Finite Group Databasebeta

← #15683192

Subgroups — #15683192

Order 2944.

440 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13092973C211yesmaximal, characteristic, complemented
2C4×D4×D23C211yesmaximal, characteristic
3#13092718C211yesmaximal, characteristic, complemented
4#13092717C211yesmaximal, characteristic, complemented
5#13092714C211yesmaximal, characteristic, complemented
6#13092706C211yesmaximal, characteristic, complemented
7#13092705C211yesmaximal, characteristic, complemented
8#13092696C211yesmaximal, characteristic, complemented
9#13092695C211yesmaximal, characteristic, complemented
10#13092458C211yesmaximal, characteristic, complemented
11#13092456C211yesmaximal, characteristic, complemented
12#13092439C211yesmaximal, characteristic, complemented
13#13092420C211yesmaximal, characteristic
14#13092420C211yesmaximal, characteristic
15C23×#478C211yesmaximal, characteristic, complemented
16C2×D4×D23C2211yescharacteristic
17C22×C4×D23—21no—
18C23×#125C2211yescharacteristic, complemented
19C4×D4×C23C2211yescharacteristic
20D4×Dic23C2211yescharacteristic
21C4×C22⋊D23—21no—
22C2×#67262C2211yescharacteristic
23C2×#67262C2211yescharacteristic
24#10625067—21no—
25#10625067—21no—
26#10625064C2211yescharacteristic
27#10625063C2211yescharacteristic
28#10625063C2211yescharacteristic
29C4⋊C4×D23C2211yescharacteristic
30#10625059C2211yescharacteristic, complemented
31#10625059C2211yescharacteristic, complemented
32#10625058—21no—
33#10625058—21no—
34(C22⋊D23)⋊C4—21no—
35C22⋊C4×D23—21no—
36C4×D92C2211yescharacteristic
37C42×D23C2211yescharacteristic
38#10625041C2211yescharacteristic, complemented
39C23×#107C2211yescharacteristic, complemented
40C23×#106C2211yescharacteristic, complemented
41C23×C4⋊C8C2211yescharacteristic, complemented
42C23×#102C2211yescharacteristic
43C23×#102C2211yescharacteristic
44#10625014C2211yescharacteristic
45#10625014C2211yescharacteristic
46#10625003C2211yescharacteristic
47#10625003C2211yescharacteristic
48#10625000C2211yescharacteristic, complemented
49#10624999C2211yescharacteristic, complemented
50Dic23⋊C8C2211yescharacteristic, complemented
51Dic23⋊C8C2211yescharacteristic, complemented
52#10624991C2211yescharacteristic
53#10624991C2211yescharacteristic
54#10624990C2211yescharacteristic, complemented
55#10624990C2211yescharacteristic, complemented
56#10624989C2211yescharacteristic, complemented
57#10624989C2211yescharacteristic, complemented
58C4⋊(C23⋊C8)C2211yescharacteristic, complemented
59C23×D23—21no—
60C2×D4×C23C2311yescharacteristic
61C22×C4×C23—21no—
62C2×C22⋊D23—21no—
63C22×Dic23—21no—
64D4×D23—22no—
65D4×D23Q814yescomplemented
66C2×D92C2311yescharacteristic
67C2×C4×D23—21no—
68C2×C4×D23—21no—
69C2×C4×D23—21no—
70C2×C4×D23—44no—
71C2×C4×D23D411yescharacteristic
72C2×C4×D23D411yescharacteristic
73C2×C4×D23C2311yescharacteristic
74C2×Dic46—21no—
75C2×Dic46—21no—
76C2×C8×C23C2311yescharacteristic
77C2×C8×C23C2311yescharacteristic
78C4⋊C4×C23—21no—
79C4⋊C4×C23—21no—
80C4⋊C4×C23C2311yescharacteristic
81C4⋊C4×C23C2311yescharacteristic
82C4⋊C4×C23C2311yescharacteristic
83C22⋊C4×C23—21no—
84C42×C23C2311yescharacteristic
85C22⋊Dic23—21no—
86(C2×D23)⋊C4—21no—
87(C2×D23)⋊C4—21no—
88(C2×D23)⋊C4—21no—
89(C2×D23)⋊C4—21no—
90C4⋊Dic23C2311yescharacteristic
91C4⋊Dic23C2311yescharacteristic
92C4⋊Dic23C2311yescharacteristic
93Dic23⋊C4—21no—
94Dic23⋊C4—21no—
95Dic23⋊C4—21no—
96Dic23⋊C4—21no—
97Dic23⋊C4—21no—
98C4×Dic23—21no—
99C4×Dic23—21no—
100C4×Dic23D411yescharacteristic
101C4×Dic23D411yescharacteristic
102C4×Dic23C2311yescharacteristic
103C2×C23⋊C8C2311yescharacteristic
104C2×C23⋊C8C2311yescharacteristic
105#67262—22no—
106#67262—22no—
107C23×C23—21no—
108C22×D23—21no—
109C22×D23—24no—
110C22×D23—42no—
111C22×D23—42no—
112C22×D23C2×D411yescharacteristic
113D4×C23—21no—
114D4×C23C2×Q812yes—
115C2×C4×C23—21no—
116C2×C4×C23—21no—
117C2×C4×C23—21no—
118C2×C4×C23—42no—
119C2×C4×C23C2×D411yescharacteristic
120C2×C4×C23C2×D411yescharacteristic
121C2×C4×C23C2411yescharacteristic
122C22⋊D23—24no—
123C2×Dic23—21no—
124C2×Dic23—21no—
125C2×Dic23—21no—
126C2×Dic23—42no—
127C2×Dic23C2×D411yescharacteristic
128C2×Dic23C2×D411yescharacteristic
129C2×Dic23C2×D411yescharacteristic
130D92—21no—
131D92C2×Q812yes—
132C4×D23—22no—
133C4×D23—41no—
134C4×D23—42no—
135C4×D23—42no—
136C4×D23—42no—
137C4×D23C2×Q812yes—
138C4×D23#4112yes—
139Dic46—42no—
140Dic46—42no—
141C8×C23—21no—
142C8×C23—21no—
143C23⋊C8—21no—
144C23⋊C8—21no—
145#3077—231nomaximal, Sylow
146C22×C23—22no—
147C22×C23—41no—
148C22×C23—41no—
149C22×C23C22×D411yescharacteristic
150C2×D23—21no—
151C2×D23—21no—
152C2×D23—22no—
153C2×D23—48no—
154C2×D23—41no—
155C2×D23—41no—
156C2×D23C22⋊Q812yes—
157C4×C23—21no—
158C4×C23—21no—
159C4×C23—41no—
160C4×C23—41no—
161C4×C23—41no—
162C4×C23C22×Q811yescharacteristic
163C4×C23C2×#4111yescharacteristic
164Dic23—21no—
165Dic23—41no—
166Dic23—41no—
167Dic23—41no—
168Dic23C22⋊Q812yes—
169Dic23AGL(1,ℤ/8)12yes—
170#533—231no—
171C2×C4×D4—231no—
172#478—231no—
173#478—231no—
174#478—231no—
175#478D2311yescharacteristic, complemented
176#476—231no—
177#476—231no—
178#474—231no—
179#474—231no—
180#428—231no—
181#428—231no—
182#423—231no—
183#418—231no—
184#418—231no—
185C2×C23—42no—
186C2×C23C2×C22⋊Q811yescharacteristic
187C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
188C2×C23#57511yescharacteristic
189D23—22no—
190D23—42no—
191C22×D4—231no—
192C23×C4—461no—
193C2×M16—231no—
194C2×M16—231no—
195C4⋊Q8—231no—
196C4⋊Q8—231no—
197#125—231no—
198#125C2×D2311yescharacteristic, complemented
199C22⋊Q8—461no—
200C22⋊Q8—461no—
201C4×Q8—461no—
202C4×Q8—461no—
203C4×D4—231no—
204C4×D4—231no—
205C4×D4—231no—
206C4×D4—461no—
207C4×D4—461no—
208C4×D4C2×D2311yescharacteristic
209#117—231no—
210#117—231no—
211C2×C4⋊C4—231no—
212C2×C22⋊C4—461no—
213C2×C42—231no—
214#107—231no—
215#107—231no—
216#107—231no—
217#107C2×D2311yescharacteristic, complemented
218#106—231no—
219#106—231no—
220#106—231no—
221#106C2×D2311yescharacteristic, complemented
222C4⋊C8—231no—
223C4⋊C8—231no—
224C4⋊C8—231no—
225C4⋊C8C2×D2311yescharacteristic, complemented
226#102—231no—
227#102—231no—
228#102—231no—
229#102—231no—
230#102—231no—
231#102—231no—
232#102C2×D2311yescharacteristic
233#102C2×D2311yescharacteristic
234C23#307711yescharacteristic, complemented, Sylow
235C24—461no—
236C2×Q8—461no—
237C2×Q8—461no—
238C2×D4—234no—
239C2×D4—231no—
240C2×D4—462no—
241C2×D4—461no—
242C2×D4C22×D2311yescharacteristic
243C22×C4—21no—
244C22×C4—231no—
245C22×C4—231no—
246C22×C4—231no—
247C22×C4—461no—
248C22×C4—461no—
249C22×C4—461no—
250C22×C4—461no—
251C22×C4—924no—
252M16—462no—
253M16—462no—
254C2×C8—231no—
255C2×C8—231no—
256C2×C8C22×D2311yescharacteristic
257C2×C8C22×D2311yescharacteristic
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—231no—
261C4⋊C4—231no—
262C4⋊C4—231no—
263C4⋊C4—461no—
264C4⋊C4—461no—
265C4⋊C4—461no—
266C4⋊C4—461no—
267C4⋊C4—461no—
268C4⋊C4C22×D2311yescharacteristic
269C4⋊C4C22×D2311yescharacteristic
270C4⋊C4C22×D2311yescharacteristic
271C22⋊C4—21no—
272C22⋊C4—461no—
273C22⋊C4—461no—
274C22⋊C4—461no—
275C22⋊C4—461no—
276C22⋊C4—461no—
277C42—231no—
278C42—231no—
279C42—231no—
280C42—461no—
281C42—461no—
282C42C22×D2311yescharacteristic
283C23—21no—
284C23—231no—
285C23—464no—
286C23—461no—
287C23—922no—
288C23—922no—
289Q8—922no—
290Q8—922no—
291D4—21no—
292D4—232no—
293D4—464no—
294D4—461no—
295D4Q8×D2312yes—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—42no—
300C2×C4—231no—
301C2×C4—231no—
302C2×C4—232no—
303C2×C4—232no—
304C2×C4—231no—
305C2×C4—462no—
306C2×C4—461no—
307C2×C4—461no—
308C2×C4—461no—
309C2×C4—921no—
310C2×C4—922no—
311C2×C4—922no—
312C2×C4—922no—
313C2×C4—922no—
314C2×C4D4×D2311yescharacteristic
315C2×C4D4×D2311yescharacteristic
316C2×C4C23×D2311yescharacteristic
317C8—21no—
318C8—21no—
319C8—461no—
320C8—461no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—232no—
325C22—461no—
326C22—461no—
327C22—462no—
328C22—928no—
329C22—921no—
330C22—921no—
331C22C2×D4×D2311yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—232no—
338C4—232no—
339C4—461no—
340C4—921no—
341C4—921no—
342C4—921no—
343C4C2×Q8×D2311yescharacteristic
344C4#41×D2311yescharacteristic
345C2—42no—
346C2—462no—
347C2—922no—
348C2C22⋊Q8×D2311yescharacteristic
349C2AGL(1,ℤ/8)×D2311yescharacteristic
350C2#1309321411yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#478C2
socleC22×C23C22×D4
prime radicalC2×D4×D23C22
hypercenter#478D23
hypocenterC23#3077
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. #13092973C2semidirect
3. #13092718C2semidirect
4. #13092717C2semidirect
5. #13092714C2semidirect
6. #13092706C2semidirect
7. #13092705C2semidirect
8. #13092696C2semidirect
9. #13092695C2semidirect
10. #13092458C2semidirect
11. #13092456C2semidirect
12. #13092439C2semidirect
15. C23×#478C2semidirect
18. C23×#125C22semidirect
30. #10625059C22semidirect
31. #10625059C22semidirect
38. #10625041C22semidirect
39. C23×#107C22semidirect
40. C23×#106C22semidirect
41. C23×C4⋊C8C22semidirect
48. #10625000C22semidirect
49. #10624999C22semidirect
50. Dic23⋊C8C22semidirect
51. Dic23⋊C8C22semidirect
54. #10624990C22semidirect
55. #10624990C22semidirect
56. #10624989C22semidirect
57. #10624989C22semidirect
58. C4⋊(C23⋊C8)C22semidirect
65. D4×D23Q8semidirect
175. #478D23semidirect
198. #125C2×D23semidirect
217. #107C2×D23semidirect
221. #106C2×D23semidirect
225. C4⋊C8C2×D23semidirect
234. C23#3077semidirect

Maximal subgroups

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

subgroupindex
#130929732
C4×D4×D232
#130927182
#130927172
#130927142
#130927062
#130927052
#130926962
#130926952
#130924582
#130924562
#130924392
#130924202
C23×#4782
#307723