Finite Group Databasebeta

← #44398366

Subgroups — #44398366

Order 29056.

200 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 65 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#28409566C211yesmaximal, characteristic
2#28409089C211yesmaximal, characteristic, complemented
3#28408773C212yesmaximal, complemented
4#28408771C212yesmaximal, complemented
5#432×C227C211yesmaximal, characteristic, complemented
6#20300282—21no—
7#20300280C2211yescharacteristic
8#20300276C2211yescharacteristic
9#20300271—21no—
10#20300267C411yescharacteristic
11#20300262C411yescharacteristic
12C4×Dic454C411yescharacteristic
13C4×D908C411yescharacteristic
14C4×C22⋊D227—21no—
15#20300245—21no—
16C4⋊(C227⋊C8)—21no—
17C22⋊(C227⋊C8)—21no—
18#20300199C2212yes—
19C2×C42×C227C2211yescharacteristic
20C4⋊C8×C227—21no—
21C22⋊C8×C227—21no—
22#97×C227C2212yes—
23C2×Dic454C2×C411yescharacteristic
24C2×D908C2×C411yescharacteristic
25C2×C22⋊D227—21no—
26C2×C4×D227—21no—
27C2×C227⋊C8—22no—
28C4⋊Dic227C2×C411yescharacteristic
29C4⋊Dic227C2×C411yescharacteristic
30Dic227⋊C4—21no—
31Dic227⋊C4—21no—
32Dic227⋊C4—21no—
33Dic227⋊C4—21no—
34C22⋊Dic227—21no—
35(C2×D227)⋊C4—21no—
36(C2×D227)⋊C4—21no—
37(C2×D227)⋊C4—21no—
38(C2×D227)⋊C4—21no—
39C4×Dic227—21no—
40C22×C4×C227C2×C411yescharacteristic
41C22×C4×C227D411yescharacteristic
42C22×C4×C227D411yescharacteristic
43C2×C8×C227—22no—
44C42×C227C2×C411yescharacteristic
45C42×C227D411yescharacteristic
46C42×C227D411yescharacteristic
47C42×C227C2311yescharacteristic
48C22×D227—21no—
49Dic454—41no—
50D908—41no—
51C22⋊D227—42no—
52C2×Dic227—21no—
53C2×Dic227—21no—
54C2×Dic227—21no—
55C4×D227—42no—
56C227⋊C8—42no—
57C23×C227C22⋊C411yescharacteristic
58C2×C4×C227—41no—
59C2×C4×C227—41no—
60C2×C4×C227—41no—
61C2×C4×C227C22⋊C411yescharacteristic
62C2×C4×C227C22⋊C411yescharacteristic
63C2×C4×C227C22⋊C411yescharacteristic
64C2×C4×C227C22×C411yescharacteristic
65C2×C4×C227C2×D411yescharacteristic
66C2×C4×C227C2×D411yescharacteristic
67C8×C227—42no—
68C22×C227—21no—
69C22×C227—21no—
70C22×C227—21no—
71C22×C227C2×C22⋊C411yescharacteristic
72C2×D227—41no—
73C2×D227—41no—
74C2×D227—41no—
75C4×C227—21no—
76C4×C227—21no—
77C4×C227—21no—
78C4×C227—21no—
79C4×C227—21no—
80C4×C227—21no—
81Dic227—41no—
82Dic227—41no—
83Dic227—41no—
84C2×C227—41no—
85C2×C227#41311yescharacteristic
86C2×C227#42111yescharacteristic
87C2×C227#42111yescharacteristic
88D227—81no—
89C227#153511yescharacteristic, complemented, Sylow
90#1535—2271nomaximal, Sylow
91#529—2271no—
92#432—2271no—
93#432D22711yescharacteristic, complemented
94#330—2272no—
95#329—2272no—
96#126—4541no—
97#125—2271no—
98#124—2271no—
99#123—4541no—
100C22⋊Q8—2271no—
101#121—2271no—
102C4×Q8—2271no—
103C4×D4—4541no—
104C4×D4—2271no—
105#117—4541no—
106C2×C42C2×D22711yescharacteristic
107C4⋊C8—21no—
108C4⋊C8—4541no—
109C22⋊C8—21no—
110C22⋊C8—4541no—
111#97—2272no—
112#97C2×D22712yes—
113C2×Q8—2271no—
114C2×D4—4541no—
115C2×D4—2271no—
116C22×C4—4541no—
117C22×C4C4×D22711yescharacteristic
118C22×C4C22⋊D22711yescharacteristic
119C22×C4D90811yescharacteristic
120C2×C8—22no—
121C2×C8—4542no—
122C4⋊C4—4541no—
123C4⋊C4—4541no—
124C4⋊C4—4541no—
125C4⋊C4—4541no—
126C4⋊C4—2271no—
127C4⋊C4—2271no—
128C22⋊C4—4541no—
129C22⋊C4—4541no—
130C22⋊C4—4541no—
131C22⋊C4—4541no—
132C22⋊C4—4541no—
133C42—4541no—
134C42C4×D22711yescharacteristic
135C42C22⋊D22711yescharacteristic
136C42D90811yescharacteristic
137C42C22×D22711yescharacteristic
138C23—4541no—
139C23(C2×D227)⋊C411yescharacteristic
140Q8—9081no—
141D4—9081no—
142D4—9082no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—9082no—
147C2×C4—4541no—
148C2×C4—4541no—
149C2×C4—4541no—
150C2×C4(C2×D227)⋊C411yescharacteristic
151C2×C4(C2×D227)⋊C411yescharacteristic
152C2×C4(C2×D227)⋊C411yescharacteristic
153C2×C4C2×C4×D22711yescharacteristic
154C2×C4C2×C22⋊D22711yescharacteristic
155C2×C4C2×D90811yescharacteristic
156C8—42no—
157C8—9082no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—9081no—
162C22—9081no—
163C22—9081no—
164C22C2×(C2×D227)⋊C411yescharacteristic
165C4—21no—
166C4—21no—
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—9081no—
172C4—9081no—
173C4—9081no—
174C2—41no—
175C2—18161no—
176C2#2840901411yescharacteristic
177C2#2840904811yescharacteristic
178C2#2840905011yescharacteristic
subgroupG/H
centerC22C2×(C2×D227)⋊C4
commutatorC2×C4×C227C22×C4
FrattiniC42C22×D227
Fitting#432×C227C2
socleC22×C227C2×C22⋊C4
prime radical#20300262C4
cosocleC42×C227C23
hypercenter#432D227
hypocenterC227#1535
LCSG ▷ C2×C4×C227 ▷ C22×C227 ▷ C227
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #28409089C2semidirect
3. #28408773C2semidirect
4. #28408771C2semidirect
5. #432×C227C2semidirect
89. C227#1535semidirect
93. #432D227semidirect

Maximal subgroups

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

subgroupindex
#284095662
#284090892
#284087732
#284087712
#432×C2272
#1535227