Finite Group Databasebeta

← #46783883

Subgroups — #46783883

Order 33664.

326 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C2×#22554470C211yesmaximal, characteristic, complemented
2C2×#22554391C212yesmaximal
3#30681700C212yesmaximal, complemented
4#30681693C211yesmaximal, characteristic, complemented
5#390×C263C211yesmaximal, characteristic
6C22×Dic526—21no—
7C22×C263⋊C8C2212yes—
8#22554470—24no—
9C2×C4⋊Dic263—21no—
10C2×C4⋊Dic263C2212yes—
11#22554391—24no—
12C22×D4×C263C2211yescharacteristic
13C2×C4⋊C4×C263C2211yescharacteristic
14C2×C22⋊C4×C263—21no—
15C2×C22⋊C4×C263—21no—
16C2×C42×C263C2211yescharacteristic
17C2×Dic526—24no—
18C2×Dic526—42no—
19C2×Dic526—42no—
20C22×Dic263—22no—
21C2×C263⋊C8—22no—
22C2×C263⋊C8—22no—
23C2×C263⋊C8—22no—
24C4⋊Dic263—24no—
25C4⋊Dic263—22no—
26C4⋊Dic263D414yes—
27C24×C263—21no—
28C2×D4×C263—22no—
29C2×D4×C263—22no—
30C2×D4×C263—21no—
31C2×D4×C263Q812yescomplemented
32C22×C4×C263—21no—
33C22×C4×C263D411yescharacteristic
34C22×C4×C263D411yescharacteristic
35C22×C4×C263C2311yescharacteristic
36C4⋊C4×C263—22no—
37C22⋊C4×C263—42no—
38C22⋊C4×C263—42no—
39C42×C263—22no—
40Dic526—48no—
41C2×Dic263—24no—
42C2×Dic263—42no—
43C2×Dic263—42no—
44C263⋊C8—42no—
45C23×C263—22no—
46C23×C263—41no—
47C23×C263—41no—
48C23×C263—41no—
49C23×C263—41no—
50C23×C263—41no—
51C23×C263—41no—
52C23×C263C2×D411yescharacteristic
53D4×C263—24no—
54D4×C263—42no—
55C2×C4×C263—21no—
56C2×C4×C263—21no—
57C2×C4×C263—21no—
58C2×C4×C263—21no—
59C2×C4×C263—41no—
60C2×C4×C263—41no—
61C2×C4×C263—41no—
62C2×C4×C263D812yes—
63C2×C4×C263SD1612yes—
64C2×C4×C263C2×D412yes—
65C2×C4×C263C2×Q811yescharacteristic
66C2×C4×C263#4112yes—
67C2×C4×C263#4111yescharacteristic
68C22×C263—42no—
69C22×C263—42no—
70C22×C263—42no—
71C22×C263—81no—
72C22×C263—81no—
73C22×C263—81no—
74C22×C263—81no—
75C22×C263#12011yescharacteristic
76C22×C263C22⋊Q811yescharacteristic
77C22×C263#12411yescharacteristic
78C22×C263C2×D811yescharacteristic
79C22×C263C2×SD1611yescharacteristic
80C22×C263AGL(1,ℤ/8)11yescharacteristic
81C22×C263#13711yescharacteristic
82C4×C263—22no—
83C4×C263—22no—
84C4×C263—81no—
85C4×C263C22⋊Q812yes—
86C4×C263#12412yes—
87Dic263—44no—
88C2×C263—82no—
89C2×C263#39311yescharacteristic
90C2×C263#44711yescharacteristic
91C2×C263#44811yescharacteristic
92C2×C263#47411yescharacteristic
93C2×C263#47611yescharacteristic
94C2×C263#48611yescharacteristic
95C2×C263#48911yescharacteristic
96C263#202311yescharacteristic, complemented, Sylow
97#2023—2631nomaximal, Sylow
98C2×C4⋊Q8—2631no—
99C2×#102—2632no—
100#390D26311yescharacteristic
101#340—2632no—
102#336—2631no—
103C22×Q8—5261no—
104C22×D4C2×D26311yescharacteristic
105C22×C8—2632no—
106C4⋊Q8—5264no—
107C2×C4⋊C4—2632no—
108C2×C4⋊C4—5261no—
109C2×C4⋊C4C2×D26311yescharacteristic
110C2×C22⋊C4—21no—
111C2×C22⋊C4—21no—
112C2×C42C2×D26311yescharacteristic
113#102—5264no—
114C24—21no—
115C2×Q8—5264no—
116C2×Q8—10522no—
117C2×Q8—10522no—
118C2×D4—22no—
119C2×D4—22no—
120C2×D4—21no—
121C2×D4Dic52612yescomplemented
122C22×C4—21no—
123C22×C4—5262no—
124C22×C4C22⋊D26311yescharacteristic
125C22×C4C22⋊D26311yescharacteristic
126C22×C4C22×D26311yescharacteristic
127C2×C8—5262no—
128C2×C8—5262no—
129C2×C8—5262no—
130C4⋊C4—22no—
131C4⋊C4—2634no—
132C4⋊C4—5264no—
133C4⋊C4—5262no—
134C22⋊C4—42no—
135C22⋊C4—42no—
136C42—22no—
137C23—22no—
138C23—41no—
139C23—41no—
140C23—41no—
141C23—41no—
142C23—41no—
143C23—41no—
144C23C2×C22⋊D26311yescharacteristic
145Q8—10528no—
146D4—24no—
147D4—42no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—5264no—
156C2×C4—10522no—
157C2×C4—10522no—
158C2×C4#1686236112yes—
159C2×C4#1686236412yes—
160C2×C4D4×D26312yes—
161C2×C4C2×Dic52611yescharacteristic
162C2×C4#1686237512yes—
163C2×C4#1686237611yescharacteristic
164C8—10522no—
165C22—42no—
166C22—42no—
167C22—42no—
168C22—81no—
169C22—81no—
170C22—81no—
171C22—81no—
172C22#2255443811yescharacteristic
173C22#2255444911yescharacteristic
174C22#2255445711yescharacteristic
175C22C2×#1686236111yescharacteristic
176C22C2×#1686236411yescharacteristic
177C22#2255449511yescharacteristic
178C22#2255450011yescharacteristic
179C4—22no—
180C4—22no—
181C4—81no—
182C4—10524no—
183C4#2255444712yes—
184C4#2255445612yes—
185C2—82no—
186C2#3068185011yescharacteristic
187C2#3068207111yescharacteristic
188C2#3068207611yescharacteristic
189C2#3068221811yescharacteristic
190C2#3068222811yescharacteristic
191C2#3068228411yescharacteristic
192C2#3068229711yescharacteristic
subgroupG/H
centerC23C2×C22⋊D263
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#390×C263C2
socleC23×C263C2×D4
prime radicalC22×D4×C263C22
hypercenter#390D263
hypocenterC263#2023
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#22554470C2semidirect
3. #30681700C2semidirect
4. #30681693C2semidirect
31. C2×D4×C263Q8semidirect
96. C263#2023semidirect
121. C2×D4Dic526semidirect

Maximal subgroups

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

subgroupindex
C2×#225544702
C2×#225543912
#306817002
#306816932
#390×C2632
#2023263