Finite Group Databasebeta

← #15683221

Subgroups — #15683221

Order 2944.

398 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093044C211yesmaximal, characteristic, complemented
2#13092889C211yesmaximal, characteristic
3#13092720C211yesmaximal, characteristic, complemented
4#13092718C211yesmaximal, characteristic, complemented
5#13092717C211yesmaximal, characteristic, complemented
6#13092715C211yesmaximal, characteristic, complemented
7#13092705C211yesmaximal, characteristic, complemented
8#13092704C211yesmaximal, characteristic, complemented
9#13092696C211yesmaximal, characteristic, complemented
10#13092458C211yesmaximal, characteristic, complemented
11#13092454C211yesmaximal, characteristic, complemented
12#13092442C211yesmaximal, characteristic, complemented
13#13092420C211yesmaximal, characteristic
14#102×D23C211yesmaximal, characteristic
15C23×#474C211yesmaximal, characteristic, complemented
16C2×D4×D23C2211yescharacteristic
17C23×C4⋊Q8C2211yescharacteristic, complemented
18C4×D4×C23C2211yescharacteristic
19#10625117—21no—
20#10625115—21no—
21D4×Dic23C2211yescharacteristic
22C4×C22⋊D23—21no—
23C2×(C2×D23)⋊C4—21no—
24C2×#67262C2211yescharacteristic
25C2×C8×D23C2211yescharacteristic
26#10625067—21no—
27#10625064C2211yescharacteristic
28#10625063C2211yescharacteristic
29#10625063C2211yescharacteristic
30C4⋊C4×D23C2211yescharacteristic
31#10625061C2211yescharacteristic, complemented
32#10625060—21no—
33#10625059C2211yescharacteristic, complemented
34(C22⋊D23)⋊C4—21no—
35C22⋊C4×D23—21no—
36C4×D92C2211yescharacteristic
37#10625043C2211yescharacteristic
38#10625041C2211yescharacteristic, complemented
39C23×#107C2211yescharacteristic, complemented
40C23×#107C2211yescharacteristic, complemented
41C23×C4⋊C8C2211yescharacteristic, complemented
42C23×#102C2211yescharacteristic
43C23×#102C2211yescharacteristic
44#10625014C2211yescharacteristic
45#10625014C2211yescharacteristic
46#10625003C2211yescharacteristic
47#10625003C2211yescharacteristic
48#10625000C2211yescharacteristic, complemented
49#10624999C2211yescharacteristic, complemented
50Dic23⋊C8C2211yescharacteristic, complemented
51Dic23⋊C8C2211yescharacteristic, complemented
52#10624991C2211yescharacteristic
53#10624991C2211yescharacteristic
54#10624990C2211yescharacteristic, complemented
55#10624990C2211yescharacteristic, complemented
56#10624990C2211yescharacteristic, complemented
57#10624989C2211yescharacteristic, complemented
58C4⋊(C23⋊C8)C2211yescharacteristic, complemented
59C23×D23—21no—
60C2×Q8×C23—21no—
61C2×D4×C23C2311yescharacteristic
62C22×C4×C23—21no—
63C2×C22⋊D23—21no—
64C22×Dic23—21no—
65D4×D23—22no—
66D4×D23Q814yescomplemented
67C2×D92C2311yescharacteristic
68C2×C4×D23—21no—
69C2×C4×D23—21no—
70C2×C4×D23—21no—
71C2×C4×D23C2311yescharacteristic
72C2×Dic46—21no—
73C2×C8×C23C2311yescharacteristic
74C2×C8×C23C2311yescharacteristic
75C4⋊C4×C23—21no—
76C4⋊C4×C23C2311yescharacteristic
77C4⋊C4×C23C2311yescharacteristic
78C4⋊C4×C23C2311yescharacteristic
79C22⋊C4×C23—21no—
80C42×C23C2311yescharacteristic
81C22⋊Dic23—21no—
82(C2×D23)⋊C4—21no—
83(C2×D23)⋊C4—21no—
84(C2×D23)⋊C4—21no—
85(C2×D23)⋊C4—21no—
86(C2×D23)⋊C4D411yescharacteristic
87(C2×D23)⋊C4D411yescharacteristic
88C4⋊Dic23—21no—
89C4⋊Dic23C2311yescharacteristic
90C4⋊Dic23C2311yescharacteristic
91C4⋊Dic23C2311yescharacteristic
92Dic23⋊C4—21no—
93Dic23⋊C4—21no—
94Dic23⋊C4—21no—
95Dic23⋊C4—21no—
96Dic23⋊C4—21no—
97Dic23⋊C4D411yescharacteristic
98Dic23⋊C4D411yescharacteristic
99C4×Dic23—21no—
100C4×Dic23—21no—
101C4×Dic23C2311yescharacteristic
102C2×C23⋊C8C2311yescharacteristic
103C2×C23⋊C8C2311yescharacteristic
104#67262—22no—
105C8×D23—22no—
106C23×C23—21no—
107C22×D23—21no—
108C22×D23—24no—
109C22×D23—81no—
110C22×D23—81no—
111C22×D23C2×D411yescharacteristic
112Q8×C23—81no—
113D4×C23—21no—
114D4×C23C2×Q812yes—
115C2×C4×C23—21no—
116C2×C4×C23—21no—
117C2×C4×C23—21no—
118C2×C4×C23—81no—
119C2×C4×C23C2×D411yescharacteristic
120C2×C4×C23C2×D411yescharacteristic
121C2×C4×C23C2411yescharacteristic
122C22⋊D23—24no—
123C2×Dic23—21no—
124C2×Dic23—21no—
125C2×Dic23—21no—
126C2×Dic23—81no—
127C2×Dic23C2×D411yescharacteristic
128C2×Dic23C2×D411yescharacteristic
129C2×Dic23C2×D411yescharacteristic
130D92—21no—
131D92C2×Q812yes—
132C4×D23—81no—
133C4×D23—81no—
134C4×D23—81no—
135C4×D23C2×Q812yes—
136C4×D23#4112yes—
137Dic46—81no—
138C8×C23—21no—
139C8×C23—21no—
140C23⋊C8—21no—
141C23⋊C8—21no—
142#3081—231nomaximal, Sylow
143C22×C23—22no—
144C22×C23—41no—
145C22×C23—41no—
146C22×C23C22×D411yescharacteristic
147C2×D23—21no—
148C2×D23—21no—
149C2×D23—22no—
150C2×D23—41no—
151C2×D23—41no—
152C2×D23—84no—
153C2×D23C22⋊Q812yes—
154C4×C23—21no—
155C4×C23—21no—
156C4×C23—41no—
157C4×C23—41no—
158C4×C23—41no—
159C4×C23C22×Q811yescharacteristic
160C4×C23C2×#4111yescharacteristic
161Dic23—21no—
162Dic23—21no—
163Dic23—41no—
164Dic23—41no—
165Dic23—41no—
166Dic23C22⋊Q812yes—
167#544—231no—
168#518—231no—
169#478—231no—
170#478—231no—
171#478—231no—
172#478—231no—
173#476—231no—
174#476—231no—
175#474—231no—
176#474D2311yescharacteristic, complemented
177#428—231no—
178#427—231no—
179#424—231no—
180#418—231no—
181C2×#102—231no—
182C2×C23—42no—
183C2×C23C2×C22⋊Q811yescharacteristic
184C2×C23#57611yescharacteristic
185C2×C23#57711yescharacteristic
186D23—22no—
187D23—42no—
188C22×D4—231no—
189C2×M16—231no—
190C22×C8—231no—
191C4⋊Q8—231no—
192C4⋊Q8—461no—
193C4⋊Q8C2×D2311yescharacteristic, complemented
194#125—231no—
195#125—231no—
196#125—461no—
197C22⋊Q8—461no—
198C22⋊Q8—461no—
199C4×D4—231no—
200C4×D4—231no—
201C4×D4—231no—
202C4×D4—461no—
203C4×D4—461no—
204C4×D4C2×D2311yescharacteristic
205#117—231no—
206#117—231no—
207#117—231no—
208C2×C4⋊C4—231no—
209C2×C22⋊C4—461no—
210C2×C22⋊C4—461no—
211#107—231no—
212#107—231no—
213#107C2×D2311yescharacteristic, complemented
214#107C2×D2311yescharacteristic, complemented
215#106—231no—
216#106—231no—
217#106—231no—
218#106—231no—
219C4⋊C8—231no—
220C4⋊C8—231no—
221C4⋊C8—231no—
222C4⋊C8C2×D2311yescharacteristic, complemented
223#102—231no—
224#102—231no—
225#102—231no—
226#102—231no—
227#102—231no—
228#102—231no—
229#102C2×D2311yescharacteristic
230#102C2×D2311yescharacteristic
231C23#308111yescharacteristic, complemented, Sylow
232C24—461no—
233C2×Q8—21no—
234C2×Q8—461no—
235C2×D4—234no—
236C2×D4—231no—
237C2×D4—462no—
238C2×D4—461no—
239C2×D4C22×D2311yescharacteristic
240C22×C4—21no—
241C22×C4—231no—
242C22×C4—461no—
243C22×C4—461no—
244C22×C4—461no—
245C22×C4—461no—
246M16—462no—
247C2×C8—231no—
248C2×C8—231no—
249C2×C8—462no—
250C2×C8C22×D2311yescharacteristic
251C2×C8C22×D2311yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—231no—
254C4⋊C4—231no—
255C4⋊C4—231no—
256C4⋊C4—231no—
257C4⋊C4—231no—
258C4⋊C4—461no—
259C4⋊C4—461no—
260C4⋊C4—461no—
261C4⋊C4—461no—
262C4⋊C4—461no—
263C4⋊C4—461no—
264C4⋊C4C22×D2311yescharacteristic
265C4⋊C4C22×D2311yescharacteristic
266C4⋊C4C22×D2311yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—231no—
269C22⋊C4—231no—
270C22⋊C4—461no—
271C22⋊C4—461no—
272C22⋊C4—461no—
273C22⋊C4—461no—
274C22⋊C4—461no—
275C42—231no—
276C42—461no—
277C42—461no—
278C42C22×D2311yescharacteristic
279C23—21no—
280C23—231no—
281C23—464no—
282C23—461no—
283C23—1841no—
284C23—1841no—
285Q8—81no—
286Q8—1841no—
287D4—21no—
288D4—232no—
289D4—464no—
290D4—461no—
291D4Q8×D2312yes—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—81no—
296C2×C4—231no—
297C2×C4—232no—
298C2×C4—232no—
299C2×C4—231no—
300C2×C4—231no—
301C2×C4—461no—
302C2×C4—461no—
303C2×C4—461no—
304C2×C4—1841no—
305C2×C4—1841no—
306C2×C4—1841no—
307C2×C4—1841no—
308C2×C4D4×D2311yescharacteristic
309C2×C4D4×D2311yescharacteristic
310C2×C4C23×D2311yescharacteristic
311C8—21no—
312C8—21no—
313C8—461no—
314C8—461no—
315C22—22no—
316C22—41no—
317C22—41no—
318C22—232no—
319C22—461no—
320C22—461no—
321C22—462no—
322C22—921no—
323C22—921no—
324C22—1844no—
325C22C2×D4×D2311yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—232no—
332C4—461no—
333C4—461no—
334C4—921no—
335C4—921no—
336C4—921no—
337C4C2×Q8×D2311yescharacteristic
338C4#41×D2311yescharacteristic
339C2—42no—
340C2—462no—
341C2—922no—
342C2C22⋊Q8×D2311yescharacteristic
343C2#1309321811yescharacteristic
344C2#1309322611yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#474C2
socleC22×C23C22×D4
prime radicalC2×D4×D23C22
hypercenter#474D23
hypocenterC23#3081
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #13093044C2semidirect
3. #13092720C2semidirect
4. #13092718C2semidirect
5. #13092717C2semidirect
6. #13092715C2semidirect
7. #13092705C2semidirect
8. #13092704C2semidirect
9. #13092696C2semidirect
10. #13092458C2semidirect
11. #13092454C2semidirect
12. #13092442C2semidirect
15. C23×#474C2semidirect
17. C23×C4⋊Q8C22semidirect
31. #10625061C22semidirect
33. #10625059C22semidirect
38. #10625041C22semidirect
39. C23×#107C22semidirect
40. C23×#107C22semidirect
41. C23×C4⋊C8C22semidirect
48. #10625000C22semidirect
49. #10624999C22semidirect
50. Dic23⋊C8C22semidirect
51. Dic23⋊C8C22semidirect
54. #10624990C22semidirect
55. #10624990C22semidirect
56. #10624990C22semidirect
57. #10624989C22semidirect
58. C4⋊(C23⋊C8)C22semidirect
66. D4×D23Q8semidirect
176. #474D23semidirect
193. C4⋊Q8C2×D23semidirect
213. #107C2×D23semidirect
214. #107C2×D23semidirect
222. C4⋊C8C2×D23semidirect
231. C23#3081semidirect

Maximal subgroups

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

subgroupindex
#130930442
#130928892
#130927202
#130927182
#130927172
#130927152
#130927052
#130927042
#130926962
#130924582
#130924542
#130924422
#130924202
#102×D232
C23×#4742
#308123