Finite Group Databasebeta

← #44399034

Subgroups — #44399034

Order 29056.

206 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 45 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#28409786C211yesmaximal, characteristic, complemented
2#28409421C211yesmaximal, characteristic
3#28409398C211yesmaximal, characteristic, complemented
4#28409397C211yesmaximal, characteristic, complemented
5#28408773C211yesmaximal, characteristic, complemented
6#28408771C211yesmaximal, characteristic, complemented
7#330×C227C211yesmaximal, characteristic, complemented
8C2×#16813873—21no—
9C2×D1816—21no—
10#20300287—21no—
11#20300285C2211yescharacteristic
12#20300283—21no—
13#20300283—21no—
14#20300280C2211yescharacteristic
15#20300276C2211yescharacteristic
16#20300273—21no—
17#20300268—21no—
18#20300266—21no—
19#20300210—21no—
20#20300210—21no—
21#20300208—21no—
22#20300208—21no—
23#20300199C2211yescharacteristic
24#125×C227C2211yescharacteristic
25#97×C227C2211yescharacteristic
26#97×C227C2211yescharacteristic
27C2×Dic454—21no—
28C2×Dic454D411yescharacteristic
29C2×D908—21no—
30C2×D908—21no—
31C2×D908—21no—
32C2×D908D411yescharacteristic
33C2×C4×D227—21no—
34#16813873—42no—
35D1816—42no—
36C2×C227⋊C8—21no—
37C4⋊Dic227—21no—
38C4⋊Dic227D411yescharacteristic
39C4⋊Dic227D411yescharacteristic
40Dic227⋊C4—21no—
41Dic227⋊C4—21no—
42Dic227⋊C4—21no—
43(C2×D227)⋊C4—21no—
44(C2×D227)⋊C4—21no—
45(C2×D227)⋊C4—21no—
46(C2×D227)⋊C4—21no—
47(C2×D227)⋊C4—21no—
48C4×Dic227—21no—
49C2×C8×C227—21no—
50C2×C8×C227—21no—
51C4⋊C4×C227—21no—
52C4⋊C4×C227—21no—
53C4⋊C4×C227D411yescharacteristic
54C4⋊C4×C227D411yescharacteristic
55C42×C227C2311yescharacteristic
56C22×D227—21no—
57C22×D227—41no—
58Dic454—41no—
59Dic454—81no—
60D908—41no—
61D908—41no—
62D908—41no—
63D908—42no—
64D908—42no—
65C2×Dic227—21no—
66C2×Dic227—21no—
67C2×Dic227—21no—
68C4×D227—81no—
69C227⋊C8—41no—
70C2×C4×C227—21no—
71C2×C4×C227—21no—
72C2×C4×C227C2×D411yescharacteristic
73C2×C4×C227C2×D411yescharacteristic
74C2×C4×C227C2×D411yescharacteristic
75C8×C227—22no—
76C8×C227—41no—
77C22×C227#12011yescharacteristic
78C2×D227—41no—
79C2×D227—41no—
80C2×D227—41no—
81C2×D227—81no—
82C2×D227—81no—
83C2×D227—81no—
84C4×C227—21no—
85C4×C227—21no—
86C4×C227—21no—
87C4×C227—41no—
88C4×C227—41no—
89Dic227—41no—
90Dic227—41no—
91Dic227—41no—
92C2×C227#45311yescharacteristic
93C2×C227#45411yescharacteristic
94C2×C227#45411yescharacteristic
95D227—81no—
96D227—161no—
97C227#165711yescharacteristic, complemented, Sylow
98#1657—2271nomaximal, Sylow
99#563—2271no—
100#496—2271no—
101#490—2271no—
102#490—2271no—
103#330—2271no—
104#330D22711yescharacteristic, complemented
105#329—2271no—
106C2×SD16—4541no—
107C2×D8—4541no—
108C4⋊Q8—4541no—
109#127—2271no—
110#126—4541no—
111#126—4541no—
112#125—2271no—
113#125C2×D22711yescharacteristic
114#124—2271no—
115#123—4541no—
116C22⋊Q8—4541no—
117C22⋊Q8—4541no—
118#102—4541no—
119#102—4541no—
120#102—4541no—
121#102—4541no—
122#97—2271no—
123#97C2×D22711yescharacteristic
124#97C2×D22711yescharacteristic
125C2×Q8—4541no—
126C2×Q8—2271no—
127C2×D4—4541no—
128C2×D4—4541no—
129C2×D4—4541no—
130C2×D4—2271no—
131C22×C4—4541no—
132SD16—9082no—
133D8—9082no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—4541no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—4541no—
140C4⋊C4—4541no—
141C4⋊C4—4541no—
142C4⋊C4—4541no—
143C4⋊C4—2271no—
144C4⋊C4—2271no—
145C4⋊C4D90811yescharacteristic
146C4⋊C4D90811yescharacteristic
147C22⋊C4—4541no—
148C22⋊C4—4541no—
149C22⋊C4—4541no—
150C22⋊C4—4541no—
151C22⋊C4—4541no—
152C42—4541no—
153C42C22×D22711yescharacteristic
154C23—9081no—
155C23—4541no—
156Q8—18161no—
157Q8—9081no—
158D4—9081no—
159D4—9081no—
160D4—9082no—
161D4—9082no—
162D4—9081no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—18161no—
166C2×C4—4541no—
167C2×C4—4541no—
168C2×C4—4541no—
169C2×C4D4×D22711yescharacteristic
170C2×C4D4×D22711yescharacteristic
171C2×C4C2×D90811yescharacteristic
172C8—22no—
173C8—41no—
174C8—9081no—
175C22—18161no—
176C22—18161no—
177C22—18161no—
178C22—9081no—
179C22—9081no—
180C22—9081no—
181C22#2030025811yescharacteristic
182C4—21no—
183C4—21no—
184C4—21no—
185C4—41no—
186C4—41no—
187C4—9081no—
188C4—9081no—
189C4—9081no—
190C2—18161no—
191C2—36321no—
192C2#2840920111yescharacteristic
193C2#2840920611yescharacteristic
194C2#2840920711yescharacteristic
subgroupG/H
centerC22#20300258
commutator, cosocleC42×C227C23
FrattiniC42C22×D227
Fitting#330×C227C2
socleC22×C227#120
prime radical#28409421C2
hypercenter#330D227
hypocenterC227#1657
LCSG ▷ C42×C227 ▷ C22×C227 ▷ C227
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
1. #28409786C2semidirect
3. #28409398C2semidirect
4. #28409397C2semidirect
5. #28408773C2semidirect
6. #28408771C2semidirect
7. #330×C227C2semidirect
97. C227#1657semidirect
104. #330D227semidirect

Maximal subgroups

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

subgroupindex
#284097862
#284094212
#284093982
#284093972
#284087732
#284087712
#330×C2272
#1657227