Finite Group Databasebeta

← #46782852

Subgroups — #46782852

Order 33664.

262 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 81 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#41×Dic263C211yesmaximal, characteristic
2#30681912C211yesmaximal, characteristic
3#30681699C212yesmaximal, complemented
4#30681695C212yesmaximal, complemented
5#413×C263C211yesmaximal, characteristic
6Q8×Dic263—21no—
7D4×Dic263—21no—
8D4×Dic263—22no—
9#22554429C412yescomplemented
10#22554429C2212yes—
11#22554429C2211yescharacteristic
12C2×C4×Dic263C412yescomplemented
13C2×C4×Dic263C2211yescharacteristic
14#22554385—22no—
15C2×#41×C263C2211yescharacteristic
16C2×M16×C263C2212yes—
17#101×C263—21no—
18#100×C263—21no—
19C22×Dic263—22no—
20C22×Dic263—21no—
21C4⋊Dic263—22no—
22C4⋊Dic263—21no—
23C4⋊Dic263—22no—
24C22⋊Dic263—22no—
25C22⋊Dic263—21no—
26C22⋊Dic263—22no—
27C4×Dic263—22no—
28C4×Dic263—21no—
29C4×Dic263—22no—
30C4×Dic263C2×C411yescharacteristic
31C4×Dic263C2×C412yes—
32C4×Dic263C2×C411yescharacteristic
33#41×C263—22no—
34#41×C263—22no—
35C2×Q8×C263D411yescharacteristic
36C2×D4×C263D411yescharacteristic
37C2×D4×C263D412yes—
38C22×C4×C263C2×C412yes—
39C22×C4×C263C2311yescharacteristic
40M16×C263—22no—
41M16×C263—22no—
42C2×C8×C263—22no—
43C2×Dic263—21no—
44C2×Dic263—22no—
45C2×Dic263—21no—
46C2×Dic263—42no—
47C2×Dic263—44no—
48C2×Dic263—42no—
49C23×C263C22⋊C412yes—
50C23×C263C2×D411yescharacteristic
51Q8×C263—22no—
52D4×C263—24no—
53D4×C263—22no—
54C2×C4×C263—22no—
55C2×C4×C263—22no—
56C2×C4×C263C22⋊C412yes—
57C2×C4×C263C22×C411yescharacteristic
58C2×C4×C263C2×D411yescharacteristic
59C2×C4×C263#4112yes—
60C2×C4×C263#4112yes—
61C8×C263—42no—
62C22×C263—22no—
63C22×C263—41no—
64C22×C263—42no—
65C22×C263C2×C22⋊C411yescharacteristic
66C22×C263#12312yes—
67C4×C263—22no—
68C4×C263#11711yescharacteristic
69C4×C263#11711yescharacteristic
70C4×C263#12312yes—
71Dic263—22no—
72Dic263—42no—
73Dic263—41no—
74Dic263—82no—
75C2×C263—21no—
76C2×C263—22no—
77C2×C263—42no—
78C2×C263#38111yescharacteristic
79C263#182711yescharacteristic, complemented, Sylow
80#1827—2631nomaximal, Sylow
81C4×#41—2631no—
82#413D26311yescharacteristic
83#410—2631no—
84#339—2632no—
85H(3,ℤ/4)—2632no—
86C2×#41C2×D26311yescharacteristic
87C2×M16C2×D26312yes—
88C4×Q8—5261no—
89C4×D4—5261no—
90C4×D4—5262no—
91#117—2632no—
92#117—2631no—
93#117—2632no—
94C2×C42—2632no—
95C2×C42—2631no—
96#101—21no—
97#100—21no—
98#99—5262no—
99#41—22no—
100#41—22no—
101C2×Q8C22⋊D26311yescharacteristic
102C2×D4C22⋊D26311yescharacteristic
103C2×D4D105212yes—
104C22×C4—5262no—
105C22×C4—5261no—
106C22×C4C4×D26312yes—
107C22×C4C22×D26311yescharacteristic
108M16—22no—
109M16—22no—
110C2×C8—22no—
111C4⋊C4—5262no—
112C4⋊C4—5261no—
113C4⋊C4—5262no—
114C22⋊C4—5262no—
115C22⋊C4—5261no—
116C22⋊C4—5262no—
117C42—2631no—
118C42—2632no—
119C42—2631no—
120C42—5262no—
121C42—5261no—
122C42—5262no—
123C23(C2×D263)⋊C412yes—
124C23C2×D105211yescharacteristic
125Q8—22no—
126D4—24no—
127D4—22no—
128C2×C4—22no—
129C2×C4—22no—
130C2×C4—5261no—
131C2×C4—5262no—
132C2×C4—5261no—
133C2×C4—10522no—
134C2×C4—10524no—
135C2×C4—10522no—
136C2×C4(C2×D263)⋊C412yes—
137C2×C4C2×C4×D26311yescharacteristic
138C2×C4C2×C22⋊D26311yescharacteristic
139C2×C4#1686237512yes—
140C2×C4#1686237512yes—
141C8—42no—
142C22—22no—
143C22—41no—
144C22—42no—
145C22C2×(C2×D263)⋊C411yescharacteristic
146C22#2255445412yes—
147C4—22no—
148C4—5262no—
149C4—10522no—
150C4—10521no—
151C4—21042no—
152C4#2255442611yescharacteristic
153C4#2255442611yescharacteristic
154C4#2255445112yes—
155C2—21no—
156C2—22no—
157C2—42no—
158C2#3068179911yescharacteristic
subgroupG/H
centerC4#22554426
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#413×C263C2
socleC2×C263#381
prime radicalC2×#41×C263C22
cosocleC22×C4×C263C23
hypercenter#413D263
hypocenterC263#1827
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
3. #30681699C2semidirect
4. #30681695C2semidirect
9. #22554429C4semidirect
12. C2×C4×Dic263C4semidirect
79. C263#1827semidirect

Maximal subgroups

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

subgroupindex
#41×Dic2632
#306819122
#306816992
#306816952
#413×C2632
#1827263