Finite Group Databasebeta

← #15685249

Subgroups — #15685249

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#13093113C211yesmaximal, characteristic, complemented
2#13093063C211yesmaximal, characteristic, complemented
3#13092772C211yesmaximal, characteristic, complemented
4#13092753C211yesmaximal, characteristic, complemented
5#13092742C211yesmaximal, characteristic, complemented
6#13092718C211yesmaximal, characteristic, complemented
7#13092653C211yesmaximal, characteristic, complemented
8#13092646C211yesmaximal, characteristic, complemented
9#13092633C211yesmaximal, characteristic, complemented
10#13092564C211yesmaximal, characteristic, complemented
11#13092553C211yesmaximal, characteristic, complemented
12C4×D184C211yesmaximal, 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#10625110—21no—
22#10625108—21no—
23#10625101C2211yescharacteristic
24#10625101C2211yescharacteristic
25#10625101C2211yescharacteristic, complemented
26#10625097C2211yescharacteristic, complemented
27C2×C4⋊Dic23C2211yescharacteristic
28#10625095C2211yescharacteristic
29C2×D184C2211yescharacteristic
30C2×D184C2211yescharacteristic
31C2×#67263C2211yescharacteristic, complemented
32#10625069—21no—
33#10625065—21no—
34#10625055—21no—
35#10625054—21no—
36(C22⋊D23)⋊C4—21no—
37C22⋊C4×D23—21no—
38#10625046C2211yescharacteristic
39C4×D92C2211yescharacteristic
40C4×D92C2211yescharacteristic, complemented
41#10625041C2211yescharacteristic, 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#10625003C2211yescharacteristic, complemented
53#10625000C2211yescharacteristic, complemented
54#10625000C2211yescharacteristic, 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—
68#67288—22no—
69#67288—41no—
70C2×D92—22no—
71C2×D92—21no—
72C2×D92—41no—
73C2×D92C2311yescharacteristic
74C2×D92C2311yescharacteristic
75C2×D92C2311yescharacteristic
76C2×C4×D23—21no—
77C2×C4×D23—21no—
78C2×C4×D23—21no—
79C2×Dic46C2311yescharacteristic
80C2×C8×C23—41no—
81C2×C8×C23—41no—
82C2×C8×C23C2311yescharacteristic
83C2×C8×C23C2311yescharacteristic
84C2×C8×C23C2311yescharacteristic
85C2×C8×C23C2311yescharacteristic
86C4⋊C4×C23D411yescharacteristic
87C22⋊C4×C23D411yescharacteristic
88C22⋊C4×C23D411yescharacteristic
89C42×C23C2311yescharacteristic
90C22⋊Dic23—21no—
91C22⋊Dic23—21no—
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)⋊C4—21no—
99C4⋊Dic23—21no—
100C4⋊Dic23C2311yescharacteristic
101C4⋊Dic23C2311yescharacteristic
102C4⋊Dic23C2311yescharacteristic
103C4⋊Dic23C2311yescharacteristic
104Dic23⋊C4—21no—
105Dic23⋊C4—21no—
106Dic23⋊C4—21no—
107C4×Dic23—21no—
108D184—22no—
109D184—41no—
110#67263—41no—
111C23×C23C2×D411yescharacteristic
112C23×C23C2×D411yescharacteristic
113C22×D23—21no—
114C22×D23—21no—
115C22×D23—21no—
116C22×D23—42no—
117C22×D23—42no—
118C22×D23—81no—
119D4×C23—22no—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23—21no—
124C2×C4×C23C2×D411yescharacteristic
125C2×C4×C23C2×D411yescharacteristic
126C2×C4×C23C2×D411yescharacteristic
127C2×C4×C23C2×D411yescharacteristic
128C2×C4×C23C2411yescharacteristic
129C22⋊D23—42no—
130C22⋊D23—42no—
131C22⋊D23—81no—
132C22⋊D23—81no—
133C2×Dic23—21no—
134C2×Dic23—21no—
135C2×Dic23—21no—
136C2×Dic23—21no—
137C2×Dic23—21no—
138C2×Dic23—81no—
139D92—21no—
140D92—21no—
141D92—21no—
142D92—21no—
143D92—21no—
144D92—42no—
145D92#4112yes—
146C4×D23—42no—
147C4×D23—81no—
148C4×D23—81no—
149Dic46—21no—
150Dic46—21no—
151C8×C23—21no—
152C8×C23—21no—
153C8×C23—21no—
154C8×C23—21no—
155#3297—231nomaximal, Sylow
156C22×C23—21no—
157C22×C23—21no—
158C22×C23—21no—
159C22×C23—21no—
160C22×C23—21no—
161C22×C23#13512yes—
162C22×C23C22×D411yescharacteristic
163C2×D23—22no—
164C2×D23—41no—
165C2×D23—41no—
166C2×D23—41no—
167C2×D23—41no—
168C2×D23—41no—
169C2×D23—41no—
170C2×D23—41no—
171C2×D23—41no—
172C2×D23—84no—
173C4×C23—21no—
174C4×C23—21no—
175C4×C23—21no—
176C4×C23—21no—
177C4×C23C2×#4111yescharacteristic
178C4×C23H(5,𝔽2)11yescharacteristic
179Dic23—41no—
180Dic23—41no—
181Dic23—41no—
182Dic23—41no—
183Dic23—41no—
184#553—231no—
185#546—231no—
186#488—231no—
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×D4D2311yescharacteristic, complemented
197#416—231no—
198C2×#102—231no—
199C2×C23—22no—
200C2×C23—41no—
201C2×C23#54611yescharacteristic
202C2×C23C2×#13511yescharacteristic
203C2×C23#57611yescharacteristic
204D23—42no—
205D23—81no—
206D23—81no—
207C2×#41—231no—
208C22×D4—231no—
209C2×SD16—231no—
210C2×D8—231no—
211C2×D8—231no—
212C22×C8C2×D2311yescharacteristic
213C22×C8C2×D2311yescharacteristic, complemented
214#126—461no—
215#125—231no—
216#124—231no—
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—461no—
229C4×D4C2×D2311yescharacteristic
230#117—231no—
231C2×C4⋊C4—231no—
232C2×C22⋊C4—461no—
233#107—231no—
234#107—231no—
235#106—231no—
236C4⋊C8C2×D2311yescharacteristic, complemented
237#103—231no—
238#103—231no—
239#103—231no—
240#102—231no—
241#102—231no—
242#102—231no—
243#102—231no—
244#102—231no—
245#102—231no—
246#102—231no—
247C22⋊C8C2×D2311yescharacteristic
248C22⋊C8C2×D2311yescharacteristic, complemented
249C4×C8C2×D2311yescharacteristic, complemented
250C23#329711yescharacteristic, complemented, Sylow
251C24—461no—
252#41—462no—
253#41—921no—
254C2×Q8—231no—
255C2×D4—231no—
256C2×D4—231no—
257C2×D4—231no—
258C2×D4—462no—
259C2×D4—461no—
260C2×D4—461no—
261C2×D4—461no—
262C2×D4—461no—
263C2×D4—461no—
264C2×D4—921no—
265C2×D4D9211yescharacteristic
266C22×C4—461no—
267C22×C4—461no—
268C22×C4—461no—
269C22×C4—461no—
270C22×C4C22×D2311yescharacteristic
271C22×C4C22×D2311yescharacteristic
272SD16—921no—
273D8—462no—
274D8—921no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8C22×D2311yescharacteristic
278C2×C8C22×D2311yescharacteristic
279C2×C8C22×D2311yescharacteristic
280C2×C8C22×D2311yescharacteristic
281C4⋊C4—231no—
282C4⋊C4—231no—
283C4⋊C4—231no—
284C4⋊C4—231no—
285C4⋊C4—461no—
286C4⋊C4—461no—
287C4⋊C4—461no—
288C4⋊C4—461no—
289C4⋊C4D9211yescharacteristic
290C22⋊C4—461no—
291C22⋊C4—461no—
292C22⋊C4—461no—
293C22⋊C4—461no—
294C22⋊C4—461no—
295C22⋊C4—461no—
296C22⋊C4—461no—
297C22⋊C4—461no—
298C22⋊C4—461no—
299C22⋊C4D9211yescharacteristic
300C22⋊C4D9211yescharacteristic
301C42—461no—
302C42C22×D2311yescharacteristic
303C23—461no—
304C23—461no—
305C23—461no—
306C23—922no—
307C23—922no—
308C23—1841no—
309C23C2×D9211yescharacteristic
310C23C2×D9211yescharacteristic
311Q8—461no—
312Q8—461no—
313D4—22no—
314D4—232no—
315D4—461no—
316D4—461no—
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—21no—
329C2×C4—461no—
330C2×C4—461no—
331C2×C4—461no—
332C2×C4—461no—
333C2×C4—461no—
334C2×C4—922no—
335C2×C4—1841no—
336C2×C4—1841no—
337C2×C4—1841no—
338C2×C4C2×D9211yescharacteristic
339C2×C4C2×D9211yescharacteristic
340C2×C4C2×D9211yescharacteristic
341C2×C4C2×D9211yescharacteristic
342C2×C4C23×D2311yescharacteristic
343C8—21no—
344C8—21no—
345C8—21no—
346C8—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—462no—
353C22—921no—
354C22—921no—
355C22—921no—
356C22—921no—
357C22—921no—
358C22—921no—
359C22—921no—
360C22—921no—
361C22—1844no—
362C22#1062507512yes—
363C22C22×D9211yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—921no—
369C4—921no—
370C4—921no—
371C4—921no—
372C4—921no—
373C4#1062515511yescharacteristic
374C4#41×D2311yescharacteristic
375C2—22no—
376C2—41no—
377C2—922no—
378C2—1841no—
379C2—1841no—
380C2#1309306211yescharacteristic
381C2C2×#1062507511yescharacteristic
382C2#1309322211yescharacteristic
subgroupG/H
centerC22C22×D92
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC8×D4×C23C2
socleC22×C23C22×D4
hypercenterC8×D4D23
hypocenterC23#3297
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. #13093113C2semidirect
2. #13093063C2semidirect
3. #13092772C2semidirect
4. #13092753C2semidirect
5. #13092742C2semidirect
6. #13092718C2semidirect
7. #13092653C2semidirect
8. #13092646C2semidirect
9. #13092633C2semidirect
10. #13092564C2semidirect
11. #13092553C2semidirect
12. C4×D184C2semidirect
13. #13092414C2semidirect
14. C2×#10625003C2semidirect
15. C8×D4×C23C2semidirect
19. C22×C8×C23C22semidirect
25. #10625101C22semidirect
26. #10625097C22semidirect
31. C2×#67263C22semidirect
40. C4×D92C22semidirect
41. #10625041C22semidirect
42. C23×C4⋊C8C22semidirect
44. C23×C22⋊C8C22semidirect
45. C4×C8×C23C22semidirect
52. #10625003C22semidirect
53. #10625000C22semidirect
54. #10625000C22semidirect
55. #10624999C22semidirect
56. #10624998C22semidirect
57. #10624998C22semidirect
58. #10624998C22semidirect
196. C8×D4D23semidirect
213. C22×C8C2×D23semidirect
236. C4⋊C8C2×D23semidirect
248. C22⋊C8C2×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
#130931132
#130930632
#130927722
#130927532
#130927422
#130927182
#130926532
#130926462
#130926332
#130925642
#130925532
C4×D1842
#130924142
C2×#106250032
C8×D4×C232
#329723