Finite Group Databasebeta

← #22586707

Subgroups — #22586707

Order 9088.

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

normal subgroups only

This group has 214 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
1C2×#14556122C211yesmaximal, characteristic
2#17986056C211yesmaximal, characteristic, complemented
3#17985724C212yesmaximal, complemented
4#17985722C212yesmaximal
5#431×C71C211yesmaximal, characteristic, complemented
6#14556122—21no—
7#14556122—21no—
8#14556122—21no—
9#14556122—21no—
10C2×Dic71⋊C4C411yescharacteristic
11C2×Dic71⋊C4C411yescharacteristic
12C2×Dic71⋊C4C2211yescharacteristic
13C2×(C2×D71)⋊C4C411yescharacteristic
14C2×(C2×D71)⋊C4C411yescharacteristic
15C2×(C2×D71)⋊C4C2211yescharacteristic
16C4⋊(C71⋊C8)—21no—
17C22⋊(C71⋊C8)C2212yes—
18#14556039—21no—
19C2×C42×C71C2211yescharacteristic
20C4⋊C8×C71—21no—
21C22⋊C8×C71C2212yes—
22C4×C8×C71—21no—
23C23×D71C2×C411yescharacteristic
24C22×Dic71C2×C411yescharacteristic
25C22×Dic71C2×C411yescharacteristic
26C22×Dic71C2×C411yescharacteristic
27C2×C71⋊C8—22no—
28Dic71⋊C4—21no—
29Dic71⋊C4—21no—
30Dic71⋊C4—21no—
31Dic71⋊C4—21no—
32Dic71⋊C4—21no—
33Dic71⋊C4—21no—
34(C2×D71)⋊C4—21no—
35(C2×D71)⋊C4—21no—
36(C2×D71)⋊C4—21no—
37(C2×D71)⋊C4—21no—
38(C2×D71)⋊C4—21no—
39(C2×D71)⋊C4—21no—
40C22×C4×C71C2×C411yescharacteristic
41C22×C4×C71C2×C411yescharacteristic
42C22×C4×C71C2311yescharacteristic
43C2×C8×C71—22no—
44C42×C71D411yescharacteristic
45C42×C71D411yescharacteristic
46C42×C71D411yescharacteristic
47C42×C71D411yescharacteristic
48C23×C71C22×C411yescharacteristic
49C22×D71—21no—
50C22×D71—22no—
51C22×D71—41no—
52C22×D71—41no—
53C2×C4×C71—22no—
54C2×C4×C71—41no—
55C2×C4×C71—41no—
56C2×C4×C71C22⋊C411yescharacteristic
57C2×C4×C71C22⋊C411yescharacteristic
58C2×C4×C71C22⋊C411yescharacteristic
59C2×C4×C71C22⋊C411yescharacteristic
60C2×C4×C71C2×D411yescharacteristic
61C2×C4×C71C2×D411yescharacteristic
62C2×Dic71—21no—
63C2×Dic71—21no—
64C2×Dic71—21no—
65C2×Dic71—22no—
66C2×Dic71—41no—
67C2×Dic71—41no—
68C8×C71—42no—
69C71⋊C8—42no—
70C22×C71—21no—
71C22×C71—21no—
72C22×C71C2×C22⋊C411yescharacteristic
73C22×C71#13112yes—
74C2×D71—41no—
75C2×D71—41no—
76C2×D71—41no—
77C2×D71—82no—
78C4×C71—21no—
79C4×C71—21no—
80C4×C71—21no—
81C4×C71—21no—
82C4×C71—21no—
83C4×C71—21no—
84Dic71—41no—
85Dic71—41no—
86Dic71—41no—
87C2×C71—22no—
88C2×C71#40811yescharacteristic
89C2×C71#41011yescharacteristic
90C2×C71#41311yescharacteristic
91D71—81no—
92#1473—711nomaximal, Sylow
93C71#147311yescharacteristic, complemented, Sylow
94C2×#126—711no—
95#432—711no—
96#431D7111yescharacteristic, complemented
97#324—712no—
98#323—712no—
99#126—1421no—
100#126—1421no—
101#126—1421no—
102#126—1421no—
103C2×C4⋊C4—711no—
104C2×C4⋊C4—711no—
105C2×C4⋊C4—711no—
106C2×C22⋊C4—711no—
107C2×C22⋊C4—711no—
108C2×C22⋊C4—711no—
109C2×C42C2×D7111yescharacteristic
110C4⋊C8—21no—
111C4⋊C8—1421no—
112C22⋊C8—712no—
113C22⋊C8C2×D7112yes—
114#97—1421no—
115C4×C8—21no—
116C24—711no—
117C22×C4—711no—
118C22×C4—711no—
119C22×C4—711no—
120C22×C4C4×D7111yescharacteristic
121C22×C4C4×D7111yescharacteristic
122C22×C4C22×D7111yescharacteristic
123C2×C8—22no—
124C2×C8—1422no—
125C4⋊C4—1421no—
126C4⋊C4—1421no—
127C4⋊C4—1421no—
128C4⋊C4—1421no—
129C4⋊C4—1421no—
130C4⋊C4—1421no—
131C22⋊C4—1421no—
132C22⋊C4—1421no—
133C22⋊C4—1421no—
134C22⋊C4—1421no—
135C22⋊C4—1421no—
136C22⋊C4—1421no—
137C42D28411yescharacteristic
138C42D28411yescharacteristic
139C42C22⋊D7111yescharacteristic
140C42C22⋊D7111yescharacteristic
141C23—2841no—
142C23—2841no—
143C23—1421no—
144C23—1422no—
145C23C2×C4×D7111yescharacteristic
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—2841no—
150C2×C4—2841no—
151C2×C4—1421no—
152C2×C4—1421no—
153C2×C4—1421no—
154C2×C4—1422no—
155C2×C4(C2×D71)⋊C411yescharacteristic
156C2×C4(C2×D71)⋊C411yescharacteristic
157C2×C4(C2×D71)⋊C411yescharacteristic
158C2×C4(C2×D71)⋊C411yescharacteristic
159C2×C4C2×C22⋊D7111yescharacteristic
160C2×C4C2×D28411yescharacteristic
161C8—42no—
162C8—2842no—
163C22—21no—
164C22—21no—
165C22—2841no—
166C22—2841no—
167C22—2841no—
168C22—5682no—
169C22C2×(C2×D71)⋊C411yescharacteristic
170C22#1455613412yes—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—21no—
177C4—2841no—
178C4—2841no—
179C4—2841no—
180C2—22no—
181C2—5681no—
182C2#1798596511yescharacteristic
183C2#1798597211yescharacteristic
184C2#1798598111yescharacteristic
subgroupG/H
centerC22C2×(C2×D71)⋊C4
commutatorC23×C71C22×C4
FrattiniC22×C4C22×D71
Fitting#431×C71C2
socleC22×C71C2×C22⋊C4
hypercenter#431D71
hypocenterC71#1473
LCSG ▷ C23×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #17986056C2semidirect
3. #17985724C2semidirect
5. #431×C71C2semidirect
93. C71#1473semidirect
96. #431D71semidirect