Finite Group Databasebeta

← #44399031

Subgroups — #44399031

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#28409419C211yesmaximal, characteristic
3#28409396C211yesmaximal, characteristic, complemented
4#28408774C211yesmaximal, characteristic, complemented
5#28408773C211yesmaximal, characteristic, complemented
6#28408771C211yesmaximal, characteristic, complemented
7#490×C227C211yesmaximal, characteristic, complemented
8C2×#16813872—21no—
9C2×#16813869—21no—
10#20300287—21no—
11#20300283—21no—
12#20300283—21no—
13#20300280C2211yescharacteristic
14#20300276C2211yescharacteristic
15#20300273—21no—
16#20300268—21no—
17#20300266—21no—
18#20300209—21no—
19#20300209—21no—
20#20300199C2211yescharacteristic
21#20300199C2211yescharacteristic
22#127×C227C2211yescharacteristic
23#125×C227C2211yescharacteristic
24#102×C227—21no—
25#102×C227—21no—
26#97×C227C2211yescharacteristic
27C2×Dic454—21no—
28C2×Dic454D411yescharacteristic
29C2×D908D411yescharacteristic
30C2×C4×D227—21no—
31#16813872—42no—
32#16813869—42no—
33C2×C227⋊C8—21no—
34C2×C227⋊C8—21no—
35C4⋊Dic227—21no—
36C4⋊Dic227D411yescharacteristic
37C4⋊Dic227D411yescharacteristic
38Dic227⋊C4—21no—
39Dic227⋊C4—21no—
40Dic227⋊C4—21no—
41(C2×D227)⋊C4—21no—
42(C2×D227)⋊C4—21no—
43(C2×D227)⋊C4—21no—
44(C2×D227)⋊C4—21no—
45(C2×D227)⋊C4—21no—
46C4×Dic227—21no—
47C2×D4×C227—21no—
48C2×D4×C227—21no—
49C2×D4×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—
57Dic454—41no—
58Dic454—81no—
59D908—41no—
60C2×Dic227—21no—
61C2×Dic227—21no—
62C2×Dic227—21no—
63C4×D227—81no—
64C227⋊C8—22no—
65C227⋊C8—41no—
66C23×C227—41no—
67D4×C227—42no—
68D4×C227—42no—
69D4×C227—41no—
70D4×C227—41no—
71C2×C4×C227—21no—
72C2×C4×C227—21no—
73C2×C4×C227C2×D411yescharacteristic
74C2×C4×C227C2×D411yescharacteristic
75C2×C4×C227C2×D411yescharacteristic
76C8×C227—41no—
77C22×C227—81no—
78C22×C227—81no—
79C22×C227—81no—
80C22×C227#12011yescharacteristic
81C2×D227—41no—
82C2×D227—41no—
83C2×D227—41no—
84C4×C227—21no—
85C4×C227—21no—
86C4×C227—21no—
87C4×C227—41no—
88C4×C227—41no—
89Dic227—41no—
90Dic227—41no—
91Dic227—41no—
92C2×C227—161no—
93C2×C227#45311yescharacteristic
94C2×C227#45411yescharacteristic
95C2×C227#45411yescharacteristic
96D227—81no—
97C227#165711yescharacteristic, complemented, Sylow
98#1657—2271nomaximal, Sylow
99#563—2271no—
100#496—2271no—
101#490—2271no—
102#490D22711yescharacteristic, complemented
103#330—2271no—
104#330—2271no—
105#329—2271no—
106C2×SD16—4541no—
107C2×D8—4541no—
108C4⋊Q8—4541no—
109#127C2×D22711yescharacteristic
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—21no—
119#102—21no—
120#102—4541no—
121#102—4541no—
122#97—2271no—
123#97—2271no—
124#97C2×D22711yescharacteristic
125C2×Q8—4541no—
126C2×Q8—2271no—
127C2×D4—21no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—2271no—
131C22×C4—4541no—
132SD16—9082no—
133D8—9082no—
134C2×C8—21no—
135C2×C8—4541no—
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⋊C4C22⋊D22711yescharacteristic
146C4⋊C4C22⋊D22711yescharacteristic
147C22⋊C4—4541no—
148C22⋊C4—4541no—
149C22⋊C4—4541no—
150C22⋊C4—4541no—
151C22⋊C4—4541no—
152C42—4541no—
153C42C22×D22711yescharacteristic
154C23—41no—
155C23—4541no—
156Q8—18161no—
157Q8—9081no—
158D4—41no—
159D4—41no—
160D4—42no—
161D4—42no—
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×C22⋊D22711yescharacteristic
172C8—41no—
173C8—9081no—
174C8—4542no—
175C22—81no—
176C22—81no—
177C22—81no—
178C22—9081no—
179C22—9081no—
180C22—9081no—
181C22#2030025611yescharacteristic
182C4—21no—
183C4—21no—
184C4—21no—
185C4—41no—
186C4—41no—
187C4—9081no—
188C4—9081no—
189C4—9081no—
190C2—161no—
191C2—18161no—
192C2#2840919811yescharacteristic
193C2#2840920311yescharacteristic
194C2#2840920411yescharacteristic
subgroupG/H
centerC22#20300256
commutator, cosocleC42×C227C23
FrattiniC42C22×D227
Fitting#490×C227C2
socleC22×C227#120
prime radical#28409419C2
hypercenter#490D227
hypocenterC227#1657
LCSG ▷ C42×C227 ▷ C22×C227 ▷ C227
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #28409786C2semidirect
3. #28409396C2semidirect
4. #28408774C2semidirect
5. #28408773C2semidirect
6. #28408771C2semidirect
7. #490×C227C2semidirect
97. C227#1657semidirect
102. #490D227semidirect

Maximal subgroups

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

subgroupindex
#284097862
#284094192
#284093962
#284087742
#284087732
#284087712
#490×C2272
#1657227