Finite Group Databasebeta

← #15685342

Subgroups — #15685342

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#13093085C211yesmaximal, characteristic, complemented
3#13092762C211yesmaximal, characteristic, complemented
4#13092744C211yesmaximal, characteristic, complemented
5#13092738C211yesmaximal, characteristic, complemented
6#13092711C211yesmaximal, characteristic, complemented
7#13092652C211yesmaximal, characteristic, complemented
8#13092610C211yesmaximal, characteristic, complemented
9#13092560C211yesmaximal, characteristic, complemented
10#13092559C211yesmaximal, characteristic, complemented
11#13092508C211yesmaximal, characteristic, complemented
12C8×C22⋊D23C211yesmaximal, characteristic, complemented
13#13092414C211yesmaximal, characteristic, complemented
14#13092410C211yesmaximal, characteristic, complemented
15C23×#466C211yesmaximal, characteristic, complemented
16C2×#67290C2211yescharacteristic
17C2×#67288C2211yescharacteristic
18C2×D8×C23C2211yescharacteristic
19C22×C8×C23C2211yescharacteristic
20C23×#121C2211yescharacteristic
21C23×#121C2211yescharacteristic
22#10625111—21no—
23#10625111C2211yescharacteristic
24#10625110—21no—
25#10625110—21no—
26#10625109C2211yescharacteristic
27#10625107—21no—
28D4×Dic23C2211yescharacteristic
29C2×#67273C2211yescharacteristic
30C2×#67272C2211yescharacteristic
31C4×C22⋊D23C2211yescharacteristic
32#10625097C2211yescharacteristic
33C2×C8×D23C2211yescharacteristic
34#10625066C2211yescharacteristic
35#10625063C2211yescharacteristic
36#10625059C2211yescharacteristic
37#10625058C2211yescharacteristic
38#10625056—21no—
39#10625055—21no—
40(C22⋊D23)⋊C4—21no—
41#10625048—21no—
42C23×#107C2211yescharacteristic
43C23×#102C2211yescharacteristic
44C23×#102C2211yescharacteristic
45#10625014C2211yescharacteristic
46#10625014C2211yescharacteristic
47C22⋊(C23⋊C8)C2211yescharacteristic
48#10625003C2211yescharacteristic
49#10625003C2211yescharacteristic
50(C2×D23)⋊C8C2211yescharacteristic
51#10624998C2211yescharacteristic
52#10624998C2211yescharacteristic
53Dic23⋊C8C2211yescharacteristic
54C8×Dic23C2211yescharacteristic
55#10624992C2211yescharacteristic
56#10624991C2211yescharacteristic
57#10624990C2211yescharacteristic
58#10624989C2211yescharacteristic
59C2×D4×C23—21no—
60C2×D4×C23—21no—
61C2×D4×C23C2311yescharacteristic
62C2×D4×C23C2311yescharacteristic
63C22×C4×C23C2311yescharacteristic
64C2×C22⋊D23—21no—
65C2×C22⋊D23—21no—
66C2×C22⋊D23—21no—
67C2×C22⋊D23—21no—
68C2×C22⋊D23—21no—
69C2×C22⋊D23D411yescharacteristic
70C22×Dic23—21no—
71C22×Dic23—21no—
72#67290—22no—
73#67290—41no—
74#67288—22no—
75#67288—41no—
76C2×D92—21no—
77C2×D92C2311yescharacteristic
78C2×C4×D23—21no—
79C2×C4×D23C2311yescharacteristic
80C2×Dic46—21no—
81C2×Dic46C2311yescharacteristic
82D8×C23—41no—
83C2×C8×C23—41no—
84C2×C8×C23C2311yescharacteristic
85C2×C8×C23C2311yescharacteristic
86C4⋊C4×C23C2311yescharacteristic
87C4⋊C4×C23C2311yescharacteristic
88C22⋊C4×C23—21no—
89C22⋊C4×C23—21no—
90C22⋊Dic23—21no—
91C22⋊Dic23—21no—
92C22⋊Dic23—21no—
93C22⋊Dic23D411yescharacteristic
94#67273—22no—
95#67272—41no—
96(C2×D23)⋊C4—21no—
97(C2×D23)⋊C4—21no—
98(C2×D23)⋊C4D411yescharacteristic
99C4⋊Dic23C2311yescharacteristic
100C4⋊Dic23C2311yescharacteristic
101Dic23⋊C4—21no—
102Dic23⋊C4—21no—
103Dic23⋊C4D411yescharacteristic
104C4×Dic23—21no—
105C4×Dic23—21no—
106C4×Dic23—21no—
107C4×Dic23C2311yescharacteristic
108C2×C23⋊C8C2311yescharacteristic
109C2×C23⋊C8C2311yescharacteristic
110C8×D23—41no—
111C23×C23—21no—
112C23×C23—21no—
113C23×C23C2×D411yescharacteristic
114C22×D23—21no—
115C22×D23C2×D411yescharacteristic
116D4×C23—21no—
117D4×C23—21no—
118D4×C23—21no—
119D4×C23—21no—
120D4×C23—81no—
121D4×C23—81no—
122C2×C4×C23—21no—
123C2×C4×C23—21no—
124C2×C4×C23—21no—
125C2×C4×C23—21no—
126C2×C4×C23C2×D411yescharacteristic
127C2×C4×C23C2411yescharacteristic
128C22⋊D23—22no—
129C22⋊D23—42no—
130C22⋊D23—42no—
131C22⋊D23—42no—
132C22⋊D23—81no—
133C22⋊D23—81no—
134C2×Dic23—21no—
135C2×Dic23—21no—
136C2×Dic23—21no—
137C2×Dic23—42no—
138C2×Dic23—42no—
139C2×Dic23C2×D411yescharacteristic
140C2×Dic23C2×D411yescharacteristic
141C2×Dic23C2×D411yescharacteristic
142D92—21no—
143D92—21no—
144D92—81no—
145C4×D23—21no—
146C4×D23—21no—
147C4×D23—42no—
148Dic46—21no—
149Dic46—81no—
150Dic46#4112yes—
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—21no—
173C4×C23—41no—
174C4×C23—41no—
175C4×C23C2×#4111yescharacteristic
176C4×C23H(5,𝔽2)11yescharacteristic
177Dic23—22no—
178Dic23—21no—
179Dic23—21no—
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#466D2311yescharacteristic, complemented
191#459—231no—
192#449—231no—
193#449—231no—
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×#41—231no—
208C2×SD16—231no—
209C2×D8—231no—
210C2×D8C2×D2311yescharacteristic
211C22×C8—231no—
212C22×C8C2×D2311yescharacteristic
213C4⋊Q8—231no—
214#127—231no—
215#127—461no—
216#124—461no—
217#124—461no—
218#121—231no—
219#121—231no—
220#121—461no—
221#121—461no—
222#121—461no—
223#121C2×D2311yescharacteristic
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#107C2×D2311yescharacteristic
234#106—231no—
235C4⋊C8—231no—
236#103—231no—
237#103—231no—
238#103—231no—
239#102—231no—
240#102—231no—
241#102—231no—
242#102—231no—
243#102—231no—
244#102C2×D2311yescharacteristic
245#102C2×D2311yescharacteristic
246C22⋊C8—231no—
247C22⋊C8—231no—
248C4×C8—231no—
249C23#330511yescharacteristic, complemented, Sylow
250#41—462no—
251#41—462no—
252#41—921no—
253#41—921no—
254C2×Q8—231no—
255C2×Q8—461no—
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—231no—
269C22×C4—461no—
270C22×C4—461no—
271C22×C4—461no—
272C22×C4C22×D2311yescharacteristic
273SD16—462no—
274D8—41no—
275D8—921no—
276C2×C8—41no—
277C2×C8—231no—
278C2×C8—231no—
279C2×C8—921no—
280C2×C8C22×D2311yescharacteristic
281C2×C8C22×D2311yescharacteristic
282C4⋊C4—231no—
283C4⋊C4—231no—
284C4⋊C4—231no—
285C4⋊C4—461no—
286C4⋊C4—461no—
287C4⋊C4C22×D2311yescharacteristic
288C4⋊C4C22×D2311yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—231no—
292C22⋊C4—231no—
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—232no—
308Q8—461no—
309Q8—1841no—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—81no—
315D4—81no—
316D4—462no—
317D4—461no—
318D4—461no—
319D4—922no—
320D4—922no—
321D4—922no—
322D4—1841no—
323D4—1841no—
324D4—1841no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—231no—
330C2×C4—231no—
331C2×C4—231no—
332C2×C4—461no—
333C2×C4—461no—
334C2×C4—461no—
335C2×C4—461no—
336C2×C4—461no—
337C2×C4—922no—
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—41no—
364C4—41no—
365C4—232no—
366C4—461no—
367C4—461no—
368C4—462no—
369C4—921no—
370C4—921no—
371C4#1062515511yescharacteristic
372C4#41×D2311yescharacteristic
373C2—41no—
374C2—81no—
375C2—81no—
376C2—921no—
377C2—1841no—
378C2#1309305611yescharacteristic
379C2#135×D2311yescharacteristic
380C2#1309321811yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#466C2
socleC22×C23C22×D4
hypercenter#466D23
hypocenterC23#3305
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #13093131C2semidirect
2. #13093085C2semidirect
3. #13092762C2semidirect
4. #13092744C2semidirect
5. #13092738C2semidirect
6. #13092711C2semidirect
7. #13092652C2semidirect
8. #13092610C2semidirect
9. #13092560C2semidirect
10. #13092559C2semidirect
11. #13092508C2semidirect
12. C8×C22⋊D23C2semidirect
13. #13092414C2semidirect
14. #13092410C2semidirect
15. C23×#466C2semidirect
190. #466D23semidirect
249. C23#3305semidirect

Maximal subgroups

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

subgroupindex
#130931312
#130930852
#130927622
#130927442
#130927382
#130927112
#130926522
#130926102
#130925602
#130925592
#130925082
C8×C22⋊D232
#130924142
#130924102
C23×#4662
#330523