Finite Group Databasebeta

← #46781850

Subgroups — #46781850

Order 33664.

250 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 65 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#30682286C211yesmaximal, characteristic, complemented
2#30682138C211yesmaximal, characteristic, complemented
3#30682133C211yesmaximal, characteristic
4#30681684C211yesmaximal, characteristic, complemented
5Q8⋊(C263⋊C8)C211yesmaximal, characteristic, complemented
6D4⋊(C263⋊C8)C211yesmaximal, characteristic, complemented
7D4×Q8×C263C211yesmaximal, characteristic, complemented
8C2×#16862363—21no—
9C2×#16862361—21no—
10#22554467C2211yescharacteristic
11C4⋊(C263⋊C8)C2211yescharacteristic
12C4⋊(C263⋊C8)C2211yescharacteristic
13#22554390—21no—
14#22554390—21no—
15#22554390—22no—
16C4×C263⋊C8C2211yescharacteristic
17C22×Q8×C263—21no—
18C4⋊Q8×C263—21no—
19C4⋊Q8×C263C2211yescharacteristic
20C22⋊Q8×C263—21no—
21C22⋊Q8×C263—22no—
22C4×Q8×C263C2211yescharacteristic
23C4×D4×C263—21no—
24C4×D4×C263C2211yescharacteristic
25C2×D1052—21no—
26C2×D1052—21no—
27C2×D1052—21no—
28#16862363—42no—
29#16862361—42no—
30C2×C263⋊C8—21no—
31C2×C263⋊C8—21no—
32C2×C263⋊C8—21no—
33C2×Q8×C263—22no—
34C2×Q8×C263—21no—
35C2×Q8×C263—42no—
36C2×Q8×C263—42no—
37C2×Q8×C263D411yescharacteristic
38C2×D4×C263D411yescharacteristic
39C22×C4×C263—22no—
40C22×C4×C263—21no—
41C4⋊C4×C263—22no—
42C4⋊C4×C263—21no—
43C4⋊C4×C263—21no—
44C4⋊C4×C263D411yescharacteristic
45C4⋊C4×C263D411yescharacteristic
46C4⋊C4×C263D412yes—
47C22⋊C4×C263—22no—
48C22⋊C4×C263—21no—
49C42×C263—21no—
50C42×C263C2311yescharacteristic
51C22×D263—41no—
52D1052—42no—
53D1052—41no—
54D1052—41no—
55D1052—41no—
56D1052—41no—
57C263⋊C8—41no—
58C263⋊C8—41no—
59C263⋊C8—41no—
60C23×C263—21no—
61Q8×C263—21no—
62Q8×C263—44no—
63Q8×C263—41no—
64Q8×C263—41no—
65Q8×C263D812yescomplemented
66D4×C263—21no—
67D4×C263SD1612yescomplemented
68C2×C4×C263—21no—
69C2×C4×C263—21no—
70C2×C4×C263—22no—
71C2×C4×C263—21no—
72C2×C4×C263—44no—
73C2×C4×C263—41no—
74C2×C4×C263—41no—
75C2×C4×C263C2×D411yescharacteristic
76C2×C4×C263C2×D411yescharacteristic
77C2×C4×C263C2×D411yescharacteristic
78C22×C263—22no—
79C22×C263—41no—
80C22×C263—41no—
81C22×C263#12011yescharacteristic
82C2×D263—81no—
83C2×D263—81no—
84C2×D263—81no—
85C4×C263—22no—
86C4×C263—21no—
87C4×C263—42no—
88C4×C263—41no—
89C4×C263—41no—
90C4×C263C2×D811yescharacteristic
91C4×C263C2×SD1611yescharacteristic
92C4×C263AGL(1,ℤ/8)11yescharacteristic
93C4×C263#13711yescharacteristic
94C2×C263—42no—
95C2×C263#44711yescharacteristic
96C2×C263#44811yescharacteristic
97C2×C263#45411yescharacteristic
98D263—161no—
99C263#162711yescharacteristic, complemented, Sylow
100#1627—2631nomaximal, Sylow
101D4×Q8D26311yescharacteristic, complemented
102#486—2631no—
103#460—2631no—
104#459—2631no—
105#332—2631no—
106Q8⋊C8—2631no—
107D4⋊C8—2631no—
108C22×Q8—21no—
109C2×SD16—5261no—
110C2×D8—5261no—
111C4⋊Q8—21no—
112C4⋊Q8C2×D26311yescharacteristic
113#127—2631no—
114C22⋊Q8—21no—
115C22⋊Q8—22no—
116C4×Q8C2×D26311yescharacteristic
117C4×D4—21no—
118C4×D4C2×D26311yescharacteristic
119C4⋊C8—2631no—
120C4⋊C8—2631no—
121#102—5261no—
122#102—5261no—
123#102—5262no—
124C4×C8—2631no—
125C2×Q8—22no—
126C2×Q8—21no—
127C2×Q8—42no—
128C2×Q8—42no—
129C2×Q8C22⋊D26311yescharacteristic
130C2×D4—5261no—
131C2×D4—5261no—
132C2×D4—5261no—
133C2×D4C22⋊D26311yescharacteristic
134C22×C4—22no—
135C22×C4—21no—
136SD16—10522no—
137D8—10522no—
138C2×C8—5261no—
139C2×C8—5261no—
140C2×C8—5261no—
141C4⋊C4—22no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4C22⋊D26311yescharacteristic
145C4⋊C4C22⋊D26311yescharacteristic
146C4⋊C4C22⋊D26312yes—
147C22⋊C4—22no—
148C22⋊C4—21no—
149C42—21no—
150C42C22×D26311yescharacteristic
151C23—21no—
152C23—10521no—
153Q8—21no—
154Q8—44no—
155Q8—41no—
156Q8—41no—
157Q8#1686236112yescomplemented
158D4—21no—
159D4—10522no—
160D4—10521no—
161D4—10521no—
162D4—10521no—
163D4—10521no—
164D4#1686236312yescomplemented
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—44no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4C2×C22⋊D26311yescharacteristic
173C2×C4C2×C22⋊D26311yescharacteristic
174C2×C4C2×C22⋊D26311yescharacteristic
175C8—10521no—
176C8—10521no—
177C8—10521no—
178C22—22no—
179C22—41no—
180C22—41no—
181C22—21041no—
182C22—21041no—
183C22—21041no—
184C22#2255443911yescharacteristic
185C4—22no—
186C4—21no—
187C4—42no—
188C4—41no—
189C4—41no—
190C4C2×#1686236111yescharacteristic
191C4C2×#1686236311yescharacteristic
192C4#2255449611yescharacteristic
193C4#2255450111yescharacteristic
194C2—42no—
195C2—42081no—
196C2#3068207211yescharacteristic
197C2#3068207711yescharacteristic
198C2#3068211111yescharacteristic
subgroupG/H
centerC22#22554439
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
FittingD4×Q8×C263C2
socleC22×C263#120
prime radical#30682133C2
hypercenterD4×Q8D263
hypocenterC263#1627
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. #30682286C2semidirect
2. #30682138C2semidirect
4. #30681684C2semidirect
5. Q8⋊(C263⋊C8)C2semidirect
6. D4⋊(C263⋊C8)C2semidirect
7. D4×Q8×C263C2semidirect
65. Q8×C263D8semidirect
67. D4×C263SD16semidirect
99. C263#1627semidirect
101. D4×Q8D263semidirect
157. Q8#16862361semidirect
164. D4#16862363semidirect

Maximal subgroups

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

subgroupindex
#306822862
#306821382
#306821332
#306816842
Q8⋊(C263⋊C8)2
D4⋊(C263⋊C8)2
D4×Q8×C2632
#1627263