Finite Group Databasebeta

← #46782664

Subgroups — #46782664

Order 33664.

612 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C22×#16862376C211yesmaximal, characteristic
2C2×#22554384C214yesmaximal, complemented
3#30681801C211yesmaximal, characteristic, complemented
4#381×C263C211yesmaximal, characteristic, complemented
5C2×#16862376—28no—
6C2×#16862376—22no—
7C2×#16862376—22no—
8C22×Dic526C411yescharacteristic, complemented
9C22×D1052C411yescharacteristic, complemented
10C22×C22⋊D263C2212yes—
11C22×C4×D263C412yescomplemented
12C2×C22⋊Dic263C2212yes—
13#22554384—28no—
14C263⋊#95—22no—
15C23×C4×C263C2211yescharacteristic
16C2×C22⋊C4×C263C2212yes—
17#95×C263—22no—
18C23×D263C2×C412yes—
19#16862376—216no—
20#16862376—216no—
21C2×Dic526—24no—
22C2×Dic526—22no—
23C2×D1052—24no—
24C2×D1052—22no—
25C2×C22⋊D263—24no—
26C2×C22⋊D263—22no—
27C2×C22⋊D263—22no—
28C2×C22⋊D263D418yes—
29C22×Dic263—22no—
30C22×Dic263C2×C412yes—
31C2×C4×D263—24no—
32C2×C4×D263—24no—
33C2×C4×D263—24no—
34C22⋊Dic263—24no—
35C24×C263C2311yescharacteristic
36C22×C4×C263—24no—
37C22×C4×C263—22no—
38C22×C4×C263C2×C411yescharacteristic
39C22×C4×C263C2×C411yescharacteristic
40C22×C4×C263D412yes—
41C22×C4×C263D412yes—
42C22⋊C4×C263—24no—
43C22×D263—22no—
44C22×D263—22no—
45C22×D263—44no—
46C22×D263C22⋊C414yes—
47Dic526—28no—
48D1052—28no—
49C22⋊D263—28no—
50C22⋊D263—28no—
51C2×Dic263—22no—
52C2×Dic263—22no—
53C2×Dic263—44no—
54C2×Dic263—42no—
55C2×Dic263C22⋊C414yes—
56C4×D263—216no—
57C23×C263—42no—
58C23×C263C22×C411yescharacteristic
59C23×C263C2×D414yes—
60C23×C263C2×D411yescharacteristic
61C23×C263C2×D411yescharacteristic
62C2×C4×C263—22no—
63C2×C4×C263—22no—
64C2×C4×C263—24no—
65C2×C4×C263—24no—
66C2×C4×C263—44no—
67C2×C4×C263—42no—
68C2×C4×C263C22⋊C412yes—
69C2×C4×C263C22⋊C412yes—
70C22×C263—22no—
71C22×C263—22no—
72C22×C263—22no—
73C22×C263—44no—
74C22×C263C2×C22⋊C412yes—
75C22×C263C2×C22⋊C411yescharacteristic
76C22×C263#12012yes—
77C22×C263#12012yes—
78C2×D263—24no—
79C2×D263—44no—
80C2×D263—44no—
81C2×D263—44no—
82C4×C263—22no—
83C4×C263—22no—
84C4×C263—82no—
85Dic263—24no—
86Dic263—82no—
87C2×C263—22no—
88C2×C263—22no—
89C2×C263—22no—
90C2×C263#37911yescharacteristic
91C2×C263#41012yes—
92D263—44no—
93C263#178211yescharacteristic, complemented, Sylow
94#1782—2631nomaximal, Sylow
95C22×#41—2631no—
96C2×#99—2634no—
97#381—2631no—
98#381D26311yescharacteristic, complemented
99C2×#41—5268no—
100C2×#41—5262no—
101C2×#41—5262no—
102C22×Q8—2631no—
103C22×D4—2632no—
104C22×D4—2631no—
105C23×C4—2632no—
106C23×C4C2×D26311yescharacteristic
107C2×C22⋊C4—2632no—
108C2×C22⋊C4C2×D26312yes—
109#99—5268no—
110#95—22no—
111#95—5262no—
112C24—2632no—
113C24C22×D26311yescharacteristic
114#41—52616no—
115#41—52616no—
116C2×Q8—5264no—
117C2×Q8—5262no—
118C2×D4—2638no—
119C2×D4—5264no—
120C2×D4—5264no—
121C2×D4—5262no—
122C2×D4—5262no—
123C2×D4—5262no—
124C22×C4—24no—
125C22×C4—22no—
126C22×C4—2632no—
127C22×C4—5264no—
128C22×C4—5264no—
129C22×C4—5264no—
130C22×C4—5262no—
131C22×C4C4×D26311yescharacteristic
132C22×C4C4×D26311yescharacteristic
133C22×C4C22⋊D26312yes—
134C22×C4D105212yes—
135C22⋊C4—24no—
136C22⋊C4—5264no—
137C23—42no—
138C23—2634no—
139C23—5262no—
140C23—5262no—
141C23—10524no—
142C23C2×C4×D26311yescharacteristic
143C23D4×D26314yes—
144C23C2×C22⋊D26311yescharacteristic
145C23C2×D105211yescharacteristic
146Q8—5268no—
147D4—5268no—
148D4—5268no—
149D4—5268no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—24no—
153C2×C4—24no—
154C2×C4—44no—
155C2×C4—42no—
156C2×C4—2634no—
157C2×C4—52616no—
158C2×C4—5262no—
159C2×C4—5262no—
160C2×C4—10524no—
161C2×C4—10522no—
162C2×C4(C2×D263)⋊C412yes—
163C2×C4(C2×D263)⋊C412yes—
164C22—22no—
165C22—22no—
166C22—22no—
167C22—44no—
168C22—5264no—
169C22—10524no—
170C22—10524no—
171C22—10524no—
172C22C22⋊C4×D26312yes—
173C22C2×(C2×D263)⋊C411yescharacteristic
174C22#2255443812yes—
175C22#2255444012yes—
176C4—22no—
177C4—22no—
178C4—82no—
179C4—5264no—
180C4—21042no—
181C2—22no—
182C2—22no—
183C2—22no—
184C2—10524no—
185C2#3068179311yescharacteristic
186C2#3068191112yes—
subgroupG/H
centerC22C2×(C2×D263)⋊C4
commutatorC23×C263C22×C4
FrattiniC24C22×D263
Fitting#381×C263C2
socleC22×C263C2×C22⋊C4
prime radicalC22×#16862376C2
cosocleC24×C263C23
hypercenter#381D263
hypocenterC263#1782
LCSG ▷ C23×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C23×C4 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#22554384C2semidirect
3. #30681801C2semidirect
4. #381×C263C2semidirect
8. C22×Dic526C4semidirect
9. C22×D1052C4semidirect
11. C22×C4×D263C4semidirect
93. C263#1782semidirect
98. #381D263semidirect

Maximal subgroups

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

subgroupindex
C22×#168623762
C2×#225543842
#306818012
#381×C2632
#1782263