198C22×C4C22×D28311yescharacteristic
199Q16—5668no—
200SD16—5668no—
201C2×C8—2832no—
202C2×C8—2832no—
203C2×C8—5662no—
204C2×C8—5662no—
205C4⋊C4—24no—
206C4⋊C4—21no—
207C4⋊C4C22×D28312yes—
208C22⋊C4—24no—
209C23—22no—
210C23—22no—
211C23—22no—
212C23—5664no—
213C23—5662no—
214C23—11322no—
215C23—11322no—
216C23C2×C22⋊D28312yes—
217C23C2×C22⋊D28311yescharacteristic
218Q8—22no—
219Q8—22no—
220Q8—42no—
221Q8—2834no—
222Q8—5664no—
223Q8—5662no—
224D4—2834no—
225D4—56616no—
226D4—5664no—
227D4—5662no—
228C2×C4—22no—
229C2×C4—24no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—56616no—
237C2×C4—5664no—
238C2×C4—5662no—
239C2×C4D4×D28312yes—
240C2×C4D4×D28312yes—
241C2×C4C2×C22⋊D28312yes—
242C2×C4C2×C22⋊D28311yescharacteristic
243C2×C4C23×D28311yescharacteristic
244C8—5662no—
245C8—5662no—
246C22—22no—
247C22—22no—
248C22—22no—
249C22—44no—
250C22—5664no—
251C22—11322no—
252C22—11322no—
253C22—11328no—
254C22#2258357812yes—
255C22#2258363012yes—
256C22#2258364112yes—
257C22C22×C22⋊D28311yescharacteristic
258C4—22no—
259C4—42no—
260C4—42no—
261C4—5664no—
262C4#2258357812yes—
263C4C2×D4×D28311yescharacteristic
264C4C2×D4×D28311yescharacteristic
265C2—42no—
266C2—11324no—
267C2#3182662514yesdirect product factor
268C2C2×#2258357811yescharacteristic
269C2C2×#2258363011yescharacteristic
270C2C2×#2258364111yescharacteristic
subgroupG/H
centerC23C2×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×C22⋊Q8×C283C2
socleC23×C283C2×D4
prime radicalC22×#17985392C2
hypercenterC2×C22⋊Q8D283
hypocenterC283C2×#452
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C22×#17985382C2semidirect
3. C22×#17985379C2semidirect
4. #31826625C2direct (N × H)
5. C2×#22583533C2semidirect
6. C2×#22583530C2semidirect
7. C2×C22⋊(C283⋊C8)C2semidirect
8. C2×C22⋊Q8×C283C2semidirect
18. C2×#17985382C22semidirect
20. C2×#17985379C22semidirect
23. #22583533C22semidirect
24. #22583530C22semidirect
25. C22⋊(C283⋊C8)C22semidirect
29. C22⋊Q8×C283C22semidirect
130. C2×C283#452semidirect
135. C283C2×#452semidirect
140. C2×C22⋊Q8D283semidirect
162. C22⋊Q8C2×D283semidirect
267. C2#31826625direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#179853922
C22×#179853822
C22×#179853792
#318266252
C2×#225835332
C2×#225835302
C2×C22⋊(C283⋊C8)2
C2×C22⋊Q8×C2832
C2×#452283