Finite Group Databasebeta

← #44400124

Subgroups — #44400124

Order 29056.

324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#20300286C211yesmaximal, characteristic
2#28409509C211yesmaximal, characteristic
3#28409041C211yesmaximal, characteristic
4C2×#20300206C211yesmaximal, characteristic
5#28408793C211yesmaximal, characteristic
6#28408791C211yesmaximal, characteristic
7#419×C227C211yesmaximal, characteristic
8C22×Dic454C2211yescharacteristic
9C2×#16813868C2211yescharacteristic
10#20300286—22no—
11#20300286C414yescomplemented
12C4×Dic454—22no—
13#20300253—22no—
14#20300247C2211yescharacteristic
15#20300244—22no—
16C2×Dic227⋊C4—22no—
17C2×C4×Dic227C2211yescharacteristic
18#20300212—22no—
19#20300206—22no—
20C22×Q8×C227C2211yescharacteristic
21C2×M16×C227C2211yescharacteristic
22#117×C227C2211yescharacteristic
23#103×C227—22no—
24C2×Dic454—21no—
25C2×Dic454—21no—
26C2×Dic454—21no—
27C2×Dic454—21no—
28C2×Dic454C2×C412yes—
29C2×Dic454D412yes—
30C22×Dic227—21no—
31C22×Dic227D412yes—
32#16813868—21no—
33#16813868—21no—
34C2×C227⋊C8—21no—
35C4⋊Dic227D412yes—
36Dic227⋊C4—24no—
37Dic227⋊C4—28no—
38C22⋊Dic227—21no—
39C4×Dic227—24no—
40C4×Dic227—21no—
41C4×Dic227—21no—
42C4×Dic227C2×C412yes—
43C2×Q8×C227—21no—
44C2×Q8×C227—21no—
45C2×Q8×C227—21no—
46C2×Q8×C227—21no—
47C2×Q8×C227—21no—
48C2×Q8×C227C2×C412yes—
49C22×C4×C227—21no—
50C22×C4×C227C2311yescharacteristic
51M16×C227—21no—
52M16×C227—21no—
53C2×C8×C227—21no—
54C4⋊C4×C227D412yes—
55C22⋊C4×C227—21no—
56C42×C227—21no—
57Dic454—22no—
58Dic454—22no—
59Dic454—22no—
60Dic454—22no—
61C2×Dic227—24no—
62C2×Dic227—22no—
63C2×Dic227—22no—
64C2×Dic227—22no—
65C2×Dic227—22no—
66C2×Dic227C22⋊C414yes—
67C227⋊C8—41no—
68C23×C227C2×D411yescharacteristic
69Q8×C227—22no—
70Q8×C227—22no—
71Q8×C227—41no—
72Q8×C227—41no—
73C2×C4×C227—22no—
74C2×C4×C227—22no—
75C2×C4×C227—41no—
76C2×C4×C227—41no—
77C2×C4×C227C22×C411yescharacteristic
78C2×C4×C227C2×D411yescharacteristic
79C2×C4×C227C2×D411yescharacteristic
80C2×C4×C227C2×D411yescharacteristic
81C2×C4×C227#4111yescharacteristic
82C2×C4×C227#4111yescharacteristic
83C8×C227—41no—
84C22×C227—22no—
85C22×C227C2×C22⋊C411yescharacteristic
86C22×C227#12011yescharacteristic
87C22×C227#12311yescharacteristic
88C4×C227—42no—
89C4×C227—42no—
90C4×C227C4×D411yescharacteristic
91C4×C227C4×D411yescharacteristic
92C4×C227#12111yescharacteristic
93C4×C227#12111yescharacteristic
94Dic227—24no—
95Dic227—24no—
96Dic227—42no—
97C2×C227—21no—
98C2×C227—21no—
99C2×C227#38611yescharacteristic
100C2×C227#45612yes—
101C227#188611yescharacteristic, complemented, Sylow
102#1886—2271nomaximal, Sylow
103C2×C4⋊Q8—2271no—
104#519—2271no—
105#419—2271no—
106#419D22711yescharacteristic
107C2×#101—2271no—
108#339—2271no—
109#339—2271no—
110C22×Q8—2271no—
111C22×Q8C2×D22711yescharacteristic
112C2×M16—2271no—
113C2×M16C2×D22711yescharacteristic
114C4⋊Q8—4542no—
115C4⋊Q8—2274no—
116C4×Q8—4542no—
117C4×Q8—4542no—
118#117—4542no—
119#117—2271no—
120#117C2×D22711yescharacteristic
121C2×C4⋊C4—4542no—
122C2×C42—2271no—
123#103—22no—
124#103—4542no—
125#101—4542no—
126C2×Q8—21no—
127C2×Q8—21no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—4541no—
132C2×Q8—4541no—
133C2×Q8—4541no—
134C2×Q8—4541no—
135C2×Q8—2272no—
136C2×Q8—2272no—
137C2×Q8C4×D22712yes—
138C22×C4—21no—
139C22×C4—4541no—
140C22×C4—2272no—
141C22×C4C22×D22711yescharacteristic
142M16—21no—
143M16—21no—
144M16—4541no—
145M16—4541no—
146C2×C8—21no—
147C2×C8—4541no—
148C4⋊C4—4544no—
149C4⋊C4—4548no—
150C4⋊C4—2272no—
151C4⋊C4C22⋊D22712yes—
152C22⋊C4—21no—
153C22⋊C4—4541no—
154C42—21no—
155C42—4544no—
156C42—4541no—
157C42—4541no—
158C42—2272no—
159C23D4×D22711yescharacteristic
160Q8—22no—
161Q8—22no—
162Q8—41no—
163Q8—41no—
164Q8—4542no—
165Q8—4542no—
166Q8—4542no—
167Q8—4542no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—4542no—
173C2×C4—4544no—
174C2×C4—4542no—
175C2×C4—4542no—
176C2×C4—4542no—
177C2×C4—2274no—
178C2×C4C2×C4×D22711yescharacteristic
179C2×C4D4×D22711yescharacteristic
180C2×C4D4×D22711yescharacteristic
181C2×C4C2×C22⋊D22711yescharacteristic
182C2×C4#1681388311yescharacteristic
183C2×C4#1681388411yescharacteristic
184C8—41no—
185C8—9081no—
186C22—22no—
187C22C22⋊C4×D22711yescharacteristic
188C22#2030025611yescharacteristic
189C22#2030027011yescharacteristic
190C4—42no—
191C4—42no—
192C4—9082no—
193C4—4544no—
194C4—4544no—
195C4(C22⋊D227)⋊C411yescharacteristic
196C4C4×C22⋊D22711yescharacteristic
197C4#2030025911yescharacteristic
198C4#2030026111yescharacteristic
199C2—21no—
200C2—21no—
201C2#2840890811yescharacteristic
202C2#2840921312yes—
subgroupG/H
centerC22#20300256
commutatorC2×C4×C227C22×C4
FrattiniC22×C4C22×D227
Fitting#419×C227C2
socleC22×C227#120
prime radicalC23×C227C2×D4
cosocleC22×C4×C227C23
hypercenter#419D227
hypocenterC227#1886
LCSG ▷ C2×C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
11. #20300286C4semidirect
101. C227#1886semidirect

Maximal subgroups

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

subgroupindex
C2×#203002862
#284095092
#284090412
C2×#203002062
#284087932
#284087912
#419×C2272
#1886227