Finite Group Databasebeta

← #22588786

Subgroups — #22588786

Order 9088.

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

normal subgroups only

This group has 358 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
1#17986510C211yesmaximal, characteristic
2C2×#14556087C211yesmaximal, characteristic, complemented
3C2×#14556054C212yesmaximal, complemented
4#17985760C212yesmaximal, complemented
5#407×C71C211yesmaximal, characteristic, complemented
6C2×#11765865C2211yescharacteristic
7#14556111—21no—
8#14556107C412yescomplemented
9#14556102C412yescomplemented
10#14556097—21no—
11C4×C22⋊D71—22no—
12#14556087—24no—
13#14556087C2211yescharacteristic
14C2×C4⋊Dic71—21no—
15C2×C22⋊Dic71—21no—
16C2×C4×Dic71C2212yes—
17#14556054—24no—
18C23×C4×C71C2211yescharacteristic
19C2×M16×C71C2212yes—
20C22⋊C8×C71—22no—
21#11765865—22no—
22#11765865—22no—
23C2×Dic142C2×C411yescharacteristic
24C2×D284C2×C411yescharacteristic
25C2×C22⋊D71—22no—
26C2×C22⋊D71—21no—
27C22×Dic71—22no—
28C2×C4×D71—21no—
29C4⋊Dic71—24no—
30C4⋊Dic71C2×C412yes—
31Dic71⋊C4—22no—
32C22⋊Dic71—24no—
33C22⋊Dic71—22no—
34C22⋊Dic71—21no—
35(C2×D71)⋊C4—22no—
36C4×Dic71—22no—
37C4×Dic71—21no—
38C4×Dic71D414yescomplemented
39C24×C71D411yescharacteristic
40C22×C4×C71—22no—
41C22×C4×C71—22no—
42C22×C4×C71C2×C412yes—
43C22×C4×C71D411yescharacteristic
44C22×C4×C71D412yes—
45C22×C4×C71C2311yescharacteristic
46M16×C71—22no—
47M16×C71—22no—
48C2×C8×C71—22no—
49C23×C71—21no—
50C23×C71—21no—
51C23×C71—42no—
52C23×C71C22⋊C412yes—
53C23×C71C2×D411yescharacteristic
54C22×D71—21no—
55C2×C4×C71—21no—
56C2×C4×C71—21no—
57C2×C4×C71—24no—
58C2×C4×C71—24no—
59C2×C4×C71C22⋊C412yes—
60C2×C4×C71C22×C411yescharacteristic
61C2×C4×C71C2×D412yes—
62C2×C4×C71C2×D411yescharacteristic
63C2×C4×C71#4112yes—
64C22⋊D71—44no—
65C22⋊D71—41no—
66C22⋊D71—41no—
67C2×Dic71—22no—
68C2×Dic71—21no—
69C2×Dic71—24no—
70C2×Dic71—44no—
71D284—22no—
72C4×D71—42no—
73Dic142—22no—
74C8×C71—42no—
75C22×C71—22no—
76C22×C71—22no—
77C22×C71—22no—
78C22×C71—22no—
79C22×C71—42no—
80C22×C71—42no—
81C22×C71C2×C22⋊C411yescharacteristic
82C22×C71#12011yescharacteristic
83C22×C71#12311yescharacteristic
84C2×D71—41no—
85C2×D71—42no—
86C4×C71—22no—
87C4×C71C4×D412yes—
88C4×C71#12112yes—
89Dic71—44no—
90Dic71—41no—
91Dic71—42no—
92C2×C71—21no—
93C2×C71—21no—
94C2×C71—42no—
95C2×C71#38611yescharacteristic
96C2×C71#42112yes—
97D71—81no—
98#1897—711nomaximal, Sylow
99C71#189711yescharacteristic, complemented, Sylow
100#525—711no—
101C2×#117—711no—
102C2×#104—712no—
103#407D7111yescharacteristic, complemented
104#339—712no—
105C2×#41—711no—
106C23×C4C2×D7111yescharacteristic
107C2×M16C2×D7112yes—
108#123—1421no—
109C22⋊Q8—712no—
110#121—712no—
111#120—1421no—
112C4×D4—1422no—
113#117—711no—
114#117—1424no—
115C2×C4⋊C4—1421no—
116C2×C22⋊C4—1421no—
117C2×C42—712no—
118#104—1424no—
119C22⋊C8—22no—
120C24D28411yescharacteristic
121#41—1422no—
122#41—1422no—
123C2×Q8—711no—
124C2×D4—711no—
125C2×D4—1422no—
126C2×D4—1421no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—1422no—
130C22×C4—1421no—
131C22×C4C4×D7112yes—
132C22×C4D28411yescharacteristic
133C22×C4C22⋊D7112yes—
134C22×C4C22×D7111yescharacteristic
135M16—22no—
136M16—22no—
137C2×C8—22no—
138C4⋊C4—712no—
139C4⋊C4—1424no—
140C4⋊C4—1422no—
141C22⋊C4—1424no—
142C22⋊C4—1422no—
143C22⋊C4—1421no—
144C22⋊C4—1422no—
145C42—714no—
146C42—1422no—
147C42—1421no—
148C23—21no—
149C23—21no—
150C23—42no—
151C23—1421no—
152C23(C2×D71)⋊C412yes—
153C23C2×D28411yescharacteristic
154Q8—1422no—
155D4—2844no—
156D4—2841no—
157D4—2841no—
158D4—1422no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—2844no—
164C2×C4—2842no—
165C2×C4—1422no—
166C2×C4—1421no—
167C2×C4—1424no—
168C2×C4(C2×D71)⋊C412yes—
169C2×C4C2×C4×D7111yescharacteristic
170C2×C4D4×D7112yes—
171C2×C4C2×C22⋊D7111yescharacteristic
172C2×C4#1176586412yes—
173C8—42no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—2841no—
181C22—2842no—
182C22C2×(C2×D71)⋊C411yescharacteristic
183C22#1455609811yescharacteristic
184C22#1455611211yescharacteristic
185C4—22no—
186C4—2844no—
187C4—2841no—
188C4—2842no—
189C4(C22⋊D71)⋊C412yes—
190C4#1455610012yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—5681no—
195C2#1798587611yescharacteristic
196C2#1798601512yes—
subgroupG/H
centerC2×C4C2×C22⋊D71
commutatorC2×C4×C71C22×C4
FrattiniC22×C4C22×D71
Fitting#407×C71C2
socleC22×C71C2×C22⋊C4
hypercenter#407D71
hypocenterC71#1897
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×#14556087C2semidirect
3. C2×#14556054C2semidirect
4. #17985760C2semidirect
5. #407×C71C2semidirect
8. #14556107C4semidirect
9. #14556102C4semidirect
38. C4×Dic71D4semidirect
99. C71#1897semidirect
103. #407D71semidirect