Finite Group Databasebeta

← #22599049

Subgroups — #22599049

Order 9088.

366 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 129 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#17986533C211yesmaximal, characteristic
3#17986408C211yesmaximal, characteristic, complemented
4#17986393C211yesmaximal, characteristic, complemented
5#17986368C211yesmaximal, characteristic, complemented
6#17986359C211yesmaximal, characteristic, complemented
7#17986240C212yesmaximal, complemented
8#17986228C212yesmaximal
9#17986107C212yesmaximal, complemented
10#17986101C212yesmaximal, complemented
11C2×#97×C71C211yesmaximal, characteristic, complemented
12C2×Dic284C2212yes—
13C2×#11765854C2212yes—
14#14556128C2211yescharacteristic
15#14556128C2211yescharacteristic
16#14556122—21no—
17#14556120—21no—
18#14556120C2211yescharacteristic
19#14556116C2211yescharacteristic
20#14556111—21no—
21#14556107—21no—
22#14556107C2212yes—
23#14556107C2211yescharacteristic
24#14556102C2211yescharacteristic
25C4×Dic142—21no—
26C4×Dic142C2212yes—
27C4×Dic142C2211yescharacteristic
28C4×D284C2211yescharacteristic
29C4×C22⋊D71—21no—
30#14556087—21no—
31#14556085—21no—
32#14556062C2212yes—
33#14556060C2212yes—
34#14556053C2212yes—
35#14556053C2212yes—
36#14556053C2212yes—
37#14556050C2212yes—
38C22×C8×C71C2212yes—
39C2×C42×C71C2211yescharacteristic
40#97×C71C2212yes—
41#97×C71C2211yescharacteristic
42#97×C71C2211yescharacteristic
43C2×Dic142—21no—
44C2×Dic142C2311yescharacteristic
45C2×Dic142C2312yes—
46C2×D284C2311yescharacteristic
47C2×C22⋊D71—21no—
48C2×C4×D71—21no—
49Dic284—24no—
50#11765854—24no—
51C4⋊Dic71—21no—
52C4⋊Dic71—21no—
53C4⋊Dic71—21no—
54C4⋊Dic71C2312yes—
55C4⋊Dic71C2311yescharacteristic
56C4⋊Dic71C2311yescharacteristic
57Dic71⋊C4—21no—
58Dic71⋊C4—21no—
59Dic71⋊C4—21no—
60Dic71⋊C4—22no—
61Dic71⋊C4—22no—
62Dic71⋊C4—21no—
63C22⋊Dic71—22no—
64C22⋊Dic71—21no—
65(C2×D71)⋊C4—21no—
66(C2×D71)⋊C4—21no—
67(C2×D71)⋊C4—21no—
68(C2×D71)⋊C4—21no—
69C4×Dic71—21no—
70C4×Dic71—22no—
71C22×C4×C71D411yescharacteristic
72C22×C4×C71D411yescharacteristic
73C22×C4×C71C2311yescharacteristic
74C2×C8×C71—24no—
75C2×C8×C71C2312yes—
76C2×C8×C71C2312yes—
77C42×C71D411yescharacteristic
78C42×C71D411yescharacteristic
79C42×C71C2311yescharacteristic
80C42×C71C2311yescharacteristic
81C23×C71C2×D411yescharacteristic
82C22×D71—21no—
83C2×C4×C71—22no—
84C2×C4×C71—22no—
85C2×C4×C71—41no—
86C2×C4×C71C2×D411yescharacteristic
87C2×C4×C71C2×D411yescharacteristic
88C2×C4×C71C2×D411yescharacteristic
89C2×C4×C71C2×D411yescharacteristic
90C2×C4×C71C2×D411yescharacteristic
91C2×C4×C71C2411yescharacteristic
92C22⋊D71—42no—
93C2×Dic71—21no—
94C2×Dic71—21no—
95C2×Dic71—22no—
96C2×Dic71—22no—
97C2×Dic71—21no—
98D284—22no—
99C4×D71—42no—
100Dic142—22no—
101Dic142—22no—
102Dic142—22no—
103Dic142—42no—
104C8×C71—22no—
105C8×C71#4114yes—
106C22×C71—21no—
107C22×C71—21no—
108C22×C71#13712yes—
109C22×C71C22×D411yescharacteristic
110C2×D71—41no—
111C2×D71—41no—
112C2×D71—41no—
113C4×C71—21no—
114C4×C71—21no—
115C4×C71—21no—
116C4×C71—21no—
117C4×C71—21no—
118C4×C71C2×#4112yes—
119Dic71—42no—
120Dic71—41no—
121Dic71—41no—
122Dic71—42no—
123Dic71—41no—
124C2×C71—22no—
125C2×C71#53211yescharacteristic
126C2×C71C2×#13711yescharacteristic
127C2×C71#57511yescharacteristic
128D71—81no—
129#3181—711nomaximal, Sylow
130C71#318111yescharacteristic, complemented, Sylow
131#533—711no—
132#529—711no—
133#501—711no—
134#497—711no—
135#491—711no—
136#489—711no—
137#467—712no—
138#465—712no—
139#441—712no—
140#440—712no—
141C2×#97D7111yescharacteristic, complemented
142C2×Q16—712no—
143C2×SD16—712no—
144C22×C8C2×D7112yes—
145C4⋊Q8—711no—
146C4⋊Q8—711no—
147#126—1421no—
148#125—711no—
149#125—1421no—
150#124—711no—
151#123—1421no—
152C22⋊Q8—711no—
153C22⋊Q8—712no—
154C22⋊Q8—1421no—
155#121—711no—
156C4×Q8—711no—
157C4×Q8—712no—
158C4×Q8—1421no—
159C4×D4—711no—
160C4×D4—1421no—
161#117—1421no—
162#117—1421no—
163C2×C42C2×D7111yescharacteristic
164#107—712no—
165#106—712no—
166#103—712no—
167#103—712no—
168#103—712no—
169#102—712no—
170#97C2×D7112yes—
171#97C2×D7111yescharacteristic
172#97C2×D7111yescharacteristic
173C2×Q8—711no—
174C2×Q8—712no—
175C2×Q8—1421no—
176C2×D4—711no—
177C2×D4—1421no—
178C22×C4—1421no—
179C22×C4D28411yescharacteristic
180C22×C4D28411yescharacteristic
181C22×C4C22×D7111yescharacteristic
182Q16—1424no—
183SD16—1424no—
184C2×C8—24no—
185C2×C8C22×D7112yes—
186C2×C8C22×D7112yes—
187C4⋊C4—712no—
188C4⋊C4—711no—
189C4⋊C4—711no—
190C4⋊C4—1421no—
191C4⋊C4—1421no—
192C4⋊C4—1421no—
193C4⋊C4—1422no—
194C4⋊C4—1421no—
195C4⋊C4—1422no—
196C4⋊C4—1421no—
197C4⋊C4—1421no—
198C4⋊C4—1421no—
199C22⋊C4—1422no—
200C22⋊C4—1421no—
201C22⋊C4—1421no—
202C22⋊C4—1421no—
203C22⋊C4—1421no—
204C22⋊C4—1421no—
205C42—1421no—
206C42—1422no—
207C42D28411yescharacteristic
208C42D28411yescharacteristic
209C42C22×D7111yescharacteristic
210C42C22×D7111yescharacteristic
211C23—1421no—
212C23C2×D28411yescharacteristic
213Q8—2842no—
214Q8—1422no—
215Q8—1422no—
216Q8—1422no—
217D4—2842no—
218D4—1422no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—2842no—
223C2×C4—1421no—
224C2×C4—1421no—
225C2×C4—1422no—
226C2×C4—1422no—
227C2×C4—1421no—
228C2×C4C2×D28411yescharacteristic
229C2×C4C2×D28411yescharacteristic
230C2×C4C2×D28411yescharacteristic
231C2×C4C2×D28411yescharacteristic
232C2×C4C2×D28411yescharacteristic
233C2×C4C23×D7111yescharacteristic
234C8—22no—
235C8#1176586514yes—
236C22—21no—
237C22—21no—
238C22—2841no—
239C22—2841no—
240C22—2841no—
241C22#1455616112yes—
242C22C22×D28411yescharacteristic
243C4—21no—
244C4—21no—
245C4—21no—
246C4—21no—
247C4—21no—
248C4—2841no—
249C4—2841no—
250C4—2842no—
251C4—2841no—
252C4—2842no—
253C4C2×#1176586512yes—
254C2—22no—
255C2—5681no—
256C2#1798654911yescharacteristic
257C2C2×#1455616111yescharacteristic
258C2#1798679911yescharacteristic
subgroupG/H
centerC22C22×D284
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
FittingC2×#97×C71C2
socleC22×C71C22×D4
hypercenterC2×#97D71
hypocenterC71#3181
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
1. #17986556C2semidirect
3. #17986408C2semidirect
4. #17986393C2semidirect
5. #17986368C2semidirect
6. #17986359C2semidirect
7. #17986240C2semidirect
9. #17986107C2semidirect
10. #17986101C2semidirect
11. C2×#97×C71C2semidirect
130. C71#3181semidirect
141. C2×#97D71semidirect