Finite Group Databasebeta

← #22588796

Subgroups — #22588796

Order 9088.

378 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 89 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×#14556111C211yesmaximal, characteristic
2C2×#14556087C211yesmaximal, characteristic, complemented
3C2×#14556042C212yesmaximal
4#17985765C212yesmaximal, complemented
5#381×C71C211yesmaximal, characteristic, complemented
6C22×C22⋊D71C2211yescharacteristic
7#14556111—21no—
8#14556111—21no—
9#14556111—22no—
10#14556087—24no—
11C2×C4⋊Dic71—21no—
12C2×Dic71⋊C4C412yescomplemented
13C2×C22⋊Dic71C2211yescharacteristic
14C2×C22⋊Dic71C2212yes—
15C2×(C2×D71)⋊C4C412yescomplemented
16C2×C4×Dic71—21no—
17#14556042—24no—
18C23×C4×C71C2211yescharacteristic
19C2×C22⋊C4×C71C2212yes—
20#95×C71—22no—
21C23×D71C2×C411yescharacteristic
22C2×C22⋊D71—22no—
23C2×C22⋊D71—21no—
24C2×C22⋊D71—21no—
25C2×C22⋊D71—22no—
26C22×Dic71—22no—
27C22×Dic71C2×C411yescharacteristic
28C22×Dic71C2×C412yes—
29C4⋊Dic71—24no—
30Dic71⋊C4—22no—
31Dic71⋊C4—22no—
32C22⋊Dic71—22no—
33C22⋊Dic71—21no—
34C22⋊Dic71—21no—
35C22⋊Dic71D414yes—
36(C2×D71)⋊C4—22no—
37(C2×D71)⋊C4—22no—
38C4×Dic71—24no—
39C24×C71C2311yescharacteristic
40C22×C4×C71—22no—
41C22×C4×C71—22no—
42C22×C4×C71—22no—
43C22×C4×C71C2×C412yes—
44C22×C4×C71D411yescharacteristic
45C22×C4×C71D411yescharacteristic
46C22×C4×C71D412yes—
47C22⋊C4×C71—22no—
48C22⋊C4×C71—22no—
49C23×C71—42no—
50C23×C71C22×C411yescharacteristic
51C23×C71C2×D412yes—
52C23×C71C2×D411yescharacteristic
53C23×C71C2×D411yescharacteristic
54C23×C71#4112yes—
55C22×D71—21no—
56C22×D71—22no—
57C22×D71—42no—
58C2×C4×C71—24no—
59C2×C4×C71—21no—
60C2×C4×C71—21no—
61C2×C4×C71—24no—
62C2×C4×C71—21no—
63C2×C4×C71—21no—
64C2×C4×C71—44no—
65C2×C4×C71—42no—
66C2×C4×C71C22⋊C412yes—
67C2×C4×C71C22⋊C412yes—
68C22⋊D71—41no—
69C22⋊D71—42no—
70C22⋊D71—41no—
71C2×Dic71—22no—
72C2×Dic71—21no—
73C2×Dic71—22no—
74C2×Dic71—24no—
75C2×Dic71—44no—
76C2×Dic71—42no—
77C22×C71—22no—
78C22×C71—22no—
79C22×C71—22no—
80C22×C71—42no—
81C22×C71—42no—
82C22×C71C2×C22⋊C411yescharacteristic
83C22×C71C4×D412yes—
84C22×C71#12011yescharacteristic
85C22×C71#12112yes—
86C22×C71#12311yescharacteristic
87C2×D71—41no—
88C2×D71—42no—
89C2×D71—82no—
90C4×C71—22no—
91C4×C71—22no—
92C4×C71—82no—
93Dic71—44no—
94Dic71—41no—
95Dic71—42no—
96C2×C71—21no—
97C2×C71—22no—
98C2×C71—22no—
99C2×C71—21no—
100C2×C71#38611yescharacteristic
101C2×C71#41012yes—
102D71—81no—
103#1899—711nomaximal, Sylow
104C71#189911yescharacteristic, complemented, Sylow
105C2×#123—711no—
106C2×#117—711no—
107C2×#99—712no—
108#381D7111yescharacteristic, complemented
109#342—712no—
110C22×D4—711no—
111C23×C4C2×D7111yescharacteristic
112#123—1421no—
113#123—1421no—
114#123—1422no—
115#117—1424no—
116C2×C4⋊C4—712no—
117C2×C4⋊C4—1421no—
118C2×C22⋊C4—712no—
119C2×C22⋊C4—711no—
120C2×C22⋊C4—712no—
121C2×C22⋊C4C2×D7112yes—
122C2×C42—1421no—
123#99—1424no—
124#95—22no—
125C24—711no—
126C24C22×D7111yescharacteristic
127C2×D4—1422no—
128C2×D4—1421no—
129C2×D4—1421no—
130C2×D4—1422no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—712no—
135C22×C4—711no—
136C22×C4—1422no—
137C22×C4C4×D7112yes—
138C22×C4D28411yescharacteristic
139C22×C4D28411yescharacteristic
140C22×C4C22⋊D7112yes—
141C4⋊C4—1424no—
142C4⋊C4—1422no—
143C4⋊C4—1422no—
144C22⋊C4—22no—
145C22⋊C4—22no—
146C22⋊C4—714no—
147C22⋊C4—1422no—
148C22⋊C4—1421no—
149C22⋊C4—1421no—
150C22⋊C4—1422no—
151C22⋊C4—1422no—
152C42—1424no—
153C23—42no—
154C23—2842no—
155C23—1421no—
156C23—1422no—
157C23C2×C4×D7111yescharacteristic
158C23D4×D7112yes—
159C23C2×C22⋊D7111yescharacteristic
160C23C2×D28411yescharacteristic
161C23#1176586412yes—
162D4—2841no—
163D4—2842no—
164D4—2841no—
165C2×C4—24no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—24no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—44no—
172C2×C4—42no—
173C2×C4—2844no—
174C2×C4—2842no—
175C2×C4—1422no—
176C2×C4—1421no—
177C2×C4—1422no—
178C2×C4—1424no—
179C2×C4(C2×D71)⋊C412yes—
180C2×C4(C2×D71)⋊C412yes—
181C22—22no—
182C22—22no—
183C22—22no—
184C22—42no—
185C22—42no—
186C22—2841no—
187C22—2842no—
188C22—5682no—
189C22C2×(C2×D71)⋊C411yescharacteristic
190C22(C22⋊D71)⋊C412yes—
191C22#1455609811yescharacteristic
192C22#1455610012yes—
193C22#1455611211yescharacteristic
194C4—22no—
195C4—22no—
196C4—82no—
197C4—2844no—
198C4—2841no—
199C4—2842no—
200C2—22no—
201C2—21no—
202C2—22no—
203C2—21no—
204C2—5681no—
205C2#1798587611yescharacteristic
206C2#1798597212yes—
subgroupG/H
centerC22C2×(C2×D71)⋊C4
commutatorC23×C71C22×C4
FrattiniC24C22×D71
Fitting#381×C71C2
socleC22×C71C2×C22⋊C4
hypercenter#381D71
hypocenterC71#1899
LCSG ▷ C23×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C23×C4 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#14556087C2semidirect
4. #17985765C2semidirect
5. #381×C71C2semidirect
12. C2×Dic71⋊C4C4semidirect
15. C2×(C2×D71)⋊C4C4semidirect
104. C71#1899semidirect
108. #381D71semidirect