Finite Group Databasebeta

← #15685230

Subgroups — #15685230

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#13093102C211yesmaximal, characteristic, complemented
2#13093058C211yesmaximal, characteristic
3#13092773C211yesmaximal, characteristic, complemented
4#13092743C211yesmaximal, characteristic, complemented
5#13092716C211yesmaximal, characteristic, complemented
6#13092656C211yesmaximal, characteristic, complemented
7#13092647C211yesmaximal, characteristic, complemented
8#13092642C211yesmaximal, characteristic, complemented
9#13092582C211yesmaximal, characteristic, complemented
10#13092570C211yesmaximal, characteristic, complemented
11#13092504C211yesmaximal, characteristic, complemented
12(C22⋊D23)⋊C8C211yesmaximal, characteristic, complemented
13#13092412C211yesmaximal, characteristic, complemented
14C2×#10624991C211yesmaximal, characteristic, complemented
15C23×#483C211yesmaximal, characteristic, complemented
16C2×#67292C2211yescharacteristic
17C22×D92C2211yescharacteristic
18C23×C22⋊Q8C2211yescharacteristic
19C2×C4⋊C4×C23C2211yescharacteristic
20#10625118C2211yescharacteristic
21C2×#67275C2211yescharacteristic, complemented
22#10625100—21no—
23C4×C22⋊D23C2211yescharacteristic
24#10625097—21no—
25#10625095C2211yescharacteristic
26C22×C23⋊C8C2211yescharacteristic
27C2×#67263C2211yescharacteristic
28C2×#67263C2211yescharacteristic
29C2×C8×D23C2211yescharacteristic, complemented
30#10625069—21no—
31#10625068C2211yescharacteristic, complemented
32#10625066—21no—
33#10625066C2211yescharacteristic
34#10625065—21no—
35#10625064C2211yescharacteristic
36#10625063C2211yescharacteristic, complemented
37#10625061C2211yescharacteristic, complemented
38#10625060—21no—
39#10625058C2211yescharacteristic, complemented
40#10625053—21no—
41C22⋊C4×D23—21no—
42C23×#106C2211yescharacteristic, complemented
43C23×#106C2211yescharacteristic, complemented
44C23×#103C2211yescharacteristic, complemented
45C23×#103C2211yescharacteristic, complemented
46C23×C22⋊C8C2211yescharacteristic
47#10625017C2211yescharacteristic, complemented
48#10625003C2211yescharacteristic
49#10625003C2211yescharacteristic
50(C2×D23)⋊C8C2211yescharacteristic, complemented
51Dic23⋊C8C2211yescharacteristic, complemented
52C8×Dic23C2211yescharacteristic, complemented
53#10624992C2211yescharacteristic, complemented
54#10624991C2211yescharacteristic
55#10624991C2211yescharacteristic
56#10624991C2211yescharacteristic
57#10624991C2211yescharacteristic
58#10624989C2211yescharacteristic, complemented
59C23×D23—21no—
60C2×Q8×C23C2311yescharacteristic
61C22×C4×C23—21no—
62C22×C4×C23C2311yescharacteristic
63C2×C22⋊D23D411yescharacteristic
64#67292—22no—
65#67292—41no—
66C2×D92—22no—
67C2×D92—21no—
68C2×D92—21no—
69C2×D92—21no—
70C2×D92—41no—
71C2×D92C2311yescharacteristic
72C2×D92C2311yescharacteristic
73C2×C4×D23—21no—
74C2×C4×D23—21no—
75C2×C4×D23C2311yescharacteristic
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—
85C22⋊Dic23—21no—
86C22⋊Dic23D411yescharacteristic
87#67275—41no—
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
95C4⋊Dic23—21no—
96C4⋊Dic23—21no—
97C4⋊Dic23C2311yescharacteristic
98Dic23⋊C4—21no—
99Dic23⋊C4—21no—
100Dic23⋊C4—21no—
101Dic23⋊C4D411yescharacteristic
102C4×Dic23—21no—
103C4×Dic23—21no—
104C4×Dic23C2311yescharacteristic
105C2×C23⋊C8—41no—
106C2×C23⋊C8C2311yescharacteristic
107C2×C23⋊C8C2311yescharacteristic
108#67263—22no—
109#67263—41no—
110C8×D23—41no—
111C23×C23C2×D411yescharacteristic
112C22×D23—21no—
113C22×D23—21no—
114C22×D23—42no—
115C22×D23—42no—
116C22×D23—81no—
117C22×D23C2×D411yescharacteristic
118Q8×C23—21no—
119Q8×C23—21no—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23—21no—
124C2×C4×C23—21no—
125C2×C4×C23—21no—
126C2×C4×C23—42no—
127C2×C4×C23C2×D411yescharacteristic
128C2×C4×C23C2411yescharacteristic
129C22⋊D23—22no—
130C2×Dic23—21no—
131C2×Dic23—21no—
132C2×Dic23C2×D411yescharacteristic
133C2×Dic23C2×D411yescharacteristic
134C2×Dic23C2×D411yescharacteristic
135D92—21no—
136D92—21no—
137D92—21no—
138D92—42no—
139D92—42no—
140D92—81no—
141D92#4112yes—
142C4×D23—21no—
143C4×D23—21no—
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#13512yes—
156C22×C23C22×D411yescharacteristic
157C2×D23—21no—
158C2×D23—22no—
159C2×D23—21no—
160C2×D23—21no—
161C2×D23—41no—
162C2×D23—41no—
163C2×D23—41no—
164C2×D23—41no—
165C2×D23—41no—
166C2×D23—84no—
167C4×C23—21no—
168C4×C23—41no—
169C4×C23—41no—
170C4×C23—41no—
171C4×C23—41no—
172C4×C23C2×#4111yescharacteristic
173C4×C23H(5,𝔽2)11yescharacteristic
174Dic23—21no—
175Dic23—21no—
176Dic23—21no—
177Dic23—41no—
178Dic23—41no—
179#552—231no—
180#546—231no—
181#488—231no—
182#483D2311yescharacteristic, complemented
183#482—231no—
184#478—231no—
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—22no—
195C2×C23#54611yescharacteristic
196C2×C23C2×#13511yescharacteristic
197C2×C23#57711yescharacteristic
198D23—41no—
199D23—42no—
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—231no—
210#125—461no—
211#124—231no—
212#123—461no—
213#123—461no—
214C22⋊Q8—231no—
215C22⋊Q8—231no—
216C22⋊Q8C2×D2311yescharacteristic
217#121—231no—
218#121—461no—
219#120—461no—
220C4×Q8—231no—
221C4×D4—231no—
222C4×D4—231no—
223#117—231no—
224#117—461no—
225C2×C4⋊C4C2×D2311yescharacteristic
226C2×C22⋊C4—461no—
227#107—231no—
228#106C2×D2311yescharacteristic, complemented
229#106C2×D2311yescharacteristic, complemented
230C4⋊C8—231no—
231#103—231no—
232#103—231no—
233#103C2×D2311yescharacteristic, complemented
234#103C2×D2311yescharacteristic, complemented
235#102—231no—
236#102—231no—
237#102—231no—
238#102—231no—
239#102—231no—
240#102—231no—
241C22⋊C8—231no—
242C22⋊C8C2×D2311yescharacteristic
243C4×C8—231no—
244C23#329611yescharacteristic, complemented, Sylow
245C24—461no—
246#41—462no—
247#41—921no—
248C2×Q8—231no—
249C2×Q8C22×D2311yescharacteristic
250C2×D4—231no—
251C2×D4—231no—
252C2×D4—231no—
253C2×D4—462no—
254C2×D4—461no—
255C2×D4—461no—
256C2×D4—461no—
257C2×D4—921no—
258C22×C4—21no—
259C22×C4—231no—
260C22×C4—461no—
261C22×C4—461no—
262C22×C4C22×D2311yescharacteristic
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—231no—
295C42—461no—
296C42—461no—
297C23—231no—
298C23—461no—
299C23—461no—
300C23—922no—
301C23—922no—
302C23—1841no—
303C23D4×D2311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—461no—
307Q8—461no—
308D4—232no—
309D4—462no—
310D4—461no—
311D4—461no—
312D4—461no—
313D4—922no—
314D4—922no—
315D4—1841no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—231no—
324C2×C4—231no—
325C2×C4—231no—
326C2×C4—461no—
327C2×C4—461no—
328C2×C4—461no—
329C2×C4—461no—
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—461no—
341C22—461no—
342C22—461no—
343C22—462no—
344C22—921no—
345C22—921no—
346C22—921no—
347C22—921no—
348C22—921no—
349C22—1844no—
350C22#1062508712yes—
351C22C2×D4×D2311yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—461no—
358C4—461no—
359C4—461no—
360C4—921no—
361C4—921no—
362C4#41×D2311yescharacteristic
363C4#1062516011yescharacteristic
364C2—22no—
365C2—921no—
366C2—922no—
367C2—1841no—
368C2#1309305911yescharacteristic
369C2C2×#1062508711yescharacteristic
370C2#1309322611yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#483C2
socleC22×C23C22×D4
prime radical#13093058C2
hypercenter#483D23
hypocenterC23#3296
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #13093102C2semidirect
3. #13092773C2semidirect
4. #13092743C2semidirect
5. #13092716C2semidirect
6. #13092656C2semidirect
7. #13092647C2semidirect
8. #13092642C2semidirect
9. #13092582C2semidirect
10. #13092570C2semidirect
11. #13092504C2semidirect
12. (C22⋊D23)⋊C8C2semidirect
13. #13092412C2semidirect
14. C2×#10624991C2semidirect
15. C23×#483C2semidirect
21. C2×#67275C22semidirect
29. C2×C8×D23C22semidirect
31. #10625068C22semidirect
36. #10625063C22semidirect
37. #10625061C22semidirect
39. #10625058C22semidirect
42. C23×#106C22semidirect
43. C23×#106C22semidirect
44. C23×#103C22semidirect
45. C23×#103C22semidirect
47. #10625017C22semidirect
50. (C2×D23)⋊C8C22semidirect
51. Dic23⋊C8C22semidirect
52. C8×Dic23C22semidirect
53. #10624992C22semidirect
58. #10624989C22semidirect
182. #483D23semidirect
228. #106C2×D23semidirect
229. #106C2×D23semidirect
233. #103C2×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
#130931022
#130930582
#130927732
#130927432
#130927162
#130926562
#130926472
#130926422
#130925822
#130925702
#130925042
(C22⋊D23)⋊C82
#130924122
C2×#106249912
C23×#4832
#329623