Finite Group Databasebeta

← #44400798

Subgroups — #44400798

Order 29056.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#28409539C212yesmaximal, complemented
2#28409049C212yesmaximal, complemented
3#28408995C211yesmaximal, characteristic, complemented
4#28408789C211yesmaximal, characteristic, complemented
5#575×C227C211yesmaximal, characteristic, complemented
6C22×C4×D227C2211yescharacteristic
7C2×#16813868C2211yescharacteristic
8#20300269—22no—
9#20300264—22no—
10#20300259—22no—
11#20300256—22no—
12C4×C22⋊D227—24no—
13#20300247C2212yes—
14#20300215—24no—
15(C2×D227)⋊C8—22no—
16C2×#41×C227C2212yes—
17#137×C227—22no—
18AGL(1,ℤ/8)×C227—22no—
19#135×C227—22no—
20C2×M16×C227C2211yescharacteristic
21C23×D227D411yescharacteristic
22C2×C22⋊D227—24no—
23C22×Dic227D411yescharacteristic
24C2×C4×D227—21no—
25C2×C4×D227—22no—
26C2×C4×D227—22no—
27C2×C4×D227—21no—
28#16813868—22no—
29C2×C227⋊C8—21no—
30C4⋊Dic227—22no—
31Dic227⋊C4—24no—
32C22⋊Dic227—24no—
33C22⋊Dic227—22no—
34(C2×D227)⋊C4—24no—
35C4×Dic227D414yescomplemented
36#41×C227—22no—
37#41×C227—22no—
38#41×C227—22no—
39#41×C227—22no—
40C2×Q8×C227D412yescomplemented
41C2×D4×C227—22no—
42C2×D4×C227D412yescomplemented
43C22×C4×C227—22no—
44C22×C4×C227C2311yescharacteristic
45Q16×C227—22no—
46SD16×C227—24no—
47D8×C227—22no—
48M16×C227—22no—
49C2×C8×C227D412yescomplemented
50C22×D227—22no—
51C22×D227—21no—
52C22×D227—42no—
53C22⋊D227—48no—
54C2×Dic227—24no—
55C2×Dic227—22no—
56C2×Dic227—21no—
57C4×D227—41no—
58C4×D227—42no—
59C4×D227—41no—
60C227⋊C8—41no—
61C23×C227—22no—
62C23×C227C2×D411yescharacteristic
63Q8×C227—22no—
64Q8×C227—22no—
65D4×C227—22no—
66D4×C227—22no—
67D4×C227—42no—
68D4×C227—42no—
69C2×C4×C227—22no—
70C2×C4×C227—42no—
71C2×C4×C227—42no—
72C2×C4×C227C2×D412yes—
73C2×C4×C227C2×D411yescharacteristic
74C2×C4×C227C2×D412yes—
75C2×C4×C227#4111yescharacteristic
76C8×C227—22no—
77C22×C227—41no—
78C22×C227—44no—
79C22×C227—42no—
80C22×C227#12012yes—
81C22×C227#12111yescharacteristic
82C2×D227—24no—
83C2×D227—22no—
84C2×D227—42no—
85C2×D227—41no—
86C2×D227—41no—
87C4×C227—42no—
88C4×C227#12011yescharacteristic
89C4×C227#12112yes—
90C4×C227#12711yescharacteristic
91Dic227—44no—
92Dic227—41no—
93C2×C227—22no—
94C2×C227—21no—
95C2×C227—82no—
96C2×C227#39211yescharacteristic
97D227—42no—
98C227#201011yescharacteristic, complemented, Sylow
99#2010—2271nomaximal, Sylow
100#575D22711yescharacteristic, complemented
101#525—2272no—
102#421—2272no—
103#407—2271no—
104H(3,ℤ/4)—2271no—
105C2×#41C2×D22712yes—
106C23×C4—2271no—
107#137—22no—
108AGL(1,ℤ/8)—22no—
109#135—22no—
110C2×M16—2271no—
111C2×M16C2×D22711yescharacteristic
112#123—4542no—
113C22⋊Q8—4542no—
114#121—4542no—
115#120—4542no—
116C4×D4—4544no—
117#117—2272no—
118#104—4544no—
119C22⋊C8—4542no—
120C24—2271no—
121#41—22no—
122#41—22no—
123#41—22no—
124#41—22no—
125C2×Q8C22⋊D22712yescomplemented
126C2×D4—22no—
127C2×D4—4544no—
128C2×D4C22⋊D22712yescomplemented
129C22×C4—22no—
130C22×C4—4542no—
131C22×C4—4541no—
132C22×C4—4542no—
133C22×C4—4541no—
134C22×C4—2271no—
135C22×C4C22×D22711yescharacteristic
136Q16—22no—
137SD16—24no—
138D8—22no—
139M16—22no—
140M16—4542no—
141C2×C8—4541no—
142C2×C8C22⋊D22712yescomplemented
143C4⋊C4—4544no—
144C4⋊C4—4542no—
145C22⋊C4—4544no—
146C22⋊C4—4544no—
147C22⋊C4—4542no—
148C42—2274no—
149C23—22no—
150C23—9082no—
151C23—4542no—
152C23—4541no—
153C23D4×D22711yescharacteristic
154Q8—22no—
155Q8—22no—
156D4—22no—
157D4—22no—
158D4—42no—
159D4—42no—
160D4—9088no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—9081no—
165C2×C4—9082no—
166C2×C4—9081no—
167C2×C4—4544no—
168C2×C4—4542no—
169C2×C4—4541no—
170C2×C4D4×D22712yes—
171C2×C4C2×C22⋊D22712yes—
172C2×C4C2×C22⋊D22711yescharacteristic
173C2×C4#1681388311yescharacteristic
174C8—22no—
175C8—9081no—
176C22—41no—
177C22—44no—
178C22—42no—
179C22—9082no—
180C22—9081no—
181C22—9081no—
182C22—4544no—
183C22—4542no—
184C22#2030025612yes—
185C22#2030025911yescharacteristic
186C4—42no—
187C4—9084no—
188C4—9081no—
189C4#2030025711yescharacteristic
190C4#2030026012yes—
191C4#2030028411yescharacteristic
192C2—22no—
193C2—21no—
194C2—82no—
195C2—9082no—
196C2#2840894011yescharacteristic
subgroupG/H
centerC4#20300284
commutator, cosocleC22×C4×C227C23
FrattiniC22×C4C22×D227
Fitting#575×C227C2
socleC2×C227#392
hypercenter#575D227
hypocenterC227#2010
LCSG ▷ C22×C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #28409539C2semidirect
2. #28409049C2semidirect
3. #28408995C2semidirect
4. #28408789C2semidirect
5. #575×C227C2semidirect
35. C4×Dic227D4semidirect
40. C2×Q8×C227D4semidirect
42. C2×D4×C227D4semidirect
49. C2×C8×C227D4semidirect
98. C227#2010semidirect
100. #575D227semidirect
125. C2×Q8C22⋊D227semidirect
128. C2×D4C22⋊D227semidirect
142. C2×C8C22⋊D227semidirect

Maximal subgroups

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

subgroupindex
#284095392
#284090492
#284089952
#284087892
#575×C2272
#2010227