Finite Group Databasebeta

← #22590008

Subgroups — #22590008

Order 9088.

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

normal subgroups only

This group has 286 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#17986567C211yesmaximal, characteristic
2#99×D71C212yesmaximal, complemented
3#17985794C211yesmaximal, characteristic, complemented
4#17985791C212yesmaximal, complemented
5#354×C71C211yesmaximal, characteristic, complemented
6C2×#11765866C411yescharacteristic, complemented
7C2×D4×D71C2211yescharacteristic
8#14556125C411yescharacteristic, complemented
9#14556124C2211yescharacteristic
10#14556117C411yescharacteristic, complemented
11#14556101—22no—
12#14556098—22no—
13#14556085C411yescharacteristic, complemented
14C22⋊C4×D71—22no—
15#14556043C2212yes—
16#14556042—22no—
17#124×C71C2211yescharacteristic
18#99×C71C2212yes—
19C23×D71D412yes—
20#11765866—42no—
21C2×D284—21no—
22C2×D284—22no—
23C2×D284C2×C411yescharacteristic
24C2×D284C2×C411yescharacteristic, complemented
25C2×C22⋊D71—22no—
26C2×C22⋊D71D412yes—
27D4×D71—42no—
28C2×C4×D71—21no—
29C2×C4×D71—42no—
30C2×C4×D71C2×C411yescharacteristic
31Dic71⋊C4—21no—
32C22⋊Dic71—22no—
33(C2×D71)⋊C4—21no—
34(C2×D71)⋊C4—22no—
35(C2×D71)⋊C4—42no—
36C4×Dic71C2×C411yescharacteristic, complemented
37C2×Q8×C71C2×C411yescharacteristic, complemented
38C2×D4×C71C2311yescharacteristic
39C22⋊C4×C71—22no—
40C22⋊C4×C71—22no—
41C42×C71C2×C411yescharacteristic, complemented
42C23×C71C2×D412yes—
43C22×D71—22no—
44C22×D71—22no—
45C22×D71—21no—
46C22×D71—82no—
47C22×D71C22⋊C412yes—
48C22×D71C22⋊C411yescharacteristic
49Q8×C71—41no—
50D4×C71—41no—
51C2×C4×C71—21no—
52C2×C4×C71—21no—
53C2×C4×C71—42no—
54C2×C4×C71C22×C411yescharacteristic
55C22⋊D71—42no—
56C22⋊D71—82no—
57C2×Dic71—21no—
58C2×Dic71—42no—
59C2×Dic71C22⋊C411yescharacteristic
60D284—41no—
61D284—41no—
62D284—42no—
63D284—82no—
64C4×D71—22no—
65C4×D71—42no—
66C4×D71—84no—
67C22×C71—22no—
68C22×C71—42no—
69C22×C71C2×C22⋊C411yescharacteristic
70C2×D71—22no—
71C2×D71—41no—
72C2×D71—44no—
73C2×D71—42no—
74C2×D71—42no—
75C2×D71—41no—
76C2×D71—82no—
77C2×D71#9912yes—
78C4×C71—21no—
79C4×C71—41no—
80C4×C71—41no—
81C4×C71—82no—
82Dic71—21no—
83Dic71—41no—
84Dic71—82no—
85C2×C71—21no—
86C2×C71—42no—
87C2×C71C2×#9911yescharacteristic
88D71—22no—
89D71—42no—
90D71—81no—
91#2127—711nomaximal, Sylow
92C71#212711yescharacteristic, complemented, Sylow
93#535—711no—
94C2×#99—712no—
95#354—711no—
96#354D7111yescharacteristic, complemented
97#353—712no—
98C2×#41—711no—
99C22×D4—711no—
100#127—711no—
101#127—711no—
102#124—711no—
103#124C2×D7111yescharacteristic
104#121—1422no—
105#120—1422no—
106#117—711no—
107C2×C22⋊C4—1422no—
108#99—712no—
109#99—1422no—
110#99C2×D7112yes—
111C24—712no—
112#41—2842no—
113C2×Q8C4×D7111yescharacteristic, complemented
114C2×D4—2842no—
115C2×D4—712no—
116C2×D4—711no—
117C2×D4—711no—
118C2×D4—1421no—
119C2×D4—1422no—
120C2×D4—1422no—
121C2×D4C22×D7111yescharacteristic
122C22×C4—2842no—
123C22×C4—711no—
124C22×C4—1421no—
125C4⋊C4—1421no—
126C22⋊C4—22no—
127C22⋊C4—22no—
128C22⋊C4—2842no—
129C22⋊C4—1421no—
130C22⋊C4—1422no—
131C22⋊C4—1422no—
132C42—711no—
133C42C4×D7111yescharacteristic, complemented
134C23—5682no—
135C23—711no—
136C23—712no—
137C23—1422no—
138C23—1422no—
139C23—1421no—
140C23D4×D7112yes—
141Q8—41no—
142D4—41no—
143D4—2841no—
144D4—2841no—
145D4—2842no—
146D4—2842no—
147D4—5682no—
148D4—5682no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—42no—
152C2×C4—2842no—
153C2×C4—2842no—
154C2×C4—5684no—
155C2×C4—711no—
156C2×C4—1422no—
157C2×C4—1421no—
158C2×C4C2×C4×D7111yescharacteristic
159C22—22no—
160C22—42no—
161C22—2842no—
162C22—2842no—
163C22—2841no—
164C22—2844no—
165C22—2841no—
166C22—5682no—
167C22—712no—
168C22—1422no—
169C22C22⋊C4×D7111yescharacteristic
170C4—21no—
171C4—41no—
172C4—41no—
173C4—82no—
174C4—2841no—
175C4—5682no—
176C4—1421no—
177C2—21no—
178C2—42no—
179C2—2842no—
180C2—5681no—
181C2—1422no—
182C2#99×D7111yescharacteristic
subgroupG/H
centerC2#99×D71
commutatorC2×C4×C71C22×C4
FrattiniC2×D4C22×D71
Fitting#354×C71C2
socleC2×C71C2×#99
hypercenter#354D71
hypocenterC71#2127
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
2. #99×D71C2semidirect
3. #17985794C2semidirect
4. #17985791C2semidirect
5. #354×C71C2semidirect
6. C2×#11765866C4semidirect
8. #14556125C4semidirect
10. #14556117C4semidirect
13. #14556085C4semidirect
24. C2×D284C2×C4semidirect
36. C4×Dic71C2×C4semidirect
37. C2×Q8×C71C2×C4semidirect
41. C42×C71C2×C4semidirect
92. C71#2127semidirect
96. #354D71semidirect
113. C2×Q8C4×D71semidirect
133. C42C4×D71semidirect