Finite Group Databasebeta

← #46781236

Subgroups — #46781236

Order 33664.

304 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 77 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#30682449C211yesmaximal, characteristic
2C2×C22⋊(C263⋊C8)C211yesmaximal, characteristic, complemented
3#30681674C212yesmaximal, complemented
4#30681671C212yesmaximal, complemented
5C4×C22⋊C4×C263C211yesmaximal, characteristic, complemented
6C2×#16862376C411yescharacteristic, complemented
7C22×C263⋊C8—21no—
8#22554453—21no—
9#22554449C411yescharacteristic, complemented
10#22554449C2211yescharacteristic
11#22554444C411yescharacteristic, complemented
12#22554444C2211yescharacteristic
13#22554439—21no—
14C4×C22⋊D263—21no—
15C4×C22⋊D263—21no—
16#22554429C411yescharacteristic, complemented
17C22⋊(C263⋊C8)—21no—
18C22⋊(C263⋊C8)C2212yes—
19C23×C4×C263C2211yescharacteristic
20C2×C22⋊C4×C263—21no—
21C2×C42×C263—21no—
22#95×C263C2212yes—
23#16862376—42no—
24C2×Dic526C2×C411yescharacteristic
25C2×D1052C2×C411yescharacteristic
26C2×C22⋊D263—21no—
27C2×C22⋊D263—21no—
28C2×C22⋊D263—21no—
29C2×C4×D263—21no—
30C2×C263⋊C8—22no—
31C2×C263⋊C8—42no—
32C4⋊Dic263C2×C411yescharacteristic
33C4⋊Dic263C2×C411yescharacteristic
34Dic263⋊C4—21no—
35Dic263⋊C4—21no—
36C22⋊Dic263—21no—
37C22⋊Dic263—21no—
38C22⋊Dic263—21no—
39(C2×D263)⋊C4—21no—
40(C2×D263)⋊C4—21no—
41C4×Dic263—21no—
42C24×C263D411yescharacteristic
43C22×C4×C263—22no—
44C22×C4×C263—42no—
45C22×C4×C263C2×C411yescharacteristic
46C22×C4×C263C2×C411yescharacteristic
47C22×C4×C263D411yescharacteristic
48C22×C4×C263D411yescharacteristic
49C22×C4×C263D411yescharacteristic
50C22×C4×C263C2311yescharacteristic
51C22⋊C4×C263—24no—
52C42×C263—42no—
53C22×D263—21no—
54Dic526—41no—
55D1052—41no—
56C22⋊D263—42no—
57C22⋊D263—42no—
58C22⋊D263—42no—
59C2×Dic263—21no—
60C2×Dic263—21no—
61C2×Dic263—21no—
62C4×D263—42no—
63C263⋊C8—42no—
64C23×C263—22no—
65C23×C263—22no—
66C23×C263—41no—
67C23×C263C22⋊C411yescharacteristic
68C23×C263C22⋊C411yescharacteristic
69C23×C263C2×D411yescharacteristic
70C2×C4×C263—22no—
71C2×C4×C263—22no—
72C2×C4×C263—22no—
73C2×C4×C263—24no—
74C2×C4×C263—41no—
75C2×C4×C263—41no—
76C2×C4×C263—41no—
77C2×C4×C263—42no—
78C2×C4×C263—42no—
79C2×C4×C263C22⋊C411yescharacteristic
80C2×C4×C263C22⋊C411yescharacteristic
81C2×C4×C263C22×C411yescharacteristic
82C2×C4×C263C2×D411yescharacteristic
83C22×C263—21no—
84C22×C263—21no—
85C22×C263—21no—
86C22×C263—21no—
87C22×C263—21no—
88C22×C263—21no—
89C22×C263—21no—
90C22×C263—44no—
91C22×C263#10412yes—
92C22×C263C2×C22⋊C411yescharacteristic
93C22×C263#13512yes—
94C2×D263—41no—
95C2×D263—41no—
96C2×D263—41no—
97C4×C263—21no—
98C4×C263—21no—
99C4×C263—21no—
100C4×C263—44no—
101C4×C263#9912yes—
102Dic263—41no—
103Dic263—41no—
104Dic263—41no—
105C2×C263—22no—
106C2×C263—22no—
107C2×C263—41no—
108C2×C263C2×#9911yescharacteristic
109C2×C263#41611yescharacteristic
110C2×C263C2×#10411yescharacteristic
111D263—81no—
112C263#150111yescharacteristic, complemented, Sylow
113#1501—2631nomaximal, Sylow
114#525—2631no—
115C2×C22⋊C8—2631no—
116C4×C22⋊C4D26311yescharacteristic, complemented
117#328—2632no—
118#327—2632no—
119C2×#41—2631no—
120C23×C4C2×D26311yescharacteristic
121C22×C8—5261no—
122#123—5261no—
123C22⋊Q8—2631no—
124C22⋊Q8—2631no—
125#121—2631no—
126#121—2631no—
127#120—5261no—
128C4×D4—5261no—
129C4×D4—5261no—
130#117—2631no—
131C2×C22⋊C4—21no—
132C2×C42—21no—
133C22⋊C8—2632no—
134C22⋊C8—5261no—
135#95C2×D26312yes—
136C24C22⋊D26311yescharacteristic
137#41—10522no—
138C2×Q8—2631no—
139C2×D4—2631no—
140C2×D4—5261no—
141C2×D4—5261no—
142C2×D4—5261no—
143C22×C4—22no—
144C22×C4—42no—
145C22×C4—5261no—
146C22×C4C4×D26311yescharacteristic
147C22×C4C4×D26311yescharacteristic
148C22×C4C22⋊D26311yescharacteristic
149C22×C4D105211yescharacteristic
150C22×C4D105211yescharacteristic
151C22×C4C22×D26311yescharacteristic
152C2×C8—5262no—
153C2×C8—10522no—
154C4⋊C4—2631no—
155C4⋊C4—2631no—
156C4⋊C4—5261no—
157C4⋊C4—5261no—
158C22⋊C4—24no—
159C22⋊C4—5261no—
160C22⋊C4—5261no—
161C22⋊C4—5261no—
162C22⋊C4—5261no—
163C22⋊C4—5261no—
164C42—42no—
165C42—5261no—
166C23—22no—
167C23—22no—
168C23—41no—
169C23—5261no—
170C23(C2×D263)⋊C411yescharacteristic
171C23(C2×D263)⋊C411yescharacteristic
172C23C2×C22⋊D26311yescharacteristic
173Q8—10521no—
174D4—10521no—
175D4—10522no—
176D4—10522no—
177D4—10522no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—24no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—5261no—
188C2×C4—5261no—
189C2×C4—5261no—
190C2×C4—10522no—
191C2×C4(C2×D263)⋊C411yescharacteristic
192C2×C4(C2×D263)⋊C411yescharacteristic
193C2×C4C2×C4×D26311yescharacteristic
194C2×C4C2×D105211yescharacteristic
195C8—10522no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—44no—
204C22—10521no—
205C22—10521no—
206C22—10521no—
207C22#2255439812yes—
208C22C2×(C2×D263)⋊C411yescharacteristic
209C22#2255449012yes—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—44no—
214C4—10521no—
215C4—10521no—
216C4—10521no—
217C4#2255438412yes—
218C2—22no—
219C2—22no—
220C2—41no—
221C2—21041no—
222C2C2×#2255438411yescharacteristic
223C2#3068193211yescharacteristic
224C2C2×#2255439811yescharacteristic
subgroupG/H
centerC2×C4(C2×D263)⋊C4
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
FittingC4×C22⋊C4×C263C2
socleC22×C263C2×C22⋊C4
prime radical#30682449C2
cosocleC22×C4×C263C23
hypercenterC4×C22⋊C4D263
hypocenterC263#1501
LCSG ▷ C2×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊(C263⋊C8)C2semidirect
3. #30681674C2semidirect
4. #30681671C2semidirect
5. C4×C22⋊C4×C263C2semidirect
6. C2×#16862376C4semidirect
9. #22554449C4semidirect
11. #22554444C4semidirect
16. #22554429C4semidirect
112. C263#1501semidirect
116. C4×C22⋊C4D263semidirect

Maximal subgroups

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

subgroupindex
#306824492
C2×C22⋊(C263⋊C8)2
#306816742
#306816712
C4×C22⋊C4×C2632
#1501263