Finite Group Databasebeta

← #22598467

Subgroups — #22598467

Order 9088.

380 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 119 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#17986551C211yesmaximal, characteristic
2C2×#14556093C211yesmaximal, characteristic
3#17986329C211yesmaximal, characteristic
4#17986283C212yesmaximal, complemented
5#17986208C212yesmaximal, complemented
6#17986157C211yesmaximal, characteristic
7#17986154C211yesmaximal, characteristic
8#17986105C212yesmaximal, complemented
9#17986103C212yesmaximal, complemented
10#17986053C211yesmaximal, characteristic
11#483×C71C211yesmaximal, characteristic
12C22×Dic142C2211yescharacteristic
13C2×Dic284C2212yes—
14C2×#11765855C2212yes—
15#14556127C2211yescharacteristic
16#14556126C2211yescharacteristic
17#14556118—21no—
18#14556107C2211yescharacteristic
19#14556105—21no—
20Q8×Dic71C2211yescharacteristic
21#14556093—21no—
22#14556093—21no—
23#14556093—21no—
24#14556093C2212yes—
25#14556093C2211yescharacteristic
26#14556093C2212yes—
27#14556084—21no—
28C2×Dic71⋊C4—21no—
29C2×C4×Dic71—21no—
30C2×C4×Dic71C2211yescharacteristic
31#14556059C2212yes—
32Dic71⋊C8C2212yes—
33#14556053C2212yes—
34#14556051C2212yes—
35#14556051C2212yes—
36C22⋊(C71⋊C8)C2211yescharacteristic
37#14556038C2212yes—
38C22⋊Q8×C71C2211yescharacteristic
39C2×C4⋊C4×C71C2211yescharacteristic
40#106×C71C2212yes—
41#103×C71C2212yes—
42C22⋊C8×C71C2211yescharacteristic
43C2×Dic142—21no—
44C2×Dic142—24no—
45C2×Dic142—21no—
46C2×Dic142C2311yescharacteristic
47C2×Dic142C2312yes—
48C22×Dic71—21no—
49C22×Dic71D411yescharacteristic
50C22×Dic71D411yescharacteristic
51Dic284—24no—
52#11765855—24no—
53C2×C71⋊C8C2312yes—
54C4⋊Dic71—21no—
55C4⋊Dic71C2311yescharacteristic
56Dic71⋊C4—21no—
57Dic71⋊C4—22no—
58Dic71⋊C4—22no—
59Dic71⋊C4—21no—
60Dic71⋊C4—21no—
61Dic71⋊C4—21no—
62Dic71⋊C4—21no—
63C22⋊Dic71—21no—
64C4×Dic71—22no—
65C4×Dic71—22no—
66C4×Dic71—21no—
67C4×Dic71—21no—
68C4×Dic71D411yescharacteristic
69C4×Dic71D411yescharacteristic
70C4×Dic71C2311yescharacteristic
71C4×Dic71C2311yescharacteristic
72C2×Q8×C71C2311yescharacteristic
73C22×C4×C71—21no—
74C22×C4×C71C2311yescharacteristic
75C2×C8×C71C2312yes—
76C4⋊C4×C71—21no—
77C4⋊C4×C71—21no—
78C4⋊C4×C71C2312yes—
79C4⋊C4×C71C2311yescharacteristic
80C22⋊C4×C71—21no—
81C23×C71C2×D411yescharacteristic
82Q8×C71—22no—
83C2×C4×C71—22no—
84C2×C4×C71—21no—
85C2×C4×C71—21no—
86C2×C4×C71—22no—
87C2×C4×C71—42no—
88C2×C4×C71C2×D411yescharacteristic
89C2×C4×C71C2411yescharacteristic
90C2×Dic71—24no—
91C2×Dic71—22no—
92C2×Dic71—22no—
93C2×Dic71—22no—
94C2×Dic71—21no—
95C2×Dic71—21no—
96C2×Dic71C2×D411yescharacteristic
97C2×Dic71C2×D411yescharacteristic
98C2×Dic71C2×D411yescharacteristic
99C2×Dic71C2×D411yescharacteristic
100Dic142—24no—
101Dic142—22no—
102Dic142—22no—
103Dic142—42no—
104Dic142#4114yes—
105C8×C71—22no—
106C71⋊C8—22no—
107C22×C71—21no—
108C22×C71—21no—
109C22×C71#13712yes—
110C22×C71C22×D411yescharacteristic
111C4×C71—21no—
112C4×C71—41no—
113C4×C71—41no—
114C4×C71—42no—
115C4×C71C2×#4112yes—
116Dic71—24no—
117Dic71—21no—
118Dic71—21no—
119Dic71—21no—
120Dic71—41no—
121Dic71—41no—
122Dic71#13712yes—
123C2×C71—22no—
124C2×C71#52511yescharacteristic
125C2×C71C2×#13711yescharacteristic
126C2×C71C2×#13711yescharacteristic
127#3113—711nomaximal, Sylow
128C71#311311yescharacteristic, complemented, Sylow
129#533—711no—
130C2×C4×Q8—711no—
131#483—711no—
132#483D7111yescharacteristic
133#475—712no—
134#462—712no—
135#451—711no—
136#451—711no—
137#441—712no—
138#441—712no—
139#432—711no—
140C22×Q8—711no—
141C2×Q16—712no—
142C2×Q16—712no—
143C4⋊Q8—711no—
144C4⋊Q8—711no—
145#125—1421no—
146C22⋊Q8—711no—
147C22⋊Q8—1421no—
148C22⋊Q8C2×D7111yescharacteristic
149C4×Q8—711no—
150C4×Q8—712no—
151C4×Q8—712no—
152C4×Q8—711no—
153C4×Q8—1421no—
154C4×Q8—1421no—
155C4×Q8—1421no—
156#117—1421no—
157C2×C4⋊C4—1421no—
158C2×C4⋊C4C2×D7111yescharacteristic
159C2×C42—711no—
160C2×C42—1421no—
161#106—712no—
162#106C2×D7112yes—
163C4⋊C8—712no—
164#103—712no—
165#103—712no—
166#103—712no—
167#103C2×D7112yes—
168C22⋊C8—711no—
169C22⋊C8C2×D7111yescharacteristic
170#97—712no—
171C2×Q8—712no—
172C2×Q8—711no—
173C2×Q8—1421no—
174C2×Q8—1424no—
175C2×Q8—1421no—
176C2×Q8C22×D7111yescharacteristic
177C22×C4—21no—
178C22×C4—711no—
179C22×C4—711no—
180C22×C4—1421no—
181C22×C4C22×D7111yescharacteristic
182Q16—1424no—
183Q16—1424no—
184C2×C8—712no—
185C2×C8C22×D7112yes—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—711no—
189C4⋊C4—1422no—
190C4⋊C4—1422no—
191C4⋊C4—1421no—
192C4⋊C4—1421no—
193C4⋊C4—1421no—
194C4⋊C4—1421no—
195C4⋊C4—1421no—
196C4⋊C4—1421no—
197C4⋊C4C22×D7111yescharacteristic
198C4⋊C4C22×D7112yes—
199C22⋊C4—21no—
200C22⋊C4—1421no—
201C42—711no—
202C42—711no—
203C42—711no—
204C42—711no—
205C42—1422no—
206C42—1422no—
207C42—1421no—
208C42—1421no—
209C23D4×D7111yescharacteristic
210Q8—22no—
211Q8—2842no—
212Q8—714no—
213Q8—1424no—
214Q8—1422no—
215Q8—1422no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—42no—
221C2×C4—711no—
222C2×C4—711no—
223C2×C4—711no—
224C2×C4—711no—
225C2×C4—1421no—
226C2×C4—1421no—
227C2×C4—1422no—
228C2×C4—1424no—
229C2×C4—1422no—
230C2×C4—1422no—
231C2×C4D4×D7111yescharacteristic
232C2×C4C23×D7111yescharacteristic
233C8—22no—
234C8—1422no—
235C22—21no—
236C22—21no—
237C22#1455615712yes—
238C22C2×D4×D7111yescharacteristic
239C4—21no—
240C4—41no—
241C4—41no—
242C4—42no—
243C4—2841no—
244C4—2841no—
245C4—712no—
246C4—1424no—
247C4—1421no—
248C4—1421no—
249C4—1421no—
250C4#41×D7112yes—
251C2—22no—
252C2#1798650711yescharacteristic
253C2#137×D7111yescharacteristic
254C2C2×#1455615711yescharacteristic
subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#483×C71C2
socleC22×C71C22×D4
hypercenter#483D71
hypocenterC71#3113
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
4. #17986283C2semidirect
5. #17986208C2semidirect
8. #17986105C2semidirect
9. #17986103C2semidirect
128. C71#3113semidirect