Finite Group Databasebeta

← #46781785

Subgroups — #46781785

Order 33664.

246 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 51 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#30682515C211yesmaximal, characteristic
2#30682257C211yesmaximal, characteristic, complemented
3#30682254C211yesmaximal, characteristic, complemented
4#30681878C211yesmaximal, characteristic, complemented
5#30681671C211yesmaximal, characteristic, complemented
6#30681663C211yesmaximal, characteristic, complemented
7#327×C263C211yesmaximal, characteristic, complemented
8C2×#16862375—21no—
9#22554448—21no—
10#22554447—21no—
11#22554444C2211yescharacteristic
12#22554443—21no—
13#22554442—21no—
14#22554442—21no—
15C2×C4⋊Dic263C2211yescharacteristic
16C2×Dic263⋊C4C2211yescharacteristic
17#22554402—21no—
18#22554401—21no—
19#22554392—21no—
20#22554391—21no—
21C22⋊(C263⋊C8)C2211yescharacteristic
22C263⋊#95—21no—
23C263⋊#95—21no—
24#121×C263C2211yescharacteristic
25C22⋊C8×C263C2211yescharacteristic
26#95×C263C2211yescharacteristic
27#16862375—42no—
28#16862375—42no—
29C2×Dic526—21no—
30C2×D1052D411yescharacteristic
31C2×C22⋊D263—21no—
32C2×C22⋊D263—21no—
33C2×C22⋊D263—21no—
34C22×Dic263—21no—
35C22×Dic263—21no—
36C22×Dic263D411yescharacteristic
37C22×Dic263D411yescharacteristic
38C2×C4×D263—21no—
39C2×C263⋊C8—21no—
40C4⋊Dic263—21no—
41C4⋊Dic263—21no—
42C4⋊Dic263D411yescharacteristic
43Dic263⋊C4—21no—
44Dic263⋊C4—21no—
45Dic263⋊C4—21no—
46C22⋊Dic263—21no—
47(C2×D263)⋊C4—21no—
48(C2×D263)⋊C4—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—
57Dic526—42no—
58D1052—41no—
59C22⋊D263—42no—
60C22⋊D263—41no—
61C22⋊D263—41no—
62C22⋊D263—81no—
63C2×Dic263—21no—
64C2×Dic263—21no—
65C2×Dic263—21no—
66C2×Dic263—21no—
67C2×Dic263—42no—
68C2×Dic263—41no—
69C2×Dic263—42no—
70C2×Dic263—41no—
71C2×Dic263SD1612yes—
72C4×D263—42no—
73C263⋊C8—41no—
74C23×C263—21no—
75C23×C263C2×D411yescharacteristic
76D4×C263—41no—
77D4×C263—41no—
78D4×C263—41no—
79C2×C4×C263—21no—
80C2×C4×C263—41no—
81C2×C4×C263—41no—
82C2×C4×C263—41no—
83C2×C4×C263—41no—
84C2×C4×C263C2×D411yescharacteristic
85C2×C4×C263C2×D411yescharacteristic
86C8×C263—41no—
87C22×C263—21no—
88C22×C263—21no—
89C22×C263—41no—
90C22×C263—41no—
91C22×C263—41no—
92C22×C263#12011yescharacteristic
93C22×C263C2×SD1611yescharacteristic
94C22×C263AGL(1,ℤ/8)11yescharacteristic
95C2×D263—41no—
96C2×D263—41no—
97C2×D263—41no—
98C4×C263—21no—
99C4×C263—21no—
100C4×C263—41no—
101C4×C263—81no—
102Dic263—22no—
103Dic263—41no—
104Dic263—41no—
105Dic263—81no—
106C2×C263—21no—
107C2×C263—21no—
108C2×C263—81no—
109C2×C263#45011yescharacteristic
110C2×C263#45411yescharacteristic
111C2×C263#45811yescharacteristic
112D263—81no—
113C263#161611yescharacteristic, complemented, Sylow
114#1616—2631nomaximal, Sylow
115#537—2631no—
116#481—2631no—
117#481—2631no—
118#400—2631no—
119#327—2631no—
120#327D26311yescharacteristic, complemented
121#324—2631no—
122C2×#41—5261no—
123C22⋊Q8—5261no—
124C22⋊Q8—5261no—
125#121—2631no—
126#121—5261no—
127#121—5261no—
128#121—5261no—
129#121C2×D26311yescharacteristic
130C2×C4⋊C4—2631no—
131C2×C4⋊C4—2631no—
132#106—5261no—
133#106—5261no—
134#102—5261no—
135#102—5261no—
136C22⋊C8—2631no—
137C22⋊C8C2×D26311yescharacteristic
138#95—5261no—
139#95—5261no—
140#95C2×D26311yescharacteristic
141#41—10522no—
142#41—10522no—
143C2×Q8—5261no—
144C2×D4—21no—
145C2×D4—2631no—
146C2×D4—5261no—
147C2×D4—5261no—
148C2×D4—5261no—
149C2×D4D105211yescharacteristic
150C22×C4—21no—
151C22×C4—2631no—
152C22×C4—2631no—
153C22×C4—5261no—
154C22×C4—5261no—
155C22×C4—5261no—
156C22×C4C22×D26311yescharacteristic
157C2×C8—21no—
158C2×C8—5261no—
159C4⋊C4—2631no—
160C4⋊C4—5261no—
161C4⋊C4—5261no—
162C4⋊C4—5261no—
163C4⋊C4—5261no—
164C4⋊C4—5261no—
165C4⋊C4D105211yescharacteristic
166C22⋊C4—21no—
167C22⋊C4—5261no—
168C22⋊C4—5261no—
169C22⋊C4—5261no—
170C23—21no—
171C23—5261no—
172C23D4×D26311yescharacteristic
173Q8—10522no—
174D4—41no—
175D4—41no—
176D4—41no—
177D4—10521no—
178D4—10522no—
179D4—10521no—
180D4—10521no—
181D4—21041no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—2632no—
188C2×C4—5261no—
189C2×C4—5261no—
190C2×C4—5261no—
191C2×C4—5261no—
192C2×C4—10522no—
193C2×C4—10522no—
194C2×C4—10521no—
195C2×C4—10522no—
196C2×C4—10521no—
197C2×C4D4×D26311yescharacteristic
198C2×C4C2×D105211yescharacteristic
199C8—41no—
200C8—10521no—
201C22—21no—
202C22—21no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—10521no—
207C22—10521no—
208C22—10521no—
209C22#2255444011yescharacteristic
210C22SD16×D26311yescharacteristic
211C22#2255449411yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—81no—
216C4—5262no—
217C4—10521no—
218C4—10521no—
219C4—21041no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—21041no—
224C2#3068209011yescharacteristic
225C2#3068211211yescharacteristic
226C2#3068212911yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#327×C263C2
socleC22×C263#120
prime radical#30682515C2
hypercenter#327D263
hypocenterC263#1616
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. #30682257C2semidirect
3. #30682254C2semidirect
4. #30681878C2semidirect
5. #30681671C2semidirect
6. #30681663C2semidirect
7. #327×C263C2semidirect
113. C263#1616semidirect
120. #327D263semidirect

Maximal subgroups

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

subgroupindex
#306825152
#306822572
#306822542
#306818782
#306816712
#306816632
#327×C2632
#1616263