Finite Group Databasebeta

← #15685251

Subgroups — #15685251

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#13093061C211yesmaximal, characteristic, complemented
3#13092770C211yesmaximal, characteristic, complemented
4#13092753C211yesmaximal, characteristic, complemented
5#13092739C211yesmaximal, characteristic, complemented
6#13092715C211yesmaximal, characteristic, complemented
7#13092650C211yesmaximal, characteristic, complemented
8#13092644C211yesmaximal, characteristic, complemented
9#13092630C211yesmaximal, characteristic, complemented
10#13092559C211yesmaximal, characteristic, complemented
11D8×Dic23C211yesmaximal, characteristic, complemented
12(C22⋊D23)⋊C8C211yesmaximal, characteristic, complemented
13#13092410C211yesmaximal, characteristic, complemented
14C2×#10625014C211yesmaximal, characteristic, complemented
15C23×#447C211yesmaximal, characteristic, complemented
16C22×D4×C23C2211yescharacteristic
17C2×#67290C2211yescharacteristic
18C2×D8×C23C2211yescharacteristic
19C2×D8×C23C2211yescharacteristic
20C23×#121C2211yescharacteristic
21#10625124—21no—
22C2×C22⋊Dic23—21no—
23#10625110—21no—
24#10625110—21no—
25#10625109C2211yescharacteristic
26#10625109C2211yescharacteristic, complemented
27#10625107C2211yescharacteristic
28#10625106—21no—
29D4×Dic23—21no—
30D4×Dic23C2211yescharacteristic
31D4×Dic23C2211yescharacteristic, complemented
32C2×#67273C2211yescharacteristic, complemented
33C4×C22⋊D23C2211yescharacteristic
34C2×C4⋊Dic23C2211yescharacteristic
35#10625095C2211yescharacteristic
36C22×C23⋊C8C2211yescharacteristic
37C2×C8×D23C2211yescharacteristic, complemented
38#10625063C2211yescharacteristic, complemented
39#10625061C2211yescharacteristic, complemented
40#10625057—21no—
41#10625050—21no—
42C23×#102C2211yescharacteristic
43C23×#102C2211yescharacteristic
44C23×C22⋊C8C2211yescharacteristic
45#10625014C2211yescharacteristic
46#10625014C2211yescharacteristic
47#10625014C2211yescharacteristic
48#10625014C2211yescharacteristic
49#10625014C2211yescharacteristic, complemented
50(C2×D23)⋊C8C2211yescharacteristic, complemented
51#10625000C2211yescharacteristic, complemented
52#10625000C2211yescharacteristic, complemented
53#10624998C2211yescharacteristic, complemented
54#10624998C2211yescharacteristic, complemented
55Dic23⋊C8C2211yescharacteristic, complemented
56C8×Dic23C2211yescharacteristic, complemented
57#10624992C2211yescharacteristic, complemented
58#10624990C2211yescharacteristic, complemented
59C24×C23—21no—
60C2×D4×C23—22no—
61C2×D4×C23—21no—
62C2×D4×C23—21no—
63C2×D4×C23—41no—
64C2×D4×C23C2311yescharacteristic
65C2×D4×C23C2311yescharacteristic
66C2×D4×C23C2311yescharacteristic
67C22×C4×C23C2311yescharacteristic
68C2×C22⋊D23—21no—
69C2×C22⋊D23—21no—
70C2×C22⋊D23—21no—
71C2×C22⋊D23D411yescharacteristic
72C22×Dic23—21no—
73C22×Dic23—21no—
74C22×Dic23—21no—
75C22×Dic23—21no—
76#67290—22no—
77#67290—41no—
78C2×C4×D23C2311yescharacteristic
79C2×Dic46C2311yescharacteristic
80D8×C23—22no—
81D8×C23—41no—
82C2×C8×C23C2311yescharacteristic
83C2×C8×C23C2311yescharacteristic
84C4⋊C4×C23C2311yescharacteristic
85C22⋊C4×C23—21no—
86C22⋊Dic23—21no—
87C22⋊Dic23—21no—
88C22⋊Dic23—21no—
89C22⋊Dic23—21no—
90C22⋊Dic23—21no—
91C22⋊Dic23—21no—
92C22⋊Dic23—21no—
93C22⋊Dic23D411yescharacteristic
94#67273—41no—
95(C2×D23)⋊C4—21no—
96(C2×D23)⋊C4D411yescharacteristic
97C4⋊Dic23—21no—
98C4⋊Dic23—21no—
99C4⋊Dic23C2311yescharacteristic
100C4⋊Dic23C2311yescharacteristic
101C4⋊Dic23C2311yescharacteristic
102Dic23⋊C4—21no—
103Dic23⋊C4—21no—
104Dic23⋊C4D411yescharacteristic
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×C23—21no—
114C23×C23—42no—
115C23×C23—42no—
116C23×C23—81no—
117C23×C23C2×D411yescharacteristic
118C22×D23C2×D411yescharacteristic
119D4×C23—21no—
120D4×C23—21no—
121D4×C23—21no—
122D4×C23—21no—
123D4×C23—21no—
124D4×C23—42no—
125D4×C23—42no—
126D4×C23#4112yes—
127C2×C4×C23—21no—
128C2×C4×C23—21no—
129C2×C4×C23—21no—
130C2×C4×C23C2×D411yescharacteristic
131C2×C4×C23C2411yescharacteristic
132C22⋊D23—22no—
133C22⋊D23—42no—
134C22⋊D23—81no—
135C22⋊D23—81no—
136C2×Dic23—21no—
137C2×Dic23—21no—
138C2×Dic23—21no—
139C2×Dic23—21no—
140C2×Dic23—42no—
141C2×Dic23—81no—
142C2×Dic23—81no—
143C2×Dic23—81no—
144C2×Dic23C2×D411yescharacteristic
145C2×Dic23C2×D411yescharacteristic
146C2×Dic23C2×D411yescharacteristic
147C4×D23—21no—
148C4×D23—21no—
149Dic46—21no—
150Dic46—21no—
151C8×C23—21no—
152C8×C23—21no—
153C23⋊C8—21no—
154C23⋊C8—21no—
155#3297—231nomaximal, Sylow
156C22×C23—21no—
157C22×C23—21no—
158C22×C23—22no—
159C22×C23—41no—
160C22×C23—41no—
161C22×C23—41no—
162C22×C23—41no—
163C22×C23—41no—
164C22×C23—41no—
165C22×C23—41no—
166C22×C23—41no—
167C22×C23—84no—
168C22×C23#13512yes—
169C22×C23C22×D411yescharacteristic
170C2×D23—21no—
171C2×D23—21no—
172C2×D23—21no—
173C4×C23—21no—
174C4×C23—41no—
175C4×C23C2×#4111yescharacteristic
176C4×C23H(5,𝔽2)11yescharacteristic
177Dic23—21no—
178Dic23—21no—
179Dic23—21no—
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#447D2311yescharacteristic, complemented
195C4×D8—231no—
196C8×D4—231no—
197#416—231no—
198C2×#102—231no—
199C2×C23—22no—
200C2×C23—42no—
201C2×C23—81no—
202C2×C23—81no—
203C2×C23#54611yescharacteristic
204C2×C23C2×#13511yescharacteristic
205C2×C23#57611yescharacteristic
206D23—41no—
207C2×#41—231no—
208C22×D4C2×D2311yescharacteristic
209C2×SD16—231no—
210C2×D8C2×D2311yescharacteristic
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—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#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
247C22⋊C8—231no—
248C22⋊C8C2×D2311yescharacteristic
249C4×C8—231no—
250C23#329711yescharacteristic, complemented, Sylow
251C24—21no—
252#41—462no—
253#41—921no—
254C2×Q8—231no—
255C2×D4—22no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—41no—
259C2×D4—231no—
260C2×D4—461no—
261C2×D4—461no—
262C2×D4—461no—
263C2×D4C22×D2311yescharacteristic
264C2×D4C22×D2311yescharacteristic
265C2×D4C22×D2311yescharacteristic
266C22×C4—231no—
267C22×C4—461no—
268C22×C4—461no—
269C22×C4—461no—
270C22×C4—461no—
271C22×C4C22×D2311yescharacteristic
272SD16—921no—
273D8—22no—
274D8—41no—
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—231no—
285C4⋊C4—461no—
286C4⋊C4—461no—
287C4⋊C4—461no—
288C4⋊C4—461no—
289C4⋊C4C22×D2311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—231no—
292C22⋊C4—231no—
293C22⋊C4—461no—
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—21no—
305C23—21no—
306C23—42no—
307C23—42no—
308C23—81no—
309C23—231no—
310C23D4×D2311yescharacteristic
311Q8—461no—
312Q8—461no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—21no—
318D4—42no—
319D4—42no—
320D4—462no—
321D4—922no—
322D4—1841no—
323D4—1841no—
324D4#6729012yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—231no—
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—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—22no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—84no—
359C22—461no—
360C22—461no—
361C22—461no—
362C22#1062508312yes—
363C22C2×D4×D2311yescharacteristic
364C4—21no—
365C4—41no—
366C4—461no—
367C4—461no—
368C4—461no—
369C4—921no—
370C4—921no—
371C4—921no—
372C4—921no—
373C4C2×#6729011yescharacteristic
374C4#1062515511yescharacteristic
375C2—22no—
376C2—42no—
377C2—81no—
378C2—81no—
379C2—921no—
380C2#1309305411yescharacteristic
381C2C2×#1062508311yescharacteristic
382C2#1309322111yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#447C2
socleC22×C23C22×D4
hypercenter#447D23
hypocenterC23#3297
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #13093119C2semidirect
2. #13093061C2semidirect
3. #13092770C2semidirect
4. #13092753C2semidirect
5. #13092739C2semidirect
6. #13092715C2semidirect
7. #13092650C2semidirect
8. #13092644C2semidirect
9. #13092630C2semidirect
10. #13092559C2semidirect
11. D8×Dic23C2semidirect
12. (C22⋊D23)⋊C8C2semidirect
13. #13092410C2semidirect
14. C2×#10625014C2semidirect
15. C23×#447C2semidirect
26. #10625109C22semidirect
31. D4×Dic23C22semidirect
32. C2×#67273C22semidirect
37. C2×C8×D23C22semidirect
38. #10625063C22semidirect
39. #10625061C22semidirect
49. #10625014C22semidirect
50. (C2×D23)⋊C8C22semidirect
51. #10625000C22semidirect
52. #10625000C22semidirect
53. #10624998C22semidirect
54. #10624998C22semidirect
55. Dic23⋊C8C22semidirect
56. C8×Dic23C22semidirect
57. #10624992C22semidirect
58. #10624990C22semidirect
194. #447D23semidirect
250. C23#3297semidirect

Maximal subgroups

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

subgroupindex
#130931192
#130930612
#130927702
#130927532
#130927392
#130927152
#130926502
#130926442
#130926302
#130925592
D8×Dic232
(C22⋊D23)⋊C82
#130924102
C2×#106250142
C23×#4472
#329723