Finite Group Databasebeta

← #15683005

Subgroups — #15683005

Order 2944.

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

normal subgroups only

This group has 500 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×#10625121C211yesmaximal, characteristic, complemented
2C22×#67262C211yesmaximal, characteristic, complemented
3#13092929C211yesmaximal, characteristic, complemented
4#13092924C211yesmaximal, characteristic, complemented
5#13092674C212yesmaximal, complemented
6#13092669C212yesmaximal, complemented
7#13092666C212yesmaximal, complemented
8#13092662C212yesmaximal, complemented
9#13092453C211yesmaximal, characteristic, complemented
10#13092414C211yesmaximal, characteristic, complemented
11C23×#416C211yesmaximal, characteristic, complemented
12C2×#41×C23C2211yescharacteristic
13C2×#67288C2211yescharacteristic
14C22×C4×D23C2211yescharacteristic
15C22×C8×C23C2211yescharacteristic
16C23×#117C2211yescharacteristic
17#10625121—24no—
18#10625117C2212yes—
19C2×#67275C2211yescharacteristic, complemented
20C2×#67274C2211yescharacteristic, complemented
21#10625109C2212yes—
22#10625108—21no—
23#10625106—21no—
24C2×#67273C2211yescharacteristic, complemented
25C2×#67272C2211yescharacteristic, complemented
26C4×C22⋊D23—22no—
27#10625097C2211yescharacteristic
28C22×C23⋊C8C2211yescharacteristic
29C2×#67262—24no—
30C2×#67262C2212yes—
31C2×#67262C2212yes—
32#10625068C2212yes—
33#10625066C2212yes—
34#10625057—21no—
35#10625053—21no—
36C4×D92—22no—
37C23×#103C2212yescomplemented
38C23×#102C2212yescomplemented
39#10625003C2212yescomplemented
40#10624998C2212yescomplemented
41#10624990C2212yescomplemented
42#10624989C2212yescomplemented
43C23×D23D411yescharacteristic
44#41×C23—22no—
45#41×C23—22no—
46C2×Q8×C23C2311yescharacteristic
47C2×D4×C23—21no—
48C2×D4×C23C2311yescharacteristic
49C22×C4×C23—21no—
50C22×C4×C23C2311yescharacteristic
51C2×C22⋊D23—21no—
52C2×C22⋊D23—22no—
53C22×Dic23D411yescharacteristic
54#67288—22no—
55#67288—22no—
56C2×D92—22no—
57C2×D92C2311yescharacteristic
58C2×C4×D23—22no—
59C2×C4×D23—22no—
60C2×C4×D23—21no—
61C2×C4×D23D412yes—
62C2×C4×D23C2312yes—
63C2×Dic46C2311yescharacteristic
64C2×C8×C23—22no—
65C2×C8×C23C2312yes—
66C4⋊C4×C23C2312yes—
67C22⋊C4×C23—21no—
68C42×C23—21no—
69C22⋊Dic23—21no—
70C22⋊Dic23—22no—
71#67275—22no—
72#67274—22no—
73#67273—22no—
74#67272—22no—
75(C2×D23)⋊C4—22no—
76(C2×D23)⋊C4—22no—
77(C2×D23)⋊C4—22no—
78C4⋊Dic23—22no—
79C4⋊Dic23C2312yes—
80Dic23⋊C4—22no—
81C4×Dic23—21no—
82C2×C23⋊C8D414yescomplemented
83C2×C23⋊C8C2311yescharacteristic
84C2×C23⋊C8C2311yescharacteristic
85#67262—24no—
86#67262—24no—
87C23×C23—21no—
88C23×C23C2×D411yescharacteristic
89C22×D23—22no—
90C22×D23—21no—
91C22×D23—42no—
92C22×D23C2×D412yes—
93Q8×C23—21no—
94Q8×C23—21no—
95D4×C23—21no—
96D4×C23—21no—
97D4×C23—42no—
98C2×C4×C23—21no—
99C2×C4×C23—22no—
100C2×C4×C23—42no—
101C2×C4×C23C2×D412yes—
102C2×C4×C23C2×D411yescharacteristic
103C2×C4×C23#4112yes—
104C2×C4×C23C2411yescharacteristic
105C22⋊D23—44no—
106C22⋊D23—42no—
107C2×Dic23—22no—
108C2×Dic23—22no—
109C2×Dic23—21no—
110C2×Dic23C2×D412yes—
111D92—21no—
112D92—21no—
113D92—44no—
114C4×D23—24no—
115C4×D23—22no—
116C4×D23—22no—
117C4×D23—42no—
118Dic46—21no—
119Dic46—21no—
120C8×C23—22no—
121C23⋊C8C2×D412yes—
122C23⋊C8C2×D412yes—
123#3054—231nomaximal, Sylow
124C22×C23—22no—
125C22×C23—41no—
126C22×C23—42no—
127C22×C23#12112yes—
128C22×C23C22×D411yescharacteristic
129C2×D23—22no—
130C2×D23—22no—
131C2×D23—22no—
132C2×D23—44no—
133C2×D23—41no—
134C2×D23—42no—
135C4×C23—41no—
136C4×C23—42no—
137C4×C23#12112yes—
138C4×C23C22×D411yescharacteristic
139C4×C23C2×#4111yescharacteristic
140Dic23—22no—
141Dic23—41no—
142Dic23—42no—
143C2×#135—231no—
144C22×M16—231no—
145#525—231no—
146#525—231no—
147#470—232no—
148#469—232no—
149#468—232no—
150#468—232no—
151#427—231no—
152#416—231no—
153#416D2311yescharacteristic, complemented
154C2×C23—22no—
155C2×C23—81no—
156C2×C23C2×#12111yescharacteristic
157C2×C23#57512yes—
158D23—42no—
159D23—81no—
160C2×#41—231no—
161C2×#41C2×D2311yescharacteristic
162C23×C4—231no—
163#135—464no—
164C2×Q16—231no—
165C2×SD16—231no—
166C2×SD16—231no—
167C2×D8—231no—
168C2×M16—232no—
169C2×M16—232no—
170C2×M16—464no—
171C22×C8—231no—
172C22×C8C2×D2311yescharacteristic
173#123—461no—
174#123—461no—
175C22⋊Q8—232no—
176C22⋊Q8—232no—
177#121—232no—
178#121—232no—
179#120—461no—
180#120—461no—
181C4×D4—462no—
182C4×D4—462no—
183#117—231no—
184#117C2×D2311yescharacteristic
185#107—232no—
186#106—232no—
187#103—232no—
188#103C2×D2312yescomplemented
189#102—232no—
190#102C2×D2312yescomplemented
191C23#305411yescharacteristic, complemented, Sylow
192C24—231no—
193#41—22no—
194#41—22no—
195#41—462no—
196#41—462no—
197C2×Q8—231no—
198C2×Q8C22×D2311yescharacteristic
199C2×D4—21no—
200C2×D4—231no—
201C2×D4—462no—
202C2×D4—462no—
203C2×D4—461no—
204C2×D4C22×D2311yescharacteristic
205C22×C4—21no—
206C22×C4—231no—
207C22×C4—232no—
208C22×C4—232no—
209C22×C4—462no—
210C22×C4—462no—
211C22×C4—461no—
212C22×C4C22×D2311yescharacteristic
213Q16—462no—
214SD16—462no—
215SD16—462no—
216D8—462no—
217M16—464no—
218M16—464no—
219C2×C8—22no—
220C2×C8—234no—
221C2×C8—231no—
222C2×C8—231no—
223C2×C8C22×D2312yes—
224C4⋊C4—232no—
225C4⋊C4—462no—
226C4⋊C4—462no—
227C4⋊C4C22×D2312yes—
228C22⋊C4—21no—
229C22⋊C4—462no—
230C22⋊C4—462no—
231C22⋊C4—462no—
232C22⋊C4—462no—
233C22⋊C4—461no—
234C42—21no—
235C42—461no—
236C23—21no—
237C23—232no—
238C23—462no—
239C23—461no—
240C23—922no—
241C23D4×D2311yescharacteristic
242Q8—21no—
243Q8—21no—
244Q8—461no—
245Q8—461no—
246D4—21no—
247D4—21no—
248D4—42no—
249D4—461no—
250D4—461no—
251D4—924no—
252D4—924no—
253D4—922no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—42no—
257C2×C4—232no—
258C2×C4—462no—
259C2×C4—464no—
260C2×C4—462no—
261C2×C4—462no—
262C2×C4—462no—
263C2×C4—461no—
264C2×C4—922no—
265C2×C4#6728812yes—
266C2×C4D4×D2312yes—
267C2×C4D4×D2311yescharacteristic
268C2×C4C23×D2311yescharacteristic
269C8—22no—
270C8—232no—
271C8—232no—
272C22—22no—
273C22—41no—
274C22—42no—
275C22—462no—
276C22—462no—
277C22—462no—
278C22—924no—
279C22—921no—
280C22—922no—
281C22#1062505512yes—
282C22C2×D4×D2311yescharacteristic
283C4—41no—
284C4—42no—
285C4—462no—
286C4—921no—
287C4—922no—
288C4#1062505512yes—
289C4C2×#6728811yescharacteristic
290C4C2×D4×D2311yescharacteristic
291C2—22no—
292C2—81no—
293C2—922no—
294C2—1841no—
295C2C2×#1062505511yescharacteristic
296C2#1309321412yes—
subgroupG/H
centerC2×C4D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#416C2
socleC22×C23C22×D4
hypercenter#416D23
hypocenterC23#3054
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. C2×#10625121C2semidirect
2. C22×#67262C2semidirect
3. #13092929C2semidirect
4. #13092924C2semidirect
5. #13092674C2semidirect
6. #13092669C2semidirect
7. #13092666C2semidirect
8. #13092662C2semidirect
9. #13092453C2semidirect
10. #13092414C2semidirect
11. C23×#416C2semidirect
19. C2×#67275C22semidirect
20. C2×#67274C22semidirect
24. C2×#67273C22semidirect
25. C2×#67272C22semidirect
37. C23×#103C22semidirect
38. C23×#102C22semidirect
39. #10625003C22semidirect
40. #10624998C22semidirect
41. #10624990C22semidirect
42. #10624989C22semidirect
82. C2×C23⋊C8D4semidirect
153. #416D23semidirect
188. #103C2×D23semidirect
190. #102C2×D23semidirect
191. C23#3054semidirect

Maximal subgroups

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

subgroupindex
C2×#106251212
C22×#672622
#130929292
#130929242
#130926742
#130926692
#130926662
#130926622
#130924532
#130924142
C23×#4162
#305423