Finite Group Databasebeta

← #22586915

Subgroups — #22586915

Order 9088.

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

normal subgroups only

This group has 218 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#17986533C211yesmaximal, characteristic
2#17986052C211yesmaximal, characteristic, complemented
3#17985735C212yesmaximal, complemented
4#17985732C212yesmaximal
5#383×C71C211yesmaximal, characteristic, complemented
6#14556122—21no—
7#14556120C411yescharacteristic, complemented
8#14556116C411yescharacteristic, complemented
9#14556111—21no—
10#14556107C2211yescharacteristic
11#14556102C2211yescharacteristic
12C4×Dic142C411yescharacteristic, complemented
13C4×D284C411yescharacteristic, complemented
14C4×C22⋊D71—21no—
15#14556085—21no—
16C4⋊(C71⋊C8)—21no—
17C22⋊(C71⋊C8)C2212yes—
18C4×C71⋊C8—21no—
19C2×C42×C71C2211yescharacteristic
20#95×C71—21no—
21#95×C71—21no—
22#95×C71C2212yes—
23C2×Dic142C2×C411yescharacteristic
24C2×D284C2×C411yescharacteristic
25C2×C22⋊D71—21no—
26C2×C4×D71—21no—
27C2×C71⋊C8—22no—
28C4⋊Dic71C2×C411yescharacteristic
29C4⋊Dic71C2×C411yescharacteristic
30Dic71⋊C4—21no—
31Dic71⋊C4—21no—
32Dic71⋊C4—21no—
33Dic71⋊C4—21no—
34C22⋊Dic71—21no—
35(C2×D71)⋊C4—21no—
36(C2×D71)⋊C4—21no—
37(C2×D71)⋊C4—21no—
38(C2×D71)⋊C4—21no—
39C4×Dic71—21no—
40C22×C4×C71—22no—
41C22×C4×C71D411yescharacteristic
42C22×C4×C71D411yescharacteristic
43C22×C4×C71C2311yescharacteristic
44C42×C71C2×C411yescharacteristic
45C42×C71C2×C411yescharacteristic
46C42×C71D411yescharacteristic
47C42×C71D411yescharacteristic
48C23×C71C2×D411yescharacteristic
49C22×D71—21no—
50C2×C4×C71—22no—
51C2×C4×C71—41no—
52C2×C4×C71—41no—
53C2×C4×C71—42no—
54C2×C4×C71—42no—
55C2×C4×C71—42no—
56C2×C4×C71C22⋊C411yescharacteristic
57C2×C4×C71C22⋊C411yescharacteristic
58C2×C4×C71C22⋊C411yescharacteristic
59C2×C4×C71C22⋊C411yescharacteristic
60C2×C4×C71C22×C411yescharacteristic
61C2×C4×C71C2×D411yescharacteristic
62C22⋊D71—42no—
63C2×Dic71—21no—
64C2×Dic71—21no—
65C2×Dic71—21no—
66D284—41no—
67C4×D71—42no—
68Dic142—41no—
69C71⋊C8—42no—
70C22×C71—21no—
71C22×C71—21no—
72C22×C71C2×C22⋊C411yescharacteristic
73C22×C71#13512yes—
74C2×D71—41no—
75C2×D71—41no—
76C2×D71—41no—
77C4×C71—21no—
78C4×C71—21no—
79C4×C71—21no—
80C4×C71—21no—
81C4×C71—21no—
82C4×C71—21no—
83C4×C71—82no—
84Dic71—41no—
85Dic71—41no—
86Dic71—41no—
87C2×C71—22no—
88C2×C71#41011yescharacteristic
89C2×C71#41611yescharacteristic
90C2×C71#42111yescharacteristic
91D71—81no—
92#1521—711nomaximal, Sylow
93C71#152111yescharacteristic, complemented, Sylow
94#529—711no—
95#431—711no—
96#383D7111yescharacteristic, complemented
97#328—712no—
98#327—712no—
99#126—1421no—
100#125—711no—
101#124—711no—
102#123—1421no—
103C22⋊Q8—711no—
104#121—711no—
105C4×Q8—711no—
106C4×D4—711no—
107C4×D4—1421no—
108#117—1421no—
109C2×C42C2×D7111yescharacteristic
110C4⋊C8—1421no—
111C22⋊C8—712no—
112C4×C8—1421no—
113#95—21no—
114#95—21no—
115#95C2×D7112yes—
116C2×Q8—711no—
117C2×D4—711no—
118C2×D4—1421no—
119C22×C4—22no—
120C22×C4—1421no—
121C22×C4C22⋊D7111yescharacteristic
122C22×C4C22⋊D7111yescharacteristic
123C22×C4C22×D7111yescharacteristic
124C2×C8—1422no—
125C4⋊C4—711no—
126C4⋊C4—711no—
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—
136C42—1421no—
137C42C4×D7111yescharacteristic
138C42C4×D7111yescharacteristic
139C42D28411yescharacteristic
140C42D28411yescharacteristic
141C23—1421no—
142C23C2×C22⋊D7111yescharacteristic
143Q8—2841no—
144D4—2841no—
145D4—2842no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—42no—
150C2×C4—42no—
151C2×C4—42no—
152C2×C4—2842no—
153C2×C4—1421no—
154C2×C4—1421no—
155C2×C4—1421no—
156C2×C4(C2×D71)⋊C411yescharacteristic
157C2×C4(C2×D71)⋊C411yescharacteristic
158C2×C4(C2×D71)⋊C411yescharacteristic
159C2×C4(C2×D71)⋊C411yescharacteristic
160C2×C4C2×C4×D7111yescharacteristic
161C2×C4C2×D28411yescharacteristic
162C8—2842no—
163C22—21no—
164C22—21no—
165C22—2841no—
166C22—2841no—
167C22—2841no—
168C22C2×(C2×D71)⋊C411yescharacteristic
169C22#1455614812yes—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—82no—
177C4—2841no—
178C4—2841no—
179C4—2841no—
180C2—22no—
181C2—5681no—
182C2#1798597211yescharacteristic
183C2#1798599311yescharacteristic
184C2#1798601711yescharacteristic
subgroupG/H
centerC22C2×(C2×D71)⋊C4
commutatorC2×C4×C71C22×C4
FrattiniC22×C4C22×D71
Fitting#383×C71C2
socleC22×C71C2×C22⋊C4
hypercenter#383D71
hypocenterC71#1521
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ C2×C42 ◁ #383

Complements

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

NH ≅ G/Ntype
2. #17986052C2semidirect
3. #17985735C2semidirect
5. #383×C71C2semidirect
7. #14556120C4semidirect
8. #14556116C4semidirect
12. C4×Dic142C4semidirect
13. C4×D284C4semidirect
93. C71#1521semidirect
96. #383D71semidirect