Finite Group Databasebeta

← #15682684

Subgroups — #15682684

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×#10625158C211yesmaximal, characteristic, complemented
2C2×#10625079C211yesmaximal, characteristic, complemented
3C22×#67274C211yesmaximal, characteristic, complemented
4#13092986C211yesmaximal, characteristic, complemented
5#13092565C214yesmaximal, complemented
6#13092557C214yesmaximal, complemented
7#13092411C211yesmaximal, characteristic, complemented
8#13092385C211yesmaximal, characteristic, complemented
9C23×#419C211yesmaximal, characteristic, complemented
10C22×Q8×C23C2211yescharacteristic
11#10625158—24no—
12#10625158—24no—
13C2×#67292—21no—
14C2×#67292C2212yescomplemented
15C2×Q8×D23—21no—
16C2×Q8×D23C2212yescomplemented
17C2×#67288—22no—
18C2×#67288C2211yescharacteristic
19C2×#67288C2211yescharacteristic
20C22×D92C2211yescharacteristic
21C2×M16×C23C2211yescharacteristic
22C23×#117C2211yescharacteristic
23C2×#67274—24no—
24C2×#67274C2214yes—
25C22×C23⋊C8C2211yescharacteristic
26#10625079—24no—
27C2×D184C2212yes—
28C2×#67263C2212yes—
29#10625066C2214yes—
30#10625053—22no—
31#10625046—21no—
32#10625045—21no—
33C23×#103C2214yescomplemented
34(C2×D23)⋊C8C2214yescomplemented
35#10624992C2212yescomplemented
36#10624991C2212yescomplemented
37C23×D23—21no—
38C2×Q8×C23—21no—
39C2×Q8×C23—22no—
40C2×Q8×C23D414yescomplemented
41C2×Q8×C23C2312yes—
42C22×C4×C23—21no—
43C22×C4×C23C2311yescharacteristic
44C2×C22⋊D23—21no—
45C2×C22⋊D23D412yes—
46#67292—28no—
47#67292—24no—
48#67292—24no—
49Q8×D23—28no—
50Q8×D23—24no—
51Q8×D23—24no—
52#67288—216no—
53#67288—22no—
54#67288—22no—
55#67288—22no—
56#67288D414yescomplemented
57C2×D92—22no—
58C2×D92—22no—
59C2×D92—22no—
60C2×D92—21no—
61C2×D92—24no—
62C2×D92D411yescharacteristic
63C2×D92C2312yes—
64C2×D92C2311yescharacteristic
65C2×C4×D23—22no—
66C2×C4×D23—21no—
67C2×C4×D23—22no—
68C2×C4×D23C2312yes—
69C2×Dic46—22no—
70C2×Dic46D411yescharacteristic
71C2×Dic46C2311yescharacteristic
72M16×C23—22no—
73C2×C8×C23C2312yes—
74C4⋊C4×C23C2312yes—
75C22⋊C4×C23—21no—
76C42×C23—21no—
77#67274—28no—
78(C2×D23)⋊C4—24no—
79C2×C23⋊C8—22no—
80C2×C23⋊C8C2312yes—
81D184—24no—
82#67263—24no—
83C23×C23C2×D411yescharacteristic
84C22×D23—21no—
85C22×D23—22no—
86C22×D23—42no—
87C22×D23—82no—
88C22×D23C2×D412yes—
89Q8×C23—24no—
90Q8×C23—22no—
91Q8×C23C2×D414yes—
92C2×C4×C23—24no—
93C2×C4×C23—22no—
94C2×C4×C23—22no—
95C2×C4×C23C2×D412yes—
96C2×C4×C23C2×D411yescharacteristic
97C2×C4×C23C2×D412yes—
98C2×C4×C23C2411yescharacteristic
99C22⋊D23—24no—
100C22⋊D23—24no—
101C2×Dic23—21no—
102C2×Dic23C2×D412yes—
103D92—28no—
104D92—22no—
105D92—21no—
106D92—22no—
107D92—22no—
108D92—42no—
109D92—84no—
110D92C2×D412yes—
111C4×D23—28no—
112C4×D23—28no—
113C4×D23—24no—
114C4×D23—22no—
115C4×D23—22no—
116Dic46—28no—
117Dic46—22no—
118Dic46—21no—
119Dic46C2×D412yes—
120C8×C23—22no—
121C23⋊C8—22no—
122#3010—231nomaximal, Sylow
123C22×C23—22no—
124C22×C23#12012yes—
125C22×C23C22×D411yescharacteristic
126C2×D23—22no—
127C2×D23—22no—
128C2×D23—24no—
129C2×D23—42no—
130C2×D23—42no—
131C2×D23—44no—
132C2×D23—84no—
133C4×C23—24no—
134C4×C23—42no—
135C4×C23#12012yes—
136C4×C23C22×D411yescharacteristic
137C4×C23C22×D411yescharacteristic
138Dic23—22no—
139Dic23—22no—
140C2×2−1+4—231no—
141C2×AGL(1,ℤ/8)—231no—
142C22×SD16—231no—
143#535—231no—
144#449—234no—
145#448—234no—
146#419D2311yescharacteristic, complemented
147#416—231no—
148#408—231no—
149C2×C23—22no—
150C2×C23C2×#12011yescharacteristic
151C2×C23#57712yes—
152D23—42no—
153D23—42no—
154D23—82no—
1552−1+4—464no—
1562−1+4—464no—
157C2×#41—231no—
158C2×#41—232no—
159C2×#41—231no—
160C2×#41—462no—
161C2×#41—461no—
162C22×Q8—232no—
163C22×Q8—461no—
164C22×Q8C2×D2311yescharacteristic
165C22×D4—231no—
166AGL(1,ℤ/8)—464no—
167C2×SD16—234no—
168C2×SD16—232no—
169C2×SD16—464no—
170C2×D8—232no—
171C2×M16C2×D2311yescharacteristic
172C22×C8—231no—
173#127—461no—
174#124—461no—
175#121—234no—
176#120—462no—
177#117C2×D2311yescharacteristic
178#103—232no—
179#103C2×D2314yescomplemented
180#102—232no—
181C22⋊C8—234no—
182C23#301011yescharacteristic, complemented, Sylow
183C24—461no—
184#41—234no—
185#41—4616no—
186#41—464no—
187#41—468no—
188#41—464no—
189#41—462no—
190#41—462no—
191#41—462no—
192C2×Q8—21no—
193C2×Q8—22no—
194C2×Q8—231no—
195C2×Q8—231no—
196C2×Q8—462no—
197C2×Q8—464no—
198C2×Q8—468no—
199C2×Q8—464no—
200C2×Q8D9214yescomplemented
201C2×Q8C22×D2312yes—
202C2×D4—232no—
203C2×D4—231no—
204C2×D4—231no—
205C2×D4—232no—
206C2×D4—462no—
207C2×D4—464no—
208C2×D4—461no—
209C2×D4—462no—
210C2×D4—462no—
211C2×D4—461no—
212C22×C4—21no—
213C22×C4—232no—
214C22×C4—462no—
215C22×C4—462no—
216C22×C4—461no—
217C22×C4C22×D2311yescharacteristic
218SD16—464no—
219SD16—468no—
220D8—464no—
221M16—22no—
222C2×C8—232no—
223C2×C8—462no—
224C2×C8C22×D2312yes—
225C4⋊C4C22×D2312yes—
226C22⋊C4—21no—
227C22⋊C4—464no—
228C42—21no—
229C23—232no—
230C23—461no—
231C23—462no—
232C23—922no—
233C23—1842no—
234C23D4×D2311yescharacteristic
235Q8—24no—
236Q8—22no—
237Q8—232no—
238Q8—468no—
239Q8—462no—
240Q8—461no—
241Q8C2×D9214yes—
242D4—232no—
243D4—468no—
244D4—464no—
245D4—464no—
246D4—462no—
247D4—461no—
248D4—462no—
249D4—462no—
250D4—922no—
251D4—1844no—
252C2×C4—24no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—232no—
256C2×C4—468no—
257C2×C4—468no—
258C2×C4—461no—
259C2×C4—464no—
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—462no—
270C22—462no—
271C22—464no—
272C22—922no—
273C22—922no—
274C22—924no—
275C22—1844no—
276C22#1062505312yes—
277C22C2×D4×D2311yescharacteristic
278C4—24no—
279C4—42no—
280C4—462no—
281C4—462no—
282C4#1062505312yes—
283C4C22×D9211yescharacteristic
284C4C2×D4×D2311yescharacteristic
285C2—22no—
286C2—922no—
287C2—922no—
288C2—1842no—
289C2C2×#1062505311yescharacteristic
290C2#1309322612yes—
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#419C2
socleC22×C23C22×D4
hypercenter#419D23
hypocenterC23#3010
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
1. C2×#10625158C2semidirect
2. C2×#10625079C2semidirect
3. C22×#67274C2semidirect
4. #13092986C2semidirect
5. #13092565C2semidirect
6. #13092557C2semidirect
7. #13092411C2semidirect
8. #13092385C2semidirect
9. C23×#419C2semidirect
14. C2×#67292C22semidirect
16. C2×Q8×D23C22semidirect
33. C23×#103C22semidirect
34. (C2×D23)⋊C8C22semidirect
35. #10624992C22semidirect
36. #10624991C22semidirect
40. C2×Q8×C23D4semidirect
56. #67288D4semidirect
146. #419D23semidirect
179. #103C2×D23semidirect
182. C23#3010semidirect
200. C2×Q8D92semidirect

Maximal subgroups

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

subgroupindex
C2×#106251582
C2×#106250792
C22×#672742
#130929862
#130925652
#130925572
#130924112
#130923852
C23×#4192
#301023