Finite Group Databasebeta

← #22600980

Subgroups — #22600980

Order 9088.

370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 125 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#17986727C211yesmaximal, characteristic, complemented
2D4×Dic142C211yesmaximal, characteristic
3#17986350C211yesmaximal, characteristic, complemented
4#17986348C212yesmaximal, complemented
5#17986284C211yesmaximal, characteristic, complemented
6#17986283C212yesmaximal, complemented
7#17986204C211yesmaximal, characteristic
8#17986202C212yesmaximal
9C8×Dic142C211yesmaximal, characteristic, complemented
10#17986090C212yesmaximal
11C4×SD16×C71C211yesmaximal, characteristic
12C22×Dic142—21no—
13C2×#11765853C2212yes—
14#14556128C2211yescharacteristic
15#14556128C2211yescharacteristic
16#14556127C2212yes—
17#14556126C2212yes—
18#14556120—21no—
19#14556118—22no—
20#14556107—21no—
21#14556105—22no—
22C4×Dic142—21no—
23C4×Dic142C2211yescharacteristic
24#14556093C2212yes—
25D4×Dic71C2212yes—
26#14556059C2212yes—
27C4⋊(C71⋊C8)C2211yescharacteristic
28Dic71⋊C8C2212yes—
29#14556053C2212yes—
30#14556053C2212yes—
31#14556052C2212yes—
32#14556051C2212yes—
33C8×Dic71C2212yes—
34C2×SD16×C71C2211yescharacteristic
35C4×Q8×C71C2211yescharacteristic
36C4×D4×C71C2211yescharacteristic
37#106×C71C2211yescharacteristic
38#103×C71C2211yescharacteristic
39#102×C71C2211yescharacteristic
40C4×C8×C71C2211yescharacteristic
41C2×Dic142—21no—
42C2×Dic142—22no—
43C2×Dic142—44no—
44C2×Dic142D411yescharacteristic
45C2×Dic142C2312yes—
46C22×Dic71—22no—
47#11765853—24no—
48C2×C71⋊C8C2312yes—
49C4⋊Dic71—21no—
50C4⋊Dic71—21no—
51C4⋊Dic71—21no—
52C4⋊Dic71D411yescharacteristic
53C4⋊Dic71C2312yes—
54Dic71⋊C4—22no—
55Dic71⋊C4—22no—
56Dic71⋊C4—22no—
57Dic71⋊C4—22no—
58Dic71⋊C4D412yes—
59C22⋊Dic71—22no—
60C4×Dic71—22no—
61C4×Dic71C2312yes—
62C2×Q8×C71C2311yescharacteristic
63C2×D4×C71C2311yescharacteristic
64C22×C4×C71—21no—
65SD16×C71—22no—
66C2×C8×C71C2311yescharacteristic
67C2×C8×C71C2311yescharacteristic
68C4⋊C4×C71—21no—
69C4⋊C4×C71C2311yescharacteristic
70C4⋊C4×C71C2311yescharacteristic
71C22⋊C4×C71—21no—
72C42×C71—21no—
73C42×C71C2311yescharacteristic
74C23×C71—21no—
75Q8×C71—21no—
76Q8×C71—21no—
77D4×C71—21no—
78D4×C71#4112yes—
79C2×C4×C71—21no—
80C2×C4×C71—21no—
81C2×C4×C71—21no—
82C2×C4×C71—42no—
83C2×C4×C71C2×D411yescharacteristic
84C2×C4×C71C2×D411yescharacteristic
85C2×C4×C71C2411yescharacteristic
86C2×Dic71—22no—
87C2×Dic71—22no—
88C2×Dic71—44no—
89C2×Dic71C2×D412yes—
90C2×Dic71C2×D412yes—
91Dic142—22no—
92Dic142—22no—
93Dic142—42no—
94Dic142—44no—
95Dic142SD1614yescomplemented
96C8×C71—21no—
97C8×C71—21no—
98C71⋊C8—22no—
99C22×C71—22no—
100C22×C71—41no—
101C22×C71—41no—
102C22×C71C22×D411yescharacteristic
103C4×C71—21no—
104C4×C71—41no—
105C4×C71—41no—
106C4×C71—41no—
107C4×C71C2×SD1612yes—
108C4×C71C2×#4111yescharacteristic
109C4×C712−1+411yescharacteristic
110Dic71—22no—
111Dic71—42no—
112Dic71—42no—
113Dic71C2×SD1614yes—
114C2×C71—42no—
115C2×C71#54811yescharacteristic
116C2×C71C22×SD1611yescharacteristic
117C2×C71#57811yescharacteristic
118#3359—711nomaximal, Sylow
119C71#335911yescharacteristic, complemented, Sylow
120#557—711no—
121D4×Q8—711no—
122#487—712no—
123#487—711no—
124#475—711no—
125#475—712no—
126#461—712no—
127#461—711no—
128C8×Q8—711no—
129C4×SD16—712no—
130C4×SD16D7111yescharacteristic
131C22×Q8—1421no—
132C2×SD16—712no—
133C2×SD16C2×D7111yescharacteristic
134C4⋊Q8—712no—
135C4⋊Q8—712no—
136C4⋊Q8—711no—
137C4⋊Q8—711no—
138#125—1421no—
139#125—1422no—
140C22⋊Q8—1422no—
141C22⋊Q8—1421no—
142C4×Q8—711no—
143C4×Q8—712no—
144C4×Q8—1421no—
145C4×Q8C2×D7111yescharacteristic
146C4×D4—712no—
147C4×D4C2×D7111yescharacteristic
148#106—712no—
149#106C2×D7111yescharacteristic
150C4⋊C8—712no—
151C4⋊C8—711no—
152#103—712no—
153#103—712no—
154#103—712no—
155#103—712no—
156#103C2×D7111yescharacteristic
157#102C2×D7111yescharacteristic
158C4×C8—712no—
159C4×C8C2×D7111yescharacteristic
160C2×Q8—2844no—
161C2×Q8—711no—
162C2×Q8—712no—
163C2×Q8—1422no—
164C2×Q8—1421no—
165C2×Q8C22×D7111yescharacteristic
166C2×D4C22×D7111yescharacteristic
167C22×C4—21no—
168C22×C4—1422no—
169SD16—22no—
170SD16—1424no—
171C2×C8—712no—
172C2×C8C22×D7111yescharacteristic
173C2×C8C22×D7111yescharacteristic
174C4⋊C4—21no—
175C4⋊C4—712no—
176C4⋊C4—711no—
177C4⋊C4—712no—
178C4⋊C4—1422no—
179C4⋊C4—1422no—
180C4⋊C4—1422no—
181C4⋊C4—1422no—
182C4⋊C4—1421no—
183C4⋊C4—1421no—
184C4⋊C4—1421no—
185C4⋊C4C22×D7111yescharacteristic
186C4⋊C4C22×D7111yescharacteristic
187C22⋊C4—21no—
188C22⋊C4—1422no—
189C42—21no—
190C42—712no—
191C42—1422no—
192C42C22×D7111yescharacteristic
193C23—21no—
194Q8—21no—
195Q8—21no—
196Q8—2844no—
197Q8—2842no—
198Q8—714no—
199Q8—1422no—
200Q8—1422no—
201D4—21no—
202D4#1176586512yes—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—42no—
207C2×C4—2844no—
208C2×C4—712no—
209C2×C4—712no—
210C2×C4—1422no—
211C2×C4—1422no—
212C2×C4D4×D7111yescharacteristic
213C2×C4D4×D7111yescharacteristic
214C2×C4C23×D7111yescharacteristic
215C8—21no—
216C8—21no—
217C8—1422no—
218C22—22no—
219C22—41no—
220C22—41no—
221C22C2×D4×D7111yescharacteristic
222C4—21no—
223C4—41no—
224C4—41no—
225C4—41no—
226C4—2842no—
227C4—2842no—
228C4—714no—
229C4—1422no—
230C4SD16×D7112yes—
231C4C2×#1176586511yescharacteristic
232C4#1455617511yescharacteristic
233C2—42no—
234C2#1798665811yescharacteristic
235C2C2×SD16×D7111yescharacteristic
236C2#1798681311yescharacteristic
subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
FittingC4×SD16×C71C2
socleC22×C71C22×D4
hypercenterC4×SD16D71
hypocenterC71#3359
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #17986727C2semidirect
3. #17986350C2semidirect
4. #17986348C2semidirect
5. #17986284C2semidirect
6. #17986283C2semidirect
9. C8×Dic142C2semidirect
95. Dic142SD16semidirect
119. C71#3359semidirect