Finite Group Databasebeta

← #15682980

Subgroups — #15682980

Order 2944.

520 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 133 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×#10625090C211yesmaximal, characteristic, complemented
2C22×C8×D23C211yesmaximal, characteristic, complemented
3#13092930C212yesmaximal, complemented
4#13092655C211yesmaximal, characteristic, complemented
5#13092654C211yesmaximal, characteristic, complemented
6#13092653C211yesmaximal, characteristic, complemented
7#13092649C212yesmaximal, complemented
8#13092648C212yesmaximal, complemented
9#13092454C211yesmaximal, characteristic, complemented
10#13092412C212yesmaximal, complemented
11C23×#467C211yesmaximal, characteristic, complemented
12C2×#67292C2212yes—
13C22×C4×D23C2211yescharacteristic
14C2×Q16×C23C2211yescharacteristic, complemented
15C22×C8×C23C2211yescharacteristic
16C23×C22⋊Q8C2212yes—
17#10625117C2212yes—
18C2×#67274C2212yescomplemented
19#10625101C2212yes—
20C22×C23⋊C8C2211yescharacteristic
21#10625090—24no—
22C2×D184C2211yescharacteristic, complemented
23C2×C8×D23—24no—
24C2×C8×D23C2211yescharacteristic
25C2×C8×D23C2211yescharacteristic
26C2×C8×D23C2211yescharacteristic
27C2×C8×D23C2211yescharacteristic
28#10625066C2212yes—
29#10625065—22no—
30#10625064—22no—
31#10625063C2212yes—
32#10625053—22no—
33(C22⋊D23)⋊C4—22no—
34C23×#107C2211yescharacteristic, complemented
35C23×#103C2212yescomplemented
36#10625017C2212yescomplemented
37#10625003C2212yescomplemented
38#10625000C2211yescharacteristic, complemented
39#10624991C2212yescomplemented
40#10624990C2212yescomplemented
41C23×D23D411yescharacteristic
42C2×Q8×C23C2312yes—
43C22×C4×C23C2311yescharacteristic
44C2×C22⋊D23—22no—
45C22×Dic23D411yescharacteristic
46#67292—24no—
47#67292—24no—
48C2×D92—22no—
49C2×D92—22no—
50C2×D92C2312yes—
51C2×C4×D23—22no—
52C2×C4×D23—22no—
53C2×C4×D23—22no—
54C2×C4×D23D411yescharacteristic
55C2×C4×D23D411yescharacteristic
56C2×C4×D23C2311yescharacteristic
57C2×C4×D23C2311yescharacteristic
58Q16×C23—22no—
59C2×C8×C23—22no—
60C2×C8×C23C2311yescharacteristic
61C2×C8×C23C2311yescharacteristic
62C4⋊C4×C23—22no—
63C4⋊C4×C23C2312yes—
64C22⋊C4×C23—22no—
65#67274—24no—
66(C2×D23)⋊C4—22no—
67(C2×D23)⋊C4—22no—
68(C2×D23)⋊C4—22no—
69(C2×D23)⋊C4—22no—
70C4⋊Dic23C2312yes—
71Dic23⋊C4—22no—
72C4×Dic23—22no—
73C2×C23⋊C8—22no—
74C2×C23⋊C8C2311yescharacteristic
75C2×C23⋊C8C2311yescharacteristic
76D184—22no—
77C8×D23—22no—
78C8×D23—22no—
79C8×D23—22no—
80C8×D23D414yescomplemented
81C23×C23C2×D411yescharacteristic
82C22×D23—22no—
83C22×D23—22no—
84C22×D23—22no—
85C22×D23—22no—
86C22×D23C2×D411yescharacteristic
87C22×D23C2×D411yescharacteristic
88Q8×C23—22no—
89Q8×C23—22no—
90C2×C4×C23—21no—
91C2×C4×C23—21no—
92C2×C4×C23—22no—
93C2×C4×C23—22no—
94C2×C4×C23C2×D411yescharacteristic
95C2×C4×C23C2411yescharacteristic
96C22⋊D23—44no—
97C2×Dic23—22no—
98C2×Dic23—22no—
99C2×Dic23C2×D411yescharacteristic
100C2×Dic23C2×D411yescharacteristic
101D92—22no—
102D92—22no—
103D92—44no—
104D92—44no—
105C4×D23—22no—
106C4×D23—21no—
107C4×D23—21no—
108C4×D23—22no—
109C4×D23—44no—
110C4×D23C2×D412yes—
111C4×D23#4112yes—
112C8×C23—21no—
113C8×C23C2×D412yes—
114C23⋊C8—21no—
115C23⋊C8C2×D412yes—
116#3050—231nomaximal, Sylow
117C22×C23—21no—
118C22×C23—21no—
119C22×C23#13512yescomplemented
120C22×C23C22×D411yescharacteristic
121C2×D23—28no—
122C2×D23—21no—
123C2×D23—21no—
124C2×D23—21no—
125C2×D23—21no—
126C2×D23—42no—
127C2×D23—42no—
128C2×D23—42no—
129C2×D23#12112yes—
130C2×D23#13512yescomplemented
131C4×C23—21no—
132C4×C23—42no—
133C4×C23—42no—
134C4×C23C22×D411yescharacteristic
135C4×C23C2×#4111yescharacteristic
136Dic23—21no—
137Dic23—42no—
138Dic23#12112yes—
139C2×#135—231no—
140C23×C8—231no—
141#525—232no—
142#467—231no—
143#467D2311yescharacteristic, complemented
144#466—231no—
145#466—231no—
146#465—232no—
147#465—232no—
148#427—231no—
149#416—232no—
150C2×C23—22no—
151C2×C23C2×#12111yescharacteristic
152C2×C23C2×#13511yescharacteristic
153C2×C23C2×#13511yescharacteristic
154D23—22no—
155D23—22no—
156D23—82no—
157C2×#41—232no—
158C23×C4—231no—
159#135—464no—
160C2×Q16C2×D2311yescharacteristic, complemented
161C2×SD16—232no—
162C2×D8—231no—
163C22×C8—231no—
164C22×C8—231no—
165C22×C8—231no—
166C22×C8—231no—
167C22×C8—231no—
168C22×C8—464no—
169C22×C8C2×D2311yescharacteristic
170#123—462no—
171C22⋊Q8—232no—
172C22⋊Q8C2×D2312yes—
173#121—232no—
174#121—232no—
175#120—462no—
176C4×D4—462no—
177C4×D4—462no—
178#117—232no—
179#107—231no—
180#107C2×D2311yescharacteristic, complemented
181#106—232no—
182#103—232no—
183#103C2×D2312yescomplemented
184#102—232no—
185#102—232no—
186C23#305011yescharacteristic, complemented, Sylow
187C24—231no—
188#41—464no—
189#41—464no—
190C2×Q8C22×D2312yes—
191C2×D4—232no—
192C2×D4—462no—
193C2×D4—462no—
194C2×D4—462no—
195C22×C4—231no—
196C22×C4—231no—
197C22×C4—231no—
198C22×C4—231no—
199C22×C4—231no—
200C22×C4—462no—
201C22×C4—462no—
202C22×C4—462no—
203C22×C4C22×D2311yescharacteristic
204Q16—22no—
205SD16—464no—
206D8—462no—
207C2×C8—22no—
208C2×C8—231no—
209C2×C8—234no—
210C2×C8—231no—
211C2×C8—462no—
212C2×C8—462no—
213C2×C8—462no—
214C2×C8—462no—
215C2×C8C22×D2311yescharacteristic
216C2×C8C22×D2311yescharacteristic
217C4⋊C4—22no—
218C4⋊C4—232no—
219C4⋊C4—462no—
220C4⋊C4C22×D2312yes—
221C22⋊C4—22no—
222C22⋊C4—462no—
223C22⋊C4—462no—
224C22⋊C4—462no—
225C22⋊C4—462no—
226C42—462no—
227C23—231no—
228C23—231no—
229C23—462no—
230C23—462no—
231C23—462no—
232C23—462no—
233C23D4×D2311yescharacteristic
234Q8—22no—
235Q8—22no—
236D4—462no—
237D4—462no—
238D4—924no—
239D4—924no—
240D4—924no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—231no—
246C2×C4—232no—
247C2×C4—232no—
248C2×C4—231no—
249C2×C4—462no—
250C2×C4—462no—
251C2×C4—462no—
252C2×C4—461no—
253C2×C4—461no—
254C2×C4—462no—
255C2×C4—924no—
256C2×C4D4×D2311yescharacteristic
257C2×C4C23×D2311yescharacteristic
258C8—21no—
259C8—232no—
260C8—461no—
261C8D4×D2312yes—
262C22—21no—
263C22—21no—
264C22—232no—
265C22—232no—
266C22—468no—
267C22—461no—
268C22—461no—
269C22—461no—
270C22—461no—
271C22—922no—
272C22—922no—
273C22—922no—
274C22#1062509012yescomplemented
275C22C2×D4×D2311yescharacteristic
276C4—21no—
277C4—42no—
278C4—42no—
279C4—232no—
280C4—461no—
281C4—922no—
282C4C2×D4×D2311yescharacteristic
283C4#41×D2311yescharacteristic
284C2—22no—
285C2—462no—
286C2—462no—
287C2—1842no—
288C2#121×D2311yescharacteristic
289C2#135×D2311yescharacteristic
290C2C2×#1062509011yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#467C2
socleC22×C23C22×D4
hypercenter#467D23
hypocenterC23#3050
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. C2×#10625090C2semidirect
2. C22×C8×D23C2semidirect
3. #13092930C2semidirect
4. #13092655C2semidirect
5. #13092654C2semidirect
6. #13092653C2semidirect
7. #13092649C2semidirect
8. #13092648C2semidirect
9. #13092454C2semidirect
10. #13092412C2semidirect
11. C23×#467C2semidirect
14. C2×Q16×C23C22semidirect
18. C2×#67274C22semidirect
22. C2×D184C22semidirect
34. C23×#107C22semidirect
35. C23×#103C22semidirect
36. #10625017C22semidirect
37. #10625003C22semidirect
38. #10625000C22semidirect
39. #10624991C22semidirect
40. #10624990C22semidirect
80. C8×D23D4semidirect
119. C22×C23#135semidirect
130. C2×D23#135semidirect
143. #467D23semidirect
160. C2×Q16C2×D23semidirect
180. #107C2×D23semidirect
183. #103C2×D23semidirect
186. C23#3050semidirect
274. C22#10625090semidirect

Maximal subgroups

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

subgroupindex
C2×#106250902
C22×C8×D232
#130929302
#130926552
#130926542
#130926532
#130926492
#130926482
#130924542
#130924122
C23×#4672
#305023