Finite Group Databasebeta

← #15685351

Subgroups — #15685351

Order 2944.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093067C211yesmaximal, characteristic, complemented
2#13093055C211yesmaximal, characteristic, complemented
3#13092778C211yesmaximal, characteristic, complemented
4#13092746C211yesmaximal, characteristic, complemented
5#13092736C211yesmaximal, characteristic, complemented
6#13092705C211yesmaximal, characteristic, complemented
7#13092668C211yesmaximal, characteristic, complemented
8#13092643C211yesmaximal, characteristic, complemented
9#13092634C211yesmaximal, characteristic, complemented
10#13092549C211yesmaximal, characteristic, complemented
11#13092529C211yesmaximal, characteristic, complemented
12#13092491C211yesmaximal, characteristic, complemented
13#13092418C211yesmaximal, characteristic, complemented
14#102×D23C211yesmaximal, characteristic, complemented
15C23×#449C211yesmaximal, characteristic, complemented
16C2×#41×C23C2211yescharacteristic
17C2×#67290—21no—
18C2×D4×D23C2211yescharacteristic
19C2×SD16×C23C2211yescharacteristic, complemented
20C2×D8×C23C2211yescharacteristic
21C23×#121C2211yescharacteristic, complemented
22#10625118C2211yescharacteristic
23#10625117C2211yescharacteristic
24#10625110—21no—
25#10625109C2211yescharacteristic
26#10625108—21no—
27#10625106—21no—
28D4×Dic23C2211yescharacteristic
29D4×Dic23C2211yescharacteristic, complemented
30C2×#67272C2211yescharacteristic
31#10625101C2211yescharacteristic
32#10625100—21no—
33C4×C22⋊D23C2211yescharacteristic
34C2×(C2×D23)⋊C4—21no—
35C2×C4⋊Dic23C2211yescharacteristic, complemented
36C2×#67267C2211yescharacteristic, complemented
37C2×C8×D23C2211yescharacteristic
38C4⋊C4×D23C2211yescharacteristic
39#10625059C2211yescharacteristic, complemented
40#10625054—21no—
41#10625049—21no—
42C23×#103C2211yescharacteristic, complemented
43C23×#102C2211yescharacteristic
44C23×C22⋊C8C2211yescharacteristic, complemented
45#10625017C2211yescharacteristic, complemented
46#10625017C2211yescharacteristic, complemented
47#10625014C2211yescharacteristic
48#10625014C2211yescharacteristic
49#10625014C2211yescharacteristic, complemented
50#10625003C2211yescharacteristic
51#10625003C2211yescharacteristic
52(C2×D23)⋊C8C2211yescharacteristic
53#10624999C2211yescharacteristic, complemented
54#10624999C2211yescharacteristic, complemented
55#10624997C2211yescharacteristic, complemented
56Dic23⋊C8C2211yescharacteristic, complemented
57#10624991C2211yescharacteristic
58#10624990C2211yescharacteristic, complemented
59C23×D23—21no—
60#41×C23—22no—
61#41×C23—41no—
62C2×Q8×C23C2311yescharacteristic
63C2×D4×C23—21no—
64C2×D4×C23—21no—
65C2×D4×C23C2311yescharacteristic
66C2×D4×C23C2311yescharacteristic
67C22×C4×C23—21no—
68C22×C4×C23C2311yescharacteristic
69C2×C22⋊D23—21no—
70C2×C22⋊D23—21no—
71C2×C22⋊D23—21no—
72C2×C22⋊D23D411yescharacteristic
73C22×Dic23—21no—
74C22×Dic23—21no—
75C22×Dic23—21no—
76#67290—44no—
77D4×D23—22no—
78D4×D23—41no—
79C2×D92C2311yescharacteristic
80C2×C4×D23—21no—
81C2×C4×D23C2311yescharacteristic
82C2×Dic46—21no—
83SD16×C23—41no—
84D8×C23—22no—
85C2×C8×C23C2311yescharacteristic
86C2×C8×C23C2311yescharacteristic
87C4⋊C4×C23C2311yescharacteristic
88C22⋊C4×C23—21no—
89C22⋊Dic23—21no—
90C22⋊Dic23—21no—
91C22⋊Dic23—21no—
92C22⋊Dic23D411yescharacteristic
93#67272—41no—
94(C2×D23)⋊C4—21no—
95(C2×D23)⋊C4—21no—
96(C2×D23)⋊C4—21no—
97(C2×D23)⋊C4—21no—
98(C2×D23)⋊C4D411yescharacteristic
99C4⋊Dic23—21no—
100C4⋊Dic23C2311yescharacteristic
101C4⋊Dic23C2311yescharacteristic
102C4⋊Dic23C2311yescharacteristic
103Dic23⋊C4—21no—
104Dic23⋊C4—21no—
105Dic23⋊C4—21no—
106Dic23⋊C4D411yescharacteristic
107C4×Dic23C2311yescharacteristic
108#67267—41no—
109C2×C23⋊C8C2311yescharacteristic
110C2×C23⋊C8C2311yescharacteristic
111C8×D23—41no—
112C23×C23—21no—
113C23×C23—21no—
114C23×C23C2×D411yescharacteristic
115C22×D23—21no—
116C22×D23—42no—
117C22×D23—42no—
118C22×D23—81no—
119C22×D23C2×D411yescharacteristic
120Q8×C23—21no—
121Q8×C23—21no—
122D4×C23—21no—
123D4×C23—21no—
124D4×C23—21no—
125D4×C23—42no—
126D4×C23—42no—
127D4×C23#4112yescomplemented
128C2×C4×C23—21no—
129C2×C4×C23—21no—
130C2×C4×C23—21no—
131C2×C4×C23—21no—
132C2×C4×C23—42no—
133C2×C4×C23C2×D411yescharacteristic
134C2×C4×C23C2411yescharacteristic
135C22⋊D23—22no—
136C22⋊D23—42no—
137C22⋊D23—42no—
138C22⋊D23—81no—
139C2×Dic23—21no—
140C2×Dic23—21no—
141C2×Dic23—21no—
142C2×Dic23—42no—
143C2×Dic23—42no—
144C2×Dic23—81no—
145C2×Dic23C2×D411yescharacteristic
146C2×Dic23C2×D411yescharacteristic
147C2×Dic23C2×D411yescharacteristic
148D92—21no—
149D92—21no—
150C4×D23—21no—
151C4×D23—21no—
152C4×D23—42no—
153Dic46—42no—
154C8×C23—21no—
155C8×C23—21no—
156C23⋊C8—21no—
157C23⋊C8—21no—
158#3306—231nomaximal, Sylow
159C22×C23—22no—
160C22×C23—21no—
161C22×C23—21no—
162C22×C23—21no—
163C22×C23—41no—
164C22×C23—41no—
165C22×C23—41no—
166C22×C23—41no—
167C22×C23—41no—
168C22×C23C22×D411yescharacteristic
169C2×D23—21no—
170C2×D23—21no—
171C2×D23—41no—
172C2×D23—41no—
173C2×D23—41no—
174C2×D23—84no—
175C2×D23AGL(1,ℤ/8)12yes—
176C4×C23—21no—
177C4×C23—41no—
178C4×C23—41no—
179C4×C23C2×#4111yescharacteristic
180C4×C23H(5,𝔽2)11yescharacteristic
181Dic23—21no—
182Dic23—21no—
183Dic23—21no—
184Dic23—41no—
185Dic23—41no—
186Dic23—41no—
187#547—231no—
188#546—231no—
189#489—231no—
190#483—231no—
191#481—231no—
192#476—231no—
193#469—231no—
194#465—231no—
195#463—231no—
196#449D2311yescharacteristic, complemented
197#447—231no—
198#442—231no—
199#435—231no—
200#417—231no—
201C2×#102—231no—
202C2×C23—42no—
203C2×C23—41no—
204C2×C23—81no—
205C2×C23#54611yescharacteristic
206C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
207C2×C23#57711yescharacteristic
208D23—22no—
209D23—81no—
210C2×#41—461no—
211C2×#41C2×D2311yescharacteristic
212C22×D4—231no—
213C2×SD16C2×D2311yescharacteristic, complemented
214C2×D8—231no—
215C2×D8C2×D2311yescharacteristic
216C2×M16—231no—
217C22×C8—231no—
218C4⋊Q8—231no—
219#124—231no—
220#123—461no—
221#123—461no—
222#123—461no—
223C22⋊Q8—231no—
224C22⋊Q8—461no—
225#121—231no—
226#121—231no—
227#121—461no—
228#121C2×D2311yescharacteristic, complemented
229#120—461no—
230C4×D4—231no—
231C4×D4—231no—
232C4×D4—231no—
233C2×C4⋊C4—231no—
234C2×C4⋊C4—231no—
235C2×C22⋊C4—461no—
236#106—231no—
237#106—231no—
238#106—231no—
239C4⋊C8—231no—
240#103—231no—
241#103—231no—
242#103C2×D2311yescharacteristic, complemented
243#102—231no—
244#102—231no—
245#102—231no—
246#102—231no—
247#102—231no—
248#102—231no—
249#102C2×D2311yescharacteristic
250C22⋊C8—231no—
251C22⋊C8C2×D2311yescharacteristic, complemented
252#97—231no—
253C23#330611yescharacteristic, complemented, Sylow
254C24—461no—
255#41—22no—
256#41—41no—
257#41—924no—
258C2×Q8—461no—
259C2×Q8C22×D2311yescharacteristic
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—231no—
263C2×D4—231no—
264C2×D4—461no—
265C2×D4—462no—
266C2×D4—461no—
267C2×D4—461no—
268C2×D4—921no—
269C2×D4C22×D2311yescharacteristic
270C2×D4C22×D2311yescharacteristic
271C22×C4—21no—
272C22×C4—231no—
273C22×C4—461no—
274C22×C4—461no—
275C22×C4—461no—
276C22×C4—461no—
277C22×C4C22×D2311yescharacteristic
278SD16—41no—
279D8—22no—
280D8—921no—
281M16—921no—
282C2×C8—231no—
283C2×C8—231no—
284C2×C8—921no—
285C2×C8C22×D2311yescharacteristic
286C2×C8C22×D2311yescharacteristic
287C4⋊C4—231no—
288C4⋊C4—231no—
289C4⋊C4—231no—
290C4⋊C4—231no—
291C4⋊C4—461no—
292C4⋊C4—461no—
293C4⋊C4—461no—
294C4⋊C4—461no—
295C4⋊C4C22×D2311yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—231no—
298C22⋊C4—231no—
299C22⋊C4—461no—
300C22⋊C4—461no—
301C22⋊C4—461no—
302C22⋊C4—461no—
303C22⋊C4—461no—
304C22⋊C4—461no—
305C22⋊C4—461no—
306C42—231no—
307C23—21no—
308C23—21no—
309C23—231no—
310C23—461no—
311C23—922no—
312C23—922no—
313C23—1841no—
314C23D4×D2311yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—922no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—42no—
322D4—42no—
323D4—462no—
324D4—461no—
325D4—461no—
326D4—922no—
327D4—922no—
328D4—1841no—
329D4#6729012yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—42no—
335C2×C4—231no—
336C2×C4—231no—
337C2×C4—231no—
338C2×C4—461no—
339C2×C4—461no—
340C2×C4—461no—
341C2×C4—461no—
342C2×C4—461no—
343C2×C4—922no—
344C2×C4—922no—
345C2×C4—922no—
346C2×C4—1841no—
347C2×C4D4×D2311yescharacteristic
348C2×C4C23×D2311yescharacteristic
349C8—21no—
350C8—21no—
351C8—461no—
352C8—461no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—22no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—232no—
363C22—461no—
364C22—461no—
365C22—921no—
366C22—921no—
367C22—921no—
368C22—1844no—
369C22C2×D4×D2311yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—461no—
374C4—461no—
375C4—461no—
376C4—921no—
377C4—921no—
378C4—921no—
379C4C2×#6729011yescharacteristic
380C4#1062515511yescharacteristic
381C2—41no—
382C2—42no—
383C2—81no—
384C2—462no—
385C2—1841no—
386C2#1309305411yescharacteristic
387C2AGL(1,ℤ/8)×D2311yescharacteristic
388C2#1309322411yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#449C2
socleC22×C23C22×D4
hypercenter#449D23
hypocenterC23#3306
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #13093067C2semidirect
2. #13093055C2semidirect
3. #13092778C2semidirect
4. #13092746C2semidirect
5. #13092736C2semidirect
6. #13092705C2semidirect
7. #13092668C2semidirect
8. #13092643C2semidirect
9. #13092634C2semidirect
10. #13092549C2semidirect
11. #13092529C2semidirect
12. #13092491C2semidirect
13. #13092418C2semidirect
14. #102×D23C2semidirect
15. C23×#449C2semidirect
19. C2×SD16×C23C22semidirect
21. C23×#121C22semidirect
29. D4×Dic23C22semidirect
35. C2×C4⋊Dic23C22semidirect
36. C2×#67267C22semidirect
39. #10625059C22semidirect
42. C23×#103C22semidirect
44. C23×C22⋊C8C22semidirect
45. #10625017C22semidirect
46. #10625017C22semidirect
49. #10625014C22semidirect
53. #10624999C22semidirect
54. #10624999C22semidirect
55. #10624997C22semidirect
56. Dic23⋊C8C22semidirect
58. #10624990C22semidirect
127. D4×C23#41semidirect
196. #449D23semidirect
213. C2×SD16C2×D23semidirect
228. #121C2×D23semidirect
242. #103C2×D23semidirect
251. C22⋊C8C2×D23semidirect
253. C23#3306semidirect
329. D4#67290semidirect

Maximal subgroups

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

subgroupindex
#130930672
#130930552
#130927782
#130927462
#130927362
#130927052
#130926682
#130926432
#130926342
#130925492
#130925292
#130924912
#130924182
#102×D232
C23×#4492
#330623