Finite Group Databasebeta

← #15685227

Subgroups — #15685227

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#13093101C211yesmaximal, characteristic, complemented
2#13093064C211yesmaximal, characteristic
3#13092770C211yesmaximal, characteristic, complemented
4#13092749C211yesmaximal, characteristic, complemented
5#13092738C211yesmaximal, characteristic, complemented
6#13092716C211yesmaximal, characteristic, complemented
7#13092657C211yesmaximal, characteristic, complemented
8#13092637C211yesmaximal, characteristic, complemented
9#13092577C211yesmaximal, characteristic, complemented
10#13092566C211yesmaximal, characteristic, complemented
11#13092502C211yesmaximal, characteristic, complemented
12C8×C22⋊D23C211yesmaximal, characteristic, complemented
13#13092414C211yesmaximal, characteristic, complemented
14#102×D23C211yesmaximal, characteristic, complemented
15C23×#465C211yesmaximal, characteristic, complemented
16C2×D4×D23C2211yescharacteristic
17C2×#67288C2211yescharacteristic
18C2×SD16×C23C2211yescharacteristic
19C22×C8×C23C2211yescharacteristic, complemented
20C23×C22⋊Q8C2211yescharacteristic, complemented
21C23×#121C2211yescharacteristic
22#10625117C2211yescharacteristic
23Q8×Dic23C2211yescharacteristic, complemented
24C2×#67275C2211yescharacteristic, complemented
25C2×#67274C2211yescharacteristic
26#10625109—21no—
27#10625108—21no—
28#10625107C2211yescharacteristic
29C4×C22⋊D23C2211yescharacteristic
30#10625097C2211yescharacteristic, complemented
31C2×C8×D23C2211yescharacteristic
32#10625068C2211yescharacteristic
33#10625064C2211yescharacteristic
34#10625063—21no—
35C4⋊C4×D23C2211yescharacteristic
36#10625061C2211yescharacteristic, complemented
37#10625060—21no—
38#10625054—21no—
39#10625054—21no—
40C22⋊C4×D23—21no—
41#10625050—21no—
42C23×#106C2211yescharacteristic, complemented
43C23×#103C2211yescharacteristic, complemented
44C23×#102C2211yescharacteristic
45#10625014C2211yescharacteristic
46#10625014C2211yescharacteristic
47C22⋊(C23⋊C8)C2211yescharacteristic, complemented
48#10625003C2211yescharacteristic
49#10625003C2211yescharacteristic
50(C2×D23)⋊C8C2211yescharacteristic
51#10624998C2211yescharacteristic, complemented
52#10624998C2211yescharacteristic, complemented
53Dic23⋊C8C2211yescharacteristic, complemented
54C8×Dic23C2211yescharacteristic, complemented
55#10624992C2211yescharacteristic, complemented
56#10624991C2211yescharacteristic
57#10624990C2211yescharacteristic, complemented
58#10624989C2211yescharacteristic, complemented
59C23×D23—21no—
60C2×Q8×C23C2311yescharacteristic
61C2×D4×C23—21no—
62C2×D4×C23C2311yescharacteristic
63C22×C4×C23C2311yescharacteristic
64C2×C22⋊D23—21no—
65C2×C22⋊D23—21no—
66C2×C22⋊D23D411yescharacteristic
67D4×D23—22no—
68D4×D23—41no—
69#67288—22no—
70#67288—41no—
71C2×D92C2311yescharacteristic
72C2×C4×D23—21no—
73C2×C4×D23—21no—
74C2×C4×D23—21no—
75C2×C4×D23C2311yescharacteristic
76C2×Dic46C2311yescharacteristic
77SD16×C23—41no—
78C2×C8×C23—41no—
79C2×C8×C23C2311yescharacteristic
80C2×C8×C23C2311yescharacteristic
81C4⋊C4×C23—21no—
82C4⋊C4×C23C2311yescharacteristic
83C4⋊C4×C23C2311yescharacteristic
84C22⋊C4×C23—21no—
85C22⋊C4×C23—21no—
86C22⋊Dic23—21no—
87C22⋊Dic23—21no—
88C22⋊Dic23—21no—
89C22⋊Dic23D411yescharacteristic
90#67275—41no—
91#67274—22no—
92(C2×D23)⋊C4—21no—
93(C2×D23)⋊C4—21no—
94(C2×D23)⋊C4—21no—
95(C2×D23)⋊C4D411yescharacteristic
96C4⋊Dic23—21no—
97C4⋊Dic23—21no—
98C4⋊Dic23—21no—
99C4⋊Dic23C2311yescharacteristic
100C4⋊Dic23C2311yescharacteristic
101Dic23⋊C4—21no—
102Dic23⋊C4—21no—
103Dic23⋊C4—21no—
104Dic23⋊C4D411yescharacteristic
105C4×Dic23—21no—
106C4×Dic23—21no—
107C4×Dic23C2311yescharacteristic
108C2×C23⋊C8C2311yescharacteristic
109C2×C23⋊C8C2311yescharacteristic
110C8×D23—41no—
111C23×C23—21no—
112C23×C23C2×D411yescharacteristic
113C22×D23—21no—
114C22×D23—42no—
115C22×D23—42no—
116C22×D23—81no—
117C22×D23C2×D411yescharacteristic
118Q8×C23—21no—
119Q8×C23—21no—
120D4×C23—21no—
121D4×C23—21no—
122D4×C23—81no—
123C2×C4×C23—21no—
124C2×C4×C23—21no—
125C2×C4×C23—21no—
126C2×C4×C23—21no—
127C2×C4×C23—21no—
128C2×C4×C23C2×D411yescharacteristic
129C2×C4×C23C2411yescharacteristic
130C22⋊D23—22no—
131C22⋊D23—42no—
132C22⋊D23—42no—
133C2×Dic23—21no—
134C2×Dic23—21no—
135C2×Dic23—21no—
136C2×Dic23C2×D411yescharacteristic
137C2×Dic23C2×D411yescharacteristic
138C2×Dic23C2×D411yescharacteristic
139D92—21no—
140D92#4112yes—
141C4×D23—21no—
142C4×D23—21no—
143C4×D23—42no—
144C4×D23—42no—
145C4×D23—81no—
146Dic46—21no—
147Dic46—21no—
148C8×C23—21no—
149C8×C23—21no—
150C23⋊C8—21no—
151C23⋊C8—21no—
152#3296—231nomaximal, Sylow
153C22×C23—21no—
154C22×C23—21no—
155C22×C23—21no—
156C22×C23—41no—
157C22×C23—41no—
158C22×C23—41no—
159C22×C23C22×D411yescharacteristic
160C2×D23—21no—
161C2×D23—21no—
162C2×D23—22no—
163C2×D23—41no—
164C2×D23—41no—
165C2×D23—84no—
166C2×D23#13512yes—
167C4×C23—21no—
168C4×C23—41no—
169C4×C23—41no—
170C4×C23—41no—
171C4×C23C2×#4111yescharacteristic
172C4×C23H(5,𝔽2)11yescharacteristic
173Dic23—21no—
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#478—231no—
185#467—231no—
186#465D2311yescharacteristic, complemented
187#464—231no—
188#452—231no—
189#450—231no—
190C4×SD16—231no—
191C8×D4—231no—
192#416—231no—
193C2×#102—231no—
194C2×C23—41no—
195C2×C23—81no—
196C2×C23#54611yescharacteristic
197C2×C23C2×#13511yescharacteristic
198C2×C23#57711yescharacteristic
199D23—22no—
200D23—42no—
201C2×#41—231no—
202C22×D4—231no—
203C2×Q16—231no—
204C2×SD16—231no—
205C2×SD16C2×D2311yescharacteristic
206C22×C8—231no—
207C22×C8C2×D2311yescharacteristic, complemented
208#126—461no—
209#125—231no—
210#125—461no—
211#124—231no—
212#123—461no—
213#123—461no—
214C22⋊Q8—231no—
215C22⋊Q8—231no—
216C22⋊Q8C2×D2311yescharacteristic, complemented
217#121—461no—
218#121C2×D2311yescharacteristic
219#120—461no—
220C4×Q8—231no—
221C4×D4—231no—
222C4×D4—231no—
223#117—231no—
224#117—461no—
225C2×C4⋊C4—231no—
226C2×C22⋊C4—461no—
227#107—231no—
228#106—231no—
229#106C2×D2311yescharacteristic, complemented
230C4⋊C8—231no—
231#103—231no—
232#103—231no—
233#103—231no—
234#103C2×D2311yescharacteristic, complemented
235#102—231no—
236#102—231no—
237#102—231no—
238#102—231no—
239#102—231no—
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×Q8C22×D2311yescharacteristic
250C2×D4—21no—
251C2×D4—231no—
252C2×D4—231no—
253C2×D4—461no—
254C2×D4—462no—
255C2×D4—461no—
256C2×D4—921no—
257C2×D4C22×D2311yescharacteristic
258C22×C4—231no—
259C22×C4—461no—
260C22×C4—461no—
261C22×C4—461no—
262C22×C4C22×D2311yescharacteristic
263Q16—921no—
264SD16—41no—
265SD16—462no—
266C2×C8—41no—
267C2×C8—231no—
268C2×C8—231no—
269C2×C8—921no—
270C2×C8C22×D2311yescharacteristic
271C2×C8C22×D2311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—231no—
274C4⋊C4—231no—
275C4⋊C4—231no—
276C4⋊C4—461no—
277C4⋊C4—461no—
278C4⋊C4—461no—
279C4⋊C4—461no—
280C4⋊C4—461no—
281C4⋊C4—461no—
282C4⋊C4C22×D2311yescharacteristic
283C4⋊C4C22×D2311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—231no—
287C22⋊C4—231no—
288C22⋊C4—461no—
289C22⋊C4—461no—
290C22⋊C4—461no—
291C22⋊C4—461no—
292C22⋊C4—461no—
293C22⋊C4—461no—
294C42—231no—
295C42—461no—
296C42—461no—
297C23—21no—
298C23—231no—
299C23—461no—
300C23—922no—
301C23—922no—
302C23—1841no—
303C23D4×D2311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—461no—
307Q8—461no—
308D4—21no—
309D4—21no—
310D4—81no—
311D4—232no—
312D4—462no—
313D4—461no—
314D4—922no—
315D4—922no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—231no—
322C2×C4—231no—
323C2×C4—231no—
324C2×C4—461no—
325C2×C4—461no—
326C2×C4—461no—
327C2×C4—461no—
328C2×C4—461no—
329C2×C4—922no—
330C2×C4—922no—
331C2×C4—1841no—
332C2×C4D4×D2311yescharacteristic
333C2×C4C23×D2311yescharacteristic
334C8—21no—
335C8—21no—
336C8—461no—
337C8—461no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—232no—
345C22—461no—
346C22—461no—
347C22—462no—
348C22—921no—
349C22—921no—
350C22—1844no—
351C22C2×D4×D2311yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—461no—
357C4—461no—
358C4—461no—
359C4—921no—
360C4—921no—
361C4—921no—
362C4#1062515511yescharacteristic
363C4#41×D2311yescharacteristic
364C2—41no—
365C2—81no—
366C2—462no—
367C2—922no—
368C2#1309305611yescharacteristic
369C2#135×D2311yescharacteristic
370C2#1309322311yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#465C2
socleC22×C23C22×D4
prime radical#13093064C2
hypercenter#465D23
hypocenterC23#3296
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #13093101C2semidirect
3. #13092770C2semidirect
4. #13092749C2semidirect
5. #13092738C2semidirect
6. #13092716C2semidirect
7. #13092657C2semidirect
8. #13092637C2semidirect
9. #13092577C2semidirect
10. #13092566C2semidirect
11. #13092502C2semidirect
12. C8×C22⋊D23C2semidirect
13. #13092414C2semidirect
14. #102×D23C2semidirect
15. C23×#465C2semidirect
19. C22×C8×C23C22semidirect
20. C23×C22⋊Q8C22semidirect
23. Q8×Dic23C22semidirect
24. C2×#67275C22semidirect
30. #10625097C22semidirect
36. #10625061C22semidirect
42. C23×#106C22semidirect
43. C23×#103C22semidirect
47. C22⋊(C23⋊C8)C22semidirect
51. #10624998C22semidirect
52. #10624998C22semidirect
53. Dic23⋊C8C22semidirect
54. C8×Dic23C22semidirect
55. #10624992C22semidirect
57. #10624990C22semidirect
58. #10624989C22semidirect
186. #465D23semidirect
207. C22×C8C2×D23semidirect
216. C22⋊Q8C2×D23semidirect
229. #106C2×D23semidirect
234. #103C2×D23semidirect
244. C23#3296semidirect

Maximal subgroups

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

subgroupindex
#130931012
#130930642
#130927702
#130927492
#130927382
#130927162
#130926572
#130926372
#130925772
#130925662
#130925022
C8×C22⋊D232
#130924142
#102×D232
C23×#4652
#329623