Finite Group Databasebeta

← #22589311

Subgroups — #22589311

Order 9088.

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

normal subgroups only

This group has 276 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×#14556127C211yesmaximal, characteristic
2C2×#14556038C211yesmaximal, characteristic
3#17985864C211yesmaximal, 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×Dic71C2211yescharacteristic
16#14556038—22no—
17C71⋊#95—21no—
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⋊C8Q812yescomplemented
32C4⋊Dic71—21no—
33C4⋊Dic71—21no—
34C4⋊Dic71—21no—
35C4⋊Dic71C2×C412yes—
36Dic71⋊C4—24no—
37C4×Dic71C2×C412yes—
38C4×Dic71D412yes—
39C22×C4×C71—21no—
40C22×C4×C71—21no—
41C22×C4×C71C2311yescharacteristic
42C2×C8×C71—21no—
43C2×C8×C71—21no—
44C2×C8×C71Q812yescomplemented
45C4⋊C4×C71—21no—
46C4⋊C4×C71—21no—
47C4⋊C4×C71—21no—
48C4⋊C4×C71C2×C412yes—
49C23×C71C2×D411yescharacteristic
50C2×C4×C71—22no—
51C2×C4×C71—41no—
52C2×C4×C71—41no—
53C2×C4×C71—41no—
54C2×C4×C71—41no—
55C2×C4×C71—41no—
56C2×C4×C71C22×C411yescharacteristic
57C2×C4×C71C2×D411yescharacteristic
58C2×C4×C71C2×Q811yescharacteristic
59C2×C4×C71C2×Q811yescharacteristic
60C2×C4×C71#4111yescharacteristic
61C2×C4×C71#4111yescharacteristic
62C2×Dic71—21no—
63C2×Dic71—21no—
64C2×Dic71—21no—
65C2×Dic71—21no—
66C2×Dic71—22no—
67C2×Dic71—41no—
68C2×Dic71—41no—
69C2×Dic71—41no—
70C2×Dic71—41no—
71C2×Dic71—41no—
72C2×Dic71C22⋊C412yes—
73C2×Dic71C22⋊C412yes—
74Dic142—48no—
75C8×C71—22no—
76C71⋊C8—22no—
77C22×C71C2×C22⋊C411yescharacteristic
78C22×C71#12411yescharacteristic
79C22×C71C4⋊Q811yescharacteristic
80C22×C71AGL(1,ℤ/8)11yescharacteristic
81C22×C71AGL(1,ℤ/8)11yescharacteristic
82C22×C71#13711yescharacteristic
83C22×C71#13711yescharacteristic
84C4×C71—42no—
85C4×C71—81no—
86C4×C71C4×Q811yescharacteristic
87C4×C71C4×Q811yescharacteristic
88C4×C71C22⋊Q811yescharacteristic
89C4×C71C22⋊Q811yescharacteristic
90Dic71—22no—
91Dic71—22no—
92Dic71—42no—
93Dic71—81no—
94C2×C71#39111yescharacteristic
95C2×C71#41811yescharacteristic
96C2×C71#41911yescharacteristic
97C2×C71#48911yescharacteristic
98C2×C71#48911yescharacteristic
99C2×C71#50111yescharacteristic
100C2×C71#50111yescharacteristic
101#1993—711nomaximal, Sylow
102C71#199311yescharacteristic, complemented, Sylow
103C2×C4⋊Q8—711no—
104C2×#97—711no—
105#382—711no—
106#340—711no—
107#340—711no—
108#340—711no—
109#340D7111yescharacteristic
110C22×Q8—1421no—
111C22×C8—711no—
112C22×C8C2×D7111yescharacteristic
113C4⋊Q8—714no—
114C4⋊Q8—1422no—
115C2×C4⋊C4—711no—
116C2×C4⋊C4—711no—
117C2×C4⋊C4—1421no—
118C2×C4⋊C4C2×D7111yescharacteristic
119C2×C4⋊C4C2×D7111yescharacteristic
120C2×C42—711no—
121#97—1422no—
122#95—1421no—
123#95—1421no—
124C2×Q8—2842no—
125C2×Q8—2842no—
126C2×Q8—1424no—
127C22×C4—21no—
128C22×C4—21no—
129C22×C4—711no—
130C22×C4—711no—
131C22×C4—1421no—
132C22×C4—1421no—
133C22×C4C22×D7111yescharacteristic
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—712no—
137C2×C8—1421no—
138C2×C8—1421no—
139C2×C8Dic14212yescomplemented
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—712no—
144C4⋊C4—1424no—
145C4⋊C4—1421no—
146C4⋊C4—1421no—
147C4⋊C4—1421no—
148C4⋊C4C4×D7112yes—
149C42—712no—
150C42—712no—
151C23D4×D7111yescharacteristic
152Q8—2848no—
153C2×C4—22no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—2841no—
160C2×C4—2841no—
161C2×C4—2841no—
162C2×C4—2841no—
163C2×C4—2841no—
164C2×C4—712no—
165C2×C4—712no—
166C2×C4—1422no—
167C2×C4—1421no—
168C2×C4—1421no—
169C2×C4—1421no—
170C2×C4—1421no—
171C2×C4C2×C4×D7111yescharacteristic
172C2×C4D4×D7111yescharacteristic
173C2×C4Q8×D7111yescharacteristic
174C2×C4C2×Dic14211yescharacteristic
175C2×C4#1176586411yescharacteristic
176C2×C4#1176586511yescharacteristic
177C8—22no—
178C8—1422no—
179C22C22⋊C4×D7111yescharacteristic
180C22#1455611411yescharacteristic
181C22#1455612711yescharacteristic
182C22#1455615211yescharacteristic
183C22#1455615511yescharacteristic
184C22#1455615711yescharacteristic
185C22#1455616011yescharacteristic
186C4—42no—
187C4—81no—
188C4—2842no—
189C4—5681no—
190C4—1422no—
191C4—1422no—
192C4#1455609311yescharacteristic
193C4C4×Dic14211yescharacteristic
194C4#1455610511yescharacteristic
195C4#1455610611yescharacteristic
196C2#1798590311yescharacteristic
197C2#1798600211yescharacteristic
198C2#1798600611yescharacteristic
199C2#1798635711yescharacteristic
200C2#1798636011yescharacteristic
201C2#1798640611yescharacteristic
202C2#1798640711yescharacteristic
subgroupG/H
centerC23D4×D71
commutatorC2×C4×C71C22×C4
FrattiniC22×C4C22×D71
Fitting#340×C71C2
socleC23×C71C2×D4
hypercenter#340D71
hypocenterC71#1993
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
31. C2×C71⋊C8Q8semidirect
44. C2×C8×C71Q8semidirect
102. C71#1993semidirect
139. C2×C8Dic142semidirect