Finite Group Databasebeta

← #46782673

Subgroups — #46782673

Order 33664.

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

normal subgroups only

This group has 584 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×#22554388C212yesmaximal, complemented
3C2×#22554386C212yesmaximal, complemented
4#30681902C211yesmaximal, characteristic, complemented
5#407×C263C211yesmaximal, characteristic, complemented
6C2×#16862376—24no—
7C2×#16862376—24no—
8C2×#16862376—22no—
9C2×#16862376—22no—
10C22×Dic526C2211yescharacteristic
11C22×D1052C2211yescharacteristic
12C22×C22⋊D263C412yes—
13C22×C4×D263C412yes—
14C2×#16862360C2212yes—
15#22554388—24no—
16#22554386—24no—
17C22⋊(C263⋊C8)—22no—
18C23×C4×C263C2211yescharacteristic
19C2×M16×C263C2212yes—
20C22⋊C8×C263—22no—
21C23×D263C2×C412yes—
22#16862376—216no—
23#16862376—216no—
24C2×Dic526—22no—
25C2×Dic526—21no—
26C2×Dic526—21no—
27C2×Dic526D414yes—
28C2×D1052—22no—
29C2×D1052—21no—
30C2×D1052—21no—
31C2×D1052D414yes—
32C2×C22⋊D263—24no—
33C2×C22⋊D263—24no—
34C2×C22⋊D263—24no—
35C22×Dic263C2×C412yes—
36C2×C4×D263—24no—
37C2×C4×D263—24no—
38C2×C4×D263—24no—
39#16862360—22no—
40#16862360—22no—
41C2×C263⋊C8—22no—
42C24×C263C2×C411yescharacteristic
43C22×C4×C263—22no—
44C22×C4×C263—22no—
45C22×C4×C263C2×C411yescharacteristic
46C22×C4×C263D412yes—
47C22×C4×C263D412yes—
48C22×C4×C263C2311yescharacteristic
49M16×C263—22no—
50M16×C263—22no—
51C2×C8×C263—22no—
52C22×D263—22no—
53C22×D263—22no—
54C22×D263—44no—
55C22×D263C22⋊C414yes—
56Dic526—24no—
57Dic526—24no—
58D1052—24no—
59D1052—24no—
60C22⋊D263—216no—
61C2×Dic263—22no—
62C2×Dic263—22no—
63C2×Dic263C22⋊C414yes—
64C4×D263—216no—
65C263⋊C8—42no—
66C23×C263—21no—
67C23×C263—21no—
68C23×C263—42no—
69C23×C263C22⋊C412yes—
70C23×C263C22×C411yescharacteristic
71C2×C4×C263—21no—
72C2×C4×C263—21no—
73C2×C4×C263—24no—
74C2×C4×C263—24no—
75C2×C4×C263C22⋊C412yes—
76C2×C4×C263C2×D412yes—
77C2×C4×C263C2×D412yes—
78C2×C4×C263C2×D411yescharacteristic
79C2×C4×C263C2×D411yescharacteristic
80C8×C263—42no—
81C22×C263—22no—
82C22×C263—22no—
83C22×C263—24no—
84C22×C263—42no—
85C22×C263—42no—
86C22×C263C2×C22⋊C411yescharacteristic
87C22×C263C2×C22⋊C411yescharacteristic
88C22×C263C2×C22⋊C411yescharacteristic
89C2×D263—24no—
90C2×D263—44no—
91C2×D263—44no—
92C2×D263—44no—
93C4×C263—22no—
94C4×C263#12012yes—
95C4×C263#12012yes—
96Dic263—24no—
97C2×C263—21no—
98C2×C263—21no—
99C2×C263—42no—
100C2×C263#37911yescharacteristic
101C2×C263#41312yes—
102D263—44no—
103C263#178511yescharacteristic, complemented, Sylow
104#1785—2631nomaximal, Sylow
105C22×#41—2631no—
106C2×#101—2632no—
107C2×#100—2632no—
108#407—2631no—
109#407D26311yescharacteristic, complemented
110C2×#41—5264no—
111C2×#41—5264no—
112C2×#41—5262no—
113C2×#41—5262no—
114C22×Q8—2631no—
115C22×D4—2632no—
116C22×D4—2631no—
117C23×C4—2632no—
118C23×C4C2×D26311yescharacteristic
119C2×M16—2632no—
120C2×M16C2×D26312yes—
121#101—5264no—
122#100—5264no—
123C22⋊C8—22no—
124C22⋊C8—5262no—
125C24—2632no—
126C24C4×D26311yescharacteristic
127#41—52616no—
128#41—52616no—
129C2×Q8—2634no—
130C2×Q8—5262no—
131C2×Q8—5261no—
132C2×Q8—5261no—
133C2×D4—2634no—
134C2×D4—5264no—
135C2×D4—5264no—
136C2×D4—5264no—
137C2×D4—5262no—
138C2×D4—5261no—
139C2×D4—5261no—
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—2632no—
143C22×C4—5264no—
144C22×C4—5264no—
145C22×C4—5264no—
146C22×C4C4×D26311yescharacteristic
147C22×C4C22⋊D26312yes—
148C22×C4D105212yes—
149C22×C4C22×D26311yescharacteristic
150M16—22no—
151M16—22no—
152M16—5262no—
153M16—5262no—
154C2×C8—22no—
155C2×C8—5262no—
156C23—21no—
157C23—21no—
158C23—42no—
159C23—2634no—
160C23—5262no—
161C23—5262no—
162C23—10524no—
163C23(C2×D263)⋊C412yes—
164C23C2×C4×D26311yescharacteristic
165Q8—5264no—
166Q8—5264no—
167D4—52616no—
168D4—5264no—
169D4—5264no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—24no—
173C2×C4—24no—
174C2×C4—2634no—
175C2×C4—52616no—
176C2×C4—5262no—
177C2×C4—5262no—
178C2×C4(C2×D263)⋊C412yes—
179C2×C4D4×D26312yes—
180C2×C4D4×D26312yes—
181C2×C4C2×C22⋊D26311yescharacteristic
182C2×C4C2×D105211yescharacteristic
183C8—42no—
184C8—10522no—
185C22—22no—
186C22—24no—
187C22—22no—
188C22—42no—
189C22—42no—
190C22—5264no—
191C22—10524no—
192C22—10524no—
193C22—10524no—
194C22C22⋊C4×D26311yescharacteristic
195C22C22⋊C4×D26311yescharacteristic
196C22C2×(C2×D263)⋊C411yescharacteristic
197C4—22no—
198C4—5264no—
199C4#2255443812yes—
200C4#2255444012yes—
201C2—21no—
202C2—21no—
203C2—42no—
204C2—10524no—
205C2#3068179311yescharacteristic
206C2#3068192012yes—
subgroupG/H
centerC22C2×(C2×D263)⋊C4
commutatorC23×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#407×C263C2
socleC22×C263C2×C22⋊C4
prime radicalC22×#16862376C2
cosocleC22×C4×C263C23
hypercenter#407D263
hypocenterC263#1785
LCSG ▷ C23×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×#22554388C2semidirect
3. C2×#22554386C2semidirect
4. #30681902C2semidirect
5. #407×C263C2semidirect
103. C263#1785semidirect
109. #407D263semidirect

Maximal subgroups

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

subgroupindex
C22×#168623762
C2×#225543882
C2×#225543862
#306819022
#407×C2632
#1785263