Finite Group Databasebeta

← #46782055

Subgroups — #46782055

Order 33664.

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

normal subgroups only

This group has 228 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#30682680C211yesmaximal, characteristic
2#30682332C211yesmaximal, characteristic, complemented
3#30682298C211yesmaximal, characteristic, complemented
4#30682297C211yesmaximal, characteristic, complemented
5#30681677C211yesmaximal, characteristic, complemented
6#30681677C211yesmaximal, characteristic, complemented
7#329×C263C211yesmaximal, characteristic, complemented
8C2×Dic1052—21no—
9C2×#16862365—21no—
10#22554470C2211yescharacteristic, complemented
11#22554459—21no—
12#22554458C2211yescharacteristic
13#22554458C2211yescharacteristic
14#22554456—21no—
15#22554456—21no—
16#22554440—21no—
17#22554440—21no—
18#22554438—21no—
19#22554395—21no—
20#22554394—21no—
21#22554392—21no—
22#22554391—21no—
23#22554381C2211yescharacteristic, complemented
24#124×C263C2211yescharacteristic
25#97×C263C2211yescharacteristic, complemented
26#97×C263C2211yescharacteristic, complemented
27C23×D263—21no—
28C2×Dic526—21no—
29C2×Dic526D411yescharacteristic
30C2×Dic526D411yescharacteristic
31C2×D1052—21no—
32C2×D1052D411yescharacteristic
33C2×D1052D411yescharacteristic
34C2×C22⋊D263—21no—
35C2×C22⋊D263—21no—
36Dic1052—42no—
37#16862365—42no—
38C2×C263⋊C8—21no—
39C4⋊Dic263—21no—
40C4⋊Dic263—21no—
41C22⋊Dic263—21no—
42(C2×D263)⋊C4—21no—
43(C2×D263)⋊C4—21no—
44(C2×D263)⋊C4—21no—
45(C2×D263)⋊C4—21no—
46(C2×D263)⋊C4—21no—
47(C2×D263)⋊C4—21no—
48C4×Dic263—21no—
49C2×Q8×C263D411yescharacteristic
50C2×D4×C263D411yescharacteristic
51C2×C8×C263—21no—
52C2×C8×C263—21no—
53C22⋊C4×C263—21no—
54C22⋊C4×C263—21no—
55C42×C263C2311yescharacteristic
56C22×D263—21no—
57C22×D263—21no—
58C22×D263—81no—
59C22×D263—81no—
60C22×D263—81no—
61Dic526—41no—
62Dic526—41no—
63Dic526—41no—
64Dic526—41no—
65D1052—41no—
66D1052—41no—
67D1052—81no—
68C22⋊D263—81no—
69C22⋊D263—81no—
70C2×Dic263—21no—
71C2×Dic263—21no—
72C2×Dic263—41no—
73C263⋊C8—41no—
74C23×C263—21no—
75Q8×C263—41no—
76D4×C263—41no—
77C2×C4×C263—21no—
78C2×C4×C263C2×D411yescharacteristic
79C2×C4×C263C2×D411yescharacteristic
80C2×C4×C263C2×D411yescharacteristic
81C8×C263—22no—
82C8×C263—41no—
83C22×C263—41no—
84C22×C263—41no—
85C22×C263—41no—
86C22×C263#12011yescharacteristic
87C2×D263—41no—
88C2×D263—41no—
89C2×D263—41no—
90C2×D263—41no—
91C2×D263—41no—
92C2×D263—41no—
93C2×D263—84no—
94C4×C263—21no—
95C4×C263—21no—
96C4×C263—21no—
97C4×C263—41no—
98Dic263—41no—
99Dic263—41no—
100Dic263—81no—
101C2×C263—81no—
102C2×C263#45311yescharacteristic
103C2×C263#45511yescharacteristic
104C2×C263#45511yescharacteristic
105D263—81no—
106D263—81no—
107C263#165911yescharacteristic, complemented, Sylow
108#1659—2631nomaximal, Sylow
109H(3,𝔽4)—2631no—
110#497—2631no—
111#489—2631no—
112#489—2631no—
113#329—2631no—
114#329—2631no—
115#329D26311yescharacteristic, complemented
116C2×Q16—5261no—
117C2×SD16—5261no—
118C4⋊Q8—2631no—
119#124—2631no—
120#124—2631no—
121#124—5261no—
122#124—5261no—
123#124—5261no—
124#124C2×D26311yescharacteristic
125#120—5261no—
126#120—5261no—
127#120—5261no—
128#103—5261no—
129#103—5261no—
130#102—5261no—
131#102—5261no—
132#97—2631no—
133#97C2×D26311yescharacteristic, complemented
134#97C2×D26311yescharacteristic, complemented
135C24—5261no—
136C2×Q8—2631no—
137C2×Q8—2631no—
138C2×Q8—5261no—
139C2×Q8D105211yescharacteristic
140C2×D4—2631no—
141C2×D4—2631no—
142C2×D4—5261no—
143C2×D4—5261no—
144C2×D4—5261no—
145C2×D4D105211yescharacteristic
146Q16—10522no—
147SD16—10522no—
148C2×C8—21no—
149C2×C8—21no—
150C2×C8—5261no—
151C4⋊C4—5261no—
152C4⋊C4—5261no—
153C22⋊C4—21no—
154C22⋊C4—21no—
155C22⋊C4—5261no—
156C22⋊C4—5261no—
157C22⋊C4—5261no—
158C22⋊C4—5261no—
159C22⋊C4—5261no—
160C22⋊C4—5261no—
161C22⋊C4—5261no—
162C42—5261no—
163C42C22×D26311yescharacteristic
164C23—21no—
165C23—5261no—
166C23—5261no—
167C23—21041no—
168C23—21041no—
169C23—21041no—
170Q8—41no—
171Q8—10521no—
172Q8—10521no—
173Q8—10521no—
174Q8—10521no—
175D4—41no—
176D4—10521no—
177D4—10521no—
178D4—21041no—
179D4—21041no—
180D4—21041no—
181C2×C4—21no—
182C2×C4—5261no—
183C2×C4—5261no—
184C2×C4—10521no—
185C2×C4D4×D26311yescharacteristic
186C2×C4D4×D26311yescharacteristic
187C2×C4C2×D105211yescharacteristic
188C8—22no—
189C8—41no—
190C8—10521no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22—10521no—
195C22—10521no—
196C22—10521no—
197C22—10521no—
198C22—10521no—
199C22—10521no—
200C22—21044no—
201C22#2255444011yescharacteristic
202C4—21no—
203C4—21no—
204C4—21no—
205C4—41no—
206C4—10521no—
207C4—10521no—
208C4—21041no—
209C2—81no—
210C2—21041no—
211C2—21041no—
212C2#3068210711yescharacteristic
213C2#3068211711yescharacteristic
214C2#3068211811yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#329×C263C2
socleC22×C263#120
prime radical#30682680C2
hypercenter#329D263
hypocenterC263#1659
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #30682332C2semidirect
3. #30682298C2semidirect
4. #30682297C2semidirect
5. #30681677C2semidirect
6. #30681677C2semidirect
7. #329×C263C2semidirect
10. #22554470C22semidirect
23. #22554381C22semidirect
25. #97×C263C22semidirect
26. #97×C263C22semidirect
107. C263#1659semidirect
115. #329D263semidirect
133. #97C2×D263semidirect
134. #97C2×D263semidirect

Maximal subgroups

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

subgroupindex
#306826802
#306823322
#306822982
#306822972
#306816772
#329×C2632
#1659263