Finite Group Databasebeta

← #46781726

Subgroups — #46781726

Order 33664.

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

normal subgroups only

This group has 260 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#30682077C211yesmaximal, characteristic, complemented
3#30681849C211yesmaximal, characteristic, complemented
4#30681675C211yesmaximal, characteristic, complemented
5#30681673C211yesmaximal, characteristic, complemented
6#30681661C211yesmaximal, characteristic, complemented
7#451×C263C211yesmaximal, characteristic, complemented
8C2×#16862363—21no—
9#22554465—21no—
10#22554459—21no—
11#22554455—21no—
12#22554445—21no—
13#22554444C2211yescharacteristic
14#22554440—21no—
15(C22⋊D263)⋊C4—21no—
16C2×(C2×D263)⋊C4—21no—
17C2×(C2×D263)⋊C4C2211yescharacteristic
18#22554394—21no—
19C22⋊(C263⋊C8)C2211yescharacteristic
20C263⋊#95—21no—
21C263⋊#95C2211yescharacteristic
22C22×Q8×C263C2211yescharacteristic
23C2×Q16×C263—21no—
24C22⋊Q8×C263C2211yescharacteristic
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—
35#16862363—42no—
36C2×C263⋊C8—21no—
37C4⋊Dic263D411yescharacteristic
38Dic263⋊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—21no—
45(C2×D263)⋊C4—42no—
46C4×Dic263—21no—
47C2×Q8×C263—21no—
48C2×Q8×C263—21no—
49C2×Q8×C263—42no—
50C2×Q8×C263D411yescharacteristic
51C22×C4×C263—21no—
52C22×C4×C263C2311yescharacteristic
53Q16×C263—42no—
54C2×C8×C263—21no—
55C4⋊C4×C263—21no—
56C4⋊C4×C263D411yescharacteristic
57C22⋊C4×C263—21no—
58C22×D263—21no—
59C22×D263—21no—
60C22×D263—21no—
61C22×D263—21no—
62C22×D263—41no—
63C22×D263—41no—
64D1052—41no—
65D1052—81no—
66D1052—81no—
67C22⋊D263—41no—
68C22⋊D263—41no—
69C2×Dic263—21no—
70C2×Dic263—21no—
71C2×Dic263—41no—
72C2×Dic263—41no—
73C2×Dic263—41no—
74C2×Dic263—41no—
75C4×D263—81no—
76C263⋊C8—41no—
77C23×C263C2×D411yescharacteristic
78Q8×C263—22no—
79Q8×C263—22no—
80Q8×C263—41no—
81Q8×C263—41no—
82Q8×C263—41no—
83C2×C4×C263—22no—
84C2×C4×C263—21no—
85C2×C4×C263—21no—
86C2×C4×C263—41no—
87C2×C4×C263—41no—
88C2×C4×C263—41no—
89C2×C4×C263C2×D411yescharacteristic
90C2×C4×C263C2×D411yescharacteristic
91C8×C263—41no—
92C22×C263—21no—
93C22×C263—21no—
94C22×C263#12011yescharacteristic
95C22×C263#13511yescharacteristic
96C22×C263#13711yescharacteristic
97C2×D263—42no—
98C2×D263—41no—
99C2×D263—41no—
100C2×D263—41no—
101C2×D263—41no—
102C2×D263—41no—
103C2×D263—41no—
104C2×D263—81no—
105C4×C263—21no—
106C4×C263—21no—
107C4×C263—41no—
108C4×C263—42no—
109C4×C263—41no—
110Dic263—41no—
111Dic263—41no—
112Dic263—81no—
113C2×C263—21no—
114C2×C263—21no—
115C2×C263#45211yescharacteristic
116C2×C263#45511yescharacteristic
117C2×C263B(4,𝔽2)11yescharacteristic
118D263—81no—
119D263—81no—
120C263#160611yescharacteristic, complemented, Sylow
121#1606—2631nomaximal, Sylow
122#538—2631no—
123#451D26311yescharacteristic, complemented
124#448—2631no—
125#393—2631no—
126#328—2631no—
127#327—2631no—
128#323—2631no—
129C22×Q8C2×D26311yescharacteristic
130C2×Q16—21no—
131C2×SD16—5261no—
132#126—5261no—
133#124—5261no—
134#123—5261no—
135C22⋊Q8C2×D26311yescharacteristic
136#121—2631no—
137#121—5261no—
138#120—5261no—
139C4×D4—5261no—
140C2×C22⋊C4—2631no—
141C2×C22⋊C4—5261no—
142#103—21no—
143#103—5261no—
144C22⋊C8—2631no—
145C22⋊C8C2×D26311yescharacteristic
146#95—2631no—
147#95—5261no—
148C24—2631no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—42no—
152C2×Q8C22⋊D26311yescharacteristic
153C2×D4—2631no—
154C2×D4—5261no—
155C2×D4—5261no—
156C2×D4—5261no—
157C22×C4—21no—
158C22×C4—2631no—
159C22×C4—5261no—
160C22×C4—5261no—
161C22×C4C22×D26311yescharacteristic
162Q16—42no—
163SD16—10522no—
164C2×C8—21no—
165C2×C8—5261no—
166C4⋊C4—21no—
167C4⋊C4—2631no—
168C4⋊C4—5261no—
169C4⋊C4C22⋊D26311yescharacteristic
170C22⋊C4—21no—
171C22⋊C4—5261no—
172C22⋊C4—5261no—
173C22⋊C4—5261no—
174C22⋊C4—5261no—
175C22⋊C4—5261no—
176C22⋊C4—5261no—
177C22⋊C4—10522no—
178C42—5261no—
179C23—5261no—
180C23—5261no—
181C23—5261no—
182C23—5261no—
183C23—10521no—
184C23—10521no—
185C23D4×D26311yescharacteristic
186Q8—22no—
187Q8—22no—
188Q8—41no—
189Q8—41no—
190Q8—41no—
191D4—10521no—
192D4—10521no—
193D4—10521no—
194D4—21041no—
195D4—21041no—
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—5261no—
203C2×C4—5261no—
204C2×C4—10521no—
205C2×C4—10521no—
206C2×C4—10521no—
207C2×C4—10521no—
208C2×C4—21041no—
209C2×C4D4×D26311yescharacteristic
210C2×C4C2×C22⋊D26311yescharacteristic
211C8—41no—
212C8—10521no—
213C22—21no—
214C22—21no—
215C22—10522no—
216C22—10521no—
217C22—10521no—
218C22—10521no—
219C22—10521no—
220C22—10521no—
221C22—10521no—
222C22—21041no—
223C22#2255443811yescharacteristic
224C22#2255449311yescharacteristic
225C22#2255450211yescharacteristic
226C4—21no—
227C4—21no—
228C4—41no—
229C4—42no—
230C4—41no—
231C4—10521no—
232C4—10521no—
233C4—21041no—
234C2—21no—
235C2—21no—
236C2—21041no—
237C2—21041no—
238C2#3068209911yescharacteristic
239C2#3068211411yescharacteristic
240C2#3068212411yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#451×C263C2
socleC22×C263#120
prime radical#30682528C2
hypercenter#451D263
hypocenterC263#1606
LCSG ▷ C22×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
2. #30682077C2semidirect
3. #30681849C2semidirect
4. #30681675C2semidirect
5. #30681673C2semidirect
6. #30681661C2semidirect
7. #451×C263C2semidirect
120. C263#1606semidirect
123. #451D263semidirect

Maximal subgroups

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

subgroupindex
#306825282
#306820772
#306818492
#306816752
#306816732
#306816612
#451×C2632
#1606263