Finite Group Databasebeta

← #46783285

Subgroups — #46783285

Order 33664.

314 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 93 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#30682416C211yesmaximal, characteristic, complemented
2#30681955C212yesmaximal
3C2×#22554389C211yesmaximal, characteristic, complemented
4#30681694C212yesmaximal, complemented
5#536×C263C211yesmaximal, characteristic
6C2×#16862360C2212yes—
7Q8×Dic263—24no—
8#22554429—22no—
9#22554429C2212yes—
10#22554397—24no—
11#22554389—22no—
12C2×#41×C263C2211yescharacteristic
13C22×Q8×C263C2211yescharacteristic
14C4⋊Q8×C263C412yescomplemented
15#124×C263C412yescomplemented
16#123×C263—22no—
17C22⋊Q8×C263—22no—
18#117×C263C2211yescharacteristic
19#16862360—22no—
20#16862360—22no—
21C2×C263⋊C8—22no—
22C4⋊Dic263—24no—
23C4⋊Dic263—22no—
24C22⋊Dic263—22no—
25C4×Dic263—24no—
26C4×Dic263D414yes—
27#41×C263—22no—
28#41×C263—22no—
29C2×Q8×C263—22no—
30C2×Q8×C263—22no—
31C2×Q8×C263C2×C411yescharacteristic
32C2×Q8×C263C2×C412yes—
33C2×Q8×C263D412yes—
34C2×D4×C263—21no—
35C2×D4×C263C2×C411yescharacteristic
36C22×C4×C263—21no—
37C22×C4×C263D412yes—
38C22×C4×C263C2311yescharacteristic
39C4⋊C4×C263—24no—
40C4⋊C4×C263—21no—
41C22⋊C4×C263—21no—
42C22⋊C4×C263—24no—
43C42×C263C2×C412yes—
44C2×Dic263—24no—
45C263⋊C8—42no—
46C23×C263—21no—
47C23×C263C2×D411yescharacteristic
48Q8×C263—24no—
49Q8×C263—24no—
50Q8×C263—22no—
51D4×C263—22no—
52D4×C263—41no—
53D4×C263—41no—
54C2×C4×C263—22no—
55C2×C4×C263—22no—
56C2×C4×C263—22no—
57C2×C4×C263—21no—
58C2×C4×C263—42no—
59C2×C4×C263C22⋊C414yes—
60C2×C4×C263C22×C411yescharacteristic
61C2×C4×C263C2×D412yes—
62C2×C4×C263C2×D411yescharacteristic
63C2×C4×C263#4112yes—
64C22×C263—41no—
65C22×C263—42no—
66C22×C263—41no—
67C22×C263C2×C22⋊C411yescharacteristic
68C22×C263#12011yescharacteristic
69C22×C263#12311yescharacteristic
70C4×C263—24no—
71C4×C263—42no—
72C4×C263—41no—
73C4×C263C4×D412yes—
74C4×C263#12112yes—
75Dic263—44no—
76C2×C263—21no—
77C2×C263—21no—
78C2×C263—21no—
79C2×C263—81no—
80C2×C263#38611yescharacteristic
81C263#191211yescharacteristic, complemented, Sylow
82#1912—2631nomaximal, Sylow
83#536D26311yescharacteristic
84#519—2631no—
85#421—2632no—
86C2×#101—2631no—
87H(3,ℤ/4)—2632no—
88C2×#41C2×D26311yescharacteristic
89C22×Q8C2×D26311yescharacteristic
90C2×M16—2632no—
91C4⋊Q8Dic26312yescomplemented
92#124Dic26312yescomplemented
93#123—22no—
94C22⋊Q8—22no—
95C4×Q8—5264no—
96#117—2632no—
97#117—5262no—
98#117C2×D26311yescharacteristic
99#104—5264no—
100#101—5262no—
101#41—22no—
102#41—22no—
103C2×Q8—22no—
104C2×Q8—22no—
105C2×Q8C2×Dic26311yescharacteristic
106C2×Q8C2×Dic26312yes—
107C2×Q8C22⋊D26312yes—
108C2×D4—21no—
109C2×D4C2×Dic26311yescharacteristic
110C22×C4—21no—
111C22×C4C22⋊D26312yes—
112C22×C4C22×D26311yescharacteristic
113M16—5262no—
114M16—5262no—
115C2×C8—5262no—
116C4⋊C4—24no—
117C4⋊C4—21no—
118C4⋊C4—5264no—
119C4⋊C4—5262no—
120C22⋊C4—21no—
121C22⋊C4—24no—
122C22⋊C4—5262no—
123C42—2634no—
124C42—5264no—
125C42C2×Dic26312yes—
126C23—21no—
127C23C2×C22⋊D26311yescharacteristic
128Q8—24no—
129Q8—24no—
130Q8—22no—
131D4—22no—
132D4—41no—
133D4—41no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—22no—
137C2×C4—21no—
138C2×C4—42no—
139C2×C4—5264no—
140C2×C4C22⋊Dic26314yes—
141C2×C4C22×Dic26311yescharacteristic
142C2×C4D4×D26312yes—
143C2×C4C2×C22⋊D26311yescharacteristic
144C2×C4#1686237512yes—
145C8—10522no—
146C22—41no—
147C22—42no—
148C22—41no—
149C22C2×C22⋊Dic26311yescharacteristic
150C22#2255443811yescharacteristic
151C22#2255445111yescharacteristic
152C4—24no—
153C4—42no—
154C4—41no—
155C4—10524no—
156C4D4×Dic26312yes—
157C4#2255444212yes—
158C2—21no—
159C2—21no—
160C2—21no—
161C2—81no—
162C2#3068181811yescharacteristic
subgroupG/H
centerC2#30681818
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#536×C263C2
socleC2×C263#386
prime radicalC2×#41×C263C22
cosocleC22×C4×C263C23
hypercenter#536D263
hypocenterC263#1912
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2 ◁ C22×C4 ◁ #536

Complements

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

NH ≅ G/Ntype
1. #30682416C2semidirect
3. C2×#22554389C2semidirect
4. #30681694C2semidirect
14. C4⋊Q8×C263C4semidirect
15. #124×C263C4semidirect
81. C263#1912semidirect
91. C4⋊Q8Dic263semidirect
92. #124Dic263semidirect

Maximal subgroups

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

subgroupindex
#306824162
#306819552
C2×#225543892
#306816942
#536×C2632
#1912263