Finite Group Databasebeta

← #46783405

Subgroups — #46783405

Order 33664.

212 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 75 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#30681981C211yesmaximal, characteristic
2C2×#22554394C211yesmaximal, characteristic
3C2×#22554389C211yesmaximal, characteristic
4#30681894C211yesmaximal, characteristic
5#30681706C211yesmaximal, characteristic
6#30681702C211yesmaximal, characteristic
7#419×C263C211yesmaximal, characteristic
8C2×#16862360C2211yescharacteristic
9C2×#16862360C2211yescharacteristic
10C22×C263⋊C8C2211yescharacteristic
11C2×C4⋊Dic263C2211yescharacteristic
12#22554403—21no—
13#22554401—21no—
14#22554394—21no—
15#22554394—21no—
16#22554389C414yescomplemented
17#22554381—21no—
18C4×C263⋊C8—21no—
19C22×Q8×C263C2211yescharacteristic
20C2×M16×C263C2211yescharacteristic
21#117×C263C2211yescharacteristic
22#103×C263—21no—
23#103×C263—21no—
24C22×Dic263—21no—
25#16862360—21no—
26#16862360—21no—
27#16862360C2×C412yes—
28#16862360C2×C412yes—
29C2×C263⋊C8—21no—
30C2×C263⋊C8—21no—
31C2×C263⋊C8—21no—
32C2×C263⋊C8—21no—
33C2×C263⋊C8D411yescharacteristic
34C2×C263⋊C8D411yescharacteristic
35C4⋊Dic263—21no—
36C4⋊Dic263—21no—
37C2×Q8×C263—21no—
38C2×Q8×C263—21no—
39C2×Q8×C263—21no—
40C2×Q8×C263—21no—
41C2×Q8×C263—21no—
42C2×Q8×C263C2×C412yes—
43C22×C4×C263—21no—
44C22×C4×C263C2311yescharacteristic
45M16×C263—21no—
46M16×C263—21no—
47C2×C8×C263—21no—
48C4⋊C4×C263D411yescharacteristic
49C4⋊C4×C263D411yescharacteristic
50C22⋊C4×C263—21no—
51C42×C263—21no—
52C2×Dic263—41no—
53C2×Dic263—81no—
54C263⋊C8—22no—
55C263⋊C8—22no—
56C263⋊C8—21no—
57C263⋊C8—21no—
58C23×C263#4111yescharacteristic
59Q8×C263—22no—
60Q8×C263—22no—
61Q8×C263—41no—
62Q8×C263—41no—
63C2×C4×C263—22no—
64C2×C4×C263—21no—
65C2×C4×C263—21no—
66C2×C4×C263—41no—
67C2×C4×C263—41no—
68C2×C4×C263C22×C411yescharacteristic
69C2×C4×C263C2×D411yescharacteristic
70C2×C4×C263C2×D411yescharacteristic
71C2×C4×C263#4111yescharacteristic
72C2×C4×C263#4111yescharacteristic
73C2×C4×C263#4111yescharacteristic
74C8×C263—41no—
75C22×C263—21no—
76C22×C263—21no—
77C22×C263#11711yescharacteristic
78C22×C263#12111yescharacteristic
79C22×C263#12611yescharacteristic
80C4×C263—42no—
81C4×C263—41no—
82C4×C263—41no—
83C4×C263C4×D411yescharacteristic
84C4×C263C4×D411yescharacteristic
85C4×C263#12311yescharacteristic
86C4×C263#12411yescharacteristic
87Dic263—81no—
88C2×C263—21no—
89C2×C263—21no—
90C2×C263#38811yescharacteristic
91C2×C263#47111yescharacteristic
92C2×C263#47311yescharacteristic
93C263#193011yescharacteristic, complemented, Sylow
94#1930—2631nomaximal, Sylow
95#428—2631no—
96#419D26311yescharacteristic
97C2×#103—2631no—
98C2×#101—2631no—
99#405—2631no—
100#343—2631no—
101#341—2631no—
102C22×Q8C2×D26311yescharacteristic
103C2×M16—2631no—
104C2×M16—2631no—
105C2×M16C2×D26311yescharacteristic
106C22×C8—2631no—
107#117C2×D26311yescharacteristic
108C2×C4⋊C4—2631no—
109#107—5261no—
110#106—5261no—
111#103—21no—
112#103—21no—
113#103—5261no—
114#103—5261no—
115#101—2634no—
116#97—5261no—
117C4×C8—5261no—
118C2×Q8—21no—
119C2×Q8—21no—
120C2×Q8—21no—
121C2×Q8—21no—
122C2×Q8—21no—
123C2×Q8C4×D26312yes—
124C22×C4—21no—
125C22×C4—5261no—
126C22×C4C22×D26311yescharacteristic
127M16—21no—
128M16—21no—
129M16—2632no—
130M16—2632no—
131M16—5261no—
132M16—5261no—
133C2×C8—21no—
134C2×C8—2631no—
135C2×C8—2631no—
136C2×C8—5261no—
137C2×C8—5261no—
138C2×C8—5261no—
139C2×C8—5261no—
140C4⋊C4—5261no—
141C4⋊C4—5261no—
142C4⋊C4C22⋊D26311yescharacteristic
143C4⋊C4C22⋊D26311yescharacteristic
144C22⋊C4—21no—
145C42—21no—
146C23#1686237511yescharacteristic
147Q8—22no—
148Q8—22no—
149Q8—41no—
150Q8—41no—
151C2×C4—22no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—10521no—
157C2×C4—21041no—
158C2×C4C2×C4×D26311yescharacteristic
159C2×C4D4×D26311yescharacteristic
160C2×C4C2×C22⋊D26311yescharacteristic
161C2×C4#1686237511yescharacteristic
162C2×C4#1686237511yescharacteristic
163C2×C4#1686237611yescharacteristic
164C8—41no—
165C8—5262no—
166C8—5262no—
167C8—5261no—
168C8—5261no—
169C22—21no—
170C22—21no—
171C22#2255442611yescharacteristic
172C22#2255444211yescharacteristic
173C22#2255446311yescharacteristic
174C4—41no—
175C4—41no—
176C4—42no—
177C4—21041no—
178C4(C22⋊D263)⋊C411yescharacteristic
179C4C4×C22⋊D26311yescharacteristic
180C4#2255445211yescharacteristic
181C4#2255445711yescharacteristic
182C2—21no—
183C2—21no—
184C2#3068183211yescharacteristic
185C2#3068220311yescharacteristic
186C2#3068221111yescharacteristic
subgroupG/H
centerC22#22554442
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#419×C263C2
socleC22×C263#121
prime radicalC23×C263#41
cosocleC22×C4×C263C23
hypercenter#419D263
hypocenterC263#1930
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
16. #22554389C4semidirect
93. C263#1930semidirect

Maximal subgroups

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

subgroupindex
#306819812
C2×#225543942
C2×#225543892
#306818942
#306817062
#306817022
#419×C2632
#1930263