Finite Group Databasebeta

← #46783921

Subgroups — #46783921

Order 33664.

244 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 65 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#30682491C211yesmaximal, characteristic, complemented
2#30681955C211yesmaximal, characteristic
3C2×#22554397C211yesmaximal, characteristic
4#30681708C211yesmaximal, characteristic, complemented
5#30681697C211yesmaximal, characteristic, complemented
6#30681694C211yesmaximal, characteristic, complemented
7#410×C263C211yesmaximal, characteristic
8C2×#16862360C2211yescharacteristic
9C2×#16862360C2211yescharacteristic
10#22554469—21no—
11#22554461—21no—
12#22554447—22no—
13C4×Dic526—22no—
14#22554429C2211yescharacteristic
15C2×C4×Dic263C2211yescharacteristic
16#22554397—21no—
17#22554397—21no—
18#22554397—22no—
19C2×#41×C263C2211yescharacteristic
20#117×C263C2211yescharacteristic
21#117×C263C2211yescharacteristic
22#99×C263—22no—
23C2×Dic526—22no—
24C22×Dic263—21no—
25#16862360—21no—
26#16862360—21no—
27#16862360—21no—
28#16862360—21no—
29C2×C263⋊C8—21no—
30C2×C263⋊C8—21no—
31C4⋊Dic263—22no—
32C4⋊Dic263—21no—
33Dic263⋊C4—22no—
34Dic263⋊C4—22no—
35C22⋊Dic263—21no—
36C4×Dic263—21no—
37C4×Dic263D411yescharacteristic
38C4×Dic263D411yescharacteristic
39C4×Dic263D412yes—
40#41×C263—21no—
41#41×C263—21no—
42#41×C263—21no—
43#41×C263—21no—
44C2×Q8×C263Q811yescharacteristic, complemented
45C2×D4×C263—21no—
46C2×D4×C263Q811yescharacteristic, complemented
47C22×C4×C263—21no—
48C22×C4×C263C2311yescharacteristic
49C4⋊C4×C263—21no—
50C4⋊C4×C263—21no—
51C22⋊C4×C263—21no—
52C22⋊C4×C263D412yes—
53C42×C263—21no—
54C42×C263—21no—
55Dic526—44no—
56C2×Dic263—21no—
57C2×Dic263—21no—
58C2×Dic263—22no—
59C2×Dic263—42no—
60C263⋊C8—41no—
61C263⋊C8—41no—
62C23×C263—21no—
63C23×C263C2×D411yescharacteristic
64Q8×C263—21no—
65Q8×C263—21no—
66D4×C263—21no—
67D4×C263—21no—
68D4×C263—41no—
69D4×C263—41no—
70C2×C4×C263—22no—
71C2×C4×C263—21no—
72C2×C4×C263—41no—
73C2×C4×C263—41no—
74C2×C4×C263—41no—
75C2×C4×C263C2×D411yescharacteristic
76C2×C4×C263C2×D411yescharacteristic
77C2×C4×C263C2×Q811yescharacteristic
78C2×C4×C263#4111yescharacteristic
79C2×C4×C263#4111yescharacteristic
80C2×C4×C263#4111yescharacteristic
81C22×C263—41no—
82C22×C263—41no—
83C22×C263—81no—
84C22×C263#12011yescharacteristic
85C22×C263C22⋊Q811yescharacteristic
86C22×C263#12411yescharacteristic
87C4×C263—42no—
88C4×C263—41no—
89C4×C263—81no—
90C4×C263C22⋊Q811yescharacteristic
91C4×C263C22⋊Q811yescharacteristic
92C4×C263#12411yescharacteristic
93C4×C263#12411yescharacteristic
94Dic263—22no—
95Dic263—41no—
96Dic263—42no—
97C2×C263—21no—
98C2×C263—21no—
99C2×C263—21no—
100C2×C263—81no—
101C2×C263#39311yescharacteristic
102C263#203111yescharacteristic, complemented, Sylow
103#2031—2631nomaximal, Sylow
104#533—2631no—
105#421—2631no—
106C2×#104—2631no—
107#410D26311yescharacteristic
108#344—2631no—
109#339—2631no—
110H(3,ℤ/4)—2631no—
111C2×#41C2×D26311yescharacteristic
112C2×M16—2631no—
113C2×M16—2631no—
114C4⋊Q8—5261no—
115#125—5261no—
116C22⋊Q8—5262no—
117C4×Q8—5262no—
118#117—2631no—
119#117C2×D26311yescharacteristic
120#117C2×D26311yescharacteristic
121C2×C42—2631no—
122#104—5261no—
123#104—5261no—
124#104—5262no—
125#99—22no—
126#41—21no—
127#41—21no—
128#41—21no—
129#41—21no—
130C2×Q8—5262no—
131C2×Q8Dic52611yescharacteristic, complemented
132C2×D4—21no—
133C2×D4Dic52611yescharacteristic, complemented
134C22×C4—21no—
135C22×C4—5261no—
136C22×C4C22×D26311yescharacteristic
137M16—5261no—
138M16—5261no—
139M16—5261no—
140M16—5261no—
141C2×C8—5261no—
142C2×C8—5261no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—5262no—
146C4⋊C4—5262no—
147C4⋊C4—5262no—
148C4⋊C4—5261no—
149C22⋊C4—21no—
150C22⋊C4—5261no—
151C22⋊C4C22⋊D26312yes—
152C42—21no—
153C42—21no—
154C42—2631no—
155C42—2631no—
156C42—2632no—
157C42—5261no—
158C23—21no—
159C23C2×C22⋊D26311yescharacteristic
160Q8—21no—
161Q8—21no—
162Q8—10524no—
163D4—21no—
164D4—21no—
165D4—41no—
166D4—41no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—5261no—
173C2×C4—5261no—
174C2×C4—5262no—
175C2×C4—10522no—
176C2×C4D4×D26311yescharacteristic
177C2×C4D4×D26311yescharacteristic
178C2×C4C2×Dic52611yescharacteristic
179C2×C4#1686237511yescharacteristic
180C2×C4#1686237511yescharacteristic
181C2×C4#1686237611yescharacteristic
182C8—10521no—
183C8—10521no—
184C22—41no—
185C22—41no—
186C22—81no—
187C22#2255443811yescharacteristic
188C22#2255444911yescharacteristic
189C22#2255445711yescharacteristic
190C4—42no—
191C4—41no—
192C4—81no—
193C4—5262no—
194C4—10521no—
195C4—10522no—
196C4#2255444711yescharacteristic
197C4#2255444711yescharacteristic
198C4#2255445611yescharacteristic
199C4#2255445611yescharacteristic
200C2—21no—
201C2—21no—
202C2—21no—
203C2—81no—
204C2#3068185011yescharacteristic
subgroupG/H
centerC4#22554456
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#410×C263C2
socleC2×C263#393
prime radicalC2×#41×C263C22
hypercenter#410D263
hypocenterC263#2031
LCSG ▷ C22×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. #30682491C2semidirect
4. #30681708C2semidirect
5. #30681697C2semidirect
6. #30681694C2semidirect
44. C2×Q8×C263Q8semidirect
46. C2×D4×C263Q8semidirect
102. C263#2031semidirect
131. C2×Q8Dic526semidirect
133. C2×D4Dic526semidirect

Maximal subgroups

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

subgroupindex
#306824912
#306819552
C2×#225543972
#306817082
#306816972
#306816942
#410×C2632
#2031263