Finite Group Databasebeta

← #46783128

Subgroups — #46783128

Order 33664.

332 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 85 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#30682705C211yesmaximal, characteristic, complemented
2#30682484C211yesmaximal, characteristic
3#30681956C212yesmaximal, complemented
4#30681697C212yesmaximal, complemented
5#410×C263C211yesmaximal, characteristic, complemented
6C2×#16862376C2211yescharacteristic
7#22554477—24no—
8C2×#16862360—22no—
9C2×#16862360C2212yes—
10#22554468C411yescharacteristic, complemented
11#22554466C411yescharacteristic, complemented
12#22554459C411yescharacteristic, complemented
13#22554457C411yescharacteristic, complemented
14#22554442—22no—
15C4×C22⋊D263—22no—
16C2×C4×Dic263C2211yescharacteristic
17#22554398—24no—
18C2×#41×C263C2211yescharacteristic
19#117×C263C2212yes—
20#99×C263—22no—
21#16862376—22no—
22#16862376—22no—
23C2×Dic526C2×C411yescharacteristic
24C2×D1052C2×C411yescharacteristic
25C2×C22⋊D263—22no—
26C2×C22⋊D263—21no—
27C22×Dic263—21no—
28C2×C4×D263—21no—
29#16862360—24no—
30#16862360—22no—
31#16862360D414yescomplemented
32C2×C263⋊C8—24no—
33C2×C263⋊C8—22no—
34Dic263⋊C4—22no—
35C22⋊Dic263—22no—
36(C2×D263)⋊C4—22no—
37C4×Dic263—21no—
38C4×Dic263C2×C411yescharacteristic
39C4×Dic263C2×C411yescharacteristic
40#41×C263—22no—
41#41×C263—22no—
42C2×Q8×C263C2×C411yescharacteristic
43C2×D4×C263C2×C411yescharacteristic
44C2×D4×C263D412yes—
45C22×C4×C263D412yes—
46C22×C4×C263C2311yescharacteristic
47C4⋊C4×C263—22no—
48C22⋊C4×C263—22no—
49C42×C263—22no—
50C22×D263—21no—
51Dic526—22no—
52D1052—22no—
53C22⋊D263—44no—
54C22⋊D263—42no—
55C2×Dic263—21no—
56C2×Dic263—21no—
57C2×Dic263—21no—
58C2×Dic263—42no—
59C4×D263—41no—
60C4×D263—41no—
61C263⋊C8—24no—
62C23×C263C22⋊C412yes—
63C23×C263C2×D411yescharacteristic
64Q8×C263—22no—
65D4×C263—24no—
66D4×C263—22no—
67C2×C4×C263—22no—
68C2×C4×C263—22no—
69C2×C4×C263—42no—
70C2×C4×C263C22⋊C412yes—
71C2×C4×C263C22×C411yescharacteristic
72C2×C4×C263C2×D412yes—
73C2×C4×C263C2×D411yescharacteristic
74C2×C4×C263#4112yes—
75C22×C263—22no—
76C22×C263—41no—
77C22×C263—42no—
78C22×C263C2×C22⋊C411yescharacteristic
79C22×C263#12112yes—
80C2×D263—42no—
81C2×D263—41no—
82C4×C263—22no—
83C4×C263—82no—
84C4×C263C4×D412yes—
85C4×C263#12011yescharacteristic
86C4×C263#12311yescharacteristic
87Dic263—22no—
88Dic263—41no—
89Dic263—41no—
90C2×C263—21no—
91C2×C263—22no—
92C2×C263—42no—
93C2×C263#38611yescharacteristic
94D263—81no—
95C263#188411yescharacteristic, complemented, Sylow
96#1884—2631nomaximal, Sylow
97#568—2631no—
98#532—2631no—
99#421—2632no—
100#410D26311yescharacteristic, complemented
101#339—2632no—
102C2×#41—2631no—
103C2×#41C2×D26311yescharacteristic
104#131—5264no—
105C2×M16—2632no—
106C2×M16—5262no—
107C4⋊Q8—2631no—
108#127—2631no—
109#124—2631no—
110#124—2631no—
111#121—5262no—
112C4×D4—5262no—
113#117C2×D26312yes—
114C2×C42—2631no—
115#104—5264no—
116#99—22no—
117#41—22no—
118#41—22no—
119#41—5262no—
120#41—5262no—
121C2×Q8—2631no—
122C2×Q8C4×D26311yescharacteristic
123C2×D4—2631no—
124C2×D4—5262no—
125C2×D4—5261no—
126C2×D4C4×D26311yescharacteristic
127C2×D4C22⋊D26312yes—
128C22×C4—5261no—
129C22×C4—5261no—
130C22×C4D105212yes—
131C22×C4C22×D26311yescharacteristic
132M16—2634no—
133M16—5264no—
134M16—5262no—
135C2×C8—5264no—
136C2×C8—5262no—
137C4⋊C4—22no—
138C4⋊C4—5262no—
139C22⋊C4—22no—
140C22⋊C4—5262no—
141C22⋊C4—5262no—
142C42—22no—
143C42—2631no—
144C42—2631no—
145C42—5261no—
146C23—5261no—
147C23(C2×D263)⋊C412yes—
148C23C2×C22⋊D26311yescharacteristic
149Q8—22no—
150Q8—5262no—
151D4—24no—
152D4—22no—
153D4—5262no—
154D4—10524no—
155D4—10522no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—42no—
159C2×C4—5261no—
160C2×C4—5261no—
161C2×C4—5261no—
162C2×C4—10522no—
163C2×C4—10521no—
164C2×C4—10521no—
165C2×C4(C2×D263)⋊C412yes—
166C2×C4C2×C4×D26311yescharacteristic
167C2×C4D4×D26312yes—
168C2×C4C2×D105211yescharacteristic
169C2×C4#1686237512yes—
170C8—5264no—
171C22—22no—
172C22—41no—
173C22—42no—
174C22—10522no—
175C22—10521no—
176C22C2×(C2×D263)⋊C411yescharacteristic
177C22#2255444212yes—
178C4—22no—
179C4—82no—
180C4—5262no—
181C4—10521no—
182C4—10521no—
183C4(C22⋊D263)⋊C412yes—
184C4#2255444011yescharacteristic
185C4#2255445411yescharacteristic
186C2—22no—
187C2—21no—
188C2—42no—
189C2—21041no—
190C2#3068181511yescharacteristic
subgroupG/H
centerC4#22554440
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#410×C263C2
socleC2×C263#386
prime radical#30682484C2
cosocleC22×C4×C263C23
hypercenter#410D263
hypocenterC263#1884
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #30682705C2semidirect
3. #30681956C2semidirect
4. #30681697C2semidirect
5. #410×C263C2semidirect
10. #22554468C4semidirect
11. #22554466C4semidirect
12. #22554459C4semidirect
13. #22554457C4semidirect
31. #16862360D4semidirect
95. C263#1884semidirect
100. #410D263semidirect

Maximal subgroups

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

subgroupindex
#306827052
#306824842
#306819562
#306816972
#410×C2632
#1884263