Finite Group Databasebeta

← #15683347

Subgroups — #15683347

Order 2944.

410 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 127 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×#10625068C211yesmaximal, characteristic
2#117×D23C211yesmaximal, characteristic
3#13092761C212yesmaximal, complemented
4#13092760C212yesmaximal, complemented
5#13092754C212yesmaximal, complemented
6#13092749C212yesmaximal, complemented
7#13092457C211yesmaximal, characteristic, complemented
8#13092427C211yesmaximal, characteristic, complemented
9#13092425C211yesmaximal, characteristic, complemented
10#13092380C211yesmaximal, characteristic
11C23×#428C211yesmaximal, characteristic, complemented
12C22×C4×D23C2211yescharacteristic
13C22×Dic46C2211yescharacteristic
14C2×M16×C23C2211yescharacteristic
15C23×#117C2211yescharacteristic
16C2×C4⋊C4×C23C2211yescharacteristic
17C2×(C2×D23)⋊C4—21no—
18#10625097C2211yescharacteristic
19C2×C4⋊Dic23—21no—
20C2×#67267C2211yescharacteristic
21#10625068—21no—
22#10625068—21no—
23#10625068C2212yes—
24#10625068C2212yes—
25#10625063C2211yescharacteristic
26#10625063C2211yescharacteristic
27C4⋊C4×D23C2211yescharacteristic
28C4⋊C4×D23C2211yescharacteristic
29C22⋊C4×D23—21no—
30#10625048—21no—
31#10625043—21no—
32C42×D23—21no—
33C23×#107C2212yescomplemented
34C23×#106C2212yescomplemented
35(C2×D23)⋊C8C2212yes—
36(C2×D23)⋊C8C2212yes—
37#10624998C2212yescomplemented
38#10624998C2212yescomplemented
39#10624992C2212yescomplemented
40#10624992C2212yescomplemented
41#10624990C2212yescomplemented
42#10624989C2212yescomplemented
43C23×D23D411yescharacteristic
44C22×C4×C23—21no—
45C22×C4×C23C2311yescharacteristic
46C22×Dic23—21no—
47C22×Dic23D411yescharacteristic
48C2×C4×D23—22no—
49C2×C4×D23—22no—
50C2×C4×D23—21no—
51C2×C4×D23—21no—
52C2×C4×D23D411yescharacteristic
53C2×C4×D23D411yescharacteristic
54C2×C4×D23C2311yescharacteristic
55C2×C4×D23C2311yescharacteristic
56C2×Dic46—22no—
57C2×Dic46—22no—
58C2×Dic46—21no—
59C2×Dic46C2312yes—
60M16×C23—22no—
61C2×C8×C23C2312yes—
62C4⋊C4×C23—21no—
63C4⋊C4×C23C2311yescharacteristic
64C4⋊C4×C23C2312yes—
65C4⋊C4×C23C2311yescharacteristic
66C22⋊C4×C23—21no—
67C42×C23—21no—
68C22⋊Dic23—21no—
69(C2×D23)⋊C4—21no—
70(C2×D23)⋊C4—21no—
71(C2×D23)⋊C4—22no—
72(C2×D23)⋊C4—22no—
73C4⋊Dic23—22no—
74C4⋊Dic23—22no—
75C4⋊Dic23C2311yescharacteristic
76C4⋊Dic23C2311yescharacteristic
77Dic23⋊C4—21no—
78Dic23⋊C4—21no—
79C4×Dic23—21no—
80C4×Dic23—21no—
81C4×Dic23—21no—
82#67267—22no—
83C2×C23⋊C8C2312yes—
84C23×C23C2×D411yescharacteristic
85C22×D23—22no—
86C22×D23—22no—
87C22×D23—41no—
88C22×D23C2×D411yescharacteristic
89C22×D23C2×D411yescharacteristic
90C2×C4×C23—21no—
91C2×C4×C23—21no—
92C2×C4×C23—22no—
93C2×C4×C23—42no—
94C2×C4×C23C2×D411yescharacteristic
95C2×C4×C23#4112yes—
96C2×C4×C23#4112yes—
97C2×C4×C23C2411yescharacteristic
98C2×Dic23—22no—
99C2×Dic23—21no—
100C2×Dic23—21no—
101C2×Dic23—22no—
102C2×Dic23—42no—
103C2×Dic23C2×D411yescharacteristic
104C2×Dic23C2×D411yescharacteristic
105C4×D23—22no—
106C4×D23—22no—
107C4×D23—21no—
108C4×D23—21no—
109C4×D23—21no—
110C4×D23—21no—
111C4×D23—42no—
112C4×D23—42no—
113Dic46—22no—
114Dic46—22no—
115Dic46—42no—
116C8×C23—22no—
117C23⋊C8—22no—
118#3095—231nomaximal, Sylow
119C22×C23—21no—
120C22×C23—21no—
121C22×C23#12312yes—
122C22×C23C22×D411yescharacteristic
123C2×D23—21no—
124C2×D23—21no—
125C2×D23—21no—
126C2×D23—21no—
127C2×D23—21no—
128C2×D23—44no—
129C2×D23#13712yes—
130C4×C23—41no—
131C4×C23—41no—
132C4×C23—42no—
133C4×C23#12312yes—
134C4×C23C2×#4111yescharacteristic
135C4×C23C2×#4111yescharacteristic
136Dic23—21no—
137Dic23—21no—
138Dic23—42no—
139Dic23—41no—
140Dic23—41no—
141C2×C22⋊Q8—231no—
142C2×#117—231no—
143#485—232no—
144#485—232no—
145#484—232no—
146#483—232no—
147#428—231no—
148#428D2311yescharacteristic, complemented
149#419—231no—
150#419—231no—
151#407—231no—
152C2×C23—22no—
153C2×C23C2×#12311yescharacteristic
154C2×C23C2×#13711yescharacteristic
155C2×C23#57511yescharacteristic
156D23—22no—
157D23—41no—
158C22×Q8—231no—
159C23×C4—231no—
160C2×M16—231no—
161C2×M16C2×D2311yescharacteristic
162C22⋊Q8—232no—
163C22⋊Q8—232no—
164C22⋊Q8—461no—
165C22⋊Q8—461no—
166#117—231no—
167#117—231no—
168#117—231no—
169#117—461no—
170#117—461no—
171#117C2×D2311yescharacteristic
172C2×C4⋊C4—231no—
173C2×C4⋊C4—231no—
174C2×C4⋊C4—461no—
175C2×C4⋊C4C2×D2311yescharacteristic
176C2×C22⋊C4—461no—
177C2×C22⋊C4—461no—
178C2×C42—461no—
179#107—232no—
180#107C2×D2312yescomplemented
181#106—232no—
182#106C2×D2312yescomplemented
183#103—232no—
184#103—232no—
185#103—232no—
186#103—232no—
187C22⋊C8—232no—
188C22⋊C8—232no—
189C23#309511yescharacteristic, complemented, Sylow
190C24—231no—
191C2×Q8—232no—
192C2×Q8—461no—
193C2×Q8—462no—
194C2×Q8—462no—
195C22×C4—21no—
196C22×C4—231no—
197C22×C4—231no—
198C22×C4—231no—
199C22×C4—231no—
200C22×C4—231no—
201C22×C4—461no—
202C22×C4—461no—
203C22×C4—462no—
204C22×C4—462no—
205C22×C4—461no—
206C22×C4C22×D2311yescharacteristic
207M16—22no—
208M16—462no—
209C2×C8—232no—
210C2×C8C22×D2312yes—
211C4⋊C4—21no—
212C4⋊C4—231no—
213C4⋊C4—231no—
214C4⋊C4—461no—
215C4⋊C4—461no—
216C4⋊C4—462no—
217C4⋊C4—462no—
218C4⋊C4C22×D2311yescharacteristic
219C4⋊C4C22×D2311yescharacteristic
220C4⋊C4C22×D2312yes—
221C22⋊C4—21no—
222C22⋊C4—461no—
223C22⋊C4—461no—
224C22⋊C4—462no—
225C22⋊C4—462no—
226C22⋊C4—461no—
227C42—21no—
228C42—461no—
229C42—461no—
230C42—461no—
231C23—231no—
232C23—231no—
233C23—462no—
234C23—462no—
235C23—921no—
236C23D4×D2311yescharacteristic
237Q8—462no—
238Q8—462no—
239Q8—922no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—42no—
244C2×C4—231no—
245C2×C4—231no—
246C2×C4—462no—
247C2×C4—462no—
248C2×C4—462no—
249C2×C4—461no—
250C2×C4—461no—
251C2×C4—461no—
252C2×C4—461no—
253C2×C4—461no—
254C2×C4—461no—
255C2×C4—462no—
256C2×C4—922no—
257C2×C4—922no—
258C2×C4—922no—
259C2×C4#6728812yes—
260C2×C4D4×D2311yescharacteristic
261C2×C4#6729212yes—
262C2×C4C23×D2311yescharacteristic
263C8—22no—
264C8—462no—
265C22—21no—
266C22—21no—
267C22—232no—
268C22—461no—
269C22—461no—
270C22—461no—
271C22—461no—
272C22—461no—
273C22—924no—
274C22#1062506512yes—
275C22C2×D4×D2311yescharacteristic
276C4—41no—
277C4—42no—
278C4—41no—
279C4—461no—
280C4—461no—
281C4—922no—
282C4—921no—
283C4—921no—
284C4#1062506512yes—
285C4C2×#6728811yescharacteristic
286C4C2×#6729211yescharacteristic
287C2—22no—
288C2—462no—
289C2—921no—
290C2C2×#1062506511yescharacteristic
291C2#137×D2311yescharacteristic
292C2#1309321311yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#428C2
socleC22×C23C22×D4
prime radicalC23×D23D4
hypercenter#428D23
hypocenterC23#3095
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
3. #13092761C2semidirect
4. #13092760C2semidirect
5. #13092754C2semidirect
6. #13092749C2semidirect
7. #13092457C2semidirect
8. #13092427C2semidirect
9. #13092425C2semidirect
11. C23×#428C2semidirect
33. C23×#107C22semidirect
34. C23×#106C22semidirect
37. #10624998C22semidirect
38. #10624998C22semidirect
39. #10624992C22semidirect
40. #10624992C22semidirect
41. #10624990C22semidirect
42. #10624989C22semidirect
148. #428D23semidirect
180. #107C2×D23semidirect
182. #106C2×D23semidirect
189. C23#3095semidirect

Maximal subgroups

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

subgroupindex
C2×#106250682
#117×D232
#130927612
#130927602
#130927542
#130927492
#130924572
#130924272
#130924252
#130923802
C23×#4282
#309523