Finite Group Databasebeta

← #22599847

Subgroups — #22599847

Order 9088.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556160C211yesmaximal, characteristic, complemented
2C22×#11765854C211yesmaximal, characteristic, complemented
3#17986662C211yesmaximal, characteristic, complemented
4#17986640C211yesmaximal, characteristic
5#17986392C211yesmaximal, characteristic, complemented
6#17986246C211yesmaximal, characteristic, complemented
7#17986224C211yesmaximal, characteristic, complemented
8#17986203C211yesmaximal, characteristic, complemented
9#17986164C211yesmaximal, characteristic, complemented
10#17986154C211yesmaximal, characteristic, complemented
11#17986149C211yesmaximal, characteristic, complemented
12#17986139C211yesmaximal, characteristic, complemented
13#17986098C211yesmaximal, characteristic, complemented
14#17986070C211yesmaximal, characteristic, complemented
15#467×C71C211yesmaximal, characteristic, complemented
16C2×#11765866C2211yescharacteristic
17C22×Dic142C2211yescharacteristic
18C2×Q8×D71C2211yescharacteristic, complemented
19C22×D284C2211yescharacteristic
20#14556160—24no—
21C2×#11765855C2211yescharacteristic, complemented
22C2×#11765855C2211yescharacteristic, complemented
23C2×#11765854—24no—
24C2×#11765854C2211yescharacteristic
25C2×#11765854C2211yescharacteristic
26C2×#11765854C2211yescharacteristic
27C2×#11765854C2211yescharacteristic
28C2×#11765852C2211yescharacteristic
29C2×#11765852C2211yescharacteristic
30C2×#11765848C2211yescharacteristic, complemented
31#14556127—21no—
32#14556126C2211yescharacteristic, complemented
33#14556117C2211yescharacteristic
34#14556113—21no—
35#14556108C2211yescharacteristic, complemented
36#14556106—21no—
37#14556105—21no—
38#14556103—21no—
39#14556103C2211yescharacteristic
40#14556098—21no—
41#14556093C2211yescharacteristic, complemented
42#14556090C2211yescharacteristic
43C4×C22⋊D71C2211yescharacteristic
44(C22⋊D71)⋊C4—21no—
45C22⋊C4×D71—21no—
46Dic71⋊C8C2211yescharacteristic, complemented
47#14556051C2211yescharacteristic, complemented
48#14556051C2211yescharacteristic, complemented
49#14556048C2211yescharacteristic
50#14556048C2211yescharacteristic
51C22⋊(C71⋊C8)C2211yescharacteristic
52(C2×D71)⋊C8C2211yescharacteristic, complemented
53#14556038C2211yescharacteristic, complemented
54C2×Q16×C71C2211yescharacteristic, complemented
55C22×C8×C71C2211yescharacteristic
56C22⋊Q8×C71C2211yescharacteristic
57C22⋊Q8×C71C2211yescharacteristic
58#107×C71C2211yescharacteristic, complemented
59#103×C71C2211yescharacteristic, complemented
60#103×C71C2211yescharacteristic, complemented
61C23×D71—21no—
62#11765866—22no—
63#11765866—41no—
64C2×Dic142—22no—
65C2×Dic142—21no—
66C2×Dic142—21no—
67C2×Dic142—41no—
68C2×Dic142C2311yescharacteristic
69C2×Dic142C2311yescharacteristic
70Q8×D71—22no—
71Q8×D71—41no—
72C2×D284—22no—
73C2×D284—21no—
74C2×D284—21no—
75C2×D284—21no—
76C2×D284—41no—
77C2×D284C2311yescharacteristic
78C2×D284C2311yescharacteristic
79C2×C22⋊D71D411yescharacteristic
80C22×Dic71—21no—
81C2×C4×D71—21no—
82C2×C4×D71—21no—
83C2×C4×D71—21no—
84C2×C4×D71C2311yescharacteristic
85#11765855—22no—
86#11765855—41no—
87#11765854—22no—
88#11765854—22no—
89#11765854—22no—
90#11765854D414yescomplemented
91#11765852—22no—
92#11765852—41no—
93#11765848—22no—
94C2×C71⋊C8C2311yescharacteristic
95C2×C71⋊C8C2311yescharacteristic
96C4⋊Dic71—21no—
97Dic71⋊C4—21no—
98Dic71⋊C4—21no—
99Dic71⋊C4—21no—
100Dic71⋊C4D411yescharacteristic
101C22⋊Dic71D411yescharacteristic
102(C2×D71)⋊C4—21no—
103(C2×D71)⋊C4—21no—
104(C2×D71)⋊C4—21no—
105(C2×D71)⋊C4—21no—
106(C2×D71)⋊C4—21no—
107(C2×D71)⋊C4D411yescharacteristic
108C4×Dic71—21no—
109C4×Dic71C2311yescharacteristic
110C2×Q8×C71C2311yescharacteristic
111C2×Q8×C71C2311yescharacteristic
112C22×C4×C71C2311yescharacteristic
113Q16×C71—22no—
114C2×C8×C71—22no—
115C2×C8×C71C2311yescharacteristic
116C2×C8×C71C2311yescharacteristic
117C4⋊C4×C71—21no—
118C4⋊C4×C71—21no—
119C4⋊C4×C71C2311yescharacteristic
120C4⋊C4×C71C2311yescharacteristic
121C22⋊C4×C71—21no—
122C22⋊C4×C71—21no—
123C23×C71C2×D411yescharacteristic
124C22×D71—21no—
125C22×D71—21no—
126C22×D71—42no—
127C22×D71—42no—
128C22×D71—81no—
129C22×D71C2×D411yescharacteristic
130Q8×C71—21no—
131Q8×C71—21no—
132Q8×C71—21no—
133Q8×C71—21no—
134C2×C4×C71—21no—
135C2×C4×C71—21no—
136C2×C4×C71—21no—
137C2×C4×C71—21no—
138C2×C4×C71—21no—
139C2×C4×C71—21no—
140C2×C4×C71C2×D411yescharacteristic
141C2×C4×C71C2411yescharacteristic
142C22⋊D71—22no—
143C2×Dic71—21no—
144C2×Dic71—21no—
145C2×Dic71—42no—
146C2×Dic71C2×D411yescharacteristic
147C2×Dic71C2×D411yescharacteristic
148C2×Dic71C2×D411yescharacteristic
149D284—21no—
150D284—21no—
151D284—21no—
152D284—42no—
153D284—42no—
154D284—81no—
155D284C2×D412yes—
156C4×D71—21no—
157C4×D71—21no—
158C4×D71—42no—
159C4×D71—42no—
160C4×D71—81no—
161Dic142—21no—
162Dic142—21no—
163Dic142—21no—
164Dic142—42no—
165Dic142—42no—
166Dic142C2×D412yes—
167C8×C71—21no—
168C8×C71C2×D412yes—
169C71⋊C8—21no—
170C71⋊C8—21no—
171C22×C71—21no—
172C22×C71—21no—
173C22×C71#13712yescomplemented
174C22×C71C22×D411yescharacteristic
175C2×D71—21no—
176C2×D71—22no—
177C2×D71—21no—
178C2×D71—21no—
179C2×D71—41no—
180C2×D71—41no—
181C2×D71—41no—
182C2×D71—41no—
183C2×D71—41no—
184C2×D71—84no—
185C4×C71—21no—
186C4×C71—41no—
187C4×C71—41no—
188C4×C71—41no—
189C4×C71—41no—
190C4×C71C22×D411yescharacteristic
191C4×C71H(5,𝔽2)11yescharacteristic
192Dic71—22no—
193Dic71—21no—
194Dic71—21no—
195Dic71—21no—
196Dic71—41no—
197C2×C71—22no—
198C2×C71D4211yescharacteristic
199C2×C71C2×#13711yescharacteristic
200C2×C71#57711yescharacteristic
201D71—41no—
202D71—42no—
203D71—81no—
204#3266—711nomaximal, Sylow
205C71#326611yescharacteristic, complemented, Sylow
206C2×#137—711no—
207C22×SD16—711no—
208D4×Q8—711no—
209#546—711no—
210#497—711no—
211#468—711no—
212#467D7111yescharacteristic, complemented
213#464—711no—
214#461—711no—
215#452—711no—
216#451—711no—
217#450—711no—
218#448—711no—
219#440—711no—
220#435—711no—
221C2×#41—711no—
222C22×Q8—711no—
223C22×Q8—711no—
224C22×D4—711no—
225#137—1424no—
226C2×Q16—711no—
227C2×Q16—711no—
228C2×Q16C2×D7111yescharacteristic, complemented
229C2×SD16—711no—
230C2×SD16—711no—
231C2×SD16—711no—
232C2×SD16—711no—
233C2×SD16—711no—
234C2×SD16—711no—
235C2×SD16—1424no—
236C2×M16—711no—
237C22×C8C2×D7111yescharacteristic
238C4⋊Q8—711no—
239C4⋊Q8—1421no—
240#124—711no—
241#123—1421no—
242C22⋊Q8—711no—
243C22⋊Q8—1421no—
244C22⋊Q8—1421no—
245C22⋊Q8C2×D7111yescharacteristic
246C22⋊Q8C2×D7111yescharacteristic
247#121—711no—
248#121—1421no—
249#120—1421no—
250C4×Q8—711no—
251C4×D4—711no—
252C4×D4—711no—
253C4×D4—1421no—
254C2×C22⋊C4—1421no—
255#107C2×D7111yescharacteristic, complemented
256C4⋊C8—711no—
257#103—711no—
258#103—711no—
259#103C2×D7111yescharacteristic, complemented
260#103C2×D7111yescharacteristic, complemented
261#102—711no—
262#102—711no—
263C22⋊C8—711no—
264C22⋊C8—711no—
265#97—711no—
266C24—1421no—
267#41—2841no—
268#41—1422no—
269C2×Q8—2841no—
270C2×Q8—2841no—
271C2×Q8—711no—
272C2×Q8—711no—
273C2×Q8—1422no—
274C2×Q8—1421no—
275C2×Q8—1422no—
276C2×Q8—1421no—
277C2×Q8C22×D7111yescharacteristic
278C2×Q8C22×D7111yescharacteristic
279C2×D4—2841no—
280C2×D4—711no—
281C2×D4—711no—
282C2×D4—711no—
283C2×D4—1421no—
284C2×D4—1422no—
285C2×D4—1421no—
286C2×D4—1421no—
287C22×C4—711no—
288C22×C4—1421no—
289C22×C4—1421no—
290C22×C4—1421no—
291C22×C4—1421no—
292C22×C4C22×D7111yescharacteristic
293Q16—22no—
294Q16—2841no—
295Q16—1422no—
296SD16—2841no—
297SD16—714no—
298SD16—1422no—
299SD16—1422no—
300SD16—1422no—
301SD16—1422no—
302M16—1422no—
303C2×C8—22no—
304C2×C8—711no—
305C2×C8—711no—
306C2×C8C22×D7111yescharacteristic
307C2×C8C22×D7111yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—711no—
311C4⋊C4—1421no—
312C4⋊C4—1421no—
313C4⋊C4—1421no—
314C4⋊C4—1421no—
315C4⋊C4C22×D7111yescharacteristic
316C4⋊C4C22×D7111yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—21no—
319C22⋊C4—711no—
320C22⋊C4—711no—
321C22⋊C4—1421no—
322C22⋊C4—1421no—
323C22⋊C4—1421no—
324C22⋊C4—1421no—
325C22⋊C4—1421no—
326C42—711no—
327C42—1421no—
328C23—2842no—
329C23—2842no—
330C23—5681no—
331C23—711no—
332C23—1421no—
333C23—1421no—
334C23D4×D7111yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—2842no—
340Q8—2842no—
341Q8—712no—
342Q8—1421no—
343Q8—1421no—
344Q8—1421no—
345D4—2842no—
346D4—2842no—
347D4—5681no—
348D4—712no—
349D4—1422no—
350D4—1421no—
351D4—1421no—
352D4—1421no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—2842no—
360C2×C4—2842no—
361C2×C4—2842no—
362C2×C4—5681no—
363C2×C4—711no—
364C2×C4—711no—
365C2×C4—711no—
366C2×C4—1421no—
367C2×C4—1421no—
368C2×C4—1421no—
369C2×C4—1421no—
370C2×C4D4×D7111yescharacteristic
371C2×C4C23×D7111yescharacteristic
372C8—21no—
373C8—1421no—
374C8—1421no—
375C8D4×D7112yes—
376C22—21no—
377C22—21no—
378C22—2841no—
379C22—2841no—
380C22—2841no—
381C22—2841no—
382C22—2841no—
383C22—5684no—
384C22—1421no—
385C22—1422no—
386C22—1421no—
387C22—1421no—
388C22#1455616012yescomplemented
389C22C2×D4×D7111yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—2841no—
396C4—1421no—
397C4—1422no—
398C4—1421no—
399C4—1421no—
400C4C2×D4×D7111yescharacteristic
401C4#1455617411yescharacteristic
402C2—22no—
403C2—2842no—
404C2—2841no—
405C2—5681no—
406C2#1798663311yescharacteristic
407C2C2×#1455616011yescharacteristic
408C2#1798680611yescharacteristic
subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#467×C71C2
socleC22×C71C22×D4
hypercenter#467D71
hypocenterC71#3266
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. C2×#14556160C2semidirect
2. C22×#11765854C2semidirect
3. #17986662C2semidirect
5. #17986392C2semidirect
6. #17986246C2semidirect
7. #17986224C2semidirect
8. #17986203C2semidirect
9. #17986164C2semidirect
10. #17986154C2semidirect
11. #17986149C2semidirect
12. #17986139C2semidirect
13. #17986098C2semidirect
14. #17986070C2semidirect
15. #467×C71C2semidirect
18. C2×Q8×D71C22semidirect
21. C2×#11765855C22semidirect
22. C2×#11765855C22semidirect
30. C2×#11765848C22semidirect
32. #14556126C22semidirect
35. #14556108C22semidirect
41. #14556093C22semidirect
46. Dic71⋊C8C22semidirect
47. #14556051C22semidirect
48. #14556051C22semidirect
52. (C2×D71)⋊C8C22semidirect
53. #14556038C22semidirect
54. C2×Q16×C71C22semidirect
58. #107×C71C22semidirect
59. #103×C71C22semidirect
60. #103×C71C22semidirect
90. #11765854D4semidirect
173. C22×C71#137semidirect
205. C71#3266semidirect
212. #467D71semidirect
228. C2×Q16C2×D71semidirect
255. #107C2×D71semidirect
259. #103C2×D71semidirect
260. #103C2×D71semidirect
388. C22#14556160semidirect