Finite Group Databasebeta

← #15685211

Subgroups — #15685211

Order 2944.

494 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 139 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#13093071C211yesmaximal, characteristic, complemented
2D4×D92C211yesmaximal, characteristic, complemented
3#13092764C211yesmaximal, characteristic, complemented
4#13092731C212yesmaximal, complemented
5#13092698C211yesmaximal, characteristic, complemented
6#13092653C212yesmaximal, complemented
7#13092613C211yesmaximal, characteristic, complemented
8#13092553C212yesmaximal, complemented
9C4×D184C211yesmaximal, characteristic, complemented
10C2×#10625003C212yesmaximal, complemented
11C8×D4×C23C211yesmaximal, characteristic, complemented
12C2×#67290—21no—
13C2×D4×D23—21no—
14C22×D92C2212yes—
15C22×C8×C23C2212yescomplemented
16C4×D4×C23C2211yescharacteristic
17#10625101C2212yes—
18#10625101C2212yescomplemented
19C2×C4⋊Dic23C2212yescomplemented
20C2×D184C2211yescharacteristic
21C2×D184C2212yescomplemented
22#10625068—21no—
23#10625066—21no—
24#10625057—22no—
25#10625053—22no—
26#10625045C2211yescharacteristic
27C4×D92C2211yescharacteristic
28C4×D92C2211yescharacteristic, complemented
29#10625040C2211yescharacteristic, complemented
30C23×C4⋊C8C2211yescharacteristic, complemented
31C23×C22⋊C8C2212yescomplemented
32C4×C8×C23C2211yescharacteristic, complemented
33#10625003C2211yescharacteristic
34#10625003C2212yes—
35#10625003C2212yescomplemented
36#10625003C2211yescharacteristic, complemented
37#10625003C2212yescomplemented
38#10625003C2212yescomplemented
39#10625000C2212yescomplemented
40#10625000C2211yescharacteristic, complemented
41C23×D23—22no—
42C2×D4×C23D411yescharacteristic
43C22×C4×C23C2312yes—
44C2×C22⋊D23—22no—
45C2×C22⋊D23—22no—
46C22×Dic23—22no—
47#67290—44no—
48D4×D23—44no—
49C2×D92—24no—
50C2×D92—21no—
51C2×D92—22no—
52C2×D92—21no—
53C2×D92—42no—
54C2×D92C2311yescharacteristic
55C2×D92C2312yes—
56C2×D92C2311yescharacteristic
57C2×C4×D23—21no—
58C2×C4×D23—21no—
59C2×Dic46—21no—
60C2×C8×C23—42no—
61C2×C8×C23C2312yes—
62C2×C8×C23C2311yescharacteristic
63C2×C8×C23C2311yescharacteristic
64C4⋊C4×C23D411yescharacteristic
65C22⋊C4×C23D412yes—
66C42×C23C2311yescharacteristic
67(C2×D23)⋊C4—21no—
68(C2×D23)⋊C4—21no—
69(C2×D23)⋊C4—22no—
70(C2×D23)⋊C4—22no—
71C4⋊Dic23—21no—
72C4⋊Dic23—22no—
73C4⋊Dic23C2312yes—
74C4⋊Dic23C2311yescharacteristic
75C4⋊Dic23C2311yescharacteristic
76D184—22no—
77D184—42no—
78C23×C23C2×D412yes—
79C22×D23—21no—
80C22×D23—21no—
81C22×D23—22no—
82C22×D23—44no—
83C22×D23—44no—
84C22×D23—82no—
85D4×C23D814yescomplemented
86C2×C4×C23—22no—
87C2×C4×C23—22no—
88C2×C4×C23C2×D411yescharacteristic
89C2×C4×C23C2×D412yes—
90C2×C4×C23C2×D411yescharacteristic
91C2×C4×C23C2411yescharacteristic
92C22⋊D23—44no—
93C22⋊D23—44no—
94C2×Dic23—22no—
95C2×Dic23—21no—
96C2×Dic23—21no—
97C2×Dic23—44no—
98D92—21no—
99D92—22no—
100D92—21no—
101D92—21no—
102D92—22no—
103D92—44no—
104D92—42no—
105D92—81no—
106D92#4112yescomplemented
107C4×D23—42no—
108C4×D23—42no—
109Dic46—42no—
110C8×C23—21no—
111C8×C23—22no—
112C8×C23—21no—
113#3294—231nomaximal, Sylow
114C22×C23—22no—
115C22×C23—22no—
116C22×C23C2×D814yes—
117C22×C23C22×D411yescharacteristic
118C2×D23—22no—
119C2×D23—41no—
120C2×D23—41no—
121C2×D23—42no—
122C2×D23—41no—
123C2×D23—41no—
124C2×D23—42no—
125C2×D23—42no—
126C2×D23—41no—
127C2×D23—88no—
128C4×C23—22no—
129C4×C23—21no—
130C4×C23C2×D812yes—
131C4×C23C2×#4111yescharacteristic
132C4×C23H(5,𝔽2)11yescharacteristic
133Dic23—42no—
134Dic23—41no—
135Dic23—41no—
136#547—231no—
137D42—231no—
138#486—231no—
139#480—232no—
140#474—231no—
141#466—232no—
142#459—231no—
143#447—232no—
144C4×D8—231no—
145C8×D4D2311yescharacteristic, complemented
146C2×#102—232no—
147C2×C23—24no—
148C2×C23#54611yescharacteristic
149C2×C23C22×D811yescharacteristic
150C2×C23#57711yescharacteristic
151D23—42no—
152D23—81no—
153D23—82no—
154C2×#41—461no—
155C22×D4—232no—
156C22×D4—461no—
157C2×D8—231no—
158C2×D8—232no—
159C22×C8C2×D2312yescomplemented
160C4⋊Q8—231no—
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#107—232no—
174C4⋊C8C2×D2311yescharacteristic, complemented
175#102—231no—
176#102—232no—
177#102—232no—
178#102—232no—
179#102—231no—
180#102—232no—
181C22⋊C8C2×D2312yescomplemented
182C4×C8C2×D2311yescharacteristic, complemented
183C23#329411yescharacteristic, complemented, Sylow
184C24—462no—
185#41—924no—
186C2×Q8—461no—
187C2×D4—231no—
188C2×D4—232no—
189C2×D4—231no—
190C2×D4—464no—
191C2×D4—462no—
192C2×D4—462no—
193C2×D4—462no—
194C2×D4—461no—
195C2×D4—461no—
196C2×D4—922no—
197C2×D4—924no—
198C2×D4D9211yescharacteristic
199C22×C4—462no—
200C22×C4—461no—
201C22×C4—461no—
202C22×C4C22×D2312yes—
203D8—462no—
204D8—922no—
205C2×C8—42no—
206C2×C8C22×D2311yescharacteristic
207C2×C8C22×D2311yescharacteristic
208C2×C8C22×D2312yes—
209C4⋊C4—231no—
210C4⋊C4—232no—
211C4⋊C4—231no—
212C4⋊C4—462no—
213C4⋊C4—461no—
214C4⋊C4D9211yescharacteristic
215C22⋊C4—461no—
216C22⋊C4—461no—
217C22⋊C4—462no—
218C22⋊C4—462no—
219C22⋊C4D9212yes—
220C42C22×D2311yescharacteristic
221C23—461no—
222C23—461no—
223C23—462no—
224C23—924no—
225C23—924no—
226C23—1842no—
227C23C2×D9212yes—
228Q8—922no—
229D4—232no—
230D4—461no—
231D4—461no—
232D4—462no—
233D4—461no—
234D4—462no—
235D4—924no—
236D4—924no—
237D4—924no—
238D4—922no—
239D4—1841no—
240D4D18414yescomplemented
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—461no—
244C2×C4—461no—
245C2×C4—462no—
246C2×C4—924no—
247C2×C4—922no—
248C2×C4—922no—
249C2×C4C2×D9211yescharacteristic
250C2×C4C2×D9212yes—
251C2×C4C2×D9211yescharacteristic
252C2×C4C23×D2311yescharacteristic
253C8—21no—
254C8—22no—
255C8—21no—
256C22—22no—
257C22—22no—
258C22—462no—
259C22—921no—
260C22—921no—
261C22—921no—
262C22—922no—
263C22—922no—
264C22—921no—
265C22—922no—
266C22—921no—
267C22—1848no—
268C22C2×D18414yes—
269C22C22×D9211yescharacteristic
270C4—21no—
271C4—22no—
272C4—921no—
273C4—921no—
274C4—922no—
275C4C2×D18412yes—
276C4#1062515511yescharacteristic
277C4#41×D2311yescharacteristic
278C2—24no—
279C2—922no—
280C2—1842no—
281C2—1841no—
282C2#1309306211yescharacteristic
283C2C22×D18411yescharacteristic
284C2#1309322911yescharacteristic
subgroupG/H
centerC22C22×D92
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC8×D4×C23C2
socleC22×C23C22×D4
hypercenterC8×D4D23
hypocenterC23#3294
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #13093071C2semidirect
2. D4×D92C2semidirect
3. #13092764C2semidirect
4. #13092731C2semidirect
5. #13092698C2semidirect
6. #13092653C2semidirect
7. #13092613C2semidirect
8. #13092553C2semidirect
9. C4×D184C2semidirect
10. C2×#10625003C2semidirect
11. C8×D4×C23C2semidirect
15. C22×C8×C23C22semidirect
18. #10625101C22semidirect
19. C2×C4⋊Dic23C22semidirect
21. C2×D184C22semidirect
28. C4×D92C22semidirect
29. #10625040C22semidirect
30. C23×C4⋊C8C22semidirect
31. C23×C22⋊C8C22semidirect
32. C4×C8×C23C22semidirect
35. #10625003C22semidirect
36. #10625003C22semidirect
37. #10625003C22semidirect
38. #10625003C22semidirect
39. #10625000C22semidirect
40. #10625000C22semidirect
85. D4×C23D8semidirect
106. D92#41semidirect
145. C8×D4D23semidirect
159. C22×C8C2×D23semidirect
174. C4⋊C8C2×D23semidirect
181. C22⋊C8C2×D23semidirect
182. C4×C8C2×D23semidirect
183. C23#3294semidirect
240. D4D184semidirect

Maximal subgroups

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

subgroupindex
#130930712
D4×D922
#130927642
#130927312
#130926982
#130926532
#130926132
#130925532
C4×D1842
C2×#106250032
C8×D4×C232
#329423