Finite Group Databasebeta

← #15683748

Subgroups — #15683748

Order 2944.

404 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093044C211yesmaximal, characteristic, complemented
2#13092985C211yesmaximal, characteristic
3#13092782C211yesmaximal, characteristic, complemented
4#13092780C211yesmaximal, characteristic, complemented
5#13092778C211yesmaximal, characteristic, complemented
6#13092773C211yesmaximal, characteristic, complemented
7#13092771C211yesmaximal, characteristic, complemented
8#13092765C211yesmaximal, characteristic, complemented
9#13092762C211yesmaximal, characteristic, complemented
10#13092420C211yesmaximal, characteristic, complemented
11#13092417C211yesmaximal, characteristic, complemented
12#13092412C211yesmaximal, characteristic, complemented
13#102×D23C211yesmaximal, characteristic, complemented
14#13092374C211yesmaximal, characteristic, complemented
15C23×#489C211yesmaximal, characteristic, complemented
16C2×#67292C2211yescharacteristic
17C2×D4×D23C2211yescharacteristic
18C23×C4⋊Q8C2211yescharacteristic, complemented
19C23×#124C2211yescharacteristic
20#10625118C2211yescharacteristic
21#10625117—21no—
22#10625115—21no—
23#10625111C2211yescharacteristic
24C2×#67262C2211yescharacteristic
25C2×C8×D23C2211yescharacteristic
26#10625067—21no—
27#10625063C2211yescharacteristic
28C4⋊C4×D23C2211yescharacteristic
29#10625061C2211yescharacteristic, complemented
30#10625060—21no—
31#10625059C2211yescharacteristic, complemented
32#10625055—21no—
33#10625055—21no—
34#10625053—21no—
35#10625053—21no—
36#10625045C2211yescharacteristic
37#10625043C2211yescharacteristic
38#10625041C2211yescharacteristic, complemented
39C23×#103C2211yescharacteristic, complemented
40C23×#103C2211yescharacteristic, complemented
41C23×#102C2211yescharacteristic
42C23×#102C2211yescharacteristic
43C23×#97C2211yescharacteristic, complemented
44#10625017C2211yescharacteristic, complemented
45#10625017C2211yescharacteristic, complemented
46#10625014C2211yescharacteristic
47#10625014C2211yescharacteristic
48#10625003C2211yescharacteristic
49#10625003C2211yescharacteristic
50#10625003C2211yescharacteristic, complemented
51#10625003C2211yescharacteristic, complemented
52#10624997C2211yescharacteristic, complemented
53C8×Dic23C2211yescharacteristic, complemented
54#10624991C2211yescharacteristic
55#10624991C2211yescharacteristic
56#10624991C2211yescharacteristic, complemented
57#10624991C2211yescharacteristic, complemented
58C4×C23⋊C8C2211yescharacteristic, complemented
59C23×D23—21no—
60C2×Q8×C23—21no—
61C2×Q8×C23C2311yescharacteristic
62C2×D4×C23C2311yescharacteristic
63C2×C22⋊D23—21no—
64C2×C22⋊D23—21no—
65C2×C22⋊D23—21no—
66#67292—22no—
67#67292—22no—
68D4×D23—22no—
69D4×D23—22no—
70C2×D92—21no—
71C2×D92—21no—
72C2×D92—21no—
73C2×D92C2311yescharacteristic
74C2×D92C2311yescharacteristic
75C2×C4×D23—21no—
76C2×C4×D23—21no—
77C2×C4×D23C2311yescharacteristic
78C2×Dic46—21no—
79C2×C8×C23C2311yescharacteristic
80C2×C8×C23C2311yescharacteristic
81C4⋊C4×C23—21no—
82C4⋊C4×C23C2311yescharacteristic
83C4⋊C4×C23C2311yescharacteristic
84C22⋊C4×C23—21no—
85C22⋊C4×C23—21no—
86C42×C23C2311yescharacteristic
87(C2×D23)⋊C4—21no—
88(C2×D23)⋊C4—21no—
89(C2×D23)⋊C4—21no—
90(C2×D23)⋊C4D411yescharacteristic
91(C2×D23)⋊C4D411yescharacteristic
92C4⋊Dic23—21no—
93C4⋊Dic23C2311yescharacteristic
94C4⋊Dic23C2311yescharacteristic
95Dic23⋊C4—21no—
96Dic23⋊C4—21no—
97Dic23⋊C4—21no—
98Dic23⋊C4—21no—
99Dic23⋊C4—21no—
100Dic23⋊C4D411yescharacteristic
101Dic23⋊C4D411yescharacteristic
102C4×Dic23—21no—
103C4×Dic23C2311yescharacteristic
104C2×C23⋊C8C2311yescharacteristic
105C2×C23⋊C8C2311yescharacteristic
106#67262—22no—
107C8×D23—22no—
108C23×C23—21no—
109C22×D23—21no—
110C22×D23—21no—
111C22×D23—42no—
112C22×D23—81no—
113C22×D23—81no—
114C22×D23C2×D411yescharacteristic
115Q8×C23—21no—
116Q8×C23—21no—
117Q8×C23—81no—
118D4×C23—21no—
119D4×C23—21no—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23C2×D411yescharacteristic
124C2×C4×C23C2×D411yescharacteristic
125C2×C4×C23C2411yescharacteristic
126C22⋊D23—42no—
127C22⋊D23—81no—
128C22⋊D23—81no—
129C2×Dic23—21no—
130C2×Dic23—21no—
131C2×Dic23C2×D411yescharacteristic
132C2×Dic23C2×D411yescharacteristic
133C2×Dic23C2×D411yescharacteristic
134D92—21no—
135D92—21no—
136D92—21no—
137D92—21no—
138D92—42no—
139D92—81no—
140D92—81no—
141C4×D23—42no—
142C4×D23—81no—
143C4×D23#4112yes—
144C4×D23#4112yes—
145Dic46—81no—
146C8×C23—21no—
147C8×C23—21no—
148C23⋊C8—21no—
149C23⋊C8—21no—
150#3136—231nomaximal, Sylow
151C22×C23—41no—
152C22×C23—41no—
153C22×C23—41no—
154C22×C23C22×D411yescharacteristic
155C2×D23—21no—
156C2×D23—21no—
157C2×D23—41no—
158C2×D23—41no—
159C2×D23—41no—
160C2×D23—41no—
161C2×D23—41no—
162C2×D23—41no—
163C2×D23—84no—
164C2×D23#12412yes—
165C4×C23—21no—
166C4×C23—21no—
167C4×C23—41no—
168C4×C23—41no—
169C4×C23—41no—
170C4×C23C2×#4111yescharacteristic
171C4×C23C2×#4111yescharacteristic
172Dic23—21no—
173Dic23—21no—
174Dic23—41no—
175Dic23—41no—
176Dic23#12412yes—
177#544—231no—
178#535—231no—
179#490—231no—
180#490—231no—
181#489—231no—
182#489D2311yescharacteristic, complemented
183#488—231no—
184#488—231no—
185#486—231no—
186#486—231no—
187#418—231no—
188#417—231no—
189#416—231no—
190C2×#102—231no—
191#405—231no—
192C2×C23—81no—
193C2×C23C2×#12411yescharacteristic
194C2×C23#57611yescharacteristic
195C2×C23#57711yescharacteristic
196D23—22no—
197D23—81no—
198D23—81no—
199C2×#41—231no—
200C22×D4—231no—
201C2×M16—231no—
202C22×C8—231no—
203C4⋊Q8—231no—
204C4⋊Q8—461no—
205C4⋊Q8C2×D2311yescharacteristic, complemented
206#127—231no—
207#127—231no—
208#125—231no—
209#125—231no—
210#125—461no—
211#124—231no—
212#124C2×D2311yescharacteristic
213C22⋊Q8—461no—
214C22⋊Q8—461no—
215#121—461no—
216#121—461no—
217#120—461no—
218#120—461no—
219#117—231no—
220#117—231no—
221C2×C4⋊C4—231no—
222#103—231no—
223#103—231no—
224#103C2×D2311yescharacteristic, complemented
225#103C2×D2311yescharacteristic, complemented
226#102—231no—
227#102—231no—
228#102—231no—
229#102—231no—
230#102—231no—
231#102—231no—
232#102—231no—
233#102—231no—
234#102—231no—
235#102—231no—
236#102C2×D2311yescharacteristic
237#102C2×D2311yescharacteristic
238#97—231no—
239#97C2×D2311yescharacteristic, complemented
240C4×C8—231no—
241C4×C8—231no—
242C23#313611yescharacteristic, complemented, Sylow
243C24—461no—
244#41—462no—
245#41—462no—
246C2×Q8—21no—
247C2×Q8—461no—
248C2×Q8C22×D2311yescharacteristic
249C2×D4—231no—
250C2×D4—231no—
251C2×D4—461no—
252C2×D4—462no—
253C2×D4—462no—
254C2×D4—461no—
255C2×D4—461no—
256C2×D4—461no—
257C2×D4—461no—
258C2×D4—461no—
259C2×D4C22×D2311yescharacteristic
260C22×C4—231no—
261C22×C4—461no—
262C22×C4—461no—
263M16—462no—
264C2×C8—231no—
265C2×C8—231no—
266C2×C8—462no—
267C2×C8C22×D2311yescharacteristic
268C2×C8C22×D2311yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—231no—
271C4⋊C4—231no—
272C4⋊C4—231no—
273C4⋊C4—231no—
274C4⋊C4—461no—
275C4⋊C4—461no—
276C4⋊C4—461no—
277C4⋊C4—461no—
278C4⋊C4—461no—
279C4⋊C4—461no—
280C4⋊C4C22×D2311yescharacteristic
281C4⋊C4C22×D2311yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—231no—
285C22⋊C4—231no—
286C22⋊C4—461no—
287C22⋊C4—461no—
288C22⋊C4—461no—
289C42—231no—
290C42—461no—
291C42C22×D2311yescharacteristic
292C23—21no—
293C23—231no—
294C23—461no—
295C23—461no—
296C23—922no—
297C23—1841no—
298C23—1841no—
299Q8—21no—
300Q8—21no—
301Q8—81no—
302Q8—1841no—
303D4—21no—
304D4—21no—
305D4—461no—
306D4—461no—
307D4—461no—
308D4—461no—
309D4—922no—
310D4—922no—
311D4—1841no—
312D4—1841no—
313D4—1841no—
314D4—1841no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—231no—
319C2×C4—232no—
320C2×C4—232no—
321C2×C4—231no—
322C2×C4—231no—
323C2×C4—461no—
324C2×C4—461no—
325C2×C4—922no—
326C2×C4—1841no—
327C2×C4D4×D2311yescharacteristic
328C2×C4D4×D2311yescharacteristic
329C2×C4C23×D2311yescharacteristic
330C8—21no—
331C8—21no—
332C8—461no—
333C8—461no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—232no—
338C22—461no—
339C22—461no—
340C22—921no—
341C22—921no—
342C22—921no—
343C22—921no—
344C22—921no—
345C22—921no—
346C22—1844no—
347C22C2×D4×D2311yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—232no—
354C4—461no—
355C4—461no—
356C4—921no—
357C4—921no—
358C4#41×D2311yescharacteristic
359C4#41×D2311yescharacteristic
360C2—81no—
361C2—462no—
362C2—1841no—
363C2—1841no—
364C2#124×D2311yescharacteristic
365C2#1309322111yescharacteristic
366C2#1309322611yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#489C2
socleC22×C23C22×D4
prime radical#13092985C2
hypercenter#489D23
hypocenterC23#3136
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #13093044C2semidirect
3. #13092782C2semidirect
4. #13092780C2semidirect
5. #13092778C2semidirect
6. #13092773C2semidirect
7. #13092771C2semidirect
8. #13092765C2semidirect
9. #13092762C2semidirect
10. #13092420C2semidirect
11. #13092417C2semidirect
12. #13092412C2semidirect
13. #102×D23C2semidirect
14. #13092374C2semidirect
15. C23×#489C2semidirect
18. C23×C4⋊Q8C22semidirect
29. #10625061C22semidirect
31. #10625059C22semidirect
38. #10625041C22semidirect
39. C23×#103C22semidirect
40. C23×#103C22semidirect
43. C23×#97C22semidirect
44. #10625017C22semidirect
45. #10625017C22semidirect
50. #10625003C22semidirect
51. #10625003C22semidirect
52. #10624997C22semidirect
53. C8×Dic23C22semidirect
56. #10624991C22semidirect
57. #10624991C22semidirect
58. C4×C23⋊C8C22semidirect
182. #489D23semidirect
205. C4⋊Q8C2×D23semidirect
224. #103C2×D23semidirect
225. #103C2×D23semidirect
239. #97C2×D23semidirect
242. C23#3136semidirect

Maximal subgroups

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

subgroupindex
#130930442
#130929852
#130927822
#130927802
#130927782
#130927732
#130927712
#130927652
#130927622
#130924202
#130924172
#130924122
#102×D232
#130923742
C23×#4892
#313623