Finite Group Databasebeta

← #22589296

Subgroups — #22589296

Order 9088.

260 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 99 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×#14556119C211yesmaximal, characteristic
2C2×Dic71⋊C8C211yesmaximal, characteristic
3C4⋊C4×Dic71C211yesmaximal, characteristic
4#17985762C211yesmaximal, characteristic
5#17985761C211yesmaximal, characteristic
6#17985761C211yesmaximal, characteristic
7#340×C71C211yesmaximal, characteristic
8C22×C71⋊C8C2211yescharacteristic
9#14556119—22no—
10#14556119C414yescomplemented
11C2×C4⋊Dic71—21no—
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
22C22×Dic71—21no—
23C22×Dic71—21no—
24C22×Dic71D411yescharacteristic
25C22×Dic71D411yescharacteristic
26C2×C71⋊C8—21no—
27C2×C71⋊C8—21no—
28C2×C71⋊C8—21no—
29C4⋊Dic71—21no—
30C4⋊Dic71—21no—
31C4⋊Dic71—24no—
32C4⋊Dic71C2×C412yes—
33C4⋊Dic71Q812yes—
34Dic71⋊C4—24no—
35C4×Dic71—42no—
36C4×Dic71C2×C412yes—
37C4×Dic71D412yes—
38C22×C4×C71—21no—
39C22×C4×C71—21no—
40C22×C4×C71C2311yescharacteristic
41C2×C8×C71—21no—
42C2×C8×C71—21no—
43C2×C8×C71—21no—
44C4⋊C4×C71—21no—
45C4⋊C4×C71—21no—
46C4⋊C4×C71C2×C412yes—
47C4⋊C4×C71Q812yes—
48C23×C71C2×D411yescharacteristic
49C2×C4×C71—22no—
50C2×C4×C71—22no—
51C2×C4×C71—41no—
52C2×C4×C71—41no—
53C2×C4×C71—41no—
54C2×C4×C71—41no—
55C2×C4×C71C22×C411yescharacteristic
56C2×C4×C71C2×D411yescharacteristic
57C2×C4×C71C2×Q811yescharacteristic
58C2×C4×C71C2×Q811yescharacteristic
59C2×C4×C71#4111yescharacteristic
60C2×C4×C71#4111yescharacteristic
61C2×Dic71—21no—
62C2×Dic71—21no—
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—
73C8×C71—41no—
74C71⋊C8—41no—
75C22×C71C2×C22⋊C411yescharacteristic
76C22×C71C22⋊Q811yescharacteristic
77C22×C71C22⋊Q811yescharacteristic
78C22×C71#13511yescharacteristic
79C22×C71#13511yescharacteristic
80C22×C71AGL(1,ℤ/8)11yescharacteristic
81C22×C71#13711yescharacteristic
82C4×C71—42no—
83C4×C71—42no—
84C4×C71C4×Q811yescharacteristic
85C4×C71C4×Q811yescharacteristic
86C4×C71#12411yescharacteristic
87C4×C71C4⋊Q811yescharacteristic
88Dic71—22no—
89Dic71—22no—
90Dic71—42no—
91Dic71—42no—
92C2×C71#39111yescharacteristic
93C2×C71#41611yescharacteristic
94C2×C71#41711yescharacteristic
95C2×C71#47811yescharacteristic
96C2×C71#47811yescharacteristic
97C2×C71#47911yescharacteristic
98C2×C71#47911yescharacteristic
99#1989—711nomaximal, Sylow
100C71#198911yescharacteristic, complemented, Sylow
101C2×#125—711no—
102C2×C4⋊C8—711no—
103C4×C4⋊C4—711no—
104#340—711no—
105#340—711no—
106#340—711no—
107#340D7111yescharacteristic
108C22×C8—711no—
109C22×C8C2×D7111yescharacteristic
110#125—714no—
111#125—1422no—
112C2×C4⋊C4—711no—
113C2×C4⋊C4—711no—
114C2×C4⋊C4—1421no—
115C2×C4⋊C4—1421no—
116C2×C4⋊C4C2×D7111yescharacteristic
117C2×C4⋊C4C2×D7111yescharacteristic
118C2×C42—711no—
119C2×C42—1421no—
120C4⋊C8—1422no—
121#95—1421no—
122C22×C4—21no—
123C22×C4—21no—
124C22×C4—711no—
125C22×C4—711no—
126C22×C4—1421no—
127C22×C4—1421no—
128C22×C4C22×D7111yescharacteristic
129C2×C8—21no—
130C2×C8—21no—
131C2×C8—21no—
132C2×C8—1421no—
133C2×C8—1421no—
134C2×C8—1421no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—712no—
138C4⋊C4—712no—
139C4⋊C4—1424no—
140C4⋊C4—1424no—
141C4⋊C4—1421no—
142C4⋊C4—1421no—
143C4⋊C4Dic14212yes—
144C4⋊C4C4×D7112yes—
145C42—2842no—
146C42—712no—
147C42—712no—
148C23D4×D7111yescharacteristic
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—2841no—
156C2×C4—2841no—
157C2×C4—2841no—
158C2×C4—2841no—
159C2×C4—712no—
160C2×C4—712no—
161C2×C4—1422no—
162C2×C4—1422no—
163C2×C4—1421no—
164C2×C4—1421no—
165C2×C4—1421no—
166C2×C4—1421no—
167C2×C4C2×C4×D7111yescharacteristic
168C2×C4D4×D7111yescharacteristic
169C2×C4Q8×D7111yescharacteristic
170C2×C4C2×Dic14211yescharacteristic
171C2×C4#1176586411yescharacteristic
172C2×C4#1176586511yescharacteristic
173C8—41no—
174C8—2841no—
175C22C22⋊C4×D7111yescharacteristic
176C22#1455610511yescharacteristic
177C22#1455610611yescharacteristic
178C22#1455614711yescharacteristic
179C22#1455614911yescharacteristic
180C22#1455615511yescharacteristic
181C22#1455616011yescharacteristic
182C4—42no—
183C4—42no—
184C4—2842no—
185C4—2842no—
186C4—1422no—
187C4—1422no—
188C4#1455609311yescharacteristic
189C4C4×Dic14211yescharacteristic
190C4#1455611411yescharacteristic
191C4#1455612711yescharacteristic
192C2#1798590311yescharacteristic
193C2#1798599211yescharacteristic
194C2#1798599911yescharacteristic
195C2#1798629711yescharacteristic
196C2#1798629811yescharacteristic
197C2#1798630411yescharacteristic
198C2#1798630511yescharacteristic
subgroupG/H
centerC23D4×D71
commutatorC2×C4×C71C22×C4
FrattiniC22×C4C22×D71
Fitting#340×C71C2
socleC23×C71C2×D4
hypercenter#340D71
hypocenterC71#1989
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
10. #14556119C4semidirect
100. C71#1989semidirect