Finite Group Databasebeta

← #15685253

Subgroups — #15685253

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#13093119C211yesmaximal, characteristic, complemented
2#13093058C211yesmaximal, characteristic, complemented
3#13092773C211yesmaximal, characteristic, complemented
4#13092750C211yesmaximal, characteristic, complemented
5#13092743C211yesmaximal, characteristic, complemented
6#13092716C211yesmaximal, characteristic, complemented
7#13092652C211yesmaximal, characteristic, complemented
8#13092634C211yesmaximal, characteristic, complemented
9#13092561C211yesmaximal, characteristic, complemented
10#13092550C211yesmaximal, characteristic, complemented
11#13092497C211yesmaximal, characteristic, complemented
12C8×C22⋊D23C211yesmaximal, characteristic, complemented
13#13092412C211yesmaximal, characteristic, complemented
14C2×#10625003C211yesmaximal, characteristic, complemented
15C23×#465C211yesmaximal, characteristic, complemented
16C2×#67292C2211yescharacteristic
17C22×D92C2211yescharacteristic
18C2×SD16×C23C2211yescharacteristic, complemented
19C22×C8×C23C2211yescharacteristic
20C23×C22⋊Q8C2211yescharacteristic
21C23×#121C2211yescharacteristic
22#10625118C2211yescharacteristic
23#10625110—21no—
24#10625109C2211yescharacteristic, complemented
25D4×Dic23—21no—
26D4×Dic23C2211yescharacteristic, complemented
27C2×#67272C2211yescharacteristic
28C2×#67272C2211yescharacteristic
29C4×C22⋊D23C2211yescharacteristic
30C2×C4⋊Dic23C2211yescharacteristic
31C2×C8×D23C2211yescharacteristic, complemented
32#10625066—21no—
33#10625066C2211yescharacteristic
34#10625065—21no—
35#10625064C2211yescharacteristic
36#10625063C2211yescharacteristic, complemented
37#10625061C2211yescharacteristic, complemented
38#10625057—21no—
39#10625053—21no—
40C22⋊C4×D23—21no—
41#10625050—21no—
42C23×#106C2211yescharacteristic, complemented
43C23×#103C2211yescharacteristic, complemented
44C23×#102C2211yescharacteristic, complemented
45#10625017C2211yescharacteristic, complemented
46#10625017C2211yescharacteristic, complemented
47C22⋊(C23⋊C8)C2211yescharacteristic
48#10625003C2211yescharacteristic
49#10625003C2211yescharacteristic
50#10625003C2211yescharacteristic
51#10625003C2211yescharacteristic
52(C2×D23)⋊C8C2211yescharacteristic, complemented
53Dic23⋊C8C2211yescharacteristic, complemented
54C8×Dic23C2211yescharacteristic, complemented
55#10624991C2211yescharacteristic
56#10624991C2211yescharacteristic
57#10624989C2211yescharacteristic, complemented
58#10624989C2211yescharacteristic, complemented
59C23×D23—21no—
60C2×Q8×C23C2311yescharacteristic
61C2×D4×C23—21no—
62C2×D4×C23C2311yescharacteristic
63C22×C4×C23C2311yescharacteristic
64C2×C22⋊D23—21no—
65C2×C22⋊D23D411yescharacteristic
66C22×Dic23—21no—
67C22×Dic23—21no—
68#67292—22no—
69#67292—41no—
70C2×D92—22no—
71C2×D92—21no—
72C2×D92—21no—
73C2×D92—21no—
74C2×D92—41no—
75C2×D92C2311yescharacteristic
76C2×D92C2311yescharacteristic
77C2×C4×D23—21no—
78C2×C4×D23—21no—
79C2×C4×D23C2311yescharacteristic
80SD16×C23—41no—
81C2×C8×C23—41no—
82C2×C8×C23C2311yescharacteristic
83C2×C8×C23C2311yescharacteristic
84C4⋊C4×C23—21no—
85C4⋊C4×C23C2311yescharacteristic
86C4⋊C4×C23C2311yescharacteristic
87C22⋊C4×C23—21no—
88C22⋊C4×C23—21no—
89C22⋊Dic23—21no—
90C22⋊Dic23—21no—
91C22⋊Dic23D411yescharacteristic
92#67272—22no—
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)⋊C4—21no—
99(C2×D23)⋊C4D411yescharacteristic
100C4⋊Dic23—21no—
101C4⋊Dic23—21no—
102C4⋊Dic23C2311yescharacteristic
103C4⋊Dic23C2311yescharacteristic
104Dic23⋊C4—21no—
105Dic23⋊C4D411yescharacteristic
106C4×Dic23—21no—
107C4×Dic23C2311yescharacteristic
108C2×C23⋊C8C2311yescharacteristic
109C2×C23⋊C8C2311yescharacteristic
110C8×D23—41no—
111C23×C23—21no—
112C23×C23C2×D411yescharacteristic
113C22×D23—21no—
114C22×D23—21no—
115C22×D23—42no—
116C22×D23—42no—
117C22×D23—81no—
118C22×D23C2×D411yescharacteristic
119Q8×C23—21no—
120Q8×C23—21no—
121D4×C23—21no—
122D4×C23—21no—
123D4×C23—42no—
124C2×C4×C23—21no—
125C2×C4×C23—21no—
126C2×C4×C23—21no—
127C2×C4×C23—21no—
128C2×C4×C23—21no—
129C2×C4×C23C2×D411yescharacteristic
130C2×C4×C23C2411yescharacteristic
131C22⋊D23—22no—
132C22⋊D23—81no—
133C2×Dic23—21no—
134C2×Dic23—21no—
135C2×Dic23—81no—
136C2×Dic23—81no—
137C2×Dic23C2×D411yescharacteristic
138C2×Dic23C2×D411yescharacteristic
139C2×Dic23C2×D411yescharacteristic
140D92—21no—
141D92—21no—
142D92—21no—
143D92—42no—
144D92—42no—
145D92—81no—
146D92#4112yes—
147C4×D23—21no—
148C4×D23—21no—
149C4×D23—42no—
150C4×D23—81no—
151C8×C23—21no—
152C8×C23—21no—
153C23⋊C8—21no—
154C23⋊C8—21no—
155#3297—231nomaximal, Sylow
156C22×C23—21no—
157C22×C23—21no—
158C22×C23—41no—
159C22×C23—41no—
160C22×C23—41no—
161C22×C23#13512yes—
162C22×C23C22×D411yescharacteristic
163C2×D23—21no—
164C2×D23—22no—
165C2×D23—21no—
166C2×D23—21no—
167C2×D23—41no—
168C2×D23—41no—
169C2×D23—41no—
170C2×D23—41no—
171C2×D23—41no—
172C2×D23—84no—
173C4×C23—21no—
174C4×C23—41no—
175C4×C23—41no—
176C4×C23—41no—
177C4×C23C2×#4111yescharacteristic
178C4×C23H(5,𝔽2)11yescharacteristic
179Dic23—21no—
180Dic23—21no—
181Dic23—21no—
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#465D2311yescharacteristic, complemented
192#463—231no—
193#449—231no—
194#447—231no—
195C4×D8—231no—
196C8×D4—231no—
197#416—231no—
198C2×#102—231no—
199C2×C23—22no—
200C2×C23—81no—
201C2×C23#54611yescharacteristic
202C2×C23C2×#13511yescharacteristic
203C2×C23#57611yescharacteristic
204D23—41no—
205D23—42no—
206D23—81no—
207C2×#41—231no—
208C22×D4—231no—
209C2×SD16C2×D2311yescharacteristic, complemented
210C2×D8—231no—
211C2×D8—231no—
212C22×C8—231no—
213C22×C8C2×D2311yescharacteristic
214#126—461no—
215#125—231no—
216#124—231no—
217#123—461no—
218#123—461no—
219C22⋊Q8C2×D2311yescharacteristic
220#121—231no—
221#121—231no—
222#121—461no—
223#121—461no—
224#121C2×D2311yescharacteristic
225#120—461no—
226C4×D4—231no—
227C4×D4—231no—
228C4×D4—231no—
229C4×D4—461no—
230#117—231no—
231C2×C4⋊C4—231no—
232C2×C22⋊C4—461no—
233#107—231no—
234#107—231no—
235#106C2×D2311yescharacteristic, complemented
236C4⋊C8—231no—
237#103—231no—
238#103—231no—
239#103C2×D2311yescharacteristic, complemented
240#102—231no—
241#102—231no—
242#102—231no—
243#102—231no—
244#102—231no—
245#102—231no—
246#102C2×D2311yescharacteristic, complemented
247C22⋊C8—231no—
248C22⋊C8—231no—
249C4×C8—231no—
250C23#329711yescharacteristic, complemented, Sylow
251C24—461no—
252#41—462no—
253#41—921no—
254C2×Q8C22×D2311yescharacteristic
255C2×D4—21no—
256C2×D4—231no—
257C2×D4—231no—
258C2×D4—231no—
259C2×D4—462no—
260C2×D4—461no—
261C2×D4—461no—
262C2×D4—461no—
263C2×D4—461no—
264C2×D4—921no—
265C2×D4C22×D2311yescharacteristic
266C22×C4—231no—
267C22×C4—461no—
268C22×C4—461no—
269C22×C4—461no—
270C22×C4—461no—
271C22×C4C22×D2311yescharacteristic
272SD16—41no—
273D8—462no—
274D8—921no—
275C2×C8—41no—
276C2×C8—231no—
277C2×C8—231no—
278C2×C8—921no—
279C2×C8C22×D2311yescharacteristic
280C2×C8C22×D2311yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—231no—
283C4⋊C4—231no—
284C4⋊C4—231no—
285C4⋊C4—461no—
286C4⋊C4—461no—
287C4⋊C4—461no—
288C4⋊C4C22×D2311yescharacteristic
289C4⋊C4C22×D2311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—231no—
293C22⋊C4—231no—
294C22⋊C4—461no—
295C22⋊C4—461no—
296C22⋊C4—461no—
297C22⋊C4—461no—
298C22⋊C4—461no—
299C22⋊C4—461no—
300C22⋊C4—461no—
301C42—231no—
302C42—461no—
303C23—21no—
304C23—231no—
305C23—461no—
306C23—461no—
307C23—922no—
308C23—922no—
309C23—1841no—
310C23D4×D2311yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—21no—
315D4—42no—
316D4—232no—
317D4—462no—
318D4—461no—
319D4—461no—
320D4—461no—
321D4—922no—
322D4—922no—
323D4—1841no—
324D4—1841no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—231no—
331C2×C4—231no—
332C2×C4—231no—
333C2×C4—461no—
334C2×C4—461no—
335C2×C4—461no—
336C2×C4—461no—
337C2×C4—922no—
338C2×C4—1841no—
339C2×C4—1841no—
340C2×C4—1841no—
341C2×C4D4×D2311yescharacteristic
342C2×C4C23×D2311yescharacteristic
343C8—21no—
344C8—21no—
345C8—461no—
346C8—461no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—461no—
353C22—461no—
354C22—461no—
355C22—462no—
356C22—921no—
357C22—921no—
358C22—921no—
359C22—921no—
360C22—921no—
361C22—1844no—
362C22#1062508712yes—
363C22C2×D4×D2311yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—461no—
369C4—461no—
370C4—461no—
371C4—921no—
372C4—921no—
373C4#1062515511yescharacteristic
374C4#41×D2311yescharacteristic
375C2—22no—
376C2—81no—
377C2—921no—
378C2—922no—
379C2—1841no—
380C2#1309305611yescharacteristic
381C2C2×#1062508711yescharacteristic
382C2#1309321911yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#465C2
socleC22×C23C22×D4
hypercenter#465D23
hypocenterC23#3297
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #13093119C2semidirect
2. #13093058C2semidirect
3. #13092773C2semidirect
4. #13092750C2semidirect
5. #13092743C2semidirect
6. #13092716C2semidirect
7. #13092652C2semidirect
8. #13092634C2semidirect
9. #13092561C2semidirect
10. #13092550C2semidirect
11. #13092497C2semidirect
12. C8×C22⋊D23C2semidirect
13. #13092412C2semidirect
14. C2×#10625003C2semidirect
15. C23×#465C2semidirect
18. C2×SD16×C23C22semidirect
24. #10625109C22semidirect
26. D4×Dic23C22semidirect
31. C2×C8×D23C22semidirect
36. #10625063C22semidirect
37. #10625061C22semidirect
42. C23×#106C22semidirect
43. C23×#103C22semidirect
44. C23×#102C22semidirect
45. #10625017C22semidirect
46. #10625017C22semidirect
52. (C2×D23)⋊C8C22semidirect
53. Dic23⋊C8C22semidirect
54. C8×Dic23C22semidirect
57. #10624989C22semidirect
58. #10624989C22semidirect
191. #465D23semidirect
209. C2×SD16C2×D23semidirect
235. #106C2×D23semidirect
239. #103C2×D23semidirect
246. #102C2×D23semidirect
250. C23#3297semidirect

Maximal subgroups

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

subgroupindex
#130931192
#130930582
#130927732
#130927502
#130927432
#130927162
#130926522
#130926342
#130925612
#130925502
#130924972
C8×C22⋊D232
#130924122
C2×#106250032
C23×#4652
#329723