Finite Group Databasebeta

← #46783091

Subgroups — #46783091

Order 33664.

338 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 103 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
1C22×#16862366C211yesmaximal, characteristic
2C2×C4×Dic526C211yesmaximal, characteristic
3C2×#22554394C211yesmaximal, characteristic
4C2×#22554393C211yesmaximal, characteristic
5#30681700C211yesmaximal, characteristic
6#30681693C211yesmaximal, characteristic
7#391×C263C211yesmaximal, characteristic
8C22×Dic526C2211yescharacteristic
9C2×#16862366—22no—
10C2×#16862366—22no—
11C2×#16862366C414yescomplemented
12C22×C263⋊C8C2211yescharacteristic
13C22×C263⋊C8C2211yescharacteristic
14C4×Dic526—22no—
15C4×Dic526—22no—
16C2×C4⋊Dic263C2211yescharacteristic
17C2×Dic263⋊C4—21no—
18C2×C4×Dic263—21no—
19#22554394—22no—
20#22554393—22no—
21C22×Q8×C263C2211yescharacteristic
22C2×C4⋊C4×C263C2211yescharacteristic
23C2×C42×C263C2211yescharacteristic
24#95×C263—21no—
25#95×C263—21no—
26C2×Dic526—21no—
27C2×Dic526—21no—
28C2×Dic526—21no—
29C2×Dic526C2×C412yes—
30C2×Dic526D412yes—
31C2×Dic526D412yes—
32C22×Dic263—21no—
33C22×Dic263—21no—
34#16862366—28no—
35C2×C263⋊C8—21no—
36C2×C263⋊C8—21no—
37C2×C263⋊C8—21no—
38C2×C263⋊C8—21no—
39C2×C263⋊C8—21no—
40C2×C263⋊C8C2×C412yes—
41C4⋊Dic263—21no—
42C4⋊Dic263D412yes—
43Dic263⋊C4—24no—
44C4×Dic263—24no—
45C2×Q8×C263—21no—
46C2×Q8×C263—21no—
47C2×Q8×C263—21no—
48C2×Q8×C263—21no—
49C2×Q8×C263—21no—
50C2×Q8×C263C2×C412yes—
51C22×C4×C263—21no—
52C22×C4×C263—21no—
53C22×C4×C263D411yescharacteristic
54C22×C4×C263D411yescharacteristic
55C22×C4×C263C2311yescharacteristic
56C4⋊C4×C263—21no—
57C4⋊C4×C263—21no—
58C42×C263—21no—
59C42×C263—21no—
60Dic526—22no—
61Dic526—22no—
62Dic526—22no—
63Dic526C22⋊C414yes—
64C2×Dic263—22no—
65C2×Dic263—22no—
66C2×Dic263—22no—
67C2×Dic263—22no—
68C2×Dic263—41no—
69C2×Dic263—41no—
70C263⋊C8—22no—
71C263⋊C8—41no—
72C23×C263C2×D411yescharacteristic
73Q8×C263—22no—
74Q8×C263—22no—
75Q8×C263—41no—
76Q8×C263—41no—
77C2×C4×C263—21no—
78C2×C4×C263—21no—
79C2×C4×C263—22no—
80C2×C4×C263—21no—
81C2×C4×C263—21no—
82C2×C4×C263—21no—
83C2×C4×C263—41no—
84C2×C4×C263—41no—
85C2×C4×C263—41no—
86C2×C4×C263—41no—
87C2×C4×C263—41no—
88C2×C4×C263Q1612yescomplemented
89C2×C4×C263C22×C411yescharacteristic
90C2×C4×C263C2×D411yescharacteristic
91C2×C4×C263C2×D411yescharacteristic
92C2×C4×C263C2×D411yescharacteristic
93C2×C4×C263#4111yescharacteristic
94C2×C4×C263#4111yescharacteristic
95C22×C263C4×D411yescharacteristic
96C22×C263#12011yescharacteristic
97C22×C263#12111yescharacteristic
98C22×C263C2×Q1611yescharacteristic
99C22×C263#13511yescharacteristic
100C22×C263#13711yescharacteristic
101C22×C263#13711yescharacteristic
102C4×C263—22no—
103C4×C263—42no—
104C4×C263—41no—
105C4×C263—81no—
106C4×C263C2×C22⋊C411yescharacteristic
107C4×C263C4×D411yescharacteristic
108C4×C263#12111yescharacteristic
109C4×C263#12311yescharacteristic
110Dic263—24no—
111Dic263—42no—
112C2×C263#38611yescharacteristic
113C2×C263C4×Q1611yescharacteristic
114C2×C263#44111yescharacteristic
115C2×C263#45111yescharacteristic
116C2×C263#45211yescharacteristic
117C2×C263#46211yescharacteristic
118C2×C263#46411yescharacteristic
119C263#187811yescharacteristic, complemented, Sylow
120#1878—2631nomaximal, Sylow
121C22×Q16—2631no—
122C2×C4×Q8—2631no—
123C2×#103—2631no—
124C2×#103—2631no—
125#391D26311yescharacteristic
126#340—2631no—
127#336—2631no—
128C22×Q8—2631no—
129C22×Q8C2×D26311yescharacteristic
130C2×Q16—2634no—
131C2×Q16—5262no—
132C2×Q16—5262no—
133C22×C8—2631no—
134C22×C8—2631no—
135C4×Q8—5262no—
136C4×Q8—5262no—
137C2×C4⋊C4—2631no—
138C2×C4⋊C4—5261no—
139C2×C4⋊C4C2×D26311yescharacteristic
140C2×C42—5261no—
141C2×C42C2×D26311yescharacteristic
142#103—5262no—
143#103—5262no—
144#95—21no—
145#95—21no—
146C2×Q8—21no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—2632no—
152C2×Q8—2632no—
153C2×Q8—2632no—
154C2×Q8—5261no—
155C2×Q8—5261no—
156C2×Q8—5261no—
157C2×Q8C4×D26312yes—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—5261no—
161C22×C4—5261no—
162C22×C4C22⋊D26311yescharacteristic
163C22×C4C22⋊D26311yescharacteristic
164C22×C4C22×D26311yescharacteristic
165Q16—5268no—
166C2×C8—2632no—
167C2×C8—5261no—
168C2×C8—5261no—
169C2×C8—5261no—
170C2×C8—5261no—
171C2×C8—5261no—
172C4⋊C4—21no—
173C4⋊C4—21no—
174C4⋊C4—2632no—
175C4⋊C4—5264no—
176C4⋊C4—5261no—
177C42—21no—
178C42—21no—
179C42—5264no—
180C23C2×C22⋊D26311yescharacteristic
181Q8—22no—
182Q8—22no—
183Q8—41no—
184Q8—41no—
185Q8—2634no—
186Q8—5262no—
187Q8—5262no—
188Q8—5262no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—5262no—
201C2×C4—5262no—
202C2×C4—5262no—
203C2×C4—5262no—
204C2×C4—10521no—
205C2×C4—10521no—
206C2×C4#1686236612yescomplemented
207C2×C4C2×C4×D26311yescharacteristic
208C2×C4D4×D26311yescharacteristic
209C2×C4D4×D26311yescharacteristic
210C2×C4D4×D26311yescharacteristic
211C2×C4#1686237511yescharacteristic
212C2×C4#1686237611yescharacteristic
213C8—5262no—
214C8—10521no—
215C22C4×C22⋊D26311yescharacteristic
216C22#2255443811yescharacteristic
217C22#2255444111yescharacteristic
218C22C2×#1686236611yescharacteristic
219C22#2255449011yescharacteristic
220C22#2255450011yescharacteristic
221C22#2255450111yescharacteristic
222C4—22no—
223C4—42no—
224C4—41no—
225C4—81no—
226C4—5264no—
227C4—10522no—
228C4C22⋊C4×D26311yescharacteristic
229C4(C22⋊D263)⋊C411yescharacteristic
230C4#2255444311yescharacteristic
231C4#2255445211yescharacteristic
232C2#3068181411yescharacteristic
233C2C4×#1686236611yescharacteristic
234C2#3068204311yescharacteristic
235C2#3068209311yescharacteristic
236C2#3068209811yescharacteristic
237C2#3068214511yescharacteristic
238C2#3068215711yescharacteristic
subgroupG/H
centerC23C2×C22⋊D263
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#391×C263C2
socle, prime radicalC23×C263C2×D4
cosocleC22×C4×C263C23
hypercenter#391D263
hypocenterC263#1878
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
11. C2×#16862366C4semidirect
88. C2×C4×C263Q16semidirect
119. C263#1878semidirect
206. C2×C4#16862366semidirect

Maximal subgroups

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

subgroupindex
C22×#168623662
C2×C4×Dic5262
C2×#225543942
C2×#225543932
#306817002
#306816932
#391×C2632
#1878263