Finite Group Databasebeta

← #46783251

Subgroups — #46783251

Order 33664.

332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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#30682736C211yesmaximal, characteristic
2C4×#16862376C211yesmaximal, characteristic, complemented
3#30681954C211yesmaximal, characteristic, complemented
4#30681912C211yesmaximal, characteristic, complemented
5#30681709C211yesmaximal, characteristic, complemented
6#30681698C211yesmaximal, characteristic, complemented
7C2×#104×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9#22554501C412yescomplemented
10#22554500—21no—
11#22554496C412yescomplemented
12#22554495—21no—
13#22554490—22no—
14C2×#16862360C2211yescharacteristic
15C4×Dic526—21no—
16C4×D1052—21no—
17C4×C22⋊D263—22no—
18#22554429C2211yescharacteristic
19#22554429C2211yescharacteristic
20#22554427—21no—
21C42×D263—21no—
22#22554396—22no—
23#22554385—22no—
24C2×#41×C263C2211yescharacteristic
25C2×M16×C263C2211yescharacteristic
26C2×C42×C263C2211yescharacteristic
27#104×C263—21no—
28#104×C263—21no—
29#16862376—21no—
30#16862376—21no—
31#16862376C2×C412yes—
32#16862376D412yes—
33C2×Dic526D411yescharacteristic
34C2×D1052D411yescharacteristic
35C2×C22⋊D263—21no—
36C2×C4×D263—22no—
37C2×C4×D263—21no—
38#16862366—22no—
39#16862364—22no—
40#16862363—22no—
41#16862361—22no—
42#16862360—21no—
43#16862360C2×C412yescomplemented
44C2×C263⋊C8—21no—
45C4⋊Dic263—21no—
46C4⋊Dic263—21no—
47Dic263⋊C4—22no—
48C22⋊Dic263—21no—
49C22⋊Dic263D412yes—
50(C2×D263)⋊C4—22no—
51C4×Dic263—22no—
52C4×Dic263—21no—
53C4×Dic263—21no—
54#41×C263—21no—
55#41×C263—21no—
56#41×C263—21no—
57#41×C263—21no—
58C2×Q8×C263C2×C411yescharacteristic, complemented
59C2×D4×C263—21no—
60C2×D4×C263C2×C411yescharacteristic, complemented
61C22×C4×C263—21no—
62C22×C4×C263—21no—
63C22×C4×C263C2311yescharacteristic
64M16×C263—21no—
65M16×C263—21no—
66C2×C8×C263—21no—
67C42×C263—21no—
68C42×C263D411yescharacteristic
69C42×C263D411yescharacteristic
70C22×D263—21no—
71Dic526—21no—
72Dic526C22⋊C412yes—
73D1052—21no—
74D1052C22⋊C412yes—
75C22⋊D263—22no—
76C22⋊D263—22no—
77C2×Dic263—21no—
78C2×Dic263—22no—
79C2×Dic263—41no—
80C4×D263—22no—
81C4×D263—22no—
82C4×D263—44no—
83C263⋊C8—22no—
84C23×C263—21no—
85C23×C263C2×D411yescharacteristic
86Q8×C263—21no—
87Q8×C263—21no—
88D4×C263—21no—
89D4×C263—21no—
90D4×C263—41no—
91D4×C263—41no—
92C2×C4×C263—21no—
93C2×C4×C263—21no—
94C2×C4×C263—21no—
95C2×C4×C263—42no—
96C2×C4×C263—41no—
97C2×C4×C263—41no—
98C2×C4×C263C22×C411yescharacteristic
99C2×C4×C263C2×D411yescharacteristic
100C2×C4×C263C2×D411yescharacteristic
101C2×C4×C263C2×D411yescharacteristic
102C2×C4×C263#4111yescharacteristic
103C2×C4×C263#4111yescharacteristic
104C8×C263—41no—
105C22×C263—41no—
106C22×C263—41no—
107C22×C263—81no—
108C22×C263C4×D411yescharacteristic
109C22×C263#12011yescharacteristic
110C22×C263#12111yescharacteristic
111C2×D263—22no—
112C2×D263—42no—
113C4×C263—22no—
114C4×C263—41no—
115C4×C263—41no—
116C4×C263C2×C22⋊C411yescharacteristic
117C4×C263C4×D411yescharacteristic
118C4×C263#12111yescharacteristic
119C4×C263#12311yescharacteristic
120Dic263—22no—
121Dic263—42no—
122Dic263—81no—
123C2×C263—21no—
124C2×C263—21no—
125C2×C263—21no—
126C2×C263—81no—
127C2×C263#38611yescharacteristic
128D263—42no—
129C263#190611yescharacteristic, complemented, Sylow
130#1906—2631nomaximal, Sylow
131#575—2631no—
132C4×#41—2631no—
133#421—2631no—
134C2×#104D26311yescharacteristic, complemented
135#410—2631no—
136#344—2631no—
137#339—2631no—
138C2×#41—2631no—
139C2×#41C2×D26311yescharacteristic
140#137—2632no—
141#137—5261no—
142AGL(1,ℤ/8)—2632no—
143AGL(1,ℤ/8)—5261no—
144#135—5262no—
145C2×M16—2631no—
146C2×M16C2×D26311yescharacteristic
147C4×Q8—5261no—
148C4×D4—5261no—
149C4×D4—5262no—
150#117—2631no—
151#117—2631no—
152#117—5261no—
153C2×C42—5261no—
154C2×C42C2×D26311yescharacteristic
155#104—21no—
156#104—21no—
157#104—5262no—
158#99—5262no—
159#41—21no—
160#41—21no—
161#41—21no—
162#41—21no—
163#41—2632no—
164#41—2632no—
165#41—5261no—
166#41—5261no—
167C2×Q8—2631no—
168C2×Q8C4×D26311yescharacteristic, complemented
169C2×D4—21no—
170C2×D4—2631no—
171C2×D4—5261no—
172C2×D4C4×D26311yescharacteristic, complemented
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—5262no—
176C22×C4—5261no—
177C22×C4C22×D26311yescharacteristic
178Q16—5262no—
179SD16—5262no—
180SD16—5262no—
181D8—5262no—
182M16—21no—
183M16—21no—
184M16—2632no—
185M16—5261no—
186C2×C8—21no—
187C2×C8—5261no—
188C4⋊C4—5262no—
189C4⋊C4—5261no—
190C4⋊C4—5261no—
191C22⋊C4—2632no—
192C22⋊C4—5262no—
193C22⋊C4—5261no—
194C42—21no—
195C42—5262no—
196C42—5261no—
197C42—5261no—
198C42C22⋊D26311yescharacteristic
199C42C22⋊D26311yescharacteristic
200C23—21no—
201C23—5261no—
202C23D4×D26311yescharacteristic
203Q8—21no—
204Q8—21no—
205Q8—2632no—
206Q8—5261no—
207D4—21no—
208D4—21no—
209D4—41no—
210D4—41no—
211D4—2632no—
212D4—5262no—
213D4—5262no—
214D4—5261no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—42no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—5261no—
222C2×C4—5262no—
223C2×C4—5262no—
224C2×C4—5262no—
225C2×C4—10524no—
226C2×C4—10521no—
227C2×C4C2×C4×D26311yescharacteristic
228C2×C4D4×D26311yescharacteristic
229C2×C4D4×D26311yescharacteristic
230C2×C4C2×C22⋊D26311yescharacteristic
231C2×C4#1686237511yescharacteristic
232C2×C4#1686237611yescharacteristic
233C8—41no—
234C8—5262no—
235C22—41no—
236C22—41no—
237C22—81no—
238C22—5262no—
239C22—10522no—
240C22(C22⋊D263)⋊C411yescharacteristic
241C22#2255443811yescharacteristic
242C22#2255444311yescharacteristic
243C4—22no—
244C4—41no—
245C4—41no—
246C4—5262no—
247C4—10522no—
248C4—21041no—
249C4C22⋊C4×D26311yescharacteristic
250C4C4×C22⋊D26311yescharacteristic
251C4#2255444111yescharacteristic
252C4#2255445211yescharacteristic
253C2—21no—
254C2—21no—
255C2—21no—
256C2—81no—
257C2—10522no—
258C2#3068181411yescharacteristic
subgroupG/H
centerC4#22554441
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
FittingC2×#104×C263C2
socleC2×C263#386
prime radical#30682736C2
cosocleC22×C4×C263C23
hypercenterC2×#104D263
hypocenterC263#1906
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C4×#16862376C2semidirect
3. #30681954C2semidirect
4. #30681912C2semidirect
5. #30681709C2semidirect
6. #30681698C2semidirect
7. C2×#104×C263C2semidirect
9. #22554501C4semidirect
11. #22554496C4semidirect
43. #16862360C2×C4semidirect
58. C2×Q8×C263C2×C4semidirect
60. C2×D4×C263C2×C4semidirect
129. C263#1906semidirect
134. C2×#104D263semidirect
168. C2×Q8C4×D263semidirect
172. C2×D4C4×D263semidirect

Maximal subgroups

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

subgroupindex
#306827362
C4×#168623762
#306819542
#306819122
#306817092
#306816982
C2×#104×C2632
#1906263