Finite Group Databasebeta

← #15685236

Subgroups — #15685236

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#13093109C211yesmaximal, characteristic, complemented
2#13093061C211yesmaximal, characteristic
3#13092770C211yesmaximal, characteristic, complemented
4#13092748C211yesmaximal, characteristic, complemented
5#13092740C211yesmaximal, characteristic, complemented
6#13092719C211yesmaximal, characteristic, complemented
7#13092656C211yesmaximal, characteristic, complemented
8#13092643C211yesmaximal, characteristic, complemented
9#13092637C211yesmaximal, characteristic, complemented
10#13092576C211yesmaximal, characteristic, complemented
11SD16×Dic23C211yesmaximal, characteristic, complemented
12(C22⋊D23)⋊C8C211yesmaximal, characteristic, complemented
13#13092410C211yesmaximal, characteristic, complemented
14C2×#10625014C211yesmaximal, characteristic, complemented
15C23×#450C211yesmaximal, characteristic, complemented
16C22×D4×C23C2211yescharacteristic
17C2×#67290C2211yescharacteristic
18C2×SD16×C23C2211yescharacteristic
19C2×SD16×C23C2211yescharacteristic
20C23×C22⋊Q8C2211yescharacteristic
21#10625124—21no—
22C2×C22⋊Dic23—21no—
23#10625117C2211yescharacteristic, complemented
24Q8×Dic23C2211yescharacteristic, complemented
25C2×#67275C2211yescharacteristic, complemented
26#10625110—21no—
27#10625109C2211yescharacteristic
28#10625107C2211yescharacteristic
29#10625106—21no—
30D4×Dic23C2211yescharacteristic
31C4×C22⋊D23C2211yescharacteristic
32C2×C4⋊Dic23C2211yescharacteristic
33#10625095C2211yescharacteristic
34C22×C23⋊C8C2211yescharacteristic
35C2×C8×D23C2211yescharacteristic, complemented
36#10625069—21no—
37#10625063C2211yescharacteristic, complemented
38#10625061—21no—
39#10625061C2211yescharacteristic, complemented
40#10625057—21no—
41#10625048—21no—
42C23×#102C2211yescharacteristic
43C23×#102C2211yescharacteristic
44C23×C22⋊C8C2211yescharacteristic
45#10625017C2211yescharacteristic, complemented
46#10625014C2211yescharacteristic
47#10625014C2211yescharacteristic
48#10625014C2211yescharacteristic
49#10625014C2211yescharacteristic
50(C2×D23)⋊C8C2211yescharacteristic, complemented
51#10624999C2211yescharacteristic, complemented
52#10624999C2211yescharacteristic, complemented
53#10624998C2211yescharacteristic, complemented
54#10624998C2211yescharacteristic, complemented
55Dic23⋊C8C2211yescharacteristic, complemented
56C8×Dic23C2211yescharacteristic, complemented
57#10624992C2211yescharacteristic, complemented
58#10624989C2211yescharacteristic, complemented
59C24×C23—21no—
60C2×Q8×C23C2311yescharacteristic
61C2×D4×C23—22no—
62C2×D4×C23—21no—
63C2×D4×C23—41no—
64C2×D4×C23C2311yescharacteristic
65C2×D4×C23C2311yescharacteristic
66C22×C4×C23C2311yescharacteristic
67C2×C22⋊D23—21no—
68C2×C22⋊D23—21no—
69C2×C22⋊D23D411yescharacteristic
70C22×Dic23—21no—
71C22×Dic23—21no—
72C22×Dic23—21no—
73#67290—22no—
74#67290—41no—
75C2×C4×D23C2311yescharacteristic
76C2×Dic46C2311yescharacteristic
77SD16×C23—22no—
78SD16×C23—41no—
79C2×C8×C23C2311yescharacteristic
80C2×C8×C23C2311yescharacteristic
81C4⋊C4×C23—21no—
82C4⋊C4×C23C2311yescharacteristic
83C22⋊C4×C23—21no—
84C22⋊Dic23—21no—
85C22⋊Dic23—21no—
86C22⋊Dic23—21no—
87C22⋊Dic23—21no—
88C22⋊Dic23—21no—
89C22⋊Dic23D411yescharacteristic
90#67275—41no—
91(C2×D23)⋊C4—21no—
92(C2×D23)⋊C4—21no—
93(C2×D23)⋊C4D411yescharacteristic
94C4⋊Dic23—21no—
95C4⋊Dic23—21no—
96C4⋊Dic23—21no—
97C4⋊Dic23C2311yescharacteristic
98C4⋊Dic23C2311yescharacteristic
99C4⋊Dic23C2311yescharacteristic
100Dic23⋊C4—21no—
101Dic23⋊C4—21no—
102Dic23⋊C4—21no—
103Dic23⋊C4D411yescharacteristic
104C4×Dic23—21no—
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—42no—
114C23×C23—42no—
115C23×C23—81no—
116C23×C23C2×D411yescharacteristic
117C22×D23C2×D411yescharacteristic
118Q8×C23—21no—
119Q8×C23—21no—
120D4×C23—21no—
121D4×C23—21no—
122D4×C23—21no—
123D4×C23—42no—
124D4×C23#4112yes—
125C2×C4×C23—21no—
126C2×C4×C23—21no—
127C2×C4×C23—21no—
128C2×C4×C23—21no—
129C2×C4×C23C2×D411yescharacteristic
130C2×C4×C23C2411yescharacteristic
131C22⋊D23—22no—
132C22⋊D23—42no—
133C22⋊D23—81no—
134C2×Dic23—21no—
135C2×Dic23—21no—
136C2×Dic23—21no—
137C2×Dic23—21no—
138C2×Dic23—42no—
139C2×Dic23—42no—
140C2×Dic23—81no—
141C2×Dic23C2×D411yescharacteristic
142C2×Dic23C2×D411yescharacteristic
143C2×Dic23C2×D411yescharacteristic
144C4×D23—21no—
145C4×D23—21no—
146Dic46—21no—
147Dic46—21no—
148C8×C23—21no—
149C8×C23—21no—
150C23⋊C8—21no—
151C23⋊C8—21no—
152#3296—231nomaximal, Sylow
153C22×C23—21no—
154C22×C23—21no—
155C22×C23—22no—
156C22×C23—41no—
157C22×C23—41no—
158C22×C23—41no—
159C22×C23—41no—
160C22×C23—41no—
161C22×C23—84no—
162C22×C23#13512yes—
163C22×C23C22×D411yescharacteristic
164C2×D23—21no—
165C2×D23—21no—
166C2×D23—21no—
167C4×C23—21no—
168C4×C23—41no—
169C4×C23—41no—
170C4×C23C2×#4111yescharacteristic
171C4×C23H(5,𝔽2)11yescharacteristic
172Dic23—21no—
173Dic23—21no—
174Dic23—21no—
175Dic23—41no—
176Dic23—41no—
177Dic23—41no—
178Dic23—41no—
179#552—231no—
180#546—231no—
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#450D2311yescharacteristic, complemented
190C4×SD16—231no—
191C8×D4—231no—
192#416—231no—
193C2×#102—231no—
194C2×C23—22no—
195C2×C23—42no—
196C2×C23—81no—
197C2×C23#54611yescharacteristic
198C2×C23C2×#13511yescharacteristic
199C2×C23#57711yescharacteristic
200D23—41no—
201C2×#41—231no—
202C22×D4C2×D2311yescharacteristic
203C2×Q16—231no—
204C2×SD16C2×D2311yescharacteristic
205C2×SD16C2×D2311yescharacteristic
206C22×C8—231no—
207C22×C8—231no—
208#126—461no—
209#125—231no—
210#125—461no—
211#124—231no—
212#123—461no—
213#123—461no—
214C22⋊Q8—231no—
215C22⋊Q8—231no—
216C22⋊Q8C2×D2311yescharacteristic
217#121—231no—
218#121—461no—
219#120—461no—
220C4×Q8—231no—
221C4×D4—231no—
222C4×D4—231no—
223#117—231no—
224#117—461no—
225C2×C4⋊C4—231no—
226C2×C22⋊C4—461no—
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#102C2×D2311yescharacteristic
240#102C2×D2311yescharacteristic
241C22⋊C8—231no—
242C22⋊C8C2×D2311yescharacteristic
243C4×C8—231no—
244C23#329611yescharacteristic, complemented, Sylow
245C24—21no—
246#41—462no—
247#41—921no—
248C2×Q8—231no—
249C2×Q8C22×D2311yescharacteristic
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—41no—
253C2×D4—231no—
254C2×D4—461no—
255C2×D4—461no—
256C2×D4C22×D2311yescharacteristic
257C2×D4C22×D2311yescharacteristic
258C22×C4—231no—
259C22×C4—461no—
260C22×C4—461no—
261C22×C4—461no—
262C22×C4C22×D2311yescharacteristic
263Q16—921no—
264SD16—22no—
265SD16—41no—
266C2×C8—231no—
267C2×C8—231no—
268C2×C8—921no—
269C2×C8—921no—
270C2×C8C22×D2311yescharacteristic
271C2×C8C22×D2311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—231no—
274C4⋊C4—231no—
275C4⋊C4—231no—
276C4⋊C4—231no—
277C4⋊C4—461no—
278C4⋊C4—461no—
279C4⋊C4—461no—
280C4⋊C4—461no—
281C4⋊C4—461no—
282C4⋊C4—461no—
283C4⋊C4C22×D2311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—231no—
286C22⋊C4—231no—
287C22⋊C4—461no—
288C22⋊C4—461no—
289C22⋊C4—461no—
290C22⋊C4—461no—
291C22⋊C4—461no—
292C22⋊C4—461no—
293C22⋊C4—461no—
294C42—231no—
295C42—461no—
296C42—461no—
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23—231no—
303C23D4×D2311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—461no—
307Q8—461no—
308D4—21no—
309D4—21no—
310D4—21no—
311D4—42no—
312D4—462no—
313D4—922no—
314D4—1841no—
315D4#6729012yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—231no—
321C2×C4—231no—
322C2×C4—231no—
323C2×C4—461no—
324C2×C4—461no—
325C2×C4—461no—
326C2×C4—461no—
327C2×C4—461no—
328C2×C4—461no—
329C2×C4—922no—
330C2×C4—922no—
331C2×C4—1841no—
332C2×C4D4×D2311yescharacteristic
333C2×C4C23×D2311yescharacteristic
334C8—21no—
335C8—21no—
336C8—461no—
337C8—461no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—84no—
347C22—461no—
348C22—461no—
349C22—461no—
350C22#1062508712yes—
351C22C2×D4×D2311yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—461no—
356C4—461no—
357C4—461no—
358C4—921no—
359C4—921no—
360C4—921no—
361C4—921no—
362C4C2×#6729011yescharacteristic
363C4#1062515511yescharacteristic
364C2—22no—
365C2—42no—
366C2—81no—
367C2—921no—
368C2#1309305411yescharacteristic
369C2C2×#1062508711yescharacteristic
370C2#1309322711yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#450C2
socleC22×C23C22×D4
prime radical#13093061C2
hypercenter#450D23
hypocenterC23#3296
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #13093109C2semidirect
3. #13092770C2semidirect
4. #13092748C2semidirect
5. #13092740C2semidirect
6. #13092719C2semidirect
7. #13092656C2semidirect
8. #13092643C2semidirect
9. #13092637C2semidirect
10. #13092576C2semidirect
11. SD16×Dic23C2semidirect
12. (C22⋊D23)⋊C8C2semidirect
13. #13092410C2semidirect
14. C2×#10625014C2semidirect
15. C23×#450C2semidirect
23. #10625117C22semidirect
24. Q8×Dic23C22semidirect
25. C2×#67275C22semidirect
35. C2×C8×D23C22semidirect
37. #10625063C22semidirect
39. #10625061C22semidirect
45. #10625017C22semidirect
50. (C2×D23)⋊C8C22semidirect
51. #10624999C22semidirect
52. #10624999C22semidirect
53. #10624998C22semidirect
54. #10624998C22semidirect
55. Dic23⋊C8C22semidirect
56. C8×Dic23C22semidirect
57. #10624992C22semidirect
58. #10624989C22semidirect
189. #450D23semidirect
244. C23#3296semidirect

Maximal subgroups

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

subgroupindex
#130931092
#130930612
#130927702
#130927482
#130927402
#130927192
#130926562
#130926432
#130926372
#130925762
SD16×Dic232
(C22⋊D23)⋊C82
#130924102
C2×#106250142
C23×#4502
#329623