Finite Group Databasebeta

← #44401690

Subgroups — #44401690

Order 29056.

220 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 47 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#28409833C211yesmaximal, characteristic, complemented
2#28409468C211yesmaximal, characteristic, complemented
3#28409299C211yesmaximal, characteristic, complemented
4#28408845C211yesmaximal, characteristic, complemented
5#28408840C211yesmaximal, characteristic, complemented
6#28408815C211yesmaximal, characteristic, complemented
7C2×D16×C227C211yesmaximal, characteristic, complemented
8#20300333—21no—
9#20300314—21no—
10#20300314—21no—
11#20300312—22no—
12#20300310C2211yescharacteristic
13#20300307—21no—
14D8×D227—21no—
15#20300294C2211yescharacteristic
16#20300232—21no—
17#20300229—21no—
18#20300228C2211yescharacteristic, complemented
19#20300224C2211yescharacteristic, complemented
20#20300205—21no—
21C2×D8×C227C2211yescharacteristic
22C2×D8×C227C2211yescharacteristic, complemented
23D16×C227—22no—
24C2×C16×C227C2211yescharacteristic, complemented
25#16813884—21no—
26#16813884D411yescharacteristic
27#16813883—22no—
28#16813883—41no—
29C2×C22⋊D227—42no—
30D4×D227—22no—
31D4×D227—41no—
32Dic908D411yescharacteristic
33#16813873—21no—
34#16813872—22no—
35#16813872—41no—
36D1816D411yescharacteristic
37#16813869—22no—
38#16813869—41no—
39#16813868—21no—
40#16813868D411yescharacteristic
41#16813867—21no—
42C8×D227—21no—
43C227⋊C16—21no—
44C2×D4×C227—21no—
45C2×D4×C227—21no—
46D8×C227—21no—
47D8×C227—21no—
48D8×C227—21no—
49D8×C227D412yes—
50C2×C8×C227C2311yescharacteristic
51C16×C227—21no—
52C22×D227—42no—
53Dic454—21no—
54Dic454D811yescharacteristic
55D908—21no—
56D908D811yescharacteristic
57C22⋊D227—21no—
58C22⋊D227—42no—
59C22⋊D227—42no—
60C22⋊D227—41no—
61C2×Dic227—42no—
62C4×D227—21no—
63C4×D227—41no—
64C227⋊C8—21no—
65C227⋊C8—41no—
66C23×C227—41no—
67C23×C227—41no—
68D4×C227—22no—
69D4×C227—41no—
70D4×C227—41no—
71D4×C227—41no—
72C2×C4×C227C2×D411yescharacteristic
73C8×C227C2×D411yescharacteristic
74C8×C227C2×D411yescharacteristic
75C22×C227—42no—
76C22×C227—81no—
77C22×C227—161no—
78C22×C227—161no—
79C22×C227AGL(1,ℤ/8)11yescharacteristic
80C2×D227—21no—
81C2×D227—41no—
82C2×D227—162no—
83C4×C227#12011yescharacteristic
84C4×C227C2×D811yescharacteristic
85Dic227—21no—
86Dic227—41no—
87C2×C227—21no—
88C2×C227—82no—
89C2×C227—161no—
90C2×C227#44711yescharacteristic
91D227—41no—
92D227—81no—
93C227#219211yescharacteristic, complemented, Sylow
94#2192—2271nomaximal, Sylow
95#576—2271no—
96#509—2271no—
97C2×D16D22711yescharacteristic, complemented
98#472—2271no—
99#361—2271no—
100#359—2271no—
101#350—2271no—
102H(5,𝔽2)—4541no—
103AGL(1,ℤ/8)—4541no—
104AGL(1,ℤ/8)—4542no—
105AGL(1,ℤ/8)—4541no—
106#135—4541no—
107#135—2271no—
108C2×D8—4541no—
109C2×D8C2×D22711yescharacteristic
110C2×D8C2×D22711yescharacteristic, complemented
111#131—2271no—
112SD32—4541no—
113D16—22no—
114D16—4541no—
115M32—2271no—
116C2×C16C2×D22711yescharacteristic, complemented
117#108—2271no—
118#100—4541no—
119#41—9081no—
120#41—4542no—
121#41—4541no—
122#41—2271no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—9081no—
126C2×D4—9082no—
127C2×D4—4542no—
128Q16—2271no—
129SD16—9081no—
130SD16—4542no—
131SD16—4541no—
132D8—21no—
133D8—21no—
134D8—21no—
135D8—9081no—
136D8—4542no—
137D8—2271no—
138D8C22⋊D22712yes—
139M16—4541no—
140M16—4541no—
141M16—2271no—
142C2×C8—4541no—
143C2×C8C22×D22711yescharacteristic
144C16—21no—
145C16—4541no—
146C23—41no—
147C23—41no—
148C23—9082no—
149Q8—4541no—
150Q8—2271no—
151D4—22no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—9082no—
156D4—9081no—
157D4—9082no—
158D4—4541no—
159D4—4541no—
160D4—2271no—
161C2×C4—9082no—
162C2×C4—9081no—
163C2×C4—4541no—
164C2×C4D4×D22711yescharacteristic
165C8—9081no—
166C8—4541no—
167C8D4×D22711yescharacteristic
168C8C2×C22⋊D22711yescharacteristic
169C22—42no—
170C22—81no—
171C22—161no—
172C22—161no—
173C22—36322no—
174C22—9081no—
175C22—4541no—
176C22#2030031211yescharacteristic
177C4—9081no—
178C4—4541no—
179C4#2030025611yescharacteristic
180C4D8×D22711yescharacteristic
181C2—21no—
182C2—82no—
183C2—161no—
184C2—18161no—
185C2—9081no—
186C2#2840916411yescharacteristic
subgroupG/H
centerC2#28409164
commutator, cosocleC2×C8×C227C23
FrattiniC2×C8C22×D227
FittingC2×D16×C227C2
socleC2×C227#447
hypercenterC2×D16D227
hypocenterC227#2192
LCSG ▷ C2×C8×C227 ▷ C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. #28409833C2semidirect
2. #28409468C2semidirect
3. #28409299C2semidirect
4. #28408845C2semidirect
5. #28408840C2semidirect
6. #28408815C2semidirect
7. C2×D16×C227C2semidirect
18. #20300228C22semidirect
19. #20300224C22semidirect
22. C2×D8×C227C22semidirect
24. C2×C16×C227C22semidirect
93. C227#2192semidirect
97. C2×D16D227semidirect
110. C2×D8C2×D227semidirect
116. C2×C16C2×D227semidirect

Maximal subgroups

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

subgroupindex
#284098332
#284094682
#284092992
#284088452
#284088402
#284088152
C2×D16×C2272
#2192227