Finite Group Databasebeta

← #46783631

Subgroups — #46783631

Order 33664.

340 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 99 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×#16862363C211yesmaximal, characteristic
2C2×#22554403C211yesmaximal, characteristic, complemented
3C2×#22554394C211yesmaximal, characteristic, complemented
4C2×#22554390C211yesmaximal, characteristic
5C2×#22554381C211yesmaximal, characteristic, complemented
6#30681840C211yesmaximal, characteristic
7#391×C263C211yesmaximal, characteristic, complemented
8C22×D1052C2211yescharacteristic
9C2×#16862363—22no—
10C2×#16862363—22no—
11C2×#16862363C414yescomplemented
12C22×C263⋊C8C2211yescharacteristic
13C22×C263⋊C8C2211yescharacteristic
14C2×C4⋊Dic263C2211yescharacteristic
15C2×(C2×D263)⋊C4—22no—
16#22554403—22no—
17#22554394—22no—
18#22554390—22no—
19#22554381—22no—
20C22×Q8×C263C2211yescharacteristic
21C2×C4⋊C4×C263C2211yescharacteristic
22C2×C42×C263C2211yescharacteristic
23#95×C263—22no—
24C23×D263—21no—
25C2×D1052—21no—
26C2×D1052—21no—
27C2×D1052—21no—
28C2×D1052—21no—
29C2×D1052—21no—
30C2×D1052C2×C412yes—
31C22×Dic263—21no—
32#16862363—28no—
33C2×C263⋊C8—21no—
34C2×C263⋊C8—21no—
35C2×C263⋊C8C2×C412yes—
36C2×C263⋊C8D412yes—
37C2×C263⋊C8D412yes—
38C2×C263⋊C8D412yes—
39C4⋊Dic263—21no—
40C4⋊Dic263—21no—
41(C2×D263)⋊C4—44no—
42C2×Q8×C263—21no—
43C2×Q8×C263—21no—
44C2×Q8×C263—21no—
45C2×Q8×C263—21no—
46C2×Q8×C263—21no—
47C2×Q8×C263C2×C412yes—
48C22×C4×C263—21no—
49C22×C4×C263—21no—
50C22×C4×C263D412yes—
51C22×C4×C263C2311yescharacteristic
52C4⋊C4×C263—21no—
53C4⋊C4×C263—21no—
54C42×C263—21no—
55C42×C263—21no—
56C22×D263—22no—
57C22×D263—41no—
58C22×D263—41no—
59C22×D263—42no—
60C22×D263—42no—
61D1052—22no—
62D1052—22no—
63D1052—41no—
64D1052—41no—
65C2×Dic263—41no—
66C2×Dic263—42no—
67C263⋊C8—22no—
68C263⋊C8C22⋊C414yescomplemented
69C23×C263C2×D411yescharacteristic
70Q8×C263—22no—
71Q8×C263—22no—
72Q8×C263—41no—
73Q8×C263—41no—
74C2×C4×C263—22no—
75C2×C4×C263—22no—
76C2×C4×C263—22no—
77C2×C4×C263—22no—
78C2×C4×C263—41no—
79C2×C4×C263—41no—
80C2×C4×C263—41no—
81C2×C4×C263—42no—
82C2×C4×C263C22×C411yescharacteristic
83C2×C4×C263C2×D411yescharacteristic
84C2×C4×C263C2×D411yescharacteristic
85C2×C4×C263C2×D411yescharacteristic
86C2×C4×C263#4111yescharacteristic
87C2×C4×C263#4111yescharacteristic
88C22×C263C4×D411yescharacteristic
89C22×C263#12111yescharacteristic
90C22×C263#12711yescharacteristic
91C22×C263AGL(1,ℤ/8)12yes—
92C22×C263#13712yes—
93C2×D263—42no—
94C2×D263—44no—
95C2×D263—82no—
96C2×D263—81no—
97C2×D263—81no—
98C4×C263—42no—
99C4×C263—42no—
100C4×C263—81no—
101C4×C263C2×C22⋊C411yescharacteristic
102C4×C263C4×D411yescharacteristic
103C4×C263#12111yescharacteristic
104C4×C263#12411yescharacteristic
105Dic263—81no—
106C2×C263#39011yescharacteristic
107C2×C263#44012yes—
108C2×C263#46812yes—
109C2×C263#49611yescharacteristic
110C2×C263#49711yescharacteristic
111D263—82no—
112C263#197311yescharacteristic, complemented, Sylow
113#1973—2631nomaximal, Sylow
114C22×SD16—2631no—
115C2×#107—2631no—
116C2×#103—2631no—
117C2×#102—2631no—
118C2×#97—2631no—
119#391D26311yescharacteristic, complemented
120#390—2631no—
121C22×Q8C2×D26311yescharacteristic
122C22×D4—2631no—
123C2×SD16—2634no—
124C2×SD16—5262no—
125C2×SD16—5262no—
126C22×C8—2631no—
127C22×C8—2631no—
128C2×C4⋊C4—2631no—
129C2×C4⋊C4C2×D26311yescharacteristic
130C2×C22⋊C4—5262no—
131C2×C42C2×D26311yescharacteristic
132#107—5262no—
133#103—5262no—
134#102—5262no—
135#97—5262no—
136#95—22no—
137C24—5261no—
138C2×Q8—21no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—21no—
143C2×Q8C4×D26312yes—
144C2×D4—2632no—
145C2×D4—5261no—
146C2×D4—5261no—
147C2×D4—5261no—
148C2×D4—5261no—
149C2×D4—5261no—
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—5261no—
153C22×C4C22⋊D26312yes—
154C22×C4C22×D26311yescharacteristic
155SD16—5268no—
156C2×C8—2632no—
157C2×C8—2632no—
158C2×C8—2632no—
159C2×C8—2632no—
160C2×C8—5261no—
161C2×C8—5261no—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—5261no—
165C4⋊C4—5261no—
166C22⋊C4—10524no—
167C42—21no—
168C42—21no—
169C23—5262no—
170C23—10521no—
171C23—10521no—
172C23—10522no—
173C23—10522no—
174C23C2×C22⋊D26311yescharacteristic
175Q8—22no—
176Q8—22no—
177Q8—41no—
178Q8—41no—
179D4—5262no—
180D4—5262no—
181D4—10521no—
182D4—10521no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—42no—
191C2×C4—10521no—
192C2×C4—10522no—
193C2×C4C2×C4×D26311yescharacteristic
194C2×C4D4×D26311yescharacteristic
195C2×C4D4×D26311yescharacteristic
196C2×C4D4×D26311yescharacteristic
197C2×C4#1686237511yescharacteristic
198C2×C4#1686237611yescharacteristic
199C8—2634no—
200C8—5262no—
201C22—10524no—
202C22—10522no—
203C22—21042no—
204C22—21041no—
205C22—21041no—
206C22C4×C22⋊D26311yescharacteristic
207C22#2255444211yescharacteristic
208C22#2255446611yescharacteristic
209C22#2255449512yes—
210C22#2255450112yes—
211C4—42no—
212C4—42no—
213C4—81no—
214C4—21041no—
215C4C22⋊C4×D26311yescharacteristic
216C4(C22⋊D263)⋊C411yescharacteristic
217C4#2255444311yescharacteristic
218C4#2255445611yescharacteristic
219C2—21042no—
220C2#3068183811yescharacteristic
221C2#3068203612yes—
222C2#3068218612yes—
223C2#3068232811yescharacteristic
224C2#3068233011yescharacteristic
subgroupG/H
centerC23C2×C22⋊D263
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#391×C263C2
socleC23×C263C2×D4
prime radicalC22×D1052C22
cosocleC22×C4×C263C23
hypercenter#391D263
hypocenterC263#1973
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
2. C2×#22554403C2semidirect
3. C2×#22554394C2semidirect
5. C2×#22554381C2semidirect
7. #391×C263C2semidirect
11. C2×#16862363C4semidirect
68. C263⋊C8C22⋊C4semidirect
112. C263#1973semidirect
119. #391D263semidirect

Maximal subgroups

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

subgroupindex
C22×#168623632
C2×#225544032
C2×#225543942
C2×#225543902
C2×#225543812
#306818402
#391×C2632
#1973263