Finite Group Databasebeta

← #22594298

Subgroups — #22594298

Order 9088.

462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 123 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#17985941C213yesmaximal, complemented
2#17985926C213yesmaximal, complemented
3#17985923C211yesmaximal, characteristic, complemented
4#17985877C213yesmaximal
5#17985873C213yesmaximal, complemented
6#95×D71C211yesmaximal, characteristic, complemented
7#401×C71C211yesmaximal, characteristic, complemented
8C22×D284C2211yescharacteristic
9C22×C4×D71C2213yes—
10C2×C4⋊Dic71C2213yes—
11C2×Dic71⋊C4C2213yes—
12C2×(C2×D71)⋊C4C2213yes—
13C2×(C2×D71)⋊C4C2213yes—
14C2×(C2×D71)⋊C4C2213yes—
15C71⋊#95C2213yes—
16C71⋊#95C2213yes—
17C71⋊#95C2213yes—
18#95×C71C2211yescharacteristic
19#95×C71C2213yes—
20#95×C71C2213yes—
21C23×D71C2311yescharacteristic
22C23×D71C2311yescharacteristic
23C2×D284—26no—
24C22×Dic71C2313yes—
25C22×Dic71C2313yes—
26C2×C4×D71—26no—
27C2×C4×D71—43no—
28C2×C4×D71—43no—
29C4⋊Dic71—43no—
30Dic71⋊C4—43no—
31(C2×D71)⋊C4—26no—
32(C2×D71)⋊C4—43no—
33(C2×D71)⋊C4—43no—
34C22×C4×C71C2313yes—
35C22×C4×C71C2311yescharacteristic
36C22×C4×C71C2313yes—
37C23×C71C2411yescharacteristic
38C22×D71—23no—
39C22×D71—21no—
40C22×D71—23no—
41C22×D71—23no—
42C22×D71—21no—
43C22×D71#4116yes—
44C2×C4×C71—23no—
45C2×C4×C71—23no—
46C2×C4×C71—23no—
47C2×C4×C71—23no—
48C2×C4×C71—23no—
49C2×C4×C71—23no—
50C2×C4×C71—23no—
51C2×Dic71—23no—
52C2×Dic71—23no—
53C2×Dic71—23no—
54C2×Dic71—23no—
55C2×Dic71—23no—
56C2×Dic71—23no—
57D284—44no—
58C4×D71—412no—
59C22×C71C2×#4113yes—
60C22×C71H(5,𝔽2)13yes—
61C22×C712−1+411yescharacteristic
62C2×D71—26no—
63C2×D71—26no—
64C2×D71—41no—
65C2×D71—43no—
66C2×D71—43no—
67C2×D71#12614yes—
68C4×C71—41no—
69C4×C71—43no—
70C4×C71—43no—
71Dic71—43no—
72Dic71—43no—
73C2×C71C2×#12611yescharacteristic
74C2×C71#53813yes—
75C2×C71#53913yes—
76D71—24no—
77D71—81no—
78#2643—711nomaximal, Sylow
79C71#264311yescharacteristic, complemented, Sylow
80#401D7111yescharacteristic, complemented
81#400—713no—
82#397—713no—
83#396—711no—
84#386—713no—
85#385—713no—
86C2×#95—711no—
87C22×D4—711no—
88C23×C4—713no—
89C2×C4⋊C4—713no—
90C2×C4⋊C4—713no—
91C2×C22⋊C4—713no—
92C2×C22⋊C4—713no—
93C2×C22⋊C4—713no—
94#95—713no—
95#95—713no—
96#95—713no—
97#95C2×D7111yescharacteristic
98#95C2×D7113yes—
99#95C2×D7113yes—
100C24—711no—
101C24—711no—
102C2×D4—1426no—
103C22×C4—2843no—
104C22×C4—2843no—
105C22×C4—713no—
106C22×C4—713no—
107C22×C4—1426no—
108C22×C4C22×D7111yescharacteristic
109C22×C4C22×D7113yes—
110C22×C4C22×D7113yes—
111C4⋊C4—2843no—
112C4⋊C4—2843no—
113C22⋊C4—2843no—
114C22⋊C4—2843no—
115C22⋊C4—1426no—
116C23—716no—
117C23—1423no—
118C23—1423no—
119C23—1421no—
120C23—1423no—
121C23—1421no—
122C23C23×D7111yescharacteristic
123D4—2844no—
124C2×C4—23no—
125C2×C4—23no—
126C2×C4—23no—
127C2×C4—23no—
128C2×C4—23no—
129C2×C4—23no—
130C2×C4—23no—
131C2×C4—28412no—
132C2×C4—1423no—
133C2×C4—1423no—
134C2×C4—1423no—
135C2×C4—1423no—
136C2×C4—1423no—
137C2×C4—1423no—
138C22—2843no—
139C22—2843no—
140C22—2841no—
141C22—714no—
142C22—1426no—
143C22—1426no—
144C22#41×D7113yes—
145C22#1455617413yes—
146C22#1455617511yescharacteristic
147C4—43no—
148C4—43no—
149C4—41no—
150C4—2843no—
151C4—2843no—
152C2—5681no—
153C2—1424no—
154C2#126×D7111yescharacteristic
155C2#1798658813yes—
156C2#1798659013yes—
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
Fitting#401×C71C2
hypercenter#401D71
hypocenterC71#2643
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #401

Complements

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

NH ≅ G/Ntype
1. #17985941C2semidirect
2. #17985926C2semidirect
3. #17985923C2semidirect
5. #17985873C2semidirect
6. #95×D71C2semidirect
7. #401×C71C2semidirect
79. C71#2643semidirect
80. #401D71semidirect