Finite Group Databasebeta

← #46783885

Subgroups — #46783885

Order 33664.

290 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C2×#22554393C212yesmaximal
2#30681844C211yesmaximal, characteristic
3#30681700C212yesmaximal
4#30681693C211yesmaximal, characteristic
5C2×C4⋊Q8×C263C211yesmaximal, characteristic
6C22×Dic526C2211yescharacteristic
7C22×C263⋊C8C2212yes—
8C2×C4⋊Dic263C2211yescharacteristic
9#22554393—24no—
10C263⋊#95—21no—
11C263⋊#95—21no—
12C22×Q8×C263—21no—
13C4⋊Q8×C263—24no—
14C2×C4⋊C4×C263—21no—
15C2×C4⋊C4×C263C2212yes—
16C2×C42×C263C2211yescharacteristic
17C2×Dic526—22no—
18C2×Dic526—21no—
19C2×Dic526—22no—
20C2×Dic526Q812yescomplemented
21C22×Dic263—21no—
22C22×Dic263—21no—
23C2×C263⋊C8—22no—
24C2×C263⋊C8—22no—
25C2×C263⋊C8—22no—
26C4⋊Dic263—22no—
27C2×Q8×C263—24no—
28C2×Q8×C263—42no—
29C2×Q8×C263—42no—
30C22×C4×C263—22no—
31C22×C4×C263D411yescharacteristic
32C22×C4×C263D411yescharacteristic
33C22×C4×C263C2311yescharacteristic
34C4⋊C4×C263—24no—
35C4⋊C4×C263—22no—
36C4⋊C4×C263D414yes—
37C42×C263—22no—
38Dic526—24no—
39Dic526—42no—
40C2×Dic263—22no—
41C2×Dic263—41no—
42C2×Dic263—41no—
43C2×Dic263—41no—
44C2×Dic263—41no—
45C2×Dic263—41no—
46C263⋊C8—42no—
47C23×C263C2×D411yescharacteristic
48Q8×C263—48no—
49C2×C4×C263—21no—
50C2×C4×C263—21no—
51C2×C4×C263—21no—
52C2×C4×C263—21no—
53C2×C4×C263—24no—
54C2×C4×C263—42no—
55C2×C4×C263—42no—
56C2×C4×C263SD1612yes—
57C2×C4×C263Q1612yes—
58C2×C4×C263C2×D412yes—
59C2×C4×C263C2×Q811yescharacteristic
60C2×C4×C263#4112yes—
61C2×C4×C263#4111yescharacteristic
62C22×C263#12011yescharacteristic
63C22×C263C22⋊Q811yescharacteristic
64C22×C263#12411yescharacteristic
65C22×C263C2×SD1611yescharacteristic
66C22×C263C2×Q1611yescharacteristic
67C22×C263AGL(1,ℤ/8)11yescharacteristic
68C22×C263#13711yescharacteristic
69C4×C263—22no—
70C4×C263—22no—
71C4×C263—44no—
72C4×C263C22⋊Q812yes—
73C4×C263#12412yes—
74Dic263—42no—
75Dic263—81no—
76C2×C263#39311yescharacteristic
77C2×C263#45011yescharacteristic
78C2×C263#45111yescharacteristic
79C2×C263#47511yescharacteristic
80C2×C263#47711yescharacteristic
81C2×C263#48711yescharacteristic
82C2×C263#48911yescharacteristic
83C263#202411yescharacteristic, complemented, Sylow
84#2024—2631nomaximal, Sylow
85C2×C4⋊Q8D26311yescharacteristic
86C2×#103—2632no—
87#391—2631no—
88#340—2632no—
89#336—2631no—
90C22×Q8—21no—
91C22×Q8—2631no—
92C22×C8—2632no—
93C4⋊Q8—24no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—2631no—
96C2×C4⋊C4C2×D26312yes—
97C2×C42C2×D26311yescharacteristic
98#103—5264no—
99#95—5261no—
100#95—5261no—
101C2×Q8—24no—
102C2×Q8—42no—
103C2×Q8—42no—
104C2×Q8—2632no—
105C2×Q8—5261no—
106C2×Q8—5262no—
107C2×Q8—5262no—
108C22×C4—22no—
109C22×C4—5261no—
110C22×C4—5261no—
111C22×C4C22⋊D26311yescharacteristic
112C22×C4C22⋊D26311yescharacteristic
113C22×C4C22×D26311yescharacteristic
114C2×C8—5262no—
115C2×C8—5262no—
116C2×C8—5262no—
117C4⋊C4—24no—
118C4⋊C4—22no—
119C4⋊C4—5262no—
120C4⋊C4C22⋊D26314yes—
121C42—22no—
122C23C2×C22⋊D26311yescharacteristic
123Q8—48no—
124Q8—5264no—
125Q8—10522no—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—24no—
131C2×C4—42no—
132C2×C4—42no—
133C2×C4—5262no—
134C2×C4—10521no—
135C2×C4—10521no—
136C2×C4—10521no—
137C2×C4—10521no—
138C2×C4—10521no—
139C2×C4#1686236412yes—
140C2×C4#1686236612yes—
141C2×C4C2×C22⋊D26312yes—
142C2×C4Q8×D26311yescharacteristic
143C2×C4#1686237712yes—
144C2×C4#1686237711yescharacteristic
145C8—10522no—
146C22#2255443911yescharacteristic
147C22#2255444611yescharacteristic
148C22#2255445911yescharacteristic
149C22C2×#1686236411yescharacteristic
150C22C2×#1686236611yescharacteristic
151C22#2255449611yescharacteristic
152C22#2255450111yescharacteristic
153C4—22no—
154C4—22no—
155C4—44no—
156C4—10522no—
157C4—21041no—
158C4#2255444612yes—
159C4#2255445912yes—
160C2#3068184911yescharacteristic
161C2#3068208911yescharacteristic
162C2#3068209411yescharacteristic
163C2#3068222011yescharacteristic
164C2#3068223011yescharacteristic
165C2#3068229011yescharacteristic
166C2#3068230011yescharacteristic
subgroupG/H
centerC23C2×C22⋊D263
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
FittingC2×C4⋊Q8×C263C2
socle, prime radicalC23×C263C2×D4
hypercenterC2×C4⋊Q8D263
hypocenterC263#2024
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
20. C2×Dic526Q8semidirect
83. C263#2024semidirect

Maximal subgroups

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

subgroupindex
C2×#225543932
#306818442
#306817002
#306816932
C2×C4⋊Q8×C2632
#2024263