Finite Group Databasebeta

← #44399013

Subgroups — #44399013

Order 29056.

194 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 57 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#28409761C211yesmaximal, characteristic
2#28409430C211yesmaximal, characteristic
3#28409318C211yesmaximal, characteristic
4#28409242C211yesmaximal, characteristic
5#28408779C211yesmaximal, characteristic
6#28408764C211yesmaximal, characteristic
7Q8⋊C8×C227C211yesmaximal, characteristic
8C2×#16813874—21no—
9#20300288—21no—
10#20300288C2211yescharacteristic
11#20300288C2211yescharacteristic
12#20300279—22no—
13#20300279—21no—
14Q8×Dic227—21no—
15C4×Dic454—21no—
16C4×Dic454C2211yescharacteristic
17#20300220—22no—
18#20300220—21no—
19C4⋊(C227⋊C8)C2211yescharacteristic
20#20300213—21no—
21#20300211—21no—
22C4×Q8×C227C2211yescharacteristic
23C4⋊C8×C227C2211yescharacteristic
24C4×C8×C227C2211yescharacteristic
25C2×Dic454—21no—
26C2×Dic454—21no—
27C2×Dic454D411yescharacteristic
28#16813874—42no—
29C2×C227⋊C8—21no—
30C4⋊Dic227—22no—
31C4⋊Dic227—22no—
32C4⋊Dic227—21no—
33C4⋊Dic227—21no—
34C4⋊Dic227—21no—
35C4⋊Dic227D412yes—
36C4⋊Dic227D411yescharacteristic
37Dic227⋊C4—22no—
38Dic227⋊C4—21no—
39C4×Dic227—22no—
40C4×Dic227—21no—
41C2×Q8×C227D411yescharacteristic
42C2×C8×C227—21no—
43C2×C8×C227—21no—
44C4⋊C4×C227—21no—
45C4⋊C4×C227D411yescharacteristic
46C42×C227—21no—
47C42×C227C2311yescharacteristic
48Dic454—21no—
49Dic454—21no—
50Dic454—41no—
51Dic454—41no—
52Dic454—41no—
53Dic454—41no—
54C2×Dic227—21no—
55C2×Dic227—21no—
56C2×Dic227—22no—
57C2×Dic227—41no—
58C227⋊C8—41no—
59Q8×C227—21no—
60Q8×C227SD1612yes—
61C2×C4×C227—21no—
62C2×C4×C227—21no—
63C2×C4×C227C2×D411yescharacteristic
64C2×C4×C227C2×D411yescharacteristic
65C2×C4×C227C2×D411yescharacteristic
66C8×C227—22no—
67C8×C227—41no—
68C22×C227#12011yescharacteristic
69C4×C227—22no—
70C4×C227—21no—
71C4×C227—41no—
72C4×C227C2×SD1611yescharacteristic
73C4×C227#13511yescharacteristic
74C4×C227#13711yescharacteristic
75C4×C227#13711yescharacteristic
76Dic227—41no—
77Dic227—42no—
78Dic227—41no—
79Dic227—81no—
80C2×C227#44811yescharacteristic
81C2×C227#45211yescharacteristic
82C2×C227#45611yescharacteristic
83C227#165311yescharacteristic, complemented, Sylow
84#1653—2271nomaximal, Sylow
85#557—2271no—
86#498—2271no—
87#475—2271no—
88#462—2271no—
89#332—2271no—
90Q8⋊C8—2271no—
91Q8⋊C8D22711yescharacteristic
92C2×Q16—4541no—
93C4⋊Q8—4541no—
94C4⋊Q8—2271no—
95C4⋊Q8—2271no—
96#125—4542no—
97#125—4541no—
98C4×Q8—4541no—
99C4×Q8—4541no—
100C4×Q8—2271no—
101C4×Q8C2×D22711yescharacteristic
102#106—4541no—
103#106—4542no—
104C4⋊C8—2271no—
105C4⋊C8C2×D22711yescharacteristic
106#103—4541no—
107#103—4541no—
108C4×C8C2×D22711yescharacteristic
109C2×Q8—4541no—
110C2×Q8—4541no—
111C2×Q8—2271no—
112C2×Q8D90811yescharacteristic
113Q16—9082no—
114C2×C8—21no—
115C2×C8—21no—
116C2×C8—4541no—
117C4⋊C4—21no—
118C4⋊C4—4542no—
119C4⋊C4—4542no—
120C4⋊C4—4542no—
121C4⋊C4—4541no—
122C4⋊C4—4541no—
123C4⋊C4—4541no—
124C4⋊C4—4541no—
125C4⋊C4—2271no—
126C4⋊C4—2272no—
127C4⋊C4D90811yescharacteristic
128C42—21no—
129C42—4542no—
130C42—4541no—
131C42C22×D22711yescharacteristic
132Q8—21no—
133Q8—9081no—
134Q8—9081no—
135Q8—9081no—
136Q8—9081no—
137Q8—4541no—
138Q8—4541no—
139Q8#1681387312yes—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—9081no—
143C2×C4—4541no—
144C2×C4—4541no—
145C2×C4—4542no—
146C2×C4D4×D22711yescharacteristic
147C2×C4D4×D22711yescharacteristic
148C2×C4C2×D90811yescharacteristic
149C8—22no—
150C8—41no—
151C8—9081no—
152C22#2030025811yescharacteristic
153C4—22no—
154C4—21no—
155C4—41no—
156C4—18161no—
157C4—9082no—
158C4—9081no—
159C4—9081no—
160C4C2×#1681387311yescharacteristic
161C4#2030030911yescharacteristic
162C4#2030032011yescharacteristic
163C4#2030032111yescharacteristic
164C2#2840917311yescharacteristic
165C2#2840919711yescharacteristic
166C2#2840921611yescharacteristic
subgroupG/H
centerC22#20300258
commutator, cosocleC42×C227C23
FrattiniC42C22×D227
FittingQ8⋊C8×C227C2
socle, prime radicalC22×C227#120
hypercenterQ8⋊C8D227
hypocenterC227#1653
LCSG ▷ C42×C227 ▷ C22×C227 ▷ C227
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
83. C227#1653semidirect

Maximal subgroups

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

subgroupindex
#284097612
#284094302
#284093182
#284092422
#284087792
#284087642
Q8⋊C8×C2272
#1653227