Finite Group Databasebeta

← #44401424

Subgroups — #44401424

Order 29056.

262 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 55 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#28409600C211yesmaximal, characteristic
2#28409015C212yesmaximal, complemented
3#28408829C211yesmaximal, characteristic, complemented
4#28408828C212yesmaximal, complemented
5#355×C227C211yesmaximal, characteristic, complemented
6C2×#16813885C2211yescharacteristic
7C2×D4×D227C411yescharacteristic
8M16×D227—22no—
9#20300285C411yescharacteristic
10#20300284C411yescharacteristic
11#20300277C2211yescharacteristic
12#20300261—22no—
13#20300258—22no—
14#20300245C411yescharacteristic
15#20300207C2212yescomplemented
16#20300204—22no—
17#124×C227C2211yescharacteristic
18#101×C227C2212yescomplemented
19C23×D227—21no—
20#16813885—42no—
21C2×D908—22no—
22C2×D908C2×C411yescharacteristic
23C2×D908C2×C411yescharacteristic
24C2×D908D412yes—
25C2×C22⋊D227—22no—
26C2×C22⋊D227—21no—
27D4×D227—42no—
28C2×C4×D227C2×C411yescharacteristic
29C2×C4×D227D412yes—
30#16813868—22no—
31#16813867—42no—
32C8×D227—42no—
33Dic227⋊C4—21no—
34(C2×D227)⋊C4—21no—
35(C2×D227)⋊C4—22no—
36C4×Dic227C2×C411yescharacteristic
37C2×Q8×C227C2311yescharacteristic
38C2×D4×C227C2×C411yescharacteristic
39M16×C227—22no—
40C22⋊C4×C227—22no—
41C42×C227C2×C411yescharacteristic
42C22×D227—21no—
43C22×D227—42no—
44C22×D227—82no—
45C22×D227C22⋊C411yescharacteristic
46C22×D227C22⋊C412yes—
47D908—41no—
48D908—42no—
49D908—41no—
50D908—82no—
51C22⋊D227—42no—
52C22⋊D227—82no—
53C2×Dic227—21no—
54C2×Dic227C22⋊C411yescharacteristic
55C4×D227—22no—
56C4×D227—22no—
57C4×D227—22no—
58C227⋊C8—42no—
59C23×C227—21no—
60Q8×C227—41no—
61D4×C227—41no—
62C2×C4×C227—21no—
63C2×C4×C227C22×C411yescharacteristic
64C2×C4×C227C2×D412yes—
65C8×C227—42no—
66C22×C227—42no—
67C22×C227—41no—
68C22×C227C2×C22⋊C411yescharacteristic
69C2×D227—21no—
70C2×D227—22no—
71C2×D227—42no—
72C2×D227—41no—
73C2×D227—42no—
74C2×D227—41no—
75C2×D227—84no—
76C4×C227—22no—
77C4×C227—21no—
78C4×C227—41no—
79Dic227—41no—
80Dic227#9912yes—
81C2×C227—21no—
82C2×C227—81no—
83C2×C227C2×#9911yescharacteristic
84D227—42no—
85D227—41no—
86D227—81no—
87C227#213411yescharacteristic, complemented, Sylow
88#2134—2271nomaximal, Sylow
89#535—2271no—
90#413—2272no—
91#355—2271no—
92#355—2272no—
93#355D22711yescharacteristic, complemented
94C2×#41—2271no—
95C22×D4—2271no—
96C2×M16—4542no—
97#127—2271no—
98#127—2271no—
99#124—2271no—
100#124C2×D22711yescharacteristic
101#121—4542no—
102#120—4542no—
103#117—2271no—
104#101—2272no—
105#101C2×D22712yescomplemented
106#100—4542no—
107C24—4541no—
108#41—9082no—
109C2×Q8C22×D22711yescharacteristic
110C2×D4—9082no—
111C2×D4—4542no—
112C2×D4—4542no—
113C2×D4—4541no—
114C2×D4—2271no—
115C2×D4—2271no—
116C2×D4—2272no—
117C2×D4C4×D22711yescharacteristic
118C22×C4—2271no—
119C22×C4—2272no—
120M16—22no—
121M16—9082no—
122M16—4542no—
123C2×C8—9082no—
124C4⋊C4—4541no—
125C22⋊C4—22no—
126C22⋊C4—4541no—
127C22⋊C4—4542no—
128C42—2271no—
129C42C4×D22711yescharacteristic
130C23—21no—
131C23—18162no—
132C23—9082no—
133C23—4541no—
134C23—2271no—
135C23—2272no—
136Q8—41no—
137D4—41no—
138D4—18162no—
139D4—18162no—
140D4—9081no—
141D4—9082no—
142D4—9081no—
143D4—9082no—
144C2×C4—21no—
145C2×C4—4542no—
146C2×C4—4542no—
147C2×C4—4542no—
148C2×C4—4541no—
149C2×C4—2271no—
150C2×C4C2×C4×D22711yescharacteristic
151C2×C4D4×D22712yes—
152C8—42no—
153C8—9082no—
154C22—42no—
155C22—41no—
156C22—18164no—
157C22—9082no—
158C22—9082no—
159C22—9081no—
160C22—9081no—
161C22—4541no—
162C22—4542no—
163C22C22⋊C4×D22711yescharacteristic
164C4—22no—
165C4—21no—
166C4—41no—
167C4—9081no—
168C4—2272no—
169C2—21no—
170C2—81no—
171C2—18161no—
172C2—9081no—
173C2—9082no—
174C2#99×D22711yescharacteristic
subgroupG/H
centerC2#99×D227
commutatorC2×C4×C227C22×C4
FrattiniC2×Q8C22×D227
Fitting#355×C227C2
socleC2×C227C2×#99
prime radical#28409600C2
cosocleC2×Q8×C227C23
hypercenter#355D227
hypocenterC227#2134
LCSG ▷ C2×C4×C227 ▷ C22×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #28409015C2semidirect
3. #28408829C2semidirect
4. #28408828C2semidirect
5. #355×C227C2semidirect
15. #20300207C22semidirect
18. #101×C227C22semidirect
87. C227#2134semidirect
93. #355D227semidirect
105. #101C2×D227semidirect

Maximal subgroups

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

subgroupindex
#284096002
#284090152
#284088292
#284088282
#355×C2272
#2134227