Finite Group Databasebeta

← #46783277

Subgroups — #46783277

Order 33664.

362 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 85 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#30682505C211yesmaximal, characteristic
2#30682413C211yesmaximal, characteristic, complemented
3#30681954C212yesmaximal, complemented
4#30681695C212yesmaximal, complemented
5C2×#100×C263C211yesmaximal, characteristic, complemented
6C2×#16862376C2211yescharacteristic
7#22554466C412yescomplemented
8#22554457C412yescomplemented
9#22554441—22no—
10#22554439—22no—
11D4×Dic263—24no—
12#22554429C2211yescharacteristic
13#22554429C2212yes—
14C2×C22⋊Dic263—22no—
15#22554396—24no—
16C22×D4×C263C2211yescharacteristic
17C2×M16×C263C2212yes—
18#100×C263—22no—
19#16862376—22no—
20#16862376—22no—
21C2×Dic526C2×C411yescharacteristic, complemented
22C2×D1052C2×C411yescharacteristic, complemented
23C2×C22⋊D263—24no—
24C2×C22⋊D263—21no—
25C22×Dic263—24no—
26C2×C4×D263—21no—
27C4⋊Dic263—22no—
28C4⋊Dic263—21no—
29C22⋊Dic263—24no—
30C22⋊Dic263—24no—
31C22⋊Dic263—22no—
32C22⋊Dic263—21no—
33C4×Dic263C2×C412yescomplemented
34C4×Dic263D414yescomplemented
35C24×C263D412yes—
36C2×D4×C263—22no—
37C2×D4×C263—22no—
38C2×D4×C263C2×C412yes—
39C2×D4×C263D412yes—
40C22×C4×C263C2311yescharacteristic
41M16×C263—22no—
42M16×C263—22no—
43C2×C8×C263—22no—
44C22×D263—21no—
45Dic526—22no—
46D1052—22no—
47C22⋊D263—41no—
48C22⋊D263—41no—
49C22⋊D263—84no—
50C2×Dic263—22no—
51C2×Dic263—21no—
52C2×Dic263—24no—
53C2×Dic263—84no—
54C4×D263—42no—
55C23×C263—22no—
56C23×C263—22no—
57C23×C263—82no—
58C23×C263C22⋊C414yes—
59C23×C263C2×D411yescharacteristic
60D4×C263—24no—
61D4×C263—24no—
62C2×C4×C263C22×C411yescharacteristic
63C2×C4×C263C2×D412yes—
64C2×C4×C263C2×D411yescharacteristic
65C2×C4×C263#4112yes—
66C8×C263—42no—
67C22×C263—24no—
68C22×C263—41no—
69C22×C263—44no—
70C22×C263—44no—
71C22×C263—82no—
72C22×C263C2×C22⋊C411yescharacteristic
73C22×C263#12011yescharacteristic
74C22×C263#12311yescharacteristic
75C2×D263—42no—
76C2×D263—41no—
77C4×C263C4×D412yes—
78C4×C263#12112yes—
79Dic263—44no—
80Dic263—42no—
81Dic263—41no—
82C2×C263—21no—
83C2×C263—21no—
84C2×C263—21no—
85C2×C263—44no—
86C2×C263#38611yescharacteristic
87D263—81no—
88C263#191111yescharacteristic, complemented, Sylow
89#1911—2631nomaximal, Sylow
90#535—2631no—
91#518—2631no—
92#421—2632no—
93C2×#100D26311yescharacteristic, complemented
94H(3,ℤ/4)—2632no—
95C2×#41—2631no—
96C22×D4C2×D26311yescharacteristic
97C2×M16C2×D26312yes—
98#127—2632no—
99#124—2632no—
100#121—5262no—
101#120—5262no—
102C4×D4—5264no—
103#117—2632no—
104#117—2631no—
105C2×C22⋊C4—5262no—
106#104—5264no—
107#100—22no—
108C24D105212yes—
109#41—5262no—
110#41—5262no—
111C2×Q8—2631no—
112C2×D4—22no—
113C2×D4—22no—
114C2×D4—2631no—
115C2×D4—5261no—
116C2×D4—5264no—
117C2×D4C4×D26312yes—
118C2×D4C22⋊D26312yes—
119C22×C4—5264no—
120C22×C4—5261no—
121C22×C4C22×D26311yescharacteristic
122M16—22no—
123M16—22no—
124C2×C8—22no—
125C4⋊C4—5262no—
126C4⋊C4—5261no—
127C22⋊C4—5264no—
128C22⋊C4—5264no—
129C22⋊C4—5262no—
130C22⋊C4—5261no—
131C42—2632no—
132C42—2634no—
133C23—22no—
134C23—22no—
135C23—82no—
136C23—5261no—
137C23(C2×D263)⋊C414yes—
138C23C2×D105211yescharacteristic
139Q8—5262no—
140D4—24no—
141D4—24no—
142D4—5262no—
143D4—10521no—
144D4—10521no—
145D4—21044no—
146C2×C4—5262no—
147C2×C4—5261no—
148C2×C4—5264no—
149C2×C4—10522no—
150C2×C4—21044no—
151C2×C4C2×C4×D26311yescharacteristic
152C2×C4D4×D26312yes—
153C2×C4C2×C22⋊D26311yescharacteristic
154C2×C4#1686237512yes—
155C8—42no—
156C22—24no—
157C22—41no—
158C22—44no—
159C22—44no—
160C22—82no—
161C22—10522no—
162C22—10521no—
163C22C2×(C2×D263)⋊C411yescharacteristic
164C22#2255444011yescharacteristic
165C22#2255445411yescharacteristic
166C4—10524no—
167C4—10522no—
168C4—10521no—
169C4(C22⋊D263)⋊C412yes—
170C4#2255444212yes—
171C2—21no—
172C2—21no—
173C2—21no—
174C2—44no—
175C2—21041no—
176C2#3068181511yescharacteristic
subgroupG/H
centerC2#30681815
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
FittingC2×#100×C263C2
socleC2×C263#386
prime radical#30682505C2
cosocleC22×C4×C263C23
hypercenterC2×#100D263
hypocenterC263#1911
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
2. #30682413C2semidirect
3. #30681954C2semidirect
4. #30681695C2semidirect
5. C2×#100×C263C2semidirect
7. #22554466C4semidirect
8. #22554457C4semidirect
21. C2×Dic526C2×C4semidirect
22. C2×D1052C2×C4semidirect
33. C4×Dic263C2×C4semidirect
34. C4×Dic263D4semidirect
88. C263#1911semidirect
93. C2×#100D263semidirect

Maximal subgroups

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

subgroupindex
#306825052
#306824132
#306819542
#306816952
C2×#100×C2632
#1911263