Finite Group Databasebeta

← #22590010

Subgroups — #22590010

Order 9088.

270 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 55 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#17986562C211yesmaximal, characteristic
2#17985971C212yesmaximal, complemented
3#17985792C211yesmaximal, characteristic, complemented
4#17985791C212yesmaximal, complemented
5#353×C71C211yesmaximal, characteristic, complemented
6C2×#11765864C2211yescharacteristic
7C2×D4×D71C411yescharacteristic, complemented
8#14556124C2211yescharacteristic
9#14556116C411yescharacteristic, complemented
10#14556115C411yescharacteristic, complemented
11#14556100—22no—
12#14556096—22no—
13#14556085C411yescharacteristic, complemented
14#14556084—22no—
15#14556043C2212yescomplemented
16#14556042—22no—
17#127×C71C2211yescharacteristic
18#99×C71C2212yescomplemented
19C23×D71—21no—
20#11765864—42no—
21C2×Dic142C2×C411yescharacteristic
22C2×D284C2×C411yescharacteristic
23C2×C22⋊D71—22no—
24C2×C22⋊D71—21no—
25C2×C22⋊D71D412yes—
26D4×D71—42no—
27C22×Dic71D412yes—
28C2×C4×D71C2×C411yescharacteristic
29Dic71⋊C4—21no—
30Dic71⋊C4—42no—
31C22⋊Dic71—22no—
32C22⋊Dic71—22no—
33(C2×D71)⋊C4—21no—
34(C2×D71)⋊C4—22no—
35C4×Dic71—42no—
36C4×Dic71C2×C411yescharacteristic
37C2×D4×C71—22no—
38C2×D4×C71C2×C411yescharacteristic
39C2×D4×C71C2311yescharacteristic
40C22⋊C4×C71—22no—
41C42×C71C2×C411yescharacteristic
42C23×C71—21no—
43C23×C71C2×D412yes—
44C22×D71—21no—
45C22×D71—42no—
46C22×D71—82no—
47C22×D71C22⋊C411yescharacteristic
48D4×C71—41no—
49D4×C71—41no—
50D4×C71—82no—
51C2×C4×C71—21no—
52C2×C4×C71—42no—
53C2×C4×C71C22×C411yescharacteristic
54C22⋊D71—42no—
55C22⋊D71—42no—
56C22⋊D71—82no—
57C2×Dic71—22no—
58C2×Dic71—22no—
59C2×Dic71—21no—
60C2×Dic71—42no—
61C2×Dic71C22⋊C412yes—
62C2×Dic71C22⋊C411yescharacteristic
63D284—41no—
64C4×D71—22no—
65Dic142—41no—
66C22×C71—22no—
67C22×C71—42no—
68C22×C71—42no—
69C22×C71—41no—
70C22×C71C2×C22⋊C411yescharacteristic
71C2×D71—21no—
72C2×D71—41no—
73C2×D71—42no—
74C2×D71—41no—
75C2×D71—84no—
76C4×C71—21no—
77C4×C71—41no—
78C4×C71—82no—
79Dic71—22no—
80Dic71—41no—
81Dic71—82no—
82Dic71#9912yes—
83C2×C71—21no—
84C2×C71—42no—
85C2×C71—81no—
86C2×C71C2×#9911yescharacteristic
87D71—41no—
88D71—81no—
89#2128—711nomaximal, Sylow
90C71#212811yescharacteristic, complemented, Sylow
91#535—711no—
92#410—712no—
93#353—711no—
94#353—712no—
95#353D7111yescharacteristic, complemented
96C2×#41—711no—
97C22×D4—711no—
98#127—711no—
99#127C2×D7111yescharacteristic
100#124—711no—
101#124—711no—
102#121—1422no—
103#120—1422no—
104#117—711no—
105#117—1422no—
106#99—712no—
107#99—1422no—
108#99C2×D7112yescomplemented
109C24—1421no—
110#41—2842no—
111C2×Q8—711no—
112C2×D4—22no—
113C2×D4—2842no—
114C2×D4—712no—
115C2×D4—711no—
116C2×D4—1421no—
117C2×D4—1422no—
118C2×D4C4×D7111yescharacteristic
119C2×D4C22×D7111yescharacteristic
120C22×C4—712no—
121C22×C4—711no—
122C4⋊C4—2842no—
123C4⋊C4—1421no—
124C22⋊C4—22no—
125C22⋊C4—1422no—
126C22⋊C4—1421no—
127C22⋊C4—1422no—
128C22⋊C4—1422no—
129C42—2842no—
130C42—711no—
131C42C4×D7111yescharacteristic
132C23—21no—
133C23—2842no—
134C23—5682no—
135C23—711no—
136C23—1421no—
137C23D4×D7112yes—
138Q8—2841no—
139D4—41no—
140D4—41no—
141D4—82no—
142D4—2841no—
143D4—2842no—
144D4—2842no—
145D4—5682no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—2842no—
149C2×C4—711no—
150C2×C4—712no—
151C2×C4—1422no—
152C2×C4—1421no—
153C2×C4—1422no—
154C2×C4—1422no—
155C2×C4C2×C4×D7111yescharacteristic
156C22—22no—
157C22—42no—
158C22—42no—
159C22—41no—
160C22—2841no—
161C22—2842no—
162C22—2841no—
163C22—5684no—
164C22—1421no—
165C22C22⋊C4×D7111yescharacteristic
166C4—21no—
167C4—41no—
168C4—82no—
169C4—2841no—
170C4—5682no—
171C4—712no—
172C4—1422no—
173C2—21no—
174C2—42no—
175C2—81no—
176C2—2841no—
177C2—5681no—
178C2#99×D7111yescharacteristic
subgroupG/H
centerC2#99×D71
commutatorC2×C4×C71C22×C4
FrattiniC2×D4C22×D71
Fitting#353×C71C2
socleC2×C71C2×#99
hypercenter#353D71
hypocenterC71#2128
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #17985971C2semidirect
3. #17985792C2semidirect
4. #17985791C2semidirect
5. #353×C71C2semidirect
7. C2×D4×D71C4semidirect
9. #14556116C4semidirect
10. #14556115C4semidirect
13. #14556085C4semidirect
15. #14556043C22semidirect
18. #99×C71C22semidirect
90. C71#2128semidirect
95. #353D71semidirect
108. #99C2×D71semidirect