Finite Group Databasebeta

← #46781816

Subgroups — #46781816

Order 33664.

236 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 55 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#30682649C211yesmaximal, characteristic, complemented
2#30682135C211yesmaximal, characteristic, complemented
3#30682130C211yesmaximal, characteristic
4#30681687C211yesmaximal, characteristic, complemented
5#30681670C211yesmaximal, characteristic, complemented
6#30681667C211yesmaximal, characteristic, complemented
7#492×C263C211yesmaximal, characteristic, complemented
8C2×#16862364—21no—
9C2×#16862361—21no—
10#22554461—21no—
11#22554450—21no—
12#22554446—22no—
13C4×Dic526C2211yescharacteristic
14C4×D1052C2211yescharacteristic
15#22554432—21no—
16C4⋊C4×D263—21no—
17C4⋊(C263⋊C8)C2211yescharacteristic
18C4⋊(C263⋊C8)C2211yescharacteristic
19#22554391—21no—
20#22554391—21no—
21C2×SD16×C263—22no—
22C4⋊Q8×C263C2211yescharacteristic
23#127×C263C2211yescharacteristic
24C4×C8×C263C2211yescharacteristic
25C2×Dic526D411yescharacteristic
26C2×D1052D411yescharacteristic
27C2×C4×D263—22no—
28C2×C4×D263—21no—
29#16862364—42no—
30#16862361—42no—
31C2×C263⋊C8—21no—
32C2×C263⋊C8—21no—
33C4⋊Dic263—22no—
34C4⋊Dic263D411yescharacteristic
35C4⋊Dic263D411yescharacteristic
36Dic263⋊C4—22no—
37Dic263⋊C4—21no—
38(C2×D263)⋊C4—22no—
39(C2×D263)⋊C4—21no—
40C4×Dic263—21no—
41C2×Q8×C263D412yes—
42C2×D4×C263—21no—
43C2×D4×C263—21no—
44C2×D4×C263—21no—
45SD16×C263—44no—
46C2×C8×C263—21no—
47C4⋊C4×C263—21no—
48C4⋊C4×C263—21no—
49C42×C263C2311yescharacteristic
50C22×D263—21no—
51Dic526—21no—
52Dic526—21no—
53D1052—21no—
54D1052SD1612yescomplemented
55C2×Dic263—21no—
56C2×Dic263—21no—
57C2×Dic263—21no—
58C4×D263—41no—
59C4×D263—41no—
60C4×D263—82no—
61C263⋊C8—41no—
62C263⋊C8—41no—
63C23×C263—41no—
64Q8×C263—42no—
65D4×C263—42no—
66D4×C263—41no—
67D4×C263—41no—
68D4×C263—41no—
69D4×C263—41no—
70C2×C4×C263—22no—
71C2×C4×C263C2×D411yescharacteristic
72C2×C4×C263C2×D411yescharacteristic
73C2×C4×C263C2×D411yescharacteristic
74C8×C263—22no—
75C22×C263—81no—
76C22×C263—81no—
77C22×C263—81no—
78C22×C263#12011yescharacteristic
79C2×D263—22no—
80C2×D263—41no—
81C2×D263—41no—
82C4×C263—21no—
83C4×C263—42no—
84C4×C263C2×SD1611yescharacteristic
85C4×C263#13511yescharacteristic
86C4×C263AGL(1,ℤ/8)11yescharacteristic
87C4×C263#13711yescharacteristic
88Dic263—41no—
89Dic263—41no—
90Dic263—41no—
91C2×C263—161no—
92C2×C263#44811yescharacteristic
93C2×C263#44911yescharacteristic
94C2×C263#45311yescharacteristic
95D263—42no—
96C263#162211yescharacteristic, complemented, Sylow
97#1622—2631nomaximal, Sylow
98#554—2631no—
99#492D26311yescharacteristic, complemented
100#460—2631no—
101#459—2631no—
102#333—2631no—
103Q8⋊C8—2631no—
104D4⋊C8—2631no—
105C2×SD16—22no—
106C2×SD16—5261no—
107C2×D8—5261no—
108C4⋊Q8C2×D26311yescharacteristic
109#127C2×D26311yescharacteristic
110#125—5261no—
111C22⋊Q8—5261no—
112C22⋊Q8—5262no—
113C4×Q8—2631no—
114C4×D4—2631no—
115C4×D4—5261no—
116C2×C4⋊C4—5261no—
117C4⋊C8—2631no—
118C4⋊C8—2631no—
119#102—5261no—
120#102—5261no—
121C4×C8C2×D26311yescharacteristic
122C2×Q8—2631no—
123C2×Q8C22⋊D26312yes—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4—2631no—
128C22×C4—5262no—
129C22×C4—5261no—
130SD16—44no—
131SD16—10522no—
132D8—10522no—
133C2×C8—21no—
134C2×C8—5261no—
135C2×C8—5261no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—2631no—
139C4⋊C4—2631no—
140C4⋊C4—5262no—
141C4⋊C4—5262no—
142C4⋊C4—5261no—
143C22⋊C4—5262no—
144C22⋊C4—5261no—
145C42—5261no—
146C42C22×D26311yescharacteristic
147C23—41no—
148C23—5261no—
149Q8—42no—
150Q8—5261no—
151Q8—5261no—
152D4—42no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—2632no—
158D4—5261no—
159C2×C4—22no—
160C2×C4—5261no—
161C2×C4—5261no—
162C2×C4—5261no—
163C2×C4—10521no—
164C2×C4—10521no—
165C2×C4—21042no—
166C2×C4D4×D26311yescharacteristic
167C2×C4D4×D26311yescharacteristic
168C2×C4C2×C22⋊D26311yescharacteristic
169C8—22no—
170C8—10521no—
171C8—10521no—
172C22—81no—
173C22—81no—
174C22—81no—
175C22—5262no—
176C22—10521no—
177C22—10521no—
178C22#2255443811yescharacteristic
179C4—21no—
180C4—42no—
181C4—10521no—
182C4—10521no—
183C4—10521no—
184C4SD16×D26311yescharacteristic
185C4#2255449111yescharacteristic
186C4#2255449711yescharacteristic
187C4#2255449911yescharacteristic
188C2—161no—
189C2—10522no—
190C2#3068207511yescharacteristic
191C2#3068208211yescharacteristic
192C2#3068210511yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#492×C263C2
socleC22×C263#120
prime radical#30682130C2
hypercenter#492D263
hypocenterC263#1622
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #30682649C2semidirect
2. #30682135C2semidirect
4. #30681687C2semidirect
5. #30681670C2semidirect
6. #30681667C2semidirect
7. #492×C263C2semidirect
54. D1052SD16semidirect
96. C263#1622semidirect
99. #492D263semidirect

Maximal subgroups

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

subgroupindex
#306826492
#306821352
#306821302
#306816872
#306816702
#306816672
#492×C2632
#1622263