Finite Group Databasebeta

← #21435612

Subgroups — #21435612

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
2C2×SD16×D59C211yesmaximal, characteristic, complemented
3#16838067C211yesmaximal, characteristic, complemented
4#16838047C211yesmaximal, characteristic
5#16837794C211yesmaximal, characteristic, complemented
6#16837651C211yesmaximal, characteristic, complemented
7#16837642C211yesmaximal, characteristic, complemented
8#16837625C211yesmaximal, characteristic, complemented
9#16837561C211yesmaximal, characteristic, complemented
10#16837559C211yesmaximal, characteristic, complemented
11#16837551C211yesmaximal, characteristic, complemented
12#16837542C211yesmaximal, characteristic, complemented
13#16837502C211yesmaximal, characteristic, complemented
14#16837472C211yesmaximal, characteristic, complemented
15C59×#461C211yesmaximal, characteristic, complemented
16C2×#11745687C2211yescharacteristic
17C2×Q8×D59C2211yescharacteristic
18C2×Q8×D59C2211yescharacteristic, complemented
19C2×D4×D59C2211yescharacteristic
20#14273756—24no—
21C2×Dic236C2211yescharacteristic, complemented
22C2×#11745672C2211yescharacteristic, complemented
23C2×#11745672C2211yescharacteristic, complemented
24C2×#11745660C2211yescharacteristic
25C2×#11745670C2211yescharacteristic
26C2×#11745671C2211yescharacteristic
27C2×#11745671C2211yescharacteristic
28SD16×D59—24no—
29C2×#11745659C2211yescharacteristic, complemented
30C2×C8×D59C2211yescharacteristic
31#14273726—21no—
32#14273715C2211yescharacteristic
33#14273711—21no—
34#14273707C2211yescharacteristic
35#14273705—21no—
36#14273705—21no—
37#14273703C2211yescharacteristic
38#14273703C2211yescharacteristic, complemented
39#14273702C2211yescharacteristic
40#14273701—21no—
41#14273697—21no—
42C4×Dic118C2211yescharacteristic, complemented
43C4×D236C2211yescharacteristic
44#14273689—21no—
45C2×(C2×D59)⋊C4—21no—
46#14273660C2211yescharacteristic, complemented
47#14273652C2211yescharacteristic, complemented
48#14273650C2211yescharacteristic, complemented
49#14273649C2211yescharacteristic
50#14273648C2211yescharacteristic
51(C2×D59)⋊C8C2211yescharacteristic
52(C2×D59)⋊C8C2211yescharacteristic, complemented
53#14273638C2211yescharacteristic, complemented
54C2×SD16×C59C2211yescharacteristic
55C2×SD16×C59C2211yescharacteristic
56C4⋊Q8×C59C2211yescharacteristic, complemented
57C4×D4×C59C2211yescharacteristic
58C4⋊C8×C59C2211yescharacteristic, complemented
59#103×C59C2211yescharacteristic, complemented
60#103×C59C2211yescharacteristic, complemented
61C23×D59—21no—
62C2×Q8×C59C2311yescharacteristic
63C2×Q8×C59C2311yescharacteristic
64C2×D4×C59C2311yescharacteristic
65C22×C4×C59—21no—
66C2×C22⋊D59—21no—
67C2×C22⋊D59—21no—
68C22×Dic59—21no—
69Q8×D59—22no—
70Q8×D59—22no—
71Q8×D59—41no—
72Q8×D59—41no—
73#11745687—22no—
74#11745687—41no—
75D4×D59—22no—
76D4×D59—41no—
77C2×D236—21no—
78C2×D236D411yescharacteristic
79C2×D236C2311yescharacteristic
80C2×C4×D59—21no—
81C2×C4×D59—21no—
82C2×C4×D59C2311yescharacteristic
83C2×C4×D59C2311yescharacteristic
84C2×Dic118—21no—
85C2×Dic118—21no—
86C2×Dic118C2311yescharacteristic
87C2×Dic118C2311yescharacteristic
88SD16×C59—22no—
89SD16×C59—22no—
90C2×C8×C59C2311yescharacteristic
91C2×C8×C59C2311yescharacteristic
92C4⋊C4×C59—21no—
93C4⋊C4×C59—21no—
94C4⋊C4×C59C2311yescharacteristic
95C22⋊C4×C59—21no—
96C42×C59C2311yescharacteristic
97#11745672—22no—
98#11745672—41no—
99#11745671—22no—
100#11745671—41no—
101#11745670D414yescomplemented
102(C2×D59)⋊C4—21no—
103(C2×D59)⋊C4—21no—
104(C2×D59)⋊C4—21no—
105(C2×D59)⋊C4—21no—
106(C2×D59)⋊C4—21no—
107(C2×D59)⋊C4—21no—
108(C2×D59)⋊C4D411yescharacteristic
109(C2×D59)⋊C4D411yescharacteristic
110C4⋊Dic59—21no—
111C4⋊Dic59D411yescharacteristic
112C4⋊Dic59C2311yescharacteristic
113Dic59⋊C4—21no—
114Dic59⋊C4—21no—
115Dic59⋊C4—21no—
116C4×Dic59—21no—
117C2×C59⋊C8C2311yescharacteristic
118C2×C59⋊C8C2311yescharacteristic
119Dic236—22no—
120#11745660—22no—
121#11745659—22no—
122C8×D59—22no—
123C23×C59—21no—
124C22×D59—21no—
125C22×D59—42no—
126C22×D59—42no—
127C22×D59—81no—
128C22×D59C2×D411yescharacteristic
129C22×D59C2×D411yescharacteristic
130Q8×C59—21no—
131Q8×C59—21no—
132Q8×C59—21no—
133Q8×C59—21no—
134D4×C59—21no—
135D4×C59C2×D412yes—
136C2×C4×C59—21no—
137C2×C4×C59—21no—
138C2×C4×C59—21no—
139C2×C4×C59—81no—
140C2×C4×C59C2×D411yescharacteristic
141C2×C4×C59C2×D411yescharacteristic
142C2×C4×C59C2411yescharacteristic
143C22⋊D59—42no—
144C22⋊D59—42no—
145C2×Dic59—21no—
146C2×Dic59—21no—
147C2×Dic59—21no—
148C2×Dic59—42no—
149C2×Dic59C2×D411yescharacteristic
150C2×Dic59C2×D411yescharacteristic
151D236—22no—
152D236—21no—
153D236—21no—
154D236—81no—
155C4×D59—21no—
156C4×D59—21no—
157C4×D59—21no—
158C4×D59—21no—
159C4×D59—42no—
160C4×D59—42no—
161Dic118—21no—
162Dic118—21no—
163Dic118—21no—
164Dic118—42no—
165Dic118—42no—
166Dic118C2×D412yes—
167C8×C59—21no—
168C8×C59—21no—
169C59⋊C8—21no—
170C59⋊C8C2×D412yes—
171C22×C59—22no—
172C22×C59—41no—
173C22×C59—41no—
174C22×C59C22×D411yescharacteristic
175C2×D59—21no—
176C2×D59—21no—
177C2×D59—21no—
178C2×D59—21no—
179C2×D59—21no—
180C2×D59—41no—
181C2×D59—41no—
182C2×D59—41no—
183C2×D59—84no—
184C2×D59#13712yescomplemented
185C4×C59—21no—
186C4×C59—21no—
187C4×C59—41no—
188C4×C59—41no—
189C4×C59—41no—
190C4×C59C22×D411yescharacteristic
191C4×C59H(5,𝔽2)11yescharacteristic
192Dic59—22no—
193Dic59—21no—
194Dic59—21no—
195Dic59—41no—
196Dic59—41no—
197#3266—591nomaximal, Sylow
198C2×C59—42no—
199C2×C59D4211yescharacteristic
200C2×C59C2×#13711yescharacteristic
201C2×C59#57711yescharacteristic
202D59—22no—
203D59—41no—
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#461D5911yescharacteristic, complemented
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×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—1184no—
234C2×SD16C2×D5911yescharacteristic
235C2×SD16C2×D5911yescharacteristic
236C2×M16—591no—
237C22×C8—591no—
238C4⋊Q8—1181no—
239C4⋊Q8C2×D5911yescharacteristic, complemented
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#103C2×D5911yescharacteristic, complemented
260#103C2×D5911yescharacteristic, complemented
261#102—591no—
262#102—591no—
263C22⋊C8—591no—
264C22⋊C8—591no—
265#97—591no—
266C24—1181no—
267#41—1182no—
268#41—2361no—
269C2×Q8—591no—
270C2×Q8—591no—
271C2×Q8—1181no—
272C2×Q8—1181no—
273C2×Q8—1182no—
274C2×Q8—1182no—
275C2×Q8—2361no—
276C2×Q8—2361no—
277C2×Q8C22×D5911yescharacteristic
278C2×Q8C22×D5911yescharacteristic
279C2×D4—591no—
280C2×D4—591no—
281C2×D4—1181no—
282C2×D4—1181no—
283C2×D4—1182no—
284C2×D4—1181no—
285C2×D4—2361no—
286C2×D4C22×D5911yescharacteristic
287C22×C4—21no—
288C22×C4—591no—
289C22×C4—591no—
290C22×C4—1181no—
291C22×C4—1181no—
292C22×C4—1181no—
293Q16—1182no—
294Q16—1182no—
295Q16—2361no—
296SD16—22no—
297SD16—22no—
298SD16—594no—
299SD16—1182no—
300SD16—1182no—
301SD16—2361no—
302M16—1182no—
303C2×C8—591no—
304C2×C8—591no—
305C2×C8—1182no—
306C2×C8C22×D5911yescharacteristic
307C2×C8C22×D5911yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—591no—
311C4⋊C4—591no—
312C4⋊C4—1181no—
313C4⋊C4—1181no—
314C4⋊C4—1181no—
315C4⋊C4—1181no—
316C4⋊C4C22×D5911yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—591no—
319C22⋊C4—591no—
320C22⋊C4—1181no—
321C22⋊C4—1181no—
322C22⋊C4—1181no—
323C22⋊C4—1181no—
324C22⋊C4—1181no—
325C22⋊C4—1181no—
326C42—1181no—
327C42C22×D5911yescharacteristic
328C23—21no—
329C23—591no—
330C23—591no—
331C23—1181no—
332C23—4721no—
333C23—2362no—
334C23—2362no—
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—592no—
340Q8—1181no—
341Q8—1181no—
342Q8—1181no—
343Q8—2362no—
344Q8—2362no—
345D4—21no—
346D4—1182no—
347D4—1181no—
348D4—1181no—
349D4—4721no—
350D4—2362no—
351D4—2362no—
352D4D4×D5912yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—81no—
357C2×C4—591no—
358C2×C4—591no—
359C2×C4—1181no—
360C2×C4—1181no—
361C2×C4—1181no—
362C2×C4—1181no—
363C2×C4—1181no—
364C2×C4—1181no—
365C2×C4—1181no—
366C2×C4—2362no—
367C2×C4—2362no—
368C2×C4—2362no—
369C2×C4D4×D5911yescharacteristic
370C2×C4D4×D5911yescharacteristic
371C2×C4C23×D5911yescharacteristic
372C8—21no—
373C8—21no—
374C8—592no—
375C8—1181no—
376C22—22no—
377C22—41no—
378C22—41no—
379C22—592no—
380C22—1181no—
381C22—1181no—
382C22—1181no—
383C22—1181no—
384C22—1181no—
385C22—4724no—
386C22—2361no—
387C22—2361no—
388C22—2361no—
389C22C2×D4×D5911yescharacteristic
390C4—21no—
391C4—21no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—1181no—
396C4—1181no—
397C4—1182no—
398C4—2361no—
399C4—2361no—
400C4C2×D4×D5911yescharacteristic
401C4#1427377311yescharacteristic
402C2—42no—
403C2—1182no—
404C2—4721no—
405C2—2361no—
406C2#1683803611yescharacteristic
407C2#137×D5911yescharacteristic
408C2#1683820811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#461C2
socleC22×C59C22×D4
hypercenter#461D59
hypocenterC59#3266
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. C2×#14273756C2semidirect
2. C2×SD16×D59C2semidirect
3. #16838067C2semidirect
5. #16837794C2semidirect
6. #16837651C2semidirect
7. #16837642C2semidirect
8. #16837625C2semidirect
9. #16837561C2semidirect
10. #16837559C2semidirect
11. #16837551C2semidirect
12. #16837542C2semidirect
13. #16837502C2semidirect
14. #16837472C2semidirect
15. C59×#461C2semidirect
18. C2×Q8×D59C22semidirect
21. C2×Dic236C22semidirect
22. C2×#11745672C22semidirect
23. C2×#11745672C22semidirect
29. C2×#11745659C22semidirect
38. #14273703C22semidirect
42. C4×Dic118C22semidirect
46. #14273660C22semidirect
47. #14273652C22semidirect
48. #14273650C22semidirect
52. (C2×D59)⋊C8C22semidirect
53. #14273638C22semidirect
56. C4⋊Q8×C59C22semidirect
58. C4⋊C8×C59C22semidirect
59. #103×C59C22semidirect
60. #103×C59C22semidirect
101. #11745670D4semidirect
184. C2×D59#137semidirect
213. #461D59semidirect
220. C59#3266semidirect
239. C4⋊Q8C2×D59semidirect
256. C4⋊C8C2×D59semidirect
259. #103C2×D59semidirect
260. #103C2×D59semidirect