Finite Group Databasebeta

← #46783042

Subgroups — #46783042

Order 33664.

408 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 109 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
1C22×#16862360C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊D263C211yesmaximal, characteristic
3C2×(C2×D263)⋊C8C212yesmaximal, complemented
4#30681692C212yesmaximal, complemented
5C2×C22⋊C8×C263C211yesmaximal, characteristic, complemented
6C22×C22⋊D263C411yescharacteristic
7C22×C4×D263C2211yescharacteristic
8C2×#16862360—24no—
9C2×#16862360—22no—
10C22×C263⋊C8C2212yes—
11C4×C22⋊D263—22no—
12C4×C22⋊D263—22no—
13C2×Dic263⋊C4C411yescharacteristic
14C2×C22⋊Dic263C411yescharacteristic
15C2×(C2×D263)⋊C4C411yescharacteristic
16C2×C4×Dic263C2211yescharacteristic
17(C2×D263)⋊C8—24no—
18C23×C4×C263C2211yescharacteristic
19C22×C8×C263C2212yes—
20C22⋊C8×C263—22no—
21C23×D263C2×C411yescharacteristic
22C2×C22⋊D263—22no—
23C2×C22⋊D263—22no—
24C2×C22⋊D263—22no—
25C22×Dic263C2×C411yescharacteristic
26C22×Dic263C2×C411yescharacteristic
27C22×Dic263C2×C411yescharacteristic
28C2×C4×D263—22no—
29C2×C4×D263—21no—
30C2×C4×D263—21no—
31C2×C4×D263—22no—
32#16862360—28no—
33C2×C263⋊C8—22no—
34C2×C263⋊C8—22no—
35C2×C263⋊C8D414yescomplemented
36Dic263⋊C4—22no—
37C22⋊Dic263—22no—
38(C2×D263)⋊C4—22no—
39C4×Dic263—21no—
40C4×Dic263—21no—
41C24×C263C2×C411yescharacteristic
42C22×C4×C263—22no—
43C22×C4×C263—22no—
44C22×C4×C263C2×C411yescharacteristic
45C22×C4×C263D412yes—
46C22×C4×C263D412yes—
47C22×C4×C263C2311yescharacteristic
48C2×C8×C263—22no—
49C2×C8×C263—22no—
50C2×C8×C263—22no—
51C22×D263—21no—
52C22×D263—22no—
53C22×D263—21no—
54C22×D263—22no—
55C22×D263M1612yescomplemented
56C22⋊D263—28no—
57C2×Dic263—21no—
58C2×Dic263—21no—
59C2×Dic263—21no—
60C2×Dic263—21no—
61C2×Dic263—22no—
62C2×Dic263—22no—
63C2×Dic263M1612yescomplemented
64C4×D263—41no—
65C4×D263—42no—
66C4×D263—41no—
67C263⋊C8—24no—
68C23×C263—22no—
69C23×C263—21no—
70C23×C263—21no—
71C23×C263—22no—
72C23×C263C22⋊C412yes—
73C23×C263C22×C411yescharacteristic
74C2×C4×C263—22no—
75C2×C4×C263—22no—
76C2×C4×C263—24no—
77C2×C4×C263—22no—
78C2×C4×C263C22⋊C412yes—
79C2×C4×C263C2×D412yes—
80C2×C4×C263C2×D411yescharacteristic
81C2×C4×C263C2×D411yescharacteristic
82C2×C4×C263#4112yes—
83C8×C263—42no—
84C22×C263—22no—
85C22×C263—22no—
86C22×C263—22no—
87C22×C263—42no—
88C22×C263—42no—
89C22×C263C2×C22⋊C411yescharacteristic
90C22×C263C4×D412yes—
91C22×C263C2×M1611yescharacteristic
92C22×C263C2×M1611yescharacteristic
93C22×C263#13112yes—
94C2×D263—22no—
95C2×D263—24no—
96C2×D263—41no—
97C2×D263—41no—
98C2×D263—42no—
99C4×C263—22no—
100C4×C263#12011yescharacteristic
101C4×C263#12112yes—
102C4×C263#12311yescharacteristic
103Dic263—22no—
104Dic263—41no—
105Dic263—41no—
106C2×C263—42no—
107C2×C263#38611yescharacteristic
108C2×C263#40711yescharacteristic
109C2×C263#40811yescharacteristic
110C2×C263#43512yes—
111C2×C263#43612yes—
112D263—42no—
113C263#187011yescharacteristic, complemented, Sylow
114#1870—2631nomaximal, Sylow
115C22×M16—2631no—
116C2×C4×D4—2631no—
117C2×C22⋊C8—2632no—
118C2×C22⋊C8D26311yescharacteristic, complemented
119#336—2632no—
120C22×D4—2631no—
121C23×C4—2631no—
122C23×C4C2×D26311yescharacteristic
123C2×M16—5264no—
124C2×M16—5262no—
125C22×C8—2632no—
126C22×C8C2×D26312yes—
127C4×D4—5262no—
128C4×D4—5262no—
129C2×C4⋊C4—2631no—
130C2×C22⋊C4—2631no—
131C2×C22⋊C4—2631no—
132C2×C42—2631no—
133C22⋊C8—22no—
134C22⋊C8—5264no—
135C24—2631no—
136C24C4×D26311yescharacteristic
137C2×D4—5262no—
138C2×D4—5262no—
139C2×D4—5262no—
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—2631no—
143C22×C4—2631no—
144C22×C4—2631no—
145C22×C4—5262no—
146C22×C4—5261no—
147C22×C4—5261no—
148C22×C4—5262no—
149C22×C4C4×D26311yescharacteristic
150C22×C4C22⋊D26312yes—
151C22×C4D105212yes—
152C22×C4C22×D26311yescharacteristic
153M16—5268no—
154C2×C8—22no—
155C2×C8—22no—
156C2×C8—22no—
157C2×C8—2634no—
158C2×C8—5262no—
159C2×C8—5262no—
160C4⋊C4—5262no—
161C22⋊C4—5262no—
162C22⋊C4—5262no—
163C42—5261no—
164C42—5261no—
165C23—22no—
166C23—21no—
167C23—21no—
168C23—22no—
169C23—2632no—
170C23—5261no—
171C23—5262no—
172C23—5261no—
173C23—5262no—
174C23(C2×D263)⋊C412yes—
175C23C2×C4×D26311yescharacteristic
176D4—5268no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—24no—
180C2×C4—22no—
181C2×C4—2632no—
182C2×C4—5261no—
183C2×C4—5261no—
184C2×C4—5261no—
185C2×C4—5261no—
186C2×C4—5262no—
187C2×C4—5262no—
188C2×C4—10521no—
189C2×C4—10522no—
190C2×C4—10521no—
191C2×C4(C2×D263)⋊C412yes—
192C2×C4D4×D26312yes—
193C2×C4C2×C22⋊D26311yescharacteristic
194C2×C4C2×D105211yescharacteristic
195C2×C4#1686237512yes—
196C8—42no—
197C8—5264no—
198C22—22no—
199C22—22no—
200C22—22no—
201C22—42no—
202C22—42no—
203C22—5262no—
204C22—5264no—
205C22—10521no—
206C22—10522no—
207C22—10521no—
208C22C2×(C2×D263)⋊C411yescharacteristic
209C22(C22⋊D263)⋊C412yes—
210C22M16×D26311yescharacteristic
211C22M16×D26311yescharacteristic
212C22#2255447612yes—
213C4—22no—
214C4—5262no—
215C4—10521no—
216C4—10521no—
217C4#2255444011yescharacteristic
218C4#2255444212yes—
219C4#2255445411yescharacteristic
220C2—42no—
221C2—10522no—
222C2#3068181511yescharacteristic
223C2#3068190111yescharacteristic
224C2#3068190411yescharacteristic
225C2#3068201212yes—
226C2#3068201312yes—
subgroupG/H
center, FrattiniC22×C4C22×D263
commutator, socleC23×C263C22×C4
FittingC2×C22⋊C8×C263C2
prime radicalC22×C22⋊D263C4
cosocleC22×C4×C263C23
hypercenterC2×C22⋊C8D263
hypocenterC263#1870
LCSG ▷ C23×C263 ▷ C263
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C22×#16862360C2semidirect
3. C2×(C2×D263)⋊C8C2semidirect
4. #30681692C2semidirect
5. C2×C22⋊C8×C263C2semidirect
35. C2×C263⋊C8D4semidirect
55. C22×D263M16semidirect
63. C2×Dic263M16semidirect
113. C263#1870semidirect
118. C2×C22⋊C8D263semidirect

Maximal subgroups

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

subgroupindex
C22×#168623602
C2×C4×C22⋊D2632
C2×(C2×D263)⋊C82
#306816922
C2×C22⋊C8×C2632
#1870263