Finite Group Databasebeta

← #15685232

Subgroups — #15685232

Order 2944.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093107C211yesmaximal, characteristic, complemented
2#13092771C211yesmaximal, characteristic, complemented
3#13092745C211yesmaximal, characteristic, complemented
4#13092738C211yesmaximal, characteristic, complemented
5#13092717C211yesmaximal, characteristic, complemented
6#13092656C211yesmaximal, characteristic, complemented
7#13092644C211yesmaximal, characteristic, complemented
8#13092636C211yesmaximal, characteristic, complemented
9#13092579C211yesmaximal, characteristic, complemented
10#13092568C211yesmaximal, characteristic, complemented
11C4×#67273C211yesmaximal, characteristic, complemented
12D4×C23⋊C8C211yesmaximal, characteristic, complemented
13#13092413C211yesmaximal, characteristic, complemented
14C2×#10625014C211yesmaximal, characteristic, complemented
15C23×#546C211yesmaximal, characteristic
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×#67275C2211yescharacteristic, complemented
28#10625106—21no—
29C2×#67273C2211yescharacteristic
30C2×#67273C2211yescharacteristic
31#10625097C2211yescharacteristic, complemented
32C2×C4⋊Dic23C2211yescharacteristic
33#10625095C2211yescharacteristic
34#10625095C2211yescharacteristic, complemented
35C22×C23⋊C8C2211yescharacteristic
36C22×C23⋊C8C2211yescharacteristic, complemented
37#10625060—21no—
38#10625050—21no—
39#10625048—21no—
40#10625041C2211yescharacteristic, complemented
41C4×Dic46C2211yescharacteristic, 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#10624992C2211yescharacteristic, complemented
54#10624990C2211yescharacteristic, complemented
55#10624990C2211yescharacteristic, 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
75C22×Dic23—21no—
76C2×Dic46C2311yescharacteristic
77C4⋊C4×C23—21no—
78C4⋊C4×C23D411yescharacteristic
79C4⋊C4×C23C2311yescharacteristic
80C22⋊C4×C23—21no—
81C22⋊C4×C23—21no—
82C22⋊C4×C23—21no—
83C22⋊C4×C23—21no—
84C22⋊C4×C23—21no—
85C22⋊C4×C23D411yescharacteristic
86C22⋊C4×C23D411yescharacteristic
87C42×C23C2311yescharacteristic
88C22⋊Dic23—21no—
89C22⋊Dic23—21no—
90C22⋊Dic23—21no—
91#67275—41no—
92#67273—22no—
93#67273—41no—
94C4⋊Dic23—21no—
95C4⋊Dic23C2311yescharacteristic
96C4⋊Dic23C2311yescharacteristic
97C4⋊Dic23C2311yescharacteristic
98Dic23⋊C4—21no—
99Dic23⋊C4—21no—
100Dic23⋊C4—21no—
101Dic23⋊C4—21no—
102Dic23⋊C4—21no—
103C4×Dic23—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
118Q8×C23—21no—
119Q8×C23—21no—
120D4×C23—22no—
121D4×C23—21no—
122D4×C23—21no—
123D4×C23—21no—
124D4×C23—42no—
125D4×C23—42no—
126D4×C23—81no—
127D4×C23#4112yes—
128C2×C4×C23—21no—
129C2×C4×C23—21no—
130C2×C4×C23—21no—
131C2×C4×C23—21no—
132C2×C4×C23—21no—
133C2×C4×C23—21no—
134C2×C4×C23—42no—
135C2×C4×C23—81no—
136C2×C4×C23C2×D411yescharacteristic
137C2×C4×C23C2×D411yescharacteristic
138C2×C4×C23C2×D411yescharacteristic
139C2×C4×C23C2×D411yescharacteristic
140C2×C4×C23C2411yescharacteristic
141C2×Dic23—21no—
142C2×Dic23—21no—
143C2×Dic23—21no—
144C2×Dic23—21no—
145C2×Dic23—42no—
146Dic46—21no—
147Dic46—21no—
148C23⋊C8—21no—
149C23⋊C8—21no—
150C23⋊C8—21no—
151C23⋊C8—21no—
152#3296—231nomaximal, Sylow
153C22×C23—21no—
154C22×C23—21no—
155C22×C23—21no—
156C22×C23—22no—
157C22×C23—21no—
158C22×C23—21no—
159C22×C23—41no—
160C22×C23—41no—
161C22×C23—41no—
162C22×C23—41no—
163C22×C23—41no—
164C22×C23—84no—
165C22×C23#13512yes—
166C22×C23C22×D411yescharacteristic
167C4×C23—21no—
168C4×C23—21no—
169C4×C23—21no—
170C4×C23—21no—
171C4×C23—41no—
172C4×C23—41no—
173C4×C23C2×#4111yescharacteristic
174C4×C23H(5,𝔽2)11yescharacteristic
175Dic23—41no—
176Dic23—41no—
177Dic23—41no—
178Dic23—41no—
179#552—231no—
180#546D2311yescharacteristic
181#488—231no—
182#483—231no—
183#482—231no—
184#478—231no—
185#467—231no—
186#465—231no—
187#464—231no—
188#452—231no—
189#450—231no—
190C4×SD16—231no—
191C8×D4—231no—
192#416—231no—
193C2×#102—231no—
194C2×C23—22no—
195C2×C23—41no—
196C2×C23—42no—
197C2×C23—81no—
198C2×C23#54611yescharacteristic
199C2×C23C2×#13511yescharacteristic
200C2×C23#57711yescharacteristic
201C2×#41C2×D2311yescharacteristic
202C22×D4C2×D2311yescharacteristic
203C2×Q16—231no—
204C2×SD16—231no—
205C2×SD16—231no—
206C22×C8—231no—
207C22×C8—231no—
208#126—461no—
209#125—231no—
210#125—461no—
211#124C2×D2311yescharacteristic
212#123—21no—
213#123—461no—
214C22⋊Q8—231no—
215C22⋊Q8—231no—
216C22⋊Q8C2×D2311yescharacteristic
217#121—21no—
218#121C2×D2311yescharacteristic
219#120—21no—
220C4×Q8—231no—
221C4×D4C2×D2311yescharacteristic
222C4×D4C2×D2311yescharacteristic
223#117—231no—
224#117—461no—
225C2×C4⋊C4—231no—
226C2×C22⋊C4—21no—
227#107—231no—
228#106—231no—
229#106—231no—
230C4⋊C8—231no—
231#103—231no—
232#103—231no—
233#103—231no—
234#103—231no—
235#102—231no—
236#102—231no—
237#102—231no—
238#102—231no—
239#102—231no—
240#102—231no—
241C22⋊C8—231no—
242C22⋊C8—231no—
243C4×C8—231no—
244C23#329611yescharacteristic, complemented, Sylow
245C24—21no—
246#41—22no—
247#41—41no—
248C2×Q8—231no—
249C2×Q8C22×D2311yescharacteristic
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—41no—
255C2×D4C22⋊D2311yescharacteristic
256C2×D4C22×D2311yescharacteristic
257C2×D4C22×D2311yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—461no—
261C22×C4C22×D2311yescharacteristic
262C22×C4C22×D2311yescharacteristic
263Q16—921no—
264SD16—462no—
265SD16—921no—
266C2×C8—231no—
267C2×C8—231no—
268C2×C8—231no—
269C2×C8—231no—
270C2×C8—921no—
271C2×C8—921no—
272C4⋊C4—21no—
273C4⋊C4—231no—
274C4⋊C4—231no—
275C4⋊C4—231no—
276C4⋊C4—461no—
277C4⋊C4—461no—
278C4⋊C4—461no—
279C4⋊C4—461no—
280C4⋊C4—461no—
281C4⋊C4—461no—
282C4⋊C4C22⋊D2311yescharacteristic
283C4⋊C4C22×D2311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—461no—
290C22⋊C4—461no—
291C22⋊C4—461no—
292C22⋊C4C22⋊D2311yescharacteristic
293C22⋊C4C22⋊D2311yescharacteristic
294C42—461no—
295C42—461no—
296C42C22×D2311yescharacteristic
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23C2×C22⋊D2311yescharacteristic
303C23C2×C22⋊D2311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—461no—
307Q8—461no—
308D4—22no—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—42no—
313D4—42no—
314D4—81no—
315D4#6729012yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—81no—
324C2×C4—461no—
325C2×C4—461no—
326C2×C4—461no—
327C2×C4—461no—
328C2×C4—922no—
329C2×C4C2×C22⋊D2311yescharacteristic
330C2×C4C2×C22⋊D2311yescharacteristic
331C2×C4C2×C22⋊D2311yescharacteristic
332C2×C4C2×C22⋊D2311yescharacteristic
333C2×C4C23×D2311yescharacteristic
334C8—461no—
335C8—461no—
336C8—461no—
337C8—461no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—22no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—84no—
350C22#1062512112yes—
351C22C22×C22⋊D2311yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—921no—
359C4—921no—
360C4—921no—
361C4—921no—
362C4C2×#6729011yescharacteristic
363C4#1062515511yescharacteristic
364C2—22no—
365C2—41no—
366C2—42no—
367C2—81no—
368C2#1309306111yescharacteristic
369C2C2×#1062512111yescharacteristic
370C2#1309322811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
Fitting, prime radicalC23×#546C2
socleC22×C23C22×D4
hypercenter#546D23
hypocenterC23#3296
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. #13093107C2semidirect
2. #13092771C2semidirect
3. #13092745C2semidirect
4. #13092738C2semidirect
5. #13092717C2semidirect
6. #13092656C2semidirect
7. #13092644C2semidirect
8. #13092636C2semidirect
9. #13092579C2semidirect
10. #13092568C2semidirect
11. C4×#67273C2semidirect
12. D4×C23⋊C8C2semidirect
13. #13092413C2semidirect
14. C2×#10625014C2semidirect
27. C2×#67275C22semidirect
31. #10625097C22semidirect
34. #10625095C22semidirect
36. C22×C23⋊C8C22semidirect
40. #10625041C22semidirect
41. C4×Dic46C22semidirect
42. #10625017C22semidirect
43. #10625017C22semidirect
44. #10625017C22semidirect
52. C22⋊(C23⋊C8)C22semidirect
53. #10624992C22semidirect
54. #10624990C22semidirect
55. #10624990C22semidirect
56. #10624989C22semidirect
57. C4⋊(C23⋊C8)C22semidirect
58. C4×C23⋊C8C22semidirect
244. C23#3296semidirect

Maximal subgroups

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

subgroupindex
#130931072
#130927712
#130927452
#130927382
#130927172
#130926562
#130926442
#130926362
#130925792
#130925682
C4×#672732
D4×C23⋊C82
#130924132
C2×#106250142
C23×#5462
#329623