Finite Group Databasebeta

← #46782674

Subgroups — #46782674

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×#16862377C211yesmaximal, characteristic
2C2×#22554389C211yesmaximal, characteristic, complemented
3C2×#22554386C212yesmaximal, complemented
4#30681901C212yesmaximal, complemented
5C2×#101×C263C211yesmaximal, characteristic, complemented
6C2×#16862377—24no—
7C2×#16862377—24no—
8C2×#16862377—22no—
9C2×#16862377—22no—
10C22×D1052C412yes—
11C22×D1052C2211yescharacteristic
12C22×C4×D263C412yes—
13C22×C4×D263C2211yescharacteristic
14C2×#16862360C2212yes—
15#22554389—22no—
16#22554386—24no—
17(C2×D263)⋊C8—24no—
18C22×Q8×C263C2211yescharacteristic
19C2×M16×C263C2212yes—
20#101×C263—22no—
21C23×D263C2×C412yes—
22C23×D263C2×C411yescharacteristic
23#16862377—216no—
24#16862377—216no—
25C2×D1052—24no—
26C2×D1052—24no—
27C2×D1052—24no—
28C2×D1052—22no—
29C2×D1052—21no—
30C2×D1052—21no—
31C2×D1052D414yes—
32C22×Dic263C2×C411yescharacteristic
33C2×C4×D263—24no—
34C2×C4×D263—24no—
35C2×C4×D263—24no—
36C2×C4×D263—22no—
37C2×C4×D263—21no—
38C2×C4×D263—21no—
39C2×C4×D263D414yes—
40#16862360—22no—
41#16862360—22no—
42C2×C263⋊C8—22no—
43C2×Q8×C263—22no—
44C2×Q8×C263—22no—
45C2×Q8×C263D412yes—
46C2×Q8×C263D412yes—
47C22×C4×C263C2×C412yes—
48C22×C4×C263C2311yescharacteristic
49M16×C263—22no—
50M16×C263—22no—
51C2×C8×C263—22no—
52C22×D263—21no—
53C22×D263—22no—
54C22×D263—22no—
55C22×D263—21no—
56C22×D263—42no—
57C22×D263—44no—
58C22×D263C22⋊C412yes—
59C22×D263C22⋊C414yes—
60D1052—216no—
61D1052—24no—
62D1052—24no—
63C2×Dic263—21no—
64C2×Dic263—21no—
65C2×Dic263C22⋊C412yes—
66C4×D263—216no—
67C4×D263—24no—
68C4×D263—24no—
69C263⋊C8—42no—
70C23×C263C22×C411yescharacteristic
71Q8×C263—24no—
72Q8×C263—24no—
73C2×C4×C263—22no—
74C2×C4×C263—22no—
75C2×C4×C263C22⋊C414yes—
76C2×C4×C263C2×D412yes—
77C2×C4×C263C2×D412yes—
78C2×C4×C263C2×D411yescharacteristic
79C2×C4×C263C2×D411yescharacteristic
80C8×C263—42no—
81C22×C263—22no—
82C22×C263C2×C22⋊C411yescharacteristic
83C22×C263C2×C22⋊C411yescharacteristic
84C22×C263C2×C22⋊C411yescharacteristic
85C2×D263—22no—
86C2×D263—24no—
87C2×D263—24no—
88C2×D263—42no—
89C2×D263—42no—
90C2×D263—44no—
91C2×D263—44no—
92C2×D263—44no—
93C4×C263—24no—
94C4×C263#12012yes—
95C4×C263#12012yes—
96Dic263—22no—
97C2×C263—21no—
98C2×C263—21no—
99C2×C263#37911yescharacteristic
100C2×C263#41312yes—
101D263—42no—
102D263—44no—
103C263#178511yescharacteristic, complemented, Sylow
104#1785—2631nomaximal, Sylow
105C22×#41—2631no—
106C2×#101—2631no—
107C2×#101D26311yescharacteristic, complemented
108C2×#100—2632no—
109#407—2632no—
110C2×#41—5264no—
111C2×#41—5264no—
112C2×#41—5262no—
113C2×#41—5262no—
114C22×Q8C2×D26311yescharacteristic
115C22×D4—2632no—
116C22×D4—2631no—
117C23×C4—2631no—
118C23×C4—2632no—
119C2×M16—2632no—
120C2×M16C2×D26312yes—
121#101—22no—
122#101—5262no—
123#100—5264no—
124C22⋊C8—5264no—
125C24—2631no—
126C24—2632no—
127#41—52616no—
128#41—52616no—
129C2×Q8—22no—
130C2×Q8—22no—
131C2×Q8C22⋊D26312yes—
132C2×Q8D105212yes—
133C2×D4—2634no—
134C2×D4—5264no—
135C2×D4—5264no—
136C2×D4—5264no—
137C2×D4—5262no—
138C2×D4—5261no—
139C2×D4—5261no—
140C22×C4—2631no—
141C22×C4—2634no—
142C22×C4—5264no—
143C22×C4—5264no—
144C22×C4—5264no—
145C22×C4—5262no—
146C22×C4—5261no—
147C22×C4—5261no—
148C22×C4C4×D26312yes—
149C22×C4C22×D26311yescharacteristic
150M16—22no—
151M16—22no—
152M16—5262no—
153M16—5262no—
154C2×C8—22no—
155C2×C8—5262no—
156C23—2632no—
157C23—2634no—
158C23—5261no—
159C23—5262no—
160C23—5262no—
161C23—5261no—
162C23—10522no—
163C23—10524no—
164C23C2×C4×D26311yescharacteristic
165Q8—24no—
166Q8—24no—
167D4—52616no—
168D4—5264no—
169D4—5264no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—2632no—
173C2×C4—52616no—
174C2×C4—5261no—
175C2×C4—5261no—
176C2×C4—5264no—
177C2×C4—5264no—
178C2×C4(C2×D263)⋊C414yes—
179C2×C4D4×D26312yes—
180C2×C4D4×D26312yes—
181C2×C4C2×C22⋊D26311yescharacteristic
182C2×C4C2×D105211yescharacteristic
183C8—42no—
184C8—10522no—
185C22—22no—
186C22—5264no—
187C22—5262no—
188C22—5264no—
189C22—10524no—
190C22—10522no—
191C22—10522no—
192C22—10524no—
193C22—10524no—
194C22C22⋊C4×D26311yescharacteristic
195C22C22⋊C4×D26311yescharacteristic
196C22C2×(C2×D263)⋊C411yescharacteristic
197C4—24no—
198C4—5262no—
199C4#2255443812yes—
200C4#2255444012yes—
201C2—21no—
202C2—21no—
203C2—10522no—
204C2—10524no—
205C2#3068179311yescharacteristic
206C2#3068192112yes—
subgroupG/H
centerC22C22⋊C4×D263
commutatorC23×C263C22×C4
FrattiniC22×C4C22×D263
FittingC2×#101×C263C2
socleC22×C263C2×C22⋊C4
prime radicalC22×#16862377C2
cosocleC22×C4×C263C23
hypercenterC2×#101D263
hypocenterC263#1785
LCSG ▷ C23×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×#22554389C2semidirect
3. C2×#22554386C2semidirect
4. #30681901C2semidirect
5. C2×#101×C263C2semidirect
103. C263#1785semidirect
107. C2×#101D263semidirect

Maximal subgroups

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

subgroupindex
C22×#168623772
C2×#225543892
C2×#225543862
#306819012
C2×#101×C2632
#1785263