Finite Group Databasebeta

← #46783907

Subgroups — #46783907

Order 33664.

246 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 67 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
1#30682566C211yesmaximal, characteristic
2#30681948C211yesmaximal, characteristic
3#30681946C211yesmaximal, characteristic
4#30681844C211yesmaximal, characteristic
5#30681706C211yesmaximal, characteristic
6#30681698C211yesmaximal, characteristic
7#339×C263C211yesmaximal, characteristic
8C22×Dic526C2211yescharacteristic
9C2×#16862360C2211yescharacteristic
10#22554470—21no—
11#22554469—21no—
12#22554462—21no—
13#22554461—21no—
14#22554447—22no—
15#22554429C2211yescharacteristic
16C2×C4⋊Dic263C2211yescharacteristic
17#22554395—21no—
18#22554395—21no—
19#22554393—21no—
20#22554393—21no—
21C263⋊#95—22no—
22C2×M16×C263C2211yescharacteristic
23#117×C263C2211yescharacteristic
24C2×C42×C263C2211yescharacteristic
25C2×Dic526—22no—
26C2×Dic526—21no—
27C2×Dic526—21no—
28C2×Dic526—21no—
29C2×Dic526—21no—
30C2×Dic526—21no—
31C2×Dic526Q812yescomplemented
32C22×Dic263—21no—
33C22×Dic263D412yes—
34#16862360—21no—
35#16862360—21no—
36C2×C263⋊C8—21no—
37C4⋊Dic263—22no—
38C4⋊Dic263—21no—
39C4⋊Dic263—21no—
40C4⋊Dic263D411yescharacteristic
41C4⋊Dic263D411yescharacteristic
42Dic263⋊C4—22no—
43Dic263⋊C4—22no—
44C22⋊Dic263—21no—
45C4×Dic263—21no—
46C22×C4×C263—21no—
47C22×C4×C263C2311yescharacteristic
48M16×C263—21no—
49M16×C263—21no—
50C2×C8×C263—21no—
51C4⋊C4×C263D411yescharacteristic
52C4⋊C4×C263D411yescharacteristic
53C22⋊C4×C263—21no—
54C42×C263—21no—
55C42×C263—21no—
56C42×C263—21no—
57Dic526—22no—
58Dic526—22no—
59Dic526—41no—
60Dic526—41no—
61Dic526—82no—
62C2×Dic263—21no—
63C2×Dic263—21no—
64C2×Dic263—22no—
65C2×Dic263—22no—
66C2×Dic263—41no—
67C2×Dic263—41no—
68C2×Dic263—42no—
69C263⋊C8—41no—
70C23×C263C2×D411yescharacteristic
71C2×C4×C263—22no—
72C2×C4×C263—21no—
73C2×C4×C263—21no—
74C2×C4×C263—41no—
75C2×C4×C263—41no—
76C2×C4×C263C2×D411yescharacteristic
77C2×C4×C263C2×D411yescharacteristic
78C2×C4×C263C2×Q811yescharacteristic
79C2×C4×C263#4111yescharacteristic
80C2×C4×C263#4111yescharacteristic
81C2×C4×C263#4111yescharacteristic
82C8×C263—41no—
83C22×C263—21no—
84C22×C263—21no—
85C22×C263#12011yescharacteristic
86C22×C263C22⋊Q811yescharacteristic
87C22×C263#12411yescharacteristic
88C4×C263—42no—
89C4×C263—41no—
90C4×C263—41no—
91C4×C263C22⋊Q811yescharacteristic
92C4×C263C22⋊Q811yescharacteristic
93C4×C263#12411yescharacteristic
94C4×C263#12411yescharacteristic
95Dic263—42no—
96Dic263—42no—
97Dic263—41no—
98Dic263—41no—
99C2×C263—21no—
100C2×C263—21no—
101C2×C263#39311yescharacteristic
102C2×C263#45511yescharacteristic
103C2×C263#45611yescharacteristic
104C263#202811yescharacteristic, complemented, Sylow
105#2028—2631nomaximal, Sylow
106#544—2631no—
107#419—2631no—
108#419—2631no—
109#391—2631no—
110#343—2631no—
111#339—2631no—
112#339D26311yescharacteristic
113C22×Q8—2631no—
114C2×M16—2631no—
115C2×M16C2×D26311yescharacteristic
116C4⋊Q8—5261no—
117C4⋊Q8—5261no—
118#125—5261no—
119#125—5261no—
120C22⋊Q8—5262no—
121#117—2631no—
122#117C2×D26311yescharacteristic
123C2×C4⋊C4—2631no—
124C2×C42C2×D26311yescharacteristic
125#103—5261no—
126#103—5261no—
127#103—5261no—
128#103—5261no—
129#95—5262no—
130C2×Q8—2632no—
131C2×Q8—5262no—
132C2×Q8—5261no—
133C2×Q8—5261no—
134C2×Q8—5261no—
135C2×Q8—5261no—
136C2×Q8—5261no—
137C22×C4—21no—
138C22×C4—2632no—
139C22×C4—5261no—
140C22×C4C22×D26311yescharacteristic
141M16—21no—
142M16—21no—
143M16—5261no—
144M16—5261no—
145C2×C8—21no—
146C2×C8—5261no—
147C4⋊C4—2631no—
148C4⋊C4—2631no—
149C4⋊C4—5262no—
150C4⋊C4—5262no—
151C4⋊C4—5262no—
152C4⋊C4—5261no—
153C4⋊C4—5261no—
154C4⋊C4D105211yescharacteristic
155C4⋊C4D105211yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—5261no—
158C42—21no—
159C42—21no—
160C42—21no—
161C42—5261no—
162C23D4×D26311yescharacteristic
163Q8—5262no—
164Q8—5262no—
165Q8—10521no—
166Q8—10521no—
167Q8—21042no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—5261no—
174C2×C4—5261no—
175C2×C4—5262no—
176C2×C4—5262no—
177C2×C4—10521no—
178C2×C4—10521no—
179C2×C4—10522no—
180C2×C4D4×D26311yescharacteristic
181C2×C4C2×D105211yescharacteristic
182C2×C4Q8×D26311yescharacteristic
183C2×C4#1686237511yescharacteristic
184C2×C4#1686237611yescharacteristic
185C2×C4#1686237611yescharacteristic
186C8—41no—
187C8—10521no—
188C22—21no—
189C22—21no—
190C22#2255444011yescharacteristic
191C22#2255444811yescharacteristic
192C22#2255445611yescharacteristic
193C4—42no—
194C4—41no—
195C4—41no—
196C4—10522no—
197C4—10521no—
198C4—10521no—
199C4—10522no—
200C4#2255444811yescharacteristic
201C4#2255445011yescharacteristic
202C4#2255445611yescharacteristic
203C4#2255445811yescharacteristic
204C2—21no—
205C2—21no—
206C2#3068185111yescharacteristic
207C2#3068211711yescharacteristic
208C2#3068212211yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#339×C263C2
socleC22×C263#120
prime radicalC23×C263C2×D4
hypercenter#339D263
hypocenterC263#2028
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
31. C2×Dic526Q8semidirect
104. C263#2028semidirect

Maximal subgroups

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

subgroupindex
#306825662
#306819482
#306819462
#306818442
#306817062
#306816982
#339×C2632
#2028263