Finite Group Databasebeta

← #22598733

Subgroups — #22598733

Order 9088.

424 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14556128C211yesmaximal, characteristic, complemented
2#17986358C214yesmaximal, complemented
3#17986349C212yesmaximal, complemented
4#17986345C212yesmaximal, complemented
5#17986000C214yesmaximal, complemented
6C4×#11765849C211yesmaximal, characteristic, complemented
7#532×C71C211yesmaximal, characteristic
8C22×Dic142—21no—
9C2×#11765849C2212yes—
10#14556128—21no—
11#14556128—21no—
12#14556128C2212yes—
13#14556128C2212yes—
14C2×C4⋊Dic71—21no—
15C2×C4⋊Dic71C2212yes—
16#14556052C2218yes—
17#14556049C2218yes—
18#14556039C2212yes—
19C4×C71⋊C8C2212yes—
20C2×#41×C71C2212yes—
21C4⋊Q8×C71C2211yescharacteristic
22#127×C71C2211yescharacteristic
23#124×C71C2212yes—
24#121×C71—21no—
25#121×C71—21no—
26C4×D4×C71—21no—
27C4×D4×C71—21no—
28C2×C42×C71C2211yescharacteristic
29C2×Dic142—22no—
30C2×Dic142—22no—
31C2×Dic142—44no—
32C22×Dic71—22no—
33#11765849—24no—
34C2×C71⋊C8C2314yes—
35C4⋊Dic71—22no—
36C4⋊Dic71—22no—
37C4⋊Dic71—22no—
38C4⋊Dic71C2314yes—
39#41×C71—28no—
40C2×Q8×C71C2312yes—
41C2×D4×C71—22no—
42C2×D4×C71—21no—
43C2×D4×C71—21no—
44C2×D4×C71C2312yes—
45C22×C4×C71—22no—
46C22×C4×C71D411yescharacteristic
47C22×C4×C71D411yescharacteristic
48C22×C4×C71C2311yescharacteristic
49C4⋊C4×C71—21no—
50C4⋊C4×C71—21no—
51C22⋊C4×C71—22no—
52C22⋊C4×C71—22no—
53C42×C71D411yescharacteristic
54C42×C71D411yescharacteristic
55C42×C71C2311yescharacteristic
56C42×C71C2311yescharacteristic
57C23×C71—22no—
58C23×C71C2×D411yescharacteristic
59Q8×C71—24no—
60D4×C71—24no—
61D4×C71—44no—
62D4×C71—42no—
63D4×C71—42no—
64C2×C4×C71—22no—
65C2×C4×C71—22no—
66C2×C4×C71—22no—
67C2×C4×C71—44no—
68C2×C4×C71C2×D411yescharacteristic
69C2×C4×C71C2×D411yescharacteristic
70C2×C4×C71C2×D411yescharacteristic
71C2×C4×C71C2×D411yescharacteristic
72C2×C4×C71C2×D411yescharacteristic
73C2×C4×C71#4114yes—
74C2×C4×C71C2411yescharacteristic
75C2×Dic71—24no—
76C2×Dic71—44no—
77Dic142—44no—
78Dic142—44no—
79C71⋊C8—24no—
80C22×C71—21no—
81C22×C71—21no—
82C22×C71—42no—
83C22×C71—42no—
84C22×C71—42no—
85C22×C71#12412yes—
86C22×C71C22×D411yescharacteristic
87C4×C71—21no—
88C4×C71—21no—
89C4×C71—42no—
90C4×C71#12412yes—
91C4×C71AGL(1,ℤ/8)12yes—
92C4×C71#13712yes—
93C4×C71C2×#4112yes—
94Dic71—44no—
95C2×C71—22no—
96C2×C71—82no—
97C2×C71C2×#12411yescharacteristic
98C2×C71C2×AGL(1,ℤ/8)11yescharacteristic
99C2×C71C2×#13711yescharacteristic
100#3141—711nomaximal, Sylow
101C71#314111yescharacteristic, complemented, Sylow
102#532D7111yescharacteristic
103C2×C4⋊Q8—711no—
104#489—714no—
105#487—712no—
106#486—712no—
107#417—714no—
108C4×M16—711no—
109C2×#41C2×D7112yes—
110C22×Q8—1421no—
111C2×M16—712no—
112C4⋊Q8—712no—
113C4⋊Q8—712no—
114C4⋊Q8—1421no—
115C4⋊Q8—1421no—
116C4⋊Q8C2×D7111yescharacteristic
117#127C2×D7111yescharacteristic
118#124C2×D7112yes—
119#121—21no—
120#121—21no—
121C4×D4—21no—
122C4×D4—21no—
123C2×C4⋊C4—712no—
124C2×C4⋊C4—1421no—
125C2×C42C2×D7111yescharacteristic
126#103—718no—
127#102—718no—
128#97—712no—
129C4×C8—712no—
130#41—28no—
131C2×Q8—2844no—
132C2×Q8—1422no—
133C2×Q8—1422no—
134C2×Q8C22×D7112yes—
135C2×D4—22no—
136C2×D4—21no—
137C2×D4—21no—
138C2×D4C22×D7112yes—
139C22×C4—22no—
140C22×C4—1422no—
141C22×C4C22⋊D7111yescharacteristic
142C22×C4C22⋊D7111yescharacteristic
143C22×C4C22×D7111yescharacteristic
144M16—1424no—
145C2×C8—714no—
146C4⋊C4—21no—
147C4⋊C4—21no—
148C4⋊C4—714no—
149C4⋊C4—1422no—
150C4⋊C4—1422no—
151C4⋊C4—1422no—
152C22⋊C4—22no—
153C22⋊C4—22no—
154C42C22⋊D7111yescharacteristic
155C42C22⋊D7111yescharacteristic
156C42C22×D7111yescharacteristic
157C42C22×D7111yescharacteristic
158C23—22no—
159C23C2×C22⋊D7111yescharacteristic
160Q8—24no—
161Q8—2844no—
162Q8—2844no—
163D4—24no—
164D4—44no—
165D4—42no—
166D4—42no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—44no—
171C2×C4—2844no—
172C2×C4—1424no—
173C2×C4C2×C22⋊D7111yescharacteristic
174C2×C4C2×C22⋊D7111yescharacteristic
175C2×C4C2×C22⋊D7111yescharacteristic
176C2×C4C2×C22⋊D7111yescharacteristic
177C2×C4C2×C22⋊D7111yescharacteristic
178C2×C4#1176586414yes—
179C2×C4C23×D7111yescharacteristic
180C8—1424no—
181C22—21no—
182C22—21no—
183C22—42no—
184C22—42no—
185C22—42no—
186C22#1455611512yes—
187C22C22×C22⋊D7111yescharacteristic
188C4—21no—
189C4—21no—
190C4—42no—
191C4—2844no—
192C4#1455611512yes—
193C4#1455615312yes—
194C4#1455615812yes—
195C4C2×#1176586412yes—
196C2—22no—
197C2—82no—
198C2C2×#1455611511yescharacteristic
199C2C2×#1455615311yescharacteristic
200C2C2×#1455615811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#532×C71C2
socleC22×C71C22×D4
hypercenter#532D71
hypocenterC71#3141
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. C2×#14556128C2semidirect
2. #17986358C2semidirect
3. #17986349C2semidirect
4. #17986345C2semidirect
5. #17986000C2semidirect
6. C4×#11765849C2semidirect
101. C71#3141semidirect