Finite Group Databasebeta

← #46783267

Subgroups — #46783267

Order 33664.

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

normal subgroups only

This group has 312 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#30682705C211yesmaximal, characteristic
2#30682509C211yesmaximal, characteristic
3#30681946C212yesmaximal, complemented
4#30681694C212yesmaximal, complemented
5#410×C263C211yesmaximal, characteristic
6C22×Dic526C2211yescharacteristic
7#22554477—24no—
8C2×#16862360—22no—
9C2×#16862360C2212yes—
10#22554468C412yescomplemented
11#22554457C412yescomplemented
12#22554451—22no—
13#22554449—22no—
14#22554429C2211yescharacteristic
15#22554393—24no—
16C2×#41×C263C2211yescharacteristic
17#117×C263C2212yes—
18#99×C263—22no—
19C2×Dic526—21no—
20C2×Dic526—22no—
21C2×Dic526—22no—
22C2×Dic526C2×C412yes—
23C22×Dic263—21no—
24#16862360—24no—
25#16862360—22no—
26#16862360—22no—
27C2×C263⋊C8—24no—
28C2×C263⋊C8D414yes—
29C4⋊Dic263—21no—
30Dic263⋊C4—24no—
31C22⋊Dic263—24no—
32C22⋊Dic263—21no—
33C4×Dic263C2×C412yes—
34#41×C263—22no—
35#41×C263—22no—
36C2×Q8×C263C2×C411yescharacteristic
37C2×D4×C263C2×C411yescharacteristic
38C2×D4×C263D412yes—
39C22×C4×C263D412yes—
40C22×C4×C263C2311yescharacteristic
41C4⋊C4×C263—22no—
42C22⋊C4×C263—22no—
43C42×C263—22no—
44Dic526—24no—
45Dic526—41no—
46Dic526—41no—
47C2×Dic263—22no—
48C2×Dic263—22no—
49C2×Dic263—42no—
50C263⋊C8—24no—
51C23×C263C22⋊C412yes—
52C23×C263C2×D411yescharacteristic
53Q8×C263—22no—
54D4×C263—24no—
55D4×C263—22no—
56C2×C4×C263—22no—
57C2×C4×C263—22no—
58C2×C4×C263—42no—
59C2×C4×C263C22⋊C412yes—
60C2×C4×C263C22×C411yescharacteristic
61C2×C4×C263C2×D412yes—
62C2×C4×C263C2×D411yescharacteristic
63C2×C4×C263#4112yes—
64C22×C263—22no—
65C22×C263—41no—
66C22×C263—42no—
67C22×C263C2×C22⋊C411yescharacteristic
68C22×C263#12112yes—
69C4×C263—22no—
70C4×C263—82no—
71C4×C263C4×D412yes—
72C4×C263#12011yescharacteristic
73C4×C263#12311yescharacteristic
74Dic263—42no—
75Dic263—42no—
76C2×C263—21no—
77C2×C263—22no—
78C2×C263—42no—
79C2×C263#38611yescharacteristic
80C263#190911yescharacteristic, complemented, Sylow
81#1909—2631nomaximal, Sylow
82#568—2631no—
83#536—2631no—
84#419—2632no—
85#410D26311yescharacteristic
86H(3,ℤ/4)—2632no—
87C2×#41C2×D26311yescharacteristic
88C22×Q8—2631no—
89#131—5264no—
90C2×M16—2632no—
91C2×M16—5262no—
92C4⋊Q8—2632no—
93#124—2632no—
94#123—5262no—
95C22⋊Q8—5262no—
96#117—2631no—
97#117C2×D26312yes—
98#103—5264no—
99#99—22no—
100#41—22no—
101#41—22no—
102C2×Q8—2632no—
103C2×Q8—5261no—
104C2×Q8—5262no—
105C2×Q8—5262no—
106C2×Q8C4×D26311yescharacteristic
107C2×D4C4×D26311yescharacteristic
108C2×D4C22⋊D26312yes—
109C22×C4—5261no—
110C22×C4D105212yes—
111C22×C4C22×D26311yescharacteristic
112M16—5264no—
113M16—5262no—
114M16—5262no—
115C2×C8—2634no—
116C2×C8—5264no—
117C4⋊C4—22no—
118C4⋊C4—5264no—
119C4⋊C4—5261no—
120C22⋊C4—22no—
121C22⋊C4—5264no—
122C22⋊C4—5261no—
123C42—22no—
124C42—2632no—
125C23(C2×D263)⋊C412yes—
126C23C2×C22⋊D26311yescharacteristic
127Q8—22no—
128Q8—5264no—
129Q8—10521no—
130Q8—10521no—
131D4—24no—
132D4—22no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—42no—
136C2×C4—5262no—
137C2×C4—5262no—
138C2×C4—10522no—
139C2×C4(C2×D263)⋊C412yes—
140C2×C4C2×C4×D26311yescharacteristic
141C2×C4D4×D26312yes—
142C2×C4C2×D105211yescharacteristic
143C2×C4#1686237512yes—
144C8—5264no—
145C22—22no—
146C22—41no—
147C22—42no—
148C22C2×(C2×D263)⋊C411yescharacteristic
149C22#2255444212yes—
150C4—22no—
151C4—82no—
152C4—10522no—
153C4—10522no—
154C4(C22⋊D263)⋊C412yes—
155C4#2255444011yescharacteristic
156C4#2255445411yescharacteristic
157C2—22no—
158C2—21no—
159C2—42no—
160C2#3068181511yescharacteristic
subgroupG/H
centerC2#30681815
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#410×C263C2
socleC2×C263#386
prime radicalC2×#41×C263C22
cosocleC22×C4×C263C23
hypercenter#410D263
hypocenterC263#1909
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
3. #30681946C2semidirect
4. #30681694C2semidirect
10. #22554468C4semidirect
11. #22554457C4semidirect
80. C263#1909semidirect

Maximal subgroups

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

subgroupindex
#306827052
#306825092
#306819462
#306816942
#410×C2632
#1909263