Finite Group Databasebeta

← #46782038

Subgroups — #46782038

Order 33664.

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

normal subgroups only

This group has 230 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, complemented
2#30682325C211yesmaximal, characteristic, complemented
3#30682302C211yesmaximal, characteristic, complemented
4#30681679C211yesmaximal, characteristic, complemented
5#30681678C211yesmaximal, characteristic, complemented
6#30681677C211yesmaximal, characteristic, complemented
7#496×C263C211yesmaximal, characteristic, complemented
8C2×#16862364—21no—
9C2×#16862361—21no—
10#22554462C2211yescharacteristic
11#22554458C2211yescharacteristic
12#22554454—21no—
13#22554452—21no—
14#22554447—21no—
15#22554446—21no—
16#22554443—21no—
17#22554442—21no—
18#22554391—21no—
19#22554391—21no—
20#22554381C2211yescharacteristic
21#22554381C2211yescharacteristic
22C2×SD16×C263—21no—
23C2×D8×C263—21no—
24#127×C263C2211yescharacteristic
25#124×C263C2211yescharacteristic
26#97×C263C2211yescharacteristic
27C2×Dic526D411yescharacteristic
28C2×D1052D411yescharacteristic
29C2×C22⋊D263—21no—
30C2×C22⋊D263—21no—
31C22×Dic263—21no—
32C2×C4×D263—21no—
33#16862364—42no—
34#16862361—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×C263D411yescharacteristic
48C2×D4×C263—21no—
49C2×D4×C263—21no—
50C2×D4×C263—21no—
51C2×D4×C263D411yescharacteristic
52SD16×C263—42no—
53D8×C263—42no—
54C2×C8×C263—21no—
55C22⋊C4×C263—21no—
56C22⋊C4×C263—21no—
57C42×C263C2311yescharacteristic
58C22×D263—21no—
59Dic526—41no—
60D1052—41no—
61C22⋊D263—81no—
62C22⋊D263—81no—
63C2×Dic263—21no—
64C2×Dic263—21no—
65C2×Dic263—21no—
66C2×Dic263—81no—
67C4×D263—81no—
68C263⋊C8—22no—
69C263⋊C8—41no—
70C23×C263—21no—
71C23×C263—41no—
72Q8×C263—41no—
73D4×C263—41no—
74D4×C263—41no—
75D4×C263—41no—
76D4×C263—42no—
77D4×C263—41no—
78D4×C263—41no—
79C2×C4×C263—21no—
80C2×C4×C263C2×D411yescharacteristic
81C2×C4×C263C2×D411yescharacteristic
82C2×C4×C263C2×D411yescharacteristic
83C8×C263—22no—
84C22×C263—41no—
85C22×C263—41no—
86C22×C263—41no—
87C22×C263—81no—
88C22×C263—81no—
89C22×C263—81no—
90C22×C263#12011yescharacteristic
91C2×D263—41no—
92C2×D263—41no—
93C2×D263—41no—
94C4×C263—21no—
95C4×C263—21no—
96C4×C263—21no—
97C4×C263—41no—
98Dic263—41no—
99Dic263—41no—
100Dic263—41no—
101C2×C263—81no—
102C2×C263—161no—
103C2×C263#45311yescharacteristic
104C2×C263#45311yescharacteristic
105C2×C263#45411yescharacteristic
106D263—81no—
107C263#165611yescharacteristic, complemented, Sylow
108#1656—2631nomaximal, Sylow
109#562—2631no—
110#496—2631no—
111#496D26311yescharacteristic, complemented
112#490—2631no—
113#330—2631no—
114#329—2631no—
115#329—2631no—
116C2×SD16—21no—
117C2×SD16—5261no—
118C2×D8—21no—
119C2×D8—5261no—
120#127C2×D26311yescharacteristic
121#125—2631no—
122#124—2631no—
123#124C2×D26311yescharacteristic
124#123—5261no—
125#123—5261no—
126C22⋊Q8—5261no—
127C22⋊Q8—5261no—
128#121—5261no—
129#121—5261no—
130#102—5261no—
131#102—5261no—
132#97—2631no—
133#97—2631no—
134#97C2×D26311yescharacteristic
135C2×Q8—2631no—
136C2×Q8C22⋊D26311yescharacteristic
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—21no—
140C2×D4—2631no—
141C2×D4—5261no—
142C2×D4—5261no—
143C2×D4C22⋊D26311yescharacteristic
144C22×C4—5261no—
145C22×C4—5261no—
146SD16—42no—
147SD16—10522no—
148D8—42no—
149D8—10522no—
150C2×C8—21no—
151C2×C8—5261no—
152C2×C8—5261no—
153C4⋊C4—2631no—
154C4⋊C4—2631no—
155C4⋊C4—5261no—
156C4⋊C4—5261no—
157C4⋊C4—5261no—
158C4⋊C4—5261no—
159C22⋊C4—21no—
160C22⋊C4—21no—
161C22⋊C4—5261no—
162C22⋊C4—5261no—
163C22⋊C4—5261no—
164C22⋊C4—5261no—
165C42C22×D26311yescharacteristic
166C23—21no—
167C23—41no—
168C23—5261no—
169Q8—41no—
170Q8—10521no—
171D4—41no—
172D4—41no—
173D4—41no—
174D4—41no—
175D4—41no—
176D4—42no—
177D4—10521no—
178D4—21041no—
179D4—21041no—
180C2×C4—21no—
181C2×C4—5261no—
182C2×C4—5261no—
183C2×C4—5261no—
184C2×C4—21041no—
185C2×C4—21041no—
186C2×C4D4×D26311yescharacteristic
187C2×C4D4×D26311yescharacteristic
188C2×C4C2×C22⋊D26311yescharacteristic
189C8—22no—
190C8—5262no—
191C8—10521no—
192C22—41no—
193C22—41no—
194C22—41no—
195C22—81no—
196C22—81no—
197C22—81no—
198C22—10521no—
199C22—10521no—
200C22—10521no—
201C22#2255443811yescharacteristic
202C4—21no—
203C4—21no—
204C4—21no—
205C4—41no—
206C4—10521no—
207C4—10521no—
208C4—10521no—
209C2—81no—
210C2—161no—
211C2—21041no—
212C2#3068210411yescharacteristic
213C2#3068210511yescharacteristic
214C2#3068210911yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#496×C263C2
socleC22×C263#120
hypercenter#496D263
hypocenterC263#1656
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #30682682C2semidirect
2. #30682325C2semidirect
3. #30682302C2semidirect
4. #30681679C2semidirect
5. #30681678C2semidirect
6. #30681677C2semidirect
7. #496×C263C2semidirect
107. C263#1656semidirect
111. #496D263semidirect

Maximal subgroups

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

subgroupindex
#306826822
#306823252
#306823022
#306816792
#306816782
#306816772
#496×C2632
#1656263