Finite Group Databasebeta

← #44400182

Subgroups — #44400182

Order 29056.

358 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 93 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#28409543C211yesmaximal, characteristic
2C2×#20300216C212yesmaximal, complemented
3#28408996C211yesmaximal, characteristic, complemented
4#28408792C212yesmaximal, complemented
5C2×#117×C227C211yesmaximal, characteristic, complemented
6C2×#16813884C2211yescharacteristic
7C2×#16813868C2212yes—
8#20300271—21no—
9#20300267C412yescomplemented
10#20300262C412yescomplemented
11#20300257—21no—
12C4×C22⋊D227—22no—
13#20300247C2211yescharacteristic
14#20300216—24no—
15C22⋊(C227⋊C8)—22no—
16C23×C4×C227C2211yescharacteristic
17#117×C227—24no—
18C2×C4⋊C4×C227—21no—
19C2×C22⋊C4×C227—21no—
20C2×C42×C227C2212yes—
21#16813884—22no—
22#16813884—22no—
23C2×Dic454C2×C411yescharacteristic
24C2×D908C2×C411yescharacteristic
25C2×C22⋊D227—22no—
26C2×C22⋊D227—21no—
27C2×C4×D227—21no—
28#16813868—22no—
29#16813868—22no—
30C2×C227⋊C8—22no—
31C4⋊Dic227C2×C412yes—
32Dic227⋊C4—22no—
33C22⋊Dic227—22no—
34C22⋊Dic227—21no—
35(C2×D227)⋊C4—22no—
36C4×Dic227—21no—
37C24×C227D411yescharacteristic
38C22×C4×C227—22no—
39C22×C4×C227—22no—
40C22×C4×C227—22no—
41C22×C4×C227C2×C412yes—
42C22×C4×C227D411yescharacteristic
43C22×C4×C227D412yes—
44C22×C4×C227C2311yescharacteristic
45C4⋊C4×C227—24no—
46C22⋊C4×C227—24no—
47C42×C227—22no—
48C42×C227D414yescomplemented
49C22×D227—21no—
50Dic454—22no—
51D908—22no—
52C22⋊D227—44no—
53C22⋊D227—41no—
54C22⋊D227—41no—
55C2×Dic227—22no—
56C2×Dic227—21no—
57C4×D227—42no—
58C227⋊C8—42no—
59C23×C227—21no—
60C23×C227—21no—
61C23×C227—42no—
62C23×C227C22⋊C412yes—
63C23×C227C2×D411yescharacteristic
64C2×C4×C227—21no—
65C2×C4×C227—21no—
66C2×C4×C227—24no—
67C2×C4×C227—24no—
68C2×C4×C227—24no—
69C2×C4×C227—44no—
70C2×C4×C227C22⋊C412yes—
71C2×C4×C227C22×C411yescharacteristic
72C2×C4×C227C2×D412yes—
73C2×C4×C227C2×D411yescharacteristic
74C2×C4×C227#4112yes—
75C22×C227—22no—
76C22×C227—22no—
77C22×C227—22no—
78C22×C227—22no—
79C22×C227—42no—
80C22×C227—42no—
81C22×C227C2×C22⋊C411yescharacteristic
82C22×C227#12011yescharacteristic
83C22×C227#12311yescharacteristic
84C2×D227—41no—
85C2×D227—42no—
86C4×C227—22no—
87C4×C227—44no—
88C4×C227C4×D412yes—
89C4×C227#12112yes—
90Dic227—41no—
91Dic227—42no—
92C2×C227—21no—
93C2×C227—21no—
94C2×C227—42no—
95C2×C227#38611yescharacteristic
96C2×C227#42112yes—
97D227—81no—
98C227#189711yescharacteristic, complemented, Sylow
99#1897—2271nomaximal, Sylow
100#525—2271no—
101C2×#117D22711yescharacteristic, complemented
102C2×#104—2272no—
103#407—2271no—
104#339—2272no—
105C2×#41—2271no—
106C23×C4C2×D22711yescharacteristic
107C2×M16—2272no—
108#123—4541no—
109C22⋊Q8—2272no—
110#121—2272no—
111#120—4541no—
112C4×D4—4542no—
113#117—24no—
114#117—2271no—
115C2×C4⋊C4—21no—
116C2×C22⋊C4—21no—
117C2×C42C2×D22712yes—
118#104—4544no—
119C22⋊C8—4542no—
120C24C22⋊D22711yescharacteristic
121#41—4542no—
122#41—4542no—
123C2×Q8—2271no—
124C2×D4—4542no—
125C2×D4—4541no—
126C2×D4—2271no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—4541no—
131C22×C4C4×D22712yes—
132C22×C4C22⋊D22711yescharacteristic
133C22×C4D90812yes—
134C22×C4C22×D22711yescharacteristic
135M16—4542no—
136M16—4542no—
137C2×C8—4542no—
138C4⋊C4—24no—
139C4⋊C4—4542no—
140C4⋊C4—2272no—
141C22⋊C4—24no—
142C22⋊C4—4542no—
143C22⋊C4—4541no—
144C22⋊C4—4542no—
145C42—22no—
146C42—4541no—
147C42C22⋊D22714yescomplemented
148C23—21no—
149C23—21no—
150C23—42no—
151C23—4541no—
152C23(C2×D227)⋊C412yes—
153C23C2×C22⋊D22711yescharacteristic
154Q8—4542no—
155D4—9084no—
156D4—9081no—
157D4—9081no—
158D4—4542no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—24no—
164C2×C4—44no—
165C2×C4—9082no—
166C2×C4—4542no—
167C2×C4—4541no—
168C2×C4(C2×D227)⋊C412yes—
169C2×C4C2×C4×D22711yescharacteristic
170C2×C4C2×C22⋊D22712yes—
171C2×C4C2×D90811yescharacteristic
172C2×C4#1681388412yes—
173C8—9082no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—9081no—
181C22—9082no—
182C22C2×(C2×D227)⋊C411yescharacteristic
183C22#2030025711yescharacteristic
184C22#2030027111yescharacteristic
185C4—22no—
186C4—44no—
187C4—9081no—
188C4—9082no—
189C4C4×C22⋊D22712yes—
190C4#2030026212yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—18161no—
195C2#2840891111yescharacteristic
196C2#2840905012yes—
subgroupG/H
centerC2×C4C2×D908
commutatorC2×C4×C227C22×C4
FrattiniC22×C4C22×D227
FittingC2×#117×C227C2
socleC22×C227C2×C22⋊C4
prime radical#28409543C2
cosocleC22×C4×C227C23
hypercenterC2×#117D227
hypocenterC227#1897
LCSG ▷ C2×C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. C2×#20300216C2semidirect
3. #28408996C2semidirect
4. #28408792C2semidirect
5. C2×#117×C227C2semidirect
9. #20300267C4semidirect
10. #20300262C4semidirect
48. C42×C227D4semidirect
98. C227#1897semidirect
101. C2×#117D227semidirect
147. C42C22⋊D227semidirect

Maximal subgroups

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

subgroupindex
#284095432
C2×#203002162
#284089962
#284087922
C2×#117×C2272
#1897227