Finite Group Databasebeta

← #22586798

Subgroups — #22586798

Order 9088.

230 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 77 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
2C2×C4×C71⋊C8C211yesmaximal, characteristic, complemented
3#17985729C212yesmaximal, complemented
4#17985726C212yesmaximal, complemented
5#432×C71C211yesmaximal, characteristic, complemented
6C22×C71⋊C8—21no—
7#14556122—21no—
8#14556120C411yescharacteristic
9#14556116C411yescharacteristic
10#14556111—21no—
11#14556107C411yescharacteristic
12#14556102C411yescharacteristic
13C4×Dic142C2211yescharacteristic
14C4×D284C2211yescharacteristic
15C4×C22⋊D71—21no—
16#14556085—21no—
17C4×C71⋊C8—21no—
18C4×C71⋊C8C2212yes—
19C2×C42×C71C2211yescharacteristic
20C4⋊C8×C71C2212yes—
21C22⋊C8×C71—21no—
22#97×C71—21no—
23C2×Dic142C2×C411yescharacteristic
24C2×D284C2×C411yescharacteristic
25C2×C22⋊D71—21no—
26C2×C4×D71—21no—
27C2×C71⋊C8—24no—
28C2×C71⋊C8—22no—
29C4⋊Dic71C2×C411yescharacteristic
30C4⋊Dic71C2×C411yescharacteristic
31Dic71⋊C4—21no—
32Dic71⋊C4—21no—
33Dic71⋊C4—21no—
34Dic71⋊C4—21no—
35C22⋊Dic71—21no—
36(C2×D71)⋊C4—21no—
37(C2×D71)⋊C4—21no—
38(C2×D71)⋊C4—21no—
39(C2×D71)⋊C4—21no—
40C4×Dic71—21no—
41C22×C4×C71C2×C411yescharacteristic
42C22×C4×C71D411yescharacteristic
43C22×C4×C71D411yescharacteristic
44C2×C8×C71—22no—
45C42×C71C2×C411yescharacteristic
46C42×C71D411yescharacteristic
47C42×C71D411yescharacteristic
48C42×C71C2311yescharacteristic
49C23×C71C22⋊C411yescharacteristic
50C22×D71—21no—
51C2×C4×C71—22no—
52C2×C4×C71—22no—
53C2×C4×C71—22no—
54C2×C4×C71C22⋊C411yescharacteristic
55C2×C4×C71C22⋊C411yescharacteristic
56C2×C4×C71C22⋊C411yescharacteristic
57C2×C4×C71C22×C411yescharacteristic
58C2×C4×C71C2×D411yescharacteristic
59C2×C4×C71C2×D411yescharacteristic
60C22⋊D71—42no—
61C2×Dic71—21no—
62C2×Dic71—21no—
63C2×Dic71—21no—
64D284—22no—
65C4×D71—42no—
66Dic142—22no—
67C8×C71—42no—
68C71⋊C8—24no—
69C22×C71—21no—
70C22×C71—21no—
71C22×C71#10412yes—
72C22×C71C2×C22⋊C411yescharacteristic
73C2×D71—41no—
74C2×D71—41no—
75C2×D71—41no—
76C4×C71—21no—
77C4×C71—21no—
78C4×C71—21no—
79C4×C71—21no—
80C4×C71#13112yes—
81C4×C71#13512yes—
82Dic71—41no—
83Dic71—41no—
84Dic71—41no—
85C2×C71—22no—
86C2×C71#40811yescharacteristic
87C2×C71#41611yescharacteristic
88C2×C71C2×#10411yescharacteristic
89D71—81no—
90#1494—711nomaximal, Sylow
91C71#149411yescharacteristic, complemented, Sylow
92#529—711no—
93#432D7111yescharacteristic, complemented
94C2×C4×C8—711no—
95Q8⋊C8—712no—
96D4⋊C8—712no—
97C22×C8—1421no—
98#126—1421no—
99#125—711no—
100#124—711no—
101#123—1421no—
102C22⋊Q8—711no—
103#121—711no—
104C4×Q8—711no—
105C4×D4—711no—
106C4×D4—1421no—
107#117—1421no—
108C2×C42C2×D7111yescharacteristic
109C4⋊C8C2×D7112yes—
110C22⋊C8—21no—
111#97—21no—
112C4×C8—712no—
113C4×C8—1421no—
114C2×Q8—711no—
115C2×D4—711no—
116C2×D4—1421no—
117C22×C4—1421no—
118C22×C4C4×D7111yescharacteristic
119C22×C4D28411yescharacteristic
120C22×C4C22⋊D7111yescharacteristic
121C2×C8—22no—
122C2×C8—1424no—
123C2×C8—1422no—
124C4⋊C4—711no—
125C4⋊C4—711no—
126C4⋊C4—1421no—
127C4⋊C4—1421no—
128C4⋊C4—1421no—
129C4⋊C4—1421no—
130C22⋊C4—1421no—
131C22⋊C4—1421no—
132C22⋊C4—1421no—
133C22⋊C4—1421no—
134C22⋊C4—1421no—
135C42—1421no—
136C42C4×D7111yescharacteristic
137C42D28411yescharacteristic
138C42C22⋊D7111yescharacteristic
139C42C22×D7111yescharacteristic
140C23—1421no—
141C23(C2×D71)⋊C411yescharacteristic
142Q8—1422no—
143D4—2842no—
144D4—1422no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—2842no—
149C2×C4—1421no—
150C2×C4—1421no—
151C2×C4—1421no—
152C2×C4(C2×D71)⋊C411yescharacteristic
153C2×C4(C2×D71)⋊C411yescharacteristic
154C2×C4(C2×D71)⋊C411yescharacteristic
155C2×C4C2×C4×D7111yescharacteristic
156C2×C4C2×C22⋊D7111yescharacteristic
157C2×C4C2×D28411yescharacteristic
158C8—42no—
159C8—1424no—
160C22—21no—
161C22—21no—
162C22—2841no—
163C22—2841no—
164C22—2841no—
165C22#1455605412yes—
166C22C2×(C2×D71)⋊C411yescharacteristic
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—2841no—
172C4—2841no—
173C4—2841no—
174C4#1455613612yes—
175C4#1455614812yes—
176C2—22no—
177C2—5681no—
178C2#1798596711yescharacteristic
179C2#1798599311yescharacteristic
180C2C2×#1455605411yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D71
commutatorC2×C4×C71C22×C4
FrattiniC42C22×D71
Fitting#432×C71C2
socleC22×C71C2×C22⋊C4
hypercenter#432D71
hypocenterC71#1494
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C2×C4×C71⋊C8C2semidirect
3. #17985729C2semidirect
4. #17985726C2semidirect
5. #432×C71C2semidirect
91. C71#1494semidirect
93. #432D71semidirect