Finite Group Databasebeta

← #15686083

Subgroups — #15686083

Order 2944.

336 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093143C211yesmaximal, characteristic, complemented
2#13093139C211yesmaximal, characteristic
3#13092773C211yesmaximal, characteristic
4#13092772C211yesmaximal, characteristic
5#13092766C211yesmaximal, characteristic, complemented
6#13092724C211yesmaximal, characteristic, complemented
7#13092723C211yesmaximal, characteristic, complemented
8#13092696C211yesmaximal, characteristic
9#13092641C211yesmaximal, characteristic
10#13092639C211yesmaximal, characteristic
11#13092625C211yesmaximal, characteristic, complemented
12C8×Dic46C211yesmaximal, characteristic, complemented
13#13092509C211yesmaximal, characteristic, complemented
14#13092502C211yesmaximal, characteristic
15C4×Q16×C23C211yesmaximal, characteristic, complemented
16C2×Q16×C23C2211yescharacteristic
17C4×Q8×C23C2211yescharacteristic
18C4×Q8×C23C2211yescharacteristic
19#10625118C2211yescharacteristic
20Q8×Dic23C2211yescharacteristic
21Q8×Dic23C2211yescharacteristic
22#10625115C2211yescharacteristic
23C2×#67275C2211yescharacteristic
24C2×#67274C2211yescharacteristic
25#10625069—21no—
26#10625067—21no—
27#10625064C2211yescharacteristic
28#10625061—21no—
29#10625061C2211yescharacteristic
30#10625059—21no—
31#10625059C2211yescharacteristic
32#10625058C2211yescharacteristic
33#10625047—21no—
34#10625046C2211yescharacteristic
35#10625043—21no—
36#10625041—21no—
37#10625041C2211yescharacteristic
38C4×Dic46—21no—
39C4×Dic46C2211yescharacteristic
40C23×#107C2211yescharacteristic
41C23×#103C2211yescharacteristic
42C23×#103C2211yescharacteristic
43C4×C8×C23C2211yescharacteristic
44#10625017C2211yescharacteristic
45#10625017C2211yescharacteristic
46#10625003C2211yescharacteristic
47#10625003C2211yescharacteristic
48#10624998C2211yescharacteristic
49#10624998C2211yescharacteristic
50Dic23⋊C8C2211yescharacteristic
51Dic23⋊C8C2211yescharacteristic
52C8×Dic23C2211yescharacteristic
53C8×Dic23C2211yescharacteristic
54#10624992C2211yescharacteristic
55#10624991C2211yescharacteristic
56#10624990C2211yescharacteristic
57#10624989C2211yescharacteristic
58C4⋊(C23⋊C8)C2211yescharacteristic
59C2×Q8×C23C2311yescharacteristic
60C2×Q8×C23C2311yescharacteristic
61C2×D92C2311yescharacteristic
62C2×C4×D23—21no—
63C2×Dic46—21no—
64C2×Dic46D411yescharacteristic
65C2×Dic46C2311yescharacteristic
66Q16×C23—22no—
67C2×C8×C23C2311yescharacteristic
68C2×C8×C23C2311yescharacteristic
69C4⋊C4×C23—21no—
70C4⋊C4×C23—21no—
71C4⋊C4×C23C2311yescharacteristic
72C4⋊C4×C23C2311yescharacteristic
73C42×C23—21no—
74C42×C23—21no—
75C42×C23C2311yescharacteristic
76#67275—22no—
77#67274—22no—
78(C2×D23)⋊C4—21no—
79(C2×D23)⋊C4—21no—
80(C2×D23)⋊C4—21no—
81(C2×D23)⋊C4—21no—
82(C2×D23)⋊C4—21no—
83C4⋊Dic23—21no—
84C4⋊Dic23—21no—
85C4⋊Dic23—21no—
86C4⋊Dic23D411yescharacteristic
87C4⋊Dic23C2311yescharacteristic
88C4⋊Dic23C2311yescharacteristic
89Dic23⋊C4—21no—
90Dic23⋊C4—21no—
91Dic23⋊C4—21no—
92Dic23⋊C4—21no—
93Dic23⋊C4—21no—
94Dic23⋊C4—21no—
95Dic23⋊C4—21no—
96Dic23⋊C4D411yescharacteristic
97Dic23⋊C4D411yescharacteristic
98C4×Dic23—21no—
99C4×Dic23—21no—
100C4×Dic23—21no—
101C4×Dic23C2311yescharacteristic
102C4×Dic23C2311yescharacteristic
103C2×C23⋊C8C2311yescharacteristic
104C2×C23⋊C8C2311yescharacteristic
105C22×D23—21no—
106Q8×C23—21no—
107Q8×C23—21no—
108Q8×C23—21no—
109Q8×C23#4112yes—
110C2×C4×C23—21no—
111C2×C4×C23—21no—
112C2×C4×C23—21no—
113C2×C4×C23—21no—
114C2×C4×C23C2×D411yescharacteristic
115C2×C4×C23C2×D411yescharacteristic
116C2×C4×C23C2411yescharacteristic
117C2×Dic23—21no—
118C2×Dic23—21no—
119C2×Dic23—21no—
120C2×Dic23C2×D411yescharacteristic
121C2×Dic23C2×D411yescharacteristic
122C2×Dic23C2×D411yescharacteristic
123C2×Dic23C2×D411yescharacteristic
124D92—21no—
125D92—21no—
126C4×D23—42no—
127Dic46—22no—
128Dic46—21no—
129Dic46—21no—
130Dic46—42no—
131C8×C23—21no—
132C8×C23—21no—
133C23⋊C8—21no—
134C23⋊C8—21no—
135#3364—231nomaximal, Sylow
136C22×C23C22×D411yescharacteristic
137C2×D23—41no—
138C2×D23—41no—
139C2×D23—41no—
140C4×C23—22no—
141C4×C23—21no—
142C4×C23—21no—
143C4×C23—41no—
144C4×C23—41no—
145C4×C23—41no—
146C4×C23C2×#4111yescharacteristic
147C4×C232−1+411yescharacteristic
148Dic23—21no—
149Dic23—21no—
150Dic23—21no—
151Dic23—41no—
152Dic23—41no—
153Dic23—41no—
154Dic23#13512yes—
155#557—231no—
156#556—231no—
157#488—231no—
158#488—231no—
159#487—231no—
160#479—231no—
161#479—231no—
162#474—231no—
163#464—231no—
164#464—231no—
165#462—231no—
166C8×Q8—231no—
167C4×Q16—231no—
168C4×Q16D2311yescharacteristic, complemented
169C4×SD16—231no—
170C2×C23#54811yescharacteristic
171C2×C23C2×#13511yescharacteristic
172C2×C23#57811yescharacteristic
173D23—81no—
174C2×Q16—231no—
175C2×Q16C2×D2311yescharacteristic
176C2×SD16—231no—
177C4⋊Q8—231no—
178C4⋊Q8—231no—
179C4⋊Q8—461no—
180#126—461no—
181#126—461no—
182#125—231no—
183#125—231no—
184#125—461no—
185#125—461no—
186#124—231no—
187#124—231no—
188C22⋊Q8—461no—
189C4×Q8—231no—
190C4×Q8—231no—
191C4×Q8—231no—
192C4×Q8—231no—
193C4×Q8—461no—
194C4×Q8C2×D2311yescharacteristic
195C4×Q8C2×D2311yescharacteristic
196C4×D4—231no—
197#117—461no—
198#107—231no—
199#107C2×D2311yescharacteristic
200#106—231no—
201C4⋊C8—231no—
202C4⋊C8—231no—
203C4⋊C8—231no—
204#103—231no—
205#103—231no—
206#103—231no—
207#103—231no—
208#103—231no—
209#103C2×D2311yescharacteristic
210#103C2×D2311yescharacteristic
211#102—231no—
212#102—231no—
213#102—231no—
214C4×C8—231no—
215C4×C8—231no—
216C4×C8C2×D2311yescharacteristic
217C23#336411yescharacteristic, complemented, Sylow
218C2×Q8—231no—
219C2×Q8—231no—
220C2×Q8—461no—
221C2×Q8C22×D2311yescharacteristic
222C2×Q8C22×D2311yescharacteristic
223C2×D4—231no—
224C22×C4—461no—
225Q16—22no—
226Q16—462no—
227SD16—462no—
228C2×C8—231no—
229C2×C8—231no—
230C2×C8C22×D2311yescharacteristic
231C2×C8C22×D2311yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—231no—
235C4⋊C4—231no—
236C4⋊C4—231no—
237C4⋊C4—231no—
238C4⋊C4—231no—
239C4⋊C4—461no—
240C4⋊C4—461no—
241C4⋊C4—461no—
242C4⋊C4—461no—
243C4⋊C4—461no—
244C4⋊C4—461no—
245C4⋊C4—461no—
246C4⋊C4—461no—
247C4⋊C4—461no—
248C4⋊C4—461no—
249C4⋊C4C22×D2311yescharacteristic
250C4⋊C4C22×D2311yescharacteristic
251C22⋊C4—461no—
252C22⋊C4—461no—
253C22⋊C4—461no—
254C22⋊C4—461no—
255C22⋊C4—461no—
256C42—21no—
257C42—21no—
258C42—231no—
259C42—231no—
260C42—461no—
261C42—461no—
262C42—461no—
263C42C22×D2311yescharacteristic
264C23—461no—
265Q8—21no—
266Q8—21no—
267Q8—21no—
268Q8—462no—
269Q8—461no—
270Q8—461no—
271Q8—922no—
272Q8#6728812yes—
273D4—461no—
274D4—461no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—231no—
280C2×C4—231no—
281C2×C4—231no—
282C2×C4—231no—
283C2×C4—461no—
284C2×C4—461no—
285C2×C4—461no—
286C2×C4—922no—
287C2×C4D4×D2311yescharacteristic
288C2×C4D4×D2311yescharacteristic
289C2×C4C23×D2311yescharacteristic
290C8—21no—
291C8—21no—
292C8—461no—
293C8—461no—
294C22—921no—
295C22—921no—
296C22—921no—
297C22C2×D4×D2311yescharacteristic
298C4—21no—
299C4—21no—
300C4—22no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—232no—
305C4—461no—
306C4—461no—
307C4—461no—
308C4—921no—
309C4—921no—
310C4—921no—
311C4C2×#6728811yescharacteristic
312C4#1062516111yescharacteristic
313C2—1841no—
314C2#1309307611yescharacteristic
315C2#135×D2311yescharacteristic
316C2#1309323011yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC4×Q16×C23C2
socleC22×C23C22×D4
prime radicalC2×D92C23
hypercenterC4×Q16D23
hypocenterC23#3364
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
1. #13093143C2semidirect
5. #13092766C2semidirect
6. #13092724C2semidirect
7. #13092723C2semidirect
11. #13092625C2semidirect
12. C8×Dic46C2semidirect
13. #13092509C2semidirect
15. C4×Q16×C23C2semidirect
168. C4×Q16D23semidirect
217. C23#3364semidirect

Maximal subgroups

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

subgroupindex
#130931432
#130931392
#130927732
#130927722
#130927662
#130927242
#130927232
#130926962
#130926412
#130926392
#130926252
C8×Dic462
#130925092
#130925022
C4×Q16×C232
#336423