Finite Group Databasebeta

← #46783915

Subgroups — #46783915

Order 33664.

290 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 67 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#30682564C211yesmaximal, characteristic
2#30681799C212yesmaximal
3#30681799C211yesmaximal, characteristic
4#30681704C212yesmaximal
5#342×C263C211yesmaximal, characteristic
6C23×Dic263C2211yescharacteristic
7#22554449—22no—
8#22554447—24no—
9C2×C22⋊Dic263C2211yescharacteristic
10C2×C22⋊Dic263C2212yes—
11C263⋊#95—24no—
12C263⋊#95—22no—
13C2×C22⋊C4×C263C2212yes—
14C2×C22⋊C4×C263C2211yescharacteristic
15C2×Dic526—22no—
16C22×Dic263—22no—
17C22×Dic263—21no—
18C22×Dic263—21no—
19C22×Dic263—21no—
20C22×Dic263—22no—
21C22×Dic263D414yes—
22C22×Dic263Q812yescomplemented
23C4⋊Dic263—22no—
24Dic263⋊C4—24no—
25C22⋊Dic263—22no—
26C22⋊Dic263—22no—
27C22⋊Dic263—22no—
28C24×C263C2311yescharacteristic
29C22×C4×C263—22no—
30C22×C4×C263D412yes—
31C22⋊C4×C263—22no—
32C22⋊C4×C263—22no—
33C22⋊C4×C263—22no—
34Dic526—82no—
35C2×Dic263—24no—
36C2×Dic263—24no—
37C2×Dic263—22no—
38C2×Dic263—41no—
39C2×Dic263—42no—
40C2×Dic263—41no—
41C2×Dic263—44no—
42C2×Dic263—42no—
43C2×Dic263—41no—
44C23×C263—42no—
45C23×C263C2×D412yes—
46C23×C263C2×D411yescharacteristic
47C23×C263C2×Q811yescharacteristic
48C23×C263#4111yescharacteristic
49C23×C263#4112yes—
50C2×C4×C263—22no—
51C2×C4×C263—42no—
52C2×C4×C263—44no—
53C2×C4×C263—42no—
54C22×C263—24no—
55C22×C263—22no—
56C22×C263—41no—
57C22×C263—41no—
58C22×C263—42no—
59C22×C263#12011yescharacteristic
60C22×C263C22⋊Q812yes—
61C22×C263C22⋊Q811yescharacteristic
62C22×C263#12412yes—
63C22×C263#12411yescharacteristic
64C4×C263—42no—
65C4×C263—82no—
66Dic263—42no—
67Dic263—44no—
68Dic263—81no—
69C2×C263—21no—
70C2×C263—22no—
71C2×C263—22no—
72C2×C263—21no—
73C2×C263#39311yescharacteristic
74C2×C263#45812yes—
75C263#203011yescharacteristic, complemented, Sylow
76#2030—2631nomaximal, Sylow
77#543—2631no—
78#381—2632no—
79#381—2631no—
80#342—2632no—
81#342D26311yescharacteristic
82C23×C4—2631no—
83C22⋊Q8—5264no—
84C22⋊Q8—5262no—
85C2×C22⋊C4—2632no—
86C2×C22⋊C4—2631no—
87C2×C22⋊C4C2×D26312yes—
88C2×C22⋊C4C2×D26311yescharacteristic
89#95—5264no—
90#95—5262no—
91C24C22×D26311yescharacteristic
92C2×Q8—5262no—
93C22×C4—22no—
94C22×C4—2632no—
95C22×C4—2634no—
96C22×C4—5262no—
97C22×C4—5261no—
98C22×C4—5261no—
99C22×C4—5262no—
100C22×C4—5261no—
101C22×C4D105212yes—
102C4⋊C4—5264no—
103C4⋊C4—5262no—
104C22⋊C4—22no—
105C22⋊C4—22no—
106C22⋊C4—22no—
107C22⋊C4—5262no—
108C22⋊C4—5262no—
109C22⋊C4—5262no—
110C23—42no—
111C23D4×D26312yes—
112C23C2×D105211yescharacteristic
113C23Q8×D26311yescharacteristic
114C23#1686237511yescharacteristic
115C23#1686237612yes—
116Q8—21042no—
117C2×C4—22no—
118C2×C4—42no—
119C2×C4—44no—
120C2×C4—42no—
121C2×C4—5264no—
122C2×C4—5264no—
123C2×C4—5262no—
124C2×C4—10521no—
125C2×C4—10522no—
126C2×C4—10521no—
127C2×C4—10524no—
128C2×C4—10522no—
129C2×C4—10521no—
130C22—24no—
131C22—22no—
132C22—41no—
133C22—41no—
134C22—42no—
135C22#2255444011yescharacteristic
136C22#2255444812yes—
137C22#2255445011yescharacteristic
138C22#2255445612yes—
139C22#2255445811yescharacteristic
140C4—42no—
141C4—82no—
142C4—10524no—
143C4—10522no—
144C4—21041no—
145C2—22no—
146C2—21no—
147C2—22no—
148C2—21no—
149C2#3068185111yescharacteristic
150C2#3068212912yes—
subgroupG/H
centerC22#22554440
commutator, prime radical, cosocleC24×C263C23
FrattiniC24C22×D263
Fitting#342×C263C2
socleC22×C263#120
hypercenter#342D263
hypocenterC263#2030
LCSG ▷ C24×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
22. C22×Dic263Q8semidirect
75. C263#2030semidirect

Maximal subgroups

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

subgroupindex
#306825642
#306817992
#306817042
#342×C2632
#2030263