Finite Group Databasebeta

← #22599855

Subgroups — #22599855

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×#14556161C211yesmaximal, characteristic, complemented
2C22×#11765854C211yesmaximal, characteristic, complemented
3D4×Dic142C211yesmaximal, characteristic, complemented
4#17986645C211yesmaximal, characteristic
5#17986393C211yesmaximal, characteristic, complemented
6#17986245C211yesmaximal, characteristic, complemented
7#17986240C211yesmaximal, characteristic, complemented
8#17986222C211yesmaximal, characteristic, complemented
9#17986205C211yesmaximal, characteristic, complemented
10#17986163C211yesmaximal, characteristic, complemented
11#17986157C211yesmaximal, characteristic, complemented
12#17986152C211yesmaximal, characteristic, complemented
13#17986140C211yesmaximal, characteristic, complemented
14#17986101C211yesmaximal, characteristic, complemented
15#435×C71C211yesmaximal, characteristic, complemented
16C2×#11765865C2211yescharacteristic
17C22×Dic142C2211yescharacteristic
18C22×Dic142C2211yescharacteristic, complemented
19C22×D284C2211yescharacteristic
20#14556161—24no—
21C2×Dic284C2211yescharacteristic, complemented
22C2×Dic284C2211yescharacteristic, complemented
23C2×Dic284C2211yescharacteristic, complemented
24C2×#11765854—24no—
25C2×#11765854C2211yescharacteristic
26C2×#11765854C2211yescharacteristic
27C2×#11765854C2211yescharacteristic
28C2×#11765854C2211yescharacteristic
29C2×#11765854C2211yescharacteristic
30C2×#11765854C2211yescharacteristic
31#14556128C2211yescharacteristic, complemented
32#14556127—21no—
33#14556116C2211yescharacteristic
34#14556113—21no—
35#14556107C2211yescharacteristic
36#14556107C2211yescharacteristic
37#14556107C2211yescharacteristic, complemented
38#14556105—21no—
39#14556105—21no—
40#14556102C2211yescharacteristic
41#14556101—21no—
42#14556096—21no—
43C4×Dic142C2211yescharacteristic, complemented
44C4×D284C2211yescharacteristic
45D4×Dic71—21no—
46C22⋊C4×D71—21no—
47#14556062C2211yescharacteristic, complemented
48#14556053C2211yescharacteristic, complemented
49#14556053C2211yescharacteristic, complemented
50#14556053C2211yescharacteristic, complemented
51#14556053C2211yescharacteristic, complemented
52#14556050C2211yescharacteristic
53#14556050C2211yescharacteristic
54C2×M16×C71C2211yescharacteristic, complemented
55C22×C8×C71C2211yescharacteristic
56C4×D4×C71C2211yescharacteristic
57C4⋊C8×C71C2211yescharacteristic, complemented
58C22⋊C8×C71C2211yescharacteristic
59C22⋊C8×C71C2211yescharacteristic, complemented
60#97×C71C2211yescharacteristic, complemented
61C23×D71—21no—
62#11765865—22no—
63#11765865—41no—
64C2×Dic142—22no—
65C2×Dic142—22no—
66C2×Dic142—21no—
67C2×Dic142—21no—
68C2×Dic142—41no—
69C2×Dic142—41no—
70C2×Dic142C2311yescharacteristic
71C2×Dic142C2311yescharacteristic
72C2×Dic142C2311yescharacteristic
73C2×Dic142C2311yescharacteristic
74C2×D284—22no—
75C2×D284—21no—
76C2×D284—41no—
77C2×D284C2311yescharacteristic
78C2×D284C2311yescharacteristic
79C2×C22⋊D71—21no—
80C2×C22⋊D71—21no—
81C22×Dic71—21no—
82C22×Dic71—21no—
83C2×C4×D71—21no—
84C2×C4×D71—21no—
85Dic284—22no—
86Dic284—22no—
87Dic284—41no—
88#11765854—22no—
89#11765854—22no—
90#11765854—22no—
91#11765854—22no—
92#11765854—41no—
93#11765854D414yescomplemented
94C4⋊Dic71—21no—
95C4⋊Dic71—21no—
96C4⋊Dic71C2311yescharacteristic
97C4⋊Dic71C2311yescharacteristic
98Dic71⋊C4—21no—
99Dic71⋊C4—21no—
100Dic71⋊C4—21no—
101Dic71⋊C4—21no—
102C22⋊Dic71—21no—
103C22⋊Dic71—21no—
104C22⋊Dic71—21no—
105(C2×D71)⋊C4—21no—
106(C2×D71)⋊C4—21no—
107(C2×D71)⋊C4—21no—
108(C2×D71)⋊C4—21no—
109C4×Dic71—21no—
110C2×D4×C71D411yescharacteristic
111C22×C4×C71C2311yescharacteristic
112C22×C4×C71C2311yescharacteristic
113M16×C71—22no—
114C2×C8×C71—22no—
115C2×C8×C71C2311yescharacteristic
116C2×C8×C71C2311yescharacteristic
117C2×C8×C71C2311yescharacteristic
118C2×C8×C71C2311yescharacteristic
119C4⋊C4×C71D411yescharacteristic
120C22⋊C4×C71D411yescharacteristic
121C22⋊C4×C71D411yescharacteristic
122C42×C71C2311yescharacteristic
123C23×C71C2×D411yescharacteristic
124C23×C71C2×D411yescharacteristic
125C22×D71—21no—
126C22×D71—21no—
127C22×D71—42no—
128C22×D71—42no—
129C22×D71—81no—
130D4×C71—22no—
131C2×C4×C71—21no—
132C2×C4×C71—21no—
133C2×C4×C71—21no—
134C2×C4×C71—21no—
135C2×C4×C71C2×D411yescharacteristic
136C2×C4×C71C2×D411yescharacteristic
137C2×C4×C71C2×D411yescharacteristic
138C2×C4×C71C2×D411yescharacteristic
139C2×C4×C71C2411yescharacteristic
140C22⋊D71—42no—
141C22⋊D71—81no—
142C2×Dic71—21no—
143C2×Dic71—21no—
144C2×Dic71—21no—
145C2×Dic71—21no—
146C2×Dic71—21no—
147C2×Dic71—21no—
148C2×Dic71—42no—
149C2×Dic71—42no—
150D284—21no—
151D284—21no—
152D284—21no—
153D284—42no—
154D284C2×D412yes—
155C4×D71—42no—
156C4×D71—81no—
157Dic142—21no—
158Dic142—21no—
159Dic142—21no—
160Dic142—21no—
161Dic142—21no—
162Dic142—21no—
163Dic142—21no—
164Dic142—42no—
165Dic142—42no—
166Dic142C2×D412yes—
167C8×C71—21no—
168C8×C71—21no—
169C8×C71—21no—
170C8×C71C2×D412yes—
171C22×C71—21no—
172C22×C71—21no—
173C22×C71—21no—
174C22×C71—21no—
175C22×C71—21no—
176C22×C71#13712yescomplemented
177C22×C71C22×D411yescharacteristic
178C2×D71—22no—
179C2×D71—41no—
180C2×D71—41no—
181C2×D71—41no—
182C2×D71—41no—
183C2×D71—41no—
184C2×D71—84no—
185C4×C71—21no—
186C4×C71—21no—
187C4×C71—21no—
188C4×C71—21no—
189C4×C71C22×D411yescharacteristic
190C4×C71H(5,𝔽2)11yescharacteristic
191Dic71—22no—
192Dic71—41no—
193Dic71—41no—
194Dic71—41no—
195Dic71—41no—
196Dic71—41no—
197C2×C71—22no—
198C2×C71—41no—
199C2×C71D4211yescharacteristic
200C2×C71C2×#13711yescharacteristic
201C2×C71#57711yescharacteristic
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#467—711no—
213#464—711no—
214#461—711no—
215#452—711no—
216#451—711no—
217#450—711no—
218#448—711no—
219#440—711no—
220#435D7111yescharacteristic, complemented
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—711no—
235C2×SD16—1424no—
236C2×M16C2×D7111yescharacteristic, complemented
237C22×C8C2×D7111yescharacteristic
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×Q8—711no—
251C4×D4—711no—
252C4×D4—1421no—
253C4×D4C2×D7111yescharacteristic
254C2×C22⋊C4—1421no—
255#107—711no—
256C4⋊C8C2×D7111yescharacteristic, complemented
257#103—711no—
258#103—711no—
259#103—711no—
260#103—711no—
261#102—711no—
262#102—711no—
263C22⋊C8C2×D7111yescharacteristic
264C22⋊C8C2×D7111yescharacteristic, complemented
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—711no—
275C2×Q8—1422no—
276C2×Q8—1422no—
277C2×Q8—1421no—
278C2×Q8—1421no—
279C2×D4—2841no—
280C2×D4—711no—
281C2×D4—711no—
282C2×D4—1422no—
283C2×D4—1421no—
284C2×D4—1421no—
285C2×D4—1421no—
286C2×D4D28411yescharacteristic
287C22×C4—1421no—
288C22×C4—1421no—
289C22×C4—1421no—
290C22×C4—1421no—
291C22×C4C22×D7111yescharacteristic
292C22×C4C22×D7111yescharacteristic
293Q16—2841no—
294Q16—1422no—
295Q16—1422no—
296SD16—2841no—
297SD16—714no—
298SD16—1422no—
299SD16—1422no—
300SD16—1422no—
301SD16—1422no—
302M16—22no—
303C2×C8—22no—
304C2×C8C22×D7111yescharacteristic
305C2×C8C22×D7111yescharacteristic
306C2×C8C22×D7111yescharacteristic
307C2×C8C22×D7111yescharacteristic
308C4⋊C4—711no—
309C4⋊C4—711no—
310C4⋊C4—1421no—
311C4⋊C4—1421no—
312C4⋊C4—1421no—
313C4⋊C4—1421no—
314C4⋊C4—1421no—
315C4⋊C4—1421no—
316C4⋊C4D28411yescharacteristic
317C22⋊C4—1421no—
318C22⋊C4—1421no—
319C22⋊C4—1421no—
320C22⋊C4—1421no—
321C22⋊C4—1421no—
322C22⋊C4—1421no—
323C22⋊C4—1421no—
324C22⋊C4D28411yescharacteristic
325C22⋊C4D28411yescharacteristic
326C42—1421no—
327C42C22×D7111yescharacteristic
328C23—2842no—
329C23—2842no—
330C23—5681no—
331C23—1421no—
332C23—1421no—
333C23C2×D28411yescharacteristic
334C23C2×D28411yescharacteristic
335Q8—2842no—
336Q8—2842no—
337Q8—712no—
338Q8—1421no—
339Q8—1421no—
340Q8—1421no—
341Q8—1421no—
342Q8—1421no—
343Q8—1421no—
344Q8—1421no—
345D4—22no—
346D4—2842no—
347D4—2842no—
348D4—5681no—
349D4—712no—
350D4—1421no—
351D4—1421no—
352D4—1421no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—2842no—
358C2×C4—2842no—
359C2×C4—2842no—
360C2×C4—5681no—
361C2×C4—1421no—
362C2×C4—1421no—
363C2×C4—1421no—
364C2×C4—1421no—
365C2×C4—1421no—
366C2×C4—1421no—
367C2×C4C2×D28411yescharacteristic
368C2×C4C2×D28411yescharacteristic
369C2×C4C2×D28411yescharacteristic
370C2×C4C2×D28411yescharacteristic
371C2×C4C23×D7111yescharacteristic
372C8—21no—
373C8—21no—
374C8—21no—
375C8D4×D7112yes—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—2841no—
382C22—2841no—
383C22—2841no—
384C22—2841no—
385C22—2841no—
386C22—5684no—
387C22—1422no—
388C22#1455616112yescomplemented
389C22C22×D28411yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—2841no—
395C4—2841no—
396C4—2841no—
397C4—2841no—
398C4—2841no—
399C4—1422no—
400C4C2×D4×D7111yescharacteristic
401C4#1455617411yescharacteristic
402C2—22no—
403C2—41no—
404C2—2842no—
405C2—5681no—
406C2D4×D28411yescharacteristic
407C2C2×#1455616111yescharacteristic
408C2#1798681111yescharacteristic
subgroupG/H
centerC22C22×D284
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#435×C71C2
socleC22×C71C22×D4
hypercenter#435D71
hypocenterC71#3266
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#14556161C2semidirect
2. C22×#11765854C2semidirect
3. D4×Dic142C2semidirect
5. #17986393C2semidirect
6. #17986245C2semidirect
7. #17986240C2semidirect
8. #17986222C2semidirect
9. #17986205C2semidirect
10. #17986163C2semidirect
11. #17986157C2semidirect
12. #17986152C2semidirect
13. #17986140C2semidirect
14. #17986101C2semidirect
15. #435×C71C2semidirect
18. C22×Dic142C22semidirect
21. C2×Dic284C22semidirect
22. C2×Dic284C22semidirect
23. C2×Dic284C22semidirect
31. #14556128C22semidirect
37. #14556107C22semidirect
43. C4×Dic142C22semidirect
47. #14556062C22semidirect
48. #14556053C22semidirect
49. #14556053C22semidirect
50. #14556053C22semidirect
51. #14556053C22semidirect
54. C2×M16×C71C22semidirect
57. C4⋊C8×C71C22semidirect
59. C22⋊C8×C71C22semidirect
60. #97×C71C22semidirect
93. #11765854D4semidirect
176. C22×C71#137semidirect
205. C71#3266semidirect
220. #435D71semidirect
236. C2×M16C2×D71semidirect
256. C4⋊C8C2×D71semidirect
264. C22⋊C8C2×D71semidirect
265. #97C2×D71semidirect
388. C22#14556161semidirect