Finite Group Databasebeta

← #22586906

Subgroups — #22586906

Order 9088.

340 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 71 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#121×D71C211yesmaximal, characteristic
2C22⋊C8×D71C211yesmaximal, characteristic, complemented
3#17985858C211yesmaximal, characteristic, complemented
4#17985734C211yesmaximal, characteristic, complemented
5#17985733C211yesmaximal, characteristic, complemented
6#17985732C211yesmaximal, characteristic, complemented
7#327×C71C211yesmaximal, characteristic, complemented
8C2×D4×D71—21no—
9C2×D4×D71C411yescharacteristic, complemented
10C22×C4×D71C2211yescharacteristic
11C2×C8×D71—21no—
12#14556103C411yescharacteristic, complemented
13#14556102C2211yescharacteristic
14#14556101—21no—
15#14556100—21no—
16#14556099C411yescharacteristic, complemented
17C2×Dic71⋊C4—21no—
18C4⋊C4×D71C411yescharacteristic, complemented
19C2×(C2×D71)⋊C4—21no—
20C22⋊C4×D71—21no—
21C22⋊(C71⋊C8)C2211yescharacteristic, complemented
22(C2×D71)⋊C8—21no—
23C71⋊#95C2211yescharacteristic, complemented
24#121×C71C2211yescharacteristic
25C22⋊C8×C71C2211yescharacteristic, complemented
26#95×C71C2211yescharacteristic, complemented
27C23×D71—21no—
28C23×D71D411yescharacteristic
29C2×D284—21no—
30C2×D284C2×C411yescharacteristic
31C2×C22⋊D71—21no—
32C2×C22⋊D71—21no—
33C2×C22⋊D71—21no—
34D4×D71—42no—
35D4×D71—42no—
36D4×D71—42no—
37C22×Dic71—21no—
38C22×Dic71D411yescharacteristic
39C2×C4×D71—21no—
40C2×C4×D71—42no—
41C2×C4×D71C2×C411yescharacteristic
42C2×C4×D71C2×C411yescharacteristic
43C2×C4×D71D411yescharacteristic
44C2×C4×D71D411yescharacteristic
45C2×C71⋊C8—21no—
46C8×D71—42no—
47C4⋊Dic71C2×C411yescharacteristic
48Dic71⋊C4—21no—
49Dic71⋊C4—42no—
50C22⋊Dic71—21no—
51(C2×D71)⋊C4—21no—
52(C2×D71)⋊C4—21no—
53(C2×D71)⋊C4—42no—
54C2×D4×C71—21no—
55C2×D4×C71C2×C411yescharacteristic
56C22×C4×C71—21no—
57C22×C4×C71C2311yescharacteristic
58C2×C8×C71—21no—
59C4⋊C4×C71C2×C411yescharacteristic
60C22⋊C4×C71—21no—
61C23×C71—21no—
62C23×C71C2×D411yescharacteristic
63C22×D71—21no—
64C22×D71—41no—
65C22×D71—41no—
66C22×D71—42no—
67C22×D71—42no—
68C22×D71—42no—
69C22×D71C22⋊C411yescharacteristic
70C22×D71C22⋊C411yescharacteristic
71C22×D71D812yes—
72C22×D71SD1612yes—
73D4×C71—41no—
74D4×C71—41no—
75D4×C71—41no—
76C2×C4×C71—21no—
77C2×C4×C71—41no—
78C2×C4×C71—41no—
79C2×C4×C71—41no—
80C2×C4×C71—41no—
81C2×C4×C71C22×C411yescharacteristic
82C2×C4×C71C2×D411yescharacteristic
83C22⋊D71—41no—
84C22⋊D71—41no—
85C22⋊D71—42no—
86C22⋊D71—42no—
87C2×Dic71—22no—
88C2×Dic71—21no—
89C2×Dic71—41no—
90C2×Dic71—41no—
91C2×Dic71—41no—
92C2×Dic71C22⋊C411yescharacteristic
93C2×Dic71C22⋊C411yescharacteristic
94D284—41no—
95D284—42no—
96C4×D71—22no—
97C4×D71—22no—
98C4×D71—41no—
99C4×D71—41no—
100C4×D71—42no—
101C8×C71—41no—
102C71⋊C8—41no—
103C22×C71—21no—
104C22×C71—21no—
105C22×C71—41no—
106C22×C71—41no—
107C22×C71—41no—
108C22×C71C2×C22⋊C411yescharacteristic
109C22×C71C2×D811yescharacteristic
110C22×C71C2×SD1611yescharacteristic
111C2×D71—21no—
112C2×D71—21no—
113C2×D71—21no—
114C2×D71—21no—
115C2×D71—42no—
116C2×D71—42no—
117C2×D71—41no—
118C2×D71—41no—
119C2×D71—41no—
120C2×D71—84no—
121C2×D71#10212yes—
122C2×D71#10212yes—
123C4×C71—21no—
124C4×C71—21no—
125C4×C71—41no—
126C4×C71—81no—
127Dic71—21no—
128Dic71—41no—
129Dic71—81no—
130Dic71#9912yes—
131C2×C71—21no—
132C2×C71—21no—
133C2×C71—81no—
134C2×C71C2×#9911yescharacteristic
135C2×C71C2×#10211yescharacteristic
136C2×C71#42111yescharacteristic
137D71—22no—
138D71—22no—
139D71—81no—
140#1519—711nomaximal, Sylow
141C71#151911yescharacteristic, complemented, Sylow
142C2×#121—711no—
143C2×C22⋊C8—711no—
144#380—711no—
145#327—711no—
146#327—711no—
147#327—711no—
148#327D7111yescharacteristic, complemented
149C22×D4—711no—
150C22×D4—1421no—
151C23×C4—711no—
152C22×C8—1421no—
153#121—711no—
154#121—711no—
155#121—711no—
156#121—1421no—
157#121—1421no—
158#121C2×D7111yescharacteristic
159C2×C4⋊C4—711no—
160C2×C4⋊C4—1421no—
161C2×C22⋊C4—1421no—
162C2×C22⋊C4—1421no—
163C22⋊C8—711no—
164C22⋊C8—1421no—
165C22⋊C8C2×D7111yescharacteristic, complemented
166#95—711no—
167#95C2×D7111yescharacteristic, complemented
168C24—711no—
169C24—1421no—
170C2×D4—21no—
171C2×D4—2842no—
172C2×D4—2842no—
173C2×D4—2842no—
174C2×D4—711no—
175C2×D4—1421no—
176C2×D4—1421no—
177C2×D4—1421no—
178C2×D4—1421no—
179C2×D4C4×D7111yescharacteristic
180C22×C4—21no—
181C22×C4—2842no—
182C22×C4—711no—
183C22×C4—711no—
184C22×C4—711no—
185C22×C4—711no—
186C22×C4—711no—
187C22×C4—1421no—
188C22×C4—1421no—
189C22×C4C22×D7111yescharacteristic
190C2×C8—21no—
191C2×C8—2842no—
192C2×C8—1421no—
193C4⋊C4—2842no—
194C4⋊C4—711no—
195C4⋊C4—1421no—
196C4⋊C4C4×D7111yescharacteristic
197C22⋊C4—21no—
198C22⋊C4—2842no—
199C22⋊C4—1421no—
200C22⋊C4—1421no—
201C22⋊C4—1421no—
202C23—21no—
203C23—2841no—
204C23—2841no—
205C23—2842no—
206C23—2842no—
207C23—2842no—
208C23—712no—
209C23—712no—
210C23—711no—
211C23—711no—
212C23—1421no—
213C23D4×D7111yescharacteristic
214D4—41no—
215D4—41no—
216D4—41no—
217D4—2841no—
218D4—2842no—
219D4—2842no—
220D4—2841no—
221D4—2841no—
222D4—2842no—
223C2×C4—21no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—2841no—
229C2×C4—2841no—
230C2×C4—2842no—
231C2×C4—2841no—
232C2×C4—2841no—
233C2×C4—2841no—
234C2×C4—711no—
235C2×C4—711no—
236C2×C4—1422no—
237C2×C4—1422no—
238C2×C4—1421no—
239C2×C4—1422no—
240C2×C4C2×C4×D7111yescharacteristic
241C2×C4D4×D7111yescharacteristic
242C8—41no—
243C8—2841no—
244C22—21no—
245C22—21no—
246C22—41no—
247C22—41no—
248C22—41no—
249C22—2842no—
250C22—2842no—
251C22—2841no—
252C22—2841no—
253C22—2841no—
254C22—5684no—
255C22—712no—
256C22—712no—
257C22—1421no—
258C22—1421no—
259C22—1421no—
260C22—1421no—
261C22C22⋊C4×D7111yescharacteristic
262C22D8×D7111yescharacteristic
263C22SD16×D7111yescharacteristic
264C4—21no—
265C4—21no—
266C4—41no—
267C4—81no—
268C4—2841no—
269C4—5681no—
270C4—712no—
271C4—1421no—
272C2—21no—
273C2—21no—
274C2—81no—
275C2—5681no—
276C2—1422no—
277C2—1422no—
278C2#99×D7111yescharacteristic
279C2#102×D7111yescharacteristic
280C2#1798601411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D71
commutatorC2×C4×C71C22×C4
FrattiniC22×C4C22×D71
Fitting#327×C71C2
socleC22×C71C2×C22⋊C4
hypercenter#327D71
hypocenterC71#1519
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×D71C2semidirect
3. #17985858C2semidirect
4. #17985734C2semidirect
5. #17985733C2semidirect
6. #17985732C2semidirect
7. #327×C71C2semidirect
9. C2×D4×D71C4semidirect
12. #14556103C4semidirect
16. #14556099C4semidirect
18. C4⋊C4×D71C4semidirect
21. C22⋊(C71⋊C8)C22semidirect
23. C71⋊#95C22semidirect
25. C22⋊C8×C71C22semidirect
26. #95×C71C22semidirect
141. C71#1519semidirect
148. #327D71semidirect
165. C22⋊C8C2×D71semidirect
167. #95C2×D71semidirect