Finite Group Databasebeta

← #46781974

Subgroups — #46781974

Order 33664.

212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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#30682653C211yesmaximal, characteristic
2#30682290C211yesmaximal, characteristic, complemented
3#30682140C211yesmaximal, characteristic, complemented
4#30681686C211yesmaximal, characteristic, complemented
5D4⋊(C263⋊C8)C211yesmaximal, characteristic, complemented
6#30681665C211yesmaximal, characteristic, complemented
7#474×C263C211yesmaximal, characteristic, complemented
8C2×#16862363—21no—
9#22554470C2211yescharacteristic
10#22554456—22no—
11#22554444—21no—
12#22554441—21no—
13C4×D1052C2211yescharacteristic
14#22554429—21no—
15#22554428—21no—
16C4⋊(C263⋊C8)C2211yescharacteristic
17#22554394—21no—
18#22554393—22no—
19C4×C263⋊C8C2211yescharacteristic
20C4⋊Q8×C263C2211yescharacteristic
21C4×D4×C263C2211yescharacteristic
22#107×C263—21no—
23C4⋊C8×C263C2211yescharacteristic
24#102×C263—21no—
25C2×Dic526D412yes—
26C2×D1052D411yescharacteristic
27C2×C22⋊D263—22no—
28C2×C4×D263—21no—
29#16862363—42no—
30C2×C263⋊C8—21no—
31C2×C263⋊C8—21no—
32C4⋊Dic263—21no—
33C4⋊Dic263—21no—
34C4⋊Dic263D411yescharacteristic
35C22⋊Dic263—22no—
36(C2×D263)⋊C4—22no—
37(C2×D263)⋊C4—21no—
38C4×Dic263—22no—
39C2×Q8×C263—21no—
40C2×D4×C263D411yescharacteristic
41C22×C4×C263—21no—
42C2×C8×C263—21no—
43C4⋊C4×C263—21no—
44C4⋊C4×C263—21no—
45C4⋊C4×C263D411yescharacteristic
46C22⋊C4×C263—21no—
47C42×C263C2311yescharacteristic
48C22×D263—21no—
49Dic526—42no—
50D1052—21no—
51D1052—21no—
52C22⋊D263—82no—
53C2×Dic263—21no—
54C2×Dic263—22no—
55C4×D263—41no—
56C4×D263—41no—
57C263⋊C8—41no—
58C263⋊C8—41no—
59C23×C263—21no—
60Q8×C263—41no—
61Q8×C263—41no—
62D4×C263—21no—
63D4×C263—21no—
64C2×C4×C263—21no—
65C2×C4×C263—41no—
66C2×C4×C263—41no—
67C2×C4×C263—41no—
68C2×C4×C263C2×D411yescharacteristic
69C2×C4×C263C2×D411yescharacteristic
70C2×C4×C263C2×D411yescharacteristic
71C8×C263—41no—
72C22×C263—41no—
73C22×C263—41no—
74C22×C263—41no—
75C22×C263#12011yescharacteristic
76C2×D263—41no—
77C2×D263—41no—
78C2×D263—41no—
79C4×C263—21no—
80C4×C263—41no—
81C4×C263—81no—
82C4×C263#13511yescharacteristic
83C4×C263#13511yescharacteristic
84C4×C263AGL(1,ℤ/8)11yescharacteristic
85C4×C263#13711yescharacteristic
86Dic263—41no—
87Dic263—42no—
88C2×C263—81no—
89C2×C263#44911yescharacteristic
90C2×C263#45211yescharacteristic
91C2×C263#45511yescharacteristic
92D263—81no—
93C263#164611yescharacteristic, complemented, Sylow
94#1646—2631nomaximal, Sylow
95#555—2631no—
96#487—2631no—
97#474D26311yescharacteristic, complemented
98#461—2631no—
99#333—2631no—
100D4⋊C8—2631no—
101D4⋊C8—2631no—
102C2×SD16—5261no—
103C4⋊Q8—2631no—
104C4⋊Q8C2×D26311yescharacteristic
105#124—5262no—
106#121—5261no—
107#121—5261no—
108C4×D4—2631no—
109C4×D4C2×D26311yescharacteristic
110#117—5261no—
111#117—5261no—
112#107—21no—
113C4⋊C8—2631no—
114C4⋊C8C2×D26311yescharacteristic
115#103—5262no—
116#103—5261no—
117#102—21no—
118C4×C8—2631no—
119C2×Q8—21no—
120C2×Q8—2632no—
121C2×D4—2631no—
122C2×D4—5262no—
123C2×D4C22⋊D26311yescharacteristic
124C22×C4—21no—
125C22×C4—5261no—
126SD16—10522no—
127C2×C8—21no—
128C2×C8—5261no—
129C2×C8—5261no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—2631no—
133C4⋊C4—5261no—
134C4⋊C4—5261no—
135C4⋊C4C22⋊D26311yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—5262no—
138C22⋊C4—5262no—
139C22⋊C4—5261no—
140C42—5262no—
141C42C22×D26311yescharacteristic
142C23—21no—
143C23—5261no—
144Q8—41no—
145Q8—41no—
146Q8—10522no—
147D4—21no—
148D4—21no—
149D4—5261no—
150D4—5261no—
151D4—21042no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—5261no—
157C2×C4—5262no—
158C2×C4—10521no—
159C2×C4—10521no—
160C2×C4D4×D26311yescharacteristic
161C2×C4D4×D26311yescharacteristic
162C2×C4C2×C22⋊D26311yescharacteristic
163C8—41no—
164C8—10521no—
165C8—10521no—
166C22—41no—
167C22—41no—
168C22—41no—
169C22—10521no—
170C22—10521no—
171C22—10521no—
172C22#2255443811yescharacteristic
173C4—21no—
174C4—41no—
175C4—81no—
176C4—10522no—
177C4—10521no—
178C4#2255448911yescharacteristic
179C4#2255449011yescharacteristic
180C4#2255449411yescharacteristic
181C4#2255450111yescharacteristic
182C2—81no—
183C2—21041no—
184C2#3068208011yescharacteristic
185C2#3068209811yescharacteristic
186C2#3068211411yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#474×C263C2
socleC22×C263#120
prime radical#30682653C2
hypercenter#474D263
hypocenterC263#1646
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
2. #30682290C2semidirect
3. #30682140C2semidirect
4. #30681686C2semidirect
5. D4⋊(C263⋊C8)C2semidirect
6. #30681665C2semidirect
7. #474×C263C2semidirect
93. C263#1646semidirect
97. #474D263semidirect

Maximal subgroups

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

subgroupindex
#306826532
#306822902
#306821402
#306816862
D4⋊(C263⋊C8)2
#306816652
#474×C2632
#1646263