Finite Group Databasebeta

← #46783755

Subgroups — #46783755

Order 33664.

392 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C22×#16862366C211yesmaximal, characteristic, complemented
2C2×#22554449C211yesmaximal, characteristic
3C2×#22554394C211yesmaximal, characteristic, complemented
4C2×#22554393C211yesmaximal, characteristic, complemented
5C2×C22⋊(C263⋊C8)C211yesmaximal, characteristic
6#30681700C211yesmaximal, characteristic, complemented
7C2×C22⋊Q8×C263C211yesmaximal, characteristic
8C22×Dic526C2211yescharacteristic
9C2×#16862366—22no—
10C2×#16862366—22no—
11C2×#16862366—22no—
12C22×C263⋊C8C2211yescharacteristic
13C22×C263⋊C8C2211yescharacteristic
14#22554449—22no—
15#22554449—22no—
16C2×C4⋊Dic263C2211yescharacteristic
17C2×Dic263⋊C4—21no—
18C2×C22⋊Dic263—21no—
19#22554394—22no—
20#22554393—22no—
21C22⋊(C263⋊C8)—22no—
22C22×Q8×C263C2211yescharacteristic
23C23×C4×C263C2211yescharacteristic
24C22⋊Q8×C263—22no—
25C22⋊Q8×C263—22no—
26C2×C4⋊C4×C263—21no—
27C2×C4⋊C4×C263C2211yescharacteristic
28C2×C22⋊C4×C263—21no—
29C2×Dic526—21no—
30C2×Dic526—21no—
31C2×Dic526—21no—
32C2×Dic526—21no—
33C2×Dic526—21no—
34C2×Dic526D412yes—
35C22×Dic263—21no—
36C22×Dic263—21no—
37#16862366—28no—
38C2×C263⋊C8—21no—
39C2×C263⋊C8—21no—
40C2×C263⋊C8—21no—
41C2×C263⋊C8—21no—
42C2×C263⋊C8—21no—
43C2×C263⋊C8D412yes—
44C4⋊Dic263—21no—
45C4⋊Dic263D412yes—
46Dic263⋊C4—24no—
47C22⋊Dic263—24no—
48C24×C263D411yescharacteristic
49C2×Q8×C263—21no—
50C2×Q8×C263—21no—
51C2×Q8×C263—21no—
52C2×Q8×C263—21no—
53C2×Q8×C263—21no—
54C2×Q8×C263D412yes—
55C22×C4×C263—21no—
56C22×C4×C263—21no—
57C22×C4×C263—21no—
58C22×C4×C263—21no—
59C22×C4×C263—21no—
60C22×C4×C263—21no—
61C22×C4×C263—21no—
62C22×C4×C263—21no—
63C22×C4×C263D411yescharacteristic
64C22×C4×C263C2311yescharacteristic
65C4⋊C4×C263—24no—
66C4⋊C4×C263—21no—
67C4⋊C4×C263D412yes—
68C22⋊C4×C263—24no—
69Dic526—22no—
70Dic526—22no—
71Dic526—41no—
72Dic526—41no—
73C2×Dic263—22no—
74C2×Dic263—22no—
75C2×Dic263—41no—
76C2×Dic263—41no—
77C2×Dic263—41no—
78C2×Dic263—41no—
79C263⋊C8—22no—
80C263⋊C8—41no—
81C23×C263—21no—
82C23×C263—21no—
83C23×C263—21no—
84C23×C263—21no—
85C23×C263—21no—
86C23×C263—21no—
87C23×C263Q1612yescomplemented
88C23×C263C2×D411yescharacteristic
89Q8×C263—22no—
90Q8×C263—22no—
91Q8×C263—41no—
92Q8×C263—41no—
93C2×C4×C263—22no—
94C2×C4×C263—22no—
95C2×C4×C263—21no—
96C2×C4×C263—21no—
97C2×C4×C263—21no—
98C2×C4×C263—41no—
99C2×C4×C263—41no—
100C2×C4×C263—41no—
101C2×C4×C263—41no—
102C2×C4×C263—41no—
103C2×C4×C263—41no—
104C2×C4×C263—41no—
105C2×C4×C263—41no—
106C2×C4×C263C2×D411yescharacteristic
107C2×C4×C263C2×D411yescharacteristic
108C2×C4×C263C2×D411yescharacteristic
109C2×C4×C263C2×D411yescharacteristic
110C2×C4×C263C2×D411yescharacteristic
111C2×C4×C263#4111yescharacteristic
112C22×C263—22no—
113C22×C263—22no—
114C22×C263—22no—
115C22×C263—41no—
116C22×C263—41no—
117C22×C263—41no—
118C22×C263—41no—
119C22×C263#12011yescharacteristic
120C22×C263#12011yescharacteristic
121C22×C263#12111yescharacteristic
122C22×C263C2×Q1611yescharacteristic
123C22×C263#13511yescharacteristic
124C22×C263#13711yescharacteristic
125C22×C263#13711yescharacteristic
126C4×C263—41no—
127C4×C263—42no—
128C4×C263—42no—
129C4×C263#12011yescharacteristic
130C4×C263#12111yescharacteristic
131C4×C263#12111yescharacteristic
132C4×C263#12711yescharacteristic
133Dic263—42no—
134Dic263—42no—
135C2×C263—42no—
136C2×C263#39211yescharacteristic
137C2×C263#45111yescharacteristic
138C2×C263#45111yescharacteristic
139C2×C263#45211yescharacteristic
140C2×C263#45211yescharacteristic
141C2×C263#46711yescharacteristic
142C2×C263#47011yescharacteristic
143C263#200111yescharacteristic, complemented, Sylow
144#2001—2631nomaximal, Sylow
145C22×Q16—2631no—
146C2×C22⋊Q8—2631no—
147C2×C22⋊Q8D26311yescharacteristic
148C2×#103—2631no—
149C2×#103—2631no—
150C2×C22⋊C8—2631no—
151#340—2631no—
152C22×Q8—2631no—
153C22×Q8C2×D26311yescharacteristic
154C23×C4C2×D26311yescharacteristic
155C2×Q16—5262no—
156C2×Q16—5262no—
157C2×Q16—5262no—
158C22×C8—2631no—
159C22×C8—2631no—
160C22⋊Q8—22no—
161C22⋊Q8—22no—
162C22⋊Q8—5262no—
163C22⋊Q8—5262no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—2631no—
166C2×C4⋊C4—5261no—
167C2×C4⋊C4C2×D26311yescharacteristic
168C2×C22⋊C4—21no—
169C2×C22⋊C4—5261no—
170#103—5262no—
171#103—5262no—
172C22⋊C8—5262no—
173C24C22⋊D26311yescharacteristic
174C2×Q8—21no—
175C2×Q8—21no—
176C2×Q8—21no—
177C2×Q8—21no—
178C2×Q8—21no—
179C2×Q8—2632no—
180C2×Q8—5261no—
181C2×Q8—5261no—
182C2×Q8—5261no—
183C2×Q8—5261no—
184C2×Q8—5261no—
185C2×Q8C22⋊D26312yes—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—5261no—
195C22×C4—5261no—
196C22×C4C22⋊D26311yescharacteristic
197C22×C4C22×D26311yescharacteristic
198Q16—5268no—
199C2×C8—2632no—
200C2×C8—5261no—
201C2×C8—5261no—
202C2×C8—5261no—
203C2×C8—5261no—
204C2×C8—5261no—
205C4⋊C4—24no—
206C4⋊C4—21no—
207C4⋊C4—2632no—
208C4⋊C4—5264no—
209C4⋊C4—5261no—
210C4⋊C4C22⋊D26312yes—
211C22⋊C4—24no—
212C22⋊C4—5264no—
213C23—21no—
214C23—21no—
215C23—21no—
216C23—21no—
217C23—21no—
218C23—21no—
219C23#1686236612yescomplemented
220C23C2×C22⋊D26311yescharacteristic
221Q8—22no—
222Q8—22no—
223Q8—41no—
224Q8—41no—
225Q8—5262no—
226Q8—5262no—
227Q8—10521no—
228Q8—10521no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—5262no—
243C2×C4—5262no—
244C2×C4—10521no—
245C2×C4—10521no—
246C2×C4—10521no—
247C2×C4—10521no—
248C2×C4D4×D26311yescharacteristic
249C2×C4D4×D26311yescharacteristic
250C2×C4D4×D26311yescharacteristic
251C2×C4C2×C22⋊D26311yescharacteristic
252C2×C4C2×C22⋊D26311yescharacteristic
253C2×C4#1686237511yescharacteristic
254C8—5262no—
255C8—10521no—
256C22—22no—
257C22—22no—
258C22—22no—
259C22—41no—
260C22—41no—
261C22—41no—
262C22—41no—
263C22#2255443811yescharacteristic
264C22#2255443911yescharacteristic
265C22#2255444211yescharacteristic
266C22C2×#1686236611yescharacteristic
267C22#2255449011yescharacteristic
268C22#2255450011yescharacteristic
269C22#2255450111yescharacteristic
270C4—42no—
271C4—41no—
272C4—42no—
273C4—10522no—
274C4—10522no—
275C4#2255443811yescharacteristic
276C4#2255444111yescharacteristic
277C4#2255444211yescharacteristic
278C4#2255446611yescharacteristic
279C2—42no—
280C2#3068184611yescharacteristic
281C2#3068209311yescharacteristic
282C2#3068209411yescharacteristic
283C2#3068209811yescharacteristic
284C2#3068210011yescharacteristic
285C2#3068217711yescharacteristic
286C2#3068219411yescharacteristic
subgroupG/H
centerC23C2×C22⋊D263
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
FittingC2×C22⋊Q8×C263C2
socleC23×C263C2×D4
prime radicalC24×C263D4
hypercenterC2×C22⋊Q8D263
hypocenterC263#2001
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#16862366C2semidirect
3. C2×#22554394C2semidirect
4. C2×#22554393C2semidirect
6. #30681700C2semidirect
87. C23×C263Q16semidirect
143. C263#2001semidirect
219. C23#16862366semidirect

Maximal subgroups

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

subgroupindex
C22×#168623662
C2×#225544492
C2×#225543942
C2×#225543932
C2×C22⋊(C263⋊C8)2
#306817002
C2×C22⋊Q8×C2632
#2001263