Finite Group Databasebeta

← #22588939

Subgroups — #22588939

Order 9088.

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

normal subgroups only

This group has 186 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#17986035C211yesmaximal, characteristic
2#17986025C211yesmaximal, characteristic
3#17985763C211yesmaximal, characteristic
4#17985760C211yesmaximal, characteristic
5#17985758C211yesmaximal, characteristic
6#17985753C211yesmaximal, characteristic
7#405×C71C211yesmaximal, characteristic
8C2×#11765849C2211yescharacteristic
9C22×C71⋊C8C2211yescharacteristic
10#14556087C2211yescharacteristic
11C2×C4×Dic71C2211yescharacteristic
12#14556061C411yescharacteristic, complemented
13#14556061C411yescharacteristic, complemented
14#14556059C411yescharacteristic, complemented
15#14556059C411yescharacteristic, complemented
16Dic71⋊C8—21no—
17Dic71⋊C8—21no—
18C2×M16×C71C2211yescharacteristic
19C22×C8×C71C2211yescharacteristic
20#117×C71C2211yescharacteristic
21#97×C71—21no—
22C4×C8×C71—21no—
23C22×Dic71—21no—
24#11765849—21no—
25#11765849—21no—
26C2×C71⋊C8—21no—
27C2×C71⋊C8—21no—
28C2×C71⋊C8—21no—
29C2×C71⋊C8C2×C411yescharacteristic
30C2×C71⋊C8C2×C411yescharacteristic
31C4⋊Dic71C2×C411yescharacteristic
32C4⋊Dic71C2×C411yescharacteristic
33C22⋊Dic71—21no—
34C4×Dic71—21no—
35C4×Dic71—21no—
36C4×Dic71—21no—
37C22×C4×C71C2311yescharacteristic
38M16×C71—21no—
39M16×C71Q812yes—
40C2×C8×C71—21no—
41C2×C8×C71—21no—
42C2×C8×C71—21no—
43C2×C8×C71D411yescharacteristic
44C2×C8×C71D411yescharacteristic
45C4⋊C4×C71C2×C411yescharacteristic
46C4⋊C4×C71C2×C411yescharacteristic
47C22⋊C4×C71—21no—
48C42×C71—21no—
49C23×C71#4111yescharacteristic
50C2×C4×C71—21no—
51C2×C4×C71—21no—
52C2×C4×C71C22×C411yescharacteristic
53C2×C4×C71C2×D411yescharacteristic
54C2×C4×C71C2×Q811yescharacteristic
55C2×C4×C71#4111yescharacteristic
56C2×C4×C71#4111yescharacteristic
57C2×C4×C71#4111yescharacteristic
58C2×Dic71—22no—
59C2×Dic71—21no—
60C2×Dic71—21no—
61C2×Dic71—41no—
62C2×Dic71—41no—
63C8×C71—22no—
64C8×C71—21no—
65C8×C71—21no—
66C71⋊C8—21no—
67C71⋊C8—21no—
68C71⋊C8—41no—
69C22×C71—21no—
70C22×C71—21no—
71C22×C71C4×D411yescharacteristic
72C22×C71#12511yescharacteristic
73C22×C71#12611yescharacteristic
74C4×C71—41no—
75C4×C71—41no—
76C4×C71#11711yescharacteristic
77C4×C71C4×Q811yescharacteristic
78C4×C71C22⋊Q811yescharacteristic
79C4×C71#12311yescharacteristic
80Dic71—42no—
81Dic71—41no—
82Dic71—41no—
83C2×C71—21no—
84C2×C71—21no—
85C2×C71#38711yescharacteristic
86C2×C71#44311yescharacteristic
87C2×C71#44411yescharacteristic
88#1922—711nomaximal, Sylow
89C71#192211yescharacteristic, complemented, Sylow
90#427—711no—
91#424—711no—
92#405D7111yescharacteristic
93#341—711no—
94#339—711no—
95#339—711no—
96#336—711no—
97C2×M16—711no—
98C2×M16C2×D7111yescharacteristic
99C22×C8—711no—
100C22×C8C2×D7111yescharacteristic
101#117—711no—
102#117C2×D7111yescharacteristic
103C2×C42—711no—
104#107—711no—
105#107—711no—
106#106—711no—
107#106—711no—
108C4⋊C8—1421no—
109C4⋊C8—1421no—
110#97—21no—
111C4×C8—21no—
112C22×C4—1421no—
113C22×C4C22×D7111yescharacteristic
114M16—21no—
115M16—1421no—
116M16—1421no—
117M16Dic14212yes—
118C2×C8—21no—
119C2×C8—21no—
120C2×C8—21no—
121C2×C8—711no—
122C2×C8—711no—
123C2×C8—1421no—
124C2×C8—1421no—
125C2×C8—1421no—
126C2×C8C22⋊D7111yescharacteristic
127C2×C8C22⋊D7111yescharacteristic
128C4⋊C4—711no—
129C4⋊C4—711no—
130C4⋊C4C4×D7111yescharacteristic
131C4⋊C4C4×D7111yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—1421no—
134C42—21no—
135C42—1421no—
136C42—1421no—
137C42—1421no—
138C23#1176586511yescharacteristic
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—2841no—
142C2×C4—2841no—
143C2×C4—1422no—
144C2×C4—1421no—
145C2×C4—1421no—
146C2×C4C2×C4×D7111yescharacteristic
147C2×C4C2×C22⋊D7111yescharacteristic
148C2×C4C2×Dic14211yescharacteristic
149C2×C4#1176586511yescharacteristic
150C2×C4#1176586511yescharacteristic
151C2×C4#1176586511yescharacteristic
152C8—22no—
153C8—21no—
154C8—21no—
155C8—2841no—
156C8—1421no—
157C8—1421no—
158C22—21no—
159C22—21no—
160C22C4×C22⋊D7111yescharacteristic
161C22#1455612011yescharacteristic
162C22#1455612211yescharacteristic
163C4—41no—
164C4—41no—
165C4—2842no—
166C4—2841no—
167C4—2841no—
168C4#1455608511yescharacteristic
169C4C4×Dic14211yescharacteristic
170C4#1455610711yescharacteristic
171C4#1455611111yescharacteristic
172C2—21no—
173C2—21no—
174C2#1798588311yescharacteristic
175C2#1798611411yescharacteristic
176C2#1798611911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D71
commutatorC2×C4×C71C22×C4
FrattiniC22×C4C22×D71
Fitting#405×C71C2
socleC22×C71C4×D4
hypercenter#405D71
hypocenterC71#1922
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #405

Complements

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

NH ≅ G/Ntype
12. #14556061C4semidirect
13. #14556061C4semidirect
14. #14556059C4semidirect
15. #14556059C4semidirect
89. C71#1922semidirect