Finite Group Databasebeta

← #46781751

Subgroups — #46781751

Order 33664.

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

normal subgroups only

This group has 254 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#30682252C211yesmaximal, characteristic, complemented
3#30682249C211yesmaximal, characteristic, complemented
4#30681870C211yesmaximal, 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⋊Dic263—21no—
16C2×C4⋊Dic263C2211yescharacteristic
17C2×Dic263⋊C4C2211yescharacteristic
18#22554404—21no—
19#22554403—21no—
20#22554392—21no—
21#22554391—21no—
22C22⋊(C263⋊C8)C2211yescharacteristic
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⋊Dic263—42no—
43C4⋊Dic263D411yescharacteristic
44Dic263⋊C4—21no—
45Dic263⋊C4—21no—
46Dic263⋊C4—21no—
47C22⋊Dic263—21no—
48(C2×D263)⋊C4—21no—
49(C2×D263)⋊C4—21no—
50C2×D4×C263—21no—
51C2×D4×C263D411yescharacteristic
52C22×C4×C263—21no—
53C22×C4×C263C2311yescharacteristic
54C2×C8×C263—21no—
55C4⋊C4×C263D411yescharacteristic
56C22⋊C4×C263—21no—
57C22×D263—21no—
58Dic526—42no—
59D1052—41no—
60C22⋊D263—42no—
61C22⋊D263—41no—
62C22⋊D263—41no—
63C22⋊D263—81no—
64C2×Dic263—21no—
65C2×Dic263—21no—
66C2×Dic263—21no—
67C2×Dic263—21no—
68C2×Dic263—42no—
69C2×Dic263—41no—
70C2×Dic263—41no—
71C2×Dic263—41no—
72C2×Dic263—41no—
73C2×Dic263D812yes—
74C4×D263—42no—
75C263⋊C8—41no—
76C23×C263—21no—
77C23×C263C2×D411yescharacteristic
78D4×C263—41no—
79D4×C263—41no—
80D4×C263—41no—
81C2×C4×C263—22no—
82C2×C4×C263—21no—
83C2×C4×C263—41no—
84C2×C4×C263—41no—
85C2×C4×C263—41no—
86C2×C4×C263C2×D411yescharacteristic
87C2×C4×C263C2×D411yescharacteristic
88C8×C263—41no—
89C22×C263—21no—
90C22×C263—21no—
91C22×C263—41no—
92C22×C263—41no—
93C22×C263—41no—
94C22×C263#12011yescharacteristic
95C22×C263C2×D811yescharacteristic
96C22×C263AGL(1,ℤ/8)11yescharacteristic
97C2×D263—41no—
98C2×D263—41no—
99C2×D263—41no—
100C4×C263—21no—
101C4×C263—21no—
102C4×C263—42no—
103C4×C263—41no—
104Dic263—22no—
105Dic263—41no—
106Dic263—41no—
107Dic263—81no—
108C2×C263—21no—
109C2×C263—21no—
110C2×C263—81no—
111C2×C263#44711yescharacteristic
112C2×C263#45611yescharacteristic
113C2×C263#45811yescharacteristic
114D263—81no—
115C263#161011yescharacteristic, complemented, Sylow
116#1610—2631nomaximal, Sylow
117#537—2631no—
118#480—2631no—
119#480—2631no—
120#398—2631no—
121#327—2631no—
122#327D26311yescharacteristic, complemented
123#324—2631no—
124C2×#41—5261no—
125C22⋊Q8—5261no—
126C22⋊Q8—5261no—
127#121—2631no—
128#121—5261no—
129#121—5261no—
130#121—5261no—
131#121C2×D26311yescharacteristic
132C2×C4⋊C4—2631no—
133C2×C4⋊C4—2631no—
134C2×C4⋊C4—5261no—
135#107—5261no—
136#107—5261no—
137#102—5261no—
138#102—5261no—
139C22⋊C8—2631no—
140C22⋊C8C2×D26311yescharacteristic
141#95—5261no—
142#95C2×D26311yescharacteristic
143#41—10522no—
144#41—10522no—
145C2×Q8—5261no—
146C2×D4—21no—
147C2×D4—2631no—
148C2×D4—5261no—
149C2×D4—5261no—
150C2×D4—5261no—
151C2×D4D105211yescharacteristic
152C22×C4—21no—
153C22×C4—2631no—
154C22×C4—2631no—
155C22×C4—5261no—
156C22×C4—5261no—
157C22×C4—5261no—
158C22×C4C22×D26311yescharacteristic
159C2×C8—21no—
160C2×C8—5261no—
161C4⋊C4—2631no—
162C4⋊C4—5261no—
163C4⋊C4—5261no—
164C4⋊C4—5261no—
165C4⋊C4—5261no—
166C4⋊C4—5261no—
167C4⋊C4—10522no—
168C4⋊C4D105211yescharacteristic
169C22⋊C4—21no—
170C22⋊C4—5261no—
171C22⋊C4—5261no—
172C22⋊C4—5261no—
173C23—21no—
174C23—5261no—
175C23D4×D26311yescharacteristic
176Q8—10522no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—10521no—
181D4—10522no—
182D4—10521no—
183D4—10521no—
184D4—21041no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—2632no—
191C2×C4—5261no—
192C2×C4—5261no—
193C2×C4—5261no—
194C2×C4—5261no—
195C2×C4—10522no—
196C2×C4—10522no—
197C2×C4—10521no—
198C2×C4—10521no—
199C2×C4—10521no—
200C2×C4—10521no—
201C2×C4D4×D26311yescharacteristic
202C2×C4C2×D105211yescharacteristic
203C8—41no—
204C8—10521no—
205C22—21no—
206C22—21no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22—10521no—
211C22—10521no—
212C22—10521no—
213C22#2255444011yescharacteristic
214C22D8×D26311yescharacteristic
215C22#2255449711yescharacteristic
216C4—21no—
217C4—21no—
218C4—42no—
219C4—41no—
220C4—5262no—
221C4—10521no—
222C4—10521no—
223C4—21041no—
224C2—21no—
225C2—21no—
226C2—81no—
227C2—21041no—
228C2#3068207311yescharacteristic
229C2#3068212211yescharacteristic
230C2#3068212911yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#327×C263C2
socleC22×C263#120
prime radical#30682515C2
hypercenter#327D263
hypocenterC263#1610
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. #30682252C2semidirect
3. #30682249C2semidirect
4. #30681870C2semidirect
5. #30681671C2semidirect
6. #30681663C2semidirect
7. #327×C263C2semidirect
115. C263#1610semidirect
122. #327D263semidirect

Maximal subgroups

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

subgroupindex
#306825152
#306822522
#306822492
#306818702
#306816712
#306816632
#327×C2632
#1610263