Finite Group Databasebeta

← #15685247

Subgroups — #15685247

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#13093113C211yesmaximal, characteristic, complemented
2#13092771C211yesmaximal, characteristic, complemented
3#13092750C211yesmaximal, characteristic, complemented
4#13092738C211yesmaximal, characteristic, complemented
5#13092717C211yesmaximal, characteristic, complemented
6#13092651C211yesmaximal, characteristic, complemented
7#13092648C211yesmaximal, characteristic, complemented
8#13092629C211yesmaximal, characteristic, complemented
9#13092562C211yesmaximal, characteristic, complemented
10#13092551C211yesmaximal, characteristic, complemented
11C4×#67272C211yesmaximal, characteristic, complemented
12D4×C23⋊C8C211yesmaximal, characteristic, complemented
13#13092413C211yesmaximal, characteristic, complemented
14C2×#10625014C211yesmaximal, characteristic, complemented
15C23×#546C211yesmaximal, characteristic, complemented
16C2×#41×C23C2211yescharacteristic
17C22×D4×C23C2211yescharacteristic
18C23×#124C2211yescharacteristic
19C23×#123—21no—
20C23×C22⋊Q8C2211yescharacteristic
21C23×#121—21no—
22C23×#121C2211yescharacteristic
23C23×#120—21no—
24C4×D4×C23C2211yescharacteristic
25C4×D4×C23C2211yescharacteristic
26C2×C22⋊C4×C23—21no—
27C2×#67274C2211yescharacteristic, complemented
28#10625110—21no—
29C2×#67272C2211yescharacteristic
30C2×#67272C2211yescharacteristic
31#10625101C2211yescharacteristic
32#10625101C2211yescharacteristic, complemented
33#10625097C2211yescharacteristic, complemented
34C2×C4⋊Dic23C2211yescharacteristic
35C22×C23⋊C8C2211yescharacteristic
36C22×C23⋊C8C2211yescharacteristic, complemented
37#10625069—21no—
38#10625054—21no—
39(C22⋊D23)⋊C4—21no—
40C4×D92C2211yescharacteristic, complemented
41#10625041C2211yescharacteristic, complemented
42#10625017C2211yescharacteristic, complemented
43#10625017C2211yescharacteristic, complemented
44#10625017C2211yescharacteristic, complemented
45#10625014C2211yescharacteristic
46#10625014C2211yescharacteristic
47#10625014C2211yescharacteristic
48#10625014C2211yescharacteristic
49#10625014C2211yescharacteristic
50#10625014C2211yescharacteristic
51C22⋊(C23⋊C8)C2211yescharacteristic
52C22⋊(C23⋊C8)C2211yescharacteristic, complemented
53#10624991C2211yescharacteristic, complemented
54#10624990C2211yescharacteristic, complemented
55#10624989C2211yescharacteristic, complemented
56#10624989C2211yescharacteristic, complemented
57C4⋊(C23⋊C8)C2211yescharacteristic, complemented
58C4×C23⋊C8C2211yescharacteristic, complemented
59C24×C23—21no—
60#41×C23—22no—
61#41×C23—41no—
62C2×Q8×C23C2311yescharacteristic
63C2×D4×C23—22no—
64C2×D4×C23—21no—
65C2×D4×C23—21no—
66C2×D4×C23—21no—
67C2×D4×C23—41no—
68C2×D4×C23D411yescharacteristic
69C2×D4×C23C2311yescharacteristic
70C2×D4×C23C2311yescharacteristic
71C22×C4×C23—21no—
72C22×C4×C23—21no—
73C22×C4×C23C2311yescharacteristic
74C22×C4×C23C2311yescharacteristic
75C2×C22⋊D23—21no—
76C2×C22⋊D23—21no—
77C22×Dic23—21no—
78C2×D92C2311yescharacteristic
79C2×C4×D23—21no—
80C4⋊C4×C23—21no—
81C4⋊C4×C23D411yescharacteristic
82C4⋊C4×C23C2311yescharacteristic
83C22⋊C4×C23—21no—
84C22⋊C4×C23—21no—
85C22⋊C4×C23—21no—
86C22⋊C4×C23—21no—
87C22⋊C4×C23—21no—
88C22⋊C4×C23D411yescharacteristic
89C22⋊C4×C23D411yescharacteristic
90C42×C23C2311yescharacteristic
91C22⋊Dic23—21no—
92#67274—41no—
93#67272—22no—
94#67272—41no—
95(C2×D23)⋊C4—21no—
96(C2×D23)⋊C4—21no—
97(C2×D23)⋊C4—21no—
98C4⋊Dic23—21no—
99C4⋊Dic23C2311yescharacteristic
100C4⋊Dic23C2311yescharacteristic
101C4⋊Dic23C2311yescharacteristic
102Dic23⋊C4—21no—
103Dic23⋊C4—21no—
104C4×Dic23—21no—
105C2×C23⋊C8—41no—
106C2×C23⋊C8—41no—
107C2×C23⋊C8C2311yescharacteristic
108C2×C23⋊C8C2311yescharacteristic
109C2×C23⋊C8C2311yescharacteristic
110C2×C23⋊C8C2311yescharacteristic
111C23×C23—21no—
112C23×C23—21no—
113C23×C23—42no—
114C23×C23—42no—
115C23×C23—81no—
116C23×C23C2×D411yescharacteristic
117C23×C23C2×D411yescharacteristic
118C22×D23—21no—
119Q8×C23—21no—
120Q8×C23—21no—
121D4×C23—22no—
122D4×C23—21no—
123D4×C23—21no—
124D4×C23—21no—
125D4×C23—42no—
126D4×C23—42no—
127D4×C23—81no—
128D4×C23#4112yes—
129C2×C4×C23—21no—
130C2×C4×C23—21no—
131C2×C4×C23—21no—
132C2×C4×C23—21no—
133C2×C4×C23—21no—
134C2×C4×C23—21no—
135C2×C4×C23—42no—
136C2×C4×C23—81no—
137C2×C4×C23C2×D411yescharacteristic
138C2×C4×C23C2×D411yescharacteristic
139C2×C4×C23C2×D411yescharacteristic
140C2×C4×C23C2×D411yescharacteristic
141C2×C4×C23C2411yescharacteristic
142C22⋊D23—42no—
143C22⋊D23—81no—
144C2×Dic23—21no—
145C2×Dic23—21no—
146C2×Dic23—21no—
147C2×Dic23—81no—
148D92—21no—
149D92—21no—
150C4×D23—81no—
151C23⋊C8—21no—
152C23⋊C8—21no—
153C23⋊C8—21no—
154C23⋊C8—21no—
155#3297—231nomaximal, Sylow
156C22×C23—21no—
157C22×C23—21no—
158C22×C23—21no—
159C22×C23—22no—
160C22×C23—21no—
161C22×C23—21no—
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—41no—
171C2×D23—41no—
172C2×D23—41no—
173C4×C23—21no—
174C4×C23—21no—
175C4×C23—21no—
176C4×C23—21no—
177C4×C23—41no—
178C4×C23—41no—
179C4×C23C2×#4111yescharacteristic
180C4×C23H(5,𝔽2)11yescharacteristic
181Dic23—41no—
182Dic23—41no—
183Dic23—41no—
184#553—231no—
185#546D2311yescharacteristic, complemented
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×D8—231no—
196C8×D4—231no—
197#416—231no—
198C2×#102—231no—
199C2×C23—22no—
200C2×C23—41no—
201C2×C23—42no—
202C2×C23—81no—
203C2×C23#54611yescharacteristic
204C2×C23C2×#13511yescharacteristic
205C2×C23#57611yescharacteristic
206D23—81no—
207C2×#41C2×D2311yescharacteristic
208C22×D4C2×D2311yescharacteristic
209C2×SD16—231no—
210C2×D8—231no—
211C2×D8—231no—
212C22×C8—231no—
213C22×C8—231no—
214#126—461no—
215#125—231no—
216#124C2×D2311yescharacteristic
217#123—21no—
218#123—461no—
219C22⋊Q8C2×D2311yescharacteristic
220#121—21no—
221#121—231no—
222#121—231no—
223#121—461no—
224#121C2×D2311yescharacteristic
225#120—21no—
226C4×D4—231no—
227C4×D4—461no—
228C4×D4C2×D2311yescharacteristic
229C4×D4C2×D2311yescharacteristic
230#117—231no—
231C2×C4⋊C4—231no—
232C2×C22⋊C4—21no—
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#102—231no—
246#102—231no—
247C22⋊C8—231no—
248C22⋊C8—231no—
249C4×C8—231no—
250C23#329711yescharacteristic, complemented, Sylow
251C24—21no—
252#41—22no—
253#41—41no—
254C2×Q8C22×D2311yescharacteristic
255C2×D4—22no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—41no—
260C2×D4—231no—
261C2×D4—461no—
262C2×D4—461no—
263C2×D4C22⋊D2311yescharacteristic
264C2×D4C22×D2311yescharacteristic
265C2×D4C22×D2311yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—461no—
269C22×C4—461no—
270C22×C4C22×D2311yescharacteristic
271C22×C4C22×D2311yescharacteristic
272SD16—921no—
273D8—462no—
274D8—921no—
275C2×C8—231no—
276C2×C8—231no—
277C2×C8—231no—
278C2×C8—231no—
279C2×C8—921no—
280C2×C8—921no—
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—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—461no—
296C22⋊C4—461no—
297C22⋊C4—461no—
298C22⋊C4—461no—
299C22⋊C4C22⋊D2311yescharacteristic
300C22⋊C4C22⋊D2311yescharacteristic
301C42—461no—
302C42C22×D2311yescharacteristic
303C23—21no—
304C23—21no—
305C23—42no—
306C23—42no—
307C23—81no—
308C23—461no—
309C23C2×C22⋊D2311yescharacteristic
310C23C2×C22⋊D2311yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—22no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—42no—
318D4—42no—
319D4—81no—
320D4—461no—
321D4—461no—
322D4—922no—
323D4—1841no—
324D4#6729012yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—42no—
332C2×C4—81no—
333C2×C4—461no—
334C2×C4—461no—
335C2×C4—461no—
336C2×C4—1841no—
337C2×C4—1841no—
338C2×C4C2×C22⋊D2311yescharacteristic
339C2×C4C2×C22⋊D2311yescharacteristic
340C2×C4C2×C22⋊D2311yescharacteristic
341C2×C4C2×C22⋊D2311yescharacteristic
342C2×C4C23×D2311yescharacteristic
343C8—461no—
344C8—461no—
345C8—461no—
346C8—461no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—22no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—84no—
359C22—921no—
360C22—921no—
361C22—921no—
362C22#1062512112yes—
363C22C22×C22⋊D2311yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—921no—
371C4—921no—
372C4—921no—
373C4C2×#6729011yescharacteristic
374C4#1062515511yescharacteristic
375C2—22no—
376C2—41no—
377C2—42no—
378C2—81no—
379C2—1841no—
380C2#1309306111yescharacteristic
381C2C2×#1062512111yescharacteristic
382C2#1309322011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#546C2
socleC22×C23C22×D4
hypercenter#546D23
hypocenterC23#3297
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #13093113C2semidirect
2. #13092771C2semidirect
3. #13092750C2semidirect
4. #13092738C2semidirect
5. #13092717C2semidirect
6. #13092651C2semidirect
7. #13092648C2semidirect
8. #13092629C2semidirect
9. #13092562C2semidirect
10. #13092551C2semidirect
11. C4×#67272C2semidirect
12. D4×C23⋊C8C2semidirect
13. #13092413C2semidirect
14. C2×#10625014C2semidirect
15. C23×#546C2semidirect
27. C2×#67274C22semidirect
32. #10625101C22semidirect
33. #10625097C22semidirect
36. C22×C23⋊C8C22semidirect
40. C4×D92C22semidirect
41. #10625041C22semidirect
42. #10625017C22semidirect
43. #10625017C22semidirect
44. #10625017C22semidirect
52. C22⋊(C23⋊C8)C22semidirect
53. #10624991C22semidirect
54. #10624990C22semidirect
55. #10624989C22semidirect
56. #10624989C22semidirect
57. C4⋊(C23⋊C8)C22semidirect
58. C4×C23⋊C8C22semidirect
185. #546D23semidirect
250. C23#3297semidirect

Maximal subgroups

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

subgroupindex
#130931132
#130927712
#130927502
#130927382
#130927172
#130926512
#130926482
#130926292
#130925622
#130925512
C4×#672722
D4×C23⋊C82
#130924132
C2×#106250142
C23×#5462
#329723