Finite Group Databasebeta

← #46781994

Subgroups — #46781994

Order 33664.

234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 59 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
1Q8×D1052C211yesmaximal, characteristic
2#30682341C211yesmaximal, characteristic, complemented
3#30682215C211yesmaximal, characteristic
4#30681685C211yesmaximal, characteristic, complemented
5Q8⋊(C263⋊C8)C211yesmaximal, characteristic, complemented
6#30681665C211yesmaximal, characteristic
7#462×C263C211yesmaximal, characteristic, complemented
8C2×Q8×D263—21no—
9#22554470—21no—
10#22554470C2211yescharacteristic
11#22554450—22no—
12#22554450—21no—
13C4×D1052—21no—
14C4×D1052C2211yescharacteristic
15#22554403—21no—
16#22554403—22no—
17C4⋊(C263⋊C8)C2211yescharacteristic
18#22554390—21no—
19C4×C263⋊C8C2211yescharacteristic
20C2×Q16×C263—21no—
21C4⋊Q8×C263C2211yescharacteristic
22C4×Q8×C263C2211yescharacteristic
23C4⋊C8×C263C2211yescharacteristic
24#103×C263—21no—
25C2×Dic526—22no—
26C2×Dic526—21no—
27Q8×D263—42no—
28Q8×D263—42no—
29C2×D1052D411yescharacteristic
30C2×C4×D263—22no—
31C2×C4×D263—21no—
32C2×C263⋊C8—21no—
33C2×C263⋊C8—21no—
34C4⋊Dic263—22no—
35C4⋊Dic263—21no—
36C4⋊Dic263D411yescharacteristic
37C4⋊Dic263D412yes—
38(C2×D263)⋊C4—22no—
39(C2×D263)⋊C4—21no—
40C2×Q8×C263—21no—
41C2×Q8×C263D411yescharacteristic
42Q16×C263—42no—
43C2×C8×C263—21no—
44C4⋊C4×C263—21no—
45C4⋊C4×C263—21no—
46C4⋊C4×C263—21no—
47C4⋊C4×C263D411yescharacteristic
48C42×C263—21no—
49C42×C263C2311yescharacteristic
50C22×D263—21no—
51Dic526—44no—
52Dic526—41no—
53Dic526—41no—
54D1052—21no—
55D1052Q1612yescomplemented
56C2×Dic263—22no—
57C2×Dic263—21no—
58C4×D263—44no—
59C4×D263—41no—
60C4×D263—41no—
61C263⋊C8—22no—
62C263⋊C8—41no—
63Q8×C263—21no—
64Q8×C263—41no—
65Q8×C263—41no—
66Q8×C263D812yes—
67C2×C4×C263—21no—
68C2×C4×C263—21no—
69C2×C4×C263—41no—
70C2×C4×C263C2×D411yescharacteristic
71C2×C4×C263C2×D411yescharacteristic
72C2×C4×C263C2×D411yescharacteristic
73C8×C263—41no—
74C22×C263#12011yescharacteristic
75C2×D263—22no—
76C2×D263—41no—
77C2×D263—41no—
78C4×C263—22no—
79C4×C263—21no—
80C4×C263—41no—
81C4×C263—81no—
82C4×C263C2×D811yescharacteristic
83C4×C263C2×Q1611yescharacteristic
84C4×C263AGL(1,ℤ/8)11yescharacteristic
85C4×C263#13711yescharacteristic
86Dic263—42no—
87Dic263—41no—
88C2×C263#44711yescharacteristic
89C2×C263#45111yescharacteristic
90C2×C263#45611yescharacteristic
91D263—42no—
92C263#164911yescharacteristic, complemented, Sylow
93#1649—2631nomaximal, Sylow
94D4×Q8—2631no—
95#500—2631no—
96#474—2631no—
97#462D26311yescharacteristic, complemented
98#332—2631no—
99Q8⋊C8—2631no—
100D4⋊C8—2631no—
101C22×Q8—5261no—
102C2×Q16—21no—
103C4⋊Q8—2631no—
104C4⋊Q8—5261no—
105C4⋊Q8C2×D26311yescharacteristic
106C22⋊Q8—5262no—
107C22⋊Q8—5261no—
108C4×Q8C2×D26311yescharacteristic
109C4×D4—2631no—
110C4×D4—5261no—
111#107—5261no—
112#107—5262no—
113C4⋊C8—2631no—
114C4⋊C8C2×D26311yescharacteristic
115#103—21no—
116#102—5261no—
117C4×C8—2631no—
118C2×Q8—21no—
119C2×Q8—5262no—
120C2×Q8—5261no—
121C2×Q8—10522no—
122C2×Q8—10522no—
123C2×Q8C22⋊D26311yescharacteristic
124C2×D4—2631no—
125C22×C4—5262no—
126C22×C4—5261no—
127Q16—42no—
128C2×C8—21no—
129C2×C8—5261no—
130C2×C8—5261no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—2631no—
135C4⋊C4—2632no—
136C4⋊C4—5262no—
137C4⋊C4—5261no—
138C4⋊C4C22⋊D26311yescharacteristic
139C22⋊C4—5262no—
140C22⋊C4—5261no—
141C42—21no—
142C42C22×D26311yescharacteristic
143C23—5261no—
144Q8—21no—
145Q8—41no—
146Q8—41no—
147Q8—10524no—
148Q8—10521no—
149Q8—10521no—
150Q8#1686236112yes—
151D4—2632no—
152D4—5261no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—5262no—
157C2×C4—5261no—
158C2×C4—10524no—
159C2×C4—10521no—
160C2×C4—10521no—
161C2×C4D4×D26311yescharacteristic
162C2×C4D4×D26311yescharacteristic
163C2×C4C2×C22⋊D26311yescharacteristic
164C8—41no—
165C8—5262no—
166C8—10521no—
167C22—5262no—
168C22—10521no—
169C22—10521no—
170C22#2255443811yescharacteristic
171C4—21no—
172C4—22no—
173C4—41no—
174C4—81no—
175C4—10522no—
176C4—10521no—
177C4C2×#1686236111yescharacteristic
178C4Q16×D26311yescharacteristic
179C4#2255449511yescharacteristic
180C4#2255450211yescharacteristic
181C2—10522no—
182C2#3068207111yescharacteristic
183C2#3068209211yescharacteristic
184C2#3068211911yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#462×C263C2
socleC22×C263#120
prime radicalC2×D1052D4
hypercenter#462D263
hypocenterC263#1649
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
2. #30682341C2semidirect
4. #30681685C2semidirect
5. Q8⋊(C263⋊C8)C2semidirect
7. #462×C263C2semidirect
55. D1052Q16semidirect
92. C263#1649semidirect
97. #462D263semidirect

Maximal subgroups

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

subgroupindex
Q8×D10522
#306823412
#306822152
#306816852
Q8⋊(C263⋊C8)2
#306816652
#462×C2632
#1649263