Finite Group Databasebeta

← #22599534

Subgroups — #22599534

Order 9088.

366 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 121 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#17986556C211yesmaximal, characteristic, complemented
2#17986405C212yesmaximal, complemented
3#17986363C212yesmaximal, complemented
4#17986320C214yesmaximal, complemented
5#17986289C212yesmaximal, complemented
6#17986279C212yesmaximal, complemented
7#17986056C211yesmaximal, characteristic, complemented
8#532×C71C211yesmaximal, characteristic
9#14556128C2211yescharacteristic
10#14556128C2211yescharacteristic
11#14556120C2212yes—
12#14556107—21no—
13#14556107—21no—
14C4×Dic142—21no—
15C4×Dic142—21no—
16#14556087C2212yes—
17#14556061C2214yes—
18#14556059C2214yes—
19C4⋊(C71⋊C8)C2212yes—
20#14556049C2214yes—
21#14556049C2214yes—
22C22⋊(C71⋊C8)C2212yes—
23#14556039C2212yes—
24C2×#41×C71—21no—
25C4⋊Q8×C71C2211yescharacteristic
26#127×C71C2211yescharacteristic
27#124×C71—21no—
28#121×C71—21no—
29#121×C71C2212yes—
30C4×D4×C71—21no—
31C4×D4×C71C2212yes—
32C2×C42×C71C2211yescharacteristic
33C2×Dic142—21no—
34C2×Dic142—21no—
35C2×C71⋊C8C2314yes—
36C4⋊Dic71—21no—
37C4⋊Dic71—21no—
38C4⋊Dic71C2312yes—
39C4⋊Dic71C2312yes—
40Dic71⋊C4—22no—
41Dic71⋊C4—22no—
42C22⋊Dic71—22no—
43C4×Dic71—22no—
44#41×C71—44no—
45C2×Q8×C71—21no—
46C2×D4×C71—22no—
47C2×D4×C71—21no—
48C2×D4×C71—21no—
49C2×D4×C71C2312yes—
50C22×C4×C71—22no—
51C22×C4×C71D411yescharacteristic
52C22×C4×C71D411yescharacteristic
53C22×C4×C71C2311yescharacteristic
54C4⋊C4×C71—21no—
55C4⋊C4×C71C2312yes—
56C22⋊C4×C71—22no—
57C22⋊C4×C71—22no—
58C42×C71D411yescharacteristic
59C42×C71D411yescharacteristic
60C42×C71C2311yescharacteristic
61C42×C71C2311yescharacteristic
62C23×C71—22no—
63C23×C71C2×D411yescharacteristic
64Q8×C71—42no—
65D4×C71—24no—
66D4×C71—42no—
67D4×C71—42no—
68D4×C71—44no—
69C2×C4×C71—22no—
70C2×C4×C71—22no—
71C2×C4×C71—22no—
72C2×C4×C71—41no—
73C2×C4×C71—44no—
74C2×C4×C71C2×D411yescharacteristic
75C2×C4×C71C2×D411yescharacteristic
76C2×C4×C71C2×D411yescharacteristic
77C2×C4×C71C2×D411yescharacteristic
78C2×C4×C71C2×D411yescharacteristic
79C2×C4×C71C2411yescharacteristic
80C2×Dic71—22no—
81C2×Dic71—22no—
82Dic142—42no—
83Dic142—42no—
84C71⋊C8—24no—
85C22×C71—21no—
86C22×C71—21no—
87C22×C71—21no—
88C22×C71—42no—
89C22×C71—42no—
90C22×C71—42no—
91C22×C71C22×D411yescharacteristic
92C4×C71—21no—
93C4×C71—21no—
94C4×C71—21no—
95C4×C71—21no—
96C4×C71—42no—
97C4×C71AGL(1,ℤ/8)12yes—
98C4×C712−1+412yes—
99Dic71—42no—
100Dic71—42no—
101C2×C71—41no—
102C2×C71—82no—
103C2×C71#53611yescharacteristic
104C2×C71C2×AGL(1,ℤ/8)11yescharacteristic
105C2×C71#57511yescharacteristic
106#3235—711nomaximal, Sylow
107C71#323511yescharacteristic, complemented, Sylow
108#533—711no—
109#532D7111yescharacteristic
110#501—712no—
111#490—712no—
112#482—714no—
113#476—712no—
114#474—712no—
115#432—711no—
116C2×#41—21no—
117C4⋊Q8—711no—
118C4⋊Q8—711no—
119C4⋊Q8C2×D7111yescharacteristic
120#127C2×D7111yescharacteristic
121#125—712no—
122#124—21no—
123C22⋊Q8—1421no—
124C22⋊Q8—1421no—
125#121—21no—
126#121C2×D7112yes—
127C4×Q8—1421no—
128C4×Q8—1421no—
129C4×D4—21no—
130C4×D4C2×D7112yes—
131#117—712no—
132C2×C42C2×D7111yescharacteristic
133#107—714no—
134#106—714no—
135C4⋊C8—712no—
136#102—714no—
137#102—714no—
138C22⋊C8—712no—
139#97—712no—
140#41—44no—
141C2×Q8—21no—
142C2×Q8—1421no—
143C2×Q8—1421no—
144C2×D4—22no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4C22×D7112yes—
148C22×C4—22no—
149C22×C4C22⋊D7111yescharacteristic
150C22×C4C22⋊D7111yescharacteristic
151C22×C4C22×D7111yescharacteristic
152C2×C8—714no—
153C4⋊C4—21no—
154C4⋊C4—712no—
155C4⋊C4—712no—
156C4⋊C4—1422no—
157C4⋊C4—1422no—
158C4⋊C4—1421no—
159C4⋊C4—1421no—
160C4⋊C4C22×D7112yes—
161C22⋊C4—22no—
162C22⋊C4—22no—
163C22⋊C4—1422no—
164C42—1422no—
165C42C22⋊D7111yescharacteristic
166C42C22⋊D7111yescharacteristic
167C42C22×D7111yescharacteristic
168C42C22×D7111yescharacteristic
169C23—22no—
170C23C2×C22⋊D7111yescharacteristic
171Q8—42no—
172Q8—2842no—
173Q8—2842no—
174D4—24no—
175D4—42no—
176D4—42no—
177D4—44no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—41no—
182C2×C4—44no—
183C2×C4—1422no—
184C2×C4—1422no—
185C2×C4C2×C22⋊D7111yescharacteristic
186C2×C4C2×C22⋊D7111yescharacteristic
187C2×C4C2×C22⋊D7111yescharacteristic
188C2×C4C2×C22⋊D7111yescharacteristic
189C2×C4C2×C22⋊D7111yescharacteristic
190C2×C4C23×D7111yescharacteristic
191C8—1424no—
192C22—21no—
193C22—21no—
194C22—21no—
195C22—42no—
196C22—42no—
197C22—42no—
198C22C22×C22⋊D7111yescharacteristic
199C4—21no—
200C4—21no—
201C4—21no—
202C4—21no—
203C4—42no—
204C4—2842no—
205C4—2842no—
206C4#1455615412yes—
207C4#1455617512yes—
208C2—41no—
209C2—82no—
210C2#1798657011yescharacteristic
211C2C2×#1455615411yescharacteristic
212C2#1798679711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#532×C71C2
socleC22×C71C22×D4
hypercenter#532D71
hypocenterC71#3235
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #17986556C2semidirect
2. #17986405C2semidirect
3. #17986363C2semidirect
4. #17986320C2semidirect
5. #17986289C2semidirect
6. #17986279C2semidirect
7. #17986056C2semidirect
107. C71#3235semidirect