Finite Group Databasebeta

← #15685360

Subgroups — #15685360

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#13093071C211yesmaximal, characteristic, complemented
2#13093063C211yesmaximal, characteristic, complemented
3#13092777C211yesmaximal, characteristic, complemented
4#13092748C211yesmaximal, characteristic, complemented
5#13092736C211yesmaximal, characteristic, complemented
6#13092708C211yesmaximal, characteristic, complemented
7#13092670C211yesmaximal, characteristic, complemented
8#13092646C211yesmaximal, characteristic, complemented
9#13092633C211yesmaximal, characteristic, complemented
10#13092564C211yesmaximal, characteristic, complemented
11#13092553C211yesmaximal, characteristic, complemented
12#13092530C211yesmaximal, characteristic, complemented
13#13092419C211yesmaximal, characteristic, complemented
14C2×#10625003C211yesmaximal, characteristic, complemented
15C23×#435C211yesmaximal, characteristic, complemented
16C2×#67290—21no—
17C2×#67288C2211yescharacteristic
18C22×D92C2211yescharacteristic
19C2×M16×C23C2211yescharacteristic, complemented
20C22×C8×C23C2211yescharacteristic
21C4×D4×C23C2211yescharacteristic
22#10625108—21no—
23#10625101C2211yescharacteristic
24#10625101C2211yescharacteristic
25#10625101C2211yescharacteristic, complemented
26C2×C4⋊Dic23C2211yescharacteristic
27C2×C4⋊Dic23C2211yescharacteristic, complemented
28#10625095C2211yescharacteristic
29C2×D184C2211yescharacteristic
30C2×D184C2211yescharacteristic
31C2×#67263C2211yescharacteristic, complemented
32#10625068—21no—
33#10625065—21no—
34#10625057—21no—
35#10625057—21no—
36#10625055—21no—
37C22⋊C4×D23—21no—
38#10625046C2211yescharacteristic
39C4×D92C2211yescharacteristic
40C4×D92C2211yescharacteristic, complemented
41#10625040C2211yescharacteristic, complemented
42C23×C4⋊C8C2211yescharacteristic, complemented
43C23×C22⋊C8C2211yescharacteristic
44C23×C22⋊C8C2211yescharacteristic, complemented
45C23×#97C2211yescharacteristic, complemented
46#10625003C2211yescharacteristic
47#10625003C2211yescharacteristic
48#10625003C2211yescharacteristic
49#10625003C2211yescharacteristic
50#10625003C2211yescharacteristic
51#10625003C2211yescharacteristic
52#10625003C2211yescharacteristic, complemented
53#10624999C2211yescharacteristic, complemented
54#10624999C2211yescharacteristic, complemented
55#10624999C2211yescharacteristic, complemented
56#10624998C2211yescharacteristic, complemented
57#10624998C2211yescharacteristic, complemented
58#10624998C2211yescharacteristic, complemented
59C23×D23—21no—
60C2×D4×C23D411yescharacteristic
61C22×C4×C23C2311yescharacteristic
62C22×C4×C23C2311yescharacteristic
63C2×C22⋊D23—21no—
64C2×C22⋊D23—21no—
65C2×C22⋊D23—21no—
66C2×C22⋊D23—21no—
67C22×Dic23—21no—
68C22×Dic23—21no—
69#67290—44no—
70#67288—22no—
71#67288—41no—
72C2×D92—22no—
73C2×D92—21no—
74C2×D92—41no—
75C2×D92C2311yescharacteristic
76C2×D92C2311yescharacteristic
77C2×D92C2311yescharacteristic
78C2×C4×D23—21no—
79C2×C4×D23—21no—
80C2×C4×D23—21no—
81C2×Dic46—21no—
82C2×Dic46C2311yescharacteristic
83M16×C23—41no—
84C2×C8×C23—41no—
85C2×C8×C23C2311yescharacteristic
86C2×C8×C23C2311yescharacteristic
87C2×C8×C23C2311yescharacteristic
88C2×C8×C23C2311yescharacteristic
89C4⋊C4×C23D411yescharacteristic
90C22⋊C4×C23D411yescharacteristic
91C22⋊C4×C23D411yescharacteristic
92C42×C23C2311yescharacteristic
93C22⋊Dic23—21no—
94(C2×D23)⋊C4—21no—
95(C2×D23)⋊C4—21no—
96(C2×D23)⋊C4—21no—
97(C2×D23)⋊C4—21no—
98(C2×D23)⋊C4—21no—
99(C2×D23)⋊C4—21no—
100(C2×D23)⋊C4—21no—
101C4⋊Dic23—21no—
102C4⋊Dic23—21no—
103C4⋊Dic23—21no—
104C4⋊Dic23C2311yescharacteristic
105C4⋊Dic23C2311yescharacteristic
106C4⋊Dic23C2311yescharacteristic
107C4⋊Dic23C2311yescharacteristic
108Dic23⋊C4—21no—
109D184—22no—
110D184—41no—
111#67263—41no—
112C23×C23C2×D411yescharacteristic
113C23×C23C2×D411yescharacteristic
114C22×D23—21no—
115C22×D23—21no—
116C22×D23—21no—
117C22×D23—42no—
118C22×D23—42no—
119C22×D23—81no—
120D4×C23—22no—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23—21no—
124C2×C4×C23—21no—
125C2×C4×C23C2×D411yescharacteristic
126C2×C4×C23C2×D411yescharacteristic
127C2×C4×C23C2×D411yescharacteristic
128C2×C4×C23C2×D411yescharacteristic
129C2×C4×C23C2411yescharacteristic
130C22⋊D23—42no—
131C22⋊D23—42no—
132C22⋊D23—42no—
133C22⋊D23—81no—
134C2×Dic23—21no—
135C2×Dic23—21no—
136C2×Dic23—21no—
137C2×Dic23—21no—
138C2×Dic23—21no—
139C2×Dic23—42no—
140C2×Dic23—42no—
141D92—21no—
142D92—21no—
143D92—21no—
144D92—21no—
145D92—21no—
146D92—42no—
147D92#4112yescomplemented
148C4×D23—42no—
149C4×D23—42no—
150C4×D23—81no—
151Dic46—21no—
152Dic46—21no—
153Dic46—42no—
154C8×C23—21no—
155C8×C23—21no—
156C8×C23—21no—
157C8×C23—21no—
158#3306—231nomaximal, Sylow
159C22×C23—21no—
160C22×C23—21no—
161C22×C23—21no—
162C22×C23—21no—
163C22×C23—21no—
164C22×C23AGL(1,ℤ/8)12yes—
165C22×C23C22×D411yescharacteristic
166C2×D23—22no—
167C2×D23—41no—
168C2×D23—41no—
169C2×D23—41no—
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×C23C2×#4111yescharacteristic
181C4×C23H(5,𝔽2)11yescharacteristic
182Dic23—41no—
183Dic23—41no—
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#449—231no—
197#447—231no—
198#442—231no—
199#435D2311yescharacteristic, complemented
200#417—231no—
201C2×#102—231no—
202C2×C23—22no—
203C2×C23—41no—
204C2×C23#54611yescharacteristic
205C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
206C2×C23#57711yescharacteristic
207D23—42no—
208D23—81no—
209D23—81no—
210C2×#41—231no—
211C2×#41—461no—
212C22×D4—231no—
213C2×SD16—231no—
214C2×D8—231no—
215C2×D8—231no—
216C2×M16C2×D2311yescharacteristic, complemented
217C22×C8C2×D2311yescharacteristic
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—231no—
228#121—461no—
229#120—461no—
230C4×D4—231no—
231C4×D4—231no—
232C4×D4C2×D2311yescharacteristic
233C2×C4⋊C4—231no—
234C2×C4⋊C4—231no—
235C2×C22⋊C4—461no—
236#106—231no—
237#106—231no—
238#106—231no—
239C4⋊C8C2×D2311yescharacteristic, complemented
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⋊C8C2×D2311yescharacteristic
251C22⋊C8C2×D2311yescharacteristic, complemented
252#97C2×D2311yescharacteristic, complemented
253C23#330611yescharacteristic, complemented, Sylow
254C24—461no—
255#41—462no—
256#41—921no—
257#41—924no—
258C2×Q8—231no—
259C2×Q8—461no—
260C2×D4—231no—
261C2×D4—231no—
262C2×D4—231no—
263C2×D4—462no—
264C2×D4—461no—
265C2×D4—461no—
266C2×D4—461no—
267C2×D4—461no—
268C2×D4—461no—
269C2×D4—921no—
270C2×D4D9211yescharacteristic
271C22×C4—461no—
272C22×C4—461no—
273C22×C4—461no—
274C22×C4—461no—
275C22×C4—461no—
276C22×C4C22×D2311yescharacteristic
277C22×C4C22×D2311yescharacteristic
278SD16—921no—
279D8—462no—
280D8—921no—
281M16—41no—
282C2×C8—41no—
283C2×C8C22×D2311yescharacteristic
284C2×C8C22×D2311yescharacteristic
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⋊C4D9211yescharacteristic
296C22⋊C4—461no—
297C22⋊C4—461no—
298C22⋊C4—461no—
299C22⋊C4—461no—
300C22⋊C4—461no—
301C22⋊C4—461no—
302C22⋊C4—461no—
303C22⋊C4—461no—
304C22⋊C4D9211yescharacteristic
305C22⋊C4D9211yescharacteristic
306C42C22×D2311yescharacteristic
307C23—461no—
308C23—461no—
309C23—461no—
310C23—922no—
311C23—922no—
312C23—1841no—
313C23C2×D9211yescharacteristic
314C23C2×D9211yescharacteristic
315Q8—461no—
316Q8—461no—
317Q8—922no—
318D4—22no—
319D4—232no—
320D4—461no—
321D4—461no—
322D4—461no—
323D4—461no—
324D4—461no—
325D4—922no—
326D4—922no—
327D4—922no—
328D4—922no—
329D4—1841no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—461no—
335C2×C4—461no—
336C2×C4—461no—
337C2×C4—461no—
338C2×C4—461no—
339C2×C4—922no—
340C2×C4—922no—
341C2×C4—922no—
342C2×C4—922no—
343C2×C4—1841no—
344C2×C4C2×D9211yescharacteristic
345C2×C4C2×D9211yescharacteristic
346C2×C4C2×D9211yescharacteristic
347C2×C4C2×D9211yescharacteristic
348C2×C4C23×D2311yescharacteristic
349C8—21no—
350C8—21no—
351C8—21no—
352C8—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—462no—
359C22—921no—
360C22—921no—
361C22—921no—
362C22—921no—
363C22—921no—
364C22—921no—
365C22—921no—
366C22—921no—
367C22—1844no—
368C22#1062507912yes—
369C22C22×D9211yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—921no—
375C4—921no—
376C4—921no—
377C4—921no—
378C4—921no—
379C4#1062515511yescharacteristic
380C4#41×D2311yescharacteristic
381C2—22no—
382C2—41no—
383C2—922no—
384C2—1841no—
385C2—1841no—
386C2#1309306211yescharacteristic
387C2C2×#1062507911yescharacteristic
388C2#1309322911yescharacteristic
subgroupG/H
centerC22C22×D92
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#435C2
socleC22×C23C22×D4
hypercenter#435D23
hypocenterC23#3306
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #13093071C2semidirect
2. #13093063C2semidirect
3. #13092777C2semidirect
4. #13092748C2semidirect
5. #13092736C2semidirect
6. #13092708C2semidirect
7. #13092670C2semidirect
8. #13092646C2semidirect
9. #13092633C2semidirect
10. #13092564C2semidirect
11. #13092553C2semidirect
12. #13092530C2semidirect
13. #13092419C2semidirect
14. C2×#10625003C2semidirect
15. C23×#435C2semidirect
19. C2×M16×C23C22semidirect
25. #10625101C22semidirect
27. C2×C4⋊Dic23C22semidirect
31. C2×#67263C22semidirect
40. C4×D92C22semidirect
41. #10625040C22semidirect
42. C23×C4⋊C8C22semidirect
44. C23×C22⋊C8C22semidirect
45. C23×#97C22semidirect
52. #10625003C22semidirect
53. #10624999C22semidirect
54. #10624999C22semidirect
55. #10624999C22semidirect
56. #10624998C22semidirect
57. #10624998C22semidirect
58. #10624998C22semidirect
147. D92#41semidirect
199. #435D23semidirect
216. C2×M16C2×D23semidirect
239. C4⋊C8C2×D23semidirect
251. C22⋊C8C2×D23semidirect
252. #97C2×D23semidirect
253. C23#3306semidirect

Maximal subgroups

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

subgroupindex
#130930712
#130930632
#130927772
#130927482
#130927362
#130927082
#130926702
#130926462
#130926332
#130925642
#130925532
#130925302
#130924192
C2×#106250032
C23×#4352
#330623