Finite Group Databasebeta

← #15685234

Subgroups — #15685234

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#13093107C211yesmaximal, characteristic, complemented
2#13093063C211yesmaximal, characteristic
3#13092772C211yesmaximal, characteristic, complemented
4#13092748C211yesmaximal, characteristic, complemented
5#13092742C211yesmaximal, characteristic, complemented
6#13092718C211yesmaximal, characteristic, complemented
7#13092658C211yesmaximal, characteristic, complemented
8#13092646C211yesmaximal, characteristic, complemented
9#13092640C211yesmaximal, characteristic, complemented
10#13092581C211yesmaximal, characteristic, complemented
11#13092570C211yesmaximal, characteristic, complemented
12C4×#67263C211yesmaximal, characteristic, complemented
13#13092414C211yesmaximal, characteristic, complemented
14C2×#10625003C211yesmaximal, characteristic, complemented
15C8×D4×C23C211yesmaximal, characteristic, complemented
16C2×#67288C2211yescharacteristic
17C22×D92C2211yescharacteristic
18C22×C8×C23C2211yescharacteristic
19C22×C8×C23C2211yescharacteristic, complemented
20C4×D4×C23C2211yescharacteristic
21#10625108—21no—
22#10625106—21no—
23#10625101C2211yescharacteristic
24#10625097C2211yescharacteristic, complemented
25C2×C4⋊Dic23C2211yescharacteristic
26#10625095C2211yescharacteristic
27#10625095C2211yescharacteristic
28#10625095C2211yescharacteristic, complemented
29C2×Dic92C2211yescharacteristic, complemented
30C2×#67263C2211yescharacteristic
31C2×#67263C2211yescharacteristic
32#10625065—21no—
33#10625060—21no—
34#10625055—21no—
35C22⋊C4×D23—21no—
36#10625050—21no—
37#10625048—21no—
38#10625046C2211yescharacteristic
39C4×D92C2211yescharacteristic
40#10625041C2211yescharacteristic, complemented
41C4×Dic46C2211yescharacteristic, complemented
42C23×C4⋊C8C2211yescharacteristic, complemented
43C23×C22⋊C8C2211yescharacteristic
44C23×C22⋊C8C2211yescharacteristic, complemented
45C4×C8×C23C2211yescharacteristic, complemented
46#10625003C2211yescharacteristic
47#10625003C2211yescharacteristic
48#10625003C2211yescharacteristic
49#10625003C2211yescharacteristic
50#10625003C2211yescharacteristic
51#10625003C2211yescharacteristic
52#10625000C2211yescharacteristic, complemented
53#10624999C2211yescharacteristic, complemented
54#10624999C2211yescharacteristic, complemented
55#10624998C2211yescharacteristic, 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—
65C22×Dic23—21no—
66#67288—22no—
67#67288—41no—
68C2×D92—22no—
69C2×D92—21no—
70C2×D92—41no—
71C2×D92C2311yescharacteristic
72C2×D92C2311yescharacteristic
73C2×C4×D23—21no—
74C2×C4×D23—21no—
75C2×Dic46C2311yescharacteristic
76C2×Dic46C2311yescharacteristic
77C2×C8×C23—41no—
78C2×C8×C23—41no—
79C2×C8×C23C2311yescharacteristic
80C2×C8×C23C2311yescharacteristic
81C2×C8×C23C2311yescharacteristic
82C2×C8×C23C2311yescharacteristic
83C4⋊C4×C23D411yescharacteristic
84C22⋊C4×C23D411yescharacteristic
85C22⋊C4×C23D411yescharacteristic
86C42×C23C2311yescharacteristic
87C22⋊Dic23—21no—
88C22⋊Dic23—21no—
89C22⋊Dic23—21no—
90C22⋊Dic23—21no—
91(C2×D23)⋊C4—21no—
92(C2×D23)⋊C4—21no—
93(C2×D23)⋊C4—21no—
94(C2×D23)⋊C4—21no—
95C4⋊Dic23—21no—
96C4⋊Dic23C2311yescharacteristic
97C4⋊Dic23C2311yescharacteristic
98C4⋊Dic23C2311yescharacteristic
99C4⋊Dic23C2311yescharacteristic
100Dic23⋊C4—21no—
101Dic23⋊C4—21no—
102Dic23⋊C4—21no—
103Dic23⋊C4—21no—
104Dic23⋊C4—21no—
105Dic23⋊C4—21no—
106C4×Dic23—21no—
107C4×Dic23—21no—
108Dic92—41no—
109#67263—22no—
110#67263—41no—
111C23×C23C2×D411yescharacteristic
112C23×C23C2×D411yescharacteristic
113C22×D23—21no—
114C22×D23—21no—
115C22×D23—42no—
116C22×D23—42no—
117C22×D23—81no—
118D4×C23—22no—
119C2×C4×C23—21no—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23C2×D411yescharacteristic
124C2×C4×C23C2×D411yescharacteristic
125C2×C4×C23C2×D411yescharacteristic
126C2×C4×C23C2×D411yescharacteristic
127C2×C4×C23C2411yescharacteristic
128C22⋊D23—42no—
129C22⋊D23—81no—
130C2×Dic23—21no—
131C2×Dic23—21no—
132C2×Dic23—21no—
133C2×Dic23—21no—
134C2×Dic23—21no—
135C2×Dic23—21no—
136C2×Dic23—42no—
137D92—21no—
138D92—21no—
139D92—21no—
140D92—42no—
141D92#4112yes—
142C4×D23—42no—
143C4×D23—81no—
144Dic46—21no—
145Dic46—21no—
146Dic46—21no—
147Dic46—21no—
148C8×C23—21no—
149C8×C23—21no—
150C8×C23—21no—
151C8×C23—21no—
152#3296—231nomaximal, Sylow
153C22×C23—21no—
154C22×C23—21no—
155C22×C23—21no—
156C22×C23—21no—
157C22×C23—21no—
158C22×C23#13512yes—
159C22×C23C22×D411yescharacteristic
160C2×D23—22no—
161C2×D23—41no—
162C2×D23—41no—
163C2×D23—41no—
164C2×D23—41no—
165C2×D23—41no—
166C2×D23—84no—
167C4×C23—21no—
168C4×C23—21no—
169C4×C23—21no—
170C4×C23—21no—
171C4×C23C2×#4111yescharacteristic
172C4×C23H(5,𝔽2)11yescharacteristic
173Dic23—41no—
174Dic23—41no—
175Dic23—41no—
176Dic23—41no—
177Dic23—41no—
178Dic23—41no—
179#552—231no—
180#546—231no—
181#488—231no—
182#483—231no—
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×D4D2311yescharacteristic, complemented
192#416—231no—
193C2×#102—231no—
194C2×C23—22no—
195C2×C23—41no—
196C2×C23#54611yescharacteristic
197C2×C23C2×#13511yescharacteristic
198C2×C23#57711yescharacteristic
199D23—42no—
200D23—81no—
201C2×#41—231no—
202C22×D4—231no—
203C2×Q16—231no—
204C2×SD16—231no—
205C2×SD16—231no—
206C22×C8C2×D2311yescharacteristic
207C22×C8C2×D2311yescharacteristic, complemented
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⋊Q8—231no—
217#121—231no—
218#121—461no—
219#120—461no—
220C4×Q8—231no—
221C4×D4—231no—
222C4×D4C2×D2311yescharacteristic
223#117—231no—
224#117—461no—
225C2×C4⋊C4—231no—
226C2×C22⋊C4—461no—
227#107—231no—
228#106—231no—
229#106—231no—
230C4⋊C8C2×D2311yescharacteristic, complemented
231#103—231no—
232#103—231no—
233#103—231no—
234#103—231no—
235#102—231no—
236#102—231no—
237#102—231no—
238#102—231no—
239#102—231no—
240#102—231no—
241C22⋊C8C2×D2311yescharacteristic
242C22⋊C8C2×D2311yescharacteristic, complemented
243C4×C8C2×D2311yescharacteristic, complemented
244C23#329611yescharacteristic, complemented, Sylow
245C24—461no—
246#41—462no—
247#41—921no—
248C2×Q8—231no—
249C2×Q8—231no—
250C2×D4—231no—
251C2×D4—231no—
252C2×D4—462no—
253C2×D4—461no—
254C2×D4—461no—
255C2×D4—461no—
256C2×D4—921no—
257C2×D4D9211yescharacteristic
258C22×C4—461no—
259C22×C4—461no—
260C22×C4—461no—
261C22×C4C22×D2311yescharacteristic
262C22×C4C22×D2311yescharacteristic
263Q16—921no—
264SD16—462no—
265SD16—921no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8C22×D2311yescharacteristic
269C2×C8C22×D2311yescharacteristic
270C2×C8C22×D2311yescharacteristic
271C2×C8C22×D2311yescharacteristic
272C4⋊C4—231no—
273C4⋊C4—231no—
274C4⋊C4—231no—
275C4⋊C4—231no—
276C4⋊C4—461no—
277C4⋊C4—461no—
278C4⋊C4—461no—
279C4⋊C4—461no—
280C4⋊C4—461no—
281C4⋊C4—461no—
282C4⋊C4—461no—
283C4⋊C4D9211yescharacteristic
284C22⋊C4—461no—
285C22⋊C4—461no—
286C22⋊C4—461no—
287C22⋊C4—461no—
288C22⋊C4—461no—
289C22⋊C4—461no—
290C22⋊C4—461no—
291C22⋊C4—461no—
292C22⋊C4D9211yescharacteristic
293C22⋊C4D9211yescharacteristic
294C42—461no—
295C42—461no—
296C42C22×D2311yescharacteristic
297C23—461no—
298C23—461no—
299C23—922no—
300C23—922no—
301C23—1841no—
302C23C2×D9211yescharacteristic
303C23C2×D9211yescharacteristic
304Q8—461no—
305Q8—461no—
306Q8—461no—
307Q8—461no—
308D4—22no—
309D4—232no—
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—461no—
321C2×C4—461no—
322C2×C4—461no—
323C2×C4—461no—
324C2×C4—461no—
325C2×C4—461no—
326C2×C4—922no—
327C2×C4—922no—
328C2×C4—1841no—
329C2×C4C2×D9211yescharacteristic
330C2×C4C2×D9211yescharacteristic
331C2×C4C2×D9211yescharacteristic
332C2×C4C2×D9211yescharacteristic
333C2×C4C23×D2311yescharacteristic
334C8—21no—
335C8—21no—
336C8—21no—
337C8—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—462no—
344C22—921no—
345C22—921no—
346C22—921no—
347C22—921no—
348C22—921no—
349C22—1844no—
350C22#1062507512yes—
351C22C22×D9211yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—921no—
357C4—921no—
358C4—921no—
359C4—921no—
360C4—921no—
361C4—921no—
362C4#1062515511yescharacteristic
363C4#41×D2311yescharacteristic
364C2—22no—
365C2—41no—
366C2—922no—
367C2—1841no—
368C2#1309306211yescharacteristic
369C2C2×#1062507511yescharacteristic
370C2#1309322911yescharacteristic
subgroupG/H
centerC22C22×D92
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC8×D4×C23C2
socleC22×C23C22×D4
prime radical#13093063C2
hypercenterC8×D4D23
hypocenterC23#3296
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #13093107C2semidirect
3. #13092772C2semidirect
4. #13092748C2semidirect
5. #13092742C2semidirect
6. #13092718C2semidirect
7. #13092658C2semidirect
8. #13092646C2semidirect
9. #13092640C2semidirect
10. #13092581C2semidirect
11. #13092570C2semidirect
12. C4×#67263C2semidirect
13. #13092414C2semidirect
14. C2×#10625003C2semidirect
15. C8×D4×C23C2semidirect
19. C22×C8×C23C22semidirect
24. #10625097C22semidirect
28. #10625095C22semidirect
29. C2×Dic92C22semidirect
40. #10625041C22semidirect
41. C4×Dic46C22semidirect
42. C23×C4⋊C8C22semidirect
44. C23×C22⋊C8C22semidirect
45. C4×C8×C23C22semidirect
52. #10625000C22semidirect
53. #10624999C22semidirect
54. #10624999C22semidirect
55. #10624998C22semidirect
56. #10624998C22semidirect
57. #10624998C22semidirect
58. #10624998C22semidirect
191. C8×D4D23semidirect
207. C22×C8C2×D23semidirect
230. C4⋊C8C2×D23semidirect
242. C22⋊C8C2×D23semidirect
243. C4×C8C2×D23semidirect
244. C23#3296semidirect

Maximal subgroups

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

subgroupindex
#130931072
#130930632
#130927722
#130927482
#130927422
#130927182
#130926582
#130926462
#130926402
#130925812
#130925702
C4×#672632
#130924142
C2×#106250032
C8×D4×C232
#329623