Finite Group Databasebeta

← #46781719

Subgroups — #46781719

Order 33664.

238 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 51 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#30682567C211yesmaximal, characteristic
2#30682094C211yesmaximal, characteristic
3#30681857C211yesmaximal, characteristic
4#30681676C211yesmaximal, characteristic
5#30681675C211yesmaximal, characteristic
6#30681663C211yesmaximal, characteristic
7#451×C263C211yesmaximal, characteristic
8C2×#16862366—21no—
9#22554469—21no—
10#22554468—21no—
11#22554460—21no—
12#22554460—21no—
13#22554449C2211yescharacteristic
14#22554447—21no—
15#22554426—21no—
16C2×Dic263⋊C4—21no—
17C2×Dic263⋊C4C2211yescharacteristic
18#22554394—21no—
19C22⋊(C263⋊C8)C2211yescharacteristic
20C263⋊#95—21no—
21C263⋊#95C2211yescharacteristic
22C22×Q8×C263C2211yescharacteristic
23C2×Q16×C263—21no—
24C22⋊Q8×C263C2211yescharacteristic
25#103×C263—21no—
26C22⋊C8×C263C2211yescharacteristic
27C2×Dic526—21no—
28C2×Dic526D411yescharacteristic
29C22×Dic263—21no—
30C22×Dic263D411yescharacteristic
31C22×Dic263D411yescharacteristic
32#16862366—42no—
33C2×C263⋊C8—21no—
34C4⋊Dic263—21no—
35C4⋊Dic263D411yescharacteristic
36Dic263⋊C4—21no—
37Dic263⋊C4—21no—
38Dic263⋊C4—21no—
39Dic263⋊C4—21no—
40Dic263⋊C4—21no—
41Dic263⋊C4—21no—
42Dic263⋊C4—21no—
43Dic263⋊C4—42no—
44C22⋊Dic263—21no—
45C4×Dic263—21no—
46C4×Dic263—21no—
47C2×Q8×C263—21no—
48C2×Q8×C263—21no—
49C2×Q8×C263—42no—
50C2×Q8×C263D411yescharacteristic
51C22×C4×C263—21no—
52C22×C4×C263C2311yescharacteristic
53Q16×C263—42no—
54C2×C8×C263—21no—
55C4⋊C4×C263—21no—
56C4⋊C4×C263D411yescharacteristic
57C22⋊C4×C263—21no—
58Dic526—41no—
59Dic526—81no—
60C2×Dic263—21no—
61C2×Dic263—21no—
62C2×Dic263—22no—
63C2×Dic263—21no—
64C2×Dic263—21no—
65C2×Dic263—21no—
66C2×Dic263—41no—
67C2×Dic263—41no—
68C2×Dic263—41no—
69C2×Dic263Q1612yescomplemented
70C263⋊C8—41no—
71C23×C263C2×D411yescharacteristic
72Q8×C263—22no—
73Q8×C263—22no—
74Q8×C263—41no—
75Q8×C263—41no—
76Q8×C263—41no—
77C2×C4×C263—22no—
78C2×C4×C263—21no—
79C2×C4×C263—21no—
80C2×C4×C263—41no—
81C2×C4×C263—41no—
82C2×C4×C263—41no—
83C2×C4×C263C2×D411yescharacteristic
84C2×C4×C263C2×D411yescharacteristic
85C8×C263—41no—
86C22×C263—21no—
87C22×C263—21no—
88C22×C263#12011yescharacteristic
89C22×C263C2×Q1611yescharacteristic
90C22×C263#13711yescharacteristic
91C4×C263—21no—
92C4×C263—21no—
93C4×C263—41no—
94C4×C263—42no—
95C4×C263—41no—
96Dic263—22no—
97Dic263—42no—
98Dic263—41no—
99Dic263—41no—
100Dic263—41no—
101C2×C263—21no—
102C2×C263—21no—
103C2×C263#45111yescharacteristic
104C2×C263#45611yescharacteristic
105C2×C263B(4,𝔽2)11yescharacteristic
106C263#160511yescharacteristic, complemented, Sylow
107#1605—2631nomaximal, Sylow
108#544—2631no—
109#451—2631no—
110#451D26311yescharacteristic
111#395—2631no—
112#328—2631no—
113#328—2631no—
114#324—2631no—
115C22×Q8C2×D26311yescharacteristic
116C2×Q16—21no—
117C2×Q16—5261no—
118C4⋊Q8—5261no—
119C4⋊Q8—5261no—
120#125—5261no—
121#125—5261no—
122C22⋊Q8—2631no—
123C22⋊Q8—5261no—
124C22⋊Q8C2×D26311yescharacteristic
125#117—5261no—
126C2×C4⋊C4—2631no—
127C2×C4⋊C4—5261no—
128#103—21no—
129#103—5261no—
130C22⋊C8—2631no—
131C22⋊C8C2×D26311yescharacteristic
132#95—2631no—
133#95—5261no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8—42no—
137C2×Q8—2631no—
138C2×Q8—5261no—
139C2×Q8C22⋊D26311yescharacteristic
140C22×C4—21no—
141C22×C4—2631no—
142C22×C4—2631no—
143C22×C4—5261no—
144C22×C4C22×D26311yescharacteristic
145Q16—42no—
146Q16—10522no—
147C2×C8—21no—
148C2×C8—5261no—
149C4⋊C4—21no—
150C4⋊C4—2631no—
151C4⋊C4—5261no—
152C4⋊C4—5261no—
153C4⋊C4—5261no—
154C4⋊C4—5261no—
155C4⋊C4—5261no—
156C4⋊C4—5261no—
157C4⋊C4—5261no—
158C4⋊C4—5261no—
159C4⋊C4—10522no—
160C4⋊C4C22⋊D26311yescharacteristic
161C22⋊C4—21no—
162C22⋊C4—5261no—
163C42—5261no—
164C42—5261no—
165C23D4×D26311yescharacteristic
166Q8—22no—
167Q8—22no—
168Q8—41no—
169Q8—41no—
170Q8—41no—
171Q8—10521no—
172Q8—21041no—
173C2×C4—22no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—2632no—
180C2×C4—5261no—
181C2×C4—5261no—
182C2×C4—5262no—
183C2×C4—5261no—
184C2×C4—5261no—
185C2×C4—5261no—
186C2×C4—10521no—
187C2×C4—10521no—
188C2×C4—10521no—
189C2×C4D4×D26311yescharacteristic
190C2×C4C2×C22⋊D26311yescharacteristic
191C8—41no—
192C8—10521no—
193C22—21no—
194C22—21no—
195C22#2255443811yescharacteristic
196C22Q16×D26311yescharacteristic
197C22#2255450211yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—42no—
202C4—41no—
203C4—5262no—
204C4—10522no—
205C4—10521no—
206C4—10521no—
207C4—10521no—
208C2—21no—
209C2—21no—
210C2#3068209211yescharacteristic
211C2#3068211911yescharacteristic
212C2#3068212411yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#451×C263C2
socleC22×C263#120
prime radicalC23×C263C2×D4
hypercenter#451D263
hypocenterC263#1605
LCSG ▷ C22×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
69. C2×Dic263Q16semidirect
106. C263#1605semidirect

Maximal subgroups

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

subgroupindex
#306825672
#306820942
#306818572
#306816762
#306816752
#306816632
#451×C2632
#1605263