Finite Group Databasebeta

← #15685252

Subgroups — #15685252

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#13093117C211yesmaximal, characteristic, complemented
2#13093062C211yesmaximal, characteristic, complemented
3#13092772C211yesmaximal, characteristic, complemented
4#13092754C211yesmaximal, characteristic, complemented
5#13092744C211yesmaximal, characteristic, complemented
6#13092717C211yesmaximal, characteristic, complemented
7#13092652C211yesmaximal, characteristic, complemented
8#13092645C211yesmaximal, characteristic, complemented
9#13092632C211yesmaximal, characteristic, complemented
10#13092559C211yesmaximal, characteristic, complemented
11#13092549C211yesmaximal, characteristic, complemented
12C8×D92C211yesmaximal, characteristic, complemented
13#13092410C211yesmaximal, characteristic, complemented
14#102×D23C211yesmaximal, characteristic, complemented
15C4×D8×C23C211yesmaximal, characteristic, complemented
16C2×#67290C2211yescharacteristic
17C2×D4×D23C2211yescharacteristic
18C2×D8×C23C2211yescharacteristic
19C4×D4×C23C2211yescharacteristic
20C4×D4×C23C2211yescharacteristic, complemented
21#10625109C2211yescharacteristic
22#10625109C2211yescharacteristic, complemented
23C2×#67273C2211yescharacteristic, complemented
24C2×#67272C2211yescharacteristic
25#10625101—21no—
26#10625100—21no—
27C4×C22⋊D23—21no—
28C2×(C2×D23)⋊C4—21no—
29C2×C8×D23C2211yescharacteristic
30C2×C8×D23C2211yescharacteristic, complemented
31#10625068C2211yescharacteristic
32#10625066C2211yescharacteristic
33#10625063C2211yescharacteristic, complemented
34C4⋊C4×D23C2211yescharacteristic
35#10625057—21no—
36#10625055—21no—
37#10625053—21no—
38#10625050—21no—
39#10625046C2211yescharacteristic
40C4×D92C2211yescharacteristic
41#10625041C2211yescharacteristic, complemented
42C23×#107C2211yescharacteristic, complemented
43C23×#102C2211yescharacteristic
44C23×#102C2211yescharacteristic, complemented
45C4×C8×C23C2211yescharacteristic, complemented
46#10625014C2211yescharacteristic
47#10625014C2211yescharacteristic
48#10625003C2211yescharacteristic
49#10625003C2211yescharacteristic
50(C2×D23)⋊C8C2211yescharacteristic
51(C2×D23)⋊C8C2211yescharacteristic, complemented
52#10624998C2211yescharacteristic, complemented
53#10624998C2211yescharacteristic, complemented
54#10624992C2211yescharacteristic, complemented
55#10624991C2211yescharacteristic
56#10624990C2211yescharacteristic, complemented
57#10624989C2211yescharacteristic, complemented
58C4⋊(C23⋊C8)C2211yescharacteristic, complemented
59C23×D23—21no—
60C2×D4×C23C2311yescharacteristic
61C2×D4×C23C2311yescharacteristic
62C22×C4×C23—21no—
63C22×C4×C23—21no—
64C2×C22⋊D23—21no—
65C2×C22⋊D23—21no—
66C2×C22⋊D23—21no—
67C2×C22⋊D23—21no—
68C22×Dic23—21no—
69#67290—22no—
70#67290—41no—
71D4×D23—22no—
72D4×D23—41no—
73C2×D92—21no—
74C2×D92D411yescharacteristic
75C2×D92C2311yescharacteristic
76C2×C4×D23—21no—
77C2×C4×D23C2311yescharacteristic
78C2×C4×D23C2311yescharacteristic
79C2×Dic46C2311yescharacteristic
80D8×C23—22no—
81C2×C8×C23C2311yescharacteristic
82C2×C8×C23C2311yescharacteristic
83C4⋊C4×C23C2311yescharacteristic
84C4⋊C4×C23C2311yescharacteristic
85C22⋊C4×C23—21no—
86C22⋊C4×C23—21no—
87C42×C23C2311yescharacteristic
88C22⋊Dic23—21no—
89C22⋊Dic23—21no—
90#67273—41no—
91#67272—41no—
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)⋊C4D411yescharacteristic
98(C2×D23)⋊C4D411yescharacteristic
99C4⋊Dic23—21no—
100C4⋊Dic23D411yescharacteristic
101C4⋊Dic23C2311yescharacteristic
102C4⋊Dic23C2311yescharacteristic
103Dic23⋊C4—21no—
104Dic23⋊C4—21no—
105Dic23⋊C4—21no—
106C4×Dic23—21no—
107C2×C23⋊C8C2311yescharacteristic
108C2×C23⋊C8C2311yescharacteristic
109C8×D23—41no—
110C8×D23—41no—
111C23×C23—21no—
112C23×C23—21no—
113C22×D23—21no—
114C22×D23—42no—
115C22×D23—42no—
116C22×D23—81no—
117C22×D23C2×D411yescharacteristic
118C22×D23C2×D411yescharacteristic
119D4×C23—21no—
120D4×C23—21no—
121D4×C23—21no—
122D4×C23#4112yes—
123C2×C4×C23—21no—
124C2×C4×C23—21no—
125C2×C4×C23—81no—
126C2×C4×C23—81no—
127C2×C4×C23C2×D411yescharacteristic
128C2×C4×C23C2×D411yescharacteristic
129C2×C4×C23C2411yescharacteristic
130C22⋊D23—42no—
131C22⋊D23—42no—
132C22⋊D23—42no—
133C22⋊D23—81no—
134C2×Dic23—21no—
135C2×Dic23—21no—
136C2×Dic23—21no—
137C2×Dic23—42no—
138C2×Dic23C2×D411yescharacteristic
139C2×Dic23C2×D411yescharacteristic
140D92—22no—
141D92—21no—
142D92—21no—
143D92—81no—
144C4×D23—21no—
145C4×D23—21no—
146C4×D23—21no—
147C4×D23—21no—
148C4×D23—81no—
149Dic46—21no—
150Dic46—21no—
151C8×C23—21no—
152C8×C23—21no—
153C23⋊C8—21no—
154C23⋊C8—21no—
155#3297—231nomaximal, Sylow
156C22×C23—22no—
157C22×C23—41no—
158C22×C23—41no—
159C22×C23—41no—
160C22×C23—41no—
161C22×C23—41no—
162C22×C23C22×D411yescharacteristic
163C2×D23—21no—
164C2×D23—21no—
165C2×D23—21no—
166C2×D23—21no—
167C2×D23—21no—
168C2×D23—41no—
169C2×D23—41no—
170C2×D23—41no—
171C2×D23—84no—
172C2×D23#13512yes—
173C4×C23—21no—
174C4×C23—21no—
175C4×C23—41no—
176C4×C23—41no—
177C4×C23C2×#4111yescharacteristic
178C4×C23H(5,𝔽2)11yescharacteristic
179Dic23—21no—
180Dic23—21no—
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×D8D2311yescharacteristic, complemented
196C8×D4—231no—
197#416—231no—
198C2×#102—231no—
199C2×C23—42no—
200C2×C23—81no—
201C2×C23#54611yescharacteristic
202C2×C23C2×#13511yescharacteristic
203C2×C23#57611yescharacteristic
204D23—22no—
205D23—41no—
206D23—81no—
207C2×#41—231no—
208C22×D4—231no—
209C2×SD16—231no—
210C2×D8—231no—
211C2×D8C2×D2311yescharacteristic
212C22×C8—231no—
213C22×C8—231no—
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—461no—
228C4×D4C2×D2311yescharacteristic
229C4×D4C2×D2311yescharacteristic, complemented
230#117—231no—
231C2×C4⋊C4—231no—
232C2×C22⋊C4—461no—
233#107—231no—
234#107C2×D2311yescharacteristic, complemented
235#106—231no—
236C4⋊C8—231no—
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#102C2×D2311yescharacteristic
246#102C2×D2311yescharacteristic, complemented
247C22⋊C8—231no—
248C22⋊C8—231no—
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—461no—
258C2×D4—461no—
259C2×D4—462no—
260C2×D4—461no—
261C2×D4—461no—
262C2×D4—461no—
263C2×D4—921no—
264C2×D4C22×D2311yescharacteristic
265C2×D4C22×D2311yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—231no—
269C22×C4—231no—
270C22×C4—461no—
271C22×C4—461no—
272SD16—921no—
273D8—22no—
274D8—921no—
275C2×C8—231no—
276C2×C8—231no—
277C2×C8—921no—
278C2×C8—921no—
279C2×C8C22×D2311yescharacteristic
280C2×C8C22×D2311yescharacteristic
281C4⋊C4—231no—
282C4⋊C4—231no—
283C4⋊C4—231no—
284C4⋊C4—461no—
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—461no—
302C42C22×D2311yescharacteristic
303C23—21no—
304C23—21no—
305C23—231no—
306C23—231no—
307C23—461no—
308C23—922no—
309C23—922no—
310C23—1841no—
311Q8—461no—
312Q8—461no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—462no—
317D4—461no—
318D4—461no—
319D4—922no—
320D4—922no—
321D4—922no—
322D4—1841no—
323D4—1841no—
324D4#6728812yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—231no—
330C2×C4—231no—
331C2×C4—461no—
332C2×C4—461no—
333C2×C4—461no—
334C2×C4—461no—
335C2×C4—461no—
336C2×C4—461no—
337C2×C4—461no—
338C2×C4—922no—
339C2×C4—1841no—
340C2×C4D4×D2311yescharacteristic
341C2×C4D4×D2311yescharacteristic
342C2×C4C23×D2311yescharacteristic
343C8—21no—
344C8—21no—
345C8—461no—
346C8—461no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—232no—
354C22—461no—
355C22—461no—
356C22—461no—
357C22—461no—
358C22—461no—
359C22—921no—
360C22—921no—
361C22—921no—
362C22—1844no—
363C22C2×D4×D2311yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—461no—
369C4—461no—
370C4—921no—
371C4—921no—
372C4—921no—
373C4C2×#6728811yescharacteristic
374C4#1062516011yescharacteristic
375C2—42no—
376C2—81no—
377C2—462no—
378C2—921no—
379C2—1841no—
380C2#1309306311yescharacteristic
381C2#135×D2311yescharacteristic
382C2#1309321811yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC4×D8×C23C2
socleC22×C23C22×D4
hypercenterC4×D8D23
hypocenterC23#3297
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #13093117C2semidirect
2. #13093062C2semidirect
3. #13092772C2semidirect
4. #13092754C2semidirect
5. #13092744C2semidirect
6. #13092717C2semidirect
7. #13092652C2semidirect
8. #13092645C2semidirect
9. #13092632C2semidirect
10. #13092559C2semidirect
11. #13092549C2semidirect
12. C8×D92C2semidirect
13. #13092410C2semidirect
14. #102×D23C2semidirect
15. C4×D8×C23C2semidirect
20. C4×D4×C23C22semidirect
22. #10625109C22semidirect
23. C2×#67273C22semidirect
30. C2×C8×D23C22semidirect
33. #10625063C22semidirect
41. #10625041C22semidirect
42. C23×#107C22semidirect
44. C23×#102C22semidirect
45. C4×C8×C23C22semidirect
51. (C2×D23)⋊C8C22semidirect
52. #10624998C22semidirect
53. #10624998C22semidirect
54. #10624992C22semidirect
56. #10624990C22semidirect
57. #10624989C22semidirect
58. C4⋊(C23⋊C8)C22semidirect
195. C4×D8D23semidirect
229. C4×D4C2×D23semidirect
234. #107C2×D23semidirect
246. #102C2×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
#130931172
#130930622
#130927722
#130927542
#130927442
#130927172
#130926522
#130926452
#130926322
#130925592
#130925492
C8×D922
#130924102
#102×D232
C4×D8×C232
#329723