Finite Group Databasebeta

← #22586974

Subgroups — #22586974

Order 9088.

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

normal subgroups only

This group has 238 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#17986056C211yesmaximal, characteristic, complemented
3#17985738C214yesmaximal, complemented
4#432×C71C211yesmaximal, characteristic, complemented
5C2×#11765865C412yes—
6#14556128C411yescharacteristic
7#14556125C411yescharacteristic
8#14556116C2212yes—
9#14556102—21no—
10#14556102—21no—
11C4×D284—21no—
12C4×D284—21no—
13C4⋊(C71⋊C8)—21no—
14C22⋊(C71⋊C8)—21no—
15#14556039C2212yes—
16C2×C42×C71C2211yescharacteristic
17C4⋊C8×C71—21no—
18C22⋊C8×C71—21no—
19#97×C71C2212yes—
20#11765865—44no—
21C2×Dic142C2×C412yes—
22C2×D284—21no—
23C2×D284—21no—
24C2×D284C2×C412yes—
25C2×C22⋊D71—22no—
26C2×C4×D71—22no—
27C2×C71⋊C8—22no—
28C4⋊Dic71—21no—
29C4⋊Dic71—21no—
30(C2×D71)⋊C4—22no—
31(C2×D71)⋊C4—22no—
32C22×C4×C71C2×C411yescharacteristic
33C22×C4×C71D411yescharacteristic
34C22×C4×C71D411yescharacteristic
35C2×C8×C71—22no—
36C42×C71C2×C411yescharacteristic
37C42×C71D411yescharacteristic
38C42×C71D411yescharacteristic
39C42×C71C2311yescharacteristic
40C23×C71C22⋊C411yescharacteristic
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×C71C2×D411yescharacteristic
50C2×C4×C71C2×D411yescharacteristic
51C22⋊D71—44no—
52C2×Dic71—22no—
53D284—42no—
54D284—42no—
55D284—42no—
56C4×D71—44no—
57Dic142—42no—
58C8×C71—42no—
59C71⋊C8—42no—
60C22×C71—21no—
61C22×C71—21no—
62C22×C71—21no—
63C22×C71C2×C22⋊C411yescharacteristic
64C2×D71—42no—
65C2×D71—42no—
66C2×D71—42no—
67C4×C71—21no—
68C4×C71—21no—
69C4×C71—21no—
70C4×C71—21no—
71C4×C71—21no—
72C4×C71#10012yes—
73Dic71—42no—
74C2×C71—41no—
75C2×C71C2×#10011yescharacteristic
76C2×C71#42111yescharacteristic
77C2×C71#42111yescharacteristic
78D71—82no—
79#1536—711nomaximal, Sylow
80C71#153611yescharacteristic, complemented, Sylow
81#532—711no—
82#432—711no—
83#432D7111yescharacteristic, complemented
84#329—714no—
85C2×#41—712no—
86C4⋊Q8—711no—
87#127—711no—
88#124—712no—
89#121—1421no—
90#121—1421no—
91C4×D4—1421no—
92C4×D4—1421no—
93C2×C42C2×D7111yescharacteristic
94C4⋊C8—21no—
95C4⋊C8—1421no—
96C22⋊C8—21no—
97C22⋊C8—1421no—
98#97—712no—
99#97C2×D7112yes—
100#41—2844no—
101C2×Q8—712no—
102C2×D4—712no—
103C2×D4—1422no—
104C2×D4—1421no—
105C2×D4—1421no—
106C22×C4—1422no—
107C22×C4C4×D7111yescharacteristic
108C22×C4D28411yescharacteristic
109C22×C4C22⋊D7111yescharacteristic
110C2×C8—22no—
111C2×C8—1422no—
112C4⋊C4—1421no—
113C4⋊C4—1421no—
114C22⋊C4—1422no—
115C22⋊C4—1422no—
116C42C4×D7111yescharacteristic
117C42D28411yescharacteristic
118C42C22⋊D7111yescharacteristic
119C42C22×D7111yescharacteristic
120C23—1422no—
121C23(C2×D71)⋊C411yescharacteristic
122Q8—2842no—
123D4—2842no—
124D4—2842no—
125D4—2842no—
126D4—2844no—
127C2×C4—22no—
128C2×C4—41no—
129C2×C4—41no—
130C2×C4—2844no—
131C2×C4—1422no—
132C2×C4(C2×D71)⋊C411yescharacteristic
133C2×C4(C2×D71)⋊C411yescharacteristic
134C2×C4(C2×D71)⋊C411yescharacteristic
135C2×C4C2×C4×D7111yescharacteristic
136C2×C4C2×C22⋊D7111yescharacteristic
137C2×C4C2×D28411yescharacteristic
138C8—42no—
139C8—2842no—
140C22—21no—
141C22—21no—
142C22—21no—
143C22—2842no—
144C22—2842no—
145C22—2842no—
146C22C2×(C2×D71)⋊C411yescharacteristic
147C4—21no—
148C4—21no—
149C4—21no—
150C4—21no—
151C4—21no—
152C4—2842no—
153C4#1455604412yes—
154C2—41no—
155C2—5682no—
156C2C2×#1455604411yescharacteristic
157C2#1798601511yescharacteristic
158C2#1798601711yescharacteristic
subgroupG/H
centerC22C2×(C2×D71)⋊C4
commutatorC2×C4×C71C22×C4
FrattiniC42C22×D71
Fitting#432×C71C2
socleC22×C71C2×C22⋊C4
hypercenter#432D71
hypocenterC71#1536
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. #17986056C2semidirect
3. #17985738C2semidirect
4. #432×C71C2semidirect
80. C71#1536semidirect
83. #432D71semidirect