Finite Group Databasebeta

← #46783241

Subgroups — #46783241

Order 33664.

310 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C2×#22554501C211yesmaximal, characteristic
2#30681956C211yesmaximal, characteristic
3#30681947C211yesmaximal, characteristic, complemented
4#30681911C211yesmaximal, characteristic
5#30681708C211yesmaximal, characteristic, complemented
6#30681694C211yesmaximal, characteristic, complemented
7#519×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9#22554501—22no—
10#22554501—22no—
11C2×#16862366C412yescomplemented
12C2×#16862363C412yescomplemented
13C2×#16862360C2211yescharacteristic
14C2×#16862360C2211yescharacteristic
15#22554429C2211yescharacteristic
16#22554398—22no—
17#22554394—22no—
18#22554384—22no—
19C22×Q8×C263C2211yescharacteristic
20C4×Q8×C263—22no—
21C4×Q8×C263—22no—
22#117×C263—22no—
23#117×C263C2211yescharacteristic
24#117×C263C2211yescharacteristic
25#16862376—21no—
26#16862376—21no—
27#16862376—21no—
28#16862376—21no—
29C2×Dic526C2×C411yescharacteristic
30C2×D1052C2×C411yescharacteristic
31C2×C22⋊D263—21no—
32C2×C4×D263—21no—
33#16862366—24no—
34#16862363—24no—
35#16862360—21no—
36#16862360—21no—
37#16862360—21no—
38#16862360—21no—
39C2×C263⋊C8—21no—
40C2×C263⋊C8C2×C412yes—
41C4⋊Dic263—21no—
42C22⋊Dic263—21no—
43C4×Dic263—21no—
44C2×Q8×C263—21no—
45C2×Q8×C263—21no—
46C2×Q8×C263—21no—
47C2×Q8×C263C2×C412yes—
48C2×Q8×C263D412yes—
49C2×Q8×C263D412yes—
50C22×C4×C263—21no—
51C22×C4×C263C2311yescharacteristic
52C4⋊C4×C263—24no—
53C4⋊C4×C263—21no—
54C4⋊C4×C263—21no—
55C22⋊C4×C263—21no—
56C22⋊C4×C263D412yes—
57C42×C263—24no—
58C42×C263—21no—
59C42×C263D412yes—
60C22×D263—21no—
61Dic526—21no—
62Dic526—21no—
63D1052—21no—
64D1052—21no—
65C22⋊D263—41no—
66C22⋊D263—41no—
67C2×Dic263—21no—
68C2×Dic263—41no—
69C4×D263—41no—
70C4×D263—41no—
71C263⋊C8—22no—
72C263⋊C8—41no—
73C23×C263C2×D411yescharacteristic
74Q8×C263—22no—
75Q8×C263—22no—
76Q8×C263—22no—
77Q8×C263C22⋊C414yes—
78C2×C4×C263—22no—
79C2×C4×C263—22no—
80C2×C4×C263—22no—
81C2×C4×C263—22no—
82C2×C4×C263—22no—
83C2×C4×C263C22×C411yescharacteristic
84C2×C4×C263C2×D411yescharacteristic
85C2×C4×C263C2×D411yescharacteristic
86C2×C4×C263C2×D411yescharacteristic
87C2×C4×C263#4111yescharacteristic
88C2×C4×C263#4111yescharacteristic
89C22×C263—41no—
90C22×C263C4×D411yescharacteristic
91C22×C263#12011yescharacteristic
92C22×C263#12111yescharacteristic
93C2×D263—41no—
94C2×D263—81no—
95C4×C263—24no—
96C4×C263—42no—
97C4×C263—42no—
98C4×C263C2×C22⋊C411yescharacteristic
99C4×C263C4×D411yescharacteristic
100C4×C263#12111yescharacteristic
101C4×C263#12311yescharacteristic
102Dic263—41no—
103Dic263—81no—
104C2×C263—21no—
105C2×C263—21no—
106C2×C263—21no—
107C2×C263#38611yescharacteristic
108D263—81no—
109C263#190511yescharacteristic, complemented, Sylow
110#1905—2631nomaximal, Sylow
111C2×#137—2631no—
112#519D26311yescharacteristic, complemented
113#421—2631no—
114#419—2631no—
115#410—2631no—
116#344—2631no—
117H(3,ℤ/4)—2631no—
118C2×#41—2631no—
119C22×Q8C2×D26311yescharacteristic
120#137—5262no—
121#137—5262no—
122C2×Q16—2632no—
123C2×SD16—2632no—
124C2×M16—2631no—
125C2×M16—2631no—
126C4×Q8—22no—
127C4×Q8—22no—
128#117—22no—
129#117—2631no—
130#117C2×D26311yescharacteristic
131#117C2×D26311yescharacteristic
132#104—5262no—
133#103—5262no—
134#99—5262no—
135#41—5261no—
136#41—5261no—
137#41—5261no—
138#41—5261no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—2631no—
143C2×Q8C4×D26312yes—
144C2×Q8C22⋊D26312yes—
145C2×Q8D105212yes—
146C2×D4—2631no—
147C2×D4—5261no—
148C22×C4—21no—
149C22×C4—5261no—
150C22×C4C22×D26311yescharacteristic
151Q16—5264no—
152SD16—5264no—
153M16—5261no—
154M16—5261no—
155M16—5261no—
156M16—5261no—
157C2×C8—2632no—
158C2×C8—5261no—
159C4⋊C4—24no—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—5261no—
163C22⋊C4—21no—
164C22⋊C4—5261no—
165C22⋊C4C22⋊D26312yes—
166C42—24no—
167C42—21no—
168C42—5261no—
169C42C22⋊D26312yes—
170C23—5261no—
171C23C2×C22⋊D26311yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—22no—
175Q8—5261no—
176Q8—5261no—
177Q8(C2×D263)⋊C414yes—
178D4—5261no—
179D4—5261no—
180D4—10521no—
181D4—10521no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—5261no—
188C2×C4—10521no—
189C2×C4—10521no—
190C2×C4—10521no—
191C2×C4C2×C4×D26311yescharacteristic
192C2×C4C2×C22⋊D26311yescharacteristic
193C2×C4C2×C22⋊D26311yescharacteristic
194C2×C4C2×D105211yescharacteristic
195C2×C4#1686237611yescharacteristic
196C2×C4#1686237611yescharacteristic
197C8—5262no—
198C8—10521no—
199C22—41no—
200C22—10521no—
201C22—21041no—
202C22C4×C22⋊D26311yescharacteristic
203C22#2255443911yescharacteristic
204C22#2255444411yescharacteristic
205C4—24no—
206C4—42no—
207C4—42no—
208C4—10521no—
209C4—21041no—
210C4C2×(C2×D263)⋊C411yescharacteristic
211C4C4×C22⋊D26311yescharacteristic
212C4#2255444411yescharacteristic
213C4#2255445311yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—21041no—
218C2#3068181711yescharacteristic
subgroupG/H
centerC2#30681817
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#519×C263C2
socleC2×C263#386
prime radicalC2×#16862376C22
cosocleC22×C4×C263C23
hypercenter#519D263
hypocenterC263#1905
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2 ◁ C22×C4 ◁ #519

Complements

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

NH ≅ G/Ntype
3. #30681947C2semidirect
5. #30681708C2semidirect
6. #30681694C2semidirect
7. #519×C263C2semidirect
11. C2×#16862366C4semidirect
12. C2×#16862363C4semidirect
109. C263#1905semidirect
112. #519D263semidirect

Maximal subgroups

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

subgroupindex
C2×#225545012
#306819562
#306819472
#306819112
#306817082
#306816942
#519×C2632
#1905263