Finite Group Databasebeta

← #46783652

Subgroups — #46783652

Order 33664.

296 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 97 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×#22554406C211yesmaximal, characteristic, complemented
2#30681947C211yesmaximal, characteristic, complemented
3#30681943C211yesmaximal, characteristic
4C2×#22554389C211yesmaximal, characteristic, complemented
5C2×#22554387C211yesmaximal, characteristic
6#30681893C211yesmaximal, characteristic, complemented
7C22×SD16×C263C211yesmaximal, characteristic
8C2×#16862360C2211yescharacteristic
9C2×#16862360C2211yescharacteristic
10C2×#16862360C2211yescharacteristic
11#22554429C2211yescharacteristic
12#22554406—22no—
13#22554394—22no—
14#22554391—22no—
15#22554389—22no—
16#22554387—22no—
17#22554380—21no—
18C8×Dic263—21no—
19C22×Q8×C263C2211yescharacteristic
20C22×D4×C263C2211yescharacteristic
21C2×SD16×C263—21no—
22C2×SD16×C263—21no—
23C2×SD16×C263—22no—
24C2×SD16×C263C414yescomplemented
25C22×C8×C263C2211yescharacteristic
26#16862360—21no—
27#16862360—21no—
28#16862360—21no—
29#16862360—21no—
30#16862360—21no—
31#16862360D412yes—
32C2×C263⋊C8—21no—
33C2×C263⋊C8—21no—
34C2×C263⋊C8—21no—
35C4⋊Dic263D412yes—
36C22⋊Dic263—21no—
37C4×Dic263—21no—
38C24×C263—21no—
39C2×Q8×C263—21no—
40C2×Q8×C263—21no—
41C2×Q8×C263—21no—
42C2×Q8×C263—21no—
43C2×Q8×C263—21no—
44C2×Q8×C263C2×C412yes—
45C2×D4×C263—21no—
46C2×D4×C263—21no—
47C2×D4×C263—21no—
48C2×D4×C263—21no—
49C2×D4×C263—21no—
50C2×D4×C263C2×C412yes—
51C22×C4×C263—21no—
52C22×C4×C263C2311yescharacteristic
53SD16×C263—24no—
54SD16×C263—24no—
55C2×C8×C263C2×C412yes—
56C2×C8×C263D411yescharacteristic
57C2×C8×C263D411yescharacteristic
58C2×C8×C263D412yes—
59C2×Dic263—22no—
60C263⋊C8—22no—
61C263⋊C8—41no—
62C263⋊C8—41no—
63C23×C263—22no—
64C23×C263—41no—
65C23×C263—41no—
66C23×C263—82no—
67C23×C263#4111yescharacteristic
68Q8×C263—22no—
69Q8×C263—22no—
70Q8×C263—41no—
71Q8×C263—41no—
72D4×C263—22no—
73D4×C263—22no—
74D4×C263—41no—
75D4×C263—41no—
76C2×C4×C263—22no—
77C2×C4×C263—41no—
78C2×C4×C263—41no—
79C2×C4×C263C22×C411yescharacteristic
80C2×C4×C263C2×D411yescharacteristic
81C2×C4×C263C2×D411yescharacteristic
82C2×C4×C263C2×D411yescharacteristic
83C2×C4×C263C2×D411yescharacteristic
84C2×C4×C263#4111yescharacteristic
85C8×C263C22⋊C412yes—
86C8×C263C22⋊C412yes—
87C22×C263—22no—
88C22×C263—42no—
89C22×C263—82no—
90C22×C263—82no—
91C22×C263—82no—
92C22×C263C4×D411yescharacteristic
93C22×C263#12111yescharacteristic
94C22×C263#12411yescharacteristic
95C4×C263—42no—
96C4×C263C2×C22⋊C411yescharacteristic
97C4×C263C4×D411yescharacteristic
98C4×C263#12111yescharacteristic
99C4×C263#12711yescharacteristic
100Dic263—42no—
101C2×C263—21no—
102C2×C263—21no—
103C2×C263—82no—
104C2×C263#39011yescharacteristic
105C2×C263#47112yes—
106C263#197711yescharacteristic, complemented, Sylow
107#1977—2631nomaximal, Sylow
108C22×SD16D26311yescharacteristic
109C2×#108—2631no—
110#419—2631no—
111#418—2631no—
112C2×#101—2631no—
113C2×#100—2631no—
114#405—2631no—
115C22×Q8C2×D26311yescharacteristic
116C22×D4C2×D26311yescharacteristic
117C2×SD16—21no—
118C2×SD16—21no—
119C2×SD16—22no—
120C2×SD16Dic26314yescomplemented
121C2×M16—2631no—
122C2×M16—2631no—
123C2×M16—2631no—
124C22×C8C2×D26311yescharacteristic
125#117—2631no—
126#108—5262no—
127#103—5262no—
128#102—5262no—
129#101—5262no—
130#100—5262no—
131#97—5261no—
132C4×C8—5261no—
133C24—21no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8—21no—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8C2×Dic26312yes—
140C2×D4—21no—
141C2×D4—21no—
142C2×D4—21no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4C2×Dic26312yes—
146C22×C4—21no—
147C22×C4C22×D26311yescharacteristic
148SD16—24no—
149SD16—24no—
150M16—2632no—
151M16—5261no—
152M16—5261no—
153M16—5261no—
154M16—5261no—
155M16—5261no—
156C2×C8—5261no—
157C2×C8—5261no—
158C2×C8—5261no—
159C2×C8C2×Dic26312yes—
160C2×C8C22⋊D26311yescharacteristic
161C2×C8C22⋊D26311yescharacteristic
162C2×C8C22⋊D26312yes—
163C4⋊C4—2632no—
164C22⋊C4—5261no—
165C42—5261no—
166C23—22no—
167C23—41no—
168C23—41no—
169C23—82no—
170C23#1686237511yescharacteristic
171Q8—22no—
172Q8—22no—
173Q8—41no—
174Q8—41no—
175D4—22no—
176D4—22no—
177D4—41no—
178D4—41no—
179C2×C4—22no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—5262no—
183C2×C4C22×Dic26311yescharacteristic
184C2×C4D4×D26311yescharacteristic
185C2×C4D4×D26311yescharacteristic
186C2×C4C2×C22⋊D26311yescharacteristic
187C2×C4C2×C22⋊D26311yescharacteristic
188C2×C4#1686237511yescharacteristic
189C8—5262no—
190C8—10521no—
191C8—10521no—
192C8C22⋊Dic26312yes—
193C8C22⋊Dic26312yes—
194C22—22no—
195C22—42no—
196C22—82no—
197C22—82no—
198C22—82no—
199C22D4×Dic26311yescharacteristic
200C22#2255444111yescharacteristic
201C22#2255445711yescharacteristic
202C4—42no—
203C4—10522no—
204C4C2×C22⋊Dic26311yescharacteristic
205C4D4×Dic26311yescharacteristic
206C4#2255444111yescharacteristic
207C4#2255446611yescharacteristic
208C2—21no—
209C2—21no—
210C2—82no—
211C2#3068184111yescharacteristic
212C2#3068219812yes—
subgroupG/H
centerC22#22554441
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
FittingC22×SD16×C263C2
socleC22×C263#121
prime radicalC22×D4×C263C22
cosocleC22×C4×C263C23
hypercenterC22×SD16D263
hypocenterC263#1977
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#22554406C2semidirect
2. #30681947C2semidirect
4. C2×#22554389C2semidirect
6. #30681893C2semidirect
24. C2×SD16×C263C4semidirect
106. C263#1977semidirect
120. C2×SD16Dic263semidirect

Maximal subgroups

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

subgroupindex
C2×#225544062
#306819472
#306819432
C2×#225543892
C2×#225543872
#306818932
C22×SD16×C2632
#1977263