Finite Group Databasebeta

← #22599736

Subgroups — #22599736

Order 9088.

354 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17986533C211yesmaximal, characteristic, complemented
2#17986306C211yesmaximal, characteristic, complemented
3#17986303C211yesmaximal, characteristic, complemented
4#17986299C211yesmaximal, characteristic, complemented
5#17986296C211yesmaximal, characteristic, complemented
6#17986255C211yesmaximal, characteristic, complemented
7#17986250C211yesmaximal, characteristic
8#17986247C211yesmaximal, characteristic, complemented
9#17986243C211yesmaximal, characteristic, complemented
10#17986221C211yesmaximal, characteristic, complemented
11#17986218C211yesmaximal, characteristic, complemented
12#17986214C211yesmaximal, characteristic, complemented
13#17986211C211yesmaximal, characteristic, complemented
14#17986023C211yesmaximal, characteristic, complemented
15#529×C71C211yesmaximal, characteristic, complemented
16C2×#11765855C2211yescharacteristic
17C2×#11765853C2211yescharacteristic
18C2×#11765852C2211yescharacteristic
19C2×#11765850C2211yescharacteristic
20C2×#11765849C2211yescharacteristic
21C2×#11765849C2211yescharacteristic
22#14556122—21no—
23#14556120C2211yescharacteristic
24#14556116C2211yescharacteristic
25#14556111—21no—
26#14556107C2211yescharacteristic
27#14556102C2211yescharacteristic
28C4×Dic142C2211yescharacteristic
29C4×D284C2211yescharacteristic
30C4×C22⋊D71—21no—
31#14556085—21no—
32#14556061C2211yescharacteristic
33#14556061C2211yescharacteristic
34#14556059C2211yescharacteristic
35#14556059C2211yescharacteristic
36C4⋊(C71⋊C8)C2211yescharacteristic
37C4⋊(C71⋊C8)C2211yescharacteristic
38C4⋊(C71⋊C8)C2211yescharacteristic
39C4⋊(C71⋊C8)C2211yescharacteristic
40#14556052C2211yescharacteristic
41#14556052C2211yescharacteristic
42#14556051C2211yescharacteristic
43#14556051C2211yescharacteristic
44#14556049C2211yescharacteristic
45#14556049C2211yescharacteristic
46#14556048C2211yescharacteristic
47#14556048C2211yescharacteristic
48#126×C71—21no—
49#125×C71C2211yescharacteristic
50#124×C71C2211yescharacteristic
51#123×C71—21no—
52C22⋊Q8×C71C2211yescharacteristic
53#121×C71C2211yescharacteristic
54C4×Q8×C71C2211yescharacteristic
55C4×D4×C71—21no—
56C4×D4×C71C2211yescharacteristic
57#117×C71—21no—
58C2×C42×C71C2211yescharacteristic
59C2×Dic142C2311yescharacteristic
60C2×D284C2311yescharacteristic
61C2×C22⋊D71—21no—
62C2×C4×D71—21no—
63#11765855—41no—
64#11765853—41no—
65#11765852—41no—
66#11765850—41no—
67#11765849—41no—
68#11765849—41no—
69C2×C71⋊C8C2311yescharacteristic
70C2×C71⋊C8C2311yescharacteristic
71C2×C71⋊C8C2311yescharacteristic
72C2×C71⋊C8C2311yescharacteristic
73C4⋊Dic71C2311yescharacteristic
74C4⋊Dic71C2311yescharacteristic
75Dic71⋊C4—21no—
76Dic71⋊C4—21no—
77Dic71⋊C4—21no—
78Dic71⋊C4—21no—
79C22⋊Dic71—21no—
80(C2×D71)⋊C4—21no—
81(C2×D71)⋊C4—21no—
82(C2×D71)⋊C4—21no—
83(C2×D71)⋊C4—21no—
84C4×Dic71—21no—
85C2×Q8×C71C2311yescharacteristic
86C2×D4×C71—21no—
87C2×D4×C71C2311yescharacteristic
88C22×C4×C71—21no—
89C22×C4×C71D411yescharacteristic
90C22×C4×C71D411yescharacteristic
91C22×C4×C71C2311yescharacteristic
92C4⋊C4×C71—21no—
93C4⋊C4×C71—21no—
94C4⋊C4×C71—21no—
95C4⋊C4×C71—21no—
96C4⋊C4×C71C2311yescharacteristic
97C4⋊C4×C71C2311yescharacteristic
98C22⋊C4×C71—21no—
99C22⋊C4×C71—21no—
100C22⋊C4×C71—21no—
101C22⋊C4×C71—21no—
102C22⋊C4×C71—21no—
103C42×C71—21no—
104C42×C71D411yescharacteristic
105C42×C71D411yescharacteristic
106C42×C71C2311yescharacteristic
107C42×C71C2311yescharacteristic
108C23×C71—21no—
109C23×C71C2×D411yescharacteristic
110C22×D71—21no—
111Q8×C71—21no—
112Q8×C71—21no—
113D4×C71—21no—
114D4×C71—21no—
115D4×C71—42no—
116C2×C4×C71—21no—
117C2×C4×C71—21no—
118C2×C4×C71—21no—
119C2×C4×C71—21no—
120C2×C4×C71—21no—
121C2×C4×C71—41no—
122C2×C4×C71—41no—
123C2×C4×C71—42no—
124C2×C4×C71C2×D411yescharacteristic
125C2×C4×C71C2×D411yescharacteristic
126C2×C4×C71C2×D411yescharacteristic
127C2×C4×C71C2×D411yescharacteristic
128C2×C4×C71C2×D411yescharacteristic
129C2×C4×C71C2411yescharacteristic
130C22⋊D71—42no—
131C2×Dic71—21no—
132C2×Dic71—21no—
133C2×Dic71—21no—
134D284—21no—
135D284—21no—
136C4×D71—42no—
137Dic142—21no—
138Dic142—21no—
139C71⋊C8—21no—
140C71⋊C8—21no—
141C71⋊C8—21no—
142C71⋊C8—21no—
143C22×C71—21no—
144C22×C71—21no—
145C22×C71—21no—
146C22×C71—41no—
147C22×C71—41no—
148C22×C71—41no—
149C22×C71C22×D411yescharacteristic
150C2×D71—41no—
151C2×D71—41no—
152C2×D71—41no—
153C4×C71—21no—
154C4×C71—21no—
155C4×C71—21no—
156C4×C71—21no—
157C4×C71—21no—
158C4×C71—41no—
159C4×C71—41no—
160C4×C71—41no—
161C4×C71H(5,𝔽2)11yescharacteristic
162C4×C712−1+411yescharacteristic
163Dic71—41no—
164Dic71—41no—
165Dic71—41no—
166C2×C71—41no—
167C2×C71—81no—
168C2×C71#53711yescharacteristic
169C2×C71#57511yescharacteristic
170C2×C71#57511yescharacteristic
171D71—81no—
172#3256—711nomaximal, Sylow
173C71#325611yescharacteristic, complemented, Sylow
174#529—711no—
175#529D7111yescharacteristic, complemented
176#479—711no—
177#479—711no—
178#478—711no—
179#478—711no—
180#470—711no—
181#469—711no—
182#468—711no—
183#468—711no—
184#464—711no—
185#464—711no—
186#463—711no—
187#463—711no—
188#423—711no—
189C2×Q16—711no—
190C2×SD16—711no—
191C2×SD16—711no—
192C2×D8—711no—
193C2×M16—711no—
194C2×M16—711no—
195#126—21no—
196#126—1421no—
197#125—711no—
198#125C2×D7111yescharacteristic
199#124—711no—
200#124C2×D7111yescharacteristic
201#123—21no—
202#123—1421no—
203C22⋊Q8—711no—
204C22⋊Q8C2×D7111yescharacteristic
205#121—711no—
206#121C2×D7111yescharacteristic
207C4×Q8—711no—
208C4×Q8C2×D7111yescharacteristic
209C4×D4—21no—
210C4×D4—711no—
211C4×D4—1421no—
212C4×D4C2×D7111yescharacteristic
213#117—21no—
214#117—1421no—
215C2×C42C2×D7111yescharacteristic
216#107—711no—
217#107—711no—
218#106—711no—
219#106—711no—
220C4⋊C8—711no—
221C4⋊C8—711no—
222C4⋊C8—711no—
223C4⋊C8—711no—
224#103—711no—
225#103—711no—
226#103—711no—
227#103—711no—
228#102—711no—
229#102—711no—
230#102—711no—
231#102—711no—
232C2×Q8—711no—
233C2×Q8C22×D7111yescharacteristic
234C2×D4—21no—
235C2×D4—711no—
236C2×D4—1421no—
237C2×D4C22×D7111yescharacteristic
238C22×C4—21no—
239C22×C4—1421no—
240C22×C4C22⋊D7111yescharacteristic
241C22×C4C22⋊D7111yescharacteristic
242C22×C4C22×D7111yescharacteristic
243Q16—2841no—
244SD16—2841no—
245SD16—2841no—
246D8—2841no—
247M16—2841no—
248M16—2841no—
249C2×C8—711no—
250C2×C8—711no—
251C2×C8—711no—
252C2×C8—711no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—711no—
258C4⋊C4—711no—
259C4⋊C4—1421no—
260C4⋊C4—1421no—
261C4⋊C4—1421no—
262C4⋊C4—1421no—
263C4⋊C4C22×D7111yescharacteristic
264C4⋊C4C22×D7111yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—1421no—
271C22⋊C4—1421no—
272C22⋊C4—1421no—
273C22⋊C4—1421no—
274C22⋊C4—1421no—
275C42—21no—
276C42—1421no—
277C42C22⋊D7111yescharacteristic
278C42C22⋊D7111yescharacteristic
279C42C22×D7111yescharacteristic
280C42C22×D7111yescharacteristic
281C23—21no—
282C23—1421no—
283C23C2×C22⋊D7111yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—1421no—
287Q8—1421no—
288D4—21no—
289D4—21no—
290D4—42no—
291D4—2842no—
292D4—1421no—
293D4—1421no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—2842no—
303C2×C4—1421no—
304C2×C4—1421no—
305C2×C4—1421no—
306C2×C4C2×C22⋊D7111yescharacteristic
307C2×C4C2×C22⋊D7111yescharacteristic
308C2×C4C2×C22⋊D7111yescharacteristic
309C2×C4C2×C22⋊D7111yescharacteristic
310C2×C4C2×C22⋊D7111yescharacteristic
311C2×C4C23×D7111yescharacteristic
312C8—1421no—
313C8—1421no—
314C8—1421no—
315C8—1421no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—2841no—
323C22—2841no—
324C22—2841no—
325C22C22×C22⋊D7111yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—2841no—
335C4—2841no—
336C4—2841no—
337C4#1455617411yescharacteristic
338C4#1455617511yescharacteristic
339C2—41no—
340C2—81no—
341C2—5681no—
342C2#1798657711yescharacteristic
343C2#1798679711yescharacteristic
344C2#1798679711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#529×C71C2
socleC22×C71C22×D4
hypercenter#529D71
hypocenterC71#3256
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #17986533C2semidirect
2. #17986306C2semidirect
3. #17986303C2semidirect
4. #17986299C2semidirect
5. #17986296C2semidirect
6. #17986255C2semidirect
8. #17986247C2semidirect
9. #17986243C2semidirect
10. #17986221C2semidirect
11. #17986218C2semidirect
12. #17986214C2semidirect
13. #17986211C2semidirect
14. #17986023C2semidirect
15. #529×C71C2semidirect
173. C71#3256semidirect
175. #529D71semidirect