Finite Group Databasebeta

← #22589286

Subgroups — #22589286

Order 9088.

292 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 107 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
1C2×#14556127C211yesmaximal, characteristic
2C2×Dic71⋊C8C211yesmaximal, characteristic
3C4⋊C4×Dic71C211yesmaximal, characteristic
4#17985762C211yesmaximal, characteristic
5#17985761C211yesmaximal, characteristic
6#17985761C211yesmaximal, characteristic
7#340×C71C211yesmaximal, characteristic
8C22×Dic142—21no—
9C22×C71⋊C8C2211yescharacteristic
10#14556127—22no—
11#14556127C414yescomplemented
12C2×C4⋊Dic71C2211yescharacteristic
13C2×C4⋊Dic71C2211yescharacteristic
14C2×Dic71⋊C4—21no—
15C2×C4×Dic71—21no—
16C2×C4×Dic71C2211yescharacteristic
17Dic71⋊C8—22no—
18C71⋊#95—21no—
19C22×C8×C71C2211yescharacteristic
20C2×C4⋊C4×C71C2211yescharacteristic
21C2×C4⋊C4×C71C2211yescharacteristic
22C2×Dic142—24no—
23C2×Dic142—42no—
24C2×Dic142—42no—
25C22×Dic71—21no—
26C22×Dic71—21no—
27C22×Dic71D411yescharacteristic
28C22×Dic71D411yescharacteristic
29C2×C71⋊C8—21no—
30C2×C71⋊C8—21no—
31C2×C71⋊C8—21no—
32C4⋊Dic71—21no—
33C4⋊Dic71—21no—
34C4⋊Dic71C2×C412yes—
35C4⋊Dic71Q812yescomplemented
36Dic71⋊C4—24no—
37C4×Dic71—42no—
38C4×Dic71C2×C412yes—
39C4×Dic71D412yes—
40C22×C4×C71—21no—
41C22×C4×C71—21no—
42C22×C4×C71C2311yescharacteristic
43C2×C8×C71—21no—
44C2×C8×C71—21no—
45C2×C8×C71—21no—
46C4⋊C4×C71—21no—
47C4⋊C4×C71—21no—
48C4⋊C4×C71C2×C412yes—
49C4⋊C4×C71Q812yescomplemented
50C23×C71C2×D411yescharacteristic
51C2×C4×C71—22no—
52C2×C4×C71—22no—
53C2×C4×C71—41no—
54C2×C4×C71—41no—
55C2×C4×C71—41no—
56C2×C4×C71—41no—
57C2×C4×C71C22×C411yescharacteristic
58C2×C4×C71C2×D411yescharacteristic
59C2×C4×C71C2×Q811yescharacteristic
60C2×C4×C71C2×Q811yescharacteristic
61C2×C4×C71#4111yescharacteristic
62C2×C4×C71#4111yescharacteristic
63C2×Dic71—21no—
64C2×Dic71—21no—
65C2×Dic71—22no—
66C2×Dic71—22no—
67C2×Dic71—41no—
68C2×Dic71—41no—
69C2×Dic71—41no—
70C2×Dic71—41no—
71C2×Dic71C22⋊C412yes—
72C2×Dic71C22⋊C412yes—
73C2×Dic71SD1612yes—
74C2×Dic71Q1612yes—
75Dic142—48no—
76C8×C71—41no—
77C71⋊C8—41no—
78C22×C71C2×C22⋊C411yescharacteristic
79C22×C71C22⋊Q811yescharacteristic
80C22×C71C22⋊Q811yescharacteristic
81C22×C71C2×SD1611yescharacteristic
82C22×C71C2×Q1611yescharacteristic
83C22×C71AGL(1,ℤ/8)11yescharacteristic
84C22×C71AGL(1,ℤ/8)11yescharacteristic
85C4×C71—42no—
86C4×C71—42no—
87C4×C71C4×Q811yescharacteristic
88C4×C71C4×Q811yescharacteristic
89C4×C71#12411yescharacteristic
90C4×C71C4⋊Q811yescharacteristic
91Dic71—22no—
92Dic71—42no—
93Dic71—42no—
94Dic71#10314yes—
95C2×C71#39111yescharacteristic
96C2×C71C2×#10311yescharacteristic
97C2×C71#41811yescharacteristic
98C2×C71#47611yescharacteristic
99C2×C71#47611yescharacteristic
100C2×C71#47711yescharacteristic
101C2×C71#47711yescharacteristic
102#1987—711nomaximal, Sylow
103C71#198711yescharacteristic, complemented, Sylow
104C2×C4⋊Q8—711no—
105C2×C4⋊C8—711no—
106C4×C4⋊C4—711no—
107#340—711no—
108#340—711no—
109#340—711no—
110#340D7111yescharacteristic
111C22×Q8—1421no—
112C22×C8—711no—
113C22×C8C2×D7111yescharacteristic
114C4⋊Q8—714no—
115C4⋊Q8—1422no—
116C2×C4⋊C4—711no—
117C2×C4⋊C4—711no—
118C2×C4⋊C4—1421no—
119C2×C4⋊C4C2×D7111yescharacteristic
120C2×C4⋊C4C2×D7111yescharacteristic
121C2×C42—711no—
122C2×C42—1421no—
123C4⋊C8—1422no—
124#95—1421no—
125C2×Q8—2842no—
126C2×Q8—2842no—
127C2×Q8—1424no—
128C22×C4—21no—
129C22×C4—21no—
130C22×C4—711no—
131C22×C4—711no—
132C22×C4—1421no—
133C22×C4—1421no—
134C22×C4C22×D7111yescharacteristic
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—1421no—
139C2×C8—1421no—
140C2×C8—1421no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—712no—
144C4⋊C4—712no—
145C4⋊C4—1424no—
146C4⋊C4—1421no—
147C4⋊C4—1421no—
148C4⋊C4Dic14212yescomplemented
149C4⋊C4C4×D7112yes—
150C42—2842no—
151C42—712no—
152C42—712no—
153C23D4×D7111yescharacteristic
154Q8—2848no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—2841no—
162C2×C4—2841no—
163C2×C4—2841no—
164C2×C4—2841no—
165C2×C4—712no—
166C2×C4—712no—
167C2×C4—712no—
168C2×C4—712no—
169C2×C4—1422no—
170C2×C4—1422no—
171C2×C4—1421no—
172C2×C4—1421no—
173C2×C4C2×C4×D7111yescharacteristic
174C2×C4D4×D7111yescharacteristic
175C2×C4Q8×D7111yescharacteristic
176C2×C4C2×Dic14211yescharacteristic
177C2×C4#1176586411yescharacteristic
178C2×C4#1176586511yescharacteristic
179C8—41no—
180C8—2841no—
181C22C22⋊C4×D7111yescharacteristic
182C22#1455610511yescharacteristic
183C22#1455610611yescharacteristic
184C22SD16×D7111yescharacteristic
185C22Q16×D7111yescharacteristic
186C22#1455615211yescharacteristic
187C22#1455615511yescharacteristic
188C4—42no—
189C4—42no—
190C4—2842no—
191C4—2842no—
192C4—714no—
193C4—1422no—
194C4#1455609311yescharacteristic
195C4C4×Dic14211yescharacteristic
196C4#1455611411yescharacteristic
197C4#1455612711yescharacteristic
198C2#1798590311yescharacteristic
199C2#103×D7111yescharacteristic
200C2#1798600211yescharacteristic
201C2#1798628711yescharacteristic
202C2#1798628811yescharacteristic
203C2#1798629211yescharacteristic
204C2#1798629311yescharacteristic
subgroupG/H
centerC23D4×D71
commutatorC2×C4×C71C22×C4
FrattiniC22×C4C22×D71
Fitting#340×C71C2
socleC23×C71C2×D4
hypercenter#340D71
hypocenterC71#1987
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
11. #14556127C4semidirect
35. C4⋊Dic71Q8semidirect
49. C4⋊C4×C71Q8semidirect
103. C71#1987semidirect
148. C4⋊C4Dic142semidirect