Finite Group Databasebeta

← #46781745

Subgroups — #46781745

Order 33664.

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

normal subgroups only

This group has 216 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#30682533C211yesmaximal, characteristic
2#30682269C211yesmaximal, characteristic, complemented
3#30682249C211yesmaximal, characteristic
4#30681870C211yesmaximal, characteristic, complemented
5#30681674C211yesmaximal, characteristic, complemented
6#30681663C211yesmaximal, characteristic, complemented
7#327×C263C211yesmaximal, characteristic
8#22554463—21no—
9#22554460—21no—
10#22554451—21no—
11#22554451—21no—
12#22554449C2211yescharacteristic
13#22554447—21no—
14D4×Dic263—21no—
15C2×C4⋊Dic263—21no—
16C2×C4⋊Dic263C2211yescharacteristic
17C2×Dic263⋊C4C2211yescharacteristic
18#22554403—21no—
19#22554402—21no—
20#22554395—21no—
21#22554391—21no—
22C22⋊(C263⋊C8)C2211yescharacteristic
23C263⋊#95—21no—
24#121×C263C2211yescharacteristic
25C22⋊C8×C263C2211yescharacteristic
26#95×C263C2211yescharacteristic
27C2×Dic526D411yescharacteristic
28C22×Dic263—21no—
29C22×Dic263—21no—
30C22×Dic263D411yescharacteristic
31C22×Dic263D411yescharacteristic
32C2×C263⋊C8—21no—
33C4⋊Dic263—21no—
34C4⋊Dic263—21no—
35C4⋊Dic263—21no—
36C4⋊Dic263—42no—
37C4⋊Dic263D411yescharacteristic
38Dic263⋊C4—21no—
39Dic263⋊C4—21no—
40Dic263⋊C4—21no—
41Dic263⋊C4—21no—
42Dic263⋊C4—21no—
43C22⋊Dic263—21no—
44C22⋊Dic263—21no—
45C22⋊Dic263—21no—
46C22⋊Dic263—21no—
47C4×Dic263—21no—
48C2×D4×C263—21no—
49C2×D4×C263D411yescharacteristic
50C22×C4×C263—21no—
51C22×C4×C263C2311yescharacteristic
52C2×C8×C263—21no—
53C4⋊C4×C263D411yescharacteristic
54C22⋊C4×C263—21no—
55Dic526—41no—
56C2×Dic263—21no—
57C2×Dic263—21no—
58C2×Dic263—21no—
59C2×Dic263—21no—
60C2×Dic263—21no—
61C2×Dic263—21no—
62C2×Dic263—41no—
63C2×Dic263—41no—
64C2×Dic263—41no—
65C2×Dic263—41no—
66C2×Dic263—81no—
67C263⋊C8—41no—
68C23×C263—21no—
69C23×C263C2×D411yescharacteristic
70D4×C263—41no—
71D4×C263—41no—
72D4×C263—41no—
73C2×C4×C263—22no—
74C2×C4×C263—21no—
75C2×C4×C263—41no—
76C2×C4×C263—41no—
77C2×C4×C263—41no—
78C2×C4×C263C2×D411yescharacteristic
79C2×C4×C263C2×D411yescharacteristic
80C8×C263—41no—
81C22×C263—21no—
82C22×C263—21no—
83C22×C263—41no—
84C22×C263—41no—
85C22×C263—41no—
86C22×C263#12011yescharacteristic
87C22×C263#13511yescharacteristic
88C22×C263AGL(1,ℤ/8)11yescharacteristic
89C4×C263—21no—
90C4×C263—21no—
91C4×C263—42no—
92C4×C263—41no—
93Dic263—41no—
94Dic263—41no—
95Dic263—41no—
96Dic263—41no—
97Dic263—81no—
98C2×C263—21no—
99C2×C263—21no—
100C2×C263—81no—
101C2×C263#44911yescharacteristic
102C2×C263#45611yescharacteristic
103C2×C263#45811yescharacteristic
104C263#160911yescharacteristic, complemented, Sylow
105#1609—2631nomaximal, Sylow
106#539—2631no—
107#483—2631no—
108#480—2631no—
109#398—2631no—
110#328—2631no—
111#327D26311yescharacteristic
112#324—2631no—
113#126—5261no—
114#125—5261no—
115#123—5261no—
116#123—5261no—
117C22⋊Q8—2631no—
118C22⋊Q8—5261no—
119#121C2×D26311yescharacteristic
120C4×D4—5261no—
121C2×C4⋊C4—2631no—
122C2×C4⋊C4—2631no—
123C2×C4⋊C4—5261no—
124#107—5261no—
125#106—5261no—
126#103—5261no—
127#102—5261no—
128C22⋊C8—2631no—
129C22⋊C8C2×D26311yescharacteristic
130#95—5261no—
131#95C2×D26311yescharacteristic
132C2×Q8—2631no—
133C2×D4—21no—
134C2×D4D105211yescharacteristic
135C22×C4—21no—
136C22×C4—2631no—
137C22×C4—2631no—
138C22×C4—5261no—
139C22×C4—5261no—
140C22×C4C22×D26311yescharacteristic
141C2×C8—21no—
142C2×C8—5261no—
143C4⋊C4—2631no—
144C4⋊C4—5261no—
145C4⋊C4—5261no—
146C4⋊C4—5261no—
147C4⋊C4—5261no—
148C4⋊C4—5261no—
149C4⋊C4—5261no—
150C4⋊C4—5261no—
151C4⋊C4—5261no—
152C4⋊C4—10522no—
153C4⋊C4D105211yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—5261no—
156C22⋊C4—5261no—
157C22⋊C4—5261no—
158C22⋊C4—5261no—
159C42—5261no—
160C23—21no—
161C23D4×D26311yescharacteristic
162Q8—10521no—
163D4—41no—
164D4—41no—
165D4—41no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—5261no—
172C2×C4—5261no—
173C2×C4—5261no—
174C2×C4—5261no—
175C2×C4—5261no—
176C2×C4—5261no—
177C2×C4—10521no—
178C2×C4—10521no—
179C2×C4—10521no—
180C2×C4—10521no—
181C2×C4—21041no—
182C2×C4D4×D26311yescharacteristic
183C2×C4C2×D105211yescharacteristic
184C8—41no—
185C8—10521no—
186C22—21no—
187C22—21no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22#2255444011yescharacteristic
192C22#2255449111yescharacteristic
193C22#2255449411yescharacteristic
194C4—21no—
195C4—21no—
196C4—42no—
197C4—41no—
198C4—10521no—
199C4—10521no—
200C4—10521no—
201C4—10521no—
202C4—21041no—
203C2—21no—
204C2—21no—
205C2—81no—
206C2#3068208411yescharacteristic
207C2#3068212211yescharacteristic
208C2#3068212911yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#327×C263C2
socleC22×C263#120
prime radical#121×C263C22
hypercenter#327D263
hypocenterC263#1609
LCSG ▷ C22×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #30682269C2semidirect
4. #30681870C2semidirect
5. #30681674C2semidirect
6. #30681663C2semidirect
104. C263#1609semidirect

Maximal subgroups

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

subgroupindex
#306825332
#306822692
#306822492
#306818702
#306816742
#306816632
#327×C2632
#1609263