Finite Group Databasebeta

← #21435611

Subgroups — #21435611

Order 7552.

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×#14273760C211yesmaximal, characteristic, complemented
2C22×#11745660C211yesmaximal, characteristic, complemented
3D4×Dic118C211yesmaximal, characteristic, complemented
4#16838048C211yesmaximal, characteristic
5#16837796C211yesmaximal, characteristic, complemented
6#16837648C211yesmaximal, characteristic, complemented
7#16837643C211yesmaximal, characteristic, complemented
8#16837625C211yesmaximal, characteristic, complemented
9#16837608C211yesmaximal, characteristic, complemented
10#16837566C211yesmaximal, characteristic, complemented
11#16837560C211yesmaximal, characteristic, complemented
12#16837555C211yesmaximal, characteristic, complemented
13#16837543C211yesmaximal, characteristic, complemented
14#16837504C211yesmaximal, characteristic, complemented
15C59×#435C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C22×Dic118C2211yescharacteristic
18C22×Dic118C2211yescharacteristic, complemented
19C22×D236C2211yescharacteristic
20#14273760—24no—
21C2×Dic236C2211yescharacteristic, complemented
22C2×Dic236C2211yescharacteristic, complemented
23C2×Dic236C2211yescharacteristic, complemented
24C2×#11745660—24no—
25C2×#11745660C2211yescharacteristic
26C2×#11745660C2211yescharacteristic
27C2×#11745660C2211yescharacteristic
28C2×#11745660C2211yescharacteristic
29C2×#11745660C2211yescharacteristic
30C2×#11745660C2211yescharacteristic
31#14273727C2211yescharacteristic, complemented
32#14273726—21no—
33#14273715C2211yescharacteristic
34#14273712—21no—
35#14273706C2211yescharacteristic
36#14273706C2211yescharacteristic
37#14273706C2211yescharacteristic, complemented
38#14273704—21no—
39#14273704—21no—
40#14273701C2211yescharacteristic
41#14273700—21no—
42#14273695—21no—
43C4×Dic118C2211yescharacteristic, complemented
44C4×D236C2211yescharacteristic
45D4×Dic59—21no—
46C22⋊C4×D59—21no—
47#14273661C2211yescharacteristic, complemented
48#14273652C2211yescharacteristic, complemented
49#14273652C2211yescharacteristic, complemented
50#14273652C2211yescharacteristic, complemented
51#14273652C2211yescharacteristic, complemented
52#14273649C2211yescharacteristic
53#14273649C2211yescharacteristic
54C2×M16×C59C2211yescharacteristic, complemented
55C22×C8×C59C2211yescharacteristic
56C4×D4×C59C2211yescharacteristic
57C4⋊C8×C59C2211yescharacteristic, complemented
58C22⋊C8×C59C2211yescharacteristic
59C22⋊C8×C59C2211yescharacteristic, complemented
60#97×C59C2211yescharacteristic, complemented
61C23×D59—21no—
62C2×D4×C59D411yescharacteristic
63C22×C4×C59C2311yescharacteristic
64C22×C4×C59C2311yescharacteristic
65C2×C22⋊D59—21no—
66C2×C22⋊D59—21no—
67C22×Dic59—21no—
68C22×Dic59—21no—
69#11745685—22no—
70#11745685—41no—
71C2×D236—22no—
72C2×D236—21no—
73C2×D236—41no—
74C2×D236C2311yescharacteristic
75C2×D236C2311yescharacteristic
76C2×C4×D59—21no—
77C2×C4×D59—21no—
78C2×Dic118—22no—
79C2×Dic118—22no—
80C2×Dic118—21no—
81C2×Dic118—21no—
82C2×Dic118—41no—
83C2×Dic118—41no—
84C2×Dic118C2311yescharacteristic
85C2×Dic118C2311yescharacteristic
86C2×Dic118C2311yescharacteristic
87C2×Dic118C2311yescharacteristic
88M16×C59—22no—
89C2×C8×C59—22no—
90C2×C8×C59C2311yescharacteristic
91C2×C8×C59C2311yescharacteristic
92C2×C8×C59C2311yescharacteristic
93C2×C8×C59C2311yescharacteristic
94C4⋊C4×C59D411yescharacteristic
95C22⋊C4×C59D411yescharacteristic
96C22⋊C4×C59D411yescharacteristic
97C42×C59C2311yescharacteristic
98C22⋊Dic59—21no—
99C22⋊Dic59—21no—
100C22⋊Dic59—21no—
101(C2×D59)⋊C4—21no—
102(C2×D59)⋊C4—21no—
103(C2×D59)⋊C4—21no—
104(C2×D59)⋊C4—21no—
105C4⋊Dic59—21no—
106C4⋊Dic59—21no—
107C4⋊Dic59C2311yescharacteristic
108C4⋊Dic59C2311yescharacteristic
109Dic59⋊C4—21no—
110Dic59⋊C4—21no—
111Dic59⋊C4—21no—
112Dic59⋊C4—21no—
113C4×Dic59—21no—
114Dic236—22no—
115Dic236—22no—
116Dic236—41no—
117#11745660—22no—
118#11745660—22no—
119#11745660—22no—
120#11745660—22no—
121#11745660—41no—
122#11745660D414yescomplemented
123C23×C59C2×D411yescharacteristic
124C23×C59C2×D411yescharacteristic
125C22×D59—21no—
126C22×D59—21no—
127C22×D59—42no—
128C22×D59—42no—
129C22×D59—81no—
130D4×C59—22no—
131C2×C4×C59—21no—
132C2×C4×C59—21no—
133C2×C4×C59—21no—
134C2×C4×C59—21no—
135C2×C4×C59C2×D411yescharacteristic
136C2×C4×C59C2×D411yescharacteristic
137C2×C4×C59C2×D411yescharacteristic
138C2×C4×C59C2×D411yescharacteristic
139C2×C4×C59C2411yescharacteristic
140C22⋊D59—42no—
141C22⋊D59—81no—
142C2×Dic59—21no—
143C2×Dic59—21no—
144C2×Dic59—21no—
145C2×Dic59—21no—
146C2×Dic59—21no—
147C2×Dic59—21no—
148C2×Dic59—42no—
149C2×Dic59—42no—
150D236—21no—
151D236—21no—
152D236—21no—
153D236—42no—
154D236C2×D412yes—
155C4×D59—42no—
156C4×D59—81no—
157Dic118—21no—
158Dic118—21no—
159Dic118—21no—
160Dic118—21no—
161Dic118—21no—
162Dic118—21no—
163Dic118—21no—
164Dic118—42no—
165Dic118—42no—
166Dic118C2×D412yes—
167C8×C59—21no—
168C8×C59—21no—
169C8×C59—21no—
170C8×C59C2×D412yes—
171C22×C59—21no—
172C22×C59—21no—
173C22×C59—21no—
174C22×C59—21no—
175C22×C59—21no—
176C22×C59#13712yescomplemented
177C22×C59C22×D411yescharacteristic
178C2×D59—22no—
179C2×D59—41no—
180C2×D59—41no—
181C2×D59—41no—
182C2×D59—41no—
183C2×D59—41no—
184C2×D59—84no—
185C4×C59—21no—
186C4×C59—21no—
187C4×C59—21no—
188C4×C59—21no—
189C4×C59C22×D411yescharacteristic
190C4×C59H(5,𝔽2)11yescharacteristic
191Dic59—22no—
192Dic59—41no—
193Dic59—41no—
194Dic59—41no—
195Dic59—41no—
196Dic59—41no—
197#3266—591nomaximal, Sylow
198C2×C59—22no—
199C2×C59—41no—
200C2×C59D4211yescharacteristic
201C2×C59C2×#13711yescharacteristic
202C2×C59#57711yescharacteristic
203D59—42no—
204D59—81no—
205C2×#137—591no—
206C22×SD16—591no—
207D4×Q8—591no—
208#546—591no—
209#497—591no—
210#468—591no—
211#467—591no—
212#464—591no—
213#461—591no—
214#452—591no—
215#451—591no—
216#450—591no—
217#448—591no—
218#440—591no—
219#435D5911yescharacteristic, complemented
220C59#326611yescharacteristic, complemented, Sylow
221C2×#41—591no—
222C22×Q8—591no—
223C22×Q8—591no—
224C22×D4—591no—
225#137—1184no—
226C2×Q16—591no—
227C2×Q16—591no—
228C2×Q16—591no—
229C2×SD16—591no—
230C2×SD16—591no—
231C2×SD16—591no—
232C2×SD16—591no—
233C2×SD16—591no—
234C2×SD16—591no—
235C2×SD16—1184no—
236C2×M16C2×D5911yescharacteristic, complemented
237C22×C8C2×D5911yescharacteristic
238C4⋊Q8—591no—
239C4⋊Q8—1181no—
240#124—591no—
241#123—1181no—
242C22⋊Q8—591no—
243C22⋊Q8—591no—
244C22⋊Q8—591no—
245C22⋊Q8—1181no—
246C22⋊Q8—1181no—
247#121—591no—
248#121—1181no—
249#120—1181no—
250C4×Q8—591no—
251C4×D4—591no—
252C4×D4—1181no—
253C4×D4C2×D5911yescharacteristic
254C2×C22⋊C4—1181no—
255#107—591no—
256C4⋊C8C2×D5911yescharacteristic, complemented
257#103—591no—
258#103—591no—
259#103—591no—
260#103—591no—
261#102—591no—
262#102—591no—
263C22⋊C8C2×D5911yescharacteristic
264C22⋊C8C2×D5911yescharacteristic, complemented
265#97C2×D5911yescharacteristic, complemented
266C24—1181no—
267#41—1182no—
268#41—2361no—
269C2×Q8—591no—
270C2×Q8—591no—
271C2×Q8—591no—
272C2×Q8—591no—
273C2×Q8—1182no—
274C2×Q8—1182no—
275C2×Q8—1181no—
276C2×Q8—1181no—
277C2×Q8—2361no—
278C2×Q8—2361no—
279C2×D4—591no—
280C2×D4—591no—
281C2×D4—1182no—
282C2×D4—1181no—
283C2×D4—1181no—
284C2×D4—1181no—
285C2×D4—2361no—
286C2×D4D23611yescharacteristic
287C22×C4—1181no—
288C22×C4—1181no—
289C22×C4—1181no—
290C22×C4—1181no—
291C22×C4C22×D5911yescharacteristic
292C22×C4C22×D5911yescharacteristic
293Q16—1182no—
294Q16—1182no—
295Q16—2361no—
296SD16—594no—
297SD16—1182no—
298SD16—1182no—
299SD16—1182no—
300SD16—1182no—
301SD16—2361no—
302M16—22no—
303C2×C8—22no—
304C2×C8C22×D5911yescharacteristic
305C2×C8C22×D5911yescharacteristic
306C2×C8C22×D5911yescharacteristic
307C2×C8C22×D5911yescharacteristic
308C4⋊C4—591no—
309C4⋊C4—591no—
310C4⋊C4—1181no—
311C4⋊C4—1181no—
312C4⋊C4—1181no—
313C4⋊C4—1181no—
314C4⋊C4—1181no—
315C4⋊C4—1181no—
316C4⋊C4D23611yescharacteristic
317C22⋊C4—1181no—
318C22⋊C4—1181no—
319C22⋊C4—1181no—
320C22⋊C4—1181no—
321C22⋊C4—1181no—
322C22⋊C4—1181no—
323C22⋊C4—1181no—
324C22⋊C4D23611yescharacteristic
325C22⋊C4D23611yescharacteristic
326C42—1181no—
327C42C22×D5911yescharacteristic
328C23—1181no—
329C23—1181no—
330C23—4721no—
331C23—2362no—
332C23—2362no—
333C23C2×D23611yescharacteristic
334C23C2×D23611yescharacteristic
335Q8—592no—
336Q8—1181no—
337Q8—1181no—
338Q8—1181no—
339Q8—1181no—
340Q8—1181no—
341Q8—1181no—
342Q8—1181no—
343Q8—2362no—
344Q8—2362no—
345D4—22no—
346D4—592no—
347D4—1181no—
348D4—1181no—
349D4—1181no—
350D4—4721no—
351D4—2362no—
352D4—2362no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—1181no—
358C2×C4—1181no—
359C2×C4—1181no—
360C2×C4—1181no—
361C2×C4—1181no—
362C2×C4—1181no—
363C2×C4—4721no—
364C2×C4—2362no—
365C2×C4—2362no—
366C2×C4—2362no—
367C2×C4C2×D23611yescharacteristic
368C2×C4C2×D23611yescharacteristic
369C2×C4C2×D23611yescharacteristic
370C2×C4C2×D23611yescharacteristic
371C2×C4C23×D5911yescharacteristic
372C8—21no—
373C8—21no—
374C8—21no—
375C8D4×D5912yes—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—1182no—
382C22—4724no—
383C22—2361no—
384C22—2361no—
385C22—2361no—
386C22—2361no—
387C22—2361no—
388C22#1427376012yescomplemented
389C22C22×D23611yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—1182no—
395C4—2361no—
396C4—2361no—
397C4—2361no—
398C4—2361no—
399C4—2361no—
400C4C2×D4×D5911yescharacteristic
401C4#1427377311yescharacteristic
402C2—22no—
403C2—41no—
404C2—4721no—
405C2—2362no—
406C2D4×D23611yescharacteristic
407C2C2×#1427376011yescharacteristic
408C2#1683821411yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#435C2
socleC22×C59C22×D4
hypercenter#435D59
hypocenterC59#3266
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#14273760C2semidirect
2. C22×#11745660C2semidirect
3. D4×Dic118C2semidirect
5. #16837796C2semidirect
6. #16837648C2semidirect
7. #16837643C2semidirect
8. #16837625C2semidirect
9. #16837608C2semidirect
10. #16837566C2semidirect
11. #16837560C2semidirect
12. #16837555C2semidirect
13. #16837543C2semidirect
14. #16837504C2semidirect
15. C59×#435C2semidirect
18. C22×Dic118C22semidirect
21. C2×Dic236C22semidirect
22. C2×Dic236C22semidirect
23. C2×Dic236C22semidirect
31. #14273727C22semidirect
37. #14273706C22semidirect
43. C4×Dic118C22semidirect
47. #14273661C22semidirect
48. #14273652C22semidirect
49. #14273652C22semidirect
50. #14273652C22semidirect
51. #14273652C22semidirect
54. C2×M16×C59C22semidirect
57. C4⋊C8×C59C22semidirect
59. C22⋊C8×C59C22semidirect
60. #97×C59C22semidirect
122. #11745660D4semidirect
176. C22×C59#137semidirect
219. #435D59semidirect
220. C59#3266semidirect
236. C2×M16C2×D59semidirect
256. C4⋊C8C2×D59semidirect
264. C22⋊C8C2×D59semidirect
265. #97C2×D59semidirect
388. C22#14273760semidirect