Finite Group Databasebeta

← #15685340

Subgroups — #15685340

Order 2944.

408 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093131C211yesmaximal, characteristic, complemented
2#13093086C211yesmaximal, characteristic, complemented
3#13092762C211yesmaximal, characteristic, complemented
4#13092742C211yesmaximal, characteristic, complemented
5#13092740C211yesmaximal, characteristic, complemented
6#13092710C211yesmaximal, characteristic, complemented
7#13092651C211yesmaximal, characteristic, complemented
8#13092650C211yesmaximal, characteristic, complemented
9#13092610C211yesmaximal, characteristic, complemented
10#13092561C211yesmaximal, characteristic, complemented
11SD16×Dic23C211yesmaximal, characteristic, complemented
12(C22⋊D23)⋊C8C211yesmaximal, characteristic, complemented
13#13092413C211yesmaximal, characteristic, complemented
14#13092412C211yesmaximal, characteristic, complemented
15C23×#449C211yesmaximal, characteristic, complemented
16C2×#41×C23C2211yescharacteristic
17C2×#67292C2211yescharacteristic
18C2×SD16×C23C2211yescharacteristic
19C2×D8×C23C2211yescharacteristic
20C23×#121C2211yescharacteristic
21Q8×Dic23C2211yescharacteristic
22#10625111—21no—
23#10625111C2211yescharacteristic
24#10625110—21no—
25#10625109—21no—
26#10625109C2211yescharacteristic
27#10625109C2211yescharacteristic
28#10625107—21no—
29D4×Dic23C2211yescharacteristic
30C2×#67272C2211yescharacteristic
31#10625101—21no—
32#10625101C2211yescharacteristic
33C4×C22⋊D23—21no—
34C4×C22⋊D23C2211yescharacteristic
35#10625097C2211yescharacteristic
36C22×C23⋊C8C2211yescharacteristic
37C2×C8×D23C2211yescharacteristic
38#10625063C2211yescharacteristic
39#10625059C2211yescharacteristic
40#10625056—21no—
41#10625048—21no—
42C23×#103C2211yescharacteristic
43C23×#102C2211yescharacteristic
44C23×C22⋊C8C2211yescharacteristic
45#10625017C2211yescharacteristic
46#10625017C2211yescharacteristic
47#10625014C2211yescharacteristic
48#10625014C2211yescharacteristic
49#10625014C2211yescharacteristic
50#10625003C2211yescharacteristic
51#10625003C2211yescharacteristic
52(C2×D23)⋊C8C2211yescharacteristic
53#10625000C2211yescharacteristic
54#10624999C2211yescharacteristic
55Dic23⋊C8C2211yescharacteristic
56C8×Dic23C2211yescharacteristic
57#10624991C2211yescharacteristic
58#10624989C2211yescharacteristic
59#41×C23—22no—
60#41×C23—41no—
61C2×Q8×C23C2311yescharacteristic
62C2×D4×C23—21no—
63C2×D4×C23—21no—
64C2×D4×C23C2311yescharacteristic
65C2×D4×C23C2311yescharacteristic
66C22×C4×C23—21no—
67C22×C4×C23C2311yescharacteristic
68C2×C22⋊D23—21no—
69C2×C22⋊D23—21no—
70C2×C22⋊D23—21no—
71C2×C22⋊D23—21no—
72C2×C22⋊D23—21no—
73C2×C22⋊D23D411yescharacteristic
74C22×Dic23—21no—
75#67292—22no—
76#67292—41no—
77C2×D92—21no—
78C2×D92C2311yescharacteristic
79C2×C4×D23—21no—
80C2×C4×D23C2311yescharacteristic
81C2×Dic46—21no—
82SD16×C23—22no—
83D8×C23—41no—
84C2×C8×C23C2311yescharacteristic
85C2×C8×C23C2311yescharacteristic
86C4⋊C4×C23C2311yescharacteristic
87C22⋊C4×C23—21no—
88C22⋊Dic23—21no—
89C22⋊Dic23—21no—
90C22⋊Dic23—21no—
91C22⋊Dic23—21no—
92C22⋊Dic23D411yescharacteristic
93#67272—41no—
94(C2×D23)⋊C4—21no—
95(C2×D23)⋊C4—21no—
96(C2×D23)⋊C4D411yescharacteristic
97C4⋊Dic23—21no—
98C4⋊Dic23C2311yescharacteristic
99C4⋊Dic23C2311yescharacteristic
100C4⋊Dic23C2311yescharacteristic
101Dic23⋊C4—21no—
102Dic23⋊C4D411yescharacteristic
103C4×Dic23—21no—
104C4×Dic23—21no—
105C4×Dic23—21no—
106C4×Dic23C2311yescharacteristic
107C2×C23⋊C8—41no—
108C2×C23⋊C8C2311yescharacteristic
109C2×C23⋊C8C2311yescharacteristic
110C8×D23—41no—
111C23×C23—21no—
112C23×C23—21no—
113C23×C23C2×D411yescharacteristic
114C22×D23—21no—
115C22×D23C2×D411yescharacteristic
116Q8×C23—21no—
117Q8×C23#4112yes—
118D4×C23—21no—
119D4×C23—21no—
120D4×C23—21no—
121D4×C23—21no—
122D4×C23—42no—
123D4×C23—81no—
124C2×C4×C23—21no—
125C2×C4×C23—21no—
126C2×C4×C23—21no—
127C2×C4×C23—21no—
128C2×C4×C23—42no—
129C2×C4×C23C2×D411yescharacteristic
130C2×C4×C23C2411yescharacteristic
131C22⋊D23—22no—
132C22⋊D23—42no—
133C22⋊D23—81no—
134C22⋊D23—81no—
135C22⋊D23—81no—
136C22⋊D23—81no—
137C2×Dic23—21no—
138C2×Dic23—21no—
139C2×Dic23—21no—
140C2×Dic23—42no—
141C2×Dic23C2×D411yescharacteristic
142C2×Dic23C2×D411yescharacteristic
143C2×Dic23C2×D411yescharacteristic
144D92—21no—
145D92—21no—
146D92—42no—
147C4×D23—21no—
148C4×D23—21no—
149C4×D23—42no—
150Dic46—81no—
151C8×C23—21no—
152C8×C23—21no—
153C23⋊C8—21no—
154C23⋊C8—21no—
155#3305—231nomaximal, Sylow
156C22×C23—21no—
157C22×C23—21no—
158C22×C23—21no—
159C22×C23—41no—
160C22×C23—41no—
161C22×C23—41no—
162C22×C23—41no—
163C22×C23—41no—
164C22×C23—41no—
165C22×C23C22×D411yescharacteristic
166C2×D23—21no—
167C2×D23—21no—
168C2×D23—21no—
169C2×D23—41no—
170C2×D23—41no—
171C2×D23—41no—
172C4×C23—22no—
173C4×C23—21no—
174C4×C23—41no—
175C4×C23C2×#4111yescharacteristic
176C4×C23H(5,𝔽2)11yescharacteristic
177Dic23—21no—
178Dic23—21no—
179Dic23—41no—
180Dic23—41no—
181Dic23—41no—
182Dic23#13512yes—
183#555—231no—
184#550—231no—
185#486—231no—
186#482—231no—
187#482—231no—
188#477—231no—
189#466—231no—
190#466—231no—
191#459—231no—
192#449—231no—
193#449D2311yescharacteristic, complemented
194C4×SD16—231no—
195C8×D4—231no—
196#416—231no—
197#416—231no—
198C2×C23—41no—
199C2×C23—81no—
200C2×C23—81no—
201C2×C23#54611yescharacteristic
202C2×C23C2×#13511yescharacteristic
203C2×C23#57611yescharacteristic
204D23—41no—
205D23—81no—
206C2×#41—231no—
207C2×#41C2×D2311yescharacteristic
208C2×SD16C2×D2311yescharacteristic
209C2×D8—231no—
210C2×D8C2×D2311yescharacteristic
211C22×C8—231no—
212C22×C8—231no—
213C4⋊Q8—231no—
214#127—231no—
215#127—461no—
216#124—461no—
217#124—461no—
218#121—231no—
219#121—231no—
220#121—231no—
221#121—461no—
222#121—461no—
223#121—461no—
224#121C2×D2311yescharacteristic
225C4×Q8—231no—
226C4×D4—231no—
227C4×D4—231no—
228C4×D4—461no—
229#117—231no—
230#117—231no—
231#117—461no—
232#107—231no—
233#107—231no—
234#106—231no—
235C4⋊C8—231no—
236#103—231no—
237#103—231no—
238#103C2×D2311yescharacteristic
239#102—231no—
240#102—231no—
241#102—231no—
242#102—231no—
243#102—231no—
244#102—231no—
245#102C2×D2311yescharacteristic
246C22⋊C8—231no—
247C22⋊C8C2×D2311yescharacteristic
248C4×C8—231no—
249C23#330511yescharacteristic, complemented, Sylow
250#41—22no—
251#41—41no—
252#41—462no—
253#41—921no—
254C2×Q8—461no—
255C2×Q8C22×D2311yescharacteristic
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—231no—
259C2×D4—231no—
260C2×D4—461no—
261C2×D4—461no—
262C2×D4—461no—
263C2×D4—461no—
264C2×D4—461no—
265C2×D4—461no—
266C2×D4C22×D2311yescharacteristic
267C2×D4C22×D2311yescharacteristic
268C22×C4—21no—
269C22×C4—231no—
270C22×C4—461no—
271C22×C4—461no—
272C22×C4C22×D2311yescharacteristic
273SD16—22no—
274D8—41no—
275D8—921no—
276C2×C8—231no—
277C2×C8—231no—
278C2×C8—921no—
279C2×C8—921no—
280C2×C8C22×D2311yescharacteristic
281C2×C8C22×D2311yescharacteristic
282C4⋊C4—231no—
283C4⋊C4—231no—
284C4⋊C4—231no—
285C4⋊C4—231no—
286C4⋊C4—461no—
287C4⋊C4—461no—
288C4⋊C4C22×D2311yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—231no—
291C22⋊C4—231no—
292C22⋊C4—461no—
293C22⋊C4—461no—
294C22⋊C4—461no—
295C22⋊C4—461no—
296C22⋊C4—461no—
297C22⋊C4—461no—
298C42—231no—
299C42—461no—
300C42—461no—
301C42—461no—
302C23—21no—
303C23—21no—
304C23—231no—
305C23—461no—
306C23D4×D2311yescharacteristic
307Q8—21no—
308Q8—1841no—
309Q8#6729012yes—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—42no—
315D4—81no—
316D4—462no—
317D4—461no—
318D4—461no—
319D4—922no—
320D4—922no—
321D4—1841no—
322D4—1841no—
323D4—1841no—
324D4—1841no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—231no—
331C2×C4—231no—
332C2×C4—231no—
333C2×C4—461no—
334C2×C4—461no—
335C2×C4—461no—
336C2×C4—461no—
337C2×C4—461no—
338C2×C4—922no—
339C2×C4—922no—
340C2×C4D4×D2311yescharacteristic
341C2×C4C23×D2311yescharacteristic
342C8—21no—
343C8—21no—
344C8—461no—
345C8—461no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—461no—
356C22—461no—
357C22—461no—
358C22—921no—
359C22—921no—
360C22—921no—
361C22C2×D4×D2311yescharacteristic
362C4—21no—
363C4—22no—
364C4—41no—
365C4—232no—
366C4—461no—
367C4—461no—
368C4—921no—
369C4—921no—
370C4—921no—
371C4C2×#6729011yescharacteristic
372C4#1062515511yescharacteristic
373C2—41no—
374C2—81no—
375C2—81no—
376C2—921no—
377C2—1841no—
378C2#1309305411yescharacteristic
379C2#135×D2311yescharacteristic
380C2#1309322111yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#449C2
socleC22×C23C22×D4
hypercenter#449D23
hypocenterC23#3305
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #13093131C2semidirect
2. #13093086C2semidirect
3. #13092762C2semidirect
4. #13092742C2semidirect
5. #13092740C2semidirect
6. #13092710C2semidirect
7. #13092651C2semidirect
8. #13092650C2semidirect
9. #13092610C2semidirect
10. #13092561C2semidirect
11. SD16×Dic23C2semidirect
12. (C22⋊D23)⋊C8C2semidirect
13. #13092413C2semidirect
14. #13092412C2semidirect
15. C23×#449C2semidirect
193. #449D23semidirect
249. C23#3305semidirect

Maximal subgroups

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

subgroupindex
#130931312
#130930862
#130927622
#130927422
#130927402
#130927102
#130926512
#130926502
#130926102
#130925612
SD16×Dic232
(C22⋊D23)⋊C82
#130924132
#130924122
C23×#4492
#330523