Finite Group Databasebeta

← #22586863

Subgroups — #22586863

Order 9088.

242 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 73 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#17986533C211yesmaximal, characteristic
2#17986056C211yesmaximal, characteristic, complemented
3#17985735C212yesmaximal, complemented
4#17985732C212yesmaximal
5C4×C4⋊C4×C71C211yesmaximal, characteristic, complemented
6#14556122—21no—
7#14556120C411yescharacteristic, complemented
8#14556116C411yescharacteristic, complemented
9#14556111—21no—
10#14556107C2211yescharacteristic
11#14556102C2211yescharacteristic
12C4×Dic142C411yescharacteristic, complemented
13C4×D284C411yescharacteristic, complemented
14C4×C22⋊D71—21no—
15#14556085—21no—
16C4⋊(C71⋊C8)—21no—
17C22⋊(C71⋊C8)C2212yes—
18#14556039—21no—
19C2×C4⋊C4×C71—21no—
20C2×C42×C71—21no—
21C2×C42×C71C2211yescharacteristic
22#95×C71C2212yes—
23C2×Dic142C2×C411yescharacteristic
24C2×D284C2×C411yescharacteristic
25C2×C22⋊D71—21no—
26C2×C4×D71—21no—
27C2×C71⋊C8—22no—
28C4⋊Dic71C2×C411yescharacteristic
29C4⋊Dic71C2×C411yescharacteristic
30Dic71⋊C4—21no—
31Dic71⋊C4—21no—
32Dic71⋊C4—21no—
33Dic71⋊C4—21no—
34C22⋊Dic71—21no—
35(C2×D71)⋊C4—21no—
36(C2×D71)⋊C4—21no—
37(C2×D71)⋊C4—21no—
38(C2×D71)⋊C4—21no—
39C4×Dic71—21no—
40C22×C4×C71—22no—
41C22×C4×C71D411yescharacteristic
42C22×C4×C71D411yescharacteristic
43C22×C4×C71C2311yescharacteristic
44C4⋊C4×C71—24no—
45C42×C71—42no—
46C42×C71C2×C411yescharacteristic
47C42×C71C2×C411yescharacteristic
48C42×C71D411yescharacteristic
49C42×C71D411yescharacteristic
50C23×C71C2×D411yescharacteristic
51C22×D71—21no—
52C2×C4×C71—21no—
53C2×C4×C71—21no—
54C2×C4×C71—22no—
55C2×C4×C71—24no—
56C2×C4×C71—41no—
57C2×C4×C71—42no—
58C2×C4×C71—42no—
59C2×C4×C71C22⋊C411yescharacteristic
60C2×C4×C71C22⋊C411yescharacteristic
61C2×C4×C71C22⋊C411yescharacteristic
62C2×C4×C71C22⋊C411yescharacteristic
63C2×C4×C71C22×C411yescharacteristic
64C2×C4×C71C2×D411yescharacteristic
65C22⋊D71—41no—
66C22⋊D71—41no—
67C2×Dic71—21no—
68C2×Dic71—21no—
69C2×Dic71—21no—
70D284—41no—
71C4×D71—42no—
72Dic142—41no—
73C71⋊C8—42no—
74C22×C71—21no—
75C22×C71—21no—
76C22×C71C2×C22⋊C411yescharacteristic
77C22×C71AGL(1,ℤ/8)11yescharacteristic
78C22×C71#13711yescharacteristic
79C2×D71—41no—
80C2×D71—41no—
81C2×D71—41no—
82C4×C71—21no—
83C4×C71—21no—
84C4×C71—21no—
85C4×C71—21no—
86C4×C71—21no—
87C4×C71—44no—
88C4×C71#10412yes—
89Dic71—41no—
90Dic71—41no—
91Dic71—41no—
92C2×C71—21no—
93C2×C71—21no—
94C2×C71#41011yescharacteristic
95C2×C71#41711yescharacteristic
96C2×C71C2×#10411yescharacteristic
97D71—81no—
98#1509—711nomaximal, Sylow
99C71#150911yescharacteristic, complemented, Sylow
100#529—711no—
101#432—711no—
102C4×C4⋊C4D7111yescharacteristic, complemented
103#328—712no—
104#327—712no—
105#126—1421no—
106#125—711no—
107#124—711no—
108#123—1421no—
109C22⋊Q8—711no—
110#121—711no—
111C4×Q8—711no—
112C4×D4—711no—
113C4×D4—1421no—
114#117—1421no—
115C2×C4⋊C4—21no—
116C2×C42—21no—
117C2×C42C2×D7111yescharacteristic
118C4⋊C8—1421no—
119C22⋊C8—712no—
120#97—1421no—
121#95C2×D7112yes—
122C2×Q8—711no—
123C2×D4—711no—
124C2×D4—1421no—
125C22×C4—22no—
126C22×C4—1421no—
127C22×C4C22⋊D7111yescharacteristic
128C22×C4C22⋊D7111yescharacteristic
129C22×C4C22×D7111yescharacteristic
130C2×C8—1422no—
131C4⋊C4—24no—
132C4⋊C4—711no—
133C4⋊C4—711no—
134C4⋊C4—1421no—
135C4⋊C4—1421no—
136C4⋊C4—1421no—
137C4⋊C4—1421no—
138C22⋊C4—1421no—
139C22⋊C4—1421no—
140C22⋊C4—1421no—
141C22⋊C4—1421no—
142C22⋊C4—1421no—
143C42—42no—
144C42—1421no—
145C42C4×D7111yescharacteristic
146C42C4×D7111yescharacteristic
147C42D28411yescharacteristic
148C42D28411yescharacteristic
149C23—1421no—
150C23C2×C22⋊D7111yescharacteristic
151Q8—2841no—
152D4—2841no—
153D4—2841no—
154D4—2841no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—24no—
159C2×C4—41no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—2842no—
163C2×C4—1421no—
164C2×C4—1421no—
165C2×C4—1421no—
166C2×C4(C2×D71)⋊C411yescharacteristic
167C2×C4(C2×D71)⋊C411yescharacteristic
168C2×C4(C2×D71)⋊C411yescharacteristic
169C2×C4(C2×D71)⋊C411yescharacteristic
170C2×C4C2×C4×D7111yescharacteristic
171C2×C4C2×D28411yescharacteristic
172C8—2842no—
173C22—21no—
174C22—21no—
175C22—2841no—
176C22—2841no—
177C22—2841no—
178C22C2×(C2×D71)⋊C411yescharacteristic
179C22#1455615411yescharacteristic
180C22#1455615911yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—21no—
186C4—44no—
187C4—2841no—
188C4—2841no—
189C4—2841no—
190C4#1455605612yes—
191C2—21no—
192C2—21no—
193C2—5681no—
194C2#1798597211yescharacteristic
195C2#1798599811yescharacteristic
196C2C2×#1455605611yescharacteristic
subgroupG/H
centerC22C2×(C2×D71)⋊C4
commutatorC2×C4×C71C22×C4
FrattiniC22×C4C22×D71
FittingC4×C4⋊C4×C71C2
socleC22×C71C2×C22⋊C4
hypercenterC4×C4⋊C4D71
hypocenterC71#1509
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #17986056C2semidirect
3. #17985735C2semidirect
5. C4×C4⋊C4×C71C2semidirect
7. #14556120C4semidirect
8. #14556116C4semidirect
12. C4×Dic142C4semidirect
13. C4×D284C4semidirect
99. C71#1509semidirect
102. C4×C4⋊C4D71semidirect