Finite Group Databasebeta

← #46781401

Subgroups — #46781401

Order 33664.

212 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 73 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#30682493C211yesmaximal, characteristic
2#30681990C211yesmaximal, characteristic
3C4⋊C8×D263C211yesmaximal, characteristic
4#30681687C211yesmaximal, characteristic, complemented
5#30681685C211yesmaximal, characteristic, complemented
6#30681683C211yesmaximal, characteristic, complemented
7#333×C263C211yesmaximal, characteristic, complemented
8C2×C8×D263—21no—
9#22554470C2211yescharacteristic
10#22554461—21no—
11#22554450—21no—
12#22554446C412yes—
13Q8×Dic263C412yes—
14#22554435—21no—
15#22554428—21no—
16C42×D263C2211yescharacteristic
17C4⋊(C263⋊C8)C2211yescharacteristic
18C4⋊(C263⋊C8)C2211yescharacteristic
19Dic263⋊C8—21no—
20(C2×D263)⋊C8—21no—
21C8×Dic263—21no—
22C4⋊Q8×C263C2211yescharacteristic
23C4⋊C8×C263C2211yescharacteristic
24C4⋊C8×C263C2211yescharacteristic
25C2×Dic526—21no—
26C2×C4×D263C2×C411yescharacteristic
27C2×C4×D263D411yescharacteristic
28C2×C4×D263D411yescharacteristic
29C2×C263⋊C8—21no—
30C2×C263⋊C8—21no—
31C8×D263—42no—
32C4⋊Dic263—22no—
33C4⋊Dic263—21no—
34C4⋊Dic263C2×C412yes—
35Dic263⋊C4—22no—
36(C2×D263)⋊C4—22no—
37C4×Dic263—22no—
38C4×Dic263C2×C411yescharacteristic
39C4×Dic263D411yescharacteristic
40C4×Dic263D411yescharacteristic
41C2×Q8×C263C2×C412yes—
42C2×C8×C263—21no—
43C2×C8×C263—21no—
44C4⋊C4×C263—21no—
45C4⋊C4×C263—21no—
46C42×C263C2311yescharacteristic
47C22×D263C22⋊C411yescharacteristic
48Dic526—41no—
49Dic526—41no—
50C2×Dic263—22no—
51C2×Dic263C22⋊C411yescharacteristic
52C2×Dic263C22⋊C411yescharacteristic
53C2×Dic263C22⋊C411yescharacteristic
54C4×D263—21no—
55C4×D263—21no—
56C4×D263—41no—
57C4×D263SD1612yes—
58C4×D263Q1612yes—
59C263⋊C8—41no—
60C263⋊C8—41no—
61Q8×C263—42no—
62C2×C4×C263—22no—
63C2×C4×C263C22×C411yescharacteristic
64C2×C4×C263C2×D411yescharacteristic
65C2×C4×C263C2×D411yescharacteristic
66C8×C263—41no—
67C8×C263—41no—
68C22×C263C2×C22⋊C411yescharacteristic
69C2×D263—21no—
70C2×D263—21no—
71C2×D263#10312yes—
72C4×C263—21no—
73C4×C263—42no—
74C4×C263C2×SD1611yescharacteristic
75C4×C263C2×Q1611yescharacteristic
76C4×C263#13511yescharacteristic
77C4×C263#13511yescharacteristic
78Dic263—21no—
79Dic263—21no—
80Dic263—42no—
81Dic263#10312yes—
82C2×C263#41311yescharacteristic
83C2×C263C2×#10311yescharacteristic
84C2×C263#41611yescharacteristic
85D263—22no—
86C263#154211yescharacteristic, complemented, Sylow
87#1542—2631nomaximal, Sylow
88#533—2631no—
89#431—2631no—
90C2×C4⋊C8—2631no—
91#333—2631no—
92#333D26311yescharacteristic, complemented
93#332—2631no—
94#332—2631no—
95C22×C8—5261no—
96C4⋊Q8—2631no—
97C4⋊Q8C2×D26311yescharacteristic
98#125—5261no—
99C22⋊Q8—2632no—
100C22⋊Q8—5261no—
101C4×Q8—2632no—
102C4×Q8—5261no—
103#117—5261no—
104C2×C42—2631no—
105C4⋊C8—2631no—
106C4⋊C8—2631no—
107C4⋊C8—5261no—
108C4⋊C8C2×D26311yescharacteristic
109C4⋊C8C2×D26311yescharacteristic
110C22⋊C8—5261no—
111C4×C8—5261no—
112C2×Q8—5261no—
113C2×Q8C4×D26312yes—
114C22×C4—2631no—
115C22×C4—2631no—
116C22×C4—2631no—
117C2×C8—21no—
118C2×C8—21no—
119C2×C8—5261no—
120C2×C8—5261no—
121C2×C8—10522no—
122C4⋊C4—21no—
123C4⋊C4—21no—
124C4⋊C4—2632no—
125C4⋊C4—5262no—
126C4⋊C4—5262no—
127C4⋊C4—5261no—
128C22⋊C4—5262no—
129C42—2631no—
130C42—2631no—
131C42—2631no—
132C42—5262no—
133C42C22×D26311yescharacteristic
134C23—2631no—
135Q8—42no—
136Q8—10521no—
137Q8—10521no—
138C2×C4—22no—
139C2×C4—2631no—
140C2×C4—2632no—
141C2×C4—2632no—
142C2×C4—2631no—
143C2×C4—2631no—
144C2×C4—5261no—
145C2×C4—5261no—
146C2×C4—5262no—
147C2×C4—10521no—
148C2×C4C2×C4×D26311yescharacteristic
149C2×C4D4×D26311yescharacteristic
150C2×C4D4×D26311yescharacteristic
151C8—41no—
152C8—41no—
153C8—10521no—
154C8—10521no—
155C22—2632no—
156C22—5261no—
157C22—5261no—
158C22C22⋊C4×D26311yescharacteristic
159C4—21no—
160C4—42no—
161C4—2632no—
162C4—5261no—
163C4—5261no—
164C4—10522no—
165C4SD16×D26311yescharacteristic
166C4Q16×D26311yescharacteristic
167C4#2255449111yescharacteristic
168C4#2255449311yescharacteristic
169C2—5262no—
170C2#3068191911yescharacteristic
171C2#103×D26311yescharacteristic
172C2#3068193311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D263
commutatorC2×C4×C263C22×C4
FrattiniC42C22×D263
Fitting#333×C263C2
socleC22×C263C2×C22⋊C4
prime radicalC22×D263C22⋊C4
cosocleC42×C263C23
hypercenter#333D263
hypocenterC263#1542
LCSG ▷ C2×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
4. #30681687C2semidirect
5. #30681685C2semidirect
6. #30681683C2semidirect
7. #333×C263C2semidirect
86. C263#1542semidirect
92. #333D263semidirect

Maximal subgroups

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

subgroupindex
#306824932
#306819902
C4⋊C8×D2632
#306816872
#306816852
#306816832
#333×C2632
#1542263