Finite Group Databasebeta

← #46781709

Subgroups — #46781709

Order 33664.

244 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 49 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#30682537C211yesmaximal, characteristic
2#30682077C211yesmaximal, characteristic
3#30681857C211yesmaximal, characteristic, complemented
4#30681675C211yesmaximal, characteristic, complemented
5#30681673C211yesmaximal, characteristic
6#30681663C211yesmaximal, characteristic, complemented
7#451×C263C211yesmaximal, characteristic, complemented
8C2×#16862363—21no—
9#22554465—21no—
10#22554461—21no—
11#22554455—21no—
12#22554454—21no—
13#22554446—21no—
14#22554444C2211yescharacteristic
15(C22⋊D263)⋊C4—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×D1052D411yescharacteristic
28C2×C22⋊D263—21no—
29C22×Dic263—21no—
30C22×Dic263D411yescharacteristic
31C22×Dic263D411yescharacteristic
32C2×C4×D263—21no—
33#16862363—42no—
34C2×C263⋊C8—21no—
35C4⋊Dic263—21no—
36C4⋊Dic263—21no—
37C4⋊Dic263D411yescharacteristic
38Dic263⋊C4—21no—
39Dic263⋊C4—21no—
40Dic263⋊C4—21no—
41Dic263⋊C4—42no—
42(C2×D263)⋊C4—21no—
43(C2×D263)⋊C4—21no—
44(C2×D263)⋊C4—21no—
45(C2×D263)⋊C4—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—
58C22×D263—21no—
59D1052—41no—
60C22⋊D263—41no—
61C22⋊D263—41no—
62C2×Dic263—22no—
63C2×Dic263—21no—
64C2×Dic263—21no—
65C2×Dic263—21no—
66C2×Dic263—21no—
67C2×Dic263—21no—
68C2×Dic263—41no—
69C2×Dic263—41no—
70C2×Dic263—41no—
71C4×D263—81no—
72C263⋊C8—41no—
73C23×C263C2×D411yescharacteristic
74Q8×C263—22no—
75Q8×C263—22no—
76Q8×C263—41no—
77Q8×C263—41no—
78Q8×C263—41no—
79C2×C4×C263—22no—
80C2×C4×C263—21no—
81C2×C4×C263—21no—
82C2×C4×C263—41no—
83C2×C4×C263—41no—
84C2×C4×C263—41no—
85C2×C4×C263C2×D411yescharacteristic
86C2×C4×C263C2×D411yescharacteristic
87C8×C263—41no—
88C22×C263—21no—
89C22×C263—21no—
90C22×C263#12011yescharacteristic
91C22×C263#13511yescharacteristic
92C22×C263#13711yescharacteristic
93C2×D263—41no—
94C2×D263—41no—
95C2×D263—41no—
96C4×C263—21no—
97C4×C263—21no—
98C4×C263—41no—
99C4×C263—42no—
100C4×C263—41no—
101Dic263—42no—
102Dic263—41no—
103Dic263—41no—
104Dic263—41no—
105C2×C263—21no—
106C2×C263—21no—
107C2×C263#45211yescharacteristic
108C2×C263#45611yescharacteristic
109C2×C263B(4,𝔽2)11yescharacteristic
110D263—81no—
111C263#160311yescharacteristic, complemented, Sylow
112#1603—2631nomaximal, Sylow
113#539—2631no—
114#451D26311yescharacteristic, complemented
115#448—2631no—
116#395—2631no—
117#328—2631no—
118#327—2631no—
119#324—2631no—
120C22×Q8C2×D26311yescharacteristic
121C2×Q16—21no—
122C2×SD16—5261no—
123#126—5261no—
124#125—5261no—
125#123—5261no—
126#123—5261no—
127C22⋊Q8—5261no—
128C22⋊Q8C2×D26311yescharacteristic
129#121—2631no—
130C4×D4—5261no—
131C2×C4⋊C4—2631no—
132C2×C4⋊C4—5261no—
133#103—21no—
134#103—5261no—
135C22⋊C8—2631no—
136C22⋊C8C2×D26311yescharacteristic
137#95—2631no—
138#95—5261no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—42no—
142C2×Q8C22⋊D26311yescharacteristic
143C2×D4—2631no—
144C2×D4—5261no—
145C22×C4—21no—
146C22×C4—2631no—
147C22×C4—2631no—
148C22×C4—5261no—
149C22×C4—5261no—
150C22×C4C22×D26311yescharacteristic
151Q16—42no—
152SD16—10522no—
153C2×C8—21no—
154C2×C8—5261no—
155C4⋊C4—21no—
156C4⋊C4—2631no—
157C4⋊C4—5261no—
158C4⋊C4—5261no—
159C4⋊C4—5261no—
160C4⋊C4—5261no—
161C4⋊C4—5261no—
162C4⋊C4—10522no—
163C4⋊C4C22⋊D26311yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—5261no—
166C22⋊C4—5261no—
167C22⋊C4—5261no—
168C22⋊C4—5261no—
169C42—5261no—
170C23—5261no—
171C23D4×D26311yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—41no—
175Q8—41no—
176Q8—41no—
177D4—10521no—
178D4—10521no—
179D4—10521no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—5262no—
187C2×C4—5261no—
188C2×C4—5261no—
189C2×C4—5261no—
190C2×C4—5261no—
191C2×C4—5261no—
192C2×C4—10521no—
193C2×C4—10521no—
194C2×C4—10521no—
195C2×C4—21041no—
196C2×C4D4×D26311yescharacteristic
197C2×C4C2×C22⋊D26311yescharacteristic
198C8—41no—
199C8—10521no—
200C22—21no—
201C22—21no—
202C22—10521no—
203C22—10521no—
204C22—10521no—
205C22#2255443811yescharacteristic
206C22#2255449311yescharacteristic
207C22#2255450211yescharacteristic
208C4—21no—
209C4—21no—
210C4—41no—
211C4—42no—
212C4—41no—
213C4—10522no—
214C4—10521no—
215C4—10521no—
216C4—10521no—
217C2—21no—
218C2—21no—
219C2—21041no—
220C2#3068209911yescharacteristic
221C2#3068211911yescharacteristic
222C2#3068212411yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#451×C263C2
socleC22×C263#120
prime radical#22554444C22
hypercenter#451D263
hypocenterC263#1603
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
3. #30681857C2semidirect
4. #30681675C2semidirect
6. #30681663C2semidirect
7. #451×C263C2semidirect
111. C263#1603semidirect
114. #451D263semidirect

Maximal subgroups

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

subgroupindex
#306825372
#306820772
#306818572
#306816752
#306816732
#306816632
#451×C2632
#1603263