Finite Group Databasebeta

← #15685246

Subgroups — #15685246

Order 2944.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093120C211yesmaximal, characteristic, complemented
2#13093060C211yesmaximal, characteristic, complemented
3#13092751C211yesmaximal, characteristic, complemented
4#13092739C211yesmaximal, characteristic, complemented
5#13092714C211yesmaximal, characteristic, complemented
6#13092652C211yesmaximal, characteristic, complemented
7#13092649C211yesmaximal, characteristic, complemented
8#13092629C211yesmaximal, characteristic, complemented
9#13092565C211yesmaximal, characteristic, complemented
10#13092552C211yesmaximal, characteristic, complemented
11C4×D184C211yesmaximal, characteristic, complemented
12C8×D92C211yesmaximal, characteristic, complemented
13#13092412C211yesmaximal, characteristic, complemented
14#102×D23C211yesmaximal, characteristic, complemented
15C23×#488C211yesmaximal, characteristic, complemented
16C2×#67292C2211yescharacteristic
17C2×D4×D23C2211yescharacteristic
18C23×#125C2211yescharacteristic, complemented
19C23×#124C2211yescharacteristic
20#10625117C2211yescharacteristic
21C2×#67274C2211yescharacteristic, complemented
22#10625109C2211yescharacteristic
23C2×#67272C2211yescharacteristic
24C2×D184C2211yescharacteristic
25C2×C8×D23C2211yescharacteristic
26C2×C8×D23C2211yescharacteristic, complemented
27#10625069—21no—
28#10625066—21no—
29#10625066C2211yescharacteristic
30#10625066C2211yescharacteristic, complemented
31#10625065—21no—
32#10625064—21no—
33#10625063C2211yescharacteristic, complemented
34C4⋊C4×D23C2211yescharacteristic
35#10625055—21no—
36#10625054—21no—
37#10625053—21no—
38C22⋊C4×D23—21no—
39C4×D92C2211yescharacteristic
40C4×D92C2211yescharacteristic
41C4×D92C2211yescharacteristic, complemented
42C23×#103C2211yescharacteristic, complemented
43C23×#103C2211yescharacteristic, complemented
44C23×#102C2211yescharacteristic
45C23×#102C2211yescharacteristic
46C4×C8×C23C2211yescharacteristic, complemented
47#10625017C2211yescharacteristic, complemented
48#10625014C2211yescharacteristic
49#10625003C2211yescharacteristic
50#10625003C2211yescharacteristic, complemented
51(C2×D23)⋊C8C2211yescharacteristic
52(C2×D23)⋊C8C2211yescharacteristic, complemented
53#10625000C2211yescharacteristic, complemented
54#10624991C2211yescharacteristic
55#10624991C2211yescharacteristic
56#10624990C2211yescharacteristic, complemented
57#10624989C2211yescharacteristic, complemented
58C4⋊(C23⋊C8)C2211yescharacteristic, complemented
59C23×D23—21no—
60C2×Q8×C23C2311yescharacteristic
61C2×D4×C23C2311yescharacteristic
62C2×C22⋊D23—21no—
63C2×C22⋊D23—21no—
64#67292—22no—
65#67292—41no—
66D4×D23—22no—
67D4×D23—41no—
68C2×D92—21no—
69C2×D92—21no—
70C2×D92—21no—
71C2×D92D411yescharacteristic
72C2×D92C2311yescharacteristic
73C2×D92C2311yescharacteristic
74C2×C4×D23—21no—
75C2×C4×D23—21no—
76C2×C4×D23—21no—
77C2×C4×D23—21no—
78C2×C4×D23C2311yescharacteristic
79C2×C4×D23C2311yescharacteristic
80C2×C8×C23C2311yescharacteristic
81C2×C8×C23C2311yescharacteristic
82C4⋊C4×C23—21no—
83C4⋊C4×C23—21no—
84C4⋊C4×C23C2311yescharacteristic
85C4⋊C4×C23C2311yescharacteristic
86C22⋊C4×C23—21no—
87C22⋊C4×C23—21no—
88C42×C23C2311yescharacteristic
89C22⋊Dic23—21no—
90#67274—41no—
91#67272—41no—
92(C2×D23)⋊C4—21no—
93(C2×D23)⋊C4—21no—
94(C2×D23)⋊C4—21no—
95(C2×D23)⋊C4—21no—
96(C2×D23)⋊C4—21no—
97(C2×D23)⋊C4—21no—
98(C2×D23)⋊C4D411yescharacteristic
99(C2×D23)⋊C4D411yescharacteristic
100C4⋊Dic23D411yescharacteristic
101C4⋊Dic23C2311yescharacteristic
102C4⋊Dic23C2311yescharacteristic
103Dic23⋊C4—21no—
104Dic23⋊C4—21no—
105C4×Dic23—21no—
106C2×C23⋊C8C2311yescharacteristic
107C2×C23⋊C8C2311yescharacteristic
108D184—22no—
109C8×D23—41no—
110C8×D23—41no—
111C23×C23—21no—
112C22×D23—21no—
113C22×D23—21no—
114C22×D23—42no—
115C22×D23—42no—
116C22×D23—81no—
117C22×D23C2×D411yescharacteristic
118C22×D23C2×D411yescharacteristic
119Q8×C23—21no—
120Q8×C23—21no—
121D4×C23—21no—
122D4×C23—21no—
123C2×C4×C23—21no—
124C2×C4×C23—21no—
125C2×C4×C23—21no—
126C2×C4×C23C2×D411yescharacteristic
127C2×C4×C23C2×D411yescharacteristic
128C2×C4×C23C2411yescharacteristic
129C22⋊D23—42no—
130C22⋊D23—81no—
131C2×Dic23—21no—
132C2×Dic23—21no—
133C2×Dic23C2×D411yescharacteristic
134C2×Dic23C2×D411yescharacteristic
135D92—22no—
136D92—21no—
137D92—21no—
138D92—21no—
139D92—42no—
140D92—42no—
141D92—81no—
142D92#4112yes—
143C4×D23—21no—
144C4×D23—21no—
145C4×D23—21no—
146C4×D23—21no—
147C4×D23—42no—
148C4×D23—81no—
149C4×D23—81no—
150C4×D23—81no—
151C8×C23—21no—
152C8×C23—21no—
153C23⋊C8—21no—
154C23⋊C8—21no—
155#3297—231nomaximal, Sylow
156C22×C23—41no—
157C22×C23—41no—
158C22×C23—41no—
159C22×C23C22×D411yescharacteristic
160C2×D23—21no—
161C2×D23—21no—
162C2×D23—21no—
163C2×D23—22no—
164C2×D23—21no—
165C2×D23—21no—
166C2×D23—41no—
167C2×D23—41no—
168C2×D23—41no—
169C2×D23—41no—
170C2×D23—41no—
171C2×D23—84no—
172C2×D23#13512yes—
173C4×C23—21no—
174C4×C23—21no—
175C4×C23—41no—
176C4×C23—41no—
177C4×C23—41no—
178C4×C23C2×#4111yescharacteristic
179C4×C23H(5,𝔽2)11yescharacteristic
180Dic23—21no—
181Dic23—21no—
182Dic23—41no—
183Dic23—41no—
184#553—231no—
185#546—231no—
186#488D2311yescharacteristic, complemented
187#484—231no—
188#482—231no—
189#478—231no—
190#466—231no—
191#465—231no—
192#463—231no—
193#449—231no—
194#447—231no—
195C4×D8—231no—
196C8×D4—231no—
197#416—231no—
198C2×#102—231no—
199C2×C23—81no—
200C2×C23#54611yescharacteristic
201C2×C23C2×#13511yescharacteristic
202C2×C23#57611yescharacteristic
203D23—22no—
204D23—41no—
205D23—42no—
206D23—81no—
207C2×#41—231no—
208C22×D4—231no—
209C2×SD16—231no—
210C2×D8—231no—
211C2×D8—231no—
212C22×C8—231no—
213C22×C8—231no—
214#126—461no—
215#125C2×D2311yescharacteristic, complemented
216#124C2×D2311yescharacteristic
217#123—461no—
218#123—461no—
219C22⋊Q8—231no—
220#121—231no—
221#121—231no—
222#121—231no—
223#121—461no—
224#121—461no—
225#120—461no—
226C4×D4—231no—
227C4×D4—231no—
228C4×D4—231no—
229C4×D4—461no—
230#117—231no—
231C2×C4⋊C4—231no—
232C2×C22⋊C4—461no—
233#107—231no—
234#107—231no—
235#106—231no—
236C4⋊C8—231no—
237#103—231no—
238#103C2×D2311yescharacteristic, complemented
239#103C2×D2311yescharacteristic, complemented
240#102—231no—
241#102—231no—
242#102—231no—
243#102—231no—
244#102—231no—
245#102C2×D2311yescharacteristic
246#102C2×D2311yescharacteristic
247C22⋊C8—231no—
248C22⋊C8—231no—
249C4×C8C2×D2311yescharacteristic, complemented
250C23#329711yescharacteristic, complemented, Sylow
251C24—461no—
252#41—462no—
253#41—921no—
254C2×Q8C22×D2311yescharacteristic
255C2×D4—231no—
256C2×D4—231no—
257C2×D4—231no—
258C2×D4—461no—
259C2×D4—461no—
260C2×D4—461no—
261C2×D4—461no—
262C2×D4—462no—
263C2×D4—461no—
264C2×D4—921no—
265C2×D4C22×D2311yescharacteristic
266C22×C4—231no—
267C22×C4—231no—
268C22×C4—461no—
269C22×C4—461no—
270C22×C4—461no—
271C22×C4—461no—
272SD16—921no—
273D8—462no—
274D8—921no—
275C2×C8—231no—
276C2×C8—231no—
277C2×C8—921no—
278C2×C8—921no—
279C2×C8C22×D2311yescharacteristic
280C2×C8C22×D2311yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—231no—
284C4⋊C4—231no—
285C4⋊C4—231no—
286C4⋊C4—461no—
287C4⋊C4—461no—
288C4⋊C4C22×D2311yescharacteristic
289C4⋊C4C22×D2311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—231no—
293C22⋊C4—231no—
294C22⋊C4—461no—
295C22⋊C4—461no—
296C22⋊C4—461no—
297C22⋊C4—461no—
298C22⋊C4—461no—
299C22⋊C4—461no—
300C22⋊C4—461no—
301C42—461no—
302C42C22×D2311yescharacteristic
303C23—21no—
304C23—231no—
305C23—231no—
306C23—461no—
307C23—461no—
308C23—922no—
309C23—922no—
310C23—1841no—
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—21no—
315D4—232no—
316D4—462no—
317D4—461no—
318D4—461no—
319D4—461no—
320D4—922no—
321D4—922no—
322D4—922no—
323D4—1841no—
324D4—1841no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—231no—
329C2×C4—231no—
330C2×C4—461no—
331C2×C4—461no—
332C2×C4—461no—
333C2×C4—461no—
334C2×C4—461no—
335C2×C4—461no—
336C2×C4—922no—
337C2×C4—1841no—
338C2×C4—1841no—
339C2×C4—1841no—
340C2×C4D4×D2311yescharacteristic
341C2×C4D4×D2311yescharacteristic
342C2×C4C23×D2311yescharacteristic
343C8—21no—
344C8—21no—
345C8—461no—
346C8—461no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—232no—
351C22—461no—
352C22—461no—
353C22—461no—
354C22—461no—
355C22—461no—
356C22—462no—
357C22—921no—
358C22—921no—
359C22—921no—
360C22—921no—
361C22—921no—
362C22—1844no—
363C22C2×D4×D2311yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—461no—
370C4—461no—
371C4—921no—
372C4—921no—
373C4#41×D2311yescharacteristic
374C4#1062516011yescharacteristic
375C2—81no—
376C2—462no—
377C2—921no—
378C2—922no—
379C2—1841no—
380C2#1309306011yescharacteristic
381C2#135×D2311yescharacteristic
382C2#1309321911yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#488C2
socleC22×C23C22×D4
hypercenter#488D23
hypocenterC23#3297
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #13093120C2semidirect
2. #13093060C2semidirect
3. #13092751C2semidirect
4. #13092739C2semidirect
5. #13092714C2semidirect
6. #13092652C2semidirect
7. #13092649C2semidirect
8. #13092629C2semidirect
9. #13092565C2semidirect
10. #13092552C2semidirect
11. C4×D184C2semidirect
12. C8×D92C2semidirect
13. #13092412C2semidirect
14. #102×D23C2semidirect
15. C23×#488C2semidirect
18. C23×#125C22semidirect
21. C2×#67274C22semidirect
26. C2×C8×D23C22semidirect
30. #10625066C22semidirect
33. #10625063C22semidirect
41. C4×D92C22semidirect
42. C23×#103C22semidirect
43. C23×#103C22semidirect
46. C4×C8×C23C22semidirect
47. #10625017C22semidirect
50. #10625003C22semidirect
52. (C2×D23)⋊C8C22semidirect
53. #10625000C22semidirect
56. #10624990C22semidirect
57. #10624989C22semidirect
58. C4⋊(C23⋊C8)C22semidirect
186. #488D23semidirect
215. #125C2×D23semidirect
238. #103C2×D23semidirect
239. #103C2×D23semidirect
249. C4×C8C2×D23semidirect
250. C23#3297semidirect

Maximal subgroups

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

subgroupindex
#130931202
#130930602
#130927512
#130927392
#130927142
#130926522
#130926492
#130926292
#130925652
#130925522
C4×D1842
C8×D922
#130924122
#102×D232
C23×#4882
#329723