Finite Group Databasebeta

← #46783284

Subgroups — #46783284

Order 33664.

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

normal subgroups only

This group has 314 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#30682512C211yesmaximal, characteristic
2#30681956C212yesmaximal
3C2×#22554389C211yesmaximal, characteristic, complemented
4#30681694C212yesmaximal, complemented
5#519×C263C211yesmaximal, characteristic, complemented
6C2×#16862376C2211yescharacteristic
7C2×#16862360C2212yes—
8#22554468C412yescomplemented
9#22554459C412yescomplemented
10#22554453—22no—
11#22554446—22no—
12#22554429C2211yescharacteristic
13#22554398—24no—
14#22554389—22no—
15C22×Q8×C263C2211yescharacteristic
16C4×Q8×C263—24no—
17#117×C263—22no—
18#117×C263C2212yes—
19#16862376—22no—
20#16862376—22no—
21C2×Dic526C2×C411yescharacteristic
22C2×D1052C2×C411yescharacteristic
23C2×C22⋊D263—21no—
24C2×C4×D263—21no—
25#16862360—22no—
26#16862360—22no—
27C2×C263⋊C8—22no—
28C4⋊Dic263—21no—
29Dic263⋊C4—24no—
30C22⋊Dic263—21no—
31(C2×D263)⋊C4—24no—
32C4×Dic263C2×C412yes—
33C2×Q8×C263—22no—
34C2×Q8×C263—22no—
35C2×Q8×C263C2×C412yes—
36C2×Q8×C263D412yes—
37C22×C4×C263D412yes—
38C22×C4×C263C2311yescharacteristic
39C4⋊C4×C263—24no—
40C4⋊C4×C263—22no—
41C22⋊C4×C263—22no—
42C42×C263—24no—
43C42×C263D414yes—
44C22×D263—21no—
45Dic526—22no—
46D1052—22no—
47C22⋊D263—41no—
48C22⋊D263—41no—
49C2×Dic263—22no—
50C2×Dic263—21no—
51C4×D263—42no—
52C263⋊C8—42no—
53C23×C263C2×D411yescharacteristic
54Q8×C263—24no—
55Q8×C263—24no—
56C2×C4×C263—22no—
57C2×C4×C263—22no—
58C2×C4×C263—24no—
59C2×C4×C263C22⋊C414yes—
60C2×C4×C263C22×C411yescharacteristic
61C2×C4×C263C2×D412yes—
62C2×C4×C263C2×D411yescharacteristic
63C2×C4×C263#4112yes—
64C22×C263—41no—
65C22×C263C2×C22⋊C411yescharacteristic
66C22×C263#12011yescharacteristic
67C22×C263#12311yescharacteristic
68C2×D263—42no—
69C2×D263—41no—
70C4×C263—24no—
71C4×C263—44no—
72C4×C263C4×D412yes—
73C4×C263#12112yes—
74Dic263—42no—
75Dic263—41no—
76C2×C263—21no—
77C2×C263—21no—
78C2×C263—21no—
79C2×C263#38611yescharacteristic
80D263—81no—
81C263#191211yescharacteristic, complemented, Sylow
82#1912—2631nomaximal, Sylow
83#536—2631no—
84#519D26311yescharacteristic, complemented
85#421—2632no—
86C2×#101—2631no—
87H(3,ℤ/4)—2632no—
88C2×#41—2631no—
89C22×Q8C2×D26311yescharacteristic
90C2×M16—2632no—
91C4⋊Q8—2632no—
92#124—2632no—
93#123—5262no—
94C22⋊Q8—5262no—
95C4×Q8—24no—
96#117—22no—
97#117—2631no—
98#117C2×D26312yes—
99#104—5264no—
100#101—5262no—
101#41—5262no—
102#41—5262no—
103C2×Q8—22no—
104C2×Q8—22no—
105C2×Q8—2631no—
106C2×Q8C4×D26312yes—
107C2×Q8D105212yes—
108C2×D4—2631no—
109C2×D4—5261no—
110C22×C4—5261no—
111C22×C4C22⋊D26312yes—
112C22×C4C22×D26311yescharacteristic
113M16—5262no—
114M16—5262no—
115C2×C8—5262no—
116C4⋊C4—24no—
117C4⋊C4—22no—
118C4⋊C4—5264no—
119C4⋊C4—5261no—
120C22⋊C4—22no—
121C22⋊C4—5261no—
122C22⋊C4—5264no—
123C42—24no—
124C42—2632no—
125C42C22⋊D26314yes—
126C23—5261no—
127C23C2×C22⋊D26311yescharacteristic
128Q8—24no—
129Q8—24no—
130Q8—5262no—
131D4—5262no—
132D4—10521no—
133D4—10521no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—24no—
137C2×C4—5262no—
138C2×C4—5261no—
139C2×C4—10522no—
140C2×C4(C2×D263)⋊C414yes—
141C2×C4C2×C4×D26311yescharacteristic
142C2×C4C2×C22⋊D26312yes—
143C2×C4C2×D105211yescharacteristic
144C2×C4#1686237612yes—
145C8—10522no—
146C22—41no—
147C22—10522no—
148C22—10521no—
149C22C2×(C2×D263)⋊C411yescharacteristic
150C22#2255443911yescharacteristic
151C22#2255445311yescharacteristic
152C4—24no—
153C4—44no—
154C4—10522no—
155C4—10521no—
156C4C4×C22⋊D26312yes—
157C4#2255444412yes—
158C2—21no—
159C2—21no—
160C2—21no—
161C2—21041no—
162C2#3068181711yescharacteristic
subgroupG/H
centerC2#30681817
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#519×C263C2
socleC2×C263#386
prime radicalC2×#16862376C22
cosocleC22×C4×C263C23
hypercenter#519D263
hypocenterC263#1912
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2 ◁ C22×C4 ◁ #519

Complements

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

NH ≅ G/Ntype
3. C2×#22554389C2semidirect
4. #30681694C2semidirect
5. #519×C263C2semidirect
8. #22554468C4semidirect
9. #22554459C4semidirect
81. C263#1912semidirect
84. #519D263semidirect

Maximal subgroups

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

subgroupindex
#306825122
#306819562
C2×#225543892
#306816942
#519×C2632
#1912263