Finite Group Databasebeta

← #15685207

Subgroups — #15685207

Order 2944.

494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 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
1#13093070C211yesmaximal, characteristic, complemented
2D4×D92C211yesmaximal, characteristic, complemented
3#13092765C211yesmaximal, characteristic, complemented
4#13092732C212yesmaximal, complemented
5#13092654C212yesmaximal, complemented
6#13092613C211yesmaximal, characteristic, complemented
7#13092552C212yesmaximal, complemented
8C4×#67272C211yesmaximal, characteristic, complemented
9#13092482C211yesmaximal, characteristic, complemented
10#102×D23C212yesmaximal, complemented
11C23×#474C211yesmaximal, characteristic, complemented
12C2×#67292—21no—
13C2×D4×D23C2212yes—
14C22×D92—21no—
15C23×C4⋊Q8C2211yescharacteristic, complemented
16C4×D4×C23C2211yescharacteristic
17#10625117—21no—
18C2×#67272C2211yescharacteristic
19#10625101—21no—
20C2×D184C2212yescomplemented
21C2×C8×D23C2212yescomplemented
22#10625066C2212yes—
23#10625066C2212yescomplemented
24#10625065—22no—
25C4⋊C4×D23C2212yescomplemented
26#10625053—22no—
27#10625045C2211yescharacteristic
28C4×D92C2211yescharacteristic
29C4×D92C2211yescharacteristic, complemented
30C23×#107C2212yescomplemented
31C23×C4⋊C8C2211yescharacteristic, complemented
32C23×#102C2212yes—
33#10625014C2211yescharacteristic
34#10625003C2212yescomplemented
35(C2×D23)⋊C8C2212yescomplemented
36#10624991C2211yescharacteristic, complemented
37#10624991C2212yescomplemented
38#10624991C2212yescomplemented
39#10624989C2211yescharacteristic, complemented
40C4×C23⋊C8C2211yescharacteristic, complemented
41C23×D23—22no—
42C2×Q8×C23—21no—
43C2×D4×C23C2311yescharacteristic
44C22×C4×C23—21no—
45C2×C22⋊D23—22no—
46#67292—44no—
47D4×D23—24no—
48D4×D23—42no—
49C2×D92—22no—
50C2×D92—22no—
51C2×D92—21no—
52C2×D92—21no—
53C2×D92—44no—
54C2×D92D411yescharacteristic
55C2×D92C2311yescharacteristic
56C2×D92C2312yes—
57C2×C4×D23—22no—
58C2×C4×D23—21no—
59C2×C4×D23C2312yes—
60C2×C8×C23C2312yes—
61C4⋊C4×C23—21no—
62C4⋊C4×C23C2312yes—
63C4⋊C4×C23C2311yescharacteristic
64C22⋊C4×C23—21no—
65C42×C23C2311yescharacteristic
66#67272—22no—
67(C2×D23)⋊C4—21no—
68(C2×D23)⋊C4—22no—
69(C2×D23)⋊C4—22no—
70(C2×D23)⋊C4D412yes—
71C4⋊Dic23D411yescharacteristic
72C4⋊Dic23C2311yescharacteristic
73Dic23⋊C4—22no—
74C2×C23⋊C8C2311yescharacteristic
75C2×C23⋊C8C2311yescharacteristic
76D184—42no—
77C8×D23—42no—
78C23×C23—21no—
79C22×D23—21no—
80C22×D23—22no—
81C22×D23—44no—
82C22×D23—44no—
83C22×D23—82no—
84C22×D23C2×D412yes—
85Q8×C23—42no—
86D4×C23—21no—
87D4×C23#4112yescomplemented
88C2×C4×C23—22no—
89C2×C4×C23—21no—
90C2×C4×C23—42no—
91C2×C4×C23C2×D411yescharacteristic
92C2×C4×C23C2×D411yescharacteristic
93C2×C4×C23C2411yescharacteristic
94C22⋊D23—44no—
95C2×Dic23—21no—
96C2×Dic23C2×D412yes—
97D92—21no—
98D92—22no—
99D92—21no—
100D92—22no—
101D92—44no—
102D92—44no—
103D92—42no—
104D92—81no—
105D92D814yescomplemented
106C4×D23—22no—
107C4×D23—22no—
108C4×D23—44no—
109C4×D23—42no—
110C8×C23—22no—
111C23⋊C8—21no—
112C23⋊C8—21no—
113#3294—231nomaximal, Sylow
114C22×C23—22no—
115C22×C23—41no—
116C22×C23—41no—
117C22×C23C22×D411yescharacteristic
118C2×D23—22no—
119C2×D23—22no—
120C2×D23—42no—
121C2×D23—41no—
122C2×D23—41no—
123C2×D23—42no—
124C2×D23—42no—
125C2×D23—41no—
126C2×D23—88no—
127C2×D23C2×D814yes—
128C4×C23—21no—
129C4×C23—42no—
130C4×C23—41no—
131C4×C23C2×D812yes—
132C4×C23C2×#4111yescharacteristic
133C4×C23H(5,𝔽2)11yescharacteristic
134Dic23—22no—
135Dic23—41no—
136#547—231no—
137D42—231no—
138#486—231no—
139#480—232no—
140#474D2311yescharacteristic, complemented
141#466—232no—
142#459—231no—
143#447—232no—
144C4×D8—231no—
145C8×D4—231no—
146C2×#102—232no—
147C2×C23—42no—
148C2×C23#54611yescharacteristic
149C2×C23C22×D811yescharacteristic
150C2×C23#57711yescharacteristic
151D23—24no—
152D23—81no—
153D23—82no—
154C2×#41—461no—
155C22×D4—232no—
156C22×D4—461no—
157C2×D8—231no—
158C2×D8—232no—
159C22×C8—232no—
160C4⋊Q8C2×D2311yescharacteristic, complemented
161#127—231no—
162#123—462no—
163C22⋊Q8—461no—
164#121—232no—
165#121—232no—
166#121—461no—
167#120—462no—
168C4×D4—231no—
169C4×D4—231no—
170C4×D4C2×D2311yescharacteristic
171C2×C4⋊C4—232no—
172#107—231no—
173#107C2×D2312yescomplemented
174C4⋊C8C2×D2311yescharacteristic, complemented
175#102—231no—
176#102—232no—
177#102—232no—
178#102—231no—
179#102—232no—
180#102C2×D2312yes—
181C22⋊C8—232no—
182C4×C8—231no—
183C23#329411yescharacteristic, complemented, Sylow
184C24—462no—
185#41—924no—
186C2×Q8—21no—
187C2×D4—231no—
188C2×D4—232no—
189C2×D4—231no—
190C2×D4—462no—
191C2×D4—462no—
192C2×D4—462no—
193C2×D4—464no—
194C2×D4—461no—
195C2×D4—461no—
196C2×D4—924no—
197C2×D4—922no—
198C2×D4C22×D2311yescharacteristic
199C22×C4—21no—
200C22×C4—232no—
201C22×C4—462no—
202C22×C4—461no—
203D8—462no—
204D8—922no—
205C2×C8—231no—
206C2×C8—231no—
207C2×C8—922no—
208C2×C8C22×D2312yes—
209C4⋊C4—21no—
210C4⋊C4—231no—
211C4⋊C4—231no—
212C4⋊C4—462no—
213C4⋊C4C22×D2312yes—
214C4⋊C4C22×D2311yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—232no—
217C22⋊C4—462no—
218C22⋊C4—462no—
219C22⋊C4—461no—
220C42C22×D2311yescharacteristic
221C23—21no—
222C23—232no—
223C23—461no—
224C23—462no—
225C23—924no—
226C23—924no—
227C23—1842no—
228Q8—42no—
229D4—21no—
230D4—234no—
231D4—461no—
232D4—462no—
233D4—461no—
234D4—462no—
235D4—924no—
236D4—924no—
237D4—924no—
238D4—922no—
239D4—1841no—
240D4#6729212yescomplemented
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—42no—
244C2×C4—232no—
245C2×C4—462no—
246C2×C4—462no—
247C2×C4—461no—
248C2×C4—924no—
249C2×C4—922no—
250C2×C4D4×D2311yescharacteristic
251C2×C4D4×D2311yescharacteristic
252C2×C4C23×D2311yescharacteristic
253C8—22no—
254C8—461no—
255C8—461no—
256C22—22no—
257C22—41no—
258C22—41no—
259C22—234no—
260C22—462no—
261C22—462no—
262C22—921no—
263C22—922no—
264C22—922no—
265C22—921no—
266C22—922no—
267C22—921no—
268C22—1848no—
269C22C2×D4×D2311yescharacteristic
270C4—21no—
271C4—41no—
272C4—42no—
273C4—462no—
274C4—921no—
275C4D8×D2312yes—
276C4C2×#6729211yescharacteristic
277C4#1062516011yescharacteristic
278C2—42no—
279C2—464no—
280C2—1842no—
281C2—1841no—
282C2#1309305811yescharacteristic
283C2C2×D8×D2311yescharacteristic
284C2#1309322611yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#474C2
socleC22×C23C22×D4
hypercenter#474D23
hypocenterC23#3294
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #13093070C2semidirect
2. D4×D92C2semidirect
3. #13092765C2semidirect
4. #13092732C2semidirect
5. #13092654C2semidirect
6. #13092613C2semidirect
7. #13092552C2semidirect
8. C4×#67272C2semidirect
9. #13092482C2semidirect
10. #102×D23C2semidirect
11. C23×#474C2semidirect
15. C23×C4⋊Q8C22semidirect
20. C2×D184C22semidirect
21. C2×C8×D23C22semidirect
23. #10625066C22semidirect
25. C4⋊C4×D23C22semidirect
29. C4×D92C22semidirect
30. C23×#107C22semidirect
31. C23×C4⋊C8C22semidirect
34. #10625003C22semidirect
35. (C2×D23)⋊C8C22semidirect
36. #10624991C22semidirect
37. #10624991C22semidirect
38. #10624991C22semidirect
39. #10624989C22semidirect
40. C4×C23⋊C8C22semidirect
87. D4×C23#41semidirect
105. D92D8semidirect
140. #474D23semidirect
160. C4⋊Q8C2×D23semidirect
173. #107C2×D23semidirect
174. C4⋊C8C2×D23semidirect
183. C23#3294semidirect
240. D4#67292semidirect

Maximal subgroups

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

subgroupindex
#130930702
D4×D922
#130927652
#130927322
#130926542
#130926132
#130925522
C4×#672722
#130924822
#102×D232
C23×#4742
#329423