Finite Group Databasebeta

← #46783905

Subgroups — #46783905

Order 33664.

246 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 71 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#30681946C212yesmaximal
2#30681843C211yesmaximal, characteristic
3#30681707C211yesmaximal, characteristic
4#30681697C212yesmaximal
5#544×C263C211yesmaximal, characteristic
6C22×Dic526C2211yescharacteristic
7C2×#16862360C2212yes—
8C2×C4×Dic263C2211yescharacteristic
9#22554393—22no—
10#22554393—22no—
11C263⋊#95—22no—
12C4⋊Q8×C263—22no—
13#125×C263—22no—
14C22⋊Q8×C263—22no—
15#117×C263C2212yes—
16C2×C4⋊C4×C263C2211yescharacteristic
17C2×Dic526—22no—
18C2×Dic526—21no—
19C2×Dic526—22no—
20C2×Dic526Q812yescomplemented
21C22×Dic263—21no—
22C22×Dic263—21no—
23#16862360—22no—
24#16862360—22no—
25C2×C263⋊C8—22no—
26C4×Dic263—22no—
27C2×Q8×C263—22no—
28C22×C4×C263D412yes—
29C22×C4×C263C2311yescharacteristic
30C4⋊C4×C263—22no—
31C4⋊C4×C263—24no—
32C4⋊C4×C263—22no—
33C4⋊C4×C263D412yes—
34C4⋊C4×C263D412yes—
35C22⋊C4×C263—22no—
36C42×C263—22no—
37Dic526—24no—
38Dic526—42no—
39C2×Dic263—22no—
40C2×Dic263—22no—
41C2×Dic263—41no—
42C2×Dic263—41no—
43C2×Dic263—41no—
44C2×Dic263—41no—
45C263⋊C8—42no—
46C23×C263C2×D411yescharacteristic
47Q8×C263—82no—
48C2×C4×C263—22no—
49C2×C4×C263—22no—
50C2×C4×C263—22no—
51C2×C4×C263—42no—
52C2×C4×C263C2×D412yes—
53C2×C4×C263C2×Q811yescharacteristic
54C2×C4×C263#4112yes—
55C2×C4×C263#4111yescharacteristic
56C22×C263—21no—
57C22×C263—21no—
58C22×C263#12011yescharacteristic
59C22×C263C22⋊Q811yescharacteristic
60C22×C263#12411yescharacteristic
61C4×C263—42no—
62C4×C263—42no—
63C4×C263—42no—
64C4×C263C22⋊Q812yes—
65C4×C263#12412yes—
66Dic263—42no—
67Dic263—42no—
68C2×C263—21no—
69C2×C263—21no—
70C2×C263#39311yescharacteristic
71C2×C263#45511yescharacteristic
72C2×C263#45611yescharacteristic
73C263#202811yescharacteristic, complemented, Sylow
74#2028—2631nomaximal, Sylow
75#544D26311yescharacteristic
76#419—2632no—
77#391—2631no—
78#343—2631no—
79#339—2632no—
80C22×Q8—2631no—
81C2×M16—2632no—
82C4⋊Q8—22no—
83#125—22no—
84C22⋊Q8—22no—
85#117C2×D26312yes—
86C2×C4⋊C4C2×D26311yescharacteristic
87C2×C42—2631no—
88#103—5262no—
89#103—5262no—
90#95—5262no—
91C2×Q8—22no—
92C2×Q8—2632no—
93C2×Q8—5261no—
94C2×Q8—5262no—
95C2×Q8—5262no—
96C22×C4—5261no—
97C22×C4—5261no—
98C22×C4C22⋊D26312yes—
99C22×C4C22×D26311yescharacteristic
100M16—5262no—
101M16—5262no—
102C2×C8—5262no—
103C4⋊C4—22no—
104C4⋊C4—24no—
105C4⋊C4—22no—
106C4⋊C4C22⋊D26312yes—
107C4⋊C4C22⋊D26312yes—
108C22⋊C4—22no—
109C42—22no—
110C42—5262no—
111C23C2×C22⋊D26311yescharacteristic
112Q8—82no—
113Q8—5264no—
114Q8—10522no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—22no—
118C2×C4—42no—
119C2×C4—5262no—
120C2×C4—5262no—
121C2×C4—10521no—
122C2×C4—10521no—
123C2×C4—10521no—
124C2×C4—10521no—
125C2×C4C2×C22⋊D26312yes—
126C2×C4Q8×D26311yescharacteristic
127C2×C4#1686237712yes—
128C2×C4#1686237711yescharacteristic
129C8—10522no—
130C22—21no—
131C22—21no—
132C22#2255443911yescharacteristic
133C22#2255444611yescharacteristic
134C22#2255445911yescharacteristic
135C4—42no—
136C4—42no—
137C4—42no—
138C4—10522no—
139C4—10522no—
140C4#2255444612yes—
141C4#2255445912yes—
142C2—21no—
143C2—21no—
144C2#3068184911yescharacteristic
145C2#3068211611yescharacteristic
146C2#3068212111yescharacteristic
subgroupG/H
centerC22#22554439
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#544×C263C2
socleC22×C263#120
prime radicalC23×C263C2×D4
hypercenter#544D263
hypocenterC263#2028
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
20. C2×Dic526Q8semidirect
73. C263#2028semidirect

Maximal subgroups

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

subgroupindex
#306819462
#306818432
#306817072
#306816972
#544×C2632
#2028263