Finite Group Databasebeta

← #46783059

Subgroups — #46783059

Order 33664.

360 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 109 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×#22554449C211yesmaximal, characteristic
2C2×#22554393C212yesmaximal, complemented
3C2×C22⋊(C263⋊C8)C211yesmaximal, characteristic
4#30681700C212yesmaximal, complemented
5C2×#117×C263C211yesmaximal, characteristic
6C22×Dic526C2211yescharacteristic
7C22×C263⋊C8C2212yes—
8#22554449—22no—
9#22554449C414yescomplemented
10C2×C4⋊Dic263C2211yescharacteristic
11C2×Dic263⋊C4—21no—
12C2×C22⋊Dic263—21no—
13#22554393—24no—
14C22⋊(C263⋊C8)—22no—
15C23×C4×C263C2211yescharacteristic
16#117×C263—24no—
17C2×C4⋊C4×C263C2212yes—
18C2×C22⋊C4×C263—21no—
19C2×C42×C263—21no—
20C2×Dic526—21no—
21C2×Dic526—22no—
22C2×Dic526—22no—
23C2×Dic526C2×C412yes—
24C22×Dic263—21no—
25C22×Dic263—21no—
26C2×C263⋊C8—22no—
27C2×C263⋊C8—22no—
28C2×C263⋊C8—22no—
29C4⋊Dic263—21no—
30C4⋊Dic263C2×C412yes—
31Dic263⋊C4—24no—
32C22⋊Dic263—24no—
33C24×C263D411yescharacteristic
34C22×C4×C263—22no—
35C22×C4×C263—22no—
36C22×C4×C263—22no—
37C22×C4×C263C2×C412yes—
38C22×C4×C263D411yescharacteristic
39C22×C4×C263D412yes—
40C22×C4×C263C2311yescharacteristic
41C4⋊C4×C263—22no—
42C4⋊C4×C263D414yes—
43C22⋊C4×C263—24no—
44C42×C263—24no—
45Dic526—24no—
46Dic526—42no—
47C2×Dic263—22no—
48C2×Dic263—22no—
49C2×Dic263—41no—
50C2×Dic263—41no—
51C2×Dic263—42no—
52C263⋊C8—42no—
53C23×C263—21no—
54C23×C263—21no—
55C23×C263—22no—
56C23×C263—22no—
57C23×C263C22⋊C412yes—
58C23×C263C2×D411yescharacteristic
59C2×C4×C263—21no—
60C2×C4×C263—21no—
61C2×C4×C263—24no—
62C2×C4×C263—24no—
63C2×C4×C263—24no—
64C2×C4×C263—42no—
65C2×C4×C263—42no—
66C2×C4×C263C22⋊C412yes—
67C2×C4×C263C22×C411yescharacteristic
68C2×C4×C263C2×D412yes—
69C2×C4×C263C2×D411yescharacteristic
70C2×C4×C263#4112yes—
71C22×C263—22no—
72C22×C263—22no—
73C22×C263—22no—
74C22×C263—42no—
75C22×C263—42no—
76C22×C263C2×C22⋊C411yescharacteristic
77C22×C263#12011yescharacteristic
78C22×C263#12311yescharacteristic
79C22×C263#13512yes—
80C22×C263#13712yes—
81C4×C263—22no—
82C4×C263—44no—
83C4×C263C4×D412yes—
84C4×C263#12112yes—
85Dic263—42no—
86Dic263—42no—
87C2×C263—42no—
88C2×C263#38611yescharacteristic
89C2×C263#41611yescharacteristic
90C2×C263#41911yescharacteristic
91C2×C263#45212yes—
92C2×C263#48512yes—
93C263#187311yescharacteristic, complemented, Sylow
94#1873—2631nomaximal, Sylow
95C2×C22⋊Q8—2631no—
96C2×#117D26311yescharacteristic
97C2×#103—2632no—
98C2×C22⋊C8—2631no—
99#340—2632no—
100C22×Q8—2631no—
101C23×C4C2×D26311yescharacteristic
102C22×C8—2632no—
103C22⋊Q8—2634no—
104C22⋊Q8—5262no—
105#117—24no—
106C2×C4⋊C4—2631no—
107C2×C4⋊C4—5261no—
108C2×C4⋊C4C2×D26312yes—
109C2×C22⋊C4—21no—
110C2×C22⋊C4—5261no—
111C2×C42—21no—
112#103—5264no—
113C22⋊C8—5262no—
114C24C22⋊D26311yescharacteristic
115C2×Q8—2632no—
116C2×Q8—5261no—
117C2×Q8—5262no—
118C2×Q8—5262no—
119C22×C4—22no—
120C22×C4—22no—
121C22×C4—22no—
122C22×C4—5261no—
123C22×C4—5261no—
124C22×C4C4×D26312yes—
125C22×C4C22⋊D26311yescharacteristic
126C22×C4D105212yes—
127C22×C4C22×D26311yescharacteristic
128C2×C8—5262no—
129C2×C8—5262no—
130C2×C8—5262no—
131C4⋊C4—22no—
132C4⋊C4—2632no—
133C4⋊C4—5264no—
134C4⋊C4—5261no—
135C4⋊C4C22⋊D26314yes—
136C22⋊C4—24no—
137C22⋊C4—5264no—
138C42—24no—
139C23—21no—
140C23—21no—
141C23—22no—
142C23—22no—
143C23(C2×D263)⋊C412yes—
144C23C2×C22⋊D26311yescharacteristic
145Q8—5264no—
146Q8—10522no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—24no—
150C2×C4—24no—
151C2×C4—24no—
152C2×C4—42no—
153C2×C4—42no—
154C2×C4—5262no—
155C2×C4—5262no—
156C2×C4—10521no—
157C2×C4—10521no—
158C2×C4—10522no—
159C2×C4(C2×D263)⋊C412yes—
160C2×C4C2×C4×D26311yescharacteristic
161C2×C4C2×C22⋊D26312yes—
162C2×C4C2×D105211yescharacteristic
163C2×C4#1686237612yes—
164C8—10522no—
165C22—22no—
166C22—22no—
167C22—22no—
168C22—42no—
169C22—42no—
170C22C2×(C2×D263)⋊C411yescharacteristic
171C22#2255443911yescharacteristic
172C22#2255445311yescharacteristic
173C22#2255449012yes—
174C22#2255450012yes—
175C4—22no—
176C4—44no—
177C4—10522no—
178C4—10522no—
179C4C4×C22⋊D26312yes—
180C4#2255444412yes—
181C2—42no—
182C2#3068181711yescharacteristic
183C2#3068193211yescharacteristic
184C2#3068194611yescharacteristic
185C2#3068210012yes—
186C2#3068227912yes—
subgroupG/H
centerC23C2×C22⋊D263
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
FittingC2×#117×C263C2
socleC23×C263C2×D4
prime radicalC24×C263D4
cosocleC22×C4×C263C23
hypercenterC2×#117D263
hypocenterC263#1873
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. C2×#22554393C2semidirect
4. #30681700C2semidirect
9. #22554449C4semidirect
93. C263#1873semidirect

Maximal subgroups

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

subgroupindex
C2×#225544492
C2×#225543932
C2×C22⋊(C263⋊C8)2
#306817002
C2×#117×C2632
#1873263