Finite Group Databasebeta

← #44401697

Subgroups — #44401697

Order 29056.

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

normal subgroups only

This group has 210 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#28409845C211yesmaximal, characteristic, complemented
2#28409468C211yesmaximal, characteristic, complemented
3#28409299C211yesmaximal, characteristic, complemented
4#28408848C211yesmaximal, characteristic, complemented
5#28408840C211yesmaximal, characteristic, complemented
6#28408815C211yesmaximal, characteristic, complemented
7C2×SD32×C227C211yesmaximal, characteristic, complemented
8#20300336—21no—
9#20300320—22no—
10#20300319—21no—
11#20300314—21no—
12#20300311—21no—
13#20300310C2211yescharacteristic
14Q16×D227—21no—
15#20300294C2211yescharacteristic
16#20300232—21no—
17#20300229—21no—
18#20300228C2211yescharacteristic
19#20300224C2211yescharacteristic
20#20300205—21no—
21C2×Q16×C227C2211yescharacteristic
22C2×D8×C227C2211yescharacteristic
23SD32×C227—22no—
24C2×C16×C227C2211yescharacteristic
25#16813885—22no—
26#16813885—41no—
27#16813884—21no—
28#16813884—42no—
29#16813884D411yescharacteristic
30Q8×D227—22no—
31Q8×D227—41no—
32Dic908D411yescharacteristic
33#16813874—22no—
34#16813873—21no—
35#16813872—41no—
36#16813871—22no—
37D1816D411yescharacteristic
38#16813869—41no—
39#16813868—21no—
40#16813868D411yescharacteristic
41#16813867—21no—
42C8×D227—21no—
43C227⋊C16—21no—
44C2×Q8×C227—21no—
45C2×D4×C227—21no—
46Q16×C227—21no—
47Q16×C227D412yes—
48D8×C227—21no—
49D8×C227—21no—
50C2×C8×C227C2311yescharacteristic
51C16×C227—21no—
52Dic454—21no—
53Dic454—42no—
54Dic454D811yescharacteristic
55D908—21no—
56D908—42no—
57D908D811yescharacteristic
58C22⋊D227—21no—
59C22⋊D227—41no—
60C4×D227—21no—
61C4×D227—42no—
62C4×D227—42no—
63C4×D227—41no—
64C227⋊C8—21no—
65C227⋊C8—41no—
66C23×C227—41no—
67Q8×C227—22no—
68Q8×C227—41no—
69D4×C227—41no—
70D4×C227—41no—
71C2×C4×C227—41no—
72C2×C4×C227C2×D411yescharacteristic
73C8×C227C2×D411yescharacteristic
74C8×C227C2×D411yescharacteristic
75C22×C227—81no—
76C22×C227—161no—
77C22×C227AGL(1,ℤ/8)11yescharacteristic
78C2×D227—21no—
79C2×D227—41no—
80C4×C227—42no—
81C4×C227#12011yescharacteristic
82C4×C227C2×D811yescharacteristic
83Dic227—21no—
84Dic227—41no—
85C2×C227—21no—
86C2×C227—161no—
87C2×C227#44711yescharacteristic
88D227—41no—
89D227—81no—
90C227#219311yescharacteristic, complemented, Sylow
91#2193—2271nomaximal, Sylow
92#578—2271no—
93#509—2271no—
94C2×SD32D22711yescharacteristic, complemented
95#472—2271no—
96#362—2271no—
97#359—2271no—
98#350—2271no—
992−1+4—4541no—
100#137—4542no—
101#137—4541no—
102AGL(1,ℤ/8)—4541no—
103#135—4541no—
104#135—2271no—
105C2×Q16—4541no—
106C2×Q16C2×D22711yescharacteristic
107C2×D8C2×D22711yescharacteristic
108#131—2271no—
109SD32—22no—
110SD32—4541no—
111D16—4541no—
112M32—2271no—
113C2×C16C2×D22711yescharacteristic
114#108—2271no—
115#100—4541no—
116#41—9082no—
117#41—9081no—
118#41—4542no—
119#41—4541no—
120#41—2271no—
121C2×Q8—21no—
122C2×Q8—9081no—
123C2×Q8—4542no—
124C2×D4—21no—
125Q16—21no—
126Q16—4542no—
127Q16—2271no—
128Q16C22⋊D22712yes—
129SD16—9081no—
130SD16—4542no—
131SD16—4541no—
132D8—21no—
133D8—21no—
134D8—9081no—
135D8—2271no—
136M16—4541no—
137M16—4541no—
138M16—2271no—
139C2×C8—4541no—
140C2×C8C22×D22711yescharacteristic
141C16—21no—
142C16—4541no—
143C23—41no—
144Q8—22no—
145Q8—41no—
146Q8—9082no—
147Q8—4541no—
148Q8—2271no—
149D4—41no—
150D4—41no—
151D4—9082no—
152D4—9081no—
153D4—4541no—
154D4—4541no—
155D4—2271no—
156C2×C4—41no—
157C2×C4—9082no—
158C2×C4—9082no—
159C2×C4—9081no—
160C2×C4—4541no—
161C2×C4D4×D22711yescharacteristic
162C8—9081no—
163C8—4541no—
164C8D4×D22711yescharacteristic
165C8C2×C22⋊D22711yescharacteristic
166C22—81no—
167C22—161no—
168C22—9081no—
169C22—4541no—
170C22#2030031211yescharacteristic
171C4—42no—
172C4—9081no—
173C4—4541no—
174C4#2030025611yescharacteristic
175C4D8×D22711yescharacteristic
176C2—21no—
177C2—161no—
178C2—18161no—
179C2—9081no—
180C2#2840916411yescharacteristic
subgroupG/H
centerC2#28409164
commutator, cosocleC2×C8×C227C23
FrattiniC2×C8C22×D227
FittingC2×SD32×C227C2
socleC2×C227#447
hypercenterC2×SD32D227
hypocenterC227#2193
LCSG ▷ C2×C8×C227 ▷ C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. #28409845C2semidirect
2. #28409468C2semidirect
3. #28409299C2semidirect
4. #28408848C2semidirect
5. #28408840C2semidirect
6. #28408815C2semidirect
7. C2×SD32×C227C2semidirect
90. C227#2193semidirect
94. C2×SD32D227semidirect

Maximal subgroups

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

subgroupindex
#284098452
#284094682
#284092992
#284088482
#284088402
#284088152
C2×SD32×C2272
#2193227