Finite Group Databasebeta

← #46781871

Subgroups — #46781871

Order 33664.

256 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 55 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#30682608C211yesmaximal, characteristic
2#30682230C211yesmaximal, characteristic, complemented
3#30682225C211yesmaximal, characteristic, complemented
4#30681682C211yesmaximal, characteristic, complemented
5#30681670C211yesmaximal, characteristic, complemented
6#30681667C211yesmaximal, characteristic, complemented
7#492×C263C211yesmaximal, characteristic, complemented
8C2×#16862375—21no—
9#22554466—21no—
10#22554442—22no—
11#22554441—21no—
12C4×Dic526C2211yescharacteristic
13C4×D1052C2211yescharacteristic
14D4×Dic263—21no—
15#22554403—21no—
16#22554401—21no—
17C4⋊(C263⋊C8)C2211yescharacteristic
18C4⋊(C263⋊C8)C2211yescharacteristic
19#22554393—21no—
20#22554390—21no—
21C2×SD16×C263—22no—
22C4⋊Q8×C263C2211yescharacteristic
23#127×C263C2211yescharacteristic
24C4×C8×C263C2211yescharacteristic
25#16862375—42no—
26#16862375—42no—
27C2×Dic526D411yescharacteristic
28C2×D1052D411yescharacteristic
29C2×C22⋊D263—22no—
30C2×C22⋊D263—22no—
31C22×Dic263—22no—
32C2×C4×D263—21no—
33C2×C263⋊C8—21no—
34C2×C263⋊C8—21no—
35C4⋊Dic263D411yescharacteristic
36C4⋊Dic263D411yescharacteristic
37Dic263⋊C4—21no—
38C22⋊Dic263—22no—
39(C2×D263)⋊C4—21no—
40C4×Dic263—21no—
41C2×Q8×C263—21no—
42C2×D4×C263—21no—
43C2×D4×C263—21no—
44C2×D4×C263D412yes—
45SD16×C263—44no—
46C2×C8×C263—21no—
47C4⋊C4×C263—21no—
48C4⋊C4×C263—21no—
49C42×C263C2311yescharacteristic
50C22×D263—21no—
51Dic526—21no—
52Dic526SD1612yescomplemented
53D1052—21no—
54D1052—21no—
55C22⋊D263—44no—
56C22⋊D263—82no—
57C2×Dic263—21no—
58C2×Dic263—21no—
59C2×Dic263—21no—
60C2×Dic263—44no—
61C4×D263—41no—
62C4×D263—41no—
63C263⋊C8—41no—
64C263⋊C8—41no—
65C23×C263—22no—
66Q8×C263—42no—
67D4×C263—42no—
68D4×C263—41no—
69D4×C263—41no—
70D4×C263—41no—
71D4×C263—41no—
72C2×C4×C263—41no—
73C2×C4×C263C2×D411yescharacteristic
74C2×C4×C263C2×D411yescharacteristic
75C2×C4×C263C2×D411yescharacteristic
76C8×C263—22no—
77C22×C263—42no—
78C22×C263—42no—
79C22×C263—42no—
80C22×C263#12011yescharacteristic
81C2×D263—41no—
82C2×D263—41no—
83C2×D263—41no—
84C4×C263—21no—
85C4×C263—81no—
86C4×C263C2×SD1611yescharacteristic
87C4×C263#13511yescharacteristic
88C4×C263AGL(1,ℤ/8)11yescharacteristic
89C4×C263#13711yescharacteristic
90Dic263—22no—
91Dic263—41no—
92Dic263—41no—
93C2×C263—82no—
94C2×C263#45011yescharacteristic
95C2×C263#45211yescharacteristic
96C2×C263#45311yescharacteristic
97D263—81no—
98C263#163111yescharacteristic, complemented, Sylow
99#1631—2631nomaximal, Sylow
100#550—2631no—
101#492D26311yescharacteristic, complemented
102#477—2631no—
103#476—2631no—
104#331—2631no—
105Q8⋊C8—2631no—
106D4⋊C8—2631no—
107C2×#41—5261no—
108C2×SD16—22no—
109C4⋊Q8C2×D26311yescharacteristic
110#127—5261no—
111#127C2×D26311yescharacteristic
112#121—5261no—
113#121—5262no—
114C4×Q8—2631no—
115C4×D4—2631no—
116C4×D4—5261no—
117#107—5261no—
118#106—5261no—
119C4⋊C8—2631no—
120C4⋊C8—2631no—
121#103—5261no—
122#102—5261no—
123C4×C8C2×D26311yescharacteristic
124#41—10522no—
125#41—10522no—
126C2×Q8—21no—
127C2×Q8—2631no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—2631no—
131C2×D4—5262no—
132C2×D4—5262no—
133C2×D4C22⋊D26312yes—
134C22×C4—5262no—
135C22×C4—5261no—
136SD16—44no—
137C2×C8—21no—
138C2×C8—5261no—
139C2×C8—5261no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—2631no—
143C4⋊C4—2631no—
144C4⋊C4—5261no—
145C22⋊C4—5262no—
146C22⋊C4—5261no—
147C42—5261no—
148C42C22×D26311yescharacteristic
149C23—22no—
150C23—5261no—
151Q8—42no—
152Q8—2632no—
153Q8—5261no—
154D4—42no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—41no—
159D4—5261no—
160D4—5261no—
161D4—10524no—
162D4—21042no—
163C2×C4—41no—
164C2×C4—5261no—
165C2×C4—5261no—
166C2×C4—5261no—
167C2×C4—10524no—
168C2×C4—10521no—
169C2×C4—10521no—
170C2×C4D4×D26311yescharacteristic
171C2×C4D4×D26311yescharacteristic
172C2×C4C2×C22⋊D26311yescharacteristic
173C8—22no—
174C8—10521no—
175C8—10521no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—10521no—
180C22—10521no—
181C22—10521no—
182C22#2255443811yescharacteristic
183C4—21no—
184C4—81no—
185C4—5262no—
186C4—10521no—
187C4—10521no—
188C4SD16×D26311yescharacteristic
189C4#2255449111yescharacteristic
190C4#2255449711yescharacteristic
191C4#2255449911yescharacteristic
192C2—82no—
193C2—21041no—
194C2#3068208711yescharacteristic
195C2#3068209711yescharacteristic
196C2#3068210511yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#492×C263C2
socleC22×C263#120
prime radical#30682608C2
hypercenter#492D263
hypocenterC263#1631
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
2. #30682230C2semidirect
3. #30682225C2semidirect
4. #30681682C2semidirect
5. #30681670C2semidirect
6. #30681667C2semidirect
7. #492×C263C2semidirect
52. Dic526SD16semidirect
98. C263#1631semidirect
101. #492D263semidirect

Maximal subgroups

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

subgroupindex
#306826082
#306822302
#306822252
#306816822
#306816702
#306816672
#492×C2632
#1631263