Finite Group Databasebeta

← #46781760

Subgroups — #46781760

Order 33664.

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

normal subgroups only

This group has 232 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#30682528C211yesmaximal, characteristic
2#30682251C211yesmaximal, characteristic, complemented
3#30681864C211yesmaximal, characteristic, complemented
4#30681675C211yesmaximal, characteristic, complemented
5#30681673C211yesmaximal, characteristic, complemented
6#30681661C211yesmaximal, characteristic, complemented
7#483×C263C211yesmaximal, characteristic, complemented
8#22554465—21no—
9#22554459—21no—
10#22554455—21no—
11#22554445—21no—
12#22554444C2211yescharacteristic
13#22554440—21no—
14(C22⋊D263)⋊C4—21no—
15C2×(C2×D263)⋊C4—21no—
16C2×(C2×D263)⋊C4C2211yescharacteristic
17#22554403—21no—
18#22554390—21no—
19C22⋊(C263⋊C8)C2211yescharacteristic
20C263⋊#95—21no—
21C263⋊#95C2211yescharacteristic
22C22⋊Q8×C263C2211yescharacteristic
23C2×C4⋊C4×C263C2211yescharacteristic
24#106×C263—21no—
25#103×C263—21no—
26C22⋊C8×C263C2211yescharacteristic
27C23×D263D411yescharacteristic
28C2×D1052—21no—
29C2×D1052—21no—
30C2×D1052D411yescharacteristic
31C2×C22⋊D263—21no—
32C22×Dic263—21no—
33C22×Dic263D411yescharacteristic
34C2×C4×D263—21no—
35C2×C263⋊C8—21no—
36C4⋊Dic263D411yescharacteristic
37Dic263⋊C4—21no—
38(C2×D263)⋊C4—21no—
39(C2×D263)⋊C4—21no—
40(C2×D263)⋊C4—21no—
41(C2×D263)⋊C4—21no—
42(C2×D263)⋊C4—21no—
43(C2×D263)⋊C4—21no—
44(C2×D263)⋊C4—42no—
45C4×Dic263—21no—
46C2×Q8×C263D411yescharacteristic
47C22×C4×C263—21no—
48C22×C4×C263C2311yescharacteristic
49C2×C8×C263—21no—
50C4⋊C4×C263—21no—
51C4⋊C4×C263—21no—
52C4⋊C4×C263—21no—
53C4⋊C4×C263D411yescharacteristic
54C22⋊C4×C263—21no—
55C22×D263—21no—
56C22×D263—21no—
57C22×D263—21no—
58C22×D263—21no—
59C22×D263—41no—
60C22×D263—41no—
61D1052—41no—
62D1052—81no—
63D1052—81no—
64C22⋊D263—41no—
65C22⋊D263—41no—
66C2×Dic263—21no—
67C2×Dic263—21no—
68C2×Dic263—41no—
69C2×Dic263—41no—
70C2×Dic263—41no—
71C2×Dic263—41no—
72C4×D263—81no—
73C263⋊C8—41no—
74C23×C263C2×D411yescharacteristic
75Q8×C263—41no—
76C2×C4×C263—21no—
77C2×C4×C263—21no—
78C2×C4×C263—41no—
79C2×C4×C263—41no—
80C2×C4×C263—41no—
81C2×C4×C263—41no—
82C2×C4×C263C2×D411yescharacteristic
83C2×C4×C263C2×D411yescharacteristic
84C8×C263—41no—
85C22×C263—21no—
86C22×C263—21no—
87C22×C263#12011yescharacteristic
88C22×C263#13511yescharacteristic
89C22×C263AGL(1,ℤ/8)11yescharacteristic
90C2×D263—42no—
91C2×D263—41no—
92C2×D263—41no—
93C2×D263—41no—
94C2×D263—41no—
95C2×D263—41no—
96C2×D263—41no—
97C2×D263—81no—
98C4×C263—21no—
99C4×C263—21no—
100C4×C263—41no—
101C4×C263—41no—
102C4×C263—81no—
103Dic263—41no—
104Dic263—41no—
105Dic263—81no—
106C2×C263—21no—
107C2×C263—21no—
108C2×C263#44911yescharacteristic
109C2×C263#45511yescharacteristic
110C2×C263#45811yescharacteristic
111D263—81no—
112D263—81no—
113C263#161211yescharacteristic, complemented, Sylow
114#1612—2631nomaximal, Sylow
115#538—2631no—
116#483D26311yescharacteristic, complemented
117#480—2631no—
118#397—2631no—
119#328—2631no—
120#327—2631no—
121#323—2631no—
122#126—5261no—
123#124—5261no—
124#123—5261no—
125C22⋊Q8C2×D26311yescharacteristic
126#121—2631no—
127#121—5261no—
128#120—5261no—
129C4×D4—5261no—
130C2×C4⋊C4C2×D26311yescharacteristic
131C2×C22⋊C4—2631no—
132C2×C22⋊C4—5261no—
133#107—5261no—
134#106—21no—
135#103—21no—
136#102—5261no—
137C22⋊C8—2631no—
138C22⋊C8C2×D26311yescharacteristic
139#95—2631no—
140#95—5261no—
141C24—2631no—
142C2×Q8C22⋊D26311yescharacteristic
143C2×D4—2631no—
144C2×D4—5261no—
145C2×D4—5261no—
146C2×D4—5261no—
147C22×C4—21no—
148C22×C4—2631no—
149C22×C4—5261no—
150C22×C4—5261no—
151C22×C4C22×D26311yescharacteristic
152C2×C8—21no—
153C2×C8—5261no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—2631no—
158C4⋊C4—5261no—
159C4⋊C4C22⋊D26311yescharacteristic
160C22⋊C4—21no—
161C22⋊C4—5261no—
162C22⋊C4—5261no—
163C22⋊C4—5261no—
164C22⋊C4—5261no—
165C22⋊C4—5261no—
166C22⋊C4—5261no—
167C22⋊C4—10522no—
168C42—5261no—
169C23—5261no—
170C23—5261no—
171C23—5261no—
172C23—5261no—
173C23—10521no—
174C23—10521no—
175C23D4×D26311yescharacteristic
176Q8—41no—
177D4—10521no—
178D4—10521no—
179D4—10521no—
180D4—21041no—
181D4—21041no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—5261no—
189C2×C4—5261no—
190C2×C4—10521no—
191C2×C4—10521no—
192C2×C4—10521no—
193C2×C4—10521no—
194C2×C4—21041no—
195C2×C4D4×D26311yescharacteristic
196C2×C4C2×C22⋊D26311yescharacteristic
197C8—41no—
198C8—10521no—
199C22—21no—
200C22—21no—
201C22—10522no—
202C22—10521no—
203C22—10521no—
204C22—10521no—
205C22—10521no—
206C22—10521no—
207C22—10521no—
208C22—21041no—
209C22#2255443811yescharacteristic
210C22#2255449111yescharacteristic
211C22#2255449711yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—41no—
216C4—81no—
217C4—10521no—
218C4—10521no—
219C4—21041no—
220C2—21no—
221C2—21no—
222C2—21041no—
223C2—21041no—
224C2#3068208211yescharacteristic
225C2#3068211411yescharacteristic
226C2#3068212711yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#483×C263C2
socleC22×C263#120
prime radical#30682528C2
hypercenter#483D263
hypocenterC263#1612
LCSG ▷ C22×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
2. #30682251C2semidirect
3. #30681864C2semidirect
4. #30681675C2semidirect
5. #30681673C2semidirect
6. #30681661C2semidirect
7. #483×C263C2semidirect
113. C263#1612semidirect
116. #483D263semidirect

Maximal subgroups

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

subgroupindex
#306825282
#306822512
#306818642
#306816752
#306816732
#306816612
#483×C2632
#1612263