Finite Group Databasebeta

← #15674429

Subgroups — #15674429

Order 2944.

394 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 75 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×#10625080C211yesmaximal, characteristic, complemented
2#13092986C211yesmaximal, characteristic
3C2×#10625046C211yesmaximal, characteristic, complemented
4C2×#10624987C211yesmaximal, characteristic, complemented
5#13092425C211yesmaximal, characteristic, complemented
6C2×#10625005C211yesmaximal, characteristic, complemented
7C23×#339C211yesmaximal, characteristic, complemented
8C2×#67288C2211yescharacteristic
9C22×D92C2211yescharacteristic
10C22×Dic46C2211yescharacteristic
11C2×M16×C23C2211yescharacteristic
12C23×#117C2211yescharacteristic
13C2×C42×C23C2211yescharacteristic
14C2×(C2×D23)⋊C4—22no—
15C2×#67267C2211yescharacteristic
16#10625080—22no—
17#10625080—22no—
18C2×Dic92—21no—
19C2×#67263—21no—
20#10625066—22no—
21#10625053—22no—
22#10625046—21no—
23#10625046—22no—
24#10625046—22no—
25#10625045—21no—
26#10625005—22no—
27#10624992—22no—
28#10624987—22no—
29C23×D23D412yes—
30C22×C4×C23—21no—
31C22×C4×C23C2311yescharacteristic
32C2×C22⋊D23—21no—
33C22×Dic23—21no—
34#67288—21no—
35#67288—21no—
36#67288—21no—
37#67288—21no—
38C2×D92—21no—
39C2×D92—21no—
40C2×D92—21no—
41C2×D92—21no—
42C2×D92—21no—
43C2×D92—21no—
44C2×D92—24no—
45C2×D92D411yescharacteristic
46C2×C4×D23—21no—
47C2×Dic46—21no—
48C2×Dic46—21no—
49C2×Dic46—21no—
50C2×Dic46—21no—
51C2×Dic46—21no—
52C2×Dic46D411yescharacteristic
53C2×Dic46D412yescomplemented
54M16×C23—21no—
55M16×C23D412yescomplemented
56C2×C8×C23—21no—
57C4⋊C4×C23D412yes—
58C22⋊C4×C23—21no—
59C42×C23—21no—
60C42×C23—21no—
61C42×C23D412yescomplemented
62(C2×D23)⋊C4—28no—
63(C2×D23)⋊C4—24no—
64#67267—21no—
65#67267—21no—
66C2×C23⋊C8—21no—
67Dic92—24no—
68#67263—24no—
69C23×C23C2×D411yescharacteristic
70C22×D23—22no—
71C22×D23—22no—
72C22×D23—21no—
73C22×D23—22no—
74C22×D23—44no—
75C2×C4×C23—22no—
76C2×C4×C23—22no—
77C2×C4×C23—42no—
78C2×C4×C23C2×D411yescharacteristic
79C2×C4×C23C2×D411yescharacteristic
80C2×C4×C23C2×D411yescharacteristic
81C2×C4×C23C2×D411yescharacteristic
82C2×C4×C23C2×D411yescharacteristic
83C2×C4×C23#4111yescharacteristic
84C22⋊D23—41no—
85C22⋊D23—41no—
86C2×Dic23—22no—
87C2×Dic23—21no—
88C2×Dic23—41no—
89C2×Dic23—41no—
90D92—21no—
91D92—21no—
92D92—41no—
93D92—41no—
94D92—41no—
95D92—41no—
96D92—84no—
97C4×D23—41no—
98C4×D23—41no—
99Dic46—22no—
100Dic46—21no—
101Dic46—22no—
102Dic46—21no—
103Dic46—41no—
104Dic46—41no—
105C8×C23—22no—
106C23⋊C8—41no—
107#2004—231nomaximal, Sylow
108C22×C23—22no—
109C22×C23#12011yescharacteristic
110C22×C23#12011yescharacteristic
111C22×C23#12111yescharacteristic
112C2×D23—44no—
113C2×D23—41no—
114C2×D23—42no—
115C2×D23—42no—
116C2×D23—44no—
117C2×D23—82no—
118C4×C23—42no—
119C4×C23—42no—
120C4×C23#12011yescharacteristic
121C4×C23#12111yescharacteristic
122C4×C23#12111yescharacteristic
123C4×C23#12711yescharacteristic
124Dic23—42no—
125Dic23—41no—
126C2×#137—231no—
127#535—231no—
128C2×#124—231no—
129C2×#104—231no—
130#419—231no—
131C2×#100—231no—
132#339D2311yescharacteristic, complemented
133C2×C23—21no—
134C2×C23—21no—
135C2×C23#39211yescharacteristic
136C2×C23#45512yes—
137D23—81no—
138D23—82no—
139C2×#41—231no—
140C22×Q8—231no—
141C22×D4—231no—
142#137—462no—
143#137—462no—
144C2×Q16—461no—
145C2×SD16—461no—
146C2×M16—231no—
147C2×M16C2×D2311yescharacteristic
148#127—461no—
149#124—462no—
150#124—461no—
151#124—462no—
152#121—462no—
153#120—462no—
154#117C2×D2311yescharacteristic
155C2×C22⋊C4—462no—
156C2×C42C2×D2311yescharacteristic
157#104—462no—
158#103—462no—
159#100—462no—
160C23#200411yescharacteristic, complemented, Sylow
161C24—232no—
162#41—461no—
163#41—461no—
164#41—461no—
165#41—461no—
166C2×Q8—231no—
167C2×Q8—232no—
168C2×Q8—461no—
169C2×Q8—461no—
170C2×Q8—461no—
171C2×Q8—461no—
172C2×Q8—461no—
173C2×D4—231no—
174C2×D4—464no—
175C2×D4—461no—
176C2×D4—461no—
177C2×D4—461no—
178C2×D4—461no—
179C2×D4—461no—
180C2×D4—461no—
181C2×D4—461no—
182C22×C4—21no—
183C22×C4—461no—
184C22×C4—461no—
185C22×C4C22×D2311yescharacteristic
186Q16—464no—
187SD16—464no—
188M16—21no—
189M16—461no—
190M16—461no—
191M16D9212yescomplemented
192C2×C8—21no—
193C2×C8—461no—
194C4⋊C4D9212yes—
195C22⋊C4—21no—
196C22⋊C4—468no—
197C22⋊C4—464no—
198C42—21no—
199C42—21no—
200C42D9212yescomplemented
201C23—462no—
202C23—462no—
203C23—461no—
204C23—462no—
205C23—924no—
206C23D4×D2311yescharacteristic
207Q8—462no—
208Q8—461no—
209Q8—462no—
210Q8—461no—
211Q8—921no—
212Q8—921no—
213D4—461no—
214D4—461no—
215D4—921no—
216D4—921no—
217D4—921no—
218D4—921no—
219D4—921no—
220D4—921no—
221D4—1844no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—42no—
225C2×C4—462no—
226C2×C4—461no—
227C2×C4—921no—
228C2×C4—921no—
229C2×C4—921no—
230C2×C4—921no—
231C2×C4C2×D9211yescharacteristic
232C2×C4C2×D9211yescharacteristic
233C2×C4C2×D9211yescharacteristic
234C2×C4D4×D2311yescharacteristic
235C2×C4D4×D2311yescharacteristic
236C2×C4#6729211yescharacteristic
237C8—22no—
238C8—921no—
239C22—22no—
240C22—924no—
241C22—921no—
242C22—922no—
243C22—922no—
244C22—924no—
245C22—1842no—
246C22#1062505311yescharacteristic
247C22#1062505311yescharacteristic
248C22#1062506611yescharacteristic
249C4—42no—
250C4—42no—
251C4—921no—
252C4—922no—
253C4#1062504511yescharacteristic
254C4#1062505311yescharacteristic
255C4#1062506611yescharacteristic
256C4#1062506611yescharacteristic
257C2—21no—
258C2—21no—
259C2—1842no—
260C2—1841no—
261C2#1309232711yescharacteristic
262C2#1309259612yes—
subgroupG/H
centerC22#10625053
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#339C2
socleC22×C23#120
prime radical#13092986C2
hypercenter#339D23
hypocenterC23#2004
LCSG ▷ C22×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. C2×#10625080C2semidirect
3. C2×#10625046C2semidirect
4. C2×#10624987C2semidirect
5. #13092425C2semidirect
6. C2×#10625005C2semidirect
7. C23×#339C2semidirect
53. C2×Dic46D4semidirect
55. M16×C23D4semidirect
61. C42×C23D4semidirect
132. #339D23semidirect
160. C23#2004semidirect
191. M16D92semidirect
200. C42D92semidirect

Maximal subgroups

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

subgroupindex
C2×#106250802
#130929862
C2×#106250462
C2×#106249872
#130924252
C2×#106250052
C23×#3392
#200423