Finite Group Databasebeta

← #15685352

Subgroups — #15685352

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#13093063C211yesmaximal, characteristic, complemented
2#13092779C211yesmaximal, characteristic, complemented
3#13092747C211yesmaximal, characteristic, complemented
4#13092735C211yesmaximal, characteristic, complemented
5#13092704C211yesmaximal, characteristic, complemented
6#13092668C211yesmaximal, characteristic, complemented
7#13092644C211yesmaximal, characteristic, complemented
8#13092632C211yesmaximal, characteristic, complemented
9#13092560C211yesmaximal, characteristic, complemented
10#13092550C211yesmaximal, characteristic, complemented
11#13092527C211yesmaximal, characteristic, complemented
12#13092489C211yesmaximal, characteristic, complemented
13#13092416C211yesmaximal, characteristic, complemented
14C2×#10624991C211yesmaximal, characteristic, complemented
15C23×#547C211yesmaximal, characteristic, complemented
16C2×#41×C23—21no—
17C2×#67288C2211yescharacteristic
18C22×D92C2211yescharacteristic
19C23×C4⋊Q8C2211yescharacteristic, complemented
20C23×#123—21no—
21C23×#123—21no—
22C23×C22⋊Q8—21no—
23C23×#121C2211yescharacteristic
24C23×#121C2211yescharacteristic, complemented
25C4×D4×C23C2211yescharacteristic
26C4×D4×C23C2211yescharacteristic, complemented
27C2×C4⋊C4×C23C2211yescharacteristic
28C2×C4⋊C4×C23C2211yescharacteristic, complemented
29#10625108—21no—
30C2×#67273C2211yescharacteristic, complemented
31C2×#67272C2211yescharacteristic
32C2×#67272C2211yescharacteristic
33#10625101C2211yescharacteristic
34#10625095C2211yescharacteristic
35C2×#67267C2211yescharacteristic, complemented
36C22×C23⋊C8C2211yescharacteristic
37#10625065—21no—
38#10625055—21no—
39C22⋊C4×D23—21no—
40#10625046C2211yescharacteristic
41C4×D92C2211yescharacteristic
42#10625014C2211yescharacteristic, complemented
43C22⋊(C23⋊C8)C2211yescharacteristic
44C22⋊(C23⋊C8)C2211yescharacteristic, complemented
45#10624992C2211yescharacteristic, complemented
46#10624992C2211yescharacteristic, complemented
47#10624992C2211yescharacteristic, complemented
48#10624991C2211yescharacteristic
49#10624991C2211yescharacteristic
50#10624991C2211yescharacteristic
51#10624991C2211yescharacteristic
52#10624991C2211yescharacteristic
53#10624991C2211yescharacteristic
54#10624990C2211yescharacteristic, complemented
55#10624990C2211yescharacteristic, complemented
56#10624990C2211yescharacteristic, complemented
57C4⋊(C23⋊C8)C2211yescharacteristic, complemented
58#10624985C2211yescharacteristic, complemented
59C23×D23—21no—
60#41×C23—44no—
61C2×Q8×C23—21no—
62C2×D4×C23—21no—
63C2×D4×C23—21no—
64C2×D4×C23D411yescharacteristic
65C2×D4×C23C2311yescharacteristic
66C22×C4×C23—21no—
67C22×C4×C23—21no—
68C22×C4×C23—21no—
69C22×C4×C23C2311yescharacteristic
70C22×C4×C23C2311yescharacteristic
71C2×C22⋊D23—21no—
72C2×C22⋊D23—21no—
73#67288—22no—
74#67288—41no—
75C2×D92—22no—
76C2×D92—21no—
77C2×D92—41no—
78C2×D92C2311yescharacteristic
79C2×D92C2311yescharacteristic
80C2×C4×D23—21no—
81C2×C4×D23—21no—
82C2×Dic46C2311yescharacteristic
83C4⋊C4×C23—21no—
84C4⋊C4×C23—21no—
85C4⋊C4×C23—21no—
86C4⋊C4×C23D411yescharacteristic
87C4⋊C4×C23C2311yescharacteristic
88C4⋊C4×C23C2311yescharacteristic
89C4⋊C4×C23C2311yescharacteristic
90C22⋊C4×C23—21no—
91C22⋊C4×C23—21no—
92C22⋊C4×C23—21no—
93C22⋊C4×C23D411yescharacteristic
94C22⋊C4×C23D411yescharacteristic
95C42×C23C2311yescharacteristic
96C22⋊Dic23—21no—
97#67273—41no—
98#67272—22no—
99#67272—41no—
100(C2×D23)⋊C4—21no—
101(C2×D23)⋊C4—21no—
102(C2×D23)⋊C4—21no—
103(C2×D23)⋊C4—21no—
104C4⋊Dic23C2311yescharacteristic
105Dic23⋊C4—21no—
106#67267—41no—
107C2×C23⋊C8—41no—
108C2×C23⋊C8C2311yescharacteristic
109C2×C23⋊C8C2311yescharacteristic
110C2×C23⋊C8C2311yescharacteristic
111C2×C23⋊C8C2311yescharacteristic
112C23×C23—21no—
113C23×C23C2×D411yescharacteristic
114C23×C23C2×D411yescharacteristic
115C22×D23—21no—
116C22×D23—21no—
117C22×D23—42no—
118C22×D23—42no—
119C22×D23—81no—
120Q8×C23—42no—
121D4×C23—22no—
122D4×C23—21no—
123D4×C23—21no—
124D4×C23—42no—
125D4×C23—42no—
126C2×C4×C23—21no—
127C2×C4×C23—21no—
128C2×C4×C23—21no—
129C2×C4×C23—21no—
130C2×C4×C23—21no—
131C2×C4×C23—21no—
132C2×C4×C23—21no—
133C2×C4×C23—42no—
134C2×C4×C23—42no—
135C2×C4×C23—42no—
136C2×C4×C23C2×D411yescharacteristic
137C2×C4×C23C2×D411yescharacteristic
138C2×C4×C23C2×D411yescharacteristic
139C2×C4×C23C2×D411yescharacteristic
140C2×C4×C23C2411yescharacteristic
141C22⋊D23—42no—
142C22⋊D23—81no—
143C2×Dic23—21no—
144C2×Dic23—21no—
145D92—21no—
146D92—21no—
147D92—21no—
148D92—42no—
149D92#4112yescomplemented
150C4×D23—42no—
151C4×D23—81no—
152Dic46—21no—
153Dic46—21no—
154C23⋊C8—21no—
155C23⋊C8—21no—
156C23⋊C8—21no—
157C23⋊C8—21no—
158#3306—231nomaximal, Sylow
159C22×C23—21no—
160C22×C23—21no—
161C22×C23—21no—
162C22×C23—21no—
163C22×C23—21no—
164C22×C23—41no—
165C22×C23—41no—
166C22×C23—41no—
167C22×C23AGL(1,ℤ/8)12yes—
168C22×C23C22×D411yescharacteristic
169C2×D23—22no—
170C2×D23—41no—
171C2×D23—41no—
172C2×D23—41no—
173C2×D23—41no—
174C2×D23—41no—
175C2×D23—84no—
176C4×C23—21no—
177C4×C23—21no—
178C4×C23—21no—
179C4×C23—21no—
180C4×C23—41no—
181C4×C23—41no—
182C4×C23—41no—
183C4×C23C2×#4111yescharacteristic
184C4×C23H(5,𝔽2)11yescharacteristic
185Dic23—41no—
186Dic23—41no—
187#547D2311yescharacteristic, complemented
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#449—231no—
197#447—231no—
198#442—231no—
199#435—231no—
200#417—231no—
201C2×#102—231no—
202C2×C23—22no—
203C2×C23—41no—
204C2×C23—81no—
205C2×C23#54611yescharacteristic
206C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
207C2×C23#57711yescharacteristic
208D23—42no—
209D23—81no—
210C2×#41—21no—
211C2×#41—231no—
212C22×D4—231no—
213C2×SD16—231no—
214C2×D8—231no—
215C2×D8—231no—
216C2×M16—231no—
217C22×C8—231no—
218C4⋊Q8C2×D2311yescharacteristic, complemented
219#124—231no—
220#123—21no—
221#123—21no—
222#123—461no—
223C22⋊Q8—21no—
224C22⋊Q8—231no—
225#121—231no—
226#121—461no—
227#121C2×D2311yescharacteristic
228#121C2×D2311yescharacteristic, complemented
229#120—461no—
230C4×D4—231no—
231C4×D4C2×D2311yescharacteristic
232C4×D4C2×D2311yescharacteristic, complemented
233C2×C4⋊C4C2×D2311yescharacteristic
234C2×C4⋊C4C2×D2311yescharacteristic, complemented
235C2×C22⋊C4—461no—
236#106—231no—
237#106—231no—
238#106—231no—
239C4⋊C8—231no—
240#103—231no—
241#103—231no—
242#103—231no—
243#102—231no—
244#102—231no—
245#102—231no—
246#102—231no—
247#102—231no—
248#102—231no—
249#102—231no—
250C22⋊C8—231no—
251C22⋊C8—231no—
252#97—231no—
253C23#330611yescharacteristic, complemented, Sylow
254C24—461no—
255#41—44no—
256#41—462no—
257#41—921no—
258C2×Q8—21no—
259C2×Q8—231no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—231no—
263C2×D4—231no—
264C2×D4—462no—
265C2×D4—461no—
266C2×D4—461no—
267C2×D4—461no—
268C2×D4—921no—
269C2×D4C22⋊D2311yescharacteristic
270C2×D4C22×D2311yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—461no—
275C22×C4—461no—
276C22×C4C22×D2311yescharacteristic
277C22×C4C22×D2311yescharacteristic
278SD16—921no—
279D8—462no—
280D8—921no—
281M16—921no—
282C2×C8—231no—
283C2×C8—231no—
284C2×C8—231no—
285C2×C8—231no—
286C2×C8—921no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—231no—
291C4⋊C4—461no—
292C4⋊C4C22⋊D2311yescharacteristic
293C4⋊C4C22×D2311yescharacteristic
294C4⋊C4C22×D2311yescharacteristic
295C4⋊C4C22×D2311yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—461no—
300C22⋊C4—461no—
301C22⋊C4—461no—
302C22⋊C4—461no—
303C22⋊C4—461no—
304C22⋊C4C22⋊D2311yescharacteristic
305C22⋊C4C22⋊D2311yescharacteristic
306C42C22×D2311yescharacteristic
307C23—21no—
308C23—461no—
309C23—461no—
310C23—922no—
311C23—922no—
312C23—1841no—
313C23C2×C22⋊D2311yescharacteristic
314C23C2×C22⋊D2311yescharacteristic
315Q8—42no—
316Q8—461no—
317Q8—461no—
318D4—22no—
319D4—21no—
320D4—21no—
321D4—42no—
322D4—42no—
323D4—232no—
324D4—461no—
325D4—461no—
326D4—461no—
327D4—922no—
328D4—922no—
329D4—1841no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—461no—
341C2×C4—461no—
342C2×C4—922no—
343C2×C4—1841no—
344C2×C4C2×C22⋊D2311yescharacteristic
345C2×C4C2×C22⋊D2311yescharacteristic
346C2×C4C2×C22⋊D2311yescharacteristic
347C2×C4C2×C22⋊D2311yescharacteristic
348C2×C4C23×D2311yescharacteristic
349C8—461no—
350C8—461no—
351C8—461no—
352C8—461no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—462no—
362C22—921no—
363C22—921no—
364C22—921no—
365C22—921no—
366C22—921no—
367C22—1844no—
368C22#1062510312yes—
369C22C22×C22⋊D2311yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—921no—
378C4—921no—
379C4#41×D2311yescharacteristic
380C4#1062516011yescharacteristic
381C2—22no—
382C2—41no—
383C2—81no—
384C2—922no—
385C2—1841no—
386C2#1309305511yescharacteristic
387C2C2×#1062510311yescharacteristic
388C2#1309322511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#547C2
socleC22×C23C22×D4
hypercenter#547D23
hypocenterC23#3306
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #13093063C2semidirect
2. #13092779C2semidirect
3. #13092747C2semidirect
4. #13092735C2semidirect
5. #13092704C2semidirect
6. #13092668C2semidirect
7. #13092644C2semidirect
8. #13092632C2semidirect
9. #13092560C2semidirect
10. #13092550C2semidirect
11. #13092527C2semidirect
12. #13092489C2semidirect
13. #13092416C2semidirect
14. C2×#10624991C2semidirect
15. C23×#547C2semidirect
19. C23×C4⋊Q8C22semidirect
24. C23×#121C22semidirect
26. C4×D4×C23C22semidirect
28. C2×C4⋊C4×C23C22semidirect
30. C2×#67273C22semidirect
35. C2×#67267C22semidirect
42. #10625014C22semidirect
44. C22⋊(C23⋊C8)C22semidirect
45. #10624992C22semidirect
46. #10624992C22semidirect
47. #10624992C22semidirect
54. #10624990C22semidirect
55. #10624990C22semidirect
56. #10624990C22semidirect
57. C4⋊(C23⋊C8)C22semidirect
58. #10624985C22semidirect
149. D92#41semidirect
187. #547D23semidirect
218. C4⋊Q8C2×D23semidirect
228. #121C2×D23semidirect
232. C4×D4C2×D23semidirect
234. C2×C4⋊C4C2×D23semidirect
253. C23#3306semidirect

Maximal subgroups

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

subgroupindex
#130930632
#130927792
#130927472
#130927352
#130927042
#130926682
#130926442
#130926322
#130925602
#130925502
#130925272
#130924892
#130924162
C2×#106249912
C23×#5472
#330623