Finite Group Databasebeta

← #46783780

Subgroups — #46783780

Order 33664.

362 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 75 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#30682509C211yesmaximal, characteristic
2C2×#22554468C211yesmaximal, characteristic, complemented
3C2×#22554397C211yesmaximal, characteristic
4#30681947C211yesmaximal, characteristic, complemented
5C2×#22554388C211yesmaximal, characteristic, complemented
6#30681699C211yesmaximal, characteristic, complemented
7C2×#137×C263C211yesmaximal, characteristic
8C22×Dic526C2211yescharacteristic
9C2×#16862360C2211yescharacteristic
10#22554468—22no—
11#22554468—22no—
12#22554468—21no—
13#22554457—21no—
14#22554451—22no—
15#22554449—22no—
16#22554429C2211yescharacteristic
17C2×Dic263⋊C4—22no—
18C2×C4×Dic263C2211yescharacteristic
19#22554397—22no—
20#22554394—22no—
21#22554388—22no—
22C2×#41×C263C2211yescharacteristic
23C22×Q8×C263C2211yescharacteristic
24#137×C263—22no—
25#137×C263—22no—
26C2×Q16×C263—21no—
27C2×SD16×C263—21no—
28C2×M16×C263C2211yescharacteristic
29C2×Dic526—21no—
30C2×Dic526—21no—
31C2×Dic526—21no—
32C2×Dic526—21no—
33C2×Dic526—21no—
34C2×Dic526—21no—
35C22×Dic263—21no—
36C22×Dic263D412yes—
37#16862360—21no—
38#16862360—21no—
39C2×C263⋊C8—21no—
40C4⋊Dic263D412yes—
41Dic263⋊C4—28no—
42Dic263⋊C4—24no—
43C22⋊Dic263—24no—
44C22⋊Dic263—21no—
45C4×Dic263—21no—
46C4×Dic263—21no—
47C4×Dic263D412yes—
48#41×C263—21no—
49#41×C263—21no—
50#41×C263—21no—
51#41×C263—21no—
52C2×Q8×C263—21no—
53C2×Q8×C263—21no—
54C2×Q8×C263—21no—
55C2×Q8×C263—21no—
56C2×Q8×C263—21no—
57C2×Q8×C263D412yes—
58C2×Q8×C263D411yescharacteristic
59C2×D4×C263—21no—
60C2×D4×C263D411yescharacteristic
61C22×C4×C263—21no—
62C22×C4×C263—21no—
63C22×C4×C263C2311yescharacteristic
64Q16×C263—24no—
65SD16×C263—24no—
66M16×C263—21no—
67M16×C263D412yes—
68C2×C8×C263—21no—
69Dic526—41no—
70Dic526—41no—
71Dic526—41no—
72Dic526—41no—
73C2×Dic263—24no—
74C2×Dic263—22no—
75C2×Dic263—22no—
76C2×Dic263—22no—
77C2×Dic263—22no—
78C2×Dic263—22no—
79C263⋊C8—41no—
80C23×C263—21no—
81C23×C263C2×D411yescharacteristic
82Q8×C263—22no—
83Q8×C263—21no—
84Q8×C263—22no—
85Q8×C263—21no—
86Q8×C263—41no—
87Q8×C263—41no—
88D4×C263—21no—
89D4×C263—21no—
90D4×C263—41no—
91D4×C263—41no—
92C2×C4×C263—21no—
93C2×C4×C263—22no—
94C2×C4×C263—41no—
95C2×C4×C263—41no—
96C2×C4×C263—41no—
97C2×C4×C263—41no—
98C2×C4×C263C2×D411yescharacteristic
99C2×C4×C263C2×D411yescharacteristic
100C2×C4×C263C2×D411yescharacteristic
101C2×C4×C263C2×D411yescharacteristic
102C2×C4×C263C2×D411yescharacteristic
103C2×C4×C263#4111yescharacteristic
104C8×C263—22no—
105C22×C263—22no—
106C22×C263—41no—
107C22×C263—42no—
108C22×C263#12011yescharacteristic
109C22×C263#12011yescharacteristic
110C22×C263#12111yescharacteristic
111C4×C263—41no—
112C4×C263—42no—
113C4×C263#12011yescharacteristic
114C4×C263#12111yescharacteristic
115C4×C263#12111yescharacteristic
116C4×C263#12711yescharacteristic
117Dic263—24no—
118Dic263—42no—
119Dic263—42no—
120C2×C263—21no—
121C2×C263—21no—
122C2×C263—81no—
123C2×C263#39211yescharacteristic
124C2×C263#45612yes—
125C263#200511yescharacteristic, complemented, Sylow
126#2005—2631nomaximal, Sylow
127C2×#137D26311yescharacteristic
128#536—2631no—
129C2×C4⋊Q8—2631no—
130C2×#104—2631no—
131#419—2631no—
132C2×#101—2631no—
133#339—2631no—
134C2×#41C2×D26311yescharacteristic
135C22×Q8—2631no—
136C22×Q8C2×D26311yescharacteristic
137#137—22no—
138#137—22no—
139C2×Q16—21no—
140C2×SD16—21no—
141C2×M16—2631no—
142C2×M16C2×D26311yescharacteristic
143C4⋊Q8—5262no—
144C4⋊Q8—5262no—
145C4⋊Q8—5261no—
146#124—5261no—
147#123—5262no—
148C22⋊Q8—5262no—
149#117—2631no—
150C2×C4⋊C4—5262no—
151C2×C42—2631no—
152#104—5262no—
153#103—5262no—
154#101—5262no—
155#41—21no—
156#41—21no—
157#41—21no—
158#41—21no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8—21no—
162C2×Q8—21no—
163C2×Q8—21no—
164C2×Q8—5261no—
165C2×Q8—5261no—
166C2×Q8—5261no—
167C2×Q8—5261no—
168C2×Q8—5261no—
169C2×Q8—5261no—
170C2×Q8C22⋊D26311yescharacteristic
171C2×Q8C22⋊D26312yes—
172C2×D4—21no—
173C2×D4C22⋊D26311yescharacteristic
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—2632no—
177C22×C4—5261no—
178C22×C4C22×D26311yescharacteristic
179Q16—24no—
180SD16—24no—
181M16—21no—
182M16—5261no—
183M16—5261no—
184M16C22⋊D26312yes—
185C2×C8—21no—
186C2×C8—5261no—
187C4⋊C4—2632no—
188C4⋊C4—5268no—
189C4⋊C4—5264no—
190C22⋊C4—5264no—
191C22⋊C4—5261no—
192C42—2632no—
193C42—5261no—
194C42—5261no—
195C23—21no—
196C23D4×D26311yescharacteristic
197Q8—22no—
198Q8—21no—
199Q8—22no—
200Q8—21no—
201Q8—41no—
202Q8—41no—
203Q8—10521no—
204Q8—10521no—
205Q8—10521no—
206Q8—10521no—
207D4—21no—
208D4—21no—
209D4—41no—
210D4—41no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—5264no—
218C2×C4—5262no—
219C2×C4—5262no—
220C2×C4—5262no—
221C2×C4—5262no—
222C2×C4—5262no—
223C2×C4D4×D26311yescharacteristic
224C2×C4D4×D26311yescharacteristic
225C2×C4C2×C22⋊D26311yescharacteristic
226C2×C4C2×C22⋊D26311yescharacteristic
227C2×C4C2×C22⋊D26311yescharacteristic
228C2×C4#1686237511yescharacteristic
229C8—22no—
230C8—10521no—
231C22—22no—
232C22—42no—
233C22—41no—
234C22#2255443811yescharacteristic
235C22#2255443811yescharacteristic
236C22#2255444111yescharacteristic
237C4—41no—
238C4—42no—
239C4—5264no—
240C4—10522no—
241C4—10522no—
242C4#2255443911yescharacteristic
243C4#2255444211yescharacteristic
244C4#2255444211yescharacteristic
245C4#2255446611yescharacteristic
246C2—21no—
247C2—21no—
248C2—81no—
249C2#3068184611yescharacteristic
250C2#3068211912yes—
subgroupG/H
centerC22#22554438
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
FittingC2×#137×C263C2
socleC22×C263#120
prime radicalC2×#41×C263C22
hypercenterC2×#137D263
hypocenterC263#2005
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
2. C2×#22554468C2semidirect
4. #30681947C2semidirect
5. C2×#22554388C2semidirect
6. #30681699C2semidirect
125. C263#2005semidirect

Maximal subgroups

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

subgroupindex
#306825092
C2×#225544682
C2×#225543972
#306819472
C2×#225543882
#306816992
C2×#137×C2632
#2005263