Finite Group Databasebeta

← C2×#31826658 #49130671

Subgroups — C2×#31826658 #49130671

Order 36224.

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

normal subgroups only

This group has 648 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×#17985377C211yesmaximal, characteristic, complemented
2C2×#22583606C211yesmaximal, characteristic, complemented
3C2×D4×Dic283C211yesmaximal, characteristic, complemented
4#31826658C218yesmaximal, direct product factor
5C2×Dic283⋊C8C211yesmaximal, characteristic, complemented
6C2×#22583532C211yesmaximal, characteristic, complemented
7C2×#22583531C211yesmaximal, characteristic, complemented
8C22×D8×C283C211yesmaximal, characteristic, complemented
9C22×D1132C2211yescharacteristic
10C22×C22⋊D283—21no—
11C22×C22⋊D283—21no—
12C23×Dic283—21no—
13C2×#17985377—24no—
14C2×#17985377C2214yescomplemented
15C22×C283⋊C8C2211yescharacteristic
16#22583606—22no—
17#22583606C2214yescomplemented
18D4×Dic283—22no—
19D4×Dic283C2214yescomplemented
20C2×C4⋊Dic283C2211yescharacteristic
21C2×C22⋊Dic283—21no—
22C2×C4×Dic283C2211yescharacteristic
23Dic283⋊C8C2214yescomplemented
24#22583532C2214yescomplemented
25#22583531C2214yescomplemented
26C22×D4×C283C2211yescharacteristic
27C22×D4×C283C2211yescharacteristic
28C2×D8×C283—24no—
29C2×D8×C283C2214yescomplemented
30C22×C8×C283C2211yescharacteristic
31C23×D283—21no—
32C2×D1132—22no—
33C2×D1132—21no—
34C2×D1132—22no—
35C2×D1132C2312yes—
36C2×C22⋊D283—24no—
37C2×C22⋊D283—24no—
38C2×C22⋊D283—44no—
39C2×C22⋊D283—44no—
40C22×Dic283—24no—
41C22×Dic283—21no—
42C22×Dic283—44no—
43C22×Dic283D411yescharacteristic
44C22×Dic283D411yescharacteristic
45#17985377—28no—
46C2×C283⋊C8—22no—
47C2×C283⋊C8C2312yes—
48C4⋊Dic283—21no—
49C4⋊Dic283C2312yes—
50C22⋊Dic283—24no—
51C4×Dic283D412yes—
52C4×Dic283C2312yes—
53C24×C283—21no—
54C24×C283—21no—
55C2×D4×C283—21no—
56C2×D4×C283—22no—
57C2×D4×C283—21no—
58C2×D4×C283—22no—
59C2×D4×C283—22no—
60C2×D4×C283D414yescomplemented
61C2×D4×C283C2312yes—
62C2×D4×C283C2312yes—
63C22×C4×C283C2311yescharacteristic
64D8×C283—28no—
65C2×C8×C283—22no—
66C2×C8×C283C2312yes—
67C22×D283—22no—
68C22×D283—42no—
69C22×D283—42no—
70C22×D283—42no—
71D1132—22no—
72D1132—22no—
73D1132—42no—
74C22⋊D283—48no—
75C22⋊D283—48no—
76C2×Dic283—22no—
77C2×Dic283—22no—
78C2×Dic283—42no—
79C2×Dic283—48no—
80C2×Dic283D814yescomplemented
81C2×Dic283C2×D412yes—
82C2×Dic283C2×D412yes—
83C283⋊C8—22no—
84C23×C283—24no—
85C23×C283—22no—
86C23×C283—22no—
87C23×C283—42no—
88C23×C283—42no—
89C23×C283—42no—
90C23×C283—42no—
91C23×C283—42no—
92C23×C283C2×D411yescharacteristic
93D4×C283—24no—
94D4×C283—22no—
95D4×C283—22no—
96D4×C283—22no—
97D4×C283—42no—
98D4×C283C2×D414yescomplemented
99C2×C4×C283C2×D411yescharacteristic
100C2×C4×C283C2×D412yes—
101C2×C4×C283#4112yes—
102C2×C4×C283C2411yescharacteristic
103C8×C283—22no—
104C22×C283—24no—
105C22×C283—42no—
106C22×C283—42no—
107C22×C283—48no—
108C22×C283—42no—
109C22×C283—42no—
110C22×C283—42no—
111C22×C283—84no—
112C22×C283#12112yes—
113C22×C283C2×D812yes—
114C22×C283AGL(1,ℤ/8)12yes—
115C22×C283C22×D411yescharacteristic
116C2×D283—42no—
117C2×D283—42no—
118C2×D283—42no—
119C2×D283—84no—
120C4×C283#12112yes—
121C4×C283C22×D411yescharacteristic
122C4×C283C2×#4111yescharacteristic
123Dic283—22no—
124Dic283—42no—
125Dic283C2×D814yescomplemented
126C2×C283—44no—
127C2×C283—82no—
128C2×C283#45914yescomplemented
129C2×C283C2×#12111yescharacteristic
130C2×C283C22×D811yescharacteristic
131C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
132D283—82no—
133C283C2×#45911yescharacteristic, complemented, Sylow
134C2×#459—2831nomaximal, Sylow
135C22×D8—2831no—
136C22×D8D28311yescharacteristic, complemented
137C2×#127—2831no—
138C2×C4×D4—2831no—
139#459—2838no—
140C2×C4⋊C8—2831no—
141C2×#102—2831no—
142C2×#102—2831no—
143C22×D4—2831no—
144C22×D4—5661no—
145C22×D4—5661no—
146C22×D4C2×D28311yescharacteristic
147C22×D4C2×D28311yescharacteristic
148C23×C4—5661no—
149C2×D8—24no—
150C2×D8—2834no—
151C2×D8—5664no—
152C2×D8C2×D28314yescomplemented
153C22×C8—2831no—
154C22×C8C2×D28311yescharacteristic
155#127—2834no—
156#127—5662no—
157C4×D4—2834no—
158C4×D4—5662no—
159C2×C4⋊C4—2831no—
160C2×C22⋊C4—5661no—
161C2×C42—2831no—
162C4⋊C8—2834no—
163#102—2834no—
164#102—2834no—
165C24—21no—
166C24—21no—
167C24—5661no—
168C2×D4—21no—
169C2×D4—21no—
170C2×D4—22no—
171C2×D4—22no—
172C2×D4—22no—
173C2×D4—2832no—
174C2×D4—5664no—
175C2×D4—5664no—
176C2×D4—5661no—
177C2×D4—5662no—
178C2×D4—5662no—
179C2×D4—11324no—
180C2×D4—11324no—
181C2×D4C22⋊D28314yescomplemented
182C2×D4C22×D28312yes—
183C2×D4C22×D28312yes—
184C22×C4—2831no—
185C22×C4—2831no—
186C22×C4—5664no—
187C22×C4—5661no—
188C22×C4—11324no—
189C22×C4C22×D28311yescharacteristic
190D8—28no—
191D8—5668no—
192C2×C8—22no—
193C2×C8—2832no—
194C2×C8—5662no—
195C2×C8C22×D28312yes—
196C4⋊C4—2832no—
197C4⋊C4—5661no—
198C22⋊C4—5664no—
199C42—2832no—
200C42—2832no—
201C23—24no—
202C23—22no—
203C23—22no—
204C23—42no—
205C23—42no—
206C23—42no—
207C23—42no—
208C23—42no—
209C23—5662no—
210C23—11322no—
211C23—11322no—
212C23—11322no—
213C23D4×D28311yescharacteristic
214D4—24no—
215D4—22no—
216D4—22no—
217D4—22no—
218D4—42no—
219D4—5662no—
220D4—5662no—
221D4—11328no—
222D4—11328no—
223D4—11322no—
224D4C2×C22⋊D28314yescomplemented
225C2×C4—2834no—
226C2×C4—2832no—
227C2×C4—2832no—
228C2×C4—5662no—
229C2×C4—5662no—
230C2×C4—11328no—
231C2×C4—11322no—
232C2×C4D4×D28311yescharacteristic
233C2×C4C2×C22⋊D28312yes—
234C2×C4#1798539112yes—
235C2×C4C23×D28311yescharacteristic
236C8—22no—
237C8—5662no—
238C22—24no—
239C22—42no—
240C22—42no—
241C22—48no—
242C22—42no—
243C22—42no—
244C22—42no—
245C22—84no—
246C22—11322no—
247C22—11322no—
248C22—11322no—
249C22—22644no—
250C22#2258358212yes—
251C22D8×D28312yes—
252C22#2258363412yes—
253C22C2×D4×D28311yescharacteristic
254C4—2834no—
255C4—5662no—
256C4—11322no—
257C4#2258358212yes—
258C4C22×C22⋊D28311yescharacteristic
259C4C2×#1798539111yescharacteristic
260C2—44no—
261C2—82no—
262C2—22642no—
263C2#3182665814yesdirect product factor
264C2C2×#2258358211yescharacteristic
265C2C2×D8×D28311yescharacteristic
266C2C2×#2258363411yescharacteristic
subgroupG/H
centerC23D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC22×D8×C283C2
socleC23×C283C2×D4
hypercenterC22×D8D283
hypocenterC283C2×#459
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C22×#17985377C2semidirect
2. C2×#22583606C2semidirect
3. C2×D4×Dic283C2semidirect
4. #31826658C2direct (N × H)
5. C2×Dic283⋊C8C2semidirect
6. C2×#22583532C2semidirect
7. C2×#22583531C2semidirect
8. C22×D8×C283C2semidirect
14. C2×#17985377C22semidirect
17. #22583606C22semidirect
19. D4×Dic283C22semidirect
23. Dic283⋊C8C22semidirect
24. #22583532C22semidirect
25. #22583531C22semidirect
29. C2×D8×C283C22semidirect
60. C2×D4×C283D4semidirect
80. C2×Dic283D8semidirect
98. D4×C283C2×D4semidirect
125. Dic283C2×D8semidirect
128. C2×C283#459semidirect
133. C283C2×#459semidirect
136. C22×D8D283semidirect
152. C2×D8C2×D283semidirect
181. C2×D4C22⋊D283semidirect
224. D4C2×C22⋊D283semidirect
263. C2#31826658direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#179853772
C2×#225836062
C2×D4×Dic2832
#318266582
C2×Dic283⋊C82
C2×#225835322
C2×#225835312
C22×D8×C2832
C2×#459283