Finite Group Databasebeta

← #22599852

Subgroups — #22599852

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×#14556157C211yesmaximal, characteristic, complemented
2C2×SD16×D71C211yesmaximal, characteristic, complemented
3Q8×D284C211yesmaximal, characteristic, complemented
4#17986644C211yesmaximal, characteristic
5#17986393C211yesmaximal, characteristic, complemented
6#17986246C211yesmaximal, characteristic, complemented
7#17986241C211yesmaximal, characteristic, complemented
8#17986221C211yesmaximal, characteristic, complemented
9#17986204C211yesmaximal, characteristic, complemented
10#17986162C211yesmaximal, characteristic, complemented
11#17986156C211yesmaximal, characteristic, complemented
12#17986151C211yesmaximal, characteristic, complemented
13#17986139C211yesmaximal, characteristic, complemented
14#17986072C211yesmaximal, characteristic, complemented
15#440×C71C211yesmaximal, characteristic, complemented
16C2×#11765864C2211yescharacteristic
17C2×Q8×D71C2211yescharacteristic
18C2×Q8×D71C2211yescharacteristic, complemented
19C2×D4×D71C2211yescharacteristic
20#14556157—24no—
21C2×Dic284C2211yescharacteristic, complemented
22C2×Dic284C2211yescharacteristic, complemented
23C2×#11765855C2211yescharacteristic, complemented
24C2×#11765854C2211yescharacteristic
25C2×#11765854C2211yescharacteristic
26C2×#11765853C2211yescharacteristic
27C2×#11765853C2211yescharacteristic
28C2×#11765852C2211yescharacteristic
29SD16×D71—24no—
30C2×#11765848C2211yescharacteristic, complemented
31C2×C8×D71C2211yescharacteristic
32#14556128—21no—
33#14556128C2211yescharacteristic, complemented
34#14556116C2211yescharacteristic
35#14556112—21no—
36#14556108—21no—
37#14556108—21no—
38#14556108C2211yescharacteristic
39#14556108C2211yescharacteristic
40#14556108C2211yescharacteristic, complemented
41#14556103C2211yescharacteristic
42#14556102—21no—
43#14556098—21no—
44C4×D284—21no—
45C4×D284C2211yescharacteristic
46C2×(C2×D71)⋊C4—21no—
47C4⋊(C71⋊C8)C2211yescharacteristic, complemented
48#14556051C2211yescharacteristic, complemented
49#14556051C2211yescharacteristic, complemented
50#14556051C2211yescharacteristic, complemented
51#14556048C2211yescharacteristic
52(C2×D71)⋊C8C2211yescharacteristic
53(C2×D71)⋊C8C2211yescharacteristic, complemented
54C2×SD16×C71C2211yescharacteristic
55C4×Q8×C71C2211yescharacteristic, complemented
56C4×D4×C71C2211yescharacteristic
57#107×C71C2211yescharacteristic, complemented
58#103×C71C2211yescharacteristic, complemented
59#102×C71C2211yescharacteristic
60#97×C71C2211yescharacteristic, complemented
61C23×D71—21no—
62#11765864—22no—
63#11765864—41no—
64C2×Dic142—21no—
65C2×Dic142—21no—
66C2×Dic142C2311yescharacteristic
67C2×Dic142C2311yescharacteristic
68C2×Dic142C2311yescharacteristic
69Q8×D71—22no—
70Q8×D71—22no—
71Q8×D71—41no—
72Q8×D71—41no—
73C2×D284—21no—
74C2×D284D411yescharacteristic
75C2×D284C2311yescharacteristic
76C2×C22⋊D71—21no—
77C2×C22⋊D71—21no—
78D4×D71—22no—
79D4×D71—41no—
80C22×Dic71—21no—
81C2×C4×D71—21no—
82C2×C4×D71—21no—
83C2×C4×D71C2311yescharacteristic
84C2×C4×D71C2311yescharacteristic
85Dic284—22no—
86Dic284—41no—
87#11765855—22no—
88#11765854—22no—
89#11765854—41no—
90#11765853—22no—
91#11765853—22no—
92#11765852—22no—
93#11765848—22no—
94C2×C71⋊C8C2311yescharacteristic
95C2×C71⋊C8C2311yescharacteristic
96C8×D71—22no—
97C4⋊Dic71—21no—
98C4⋊Dic71—21no—
99C4⋊Dic71—21no—
100C4⋊Dic71—21no—
101C4⋊Dic71—21no—
102C4⋊Dic71D411yescharacteristic
103(C2×D71)⋊C4—21no—
104(C2×D71)⋊C4—21no—
105(C2×D71)⋊C4—21no—
106(C2×D71)⋊C4—21no—
107(C2×D71)⋊C4—21no—
108(C2×D71)⋊C4—21no—
109(C2×D71)⋊C4D411yescharacteristic
110(C2×D71)⋊C4D411yescharacteristic
111C2×Q8×C71C2311yescharacteristic
112C2×D4×C71C2311yescharacteristic
113C22×C4×C71—21no—
114SD16×C71D414yescomplemented
115C2×C8×C71C2311yescharacteristic
116C2×C8×C71C2311yescharacteristic
117C4⋊C4×C71—21no—
118C4⋊C4×C71C2311yescharacteristic
119C4⋊C4×C71C2311yescharacteristic
120C22⋊C4×C71—21no—
121C42×C71—21no—
122C42×C71C2311yescharacteristic
123C23×C71—21no—
124C22×D71—21no—
125C22×D71—42no—
126C22×D71—42no—
127C22×D71—81no—
128C22×D71C2×D411yescharacteristic
129C22×D71C2×D411yescharacteristic
130Q8×C71—21no—
131Q8×C71C2×D412yes—
132D4×C71—21no—
133D4×C71C2×D412yes—
134C2×C4×C71—21no—
135C2×C4×C71—21no—
136C2×C4×C71—21no—
137C2×C4×C71—81no—
138C2×C4×C71C2×D411yescharacteristic
139C2×C4×C71C2×D411yescharacteristic
140C2×C4×C71C2411yescharacteristic
141C22⋊D71—42no—
142C22⋊D71—42no—
143C2×Dic71—21no—
144C2×Dic71—21no—
145C2×Dic71—21no—
146C2×Dic71—42no—
147C2×Dic71C2×D411yescharacteristic
148C2×Dic71C2×D411yescharacteristic
149D284—22no—
150D284—21no—
151D284—21no—
152D284—81no—
153C4×D71—21no—
154C4×D71—21no—
155C4×D71—21no—
156C4×D71—21no—
157C4×D71—42no—
158C4×D71—42no—
159Dic142—21no—
160Dic142—21no—
161Dic142—21no—
162Dic142—21no—
163Dic142—21no—
164Dic142—21no—
165Dic142—42no—
166Dic142—42no—
167C8×C71—21no—
168C8×C71C2×D412yes—
169C71⋊C8—21no—
170C71⋊C8—21no—
171C22×C71—22no—
172C22×C71—41no—
173C22×C71—41no—
174C22×C71C22×D411yescharacteristic
175C2×D71—21no—
176C2×D71—21no—
177C2×D71—21no—
178C2×D71—21no—
179C2×D71—21no—
180C2×D71—41no—
181C2×D71—41no—
182C2×D71—41no—
183C2×D71—84no—
184C2×D71#13712yescomplemented
185C4×C71—22no—
186C4×C71—21no—
187C4×C71—21no—
188C4×C71—41no—
189C4×C71—41no—
190C4×C71C22×D411yescharacteristic
191C4×C71H(5,𝔽2)11yescharacteristic
192Dic71—21no—
193Dic71—21no—
194Dic71—41no—
195Dic71—41no—
196Dic71—41no—
197C2×C71—42no—
198C2×C71D4211yescharacteristic
199C2×C71C2×#13711yescharacteristic
200C2×C71#57711yescharacteristic
201D71—22no—
202D71—41no—
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#467—711no—
213#464—711no—
214#461—711no—
215#452—711no—
216#451—711no—
217#450—711no—
218#448—711no—
219#440D7111yescharacteristic, complemented
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×Q16—711no—
229C2×SD16—711no—
230C2×SD16—711no—
231C2×SD16—711no—
232C2×SD16—711no—
233C2×SD16—711no—
234C2×SD16—1424no—
235C2×SD16C2×D7111yescharacteristic
236C2×M16—711no—
237C22×C8—711no—
238C4⋊Q8—711no—
239C4⋊Q8—1421no—
240#124—711no—
241#123—1421no—
242C22⋊Q8—711no—
243C22⋊Q8—711no—
244C22⋊Q8—711no—
245C22⋊Q8—1421no—
246C22⋊Q8—1421no—
247#121—711no—
248#121—1421no—
249#120—1421no—
250C4×Q8C2×D7111yescharacteristic, complemented
251C4×D4—711no—
252C4×D4—1421no—
253C4×D4C2×D7111yescharacteristic
254C2×C22⋊C4—1421no—
255#107C2×D7111yescharacteristic, complemented
256C4⋊C8—711no—
257#103—711no—
258#103—711no—
259#103—711no—
260#103C2×D7111yescharacteristic, complemented
261#102—711no—
262#102C2×D7111yescharacteristic
263C22⋊C8—711no—
264C22⋊C8—711no—
265#97C2×D7111yescharacteristic, complemented
266C24—1421no—
267#41—2841no—
268#41—1422no—
269C2×Q8—2841no—
270C2×Q8—2841no—
271C2×Q8—711no—
272C2×Q8—711no—
273C2×Q8—711no—
274C2×Q8—1421no—
275C2×Q8—1421no—
276C2×Q8—1422no—
277C2×Q8—1422no—
278C2×Q8C22×D7111yescharacteristic
279C2×D4—2841no—
280C2×D4—711no—
281C2×D4—711no—
282C2×D4—1421no—
283C2×D4—1421no—
284C2×D4—1421no—
285C2×D4—1422no—
286C2×D4C22×D7111yescharacteristic
287C22×C4—21no—
288C22×C4—711no—
289C22×C4—711no—
290C22×C4—1421no—
291C22×C4—1421no—
292C22×C4—1421no—
293Q16—2841no—
294Q16—1422no—
295Q16—1422no—
296SD16—2841no—
297SD16—1422no—
298SD16—1422no—
299SD16—1422no—
300SD16—1422no—
301SD16D28414yescomplemented
302M16—1422no—
303C2×C8—711no—
304C2×C8—711no—
305C2×C8—1422no—
306C2×C8C22×D7111yescharacteristic
307C2×C8C22×D7111yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—711no—
310C4⋊C4—1421no—
311C4⋊C4—1421no—
312C4⋊C4—1421no—
313C4⋊C4—1421no—
314C4⋊C4—1421no—
315C4⋊C4C22×D7111yescharacteristic
316C4⋊C4C22×D7111yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—711no—
319C22⋊C4—711no—
320C22⋊C4—1421no—
321C22⋊C4—1421no—
322C22⋊C4—1421no—
323C22⋊C4—1421no—
324C22⋊C4—1421no—
325C22⋊C4—1421no—
326C42—21no—
327C42C22×D7111yescharacteristic
328C23—21no—
329C23—2842no—
330C23—2842no—
331C23—5681no—
332C23—711no—
333C23—711no—
334C23—1421no—
335Q8—21no—
336Q8—2842no—
337Q8—2842no—
338Q8—1421no—
339Q8—1421no—
340Q8—1421no—
341Q8—1421no—
342Q8—1421no—
343Q8—1421no—
344Q8C2×D28412yes—
345D4—21no—
346D4—2842no—
347D4—2842no—
348D4—5681no—
349D4—1422no—
350D4—1421no—
351D4—1421no—
352D4C2×D28412yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—81no—
357C2×C4—2842no—
358C2×C4—2842no—
359C2×C4—2842no—
360C2×C4—711no—
361C2×C4—711no—
362C2×C4—1421no—
363C2×C4—1421no—
364C2×C4—1421no—
365C2×C4—1421no—
366C2×C4—1421no—
367C2×C4—1421no—
368C2×C4—1421no—
369C2×C4D4×D7111yescharacteristic
370C2×C4D4×D7111yescharacteristic
371C2×C4C23×D7111yescharacteristic
372C8—21no—
373C8—1421no—
374C8—1421no—
375C8C2×D28412yes—
376C22—22no—
377C22—41no—
378C22—41no—
379C22—2841no—
380C22—2841no—
381C22—2841no—
382C22—5684no—
383C22—712no—
384C22—1421no—
385C22—1421no—
386C22—1421no—
387C22—1421no—
388C22—1421no—
389C22C2×D4×D7111yescharacteristic
390C4—22no—
391C4—21no—
392C4—21no—
393C4—41no—
394C4—41no—
395C4—2841no—
396C4—2841no—
397C4—2841no—
398C4—1421no—
399C4—1421no—
400C4C22×D28411yescharacteristic
401C4#1455617411yescharacteristic
402C2—42no—
403C2—2841no—
404C2—5681no—
405C2—1422no—
406C2D4×D28411yescharacteristic
407C2#137×D7111yescharacteristic
408C2#1798680911yescharacteristic
subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#440×C71C2
socleC22×C71C22×D4
hypercenter#440D71
hypocenterC71#3266
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. C2×#14556157C2semidirect
2. C2×SD16×D71C2semidirect
3. Q8×D284C2semidirect
5. #17986393C2semidirect
6. #17986246C2semidirect
7. #17986241C2semidirect
8. #17986221C2semidirect
9. #17986204C2semidirect
10. #17986162C2semidirect
11. #17986156C2semidirect
12. #17986151C2semidirect
13. #17986139C2semidirect
14. #17986072C2semidirect
15. #440×C71C2semidirect
18. C2×Q8×D71C22semidirect
21. C2×Dic284C22semidirect
22. C2×Dic284C22semidirect
23. C2×#11765855C22semidirect
30. C2×#11765848C22semidirect
33. #14556128C22semidirect
40. #14556108C22semidirect
47. C4⋊(C71⋊C8)C22semidirect
48. #14556051C22semidirect
49. #14556051C22semidirect
50. #14556051C22semidirect
53. (C2×D71)⋊C8C22semidirect
55. C4×Q8×C71C22semidirect
57. #107×C71C22semidirect
58. #103×C71C22semidirect
60. #97×C71C22semidirect
114. SD16×C71D4semidirect
184. C2×D71#137semidirect
205. C71#3266semidirect
219. #440D71semidirect
250. C4×Q8C2×D71semidirect
255. #107C2×D71semidirect
260. #103C2×D71semidirect
265. #97C2×D71semidirect
301. SD16D284semidirect