Finite Group Databasebeta

← #46783269

Subgroups — #46783269

Order 33664.

312 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 89 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#30682509C211yesmaximal, characteristic
2#30681948C212yesmaximal, complemented
3#30681912C211yesmaximal, characteristic
4#30681695C212yesmaximal, complemented
5#568×C263C211yesmaximal, characteristic
6C22×Dic526C2211yescharacteristic
7#22554468C412yescomplemented
8#22554457C412yescomplemented
9#22554451—22no—
10#22554449—22no—
11#22554429C2212yes—
12#22554429C2211yescharacteristic
13#22554395—24no—
14#22554385—22no—
15C2×#41×C263C2211yescharacteristic
16#131×C263—24no—
17C2×M16×C263—22no—
18C2×M16×C263C2212yes—
19C2×Dic526—21no—
20C2×Dic526—22no—
21C2×Dic526—22no—
22C2×Dic526C2×C412yes—
23C22×Dic263—21no—
24C4⋊Dic263—21no—
25C4⋊Dic263—22no—
26Dic263⋊C4—24no—
27C22⋊Dic263—24no—
28C22⋊Dic263—21no—
29C22⋊Dic263—22no—
30C4×Dic263—22no—
31C4×Dic263C2×C412yes—
32#41×C263—22no—
33#41×C263—22no—
34C2×Q8×C263C2×C411yescharacteristic
35C2×D4×C263C2×C411yescharacteristic
36C2×D4×C263D412yes—
37C22×C4×C263D412yes—
38C22×C4×C263C2311yescharacteristic
39M16×C263—24no—
40M16×C263—22no—
41M16×C263—22no—
42C2×C8×C263—24no—
43C2×C8×C263D414yes—
44Dic526—24no—
45Dic526—41no—
46Dic526—41no—
47C2×Dic263—22no—
48C2×Dic263—22no—
49C2×Dic263—42no—
50C2×Dic263—42no—
51C23×C263C22⋊C412yes—
52C23×C263C2×D411yescharacteristic
53Q8×C263—22no—
54D4×C263—24no—
55D4×C263—22no—
56C2×C4×C263—22no—
57C2×C4×C263—22no—
58C2×C4×C263C22⋊C412yes—
59C2×C4×C263C22×C411yescharacteristic
60C2×C4×C263C2×D412yes—
61C2×C4×C263C2×D411yescharacteristic
62C2×C4×C263#4112yes—
63C8×C263—24no—
64C22×C263—22no—
65C22×C263—41no—
66C22×C263—42no—
67C22×C263C2×C22⋊C411yescharacteristic
68C22×C263#12112yes—
69C4×C263—22no—
70C4×C263C4×D412yes—
71C4×C263#12011yescharacteristic
72C4×C263#12311yescharacteristic
73Dic263—42no—
74Dic263—42no—
75Dic263—82no—
76C2×C263—21no—
77C2×C263—22no—
78C2×C263—42no—
79C2×C263#38611yescharacteristic
80C263#190911yescharacteristic, complemented, Sylow
81#1909—2631nomaximal, Sylow
82#568D26311yescharacteristic
83#536—2631no—
84#419—2632no—
85#410—2631no—
86H(3,ℤ/4)—2632no—
87C2×#41C2×D26311yescharacteristic
88C22×Q8—2631no—
89#131—24no—
90C2×M16—22no—
91C2×M16C2×D26312yes—
92C4⋊Q8—2632no—
93#124—2632no—
94#123—5262no—
95C22⋊Q8—5262no—
96#117—2631no—
97#117—2632no—
98#103—5264no—
99#99—5262no—
100#41—22no—
101#41—22no—
102C2×Q8—2632no—
103C2×Q8—5261no—
104C2×Q8—5262no—
105C2×Q8—5262no—
106C2×Q8C4×D26311yescharacteristic
107C2×D4C4×D26311yescharacteristic
108C2×D4D105212yes—
109C22×C4—5261no—
110C22×C4C22⋊D26312yes—
111C22×C4C22×D26311yescharacteristic
112M16—24no—
113M16—22no—
114M16—22no—
115C2×C8—24no—
116C2×C8C22⋊D26314yes—
117C4⋊C4—5264no—
118C4⋊C4—5261no—
119C4⋊C4—5262no—
120C22⋊C4—5264no—
121C22⋊C4—5261no—
122C22⋊C4—5262no—
123C42—2632no—
124C42—5262no—
125C23(C2×D263)⋊C412yes—
126C23C2×D105211yescharacteristic
127Q8—22no—
128Q8—5264no—
129Q8—10521no—
130Q8—10521no—
131D4—24no—
132D4—22no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—5262no—
136C2×C4—5262no—
137C2×C4—10522no—
138C2×C4—10522no—
139C2×C4(C2×D263)⋊C412yes—
140C2×C4C2×C4×D26311yescharacteristic
141C2×C4C2×C22⋊D26312yes—
142C2×C4C2×C22⋊D26311yescharacteristic
143C2×C4#1686237612yes—
144C8—24no—
145C22—22no—
146C22—41no—
147C22—42no—
148C22C2×(C2×D263)⋊C411yescharacteristic
149C22#2255444412yes—
150C4—22no—
151C4—10522no—
152C4—10522no—
153C4—21042no—
154C4C4×C22⋊D26312yes—
155C4#2255443911yescharacteristic
156C4#2255445311yescharacteristic
157C2—21no—
158C2—22no—
159C2—42no—
160C2#3068181711yescharacteristic
subgroupG/H
centerC2#30681817
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#568×C263C2
socleC2×C263#386
prime radicalC2×#41×C263C22
cosocleC22×C4×C263C23
hypercenter#568D263
hypocenterC263#1909
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #30681948C2semidirect
4. #30681695C2semidirect
7. #22554468C4semidirect
8. #22554457C4semidirect
80. C263#1909semidirect

Maximal subgroups

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

subgroupindex
#306825092
#306819482
#306819122
#306816952
#568×C2632
#1909263