Finite Group Databasebeta

← #46783903

Subgroups — #46783903

Order 33664.

282 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 69 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#30682569C211yesmaximal, characteristic, complemented
2#30681943C212yesmaximal
3#30681707C211yesmaximal, characteristic, complemented
4#30681698C212yesmaximal, complemented
5#390×C263C211yesmaximal, characteristic
6C2×#16862360C2212yes—
7#22554469—22no—
8#22554461—22no—
9#22554449—22no—
10#22554429C2212yes—
11#22554391—22no—
12#22554391—22no—
13C22×D4×C263C2211yescharacteristic
14C2×C4⋊C4×C263C2211yescharacteristic
15C2×C22⋊C4×C263—22no—
16C2×C42×C263C2211yescharacteristic
17C2×Dic526—22no—
18#16862360—22no—
19#16862360—22no—
20C2×C263⋊C8—22no—
21C4⋊Dic263—22no—
22C4⋊Dic263D412yes—
23C4⋊Dic263D412yes—
24Dic263⋊C4—24no—
25C22⋊Dic263—22no—
26C4×Dic263—22no—
27C24×C263—21no—
28C2×D4×C263—22no—
29C2×D4×C263—22no—
30C2×D4×C263—21no—
31C2×D4×C263Q812yescomplemented
32C22×C4×C263—21no—
33C22×C4×C263D412yes—
34C22×C4×C263C2311yescharacteristic
35C4⋊C4×C263—22no—
36C22⋊C4×C263—44no—
37C42×C263—22no—
38Dic526—82no—
39C2×Dic263—22no—
40C2×Dic263—22no—
41C263⋊C8—42no—
42C23×C263—22no—
43C23×C263—42no—
44C23×C263—42no—
45C23×C263—41no—
46C23×C263—41no—
47C23×C263C2×D411yescharacteristic
48D4×C263—24no—
49D4×C263—42no—
50C2×C4×C263—22no—
51C2×C4×C263—22no—
52C2×C4×C263—41no—
53C2×C4×C263—41no—
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—44no—
62C22×C263—42no—
63C22×C263—82no—
64C22×C263—81no—
65C22×C263—81no—
66C22×C263#12011yescharacteristic
67C22×C263C22⋊Q811yescharacteristic
68C22×C263#12411yescharacteristic
69C4×C263—42no—
70C4×C263—42no—
71C4×C263C22⋊Q812yes—
72C4×C263#12412yes—
73Dic263—42no—
74Dic263—42no—
75C2×C263—21no—
76C2×C263—21no—
77C2×C263—82no—
78C2×C263#39311yescharacteristic
79C2×C263#45311yescharacteristic
80C2×C263#45411yescharacteristic
81C263#202711yescharacteristic, complemented, Sylow
82#2027—2631nomaximal, Sylow
83#544—2631no—
84#418—2632no—
85#390D26311yescharacteristic
86#343—2631no—
87#339—2632no—
88C22×D4C2×D26311yescharacteristic
89C2×M16—2632no—
90C4⋊Q8—5262no—
91#125—5262no—
92C22⋊Q8—5262no—
93#117—2632no—
94C2×C4⋊C4C2×D26311yescharacteristic
95C2×C22⋊C4—22no—
96C2×C42C2×D26311yescharacteristic
97#102—5262no—
98#102—5262no—
99C24—21no—
100C2×Q8—5262no—
101C2×D4—22no—
102C2×D4—22no—
103C2×D4—21no—
104C2×D4Dic52612yescomplemented
105C22×C4—21no—
106C22×C4C22⋊D26312yes—
107C22×C4C22×D26311yescharacteristic
108M16—5262no—
109M16—5262no—
110C2×C8—5262no—
111C4⋊C4—22no—
112C4⋊C4—2632no—
113C4⋊C4—2632no—
114C4⋊C4—5262no—
115C4⋊C4—5264no—
116C22⋊C4—44no—
117C22⋊C4—5262no—
118C42—22no—
119C42—5262no—
120C23—22no—
121C23—42no—
122C23—42no—
123C23—41no—
124C23—41no—
125C23C2×C22⋊D26311yescharacteristic
126Q8—21042no—
127D4—24no—
128D4—42no—
129C2×C4—22no—
130C2×C4—22no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—42no—
134C2×C4—5262no—
135C2×C4—5262no—
136C2×C4D4×D26312yes—
137C2×C4C2×Dic52611yescharacteristic
138C2×C4#1686237512yes—
139C2×C4#1686237611yescharacteristic
140C8—10522no—
141C22—21no—
142C22—21no—
143C22—44no—
144C22—42no—
145C22—82no—
146C22—81no—
147C22—81no—
148C22#2255443811yescharacteristic
149C22#2255444911yescharacteristic
150C22#2255445711yescharacteristic
151C4—42no—
152C4—42no—
153C4—10522no—
154C4—10522no—
155C4#2255444712yes—
156C4#2255445612yes—
157C2—21no—
158C2—21no—
159C2—82no—
160C2#3068185011yescharacteristic
161C2#3068210511yescharacteristic
162C2#3068211011yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#390×C263C2
socleC22×C263#120
prime radicalC22×D4×C263C22
hypercenter#390D263
hypocenterC263#2027
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #30682569C2semidirect
3. #30681707C2semidirect
4. #30681698C2semidirect
31. C2×D4×C263Q8semidirect
81. C263#2027semidirect
104. C2×D4Dic526semidirect

Maximal subgroups

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

subgroupindex
#306825692
#306819432
#306817072
#306816982
#390×C2632
#2027263