Finite Group Databasebeta

← #22586962

Subgroups — #22586962

Order 9088.

248 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 59 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#124×D71C211yesmaximal, characteristic
2#17986054C212yesmaximal, complemented
3#17985739C211yesmaximal, characteristic, complemented
4#17985738C212yesmaximal, complemented
5#329×C71C211yesmaximal, characteristic, complemented
6C2×Q8×D71C411yescharacteristic
7C2×D4×D71C411yescharacteristic
8#14556117C411yescharacteristic
9#14556116C2211yescharacteristic
10#14556115C411yescharacteristic
11#14556114—22no—
12C22⋊C4×D71—22no—
13C42×D71C2211yescharacteristic
14Dic71⋊C8—22no—
15(C2×D71)⋊C8—22no—
16#14556039C2212yescomplemented
17#124×C71C2211yescharacteristic
18#97×C71C2212yescomplemented
19C23×D71—21no—
20C2×Dic142—21no—
21C2×Dic142C2×C411yescharacteristic
22Q8×D71—42no—
23C2×D284C2×C411yescharacteristic
24C2×C22⋊D71—21no—
25D4×D71—42no—
26C2×C4×D71—21no—
27C2×C4×D71C2×C411yescharacteristic
28C2×C4×D71D412yes—
29C2×C71⋊C8—22no—
30C22⋊Dic71—22no—
31(C2×D71)⋊C4—22no—
32(C2×D71)⋊C4—22no—
33C4×Dic71C2×C411yescharacteristic
34C4×Dic71D412yes—
35C2×Q8×C71C2×C411yescharacteristic
36C2×D4×C71C2×C411yescharacteristic
37C2×C8×C71—22no—
38C22⋊C4×C71—22no—
39C42×C71C2311yescharacteristic
40C23×C71—21no—
41C22×D71—21no—
42C22×D71—44no—
43C22×D71—42no—
44C22×D71C22⋊C411yescharacteristic
45Q8×C71—41no—
46D4×C71—41no—
47C2×C4×C71—21no—
48C2×C4×C71C22×C411yescharacteristic
49C2×C4×C71C2×D412yes—
50C22⋊D71—42no—
51C2×Dic71—21no—
52C2×Dic71C22⋊C412yes—
53C2×Dic71C22⋊C411yescharacteristic
54D284—41no—
55C4×D71—22no—
56C4×D71—42no—
57C4×D71—42no—
58Dic142—42no—
59Dic142—41no—
60C8×C71—42no—
61C71⋊C8—42no—
62C22×C71—41no—
63C22×C71—42no—
64C22×C71C2×C22⋊C411yescharacteristic
65C2×D71—22no—
66C2×D71—41no—
67C2×D71—42no—
68C2×D71—84no—
69C2×D71#10012yes—
70C4×C71—21no—
71C4×C71—22no—
72C4×C71—41no—
73Dic71—21no—
74Dic71—22no—
75Dic71—41no—
76C2×C71—81no—
77C2×C71C2×#10011yescharacteristic
78C2×C71#42112yes—
79D71—22no—
80D71—81no—
81#1533—711nomaximal, Sylow
82C71#153311yescharacteristic, complemented, Sylow
83C2×#124—711no—
84#432—712no—
85#329—711no—
86#329—712no—
87#329D7111yescharacteristic, complemented
88C22×Q8—711no—
89C22×D4—711no—
90#124—711no—
91#124—711no—
92#124—711no—
93#124—1422no—
94#124C2×D7111yescharacteristic
95C2×C22⋊C4—1422no—
96C2×C42—711no—
97C4⋊C8—1422no—
98C22⋊C8—1422no—
99#97—712no—
100#97C2×D7112yescomplemented
101C24—1421no—
102C2×Q8—2842no—
103C2×Q8—711no—
104C2×Q8—1421no—
105C2×Q8C4×D7111yescharacteristic
106C2×D4—2842no—
107C2×D4—711no—
108C2×D4—1421no—
109C2×D4C4×D7111yescharacteristic
110C22×C4—712no—
111C22×C4—711no—
112C22×C4—1421no—
113C2×C8—22no—
114C2×C8—1422no—
115C22⋊C4—22no—
116C22⋊C4—1422no—
117C22⋊C4—1422no—
118C22⋊C4—1422no—
119C42—711no—
120C42—712no—
121C42C22×D7111yescharacteristic
122C23—21no—
123C23—2842no—
124C23—2844no—
125C23—711no—
126C23—1421no—
127Q8—41no—
128Q8—2841no—
129Q8—2842no—
130D4—41no—
131D4—2841no—
132D4—2842no—
133C2×C4—21no—
134C2×C4—2842no—
135C2×C4—2842no—
136C2×C4—712no—
137C2×C4—711no—
138C2×C4—1422no—
139C2×C4—1421no—
140C2×C4C2×C4×D7111yescharacteristic
141C2×C4D4×D7112yes—
142C8—42no—
143C8—2842no—
144C22—41no—
145C22—42no—
146C22—2841no—
147C22—2842no—
148C22—5684no—
149C22—712no—
150C22—1422no—
151C22C22⋊C4×D7111yescharacteristic
152C4—21no—
153C4—22no—
154C4—41no—
155C4—2841no—
156C4—1421no—
157C4—1422no—
158C2—81no—
159C2—5681no—
160C2—1422no—
161C2#100×D7111yescharacteristic
162C2#1798601412yes—
subgroupG/H
centerC22C22⋊C4×D71
commutatorC2×C4×C71C22×C4
FrattiniC42C22×D71
Fitting#329×C71C2
socleC22×C71C2×C22⋊C4
hypercenter#329D71
hypocenterC71#1533
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #17986054C2semidirect
3. #17985739C2semidirect
4. #17985738C2semidirect
5. #329×C71C2semidirect
16. #14556039C22semidirect
18. #97×C71C22semidirect
82. C71#1533semidirect
87. #329D71semidirect
100. #97C2×D71semidirect