Finite Group Databasebeta

← #46781796

Subgroups — #46781796

Order 33664.

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

normal subgroups only

This group has 240 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#30682525C211yesmaximal, characteristic
2#30682274C211yesmaximal, characteristic, complemented
3#30682254C211yesmaximal, characteristic, complemented
4#30681875C211yesmaximal, characteristic, complemented
5#30681674C211yesmaximal, characteristic, complemented
6#30681661C211yesmaximal, characteristic, complemented
7#327×C263C211yesmaximal, characteristic, complemented
8#22554465—21no—
9#22554456—21no—
10#22554454—21no—
11#22554449C2211yescharacteristic
12#22554442—21no—
13#22554438—21no—
14D4×Dic263—21no—
15C2×C4⋊Dic263—21no—
16C2×C4⋊Dic263C2211yescharacteristic
17C2×(C2×D263)⋊C4—21no—
18C2×(C2×D263)⋊C4C2211yescharacteristic
19#22554404—21no—
20#22554401—21no—
21#22554395—21no—
22#22554391—21no—
23C22⋊(C263⋊C8)C2211yescharacteristic
24#121×C263C2211yescharacteristic
25C22⋊C8×C263C2211yescharacteristic
26#95×C263C2211yescharacteristic
27C23×D263D411yescharacteristic
28C2×Dic526D411yescharacteristic
29C2×C22⋊D263—21no—
30C2×C22⋊D263—21no—
31C22×Dic263—21no—
32C22×Dic263—21no—
33C22×Dic263D411yescharacteristic
34C2×C263⋊C8—21no—
35C4⋊Dic263—21no—
36C4⋊Dic263—21no—
37C4⋊Dic263—21no—
38C4⋊Dic263—42no—
39C4⋊Dic263D411yescharacteristic
40Dic263⋊C4—21no—
41C22⋊Dic263—21no—
42C22⋊Dic263—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—42no—
48C4×Dic263—21no—
49C2×D4×C263—21no—
50C2×D4×C263D411yescharacteristic
51C22×C4×C263—21no—
52C22×C4×C263C2311yescharacteristic
53C2×C8×C263—21no—
54C4⋊C4×C263D411yescharacteristic
55C22⋊C4×C263—21no—
56C22×D263—21no—
57C22×D263—21no—
58C22×D263—21no—
59C22×D263—41no—
60C22×D263—41no—
61Dic526—41no—
62C22⋊D263—81no—
63C22⋊D263—81no—
64C2×Dic263—21no—
65C2×Dic263—21no—
66C2×Dic263—21no—
67C2×Dic263—41no—
68C2×Dic263—41no—
69C2×Dic263—41no—
70C2×Dic263—41no—
71C2×Dic263—81no—
72C263⋊C8—41no—
73C23×C263—21no—
74C23×C263C2×D411yescharacteristic
75D4×C263—41no—
76D4×C263—41no—
77D4×C263—41no—
78C2×C4×C263—22no—
79C2×C4×C263—21no—
80C2×C4×C263—41no—
81C2×C4×C263—41no—
82C2×C4×C263—41no—
83C2×C4×C263C2×D411yescharacteristic
84C2×C4×C263C2×D411yescharacteristic
85C8×C263—41no—
86C22×C263—21no—
87C22×C263—21no—
88C22×C263—41no—
89C22×C263—41no—
90C22×C263—41no—
91C22×C263#12011yescharacteristic
92C22×C263#13511yescharacteristic
93C22×C263#13711yescharacteristic
94C2×D263—42no—
95C2×D263—41no—
96C2×D263—41no—
97C2×D263—41no—
98C2×D263—81no—
99C4×C263—21no—
100C4×C263—21no—
101C4×C263—42no—
102C4×C263—41no—
103Dic263—41no—
104Dic263—41no—
105Dic263—41no—
106Dic263—81no—
107C2×C263—21no—
108C2×C263—21no—
109C2×C263—81no—
110C2×C263#45211yescharacteristic
111C2×C263#45311yescharacteristic
112C2×C263#45811yescharacteristic
113D263—81no—
114C263#161811yescharacteristic, complemented, Sylow
115#1618—2631nomaximal, Sylow
116#538—2631no—
117#484—2631no—
118#481—2631no—
119#399—2631no—
120#328—2631no—
121#327D26311yescharacteristic, complemented
122#323—2631no—
123#126—5261no—
124#124—5261no—
125#123—5261no—
126C22⋊Q8—2631no—
127#121—5261no—
128#121C2×D26311yescharacteristic
129#120—5261no—
130C4×D4—5261no—
131C2×C4⋊C4—2631no—
132C2×C4⋊C4—5261no—
133C2×C22⋊C4—2631no—
134C2×C22⋊C4—5261no—
135#107—5261no—
136#106—5261no—
137#103—5261no—
138#102—5261no—
139C22⋊C8—2631no—
140C22⋊C8C2×D26311yescharacteristic
141#95C2×D26311yescharacteristic
142C24—2631no—
143C2×Q8—2631no—
144C2×D4—21no—
145C2×D4—5261no—
146C2×D4—5261no—
147C2×D4D105211yescharacteristic
148C22×C4—21no—
149C22×C4—2631no—
150C22×C4—5261no—
151C22×C4—5261no—
152C22×C4C22×D26311yescharacteristic
153C2×C8—21no—
154C2×C8—5261no—
155C4⋊C4—2631no—
156C4⋊C4—5261no—
157C4⋊C4—5261no—
158C4⋊C4—5261no—
159C4⋊C4—5261no—
160C4⋊C4—10522no—
161C4⋊C4D105211yescharacteristic
162C22⋊C4—21no—
163C22⋊C4—5261no—
164C22⋊C4—5261no—
165C22⋊C4—5261no—
166C22⋊C4—5261no—
167C22⋊C4—5261no—
168C22⋊C4—5261no—
169C22⋊C4—10522no—
170C42—5261no—
171C23—21no—
172C23—5261no—
173C23—5261no—
174C23—5261no—
175C23—10521no—
176C23—10521no—
177C23D4×D26311yescharacteristic
178Q8—10521no—
179D4—41no—
180D4—41no—
181D4—41no—
182D4—21041no—
183D4—21041no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—5261no—
190C2×C4—5261no—
191C2×C4—5261no—
192C2×C4—10521no—
193C2×C4—10521no—
194C2×C4—10521no—
195C2×C4—10521no—
196C2×C4—21041no—
197C2×C4D4×D26311yescharacteristic
198C2×C4C2×D105211yescharacteristic
199C8—41no—
200C8—10521no—
201C22—21no—
202C22—21no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—10522no—
207C22—10521no—
208C22—10521no—
209C22—10521no—
210C22—21041no—
211C22#2255444011yescharacteristic
212C22#2255448911yescharacteristic
213C22#2255449911yescharacteristic
214C4—21no—
215C4—21no—
216C4—42no—
217C4—41no—
218C4—10521no—
219C4—10521no—
220C4—10521no—
221C4—21041no—
222C2—21no—
223C2—21no—
224C2—81no—
225C2—21041no—
226C2#3068210111yescharacteristic
227C2#3068210711yescharacteristic
228C2#3068212911yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#327×C263C2
socleC22×C263#120
prime radical#30682525C2
hypercenter#327D263
hypocenterC263#1618
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. #30682274C2semidirect
3. #30682254C2semidirect
4. #30681875C2semidirect
5. #30681674C2semidirect
6. #30681661C2semidirect
7. #327×C263C2semidirect
114. C263#1618semidirect
121. #327D263semidirect

Maximal subgroups

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

subgroupindex
#306825252
#306822742
#306822542
#306818752
#306816742
#306816612
#327×C2632
#1618263