Finite Group Databasebeta

← #46784082

Subgroups — #46784082

Order 33664.

250 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 91 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×#22554403C211yesmaximal, characteristic
2C2×#22554401C211yesmaximal, characteristic
3#30681836C211yesmaximal, characteristic
4#30681700C211yesmaximal, characteristic
5#30681700C211yesmaximal, characteristic
6#30681693C211yesmaximal, characteristic
7C2×#125×C263C211yesmaximal, characteristic
8C22×C263⋊C8C2211yescharacteristic
9C22×C263⋊C8C2211yescharacteristic
10C2×C4⋊Dic263C2211yescharacteristic
11C2×C4⋊Dic263C2211yescharacteristic
12C2×Dic263⋊C4—21no—
13#22554403—22no—
14#22554401—22no—
15C263⋊#95—21no—
16#125×C263—22no—
17#125×C263—22no—
18C2×C4⋊C4×C263—21no—
19C2×C4⋊C4×C263—21no—
20C2×C4⋊C4×C263C2211yescharacteristic
21C2×C4⋊C4×C263C2211yescharacteristic
22C2×C42×C263C2211yescharacteristic
23C22×Dic263—21no—
24C22×Dic263—21no—
25C2×C263⋊C8—21no—
26C2×C263⋊C8—21no—
27C2×C263⋊C8—21no—
28C2×C263⋊C8—21no—
29C2×C263⋊C8Q812yes—
30C2×C263⋊C8Q812yes—
31C4⋊Dic263—21no—
32C4⋊Dic263—21no—
33C4⋊Dic263—21no—
34C4⋊Dic263Q812yes—
35Dic263⋊C4—42no—
36C22×C4×C263—21no—
37C22×C4×C263—21no—
38C22×C4×C263D411yescharacteristic
39C22×C4×C263D411yescharacteristic
40C22×C4×C263C2311yescharacteristic
41C4⋊C4×C263—24no—
42C4⋊C4×C263—24no—
43C4⋊C4×C263—21no—
44C4⋊C4×C263—21no—
45C4⋊C4×C263D412yes—
46C4⋊C4×C263D412yes—
47C42×C263—21no—
48C42×C263—21no—
49C2×Dic263—22no—
50C2×Dic263—41no—
51C2×Dic263—41no—
52C2×Dic263—41no—
53C2×Dic263—41no—
54C2×Dic263—41no—
55C263⋊C8—22no—
56C263⋊C8—22no—
57C23×C263C2×D411yescharacteristic
58C2×C4×C263—21no—
59C2×C4×C263—21no—
60C2×C4×C263—22no—
61C2×C4×C263—22no—
62C2×C4×C263—21no—
63C2×C4×C263—21no—
64C2×C4×C263—21no—
65C2×C4×C263—21no—
66C2×C4×C263—41no—
67C2×C4×C263—41no—
68C2×C4×C263—41no—
69C2×C4×C263—41no—
70C2×C4×C263C2×D411yescharacteristic
71C2×C4×C263C2×D411yescharacteristic
72C2×C4×C263C2×Q811yescharacteristic
73C2×C4×C263C2×Q811yescharacteristic
74C2×C4×C263C2×Q811yescharacteristic
75C2×C4×C263#4111yescharacteristic
76C22×C263#12011yescharacteristic
77C22×C263C22⋊Q811yescharacteristic
78C22×C263C4⋊Q811yescharacteristic
79C22×C263#13511yescharacteristic
80C22×C263#13511yescharacteristic
81C22×C263AGL(1,ℤ/8)11yescharacteristic
82C22×C263#13711yescharacteristic
83C4×C263—41no—
84C4×C263—42no—
85C4×C263—41no—
86C4×C263—42no—
87C4×C263C22⋊Q811yescharacteristic
88C4×C263C22⋊Q811yescharacteristic
89C4×C263C4⋊Q811yescharacteristic
90C4×C263C4⋊Q811yescharacteristic
91Dic263—42no—
92Dic263—81no—
93C2×C263#39511yescharacteristic
94C2×C263#44911yescharacteristic
95C2×C263#45211yescharacteristic
96C2×C263#47811yescharacteristic
97C2×C263#47911yescharacteristic
98C2×C263#49911yescharacteristic
99C2×C263#50111yescharacteristic
100C263#205911yescharacteristic, complemented, Sylow
101#2059—2631nomaximal, Sylow
102C2×#125D26311yescharacteristic
103C2×#107—2631no—
104C2×#106—2631no—
105#389—2631no—
106#340—2631no—
107#340—2631no—
108#336—2631no—
109C22×C8—2631no—
110C22×C8—2631no—
111#125—22no—
112#125—22no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—2631no—
116C2×C4⋊C4—2631no—
117C2×C4⋊C4—5261no—
118C2×C4⋊C4C2×D26311yescharacteristic
119C2×C4⋊C4C2×D26311yescharacteristic
120C2×C42C2×D26311yescharacteristic
121#107—5262no—
122#106—5262no—
123#95—5261no—
124C22×C4—21no—
125C22×C4—21no—
126C22×C4—5261no—
127C22×C4—5261no—
128C22×C4C22⋊D26311yescharacteristic
129C22×C4C22⋊D26311yescharacteristic
130C22×C4C22×D26311yescharacteristic
131C2×C8—2632no—
132C2×C8—2632no—
133C2×C8—5261no—
134C2×C8—5261no—
135C2×C8—5261no—
136C2×C8—5261no—
137C4⋊C4—24no—
138C4⋊C4—24no—
139C4⋊C4—21no—
140C4⋊C4—21no—
141C4⋊C4—2632no—
142C4⋊C4—5261no—
143C4⋊C4—5261no—
144C4⋊C4—5261no—
145C4⋊C4—10522no—
146C4⋊C4C22⋊D26312yes—
147C4⋊C4C22⋊D26312yes—
148C42—21no—
149C42—21no—
150C23C2×C22⋊D26311yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—5262no—
164C2×C4—10521no—
165C2×C4—10521no—
166C2×C4—10521no—
167C2×C4—10521no—
168C2×C4—10521no—
169C2×C4C2×C22⋊D26311yescharacteristic
170C2×C4C2×C22⋊D26311yescharacteristic
171C2×C4Q8×D26311yescharacteristic
172C2×C4Q8×D26311yescharacteristic
173C2×C4Q8×D26311yescharacteristic
174C2×C4#1686237711yescharacteristic
175C8—5262no—
176C8—5262no—
177C22#2255443911yescharacteristic
178C22#2255444611yescharacteristic
179C22#2255446811yescharacteristic
180C22#2255449011yescharacteristic
181C22#2255449011yescharacteristic
182C22#2255449511yescharacteristic
183C22#2255450011yescharacteristic
184C4—41no—
185C4—42no—
186C4—41no—
187C4—42no—
188C4—10522no—
189C4—21041no—
190C4#2255444611yescharacteristic
191C4#2255444611yescharacteristic
192C4#2255446811yescharacteristic
193C4#2255446811yescharacteristic
194C2#3068185711yescharacteristic
195C2#3068208311yescharacteristic
196C2#3068210011yescharacteristic
197C2#3068223511yescharacteristic
198C2#3068224211yescharacteristic
199C2#3068233711yescharacteristic
200C2#3068234811yescharacteristic
subgroupG/H
centerC23C2×C22⋊D263
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
FittingC2×#125×C263C2
socle, prime radicalC23×C263C2×D4
hypercenterC2×#125D263
hypocenterC263#2059
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
100. C263#2059semidirect

Maximal subgroups

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

subgroupindex
C2×#225544032
C2×#225544012
#306818362
#306817002
#306816932
C2×#125×C2632
#2059263