Finite Group Databasebeta

← #21435606

Subgroups — #21435606

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×#14273756C211yesmaximal, characteristic, complemented
2Q8×C22⋊D59C211yesmaximal, characteristic, complemented
3#16838046C211yesmaximal, characteristic
4#16837793C211yesmaximal, characteristic, complemented
5#16837645C211yesmaximal, characteristic, complemented
6#16837643C211yesmaximal, characteristic, complemented
7#16837622C211yesmaximal, characteristic, complemented
8#16837605C211yesmaximal, characteristic, complemented
9#16837561C211yesmaximal, characteristic, complemented
10#16837558C211yesmaximal, characteristic, complemented
11#16837553C211yesmaximal, characteristic, complemented
12#16837539C211yesmaximal, characteristic, complemented
13#16837503C211yesmaximal, characteristic, complemented
14#16837473C211yesmaximal, characteristic, complemented
15C22×SD16×C59C211yesmaximal, characteristic, complemented
16C2×#11745687C2211yescharacteristic
17C2×Q8×D59C2211yescharacteristic, complemented
18#14273756—24no—
19C2×Dic236C2211yescharacteristic, complemented
20C2×#11745672C2211yescharacteristic, complemented
21C2×#11745672C2211yescharacteristic, complemented
22C2×#11745670C2211yescharacteristic
23C2×#11745670C2211yescharacteristic
24C2×#11745659C2211yescharacteristic, complemented
25#14273725—21no—
26#14273725C2211yescharacteristic, complemented
27#14273714C2211yescharacteristic
28#14273708—21no—
29#14273706—21no—
30#14273706C2211yescharacteristic
31#14273706C2211yescharacteristic
32#14273703—21no—
33#14273703C2211yescharacteristic, complemented
34#14273699—21no—
35#14273698C2211yescharacteristic
36#14273696—21no—
37Q8×Dic59C2211yescharacteristic, complemented
38D4×Dic59C2211yescharacteristic
39C4×C22⋊D59—21no—
40C4×C22⋊D59C2211yescharacteristic
41C2×C22⋊Dic59—21no—
42#14273661C2211yescharacteristic, complemented
43Dic59⋊C8C2211yescharacteristic, complemented
44#14273652C2211yescharacteristic, complemented
45#14273652C2211yescharacteristic, complemented
46#14273651C2211yescharacteristic, complemented
47#14273651C2211yescharacteristic, complemented
48#14273648C2211yescharacteristic
49#14273648C2211yescharacteristic
50C22⋊(C59⋊C8)C2211yescharacteristic
51(C2×D59)⋊C8C2211yescharacteristic, complemented
52#14273637C2211yescharacteristic, complemented
53C22×Q8×C59C2211yescharacteristic
54C22×D4×C59C2211yescharacteristic
55C2×SD16×C59—24no—
56C2×SD16×C59C2211yescharacteristic
57C2×SD16×C59C2211yescharacteristic
58C2×SD16×C59C2211yescharacteristic
59C2×SD16×C59C2211yescharacteristic
60C22×C8×C59C2211yescharacteristic
61C24×C59—21no—
62C2×Q8×C59—21no—
63C2×Q8×C59—22no—
64C2×Q8×C59—41no—
65C2×Q8×C59C2311yescharacteristic
66C2×Q8×C59C2311yescharacteristic
67C2×D4×C59—22no—
68C2×D4×C59—21no—
69C2×D4×C59—41no—
70C2×D4×C59C2311yescharacteristic
71C2×D4×C59C2311yescharacteristic
72C22×C4×C59—21no—
73C22×C4×C59C2311yescharacteristic
74C2×C22⋊D59—21no—
75C2×C22⋊D59—21no—
76C2×C22⋊D59D411yescharacteristic
77C22×Dic59—21no—
78C22×Dic59—21no—
79Q8×D59—22no—
80Q8×D59—41no—
81#11745687—22no—
82#11745687—41no—
83C2×C4×D59—21no—
84C2×C4×D59C2311yescharacteristic
85C2×Dic118—21no—
86C2×Dic118C2311yescharacteristic
87C2×Dic118C2311yescharacteristic
88SD16×C59—22no—
89SD16×C59—22no—
90SD16×C59—22no—
91SD16×C59D414yescomplemented
92C2×C8×C59—22no—
93C2×C8×C59C2311yescharacteristic
94C2×C8×C59C2311yescharacteristic
95C22⋊Dic59—21no—
96C22⋊Dic59—21no—
97C22⋊Dic59—21no—
98C22⋊Dic59—21no—
99C22⋊Dic59—21no—
100C22⋊Dic59—21no—
101C22⋊Dic59D411yescharacteristic
102#11745672—22no—
103#11745672—41no—
104#11745670—22no—
105#11745670—41no—
106(C2×D59)⋊C4—21no—
107(C2×D59)⋊C4D411yescharacteristic
108C4⋊Dic59—21no—
109C4⋊Dic59C2311yescharacteristic
110C4⋊Dic59C2311yescharacteristic
111Dic59⋊C4—21no—
112Dic59⋊C4—21no—
113Dic59⋊C4—21no—
114Dic59⋊C4—21no—
115Dic59⋊C4—21no—
116Dic59⋊C4D411yescharacteristic
117C4×Dic59—21no—
118C4×Dic59C2311yescharacteristic
119C2×C59⋊C8C2311yescharacteristic
120C2×C59⋊C8C2311yescharacteristic
121Dic236—22no—
122#11745659—22no—
123C23×C59—21no—
124C23×C59—21no—
125C23×C59—42no—
126C23×C59—42no—
127C23×C59—81no—
128C23×C59C2×D411yescharacteristic
129C22×D59C2×D411yescharacteristic
130Q8×C59—21no—
131Q8×C59—21no—
132Q8×C59—21no—
133Q8×C59—42no—
134Q8×C59C2×D412yes—
135D4×C59—21no—
136D4×C59—21no—
137D4×C59—21no—
138D4×C59—42no—
139D4×C59C2×D412yes—
140C2×C4×C59—21no—
141C2×C4×C59—21no—
142C2×C4×C59—21no—
143C2×C4×C59—21no—
144C2×C4×C59—42no—
145C2×C4×C59C2×D411yescharacteristic
146C2×C4×C59C2411yescharacteristic
147C22⋊D59—22no—
148C22⋊D59—42no—
149C22⋊D59—81no—
150C2×Dic59—21no—
151C2×Dic59—21no—
152C2×Dic59—21no—
153C2×Dic59—21no—
154C2×Dic59—42no—
155C2×Dic59—81no—
156C2×Dic59C2×D411yescharacteristic
157C2×Dic59C2×D411yescharacteristic
158C2×Dic59C2×D411yescharacteristic
159C4×D59—21no—
160C4×D59—21no—
161C4×D59—42no—
162Dic118—21no—
163Dic118—21no—
164Dic118—21no—
165Dic118—21no—
166Dic118—42no—
167C8×C59—21no—
168C8×C59C2×D412yes—
169C59⋊C8—21no—
170C59⋊C8—21no—
171C22×C59—21no—
172C22×C59—21no—
173C22×C59—22no—
174C22×C59—41no—
175C22×C59—41no—
176C22×C59—41no—
177C22×C59—41no—
178C22×C59—41no—
179C22×C59—84no—
180C22×C59#13712yescomplemented
181C22×C59C22×D411yescharacteristic
182C2×D59—21no—
183C2×D59—21no—
184C2×D59—21no—
185C4×C59—22no—
186C4×C59—21no—
187C4×C59—41no—
188C4×C59C22×D411yescharacteristic
189C4×C59H(5,𝔽2)11yescharacteristic
190Dic59—21no—
191Dic59—21no—
192Dic59—21no—
193Dic59—41no—
194Dic59—41no—
195Dic59—41no—
196Dic59—41no—
197#3266—591nomaximal, Sylow
198C2×C59—22no—
199C2×C59—42no—
200C2×C59—81no—
201C2×C59D4211yescharacteristic
202C2×C59C2×#13711yescharacteristic
203C2×C59#57711yescharacteristic
204D59—41no—
205C2×#137—591no—
206C22×SD16D5911yescharacteristic, complemented
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#435—591no—
220C59#326611yescharacteristic, complemented, Sylow
221C2×#41—591no—
222C22×Q8—591no—
223C22×Q8C2×D5911yescharacteristic
224C22×D4C2×D5911yescharacteristic
225#137—1184no—
226C2×Q16—591no—
227C2×Q16—591no—
228C2×Q16—591no—
229C2×SD16—24no—
230C2×SD16—591no—
231C2×SD16—591no—
232C2×SD16C2×D5911yescharacteristic
233C2×SD16C2×D5911yescharacteristic
234C2×SD16C2×D5911yescharacteristic
235C2×SD16C2×D5911yescharacteristic
236C2×M16—591no—
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—591no—
253C4×D4—1181no—
254C2×C22⋊C4—1181no—
255#107—591no—
256C4⋊C8—591no—
257#103—591no—
258#103—591no—
259#103—591no—
260#103—591no—
261#102—591no—
262#102—591no—
263C22⋊C8—591no—
264C22⋊C8—591no—
265#97—591no—
266C24—21no—
267#41—1182no—
268#41—2361no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—591no—
273C2×Q8—591no—
274C2×Q8—1181no—
275C2×Q8—1182no—
276C2×Q8—2361no—
277C2×Q8C22×D5911yescharacteristic
278C2×Q8C22×D5911yescharacteristic
279C2×D4—22no—
280C2×D4—21no—
281C2×D4—41no—
282C2×D4—591no—
283C2×D4—1181no—
284C2×D4—1181no—
285C2×D4C22×D5911yescharacteristic
286C2×D4C22×D5911yescharacteristic
287C22×C4—21no—
288C22×C4—591no—
289C22×C4—1181no—
290C22×C4—1181no—
291C22×C4—1181no—
292C22×C4C22×D5911yescharacteristic
293Q16—1182no—
294Q16—1182no—
295Q16—2361no—
296SD16—22no—
297SD16—22no—
298SD16—22no—
299SD16—1182no—
300SD16—2361no—
301SD16C22⋊D5914yescomplemented
302M16—1182no—
303C2×C8—22no—
304C2×C8—591no—
305C2×C8—591no—
306C2×C8C22×D5911yescharacteristic
307C2×C8C22×D5911yescharacteristic
308C4⋊C4—591no—
309C4⋊C4—591no—
310C4⋊C4—591no—
311C4⋊C4—1181no—
312C4⋊C4—1181no—
313C4⋊C4—1181no—
314C4⋊C4—1181no—
315C4⋊C4—1181no—
316C4⋊C4—1181no—
317C22⋊C4—591no—
318C22⋊C4—591no—
319C22⋊C4—1181no—
320C22⋊C4—1181no—
321C22⋊C4—1181no—
322C22⋊C4—1181no—
323C22⋊C4—1181no—
324C22⋊C4—1181no—
325C22⋊C4—1181no—
326C42—591no—
327C42—1181no—
328C23—21no—
329C23—21no—
330C23—42no—
331C23—42no—
332C23—81no—
333C23—591no—
334C23D4×D5911yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—42no—
339Q8—1181no—
340Q8—1181no—
341Q8—1181no—
342Q8—1181no—
343Q8—2362no—
344Q8C2×C22⋊D5912yes—
345D4—21no—
346D4—21no—
347D4—21no—
348D4—42no—
349D4—1182no—
350D4—4721no—
351D4—2362no—
352D4C2×C22⋊D5912yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—42no—
358C2×C4—591no—
359C2×C4—591no—
360C2×C4—591no—
361C2×C4—1181no—
362C2×C4—1181no—
363C2×C4—1181no—
364C2×C4—1181no—
365C2×C4—1181no—
366C2×C4—1181no—
367C2×C4—4721no—
368C2×C4—2362no—
369C2×C4—2362no—
370C2×C4D4×D5911yescharacteristic
371C2×C4C23×D5911yescharacteristic
372C8—21no—
373C8—1181no—
374C8—1181no—
375C8C2×C22⋊D5912yes—
376C22—21no—
377C22—21no—
378C22—22no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—84no—
385C22—1181no—
386C22—1181no—
387C22—1181no—
388C22#1427375612yescomplemented
389C22C2×D4×D5911yescharacteristic
390C4—21no—
391C4—22no—
392C4—41no—
393C4—1181no—
394C4—1181no—
395C4—1181no—
396C4—2361no—
397C4—2361no—
398C4—2361no—
399C4—2361no—
400C4C22×C22⋊D5911yescharacteristic
401C4#1427377211yescharacteristic
402C2—22no—
403C2—42no—
404C2—81no—
405C2—2361no—
406C2D4×C22⋊D5911yescharacteristic
407C2C2×#1427375611yescharacteristic
408C2#1683820811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC22×SD16×C59C2
socleC22×C59C22×D4
hypercenterC22×SD16D59
hypocenterC59#3266
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#14273756C2semidirect
2. Q8×C22⋊D59C2semidirect
4. #16837793C2semidirect
5. #16837645C2semidirect
6. #16837643C2semidirect
7. #16837622C2semidirect
8. #16837605C2semidirect
9. #16837561C2semidirect
10. #16837558C2semidirect
11. #16837553C2semidirect
12. #16837539C2semidirect
13. #16837503C2semidirect
14. #16837473C2semidirect
15. C22×SD16×C59C2semidirect
17. C2×Q8×D59C22semidirect
19. C2×Dic236C22semidirect
20. C2×#11745672C22semidirect
21. C2×#11745672C22semidirect
24. C2×#11745659C22semidirect
26. #14273725C22semidirect
33. #14273703C22semidirect
37. Q8×Dic59C22semidirect
42. #14273661C22semidirect
43. Dic59⋊C8C22semidirect
44. #14273652C22semidirect
45. #14273652C22semidirect
46. #14273651C22semidirect
47. #14273651C22semidirect
51. (C2×D59)⋊C8C22semidirect
52. #14273637C22semidirect
91. SD16×C59D4semidirect
180. C22×C59#137semidirect
206. C22×SD16D59semidirect
220. C59#3266semidirect
301. SD16C22⋊D59semidirect
388. C22#14273756semidirect