Finite Group Databasebeta

← #15682686

Subgroups — #15682686

Order 2944.

732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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×#10625161C211yesmaximal, characteristic, complemented
2C2×#10625120C211yesmaximal, characteristic, complemented
3C22×#67263C211yesmaximal, characteristic, complemented
4#13092986C211yesmaximal, characteristic, complemented
5#13092563C214yesmaximal, complemented
6#13092557C214yesmaximal, complemented
7#13092425C211yesmaximal, characteristic, complemented
8#13092383C211yesmaximal, characteristic, complemented
9C23×#416C211yesmaximal, characteristic, complemented
10C2×#41×C23C2211yescharacteristic
11#10625161—24no—
12#10625161—24no—
13C2×Q8×D23C2212yescomplemented
14C2×#67290—22no—
15C2×#67290C2212yescomplemented
16C2×#67288—21no—
17C2×#67288C2211yescharacteristic
18C22×D92C2211yescharacteristic
19C22×Dic46—21no—
20C22×Dic46C2211yescharacteristic
21C22×C8×C23C2211yescharacteristic
22C23×#117C2211yescharacteristic
23#10625120—24no—
24C2×#67274C2212yes—
25C2×#67272C2212yes—
26C2×#67267C2211yescharacteristic
27C2×#67263—24no—
28C2×#67263C2214yes—
29#10625066C2214yes—
30#10625053—22no—
31#10625046—21no—
32#10625045—21no—
33C23×#103C2212yescomplemented
34C23×#102C2212yescomplemented
35(C2×D23)⋊C8C2214yescomplemented
36#10624992C2214yescomplemented
37C23×D23—21no—
38#41×C23—22no—
39#41×C23D414yescomplemented
40C2×Q8×C23C2311yescharacteristic
41C2×D4×C23—21no—
42C2×D4×C23C2311yescharacteristic
43C22×C4×C23—21no—
44C22×C4×C23C2311yescharacteristic
45C2×C22⋊D23—22no—
46C2×C22⋊D23D412yes—
47C22×Dic23—21no—
48C22×Dic23—22no—
49Q8×D23—24no—
50Q8×D23—24no—
51#67290—216no—
52#67290—24no—
53#67290—24no—
54#67288—28no—
55#67288—22no—
56#67288—22no—
57C2×D92—22no—
58C2×D92—22no—
59C2×D92—21no—
60C2×D92—24no—
61C2×D92D411yescharacteristic
62C2×D92C2312yes—
63C2×C4×D23—22no—
64C2×C4×D23C2312yes—
65C2×Dic46—28no—
66C2×Dic46—21no—
67C2×Dic46—22no—
68C2×Dic46—22no—
69C2×Dic46D411yescharacteristic
70C2×Dic46D414yescomplemented
71C2×Dic46C2312yes—
72C2×C8×C23—22no—
73C2×C8×C23C2312yes—
74C4⋊C4×C23C2312yes—
75C22⋊C4×C23—21no—
76C42×C23—21no—
77#67274—24no—
78#67272—24no—
79(C2×D23)⋊C4—24no—
80#67267—22no—
81C2×C23⋊C8C2312yes—
82#67263—28no—
83C23×C23—21no—
84C23×C23C2×D411yescharacteristic
85C22×D23—22no—
86C22×D23—42no—
87C22×D23—82no—
88C22×D23C2×D412yes—
89Q8×C23—21no—
90Q8×C23C2×D412yes—
91D4×C23—24no—
92D4×C23—21no—
93D4×C23C2×D412yes—
94C2×C4×C23—21no—
95C2×C4×C23—24no—
96C2×C4×C23—22no—
97C2×C4×C23C2×D412yes—
98C2×C4×C23C2×D411yescharacteristic
99C2×C4×C23C2×D412yes—
100C2×C4×C23C2411yescharacteristic
101C22⋊D23—28no—
102C22⋊D23—24no—
103C2×Dic23—28no—
104C2×Dic23—24no—
105C2×Dic23—22no—
106C2×Dic23C2×D412yes—
107D92—22no—
108D92—22no—
109D92—22no—
110D92—42no—
111D92—84no—
112C4×D23—28no—
113C4×D23—22no—
114C4×D23—22no—
115Dic46—28no—
116Dic46—22no—
117Dic46—24no—
118Dic46—22no—
119Dic46C2×D414yes—
120C8×C23—22no—
121C23⋊C8—22no—
122#3010—231nomaximal, Sylow
123C22×C23—22no—
124C22×C23—22no—
125C22×C23—42no—
126C22×C23#12012yes—
127C22×C23C22×D411yescharacteristic
128C2×D23—22no—
129C2×D23—24no—
130C2×D23—42no—
131C2×D23—44no—
132C2×D23—84no—
133C4×C23—22no—
134C4×C23—42no—
135C4×C23#12012yes—
136C4×C23C22×D411yescharacteristic
137C4×C23C22×D411yescharacteristic
138Dic23—22no—
139Dic23—24no—
140C2×2−1+4—231no—
141C2×AGL(1,ℤ/8)—231no—
142C22×SD16—231no—
143#535—231no—
144#449—234no—
145#448—234no—
146#419—231no—
147#416D2311yescharacteristic, complemented
148#408—231no—
149C2×C23—22no—
150C2×C23—42no—
151C2×C23C2×#12011yescharacteristic
152C2×C23#57712yes—
153D23—42no—
154D23—82no—
1552−1+4—464no—
1562−1+4—464no—
157C2×#41—231no—
158C2×#41—232no—
159C2×#41—461no—
160C2×#41—462no—
161C2×#41C2×D2311yescharacteristic
162C22×Q8—232no—
163C22×Q8—231no—
164C22×Q8—461no—
165C22×D4—231no—
166AGL(1,ℤ/8)—464no—
167C2×SD16—232no—
168C2×SD16—234no—
169C2×SD16—464no—
170C2×D8—232no—
171C2×M16—231no—
172C22×C8C2×D2311yescharacteristic
173#127—461no—
174#124—461no—
175#121—234no—
176#120—462no—
177#117C2×D2311yescharacteristic
178#103—234no—
179#103C2×D2312yescomplemented
180#102C2×D2312yescomplemented
181C22⋊C8—234no—
182C23#301011yescharacteristic, complemented, Sylow
183C24—461no—
184#41—22no—
185#41—468no—
186#41—464no—
187#41—4616no—
188#41—464no—
189#41—462no—
190#41—462no—
191#41D9214yescomplemented
192C2×Q8—231no—
193C2×Q8—234no—
194C2×Q8—232no—
195C2×Q8—462no—
196C2×Q8—468no—
197C2×Q8—464no—
198C2×Q8—464no—
199C2×Q8—462no—
200C2×Q8—461no—
201C2×Q8C22×D2311yescharacteristic
202C2×D4—21no—
203C2×D4—232no—
204C2×D4—231no—
205C2×D4—232no—
206C2×D4—464no—
207C2×D4—462no—
208C2×D4—462no—
209C2×D4—462no—
210C2×D4—461no—
211C2×D4C22×D2311yescharacteristic
212C22×C4—21no—
213C22×C4—232no—
214C22×C4—462no—
215C22×C4—462no—
216C22×C4—461no—
217C22×C4C22×D2311yescharacteristic
218SD16—468no—
219SD16—464no—
220D8—464no—
221M16—462no—
222C2×C8—22no—
223C2×C8—232no—
224C2×C8C22×D2312yes—
225C4⋊C4C22×D2312yes—
226C22⋊C4—21no—
227C22⋊C4—464no—
228C42—21no—
229C23—21no—
230C23—232no—
231C23—462no—
232C23—922no—
233C23—1842no—
234C23D4×D2311yescharacteristic
235Q8—21no—
236Q8—234no—
237Q8—468no—
238Q8—462no—
239Q8—464no—
240Q8—462no—
241Q8C2×D9212yes—
242D4—24no—
243D4—21no—
244D4—468no—
245D4—464no—
246D4—462no—
247D4—462no—
248D4—462no—
249D4—922no—
250D4—1844no—
251D4C2×D9212yes—
252C2×C4—21no—
253C2×C4—24no—
254C2×C4—22no—
255C2×C4—232no—
256C2×C4—468no—
257C2×C4—468no—
258C2×C4—464no—
259C2×C4—462no—
260C2×C4—462no—
261C2×C4—462no—
262C2×C4C2×D9212yes—
263C2×C4D4×D2311yescharacteristic
264C2×C4D4×D2312yes—
265C2×C4C23×D2311yescharacteristic
266C8—22no—
267C8—462no—
268C22—22no—
269C22—22no—
270C22—42no—
271C22—462no—
272C22—464no—
273C22—922no—
274C22—924no—
275C22—1844no—
276C22#1062505312yes—
277C22C2×D4×D2311yescharacteristic
278C4—22no—
279C4—42no—
280C4—462no—
281C4—464no—
282C4#1062505312yes—
283C4C22×D9211yescharacteristic
284C4C2×D4×D2311yescharacteristic
285C2—22no—
286C2—42no—
287C2—922no—
288C2—1842no—
289C2C2×#1062505311yescharacteristic
290C2#1309322412yes—
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#416C2
socleC22×C23C22×D4
hypercenter#416D23
hypocenterC23#3010
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. C2×#10625161C2semidirect
2. C2×#10625120C2semidirect
3. C22×#67263C2semidirect
4. #13092986C2semidirect
5. #13092563C2semidirect
6. #13092557C2semidirect
7. #13092425C2semidirect
8. #13092383C2semidirect
9. C23×#416C2semidirect
13. C2×Q8×D23C22semidirect
15. C2×#67290C22semidirect
33. C23×#103C22semidirect
34. C23×#102C22semidirect
35. (C2×D23)⋊C8C22semidirect
36. #10624992C22semidirect
39. #41×C23D4semidirect
70. C2×Dic46D4semidirect
147. #416D23semidirect
179. #103C2×D23semidirect
180. #102C2×D23semidirect
182. C23#3010semidirect
191. #41D92semidirect

Maximal subgroups

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

subgroupindex
C2×#106251612
C2×#106251202
C22×#672632
#130929862
#130925632
#130925572
#130924252
#130923832
C23×#4162
#301023