Finite Group Databasebeta

← #22586888

Subgroups — #22586888

Order 9088.

252 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 69 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#17986549C211yesmaximal, characteristic
2#17985867C211yesmaximal, characteristic, complemented
3#17985734C214yesmaximal, complemented
4#432×C71C211yesmaximal, characteristic, complemented
5C2×#11765865—21no—
6#14556128C411yescharacteristic, complemented
7#14556125C411yescharacteristic, complemented
8#14556116—21no—
9#14556102—21no—
10#14556102C2212yes—
11C4×D284—21no—
12C4×D284C412yescomplemented
13C71⋊#95—21no—
14C71⋊#95—21no—
15C71⋊#95C2212yes—
16C2×C42×C71C2211yescharacteristic
17C4⋊C8×C71—21no—
18C22⋊C8×C71C2212yes—
19#97×C71—21no—
20#11765865—44no—
21C2×Dic142—21no—
22C2×D284—21no—
23C2×D284—21no—
24C2×D284C2×C412yes—
25C2×C22⋊D71—22no—
26C22×Dic71—22no—
27C2×C4×D71—22no—
28C4⋊Dic71—21no—
29C4⋊Dic71C2×C412yes—
30(C2×D71)⋊C4—22no—
31(C2×D71)⋊C4—22no—
32C22×C4×C71D411yescharacteristic
33C22×C4×C71D411yescharacteristic
34C22×C4×C71C2311yescharacteristic
35C2×C8×C71—22no—
36C42×C71C2×C411yescharacteristic
37C42×C71C2×C411yescharacteristic
38C42×C71D411yescharacteristic
39C42×C71D411yescharacteristic
40C23×C71C2×D411yescharacteristic
41C22×D71—22no—
42C2×C4×C71—22no—
43C2×C4×C71—41no—
44C2×C4×C71—41no—
45C2×C4×C71C22⋊C411yescharacteristic
46C2×C4×C71C22⋊C411yescharacteristic
47C2×C4×C71C22⋊C411yescharacteristic
48C2×C4×C71C22⋊C411yescharacteristic
49C2×C4×C71C22×C411yescharacteristic
50C2×C4×C71C2×D411yescharacteristic
51C22⋊D71—44no—
52C2×Dic71—22no—
53C2×Dic71—42no—
54C2×Dic71—42no—
55C2×Dic71—42no—
56D284—42no—
57D284—42no—
58D284—42no—
59C4×D71—44no—
60Dic142—42no—
61C8×C71—42no—
62C22×C71—21no—
63C22×C71—21no—
64C22×C71C2×C22⋊C411yescharacteristic
65C22×C71AGL(1,ℤ/8)12yes—
66C2×D71—42no—
67C2×D71—42no—
68C2×D71—42no—
69C4×C71—21no—
70C4×C71—21no—
71C4×C71—21no—
72C4×C71—21no—
73C4×C71—21no—
74C4×C71—21no—
75Dic71—42no—
76Dic71—82no—
77C2×C71—22no—
78C2×C71#41011yescharacteristic
79C2×C71#41811yescharacteristic
80C2×C71#42111yescharacteristic
81D71—82no—
82#1514—711nomaximal, Sylow
83C71#151411yescharacteristic, complemented, Sylow
84#532—711no—
85#432D7111yescharacteristic, complemented
86#383—711no—
87#327—714no—
88C2×#41—1421no—
89C4⋊Q8—711no—
90#127—711no—
91#124—1421no—
92#121—712no—
93#121—1421no—
94C4×D4—712no—
95C4×D4—1421no—
96C2×C42C2×D7111yescharacteristic
97C4⋊C8—21no—
98C22⋊C8C2×D7112yes—
99#97—21no—
100#95—712no—
101#95—1421no—
102#95—1421no—
103#41—2844no—
104C2×Q8—1421no—
105C2×D4—712no—
106C2×D4—1422no—
107C2×D4—1421no—
108C2×D4—1421no—
109C22×C4—1422no—
110C22×C4—1422no—
111C22×C4D28411yescharacteristic
112C22×C4D28411yescharacteristic
113C22×C4C22×D7111yescharacteristic
114C2×C8—22no—
115C4⋊C4—712no—
116C4⋊C4—1421no—
117C22⋊C4—1422no—
118C22⋊C4—1422no—
119C42C4×D7111yescharacteristic
120C42C4×D7111yescharacteristic
121C42C22⋊D7111yescharacteristic
122C42C22⋊D7111yescharacteristic
123C23—1422no—
124C23C2×D28411yescharacteristic
125Q8—2842no—
126D4—2842no—
127D4—2842no—
128D4—2842no—
129D4—2844no—
130C2×C4—22no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—2844no—
134C2×C4—2842no—
135C2×C4—2842no—
136C2×C4—2842no—
137C2×C4—1422no—
138C2×C4(C2×D71)⋊C411yescharacteristic
139C2×C4(C2×D71)⋊C411yescharacteristic
140C2×C4(C2×D71)⋊C411yescharacteristic
141C2×C4(C2×D71)⋊C411yescharacteristic
142C2×C4C2×C4×D7111yescharacteristic
143C2×C4C2×C22⋊D7111yescharacteristic
144C8—42no—
145C22—21no—
146C22—21no—
147C22—2842no—
148C22—2842no—
149C22—2842no—
150C22C2×(C2×D71)⋊C411yescharacteristic
151C22#1455615612yes—
152C4—21no—
153C4—21no—
154C4—21no—
155C4—21no—
156C4—21no—
157C4—21no—
158C4—2842no—
159C4—5682no—
160C2—22no—
161C2—5682no—
162C2#1798597211yescharacteristic
163C2#1798600511yescharacteristic
164C2#1798601511yescharacteristic
subgroupG/H
centerC22C2×(C2×D71)⋊C4
commutatorC2×C4×C71C22×C4
FrattiniC22×C4C22×D71
Fitting#432×C71C2
socleC22×C71C2×C22⋊C4
hypercenter#432D71
hypocenterC71#1514
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #17985867C2semidirect
3. #17985734C2semidirect
4. #432×C71C2semidirect
6. #14556128C4semidirect
7. #14556125C4semidirect
12. C4×D284C4semidirect
83. C71#1514semidirect
85. #432D71semidirect