Finite Group Databasebeta

← #46781158

Subgroups — #46781158

Order 33664.

234 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 77 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
2C4×#16862360C211yesmaximal, characteristic, complemented
3#30681668C212yesmaximal, complemented
4#30681665C212yesmaximal, complemented
5C2×C4⋊C8×C263C211yesmaximal, characteristic, complemented
6C2×#16862360—21no—
7#22554464—21no—
8#22554462C411yescharacteristic
9#22554458C411yescharacteristic
10#22554453—21no—
11#22554449C411yescharacteristic
12#22554444C411yescharacteristic
13C4×Dic526C2211yescharacteristic
14C4×D1052C2211yescharacteristic
15C4×C22⋊D263—21no—
16#22554427—21no—
17#22554381—21no—
18C4×C263⋊C8C2212yes—
19C22×C8×C263—21no—
20C2×C42×C263C2211yescharacteristic
21C4⋊C8×C263—21no—
22C4⋊C8×C263C2212yes—
23C2×Dic526C2×C411yescharacteristic
24C2×D1052C2×C411yescharacteristic
25C2×C22⋊D263—21no—
26C2×C4×D263—21no—
27#16862360—24no—
28C2×C263⋊C8—22no—
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×C263C2×C411yescharacteristic
42C22×C4×C263D411yescharacteristic
43C22×C4×C263D411yescharacteristic
44C2×C8×C263—22no—
45C2×C8×C263—42no—
46C42×C263C2×C411yescharacteristic
47C42×C263D411yescharacteristic
48C42×C263D411yescharacteristic
49C42×C263C2311yescharacteristic
50C22×D263—21no—
51Dic526—22no—
52D1052—22no—
53C22⋊D263—42no—
54C2×Dic263—21no—
55C2×Dic263—21no—
56C2×Dic263—21no—
57C4×D263—41no—
58C4×D263—41no—
59C263⋊C8—24no—
60C23×C263C22⋊C411yescharacteristic
61C2×C4×C263—22no—
62C2×C4×C263—22no—
63C2×C4×C263—21no—
64C2×C4×C263—21no—
65C2×C4×C263C22⋊C411yescharacteristic
66C2×C4×C263C22⋊C411yescharacteristic
67C2×C4×C263C22⋊C411yescharacteristic
68C2×C4×C263C22×C411yescharacteristic
69C2×C4×C263C2×D411yescharacteristic
70C2×C4×C263C2×D411yescharacteristic
71C8×C263—42no—
72C22×C263—21no—
73C22×C263—21no—
74C22×C263#10412yes—
75C22×C263C2×C22⋊C411yescharacteristic
76C2×D263—41no—
77C2×D263—41no—
78C2×D263—41no—
79C4×C263—21no—
80C4×C263—21no—
81C4×C263—21no—
82C4×C263—21no—
83C4×C263#13112yes—
84C4×C263AGL(1,ℤ/8)11yescharacteristic
85C4×C263#13711yescharacteristic
86Dic263—41no—
87Dic263—41no—
88Dic263—41no—
89C2×C263—22no—
90C2×C263#40811yescharacteristic
91C2×C263#41711yescharacteristic
92C2×C263C2×#10411yescharacteristic
93D263—81no—
94C263#148311yescharacteristic, complemented, Sylow
95#1483—2631nomaximal, Sylow
96#529—2631no—
97C2×C4⋊C8D26311yescharacteristic, complemented
98C4×M16—2631no—
99Q8⋊C8—2632no—
100D4⋊C8—2632no—
101C2×M16—5261no—
102C22×C8—21no—
103#126—5261no—
104#125—2631no—
105#124—2631no—
106#123—5261no—
107C22⋊Q8—2631no—
108#121—2631no—
109C4×Q8—2631no—
110C4×D4—2631no—
111C4×D4—5261no—
112#117—5261no—
113C2×C42C2×D26311yescharacteristic
114C4⋊C8—21no—
115C4⋊C8C2×D26312yes—
116#97—5261no—
117C4×C8—2632no—
118C2×Q8—2631no—
119C2×D4—2631no—
120C2×D4—5261no—
121C22×C4—5261no—
122C22×C4C4×D26311yescharacteristic
123C22×C4C22⋊D26311yescharacteristic
124C22×C4D105211yescharacteristic
125M16—5264no—
126C2×C8—22no—
127C2×C8—42no—
128C2×C8—5262no—
129C4⋊C4—2631no—
130C4⋊C4—2631no—
131C4⋊C4—5261no—
132C4⋊C4—5261no—
133C4⋊C4—5261no—
134C4⋊C4—5261no—
135C22⋊C4—5261no—
136C22⋊C4—5261no—
137C22⋊C4—5261no—
138C22⋊C4—5261no—
139C22⋊C4—5261no—
140C42—5261no—
141C42C4×D26311yescharacteristic
142C42C22⋊D26311yescharacteristic
143C42D105211yescharacteristic
144C42C22×D26311yescharacteristic
145C23—5261no—
146C23(C2×D263)⋊C411yescharacteristic
147Q8—5262no—
148D4—5262no—
149D4—10522no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—5261no—
155C2×C4—5261no—
156C2×C4—5261no—
157C2×C4—10521no—
158C2×C4—10521no—
159C2×C4(C2×D263)⋊C411yescharacteristic
160C2×C4(C2×D263)⋊C411yescharacteristic
161C2×C4(C2×D263)⋊C411yescharacteristic
162C2×C4C2×C4×D26311yescharacteristic
163C2×C4C2×C22⋊D26311yescharacteristic
164C2×C4C2×D105211yescharacteristic
165C8—42no—
166C8—5264no—
167C22—21no—
168C22—21no—
169C22—10521no—
170C22—10521no—
171C22—10521no—
172C22#2255439612yes—
173C22C2×(C2×D263)⋊C411yescharacteristic
174C4—21no—
175C4—21no—
176C4—21no—
177C4—21no—
178C4—10521no—
179C4—10521no—
180C4—10521no—
181C4#2255447612yes—
182C4#2255449611yescharacteristic
183C4#2255450111yescharacteristic
184C2—22no—
185C2—21041no—
186C2#3068190411yescharacteristic
187C2#3068193711yescharacteristic
188C2C2×#2255439611yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D263
commutatorC2×C4×C263C22×C4
FrattiniC42C22×D263
FittingC2×C4⋊C8×C263C2
socleC22×C263C2×C22⋊C4
prime radical#22554444C4
cosocleC42×C263C23
hypercenterC2×C4⋊C8D263
hypocenterC263#1483
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C4×#16862360C2semidirect
3. #30681668C2semidirect
4. #30681665C2semidirect
5. C2×C4⋊C8×C263C2semidirect
94. C263#1483semidirect
97. C2×C4⋊C8D263semidirect

Maximal subgroups

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

subgroupindex
#306824722
C4×#168623602
#306816682
#306816652
C2×C4⋊C8×C2632
#1483263