Finite Group Databasebeta

← #46782063

Subgroups — #46782063

Order 33664.

208 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 45 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#30682682C211yesmaximal, characteristic
2#30682344C211yesmaximal, characteristic, complemented
3#30682330C211yesmaximal, characteristic, complemented
4#30681679C211yesmaximal, characteristic, complemented
5#30681678C211yesmaximal, characteristic, complemented
6#30681677C211yesmaximal, characteristic, complemented
7#489×C263C211yesmaximal, characteristic, complemented
8C2×#16862366—21no—
9C2×#16862363—21no—
10#22554462C2211yescharacteristic
11#22554458C2211yescharacteristic
12#22554454—21no—
13#22554452—21no—
14#22554447—21no—
15#22554446—21no—
16#22554443—21no—
17#22554442—21no—
18#22554403—21no—
19#22554401—21no—
20#22554381C2211yescharacteristic
21#22554381C2211yescharacteristic
22C4⋊Q8×C263C2211yescharacteristic
23#124×C263C2211yescharacteristic
24#103×C263—21no—
25#102×C263—21no—
26#97×C263C2211yescharacteristic
27C2×Dic526D411yescharacteristic
28C2×D1052D411yescharacteristic
29C2×C22⋊D263—21no—
30C2×C22⋊D263—21no—
31C22×Dic263—21no—
32C2×C4×D263—21no—
33#16862366—42no—
34#16862363—42no—
35C2×C263⋊C8—21no—
36C2×C263⋊C8—21no—
37C4⋊Dic263—21no—
38C4⋊Dic263D411yescharacteristic
39C4⋊Dic263D411yescharacteristic
40Dic263⋊C4—21no—
41Dic263⋊C4—21no—
42Dic263⋊C4—21no—
43C22⋊Dic263—21no—
44(C2×D263)⋊C4—21no—
45(C2×D263)⋊C4—21no—
46(C2×D263)⋊C4—21no—
47C2×Q8×C263—21no—
48C2×Q8×C263D411yescharacteristic
49C2×D4×C263D411yescharacteristic
50C2×C8×C263—21no—
51C4⋊C4×C263—21no—
52C4⋊C4×C263—21no—
53C22⋊C4×C263—21no—
54C22⋊C4×C263—21no—
55C42×C263C2311yescharacteristic
56C22×D263—21no—
57Dic526—41no—
58D1052—41no—
59C22⋊D263—81no—
60C22⋊D263—81no—
61C2×Dic263—21no—
62C2×Dic263—21no—
63C2×Dic263—21no—
64C2×Dic263—81no—
65C4×D263—81no—
66C263⋊C8—22no—
67C263⋊C8—22no—
68C23×C263—21no—
69Q8×C263—41no—
70Q8×C263—41no—
71Q8×C263—41no—
72D4×C263—41no—
73C2×C4×C263—21no—
74C2×C4×C263—41no—
75C2×C4×C263C2×D411yescharacteristic
76C2×C4×C263C2×D411yescharacteristic
77C2×C4×C263C2×D411yescharacteristic
78C8×C263—41no—
79C22×C263—41no—
80C22×C263—41no—
81C22×C263—41no—
82C22×C263#12011yescharacteristic
83C2×D263—41no—
84C2×D263—41no—
85C2×D263—41no—
86C4×C263—21no—
87C4×C263—21no—
88C4×C263—21no—
89C4×C263—41no—
90C4×C263—81no—
91Dic263—41no—
92Dic263—41no—
93Dic263—41no—
94C2×C263—81no—
95C2×C263#45311yescharacteristic
96C2×C263#45511yescharacteristic
97C2×C263#45611yescharacteristic
98D263—81no—
99C263#166111yescharacteristic, complemented, Sylow
100#1661—2631nomaximal, Sylow
101#562—2631no—
102#501—2631no—
103#497—2631no—
104#489D26311yescharacteristic, complemented
105#330—2631no—
106#329—2631no—
107#329—2631no—
108C2×Q16—5261no—
109C2×SD16—5261no—
110C4⋊Q8C2×D26311yescharacteristic
111#125—2631no—
112#124—2631no—
113#124C2×D26311yescharacteristic
114#123—5261no—
115#123—5261no—
116C22⋊Q8—5261no—
117C22⋊Q8—5261no—
118#121—5261no—
119#121—5261no—
120#107—5261no—
121#106—5261no—
122#103—21no—
123#102—21no—
124#97—2631no—
125#97—2631no—
126#97C2×D26311yescharacteristic
127C2×Q8—21no—
128C2×Q8—2631no—
129C2×Q8C22⋊D26311yescharacteristic
130C2×D4—2631no—
131C2×D4—5261no—
132C2×D4—5261no—
133C2×D4C22⋊D26311yescharacteristic
134C22×C4—5261no—
135C22×C4—5261no—
136Q16—10522no—
137SD16—10522no—
138C2×C8—21no—
139C2×C8—5261no—
140C2×C8—5261no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—2631no—
144C4⋊C4—2631no—
145C4⋊C4—5261no—
146C4⋊C4—5261no—
147C4⋊C4—5261no—
148C4⋊C4—5261no—
149C22⋊C4—21no—
150C22⋊C4—21no—
151C22⋊C4—5261no—
152C22⋊C4—5261no—
153C22⋊C4—5261no—
154C22⋊C4—5261no—
155C42C22×D26311yescharacteristic
156C23—21no—
157C23—5261no—
158Q8—41no—
159Q8—41no—
160Q8—41no—
161Q8—10521no—
162D4—41no—
163D4—10521no—
164D4—21041no—
165D4—21041no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—5261no—
169C2×C4—5261no—
170C2×C4—5261no—
171C2×C4—21041no—
172C2×C4—21041no—
173C2×C4D4×D26311yescharacteristic
174C2×C4D4×D26311yescharacteristic
175C2×C4C2×C22⋊D26311yescharacteristic
176C8—41no—
177C8—5262no—
178C8—5262no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—10521no—
183C22—10521no—
184C22—10521no—
185C22#2255443811yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—81no—
191C4—10521no—
192C4—10521no—
193C4—10521no—
194C2—81no—
195C2—21041no—
196C2#3068210411yescharacteristic
197C2#3068211511yescharacteristic
198C2#3068211911yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#489×C263C2
socleC22×C263#120
prime radical#30682682C2
hypercenter#489D263
hypocenterC263#1661
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
2. #30682344C2semidirect
3. #30682330C2semidirect
4. #30681679C2semidirect
5. #30681678C2semidirect
6. #30681677C2semidirect
7. #489×C263C2semidirect
99. C263#1661semidirect
104. #489D263semidirect

Maximal subgroups

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

subgroupindex
#306826822
#306823442
#306823302
#306816792
#306816782
#306816772
#489×C2632
#1661263