Finite Group Databasebeta

← #46783180

Subgroups — #46783180

Order 33664.

360 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 109 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×#22554449C211yesmaximal, characteristic
2C2×#22554395C212yesmaximal, complemented
3#30681798C211yesmaximal, characteristic
4#30681701C212yesmaximal, complemented
5C22×M16×C263C211yesmaximal, characteristic
6C22×Dic526C2211yescharacteristic
7#22554449—22no—
8#22554449C414yescomplemented
9C2×C4⋊Dic263C2212yes—
10C2×C4⋊Dic263C2211yescharacteristic
11C2×Dic263⋊C4—21no—
12C2×C22⋊Dic263—21no—
13C2×C22⋊Dic263—21no—
14#22554395—24no—
15C263⋊#95—21no—
16C23×C4×C263C2211yescharacteristic
17C2×M16×C263—22no—
18C2×M16×C263—24no—
19C22×C8×C263C2212yes—
20C2×Dic526—21no—
21C2×Dic526—22no—
22C2×Dic526—22no—
23C2×Dic526C2×C412yes—
24C22×Dic263—21no—
25C22×Dic263—21no—
26C22×Dic263—22no—
27C4⋊Dic263—21no—
28C4⋊Dic263—22no—
29C4⋊Dic263—22no—
30C4⋊Dic263C2×C412yes—
31Dic263⋊C4—24no—
32C22⋊Dic263—24no—
33C22⋊Dic263—42no—
34C24×C263D411yescharacteristic
35C22×C4×C263—22no—
36C22×C4×C263—22no—
37C22×C4×C263C2×C412yes—
38C22×C4×C263D412yes—
39C22×C4×C263D411yescharacteristic
40C22×C4×C263C2311yescharacteristic
41M16×C263—28no—
42C2×C8×C263—22no—
43C2×C8×C263—22no—
44C2×C8×C263D414yes—
45Dic526—24no—
46Dic526—41no—
47Dic526—41no—
48C2×Dic263—22no—
49C2×Dic263—22no—
50C2×Dic263—42no—
51C2×Dic263—41no—
52C2×Dic263—41no—
53C2×Dic263—42no—
54C2×Dic263—42no—
55C2×Dic263—42no—
56C23×C263—22no—
57C23×C263—21no—
58C23×C263—21no—
59C23×C263—22no—
60C23×C263C22⋊C412yes—
61C23×C263C2×D411yescharacteristic
62C2×C4×C263—22no—
63C2×C4×C263—24no—
64C2×C4×C263—22no—
65C2×C4×C263—22no—
66C2×C4×C263C22⋊C412yes—
67C2×C4×C263C22×C411yescharacteristic
68C2×C4×C263C2×D412yes—
69C2×C4×C263C2×D411yescharacteristic
70C2×C4×C263#4112yes—
71C8×C263—24no—
72C22×C263—22no—
73C22×C263—22no—
74C22×C263—22no—
75C22×C263—42no—
76C22×C263—42no—
77C22×C263C2×C22⋊C411yescharacteristic
78C22×C263#12112yes—
79C22×C263AGL(1,ℤ/8)11yescharacteristic
80C22×C263#13711yescharacteristic
81C22×C263#13712yes—
82C4×C263—22no—
83C4×C263C4×D412yes—
84C4×C263#12011yescharacteristic
85C4×C263#12311yescharacteristic
86Dic263—42no—
87Dic263—42no—
88Dic263—82no—
89C2×C263—42no—
90C2×C263#38611yescharacteristic
91C2×C263#41711yescharacteristic
92C2×C263#41911yescharacteristic
93C2×C263#46812yes—
94C2×C263#47012yes—
95C263#189411yescharacteristic, complemented, Sylow
96#1894—2631nomaximal, Sylow
97C22×M16D26311yescharacteristic
98C2×C22⋊Q8—2631no—
99C2×#103—2632no—
100#380—2631no—
101#340—2632no—
102C22×Q8—2631no—
103C23×C4C2×D26311yescharacteristic
104C2×M16—22no—
105C2×M16—24no—
106C22×C8C2×D26312yes—
107C22⋊Q8—2634no—
108C22⋊Q8—5262no—
109C2×C4⋊C4—2631no—
110C2×C4⋊C4—2632no—
111C2×C4⋊C4—5261no—
112C2×C22⋊C4—5261no—
113C2×C22⋊C4—5261no—
114#103—5264no—
115#95—5261no—
116C24D105211yescharacteristic
117C2×Q8—2632no—
118C2×Q8—5261no—
119C2×Q8—5262no—
120C2×Q8—5262no—
121C22×C4—22no—
122C22×C4—22no—
123C22×C4—5261no—
124C22×C4—5261no—
125C22×C4—5262no—
126C22×C4C4×D26312yes—
127C22×C4C22⋊D26312yes—
128C22×C4D105211yescharacteristic
129C22×C4C22×D26311yescharacteristic
130M16—28no—
131C2×C8—22no—
132C2×C8—22no—
133C2×C8C22⋊D26314yes—
134C4⋊C4—2632no—
135C4⋊C4—5264no—
136C4⋊C4—5261no—
137C4⋊C4—5262no—
138C4⋊C4—5262no—
139C22⋊C4—5264no—
140C22⋊C4—10522no—
141C23—22no—
142C23—21no—
143C23—21no—
144C23—22no—
145C23(C2×D263)⋊C412yes—
146C23C2×D105211yescharacteristic
147Q8—5264no—
148Q8—10521no—
149Q8—10521no—
150C2×C4—22no—
151C2×C4—24no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—5262no—
155C2×C4—5262no—
156C2×C4—10522no—
157C2×C4—10521no—
158C2×C4—10521no—
159C2×C4—10522no—
160C2×C4—10522no—
161C2×C4—10522no—
162C2×C4(C2×D263)⋊C412yes—
163C2×C4C2×C4×D26311yescharacteristic
164C2×C4C2×C22⋊D26312yes—
165C2×C4C2×C22⋊D26311yescharacteristic
166C2×C4#1686237612yes—
167C8—24no—
168C22—22no—
169C22—22no—
170C22—22no—
171C22—42no—
172C22—42no—
173C22C2×(C2×D263)⋊C411yescharacteristic
174C22#2255444412yes—
175C22#2255449811yescharacteristic
176C22#2255450312yes—
177C22#2255450311yescharacteristic
178C4—22no—
179C4—10522no—
180C4—10522no—
181C4—21042no—
182C4C4×C22⋊D26312yes—
183C4#2255443911yescharacteristic
184C4#2255445311yescharacteristic
185C2—42no—
186C2#3068181711yescharacteristic
187C2#3068194011yescharacteristic
188C2#3068194811yescharacteristic
189C2#3068218412yes—
190C2#3068219612yes—
subgroupG/H
centerC23C2×D1052
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
FittingC22×M16×C263C2
socleC23×C263C2×D4
prime radicalC24×C263D4
cosocleC22×C4×C263C23
hypercenterC22×M16D263
hypocenterC263#1894
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
2. C2×#22554395C2semidirect
4. #30681701C2semidirect
8. #22554449C4semidirect
95. C263#1894semidirect

Maximal subgroups

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

subgroupindex
C2×#225544492
C2×#225543952
#306817982
#306817012
C22×M16×C2632
#1894263