Finite Group Databasebeta

← #44398426

Subgroups — #44398426

Order 29056.

252 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 67 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#28409580C211yesmaximal, characteristic
2#28409088C211yesmaximal, characteristic, complemented
3C4⋊C8×D227C211yesmaximal, characteristic, complemented
4#28408780C211yesmaximal, characteristic, complemented
5#28408780C211yesmaximal, characteristic, complemented
6#28408776C211yesmaximal, characteristic, complemented
7#331×C227C211yesmaximal, characteristic, complemented
8C2×#16813883C412yes—
9C2×C8×D227—21no—
10#20300288C2211yescharacteristic
11#20300275C412yes—
12#20300259—21no—
13#20300259—21no—
14D4×Dic227—21no—
15D4×Dic227—21no—
16C42×D227C2211yescharacteristic
17C4⋊(C227⋊C8)C2211yescharacteristic
18C4⋊(C227⋊C8)C2211yescharacteristic
19Dic227⋊C8—21no—
20(C2×D227)⋊C8—21no—
21#20300198—21no—
22#127×C227C2211yescharacteristic
23C4⋊C8×C227C2211yescharacteristic
24C4⋊C8×C227C2211yescharacteristic
25#16813883—44no—
26C2×Dic454C2×C412yes—
27C2×C22⋊D227—22no—
28C22×Dic227—22no—
29C2×C4×D227C2×C411yescharacteristic
30C2×C4×D227D411yescharacteristic
31C2×C4×D227D411yescharacteristic
32C2×C227⋊C8—21no—
33C2×C227⋊C8—21no—
34C8×D227—42no—
35C4⋊Dic227—21no—
36C4⋊Dic227—21no—
37C22⋊Dic227—22no—
38C22⋊Dic227—22no—
39C4×Dic227C2×C411yescharacteristic
40C4×Dic227D411yescharacteristic
41C4×Dic227D411yescharacteristic
42C2×D4×C227—21no—
43C2×D4×C227—21no—
44C2×D4×C227C2×C412yes—
45C2×C8×C227—21no—
46C2×C8×C227—21no—
47C42×C227C2311yescharacteristic
48C22×D227C22⋊C411yescharacteristic
49Dic454—42no—
50C22⋊D227—44no—
51C2×Dic227—22no—
52C2×Dic227—44no—
53C2×Dic227C22⋊C411yescharacteristic
54C2×Dic227C22⋊C411yescharacteristic
55C2×Dic227C22⋊C411yescharacteristic
56C4×D227—22no—
57C4×D227—21no—
58C4×D227—21no—
59C4×D227—21no—
60C4×D227—21no—
61C227⋊C8—41no—
62C227⋊C8—41no—
63C23×C227—22no—
64D4×C227—42no—
65D4×C227—41no—
66D4×C227—41no—
67D4×C227—41no—
68D4×C227—41no—
69C2×C4×C227C22×C411yescharacteristic
70C2×C4×C227C2×D411yescharacteristic
71C2×C4×C227C2×D411yescharacteristic
72C8×C227—41no—
73C8×C227—41no—
74C22×C227—42no—
75C22×C227—42no—
76C22×C227—42no—
77C22×C227C2×C22⋊C411yescharacteristic
78C2×D227—21no—
79C2×D227—21no—
80C2×D227#10012yes—
81C4×C227—21no—
82C4×C227#13511yescharacteristic
83C4×C227#13511yescharacteristic
84C4×C227AGL(1,ℤ/8)11yescharacteristic
85C4×C227#13711yescharacteristic
86Dic227—21no—
87Dic227—21no—
88Dic227—21no—
89Dic227—42no—
90C2×C227—82no—
91C2×C227C2×#10011yescharacteristic
92C2×C227#41611yescharacteristic
93C2×C227#41711yescharacteristic
94D227—22no—
95C227#155111yescharacteristic, complemented, Sylow
96#1551—2271nomaximal, Sylow
97#532—2271no—
98#432—2271no—
99C2×C4⋊C8—2271no—
100#333—2271no—
101#333—2271no—
102#331—2271no—
103#331D22711yescharacteristic, complemented
104C2×#41—2272no—
105C22×C8—4541no—
106C4⋊Q8—2271no—
107#127C2×D22711yescharacteristic
108#124—2272no—
109#121—4541no—
110#121—4541no—
111C4×D4—4541no—
112C4×D4—4541no—
113C2×C42—2271no—
114C4⋊C8—4541no—
115C4⋊C8—2271no—
116C4⋊C8—2271no—
117C4⋊C8C2×D22711yescharacteristic
118C4⋊C8C2×D22711yescharacteristic
119C22⋊C8—4541no—
120#97—4541no—
121#41—9084no—
122C2×Q8—2272no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—4542no—
126C2×D4C4×D22712yes—
127C22×C4—4542no—
128C22×C4—2271no—
129C22×C4—2271no—
130C22×C4—2271no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—9082no—
134C2×C8—4541no—
135C2×C8—4541no—
136C4⋊C4—4541no—
137C4⋊C4—4541no—
138C22⋊C4—4542no—
139C22⋊C4—4542no—
140C42—2271no—
141C42—2271no—
142C42—2271no—
143C42C22×D22711yescharacteristic
144C23—22no—
145C23—2271no—
146Q8—9082no—
147D4—42no—
148D4—41no—
149D4—41no—
150D4—41no—
151D4—41no—
152D4—9084no—
153C2×C4—9084no—
154C2×C4—4542no—
155C2×C4—4542no—
156C2×C4—4541no—
157C2×C4—4541no—
158C2×C4—4541no—
159C2×C4—4541no—
160C2×C4—2271no—
161C2×C4—2271no—
162C2×C4—2271no—
163C2×C4C2×C4×D22711yescharacteristic
164C2×C4D4×D22711yescharacteristic
165C2×C4D4×D22711yescharacteristic
166C8—41no—
167C8—41no—
168C8—9081no—
169C8—9081no—
170C22—42no—
171C22—42no—
172C22—42no—
173C22—4541no—
174C22—4541no—
175C22—2272no—
176C22C22⋊C4×D22711yescharacteristic
177C4—21no—
178C4—9082no—
179C4—4541no—
180C4—4541no—
181C4—4541no—
182C4#2030030711yescharacteristic
183C4#2030030911yescharacteristic
184C4#2030031211yescharacteristic
185C4#2030031711yescharacteristic
186C2—82no—
187C2—4542no—
188C2#100×D22711yescharacteristic
189C2#2840902511yescharacteristic
190C2#2840903011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D227
commutatorC2×C4×C227C22×C4
FrattiniC42C22×D227
Fitting#331×C227C2
socleC22×C227C2×C22⋊C4
prime radical#28409580C2
cosocleC42×C227C23
hypercenter#331D227
hypocenterC227#1551
LCSG ▷ C2×C4×C227 ▷ C22×C227 ▷ C227
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #28409088C2semidirect
3. C4⋊C8×D227C2semidirect
4. #28408780C2semidirect
5. #28408780C2semidirect
6. #28408776C2semidirect
7. #331×C227C2semidirect
95. C227#1551semidirect
103. #331D227semidirect

Maximal subgroups

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

subgroupindex
#284095802
#284090882
C4⋊C8×D2272
#284087802
#284087762
#331×C2272
#1551227