Finite Group Databasebeta

← #22599554

Subgroups — #22599554

Order 9088.

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

normal subgroups only

This group has 322 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
2#17986409C212yesmaximal, complemented
3#17986369C212yesmaximal, complemented
4#17986340C214yesmaximal
5#17986291C212yesmaximal, complemented
6#17986281C212yesmaximal, complemented
7#17986056C211yesmaximal, characteristic
8#533×C71C211yesmaximal, characteristic
9#14556128C2211yescharacteristic
10#14556128C2211yescharacteristic
11#14556120—21no—
12#14556107—21no—
13#14556107C2212yes—
14C4×Dic142—21no—
15C4×Dic142C2212yes—
16#14556087—21no—
17#14556061C2214yes—
18#14556059C2214yes—
19C4⋊(C71⋊C8)C2212yes—
20#14556051C2214yes—
21#14556051C2214yes—
22C22⋊(C71⋊C8)C2212yes—
23#14556039C2212yes—
24C4⋊Q8×C71C2211yescharacteristic
25C4⋊Q8×C71C2211yescharacteristic
26#125×C71C2212yes—
27C22⋊Q8×C71—21no—
28C22⋊Q8×C71—21no—
29C4×Q8×C71—21no—
30C4×Q8×C71—21no—
31#117×C71C2212yes—
32C2×C42×C71C2211yescharacteristic
33C2×Dic142—21no—
34C2×Dic142C2312yes—
35C2×C71⋊C8C2314yes—
36C4⋊Dic71—21no—
37C4⋊Dic71—21no—
38C4⋊Dic71—21no—
39C4⋊Dic71C2312yes—
40Dic71⋊C4—22no—
41Dic71⋊C4—22no—
42C22⋊Dic71—22no—
43C4×Dic71—22no—
44C2×Q8×C71—21no—
45C2×Q8×C71—21no—
46C22×C4×C71D411yescharacteristic
47C22×C4×C71D411yescharacteristic
48C22×C4×C71C2311yescharacteristic
49C4⋊C4×C71—22no—
50C4⋊C4×C71—22no—
51C4⋊C4×C71—21no—
52C4⋊C4×C71—21no—
53C4⋊C4×C71C2312yes—
54C4⋊C4×C71C2312yes—
55C22⋊C4×C71—22no—
56C42×C71—22no—
57C42×C71D411yescharacteristic
58C42×C71D411yescharacteristic
59C42×C71C2311yescharacteristic
60C42×C71C2311yescharacteristic
61C23×C71C2×D411yescharacteristic
62Q8×C71—42no—
63Q8×C71—42no—
64C2×C4×C71—22no—
65C2×C4×C71—22no—
66C2×C4×C71—22no—
67C2×C4×C71—22no—
68C2×C4×C71—41no—
69C2×C4×C71C2×D411yescharacteristic
70C2×C4×C71C2×D411yescharacteristic
71C2×C4×C71C2×D411yescharacteristic
72C2×C4×C71C2×D411yescharacteristic
73C2×C4×C71C2×D411yescharacteristic
74C2×C4×C71C2411yescharacteristic
75C2×Dic71—22no—
76C2×Dic71—22no—
77Dic142—24no—
78Dic142—42no—
79C71⋊C8—24no—
80C22×C71—21no—
81C22×C71—21no—
82C22×C71—21no—
83C22×C71C22×D411yescharacteristic
84C4×C71—21no—
85C4×C71—21no—
86C4×C71—21no—
87C4×C71—21no—
88C4×C71—42no—
89C4×C71—42no—
90C4×C71#13712yes—
91C4×C712−1+412yes—
92Dic71—42no—
93Dic71—42no—
94C2×C71—41no—
95C2×C71#53611yescharacteristic
96C2×C71C2×#13711yescharacteristic
97C2×C71#57511yescharacteristic
98#3237—711nomaximal, Sylow
99C71#323711yescharacteristic, complemented, Sylow
100#533—711no—
101#533D7111yescharacteristic
102#501—712no—
103#491—712no—
104#485—714no—
105#477—712no—
106#475—712no—
107#432—711no—
108C4⋊Q8—711no—
109C4⋊Q8—711no—
110C4⋊Q8C2×D7111yescharacteristic
111C4⋊Q8C2×D7111yescharacteristic
112#125—1421no—
113#125C2×D7112yes—
114C22⋊Q8—21no—
115C22⋊Q8—21no—
116C22⋊Q8—712no—
117C22⋊Q8—1421no—
118C4×Q8—21no—
119C4×Q8—21no—
120C4×Q8—712no—
121C4×Q8—1421no—
122#117—1421no—
123#117C2×D7112yes—
124C2×C42C2×D7111yescharacteristic
125#107—714no—
126#106—714no—
127C4⋊C8—712no—
128#103—714no—
129#103—714no—
130C22⋊C8—712no—
131#97—712no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—712no—
135C2×Q8—1421no—
136C22×C4C22⋊D7111yescharacteristic
137C22×C4C22⋊D7111yescharacteristic
138C22×C4C22×D7111yescharacteristic
139C2×C8—714no—
140C4⋊C4—22no—
141C4⋊C4—22no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—712no—
145C4⋊C4—1422no—
146C4⋊C4—1422no—
147C4⋊C4—1421no—
148C4⋊C4—1421no—
149C4⋊C4—1421no—
150C4⋊C4C22×D7112yes—
151C4⋊C4C22×D7112yes—
152C22⋊C4—22no—
153C22⋊C4—1422no—
154C42—22no—
155C42—1422no—
156C42C22⋊D7111yescharacteristic
157C42C22⋊D7111yescharacteristic
158C42C22×D7111yescharacteristic
159C42C22×D7111yescharacteristic
160C23C2×C22⋊D7111yescharacteristic
161Q8—42no—
162Q8—42no—
163Q8—2842no—
164Q8—1424no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—41no—
170C2×C4—1422no—
171C2×C4—1422no—
172C2×C4C2×C22⋊D7111yescharacteristic
173C2×C4C2×C22⋊D7111yescharacteristic
174C2×C4C2×C22⋊D7111yescharacteristic
175C2×C4C2×C22⋊D7111yescharacteristic
176C2×C4C2×C22⋊D7111yescharacteristic
177C2×C4C23×D7111yescharacteristic
178C8—1424no—
179C22—21no—
180C22—21no—
181C22—21no—
182C22C22×C22⋊D7111yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—21no—
187C4—42no—
188C4—42no—
189C4—2842no—
190C4—2842no—
191C4#1455615812yes—
192C4#1455617612yes—
193C2—41no—
194C2#1798657311yescharacteristic
195C2C2×#1455615811yescharacteristic
196C2#1798679711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#533×C71C2
socleC22×C71C22×D4
hypercenter#533D71
hypocenterC71#3237
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #17986409C2semidirect
3. #17986369C2semidirect
5. #17986291C2semidirect
6. #17986281C2semidirect
99. C71#3237semidirect