Finite Group Databasebeta

← #46782849

Subgroups — #46782849

Order 33664.

262 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 73 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#30682406C211yesmaximal, characteristic
2#30681920C211yesmaximal, characteristic
3#30681911C211yesmaximal, characteristic
4#30681699C211yesmaximal, characteristic, complemented
5#30681697C211yesmaximal, characteristic, complemented
6#30681694C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9C2×#16862360C2211yescharacteristic
10#22554435—21no—
11#22554432—21no—
12(C22⋊D263)⋊C4—22no—
13#22554429C2211yescharacteristic
14#22554427C412yescomplemented
15C2×C4×Dic263C2211yescharacteristic
16C42×D263C412yescomplemented
17#22554388—21no—
18#22554386—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×Dic526D411yescharacteristic
28C2×D1052D411yescharacteristic
29C2×C22⋊D263D412yes—
30C22×Dic263—21no—
31C2×C4×D263—22no—
32C2×C4×D263C2×C412yes—
33#16862360—21no—
34#16862360—21no—
35C2×C263⋊C8—21no—
36C4⋊Dic263—21no—
37Dic263⋊C4—22no—
38C22⋊Dic263—21no—
39(C2×D263)⋊C4—22no—
40C4×Dic263—22no—
41C4×Dic263—21no—
42C4×Dic263—21no—
43C4×Dic263C2×C411yescharacteristic
44C4×Dic263C2×C411yescharacteristic
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×C263C2×C412yes—
55C22×D263C22⋊C412yes—
56Dic526—21no—
57Dic526—21no—
58D1052—21no—
59D1052—21no—
60C22⋊D263—22no—
61C22⋊D263—22no—
62C2×Dic263—21no—
63C2×Dic263—21no—
64C2×Dic263—42no—
65C2×Dic263—41no—
66C2×Dic263C22⋊C412yes—
67C4×D263—22no—
68C4×D263—22no—
69C4×D263—44no—
70C263⋊C8—41no—
71C23×C263C2×D411yescharacteristic
72C2×C4×C263—22no—
73C2×C4×C263—41no—
74C2×C4×C263C22×C411yescharacteristic
75C2×C4×C263C2×D411yescharacteristic
76C2×C4×C263#4111yescharacteristic
77C2×C4×C263#4111yescharacteristic
78C2×C4×C263#4111yescharacteristic
79C2×C4×C263#4111yescharacteristic
80C8×C263—41no—
81C22×C263—41no—
82C22×C263C2×C22⋊C411yescharacteristic
83C22×C263#12311yescharacteristic
84C22×C263#12311yescharacteristic
85C2×D263—22no—
86C2×D263—42no—
87C4×C263—42no—
88C4×C263—81no—
89C4×C263#11711yescharacteristic
90C4×C263#11711yescharacteristic
91C4×C263#12311yescharacteristic
92C4×C263#12311yescharacteristic
93Dic263—22no—
94Dic263—22no—
95Dic263—41no—
96Dic263—81no—
97C2×C263—21no—
98C2×C263—21no—
99C2×C263—21no—
100C2×C263#38111yescharacteristic
101D263—42no—
102C263#182711yescharacteristic, complemented, Sylow
103#1827—2631nomaximal, Sylow
104C4×#41—2631no—
105#413—2631no—
106#410—2631no—
107#339—2631no—
108#339—2631no—
109H(3,ℤ/4)—2631no—
110H(3,ℤ/4)D26311yescharacteristic, complemented
111C2×#41—2631no—
112C2×M16—2631no—
113C2×M16C2×D26311yescharacteristic
114C4×Q8—5261no—
115C4×D4—5262no—
116C4×D4—5261no—
117#117—2632no—
118#117—2631no—
119#117C2×D26311yescharacteristic
120#117C2×D26311yescharacteristic
121C2×C42—2631no—
122C2×C42—2632no—
123#101—5261no—
124#100—5261no—
125#99—5262no—
126#41—5261no—
127#41—5261no—
128#41—5261no—
129#41—5261no—
130C2×Q8—2631no—
131C2×D4—2632no—
132C2×D4—2631no—
133C22×C4—2632no—
134C22×C4—5262no—
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—5261no—
147C22⋊C4—21no—
148C22⋊C4—21no—
149C22⋊C4—5262no—
150C22⋊C4—5261no—
151C42—21no—
152C42—2631no—
153C42—2631no—
154C42—5262no—
155C42—5261no—
156C42—5261no—
157C42C4×D26312yes—
158C23—2632no—
159C23D4×D26311yescharacteristic
160Q8—5261no—
161Q8—5261no—
162D4—5262no—
163D4—5262no—
164D4—5261no—
165D4—5261no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—2632no—
169C2×C4—5261no—
170C2×C4—5262no—
171C2×C4—5262no—
172C2×C4—5261no—
173C2×C4—10524no—
174C2×C4—10522no—
175C2×C4—10521no—
176C2×C4C2×C4×D26311yescharacteristic
177C2×C4D4×D26311yescharacteristic
178C2×C4#1686237511yescharacteristic
179C2×C4#1686237611yescharacteristic
180C2×C4#1686237611yescharacteristic
181C2×C4#1686237711yescharacteristic
182C8—41no—
183C8—10521no—
184C22—41no—
185C22—5262no—
186C22—10522no—
187C22C22⋊C4×D26311yescharacteristic
188C22#2255445211yescharacteristic
189C22#2255445511yescharacteristic
190C4—42no—
191C4—81no—
192C4—5262no—
193C4—5262no—
194C4—10521no—
195C4—21041no—
196C4#2255442711yescharacteristic
197C4#2255442811yescharacteristic
198C4#2255445211yescharacteristic
199C4#2255445511yescharacteristic
200C2—21no—
201C2—21no—
202C2—21no—
203C2—10522no—
204C2#3068180011yescharacteristic
subgroupG/H
centerC4#22554427
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
FittingH(3,ℤ/4)×C263C2
socleC2×C263#381
prime radicalC2×#16862376C22
cosocleC22×C4×C263C23
hypercenterH(3,ℤ/4)D263
hypocenterC263#1827
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C4 ◁ #117 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
4. #30681699C2semidirect
5. #30681697C2semidirect
6. #30681694C2semidirect
7. H(3,ℤ/4)×C263C2semidirect
14. #22554427C4semidirect
16. C42×D263C4semidirect
102. C263#1827semidirect
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
#306824062
#306819202
#306819112
#306816992
#306816972
#306816942
H(3,ℤ/4)×C2632
#1827263