Finite Group Databasebeta

← #15685144

Subgroups — #15685144

Order 2944.

472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×Q16×D23C212yesmaximal, complemented
2Q8×D92C211yesmaximal, characteristic
3#13093082C211yesmaximal, characteristic
4#13092796C211yesmaximal, characteristic, complemented
5#13092657C212yesmaximal, complemented
6#13092628C211yesmaximal, characteristic, complemented
7#13092574C212yesmaximal, complemented
8#13092571C212yesmaximal, complemented
9C4×#67275C211yesmaximal, characteristic, complemented
10#13092482C211yesmaximal, characteristic
11C23×#462C211yesmaximal, characteristic, complemented
12C2×Q8×D23C2212yes—
13C2×Q8×D23C2212yes—
14C2×Q16×C23C2212yes—
15C23×C4⋊Q8C2211yescharacteristic
16C4×Q8×C23C2211yescharacteristic
17#10625117C2212yes—
18C2×#67275C2212yes—
19C2×#67275C2212yes—
20C2×#67275C2211yescharacteristic
21Q16×D23—28no—
22C2×Dic92C2212yes—
23C2×C8×D23C2212yes—
24#10625068—22no—
25#10625068C2212yes—
26#10625067—22no—
27#10625064—21no—
28#10625059—21no—
29C4×D92—21no—
30C4×D92C2211yescharacteristic
31#10625040—21no—
32#10625040C2211yescharacteristic
33C4×Dic46C2211yescharacteristic
34C23×C4⋊C8C2211yescharacteristic
35C23×#103C2212yes—
36#10625017C2211yescharacteristic
37(C2×D23)⋊C8C2212yes—
38#10624998C2212yes—
39#10624992C2211yescharacteristic
40#10624989C2211yescharacteristic
41C4×C23⋊C8C2211yescharacteristic
42C2×Q8×C23C2312yes—
43C2×Q8×C23C2311yescharacteristic
44Q8×D23—24no—
45Q8×D23—24no—
46Q8×D23—42no—
47Q8×D23—42no—
48C2×D92D411yescharacteristic
49C2×C4×D23—22no—
50C2×C4×D23—22no—
51C2×C4×D23C2312yes—
52C2×Dic46—22no—
53C2×Dic46—22no—
54C2×Dic46C2312yes—
55C2×Dic46C2311yescharacteristic
56Q16×C23—24no—
57C2×C8×C23C2312yes—
58C4⋊C4×C23—21no—
59C4⋊C4×C23—21no—
60C4⋊C4×C23—21no—
61C4⋊C4×C23C2311yescharacteristic
62C42×C23—21no—
63C42×C23C2311yescharacteristic
64#67275—24no—
65#67275—42no—
66#67275D414yescomplemented
67(C2×D23)⋊C4—22no—
68(C2×D23)⋊C4—22no—
69(C2×D23)⋊C4D412yes—
70C4⋊Dic23—21no—
71C4⋊Dic23—21no—
72C4⋊Dic23—22no—
73C4⋊Dic23D411yescharacteristic
74C4⋊Dic23C2311yescharacteristic
75Dic23⋊C4—21no—
76Dic23⋊C4—22no—
77C4×Dic23—21no—
78C2×C23⋊C8C2311yescharacteristic
79C2×C23⋊C8C2311yescharacteristic
80Dic92—24no—
81C8×D23—24no—
82C22×D23C2×D412yes—
83Q8×C23—21no—
84Q8×C23—22no—
85Q8×C23—22no—
86Q8×C23C2×D412yes—
87C2×C4×C23—21no—
88C2×C4×C23—22no—
89C2×C4×C23—21no—
90C2×C4×C23C2×D411yescharacteristic
91C2×C4×C23C2×D411yescharacteristic
92C2×C4×C23C2411yescharacteristic
93C2×Dic23—21no—
94C2×Dic23—21no—
95C2×Dic23—22no—
96C2×Dic23C2×D412yes—
97D92Q1614yescomplemented
98C4×D23—22no—
99C4×D23—22no—
100C4×D23—44no—
101C4×D23—44no—
102Dic46—21no—
103Dic46—22no—
104Dic46—22no—
105Dic46—44no—
106Dic46—44no—
107Dic46C2×D412yes—
108C8×C23—22no—
109C23⋊C8—21no—
110C23⋊C8C2×D412yes—
111D4×Q16—231nomaximal, Sylow
112C22×C23C22×D411yescharacteristic
113C2×D23—22no—
114C2×D23—22no—
115C2×D23C2×Q1614yescomplemented
116C4×C23—22no—
117C4×C23—21no—
118C4×C23—42no—
119C4×C23—41no—
120C4×C23C2×Q1612yescomplemented
121C4×C23C22×D411yescharacteristic
122C4×C23H(5,𝔽2)11yescharacteristic
123Dic23—22no—
124Dic23—22no—
125Dic23—42no—
126Dic23—41no—
127C22×Q16—232no—
128D4×Q8—231no—
129D4×Q8—231no—
130#494—231no—
131#467—232no—
132#462—231no—
133#462D2311yescharacteristic, complemented
134#451—232no—
135#451—232no—
136C4×Q16—231no—
137C8×D4—231no—
138C2×C23D4211yescharacteristic
139C2×C23C22×Q1611yescharacteristic
140C2×C23#57811yescharacteristic
141D23—24no—
142C22×Q8—232no—
143C22×Q8—232no—
144C2×Q16—231no—
145C2×Q16—232no—
146C2×Q16—232no—
147C2×Q16—232no—
148C2×Q16—468no—
149C2×Q16C2×D2312yes—
150C22×C8—232no—
151C4⋊Q8—231no—
152C4⋊Q8—461no—
153C4⋊Q8—461no—
154C4⋊Q8C2×D2311yescharacteristic
155C22⋊Q8—232no—
156C22⋊Q8—232no—
157C22⋊Q8—462no—
158C22⋊Q8—462no—
159C4×Q8—231no—
160C4×Q8C2×D2311yescharacteristic
161C4×D4—231no—
162C4×D4—461no—
163C4×D4—461no—
164#107—231no—
165C4⋊C8C2×D2311yescharacteristic
166#103—231no—
167#103—232no—
168#103—231no—
169#103C2×D2312yes—
170C22⋊C8—232no—
171C4×C8—231no—
172C23D4×Q1611yescharacteristic, complemented, Sylow
173C2×Q8—231no—
174C2×Q8—232no—
175C2×Q8—462no—
176C2×Q8—462no—
177C2×Q8—464no—
178C2×Q8—464no—
179C2×Q8—922no—
180C2×Q8—922no—
181C2×Q8C22×D2312yes—
182C2×Q8C22×D2311yescharacteristic
183C2×D4—231no—
184C22×C4—232no—
185C22×C4—462no—
186C22×C4—462no—
187Q16—24no—
188Q16—234no—
189Q16—464no—
190Q16—464no—
191Q16—922no—
192C2×C8—231no—
193C2×C8—231no—
194C2×C8—464no—
195C2×C8C22×D2312yes—
196C4⋊C4—21no—
197C4⋊C4—21no—
198C4⋊C4—21no—
199C4⋊C4—231no—
200C4⋊C4—231no—
201C4⋊C4—462no—
202C4⋊C4—462no—
203C4⋊C4—461no—
204C4⋊C4—461no—
205C4⋊C4—461no—
206C4⋊C4C22×D2311yescharacteristic
207C22⋊C4—232no—
208C22⋊C4—462no—
209C22⋊C4—462no—
210C42—21no—
211C42—461no—
212C42C22×D2311yescharacteristic
213C23—232no—
214Q8—21no—
215Q8—22no—
216Q8—22no—
217Q8—232no—
218Q8—461no—
219Q8—462no—
220Q8—462no—
221Q8—924no—
222Q8—924no—
223Q8D4×D2312yes—
224D4—234no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—232no—
229C2×C4—461no—
230C2×C4—462no—
231C2×C4—462no—
232C2×C4—461no—
233C2×C4—462no—
234C2×C4—924no—
235C2×C4—924no—
236C2×C4D4×D2311yescharacteristic
237C2×C4D4×D2311yescharacteristic
238C2×C4C23×D2311yescharacteristic
239C8—22no—
240C8—232no—
241C8—461no—
242C22—234no—
243C22—462no—
244C22—462no—
245C22C2×D4×D2311yescharacteristic
246C4—21no—
247C4—22no—
248C4—41no—
249C4—42no—
250C4—462no—
251C4—462no—
252C4—921no—
253C4—922no—
254C4Q16×D2312yescomplemented
255C4C2×D4×D2311yescharacteristic
256C4#1062516011yescharacteristic
257C2—464no—
258C2#1309305111yescharacteristic
259C2C2×Q16×D2311yescharacteristic
260C2#1309323311yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#462C2
socleC22×C23C22×D4
prime radicalC2×D92D4
hypercenter#462D23
hypocenterC23D4×Q16
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
1. C2×Q16×D23C2semidirect
4. #13092796C2semidirect
5. #13092657C2semidirect
6. #13092628C2semidirect
7. #13092574C2semidirect
8. #13092571C2semidirect
9. C4×#67275C2semidirect
11. C23×#462C2semidirect
66. #67275D4semidirect
97. D92Q16semidirect
115. C2×D23C2×Q16semidirect
120. C4×C23C2×Q16semidirect
133. #462D23semidirect
172. C23D4×Q16semidirect
254. C4Q16×D23semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×D232
Q8×D922
#130930822
#130927962
#130926572
#130926282
#130925742
#130925712
C4×#672752
#130924822
C23×#4622
D4×Q1623