Finite Group Databasebeta

← #46783029

Subgroups — #46783029

Order 33664.

374 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#30682411C211yesmaximal, characteristic
2C2×#22554384C211yesmaximal, characteristic
3#30681815C211yesmaximal, characteristic
4#30681813C211yesmaximal, characteristic, complemented
5#30681810C211yesmaximal, characteristic, complemented
6#30681704C211yesmaximal, characteristic, complemented
7#342×C263C211yesmaximal, characteristic, complemented
8C22×C22⋊D263C2211yescharacteristic
9C23×Dic263C2211yescharacteristic
10C4×C22⋊D263—21no—
11C4×C22⋊D263—21no—
12(C22⋊D263)⋊C4—21no—
13(C22⋊D263)⋊C4—21no—
14#22554426—21no—
15C2×C4⋊Dic263—21no—
16C2×Dic263⋊C4—21no—
17C2×C22⋊Dic263C2211yescharacteristic
18C2×C22⋊Dic263C2211yescharacteristic
19C2×(C2×D263)⋊C4—21no—
20C22⋊C4×D263—21no—
21#22554384C414yescomplemented
22C263⋊#95—21no—
23C263⋊#95—21no—
24C263⋊#95—21no—
25C2×C22⋊C4×C263C2211yescharacteristic
26C2×C22⋊C4×C263C2211yescharacteristic
27C2×C22⋊C4×C263C2211yescharacteristic
28C23×D263D411yescharacteristic
29C2×C22⋊D263—21no—
30C2×C22⋊D263—21no—
31C2×C22⋊D263—21no—
32C2×C22⋊D263—21no—
33C2×C22⋊D263C2×C412yes—
34C2×C22⋊D263Q812yes—
35C22×Dic263—21no—
36C22×Dic263—21no—
37C22×Dic263—21no—
38C22×Dic263—21no—
39C22×Dic263—42no—
40C22×Dic263D411yescharacteristic
41C22×Dic263D411yescharacteristic
42C22×Dic263D411yescharacteristic
43C2×C4×D263—21no—
44C2×C4×D263—21no—
45C4⋊Dic263—42no—
46Dic263⋊C4—21no—
47Dic263⋊C4—21no—
48Dic263⋊C4—42no—
49C22⋊Dic263—21no—
50C22⋊Dic263—21no—
51C22⋊Dic263—21no—
52C22⋊Dic263C2×C412yescomplemented
53(C2×D263)⋊C4—21no—
54(C2×D263)⋊C4—21no—
55(C2×D263)⋊C4—42no—
56C4×Dic263—21no—
57C4×Dic263—21no—
58C24×C263C2311yescharacteristic
59C22×C4×C263—21no—
60C22×C4×C263—21no—
61C22×C4×C263D411yescharacteristic
62C22×C4×C263D411yescharacteristic
63C22⋊C4×C263—21no—
64C22⋊C4×C263—21no—
65C22⋊C4×C263—21no—
66C22⋊C4×C263—21no—
67C22⋊C4×C263—21no—
68C22⋊C4×C263C2×C412yescomplemented
69C22×D263—21no—
70C22×D263—21no—
71C22×D263—41no—
72C22×D263—41no—
73C22×D263C4⋊C412yescomplemented
74C22⋊D263—22no—
75C22⋊D263—22no—
76C22⋊D263—22no—
77C22⋊D263—22no—
78C2×Dic263—21no—
79C2×Dic263—21no—
80C2×Dic263—22no—
81C2×Dic263—22no—
82C2×Dic263—22no—
83C2×Dic263—22no—
84C2×Dic263—21no—
85C2×Dic263—21no—
86C2×Dic263—41no—
87C2×Dic263—41no—
88C2×Dic263—41no—
89C2×Dic263—41no—
90C2×Dic263—41no—
91C2×Dic263—41no—
92C2×Dic263—41no—
93C2×Dic263—41no—
94C2×Dic263C4⋊C412yescomplemented
95C4×D263—81no—
96C4×D263—81no—
97C23×C263—41no—
98C23×C263—41no—
99C23×C263C22×C411yescharacteristic
100C23×C263C2×D411yescharacteristic
101C23×C263C2×D411yescharacteristic
102C23×C263C2×D411yescharacteristic
103C23×C263C2×Q811yescharacteristic
104C23×C263#4111yescharacteristic
105C23×C263#4111yescharacteristic
106C2×C4×C263—22no—
107C2×C4×C263—21no—
108C2×C4×C263—21no—
109C2×C4×C263—41no—
110C2×C4×C263—41no—
111C2×C4×C263—41no—
112C2×C4×C263—41no—
113C2×C4×C263—41no—
114C2×C4×C263—41no—
115C2×C4×C263—41no—
116C22×C263—21no—
117C22×C263—21no—
118C22×C263—21no—
119C22×C263—21no—
120C22×C263—21no—
121C22×C263—21no—
122C22×C263—41no—
123C22×C263—41no—
124C22×C263—41no—
125C22×C263—41no—
126C22×C263C2×C4⋊C411yescharacteristic
127C22×C263C4×D411yescharacteristic
128C22×C263C4×D411yescharacteristic
129C22×C263#12011yescharacteristic
130C22×C263C22⋊Q811yescharacteristic
131C22×C263C22⋊Q811yescharacteristic
132C22×C263#12311yescharacteristic
133C2×D263—22no—
134C2×D263—41no—
135C2×D263—41no—
136C2×D263—42no—
137C2×D263—81no—
138C4×C263—42no—
139C4×C263—41no—
140C4×C263—41no—
141C4×C263—81no—
142Dic263—22no—
143Dic263—42no—
144Dic263—41no—
145Dic263—42no—
146Dic263—41no—
147C2×C263—21no—
148C2×C263—21no—
149C2×C263—21no—
150C2×C263—21no—
151C2×C263—21no—
152C2×C263—21no—
153C2×C263#38511yescharacteristic
154C2×C263B(4,𝔽2)11yescharacteristic
155C2×C263#45811yescharacteristic
156D263—42no—
157C263#186711yescharacteristic, complemented, Sylow
158#1867—2631nomaximal, Sylow
159#518—2631no—
160C2×#99—2631no—
161#386—2631no—
162#385—2631no—
163#385—2631no—
164#342—2631no—
165#342D26311yescharacteristic, complemented
166C22×D4—2631no—
167C23×C4—2631no—
168C4×D4—5261no—
169C4×D4—5261no—
170C4×D4—5261no—
171C4×D4—5261no—
172#117—5261no—
173C2×C4⋊C4—5261no—
174C2×C4⋊C4—5261no—
175C2×C22⋊C4—2631no—
176C2×C22⋊C4—2631no—
177C2×C22⋊C4—5261no—
178C2×C22⋊C4—5261no—
179C2×C22⋊C4C2×D26311yescharacteristic
180C2×C22⋊C4C2×D26311yescharacteristic
181C2×C22⋊C4C2×D26311yescharacteristic
182#99—2634no—
183#95—5261no—
184#95—5261no—
185#95—5261no—
186C24—2631no—
187C24C22×D26311yescharacteristic
188C2×D4—2632no—
189C2×D4—2632no—
190C2×D4—5261no—
191C2×D4—5261no—
192C2×D4—5261no—
193C2×D4—5261no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—2631no—
197C22×C4—2631no—
198C22×C4—2631no—
199C22×C4—5261no—
200C22×C4—5261no—
201C22×C4—5261no—
202C22×C4—5261no—
203C22×C4—5261no—
204C22×C4—5261no—
205C22×C4—10522no—
206C22×C4D105211yescharacteristic
207C22×C4D105211yescharacteristic
208C4⋊C4—5261no—
209C4⋊C4—5261no—
210C4⋊C4—10522no—
211C4⋊C4—10522no—
212C22⋊C4—21no—
213C22⋊C4—21no—
214C22⋊C4—21no—
215C22⋊C4—21no—
216C22⋊C4—21no—
217C22⋊C4—2632no—
218C22⋊C4—5261no—
219C22⋊C4—5261no—
220C22⋊C4—5261no—
221C22⋊C4—5261no—
222C22⋊C4—5261no—
223C22⋊C4—10522no—
224C22⋊C4C4×D26312yescomplemented
225C42—5261no—
226C42—5261no—
227C23—41no—
228C23—41no—
229C23—2632no—
230C23—5261no—
231C23—5261no—
232C23—10521no—
233C23—10521no—
234C23C2×C4×D26311yescharacteristic
235C23D4×D26311yescharacteristic
236C23D4×D26311yescharacteristic
237C23C2×D105211yescharacteristic
238C23Q8×D26311yescharacteristic
239C23#1686237511yescharacteristic
240C23#1686237611yescharacteristic
241D4—5262no—
242D4—5262no—
243D4—5262no—
244D4—5262no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—2632no—
256C2×C4—5261no—
257C2×C4—5261no—
258C2×C4—5262no—
259C2×C4—5262no—
260C2×C4—5262no—
261C2×C4—5262no—
262C2×C4—5261no—
263C2×C4—5261no—
264C2×C4—10521no—
265C2×C4—10521no—
266C2×C4—10521no—
267C2×C4—10521no—
268C2×C4—10521no—
269C2×C4—10521no—
270C2×C4—10521no—
271C2×C4—10521no—
272C2×C4—21041no—
273C2×C4—21041no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—41no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—5262no—
285C22—10522no—
286C22—10521no—
287C22—10521no—
288C22—21041no—
289C22C4⋊C4×D26311yescharacteristic
290C22(C22⋊D263)⋊C411yescharacteristic
291C22C4×D105211yescharacteristic
292C22#2255444011yescharacteristic
293C22#2255444811yescharacteristic
294C22#2255445011yescharacteristic
295C22#2255445211yescharacteristic
296C4—42no—
297C4—41no—
298C4—41no—
299C4—81no—
300C4—5262no—
301C4—10522no—
302C4—10522no—
303C4—10521no—
304C4—10521no—
305C2—21no—
306C2—21no—
307C2—21no—
308C2—21no—
309C2—21no—
310C2—21no—
311C2—10522no—
312C2#3068181211yescharacteristic
313C2#3068212611yescharacteristic
314C2#3068212911yescharacteristic
subgroupG/H
centerC22#22554440
commutatorC23×C263C22×C4
FrattiniC24C22×D263
Fitting#342×C263C2
socleC22×C263#120
prime radicalC22×C22⋊D263C22
cosocleC24×C263C23
hypercenter#342D263
hypocenterC263#1867
LCSG ▷ C23×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
4. #30681813C2semidirect
5. #30681810C2semidirect
6. #30681704C2semidirect
7. #342×C263C2semidirect
21. #22554384C4semidirect
52. C22⋊Dic263C2×C4semidirect
68. C22⋊C4×C263C2×C4semidirect
73. C22×D263C4⋊C4semidirect
94. C2×Dic263C4⋊C4semidirect
157. C263#1867semidirect
165. #342D263semidirect
224. C22⋊C4C4×D263semidirect

Maximal subgroups

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

subgroupindex
#306824112
C2×#225543842
#306818152
#306818132
#306818102
#306817042
#342×C2632
#1867263