Finite Group Databasebeta

← #46781286

Subgroups — #46781286

Order 33664.

222 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 69 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#30682472C211yesmaximal, characteristic
2#30681804C211yesmaximal, characteristic, complemented
3#30681676C212yesmaximal, complemented
4#30681673C212yesmaximal
5#432×C263C211yesmaximal, characteristic, complemented
6#22554464—21no—
7#22554462C411yescharacteristic, complemented
8#22554458C411yescharacteristic, complemented
9#22554453—21no—
10#22554449C2211yescharacteristic
11#22554444C2211yescharacteristic
12C4×Dic526C411yescharacteristic, complemented
13C4×D1052C411yescharacteristic, complemented
14C4×C22⋊D263—21no—
15#22554427—21no—
16C2×C4⋊Dic263—21no—
17C263⋊#95—21no—
18C263⋊#95C2212yes—
19C2×C42×C263C2211yescharacteristic
20C4⋊C8×C263—21no—
21C22⋊C8×C263C2212yes—
22#97×C263—21no—
23C2×Dic526C2×C411yescharacteristic
24C2×D1052C2×C411yescharacteristic
25C2×C22⋊D263—21no—
26C22×Dic263—22no—
27C2×C4×D263—21no—
28C4⋊Dic263—42no—
29C4⋊Dic263C2×C411yescharacteristic
30C4⋊Dic263C2×C411yescharacteristic
31Dic263⋊C4—21no—
32Dic263⋊C4—21no—
33Dic263⋊C4—21no—
34Dic263⋊C4—21no—
35C22⋊Dic263—21no—
36(C2×D263)⋊C4—21no—
37(C2×D263)⋊C4—21no—
38(C2×D263)⋊C4—21no—
39(C2×D263)⋊C4—21no—
40C4×Dic263—21no—
41C22×C4×C263D411yescharacteristic
42C22×C4×C263D411yescharacteristic
43C22×C4×C263C2311yescharacteristic
44C2×C8×C263—22no—
45C42×C263C2×C411yescharacteristic
46C42×C263C2×C411yescharacteristic
47C42×C263D411yescharacteristic
48C42×C263D411yescharacteristic
49C22×D263—21no—
50Dic526—41no—
51D1052—41no—
52C22⋊D263—41no—
53C22⋊D263—41no—
54C2×Dic263—21no—
55C2×Dic263—21no—
56C2×Dic263—21no—
57C2×Dic263—42no—
58C2×Dic263—42no—
59C2×Dic263—42no—
60C4×D263—42no—
61C23×C263C2×D411yescharacteristic
62C2×C4×C263—21no—
63C2×C4×C263—21no—
64C2×C4×C263—41no—
65C2×C4×C263—41no—
66C2×C4×C263C22⋊C411yescharacteristic
67C2×C4×C263C22⋊C411yescharacteristic
68C2×C4×C263C22⋊C411yescharacteristic
69C2×C4×C263C22⋊C411yescharacteristic
70C2×C4×C263C22×C411yescharacteristic
71C2×C4×C263C2×D411yescharacteristic
72C8×C263—42no—
73C22×C263—21no—
74C22×C263—21no—
75C22×C263C2×C22⋊C411yescharacteristic
76C22×C263AGL(1,ℤ/8)11yescharacteristic
77C22×C263#13711yescharacteristic
78C2×D263—41no—
79C2×D263—41no—
80C2×D263—41no—
81C4×C263—21no—
82C4×C263—21no—
83C4×C263—21no—
84C4×C263—21no—
85C4×C263—21no—
86C4×C263—21no—
87Dic263—41no—
88Dic263—41no—
89Dic263—41no—
90Dic263—82no—
91C2×C263—21no—
92C2×C263—21no—
93C2×C263#41011yescharacteristic
94C2×C263#41711yescharacteristic
95C2×C263#42111yescharacteristic
96D263—81no—
97C263#151211yescharacteristic, complemented, Sylow
98#1512—2631nomaximal, Sylow
99#529—2631no—
100#432D26311yescharacteristic, complemented
101#382—2631no—
102#328—2632no—
103#327—2632no—
104#126—5261no—
105#125—2631no—
106#124—2631no—
107#123—5261no—
108C22⋊Q8—2631no—
109#121—2631no—
110C4×Q8—2631no—
111C4×D4—2631no—
112C4×D4—5261no—
113#117—5261no—
114C2×C4⋊C4—5261no—
115C2×C42C2×D26311yescharacteristic
116C4⋊C8—21no—
117C22⋊C8C2×D26312yes—
118#97—21no—
119#95—2632no—
120#95—5261no—
121C2×Q8—2631no—
122C2×D4—2631no—
123C2×D4—5261no—
124C22×C4—5261no—
125C22×C4—5262no—
126C22×C4D105211yescharacteristic
127C22×C4D105211yescharacteristic
128C22×C4C22×D26311yescharacteristic
129C2×C8—22no—
130C4⋊C4—2631no—
131C4⋊C4—2631no—
132C4⋊C4—5261no—
133C4⋊C4—5261no—
134C4⋊C4—5261no—
135C4⋊C4—5261no—
136C4⋊C4—10522no—
137C22⋊C4—5261no—
138C22⋊C4—5261no—
139C22⋊C4—5261no—
140C22⋊C4—5261no—
141C22⋊C4—5261no—
142C42—5261no—
143C42C4×D26311yescharacteristic
144C42C4×D26311yescharacteristic
145C42C22⋊D26311yescharacteristic
146C42C22⋊D26311yescharacteristic
147C23—5261no—
148C23C2×D105211yescharacteristic
149Q8—10521no—
150D4—10521no—
151D4—10521no—
152D4—10521no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—5261no—
158C2×C4—5261no—
159C2×C4—5261no—
160C2×C4—10522no—
161C2×C4—10522no—
162C2×C4—10522no—
163C2×C4—10522no—
164C2×C4(C2×D263)⋊C411yescharacteristic
165C2×C4(C2×D263)⋊C411yescharacteristic
166C2×C4(C2×D263)⋊C411yescharacteristic
167C2×C4(C2×D263)⋊C411yescharacteristic
168C2×C4C2×C4×D26311yescharacteristic
169C2×C4C2×C22⋊D26311yescharacteristic
170C8—42no—
171C22—21no—
172C22—21no—
173C22—10521no—
174C22—10521no—
175C22—10521no—
176C22C2×(C2×D263)⋊C411yescharacteristic
177C22#2255449811yescharacteristic
178C22#2255450311yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—10521no—
186C4—10521no—
187C4—10521no—
188C4—21042no—
189C2—21no—
190C2—21no—
191C2—21041no—
192C2#3068191111yescharacteristic
193C2#3068194011yescharacteristic
194C2#3068195411yescharacteristic
subgroupG/H
centerC22C2×(C2×D263)⋊C4
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#432×C263C2
socleC22×C263C2×C22⋊C4
prime radical#22554444C22
cosocleC22×C4×C263C23
hypercenter#432D263
hypocenterC263#1512
LCSG ▷ C2×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #30681804C2semidirect
3. #30681676C2semidirect
5. #432×C263C2semidirect
7. #22554462C4semidirect
8. #22554458C4semidirect
12. C4×Dic526C4semidirect
13. C4×D1052C4semidirect
97. C263#1512semidirect
100. #432D263semidirect

Maximal subgroups

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

subgroupindex
#306824722
#306818042
#306816762
#306816732
#432×C2632
#1512263