Finite Group Databasebeta

← #46783918

Subgroups — #46783918

Order 33664.

244 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 63 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#30681956C211yesmaximal, characteristic
3C2×#22554396C211yesmaximal, characteristic
4#30681911C211yesmaximal, characteristic
5#30681710C211yesmaximal, characteristic, complemented
6#30681697C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9C2×#16862360C2211yescharacteristic
10#22554469—21no—
11#22554461—21no—
12#22554447—22no—
13C4×Dic526—22no—
14#22554429C2211yescharacteristic
15C2×C4×Dic263C2211yescharacteristic
16#22554398—22no—
17#22554396—21no—
18#22554396—21no—
19#22554384—22no—
20C2×M16×C263C2211yescharacteristic
21#117×C263C2211yescharacteristic
22#117×C263C2211yescharacteristic
23#16862376—21no—
24#16862376—21no—
25#16862376—21no—
26#16862376—21no—
27C2×Dic526—22no—
28C2×Dic526Q811yescharacteristic, complemented
29C2×D1052Q811yescharacteristic, complemented
30C2×C22⋊D263—21no—
31C22×Dic263—21no—
32C2×C4×D263—21no—
33#16862360—21no—
34#16862360—21no—
35C2×C263⋊C8—21no—
36C4⋊Dic263—22no—
37C4⋊Dic263—21no—
38Dic263⋊C4—22no—
39Dic263⋊C4—22no—
40C22⋊Dic263D412yes—
41C4×Dic263—21no—
42C4×Dic263—21no—
43C4×Dic263D411yescharacteristic
44C4×Dic263D411yescharacteristic
45C22×C4×C263C2311yescharacteristic
46M16×C263—21no—
47M16×C263—21no—
48C2×C8×C263—21no—
49C4⋊C4×C263—21no—
50C4⋊C4×C263—21no—
51C22⋊C4×C263—21no—
52C22⋊C4×C263—21no—
53C42×C263—21no—
54C42×C263D412yes—
55C22×D263—21no—
56Dic526—21no—
57Dic526—21no—
58Dic526—44no—
59D1052—21no—
60D1052—21no—
61C22⋊D263—41no—
62C22⋊D263—41no—
63C2×Dic263—21no—
64C2×Dic263—21no—
65C2×Dic263—22no—
66C2×Dic263—21no—
67C2×Dic263—42no—
68C4×D263—41no—
69C4×D263—41no—
70C263⋊C8—41no—
71C23×C263C2×D411yescharacteristic
72C2×C4×C263—22no—
73C2×C4×C263—41no—
74C2×C4×C263C2×D411yescharacteristic
75C2×C4×C263C2×D411yescharacteristic
76C2×C4×C263C2×Q811yescharacteristic
77C2×C4×C263#4111yescharacteristic
78C2×C4×C263#4111yescharacteristic
79C2×C4×C263#4111yescharacteristic
80C8×C263—41no—
81C22×C263—41no—
82C22×C263#12011yescharacteristic
83C22×C263C22⋊Q811yescharacteristic
84C22×C263#12411yescharacteristic
85C2×D263—41no—
86C2×D263—81no—
87C4×C263—42no—
88C4×C263—81no—
89C4×C263C22⋊Q811yescharacteristic
90C4×C263C22⋊Q811yescharacteristic
91C4×C263#12411yescharacteristic
92C4×C263#12411yescharacteristic
93Dic263—22no—
94Dic263—41no—
95Dic263—42no—
96Dic263—41no—
97C2×C263—21no—
98C2×C263—21no—
99C2×C263—21no—
100C2×C263#39311yescharacteristic
101D263—81no—
102C263#203111yescharacteristic, complemented, Sylow
103#2031—2631nomaximal, Sylow
104#533—2631no—
105#421—2631no—
106C2×#104—2631no—
107#410—2631no—
108#344—2631no—
109#339—2631no—
110H(3,ℤ/4)D26311yescharacteristic, complemented
111C2×#41—2631no—
112C2×M16—2631no—
113C2×M16C2×D26311yescharacteristic
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—5262no—
126#41—5261no—
127#41—5261no—
128#41—5261no—
129#41—5261no—
130C2×Q8—2631no—
131C2×Q8—5262no—
132C2×D4—2631no—
133C2×D4—5261no—
134C22×C4—5261no—
135C22×C4—5261no—
136C22×C4C22×D26311yescharacteristic
137M16—21no—
138M16—21no—
139M16—5261no—
140M16—5261no—
141C2×C8—21no—
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—21no—
151C22⋊C4—2632no—
152C42—21no—
153C42—2631no—
154C42—2631no—
155C42—5261no—
156C42—5261no—
157C42D105212yes—
158C23—5261no—
159C23D4×D26311yescharacteristic
160Q8—5261no—
161Q8—5261no—
162Q8—10524no—
163D4—5261no—
164D4—5261no—
165D4—10521no—
166D4—10521no—
167C2×C4—22no—
168C2×C4—41no—
169C2×C4—5261no—
170C2×C4—5261no—
171C2×C4—5262no—
172C2×C4—5261no—
173C2×C4—10522no—
174C2×C4—10521no—
175C2×C4—10521no—
176C2×C4D4×D26311yescharacteristic
177C2×C4C2×D105211yescharacteristic
178C2×C4Q8×D26311yescharacteristic
179C2×C4#1686237511yescharacteristic
180C2×C4#1686237611yescharacteristic
181C2×C4#1686237611yescharacteristic
182C8—41no—
183C8—10521no—
184C22—41no—
185C22—10521no—
186C22—21041no—
187C22#2255444011yescharacteristic
188C22#2255444811yescharacteristic
189C22#2255445611yescharacteristic
190C4—42no—
191C4—81no—
192C4—5262no—
193C4—10521no—
194C4—10522no—
195C4—10521no—
196C4#2255444811yescharacteristic
197C4#2255445011yescharacteristic
198C4#2255445611yescharacteristic
199C4#2255445811yescharacteristic
200C2—21no—
201C2—21no—
202C2—21no—
203C2—21041no—
204C2#3068185111yescharacteristic
subgroupG/H
centerC4#22554458
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
FittingH(3,ℤ/4)×C263C2
socleC2×C263#393
prime radicalC2×#16862376C22
hypercenterH(3,ℤ/4)D263
hypocenterC263#2031
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C4 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
1. #30682491C2semidirect
5. #30681710C2semidirect
6. #30681697C2semidirect
7. H(3,ℤ/4)×C263C2semidirect
28. C2×Dic526Q8semidirect
29. C2×D1052Q8semidirect
102. C263#2031semidirect
110. H(3,ℤ/4)D263semidirect

Maximal subgroups

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

subgroupindex
#306824912
#306819562
C2×#225543962
#306819112
#306817102
#306816972
H(3,ℤ/4)×C2632
#2031263