Finite Group Databasebeta

← #46781978

Subgroups — #46781978

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#30682289C211yesmaximal, characteristic, complemented
3#30682218C211yesmaximal, characteristic, complemented
4#30682144C211yesmaximal, characteristic, complemented
5#30681686C211yesmaximal, characteristic, complemented
6#30681667C211yesmaximal, characteristic, complemented
7D4⋊C8×C263C211yesmaximal, characteristic, complemented
8C2×#16862365—21no—
9#22554470C2211yescharacteristic
10#22554470C2211yescharacteristic
11#22554456—22no—
12#22554444—21no—
13#22554441—21no—
14C4×D1052C2211yescharacteristic
15#22554429—21no—
16#22554428—21no—
17#22554403—21no—
18C4⋊(C263⋊C8)C2211yescharacteristic
19#22554395—22no—
20#22554395—21no—
21#22554391—21no—
22C4×D4×C263C2211yescharacteristic
23C4⋊C8×C263C2211yescharacteristic
24C4×C8×C263C2211yescharacteristic
25C2×Dic526—21no—
26C2×Dic526D412yes—
27C2×D1052D411yescharacteristic
28C2×C22⋊D263—22no—
29C2×C4×D263—21no—
30#16862365—42no—
31C2×C263⋊C8—21no—
32C4⋊Dic263—21no—
33C4⋊Dic263—21no—
34C4⋊Dic263—21no—
35C4⋊Dic263—21no—
36C4⋊Dic263D411yescharacteristic
37C22⋊Dic263—22no—
38(C2×D263)⋊C4—22no—
39(C2×D263)⋊C4—21no—
40C4×Dic263—22no—
41C2×D4×C263D411yescharacteristic
42C22×C4×C263—21no—
43C2×C8×C263—21no—
44C2×C8×C263—21no—
45C4⋊C4×C263D411yescharacteristic
46C22⋊C4×C263—21no—
47C42×C263C2311yescharacteristic
48C22×D263—21no—
49Dic526—42no—
50Dic526—41no—
51Dic526—41no—
52D1052—21no—
53D1052—21no—
54C22⋊D263—82no—
55C2×Dic263—21no—
56C2×Dic263—22no—
57C2×Dic263—41no—
58C4×D263—41no—
59C4×D263—41no—
60C263⋊C8—41no—
61C23×C263—21no—
62D4×C263—21no—
63D4×C263—21no—
64C2×C4×C263—21no—
65C2×C4×C263—41no—
66C2×C4×C263—41no—
67C2×C4×C263C2×D411yescharacteristic
68C2×C4×C263C2×D411yescharacteristic
69C2×C4×C263C2×D411yescharacteristic
70C8×C263—41no—
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#13511yescharacteristic
82C4×C263#13511yescharacteristic
83C4×C263AGL(1,ℤ/8)11yescharacteristic
84C4×C263#13711yescharacteristic
85Dic263—41no—
86Dic263—42no—
87Dic263—81no—
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#474—2631no—
98#461—2631no—
99#333—2631no—
100D4⋊C8—2631no—
101D4⋊C8D26311yescharacteristic, complemented
102C2×SD16—5261no—
103C4⋊Q8—2631no—
104C4⋊Q8—2631no—
105#124—5262no—
106#121—5261no—
107#121—5261no—
108C4×D4—2631no—
109C4×D4C2×D26311yescharacteristic
110#117—5261no—
111#117—5261no—
112#107—5261no—
113C4⋊C8—2631no—
114C4⋊C8C2×D26311yescharacteristic
115#103—5261no—
116#103—5262no—
117#102—5261no—
118C4×C8C2×D26311yescharacteristic
119C2×Q8—2632no—
120C2×Q8—5261no—
121C2×D4—2631no—
122C2×D4—5262no—
123C2×D4D105211yescharacteristic
124C22×C4—21no—
125C22×C4—5261no—
126SD16—10522no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—5261no—
130C4⋊C4—2631no—
131C4⋊C4—5261no—
132C4⋊C4—5261no—
133C4⋊C4—5261no—
134C4⋊C4—5261no—
135C4⋊C4D105211yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—5262no—
138C22⋊C4—5262no—
139C22⋊C4—5261no—
140C42—5262no—
141C42C22×D26311yescharacteristic
142C23—21no—
143C23—5261no—
144Q8—10522no—
145Q8—10521no—
146Q8—10521no—
147D4—21no—
148D4—21no—
149D4—5261no—
150D4—5261no—
151D4—21042no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—5261no—
156C2×C4—5262no—
157C2×C4—10521no—
158C2×C4—10521no—
159C2×C4—10521no—
160C2×C4D4×D26311yescharacteristic
161C2×C4D4×D26311yescharacteristic
162C2×C4C2×D105211yescharacteristic
163C8—41no—
164C8—41no—
165C8—10521no—
166C22—41no—
167C22—41no—
168C22—41no—
169C22—10521no—
170C22—10521no—
171C22—10521no—
172C22#2255444011yescharacteristic
173C4—21no—
174C4—41no—
175C4—10522no—
176C4—10521no—
177C4—21041no—
178C4#2255449111yescharacteristic
179C4#2255449211yescharacteristic
180C4#2255449411yescharacteristic
181C4#2255450311yescharacteristic
182C2—81no—
183C2—21041no—
184C2#3068208411yescharacteristic
185C2#3068210211yescharacteristic
186C2#3068211711yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
FittingD4⋊C8×C263C2
socleC22×C263#120
prime radical#30682653C2
hypercenterD4⋊C8D263
hypocenterC263#1646
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #30682289C2semidirect
3. #30682218C2semidirect
4. #30682144C2semidirect
5. #30681686C2semidirect
6. #30681667C2semidirect
7. D4⋊C8×C263C2semidirect
93. C263#1646semidirect
101. D4⋊C8D263semidirect

Maximal subgroups

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

subgroupindex
#306826532
#306822892
#306822182
#306821442
#306816862
#306816672
D4⋊C8×C2632
#1646263