Finite Group Databasebeta

← #46783900

Subgroups — #46783900

Order 33664.

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

normal subgroups only

This group has 282 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#30681942C212yesmaximal
2#30681839C211yesmaximal, characteristic
3#30681707C211yesmaximal, characteristic, complemented
4#30681697C212yesmaximal, complemented
5#544×C263C211yesmaximal, characteristic, complemented
6C22×D1052C2211yescharacteristic
7C2×#16862360C2212yes—
8C2×(C2×D263)⋊C4—22no—
9C2×C4×Dic263C2211yescharacteristic
10#22554390—22no—
11#22554390—22no—
12C4⋊Q8×C263—22no—
13#125×C263—22no—
14C22⋊Q8×C263—22no—
15#117×C263C2212yes—
16C2×C4⋊C4×C263C2211yescharacteristic
17C23×D263—21no—
18C2×D1052—22no—
19C2×D1052—22no—
20C2×D1052—21no—
21C2×D1052Q812yescomplemented
22C22×Dic263—21no—
23#16862360—22no—
24#16862360—22no—
25C2×C263⋊C8—22no—
26(C2×D263)⋊C4—44no—
27C4×Dic263—22no—
28C2×Q8×C263—22no—
29C22×C4×C263D412yes—
30C22×C4×C263C2311yescharacteristic
31C4⋊C4×C263—22no—
32C4⋊C4×C263—24no—
33C4⋊C4×C263—22no—
34C4⋊C4×C263D412yes—
35C4⋊C4×C263D412yes—
36C22⋊C4×C263—22no—
37C42×C263—22no—
38C22×D263—22no—
39C22×D263—42no—
40C22×D263—42no—
41C22×D263—41no—
42C22×D263—41no—
43D1052—24no—
44D1052—42no—
45C2×Dic263—22no—
46C2×Dic263—41no—
47C2×Dic263—41no—
48C263⋊C8—42no—
49C23×C263C2×D411yescharacteristic
50Q8×C263—82no—
51C2×C4×C263—22no—
52C2×C4×C263—22no—
53C2×C4×C263—22no—
54C2×C4×C263—42no—
55C2×C4×C263C2×D412yes—
56C2×C4×C263C2×Q811yescharacteristic
57C2×C4×C263#4112yes—
58C2×C4×C263#4111yescharacteristic
59C22×C263—21no—
60C22×C263—21no—
61C22×C263#12011yescharacteristic
62C22×C263C22⋊Q811yescharacteristic
63C22×C263#12411yescharacteristic
64C2×D263—44no—
65C2×D263—42no—
66C2×D263—82no—
67C2×D263—81no—
68C2×D263—81no—
69C4×C263—42no—
70C4×C263—42no—
71C4×C263—42no—
72C4×C263C22⋊Q812yes—
73C4×C263#12412yes—
74Dic263—42no—
75C2×C263—21no—
76C2×C263—21no—
77C2×C263#39311yescharacteristic
78C2×C263#45311yescharacteristic
79C2×C263#45411yescharacteristic
80D263—82no—
81C263#202711yescharacteristic, complemented, Sylow
82#2027—2631nomaximal, Sylow
83#544D26311yescharacteristic, complemented
84#418—2632no—
85#390—2631no—
86#343—2631no—
87#339—2632no—
88C22×D4—2631no—
89C2×M16—2632no—
90C4⋊Q8—22no—
91#125—22no—
92C22⋊Q8—22no—
93#117C2×D26312yes—
94C2×C4⋊C4C2×D26311yescharacteristic
95C2×C22⋊C4—5262no—
96C2×C42—2631no—
97#102—5262no—
98#102—5262no—
99C24—5261no—
100C2×Q8—22no—
101C2×D4—2632no—
102C2×D4—5262no—
103C2×D4—5262no—
104C2×D4—5261no—
105C22×C4—5261no—
106C22×C4C22⋊D26312yes—
107C22×C4C22×D26311yescharacteristic
108M16—5262no—
109M16—5262no—
110C2×C8—5262no—
111C4⋊C4—22no—
112C4⋊C4—24no—
113C4⋊C4—22no—
114C4⋊C4C22⋊D26312yes—
115C4⋊C4C22⋊D26312yes—
116C22⋊C4—22no—
117C22⋊C4—10524no—
118C42—22no—
119C42—5262no—
120C23—5262no—
121C23—10522no—
122C23—10522no—
123C23—10521no—
124C23—10521no—
125C23C2×C22⋊D26311yescharacteristic
126Q8—82no—
127D4—5264no—
128D4—10522no—
129C2×C4—22no—
130C2×C4—22no—
131C2×C4—22no—
132C2×C4—42no—
133C2×C4—5262no—
134C2×C4—10521no—
135C2×C4—10521no—
136C2×C4C2×C22⋊D26312yes—
137C2×C4Q8×D26311yescharacteristic
138C2×C4#1686237712yes—
139C2×C4#1686237711yescharacteristic
140C8—10522no—
141C22—21no—
142C22—21no—
143C22—10524no—
144C22—10522no—
145C22—21042no—
146C22—21041no—
147C22—21041no—
148C22#2255443911yescharacteristic
149C22#2255444611yescharacteristic
150C22#2255445911yescharacteristic
151C4—42no—
152C4—42no—
153C4—42no—
154C4—10522no—
155C4#2255444612yes—
156C4#2255445912yes—
157C2—21no—
158C2—21no—
159C2—21042no—
160C2#3068184911yescharacteristic
161C2#3068210611yescharacteristic
162C2#3068211111yescharacteristic
subgroupG/H
centerC22#22554439
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#544×C263C2
socleC22×C263#120
prime radicalC22×D1052C22
hypercenter#544D263
hypocenterC263#2027
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
3. #30681707C2semidirect
4. #30681697C2semidirect
5. #544×C263C2semidirect
21. C2×D1052Q8semidirect
81. C263#2027semidirect
83. #544D263semidirect

Maximal subgroups

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

subgroupindex
#306819422
#306818392
#306817072
#306816972
#544×C2632
#2027263