Finite Group Databasebeta

← #15685229

Subgroups — #15685229

Order 2944.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093105C211yesmaximal, characteristic, complemented
2#13093062C211yesmaximal, characteristic
3#13092774C211yesmaximal, characteristic, complemented
4#13092749C211yesmaximal, characteristic, complemented
5#13092744C211yesmaximal, characteristic, complemented
6#13092659C211yesmaximal, characteristic, complemented
7#13092647C211yesmaximal, characteristic, complemented
8#13092640C211yesmaximal, characteristic, complemented
9#13092580C211yesmaximal, characteristic, complemented
10#13092569C211yesmaximal, characteristic, complemented
11C4×#67273C211yesmaximal, characteristic, complemented
12#13092482C211yesmaximal, characteristic, complemented
13#13092410C211yesmaximal, characteristic, complemented
14#102×D23C211yesmaximal, characteristic, complemented
15C23×#478C211yesmaximal, characteristic, complemented
16C2×#67290C2211yescharacteristic
17C2×D4×D23C2211yescharacteristic
18C23×#125C2211yescharacteristic, complemented
19C4×D4×C23C2211yescharacteristic
20C2×#67273C2211yescharacteristic
21#10625101—21no—
22C2×(C2×D23)⋊C4—21no—
23C2×Dic92C2211yescharacteristic, complemented
24C2×#67263C2211yescharacteristic
25C2×C8×D23C2211yescharacteristic
26C2×C8×D23C2211yescharacteristic, complemented
27#10625069—21no—
28#10625068C2211yescharacteristic
29#10625068C2211yescharacteristic
30#10625068C2211yescharacteristic, complemented
31#10625066C2211yescharacteristic
32#10625065—21no—
33#10625063—21no—
34#10625063C2211yescharacteristic, complemented
35C4⋊C4×D23C2211yescharacteristic
36#10625061—21no—
37#10625057—21no—
38#10625053—21no—
39#10625046C2211yescharacteristic
40C4×D92C2211yescharacteristic
41C4×Dic46C2211yescharacteristic, complemented
42C23×#107C2211yescharacteristic, complemented
43C23×#106C2211yescharacteristic, complemented
44C23×C4⋊C8C2211yescharacteristic, complemented
45C23×#102C2211yescharacteristic
46C23×#102C2211yescharacteristic
47#10625014C2211yescharacteristic
48#10625003C2211yescharacteristic
49(C2×D23)⋊C8C2211yescharacteristic
50(C2×D23)⋊C8C2211yescharacteristic, complemented
51#10624998C2211yescharacteristic, complemented
52#10624992C2211yescharacteristic, complemented
53#10624992C2211yescharacteristic, complemented
54#10624992C2211yescharacteristic, complemented
55#10624991C2211yescharacteristic
56#10624991C2211yescharacteristic
57#10624990C2211yescharacteristic, complemented
58C4×C23⋊C8C2211yescharacteristic, complemented
59C23×D23—21no—
60C2×D4×C23C2311yescharacteristic
61C22×C4×C23—21no—
62C2×C22⋊D23—21no—
63C2×C22⋊D23—21no—
64C22×Dic23—21no—
65#67290—22no—
66#67290—41no—
67D4×D23—22no—
68D4×D23—41no—
69C2×D92—21no—
70C2×D92D411yescharacteristic
71C2×D92C2311yescharacteristic
72C2×C4×D23—21no—
73C2×C4×D23C2311yescharacteristic
74C2×C4×D23C2311yescharacteristic
75C2×Dic46C2311yescharacteristic
76C2×Dic46C2311yescharacteristic
77C2×C8×C23C2311yescharacteristic
78C2×C8×C23C2311yescharacteristic
79C4⋊C4×C23—21no—
80C4⋊C4×C23—21no—
81C4⋊C4×C23C2311yescharacteristic
82C4⋊C4×C23C2311yescharacteristic
83C4⋊C4×C23C2311yescharacteristic
84C22⋊C4×C23—21no—
85C42×C23C2311yescharacteristic
86#67273—22no—
87(C2×D23)⋊C4—21no—
88(C2×D23)⋊C4—21no—
89(C2×D23)⋊C4—21no—
90(C2×D23)⋊C4—21no—
91(C2×D23)⋊C4—21no—
92(C2×D23)⋊C4—21no—
93(C2×D23)⋊C4—21no—
94(C2×D23)⋊C4D411yescharacteristic
95(C2×D23)⋊C4D411yescharacteristic
96C4⋊Dic23—21no—
97C4⋊Dic23—21no—
98C4⋊Dic23—21no—
99C4⋊Dic23D411yescharacteristic
100C4⋊Dic23C2311yescharacteristic
101Dic23⋊C4—21no—
102Dic23⋊C4—21no—
103C4×Dic23—21no—
104C4×Dic23—21no—
105C2×C23⋊C8C2311yescharacteristic
106C2×C23⋊C8C2311yescharacteristic
107Dic92—41no—
108#67263—41no—
109C8×D23—41no—
110C8×D23—41no—
111C23×C23—21no—
112C22×D23—21no—
113C22×D23—42no—
114C22×D23—42no—
115C22×D23—81no—
116C22×D23C2×D411yescharacteristic
117C22×D23C2×D411yescharacteristic
118D4×C23—21no—
119D4×C23#4112yes—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23—81no—
124C2×C4×C23C2×D411yescharacteristic
125C2×C4×C23C2×D411yescharacteristic
126C2×C4×C23C2411yescharacteristic
127C22⋊D23—42no—
128C22⋊D23—42no—
129C2×Dic23—21no—
130C2×Dic23—21no—
131C2×Dic23—21no—
132C2×Dic23—42no—
133C2×Dic23C2×D411yescharacteristic
134C2×Dic23C2×D411yescharacteristic
135D92—22no—
136D92—21no—
137D92—21no—
138D92—81no—
139C4×D23—21no—
140C4×D23—21no—
141C4×D23—21no—
142C4×D23—21no—
143C4×D23—42no—
144Dic46—21no—
145Dic46—21no—
146Dic46—21no—
147Dic46—21no—
148C8×C23—21no—
149C8×C23—21no—
150C23⋊C8—21no—
151C23⋊C8—21no—
152#3296—231nomaximal, Sylow
153C22×C23—22no—
154C22×C23—41no—
155C22×C23—41no—
156C22×C23C22×D411yescharacteristic
157C2×D23—21no—
158C2×D23—21no—
159C2×D23—21no—
160C2×D23—21no—
161C2×D23—21no—
162C2×D23—41no—
163C2×D23—41no—
164C2×D23—41no—
165C2×D23—84no—
166C2×D23#13512yes—
167C4×C23—21no—
168C4×C23—21no—
169C4×C23—41no—
170C4×C23—41no—
171C4×C23—41no—
172C4×C23C2×#4111yescharacteristic
173C4×C23H(5,𝔽2)11yescharacteristic
174Dic23—21no—
175Dic23—21no—
176Dic23—41no—
177Dic23—41no—
178Dic23—41no—
179#552—231no—
180#546—231no—
181#488—231no—
182#483—231no—
183#482—231no—
184#478D2311yescharacteristic, complemented
185#467—231no—
186#465—231no—
187#464—231no—
188#452—231no—
189#450—231no—
190C4×SD16—231no—
191C8×D4—231no—
192#416—231no—
193C2×#102—231no—
194C2×C23—42no—
195C2×C23#54611yescharacteristic
196C2×C23C2×#13511yescharacteristic
197C2×C23#57711yescharacteristic
198D23—22no—
199D23—41no—
200D23—81no—
201C2×#41—231no—
202C22×D4—231no—
203C2×Q16—231no—
204C2×SD16—231no—
205C2×SD16—231no—
206C22×C8—231no—
207C22×C8—231no—
208#126—461no—
209#125—461no—
210#125C2×D2311yescharacteristic, complemented
211#124—231no—
212#123—461no—
213#123—461no—
214C22⋊Q8—231no—
215C22⋊Q8—231no—
216C22⋊Q8—231no—
217#121—231no—
218#121—461no—
219#120—461no—
220C4×Q8—231no—
221C4×D4—231no—
222C4×D4C2×D2311yescharacteristic
223#117—231no—
224#117—461no—
225C2×C4⋊C4—231no—
226C2×C22⋊C4—461no—
227#107C2×D2311yescharacteristic, complemented
228#106—231no—
229#106C2×D2311yescharacteristic, complemented
230C4⋊C8C2×D2311yescharacteristic, complemented
231#103—231no—
232#103—231no—
233#103—231no—
234#103—231no—
235#102—231no—
236#102—231no—
237#102—231no—
238#102—231no—
239#102C2×D2311yescharacteristic
240#102C2×D2311yescharacteristic
241C22⋊C8—231no—
242C22⋊C8—231no—
243C4×C8—231no—
244C23#329611yescharacteristic, complemented, Sylow
245C24—461no—
246#41—462no—
247#41—921no—
248C2×Q8—231no—
249C2×Q8—231no—
250C2×D4—231no—
251C2×D4—231no—
252C2×D4—461no—
253C2×D4—461no—
254C2×D4—462no—
255C2×D4—461no—
256C2×D4—921no—
257C2×D4C22×D2311yescharacteristic
258C22×C4—21no—
259C22×C4—231no—
260C22×C4—231no—
261C22×C4—461no—
262C22×C4—461no—
263Q16—921no—
264SD16—462no—
265SD16—921no—
266C2×C8—231no—
267C2×C8—231no—
268C2×C8—921no—
269C2×C8—921no—
270C2×C8C22×D2311yescharacteristic
271C2×C8C22×D2311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—231no—
275C4⋊C4—231no—
276C4⋊C4—461no—
277C4⋊C4—461no—
278C4⋊C4—461no—
279C4⋊C4—461no—
280C4⋊C4—461no—
281C4⋊C4C22×D2311yescharacteristic
282C4⋊C4C22×D2311yescharacteristic
283C4⋊C4C22×D2311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—231no—
286C22⋊C4—231no—
287C22⋊C4—461no—
288C22⋊C4—461no—
289C22⋊C4—461no—
290C22⋊C4—461no—
291C22⋊C4—461no—
292C22⋊C4—461no—
293C22⋊C4—461no—
294C42—461no—
295C42—461no—
296C42C22×D2311yescharacteristic
297C23—21no—
298C23—231no—
299C23—231no—
300C23—461no—
301C23—922no—
302C23—922no—
303C23—1841no—
304Q8—461no—
305Q8—461no—
306Q8—461no—
307Q8—461no—
308D4—21no—
309D4—462no—
310D4—461no—
311D4—461no—
312D4—922no—
313D4—922no—
314D4—1841no—
315D4#6729212yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—231no—
321C2×C4—231no—
322C2×C4—461no—
323C2×C4—461no—
324C2×C4—461no—
325C2×C4—461no—
326C2×C4—461no—
327C2×C4—461no—
328C2×C4—461no—
329C2×C4—922no—
330C2×C4—922no—
331C2×C4D4×D2311yescharacteristic
332C2×C4D4×D2311yescharacteristic
333C2×C4C23×D2311yescharacteristic
334C8—21no—
335C8—21no—
336C8—461no—
337C8—461no—
338C22—22no—
339C22—41no—
340C22—41no—
341C22—232no—
342C22—461no—
343C22—461no—
344C22—461no—
345C22—461no—
346C22—461no—
347C22—921no—
348C22—921no—
349C22—921no—
350C22—1844no—
351C22C2×D4×D2311yescharacteristic
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—461no—
358C4—461no—
359C4—921no—
360C4—921no—
361C4—921no—
362C4C2×#6729211yescharacteristic
363C4#1062516011yescharacteristic
364C2—42no—
365C2—462no—
366C2—921no—
367C2—1841no—
368C2#1309305811yescharacteristic
369C2#135×D2311yescharacteristic
370C2#1309322711yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#478C2
socleC22×C23C22×D4
prime radical#13093062C2
hypercenter#478D23
hypocenterC23#3296
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #13093105C2semidirect
3. #13092774C2semidirect
4. #13092749C2semidirect
5. #13092744C2semidirect
6. #13092659C2semidirect
7. #13092647C2semidirect
8. #13092640C2semidirect
9. #13092580C2semidirect
10. #13092569C2semidirect
11. C4×#67273C2semidirect
12. #13092482C2semidirect
13. #13092410C2semidirect
14. #102×D23C2semidirect
15. C23×#478C2semidirect
18. C23×#125C22semidirect
23. C2×Dic92C22semidirect
26. C2×C8×D23C22semidirect
30. #10625068C22semidirect
34. #10625063C22semidirect
41. C4×Dic46C22semidirect
42. C23×#107C22semidirect
43. C23×#106C22semidirect
44. C23×C4⋊C8C22semidirect
50. (C2×D23)⋊C8C22semidirect
51. #10624998C22semidirect
52. #10624992C22semidirect
53. #10624992C22semidirect
54. #10624992C22semidirect
57. #10624990C22semidirect
58. C4×C23⋊C8C22semidirect
184. #478D23semidirect
210. #125C2×D23semidirect
227. #107C2×D23semidirect
229. #106C2×D23semidirect
230. C4⋊C8C2×D23semidirect
244. C23#3296semidirect

Maximal subgroups

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

subgroupindex
#130931052
#130930622
#130927742
#130927492
#130927442
#130926592
#130926472
#130926402
#130925802
#130925692
C4×#672732
#130924822
#130924102
#102×D232
C23×#4782
#329623