Finite Group Databasebeta

← #46784090

Subgroups — #46784090

Order 33664.

246 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 73 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#30681978C211yesmaximal, characteristic
3#30681807C211yesmaximal, characteristic
4#30681706C211yesmaximal, characteristic
5#30681699C211yesmaximal, characteristic
6#30681697C211yesmaximal, characteristic
7#428×C263C211yesmaximal, characteristic
8C2×#16862360C2211yescharacteristic
9#22554470—21no—
10#22554469—21no—
11#22554462—21no—
12#22554461—21no—
13#22554447—22no—
14#22554429C2211yescharacteristic
15C2×C4⋊Dic263C2211yescharacteristic
16C2×Dic263⋊C4—22no—
17C2×C4×Dic263C2211yescharacteristic
18#22554403—21no—
19#22554401—21no—
20C2×M16×C263C2211yescharacteristic
21#117×C263C2211yescharacteristic
22C2×C4⋊C4×C263C2211yescharacteristic
23#107×C263—21no—
24#106×C263—21no—
25C2×Dic526—22no—
26C22×Dic263—21no—
27C22×Dic263D412yes—
28#16862360—21no—
29#16862360Q812yescomplemented
30C2×C263⋊C8—21no—
31C4⋊Dic263—22no—
32C4⋊Dic263—21no—
33C4⋊Dic263—21no—
34C4⋊Dic263D411yescharacteristic
35C4⋊Dic263D411yescharacteristic
36Dic263⋊C4—22no—
37Dic263⋊C4—22no—
38Dic263⋊C4—44no—
39C22⋊Dic263—21no—
40C4×Dic263—21no—
41C4×Dic263—21no—
42C4×Dic263Q812yescomplemented
43C22×C4×C263—21no—
44C22×C4×C263C2311yescharacteristic
45M16×C263—21no—
46M16×C263Q812yescomplemented
47C2×C8×C263—21no—
48C4⋊C4×C263—21no—
49C4⋊C4×C263—21no—
50C4⋊C4×C263D411yescharacteristic
51C4⋊C4×C263D411yescharacteristic
52C22⋊C4×C263—21no—
53C42×C263—21no—
54Dic526—82no—
55C2×Dic263—22no—
56C2×Dic263—22no—
57C2×Dic263—22no—
58C2×Dic263—21no—
59C2×Dic263—21no—
60C2×Dic263—22no—
61C2×Dic263—42no—
62C263⋊C8—22no—
63C23×C263C2×D411yescharacteristic
64C2×C4×C263—21no—
65C2×C4×C263—21no—
66C2×C4×C263—42no—
67C2×C4×C263—41no—
68C2×C4×C263C2×D411yescharacteristic
69C2×C4×C263C2×D411yescharacteristic
70C2×C4×C263C2×Q811yescharacteristic
71C2×C4×C263C2×Q811yescharacteristic
72C2×C4×C263C2×Q811yescharacteristic
73C2×C4×C263#4111yescharacteristic
74C8×C263—22no—
75C22×C263—21no—
76C22×C263—21no—
77C22×C263#12011yescharacteristic
78C22×C263C22⋊Q811yescharacteristic
79C22×C263C4⋊Q811yescharacteristic
80C4×C263—41no—
81C4×C263—41no—
82C4×C263—81no—
83C4×C263C22⋊Q811yescharacteristic
84C4×C263C22⋊Q811yescharacteristic
85C4×C263C4⋊Q811yescharacteristic
86C4×C263C4⋊Q811yescharacteristic
87Dic263—24no—
88Dic263—42no—
89Dic263—41no—
90Dic263—41no—
91C2×C263—21no—
92C2×C263—21no—
93C2×C263#39511yescharacteristic
94C2×C263#45311yescharacteristic
95C2×C263#45611yescharacteristic
96C263#206011yescharacteristic, complemented, Sylow
97#2060—2631nomaximal, Sylow
98#544—2631no—
99#428—2631no—
100#428D26311yescharacteristic
101#384—2631no—
102#343—2631no—
103#339—2631no—
104#339—2631no—
105C2×M16—2631no—
106C2×M16C2×D26311yescharacteristic
107C4⋊Q8—5261no—
108C4⋊Q8—5261no—
109#125—5261no—
110#125—5261no—
111C22⋊Q8—5262no—
112#117—2631no—
113#117C2×D26311yescharacteristic
114C2×C4⋊C4—2631no—
115C2×C4⋊C4—5262no—
116C2×C4⋊C4C2×D26311yescharacteristic
117C2×C42—2631no—
118#107—21no—
119#107—5261no—
120#106—21no—
121#106—5261no—
122C2×Q8—5262no—
123C22×C4—21no—
124C22×C4—2632no—
125C22×C4—5261no—
126C22×C4C22×D26311yescharacteristic
127M16—21no—
128M16—2632no—
129M16—5261no—
130M16Dic52612yescomplemented
131C2×C8—21no—
132C2×C8—5261no—
133C4⋊C4—21no—
134C4⋊C4—21no—
135C4⋊C4—2631no—
136C4⋊C4—2631no—
137C4⋊C4—5262no—
138C4⋊C4—5262no—
139C4⋊C4—5262no—
140C4⋊C4—5261no—
141C4⋊C4—5261no—
142C4⋊C4—10524no—
143C4⋊C4C22⋊D26311yescharacteristic
144C4⋊C4C22⋊D26311yescharacteristic
145C22⋊C4—21no—
146C22⋊C4—5261no—
147C42—21no—
148C42—2632no—
149C42—5261no—
150C42—5261no—
151C23D4×D26311yescharacteristic
152Q8—21042no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—42no—
156C2×C4—41no—
157C2×C4—5262no—
158C2×C4—5262no—
159C2×C4—5262no—
160C2×C4—5261no—
161C2×C4—5261no—
162C2×C4—5262no—
163C2×C4—10522no—
164C2×C4D4×D26311yescharacteristic
165C2×C4C2×C22⋊D26311yescharacteristic
166C2×C4Q8×D26311yescharacteristic
167C2×C4Q8×D26311yescharacteristic
168C2×C4C2×Dic52611yescharacteristic
169C2×C4#1686237611yescharacteristic
170C8—22no—
171C8—5262no—
172C22—21no—
173C22—21no—
174C22#2255443811yescharacteristic
175C22#2255444811yescharacteristic
176C22#2255446911yescharacteristic
177C4—41no—
178C4—41no—
179C4—81no—
180C4—5264no—
181C4—10521no—
182C4—10522no—
183C4—10521no—
184C4#2255444811yescharacteristic
185C4#2255444911yescharacteristic
186C4#2255446811yescharacteristic
187C4#2255446911yescharacteristic
188C2—21no—
189C2—21no—
190C2#3068185811yescharacteristic
191C2#3068210411yescharacteristic
192C2#3068211911yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#428×C263C2
socleC22×C263#120
prime radicalC23×C263C2×D4
hypercenter#428D263
hypocenterC263#2060
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
29. #16862360Q8semidirect
42. C4×Dic263Q8semidirect
46. M16×C263Q8semidirect
96. C263#2060semidirect
130. M16Dic526semidirect

Maximal subgroups

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

subgroupindex
#306825662
#306819782
#306818072
#306817062
#306816992
#306816972
#428×C2632
#2060263