Finite Group Databasebeta

← #22588940

Subgroups — #22588940

Order 9088.

186 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 75 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#17986037C211yesmaximal, characteristic
2#17986025C211yesmaximal, characteristic
3#17985954C211yesmaximal, characteristic
4#17985764C211yesmaximal, characteristic
5#17985759C211yesmaximal, characteristic
6#17985759C211yesmaximal, characteristic
7#336×C71C211yesmaximal, characteristic
8C2×#11765849C2211yescharacteristic
9C2×#11765849C2211yescharacteristic
10#14556087C2211yescharacteristic
11#14556087C2211yescharacteristic
12#14556062C411yescharacteristic, complemented
13#14556062C411yescharacteristic, complemented
14#14556060C411yescharacteristic, complemented
15#14556060C411yescharacteristic, complemented
16Dic71⋊C8—21no—
17Dic71⋊C8—21no—
18#14556038—21no—
19C8×Dic71—21no—
20C22×C8×C71C2211yescharacteristic
21C22×C8×C71C2211yescharacteristic
22C2×C42×C71C2211yescharacteristic
23#11765849—21no—
24#11765849—21no—
25#11765849—21no—
26#11765849Q812yes—
27C2×C71⋊C8—21no—
28C2×C71⋊C8—21no—
29C4⋊Dic71C2×C411yescharacteristic
30C4⋊Dic71C2×C411yescharacteristic
31C4⋊Dic71C2×C411yescharacteristic
32C4⋊Dic71C2×C411yescharacteristic
33C22⋊Dic71—21no—
34C22⋊Dic71—21no—
35C4×Dic71—21no—
36C4×Dic71—21no—
37C22×C4×C71—21no—
38C22×C4×C71C2311yescharacteristic
39C2×C8×C71—21no—
40C2×C8×C71—21no—
41C2×C8×C71—21no—
42C2×C8×C71—21no—
43C2×C8×C71C2×C411yescharacteristic
44C2×C8×C71C2×C411yescharacteristic
45C2×C8×C71D411yescharacteristic
46C2×C8×C71D411yescharacteristic
47C42×C71—21no—
48C42×C71—21no—
49C23×C71#4111yescharacteristic
50C2×C4×C71—22no—
51C2×C4×C71—41no—
52C2×C4×C71—41no—
53C2×C4×C71C22×C411yescharacteristic
54C2×C4×C71C2×D411yescharacteristic
55C2×C4×C71C2×Q811yescharacteristic
56C2×C4×C71#4111yescharacteristic
57C2×C4×C71#4111yescharacteristic
58C2×C4×C71#4111yescharacteristic
59C2×Dic71—21no—
60C2×Dic71—21no—
61C2×Dic71—21no—
62C2×Dic71—21no—
63C8×C71—21no—
64C8×C71—21no—
65C8×C71—21no—
66C8×C71—21no—
67C71⋊C8—22no—
68C71⋊C8—41no—
69C22×C71—21no—
70C22×C71—21no—
71C22×C71C4×D411yescharacteristic
72C22×C71#12511yescharacteristic
73C22×C71#12611yescharacteristic
74C4×C71—42no—
75C4×C71#11711yescharacteristic
76C4×C71C4×Q811yescharacteristic
77C4×C71C22⋊Q811yescharacteristic
78C4×C71#12311yescharacteristic
79Dic71—41no—
80Dic71—41no—
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#405—711no—
93#341—711no—
94#339—711no—
95#339—711no—
96#336D7111yescharacteristic
97C2×M16—711no—
98C2×M16—711no—
99C22×C8C2×D7111yescharacteristic
100C22×C8C2×D7111yescharacteristic
101#117—711no—
102#117—711no—
103C2×C42C2×D7111yescharacteristic
104#107—711no—
105#107—711no—
106#106—711no—
107#106—711no—
108C4⋊C8—1421no—
109C4⋊C8—1421no—
110#97—1421no—
111C4×C8—1421no—
112C22×C4—21no—
113C22×C4C22×D7111yescharacteristic
114M16—712no—
115M16—1421no—
116M16—1421no—
117M16—1421no—
118C2×C8—21no—
119C2×C8—21no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—1421no—
123C2×C8—1421no—
124C2×C8C4×D7111yescharacteristic
125C2×C8C4×D7111yescharacteristic
126C2×C8D28411yescharacteristic
127C2×C8D28411yescharacteristic
128C4⋊C4—711no—
129C4⋊C4—711no—
130C4⋊C4—711no—
131C4⋊C4—711no—
132C22⋊C4—1421no—
133C22⋊C4—1421no—
134C42—21no—
135C42—21no—
136C42—1421no—
137C42—1421no—
138C23#1176586511yescharacteristic
139C2×C4—22no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—1421no—
143C2×C4—1421no—
144C2×C4—1421no—
145C2×C4—1421no—
146C2×C4C2×C4×D7111yescharacteristic
147C2×C4C2×D28411yescharacteristic
148C2×C4Q8×D7111yescharacteristic
149C2×C4#1176586411yescharacteristic
150C2×C4#1176586411yescharacteristic
151C2×C4#1176586411yescharacteristic
152C8—21no—
153C8—21no—
154C8—21no—
155C8—21no—
156C8—2841no—
157C8—1422no—
158C22—21no—
159C22—21no—
160C22C4×D28411yescharacteristic
161C22#1455611811yescharacteristic
162C22#1455612111yescharacteristic
163C4—42no—
164C4—2841no—
165C4—2841no—
166C4—2841no—
167C4—2841no—
168C4#1455608411yescharacteristic
169C4#1455609311yescharacteristic
170C4#1455610811yescharacteristic
171C4#1455611211yescharacteristic
172C2—21no—
173C2—21no—
174C2#1798588411yescharacteristic
175C2#1798611711yescharacteristic
176C2#1798612211yescharacteristic
subgroupG/H
centerC2×C4C2×D284
commutatorC2×C4×C71C22×C4
FrattiniC22×C4C22×D71
Fitting#336×C71C2
socleC22×C71C4×D4
hypercenter#336D71
hypocenterC71#1922
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #336

Complements

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

NH ≅ G/Ntype
12. #14556062C4semidirect
13. #14556062C4semidirect
14. #14556060C4semidirect
15. #14556060C4semidirect
89. C71#1922semidirect