Finite Group Databasebeta

← #21435667

Subgroups — #21435667

Order 7552.

472 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273758C211yesmaximal, characteristic, complemented
2C22×#11745672C211yesmaximal, characteristic, complemented
3#16838061C211yesmaximal, characteristic
4#16837794C211yesmaximal, characteristic, complemented
5#16837658C211yesmaximal, characteristic, complemented
6#16837633C211yesmaximal, characteristic, complemented
7#16837624C211yesmaximal, characteristic, complemented
8#16837609C211yesmaximal, characteristic, complemented
9#16837562C211yesmaximal, characteristic, complemented
10#16837558C211yesmaximal, characteristic, complemented
11#16837557C211yesmaximal, characteristic, complemented
12#16837541C211yesmaximal, characteristic, complemented
13#16837507C211yesmaximal, characteristic, complemented
14#16837474C211yesmaximal, characteristic, complemented
15D4×Q8×C59C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C22×Dic118C2211yescharacteristic
18#14273758—24no—
19C2×#11745672—24no—
20C2×#11745672C2211yescharacteristic
21C2×#11745672C2211yescharacteristic
22C2×#11745672C2211yescharacteristic
23C2×#11745672C2211yescharacteristic
24C2×#11745672C2211yescharacteristic
25C2×#11745672C2211yescharacteristic
26C2×#11745671C2211yescharacteristic
27C2×#11745671C2211yescharacteristic
28C2×#11745671C2211yescharacteristic
29C2×#11745664C2211yescharacteristic
30C22×C59⋊C8C2211yescharacteristic
31#14273715C2211yescharacteristic
32#14273713—21no—
33#14273706C2211yescharacteristic
34#14273705—21no—
35#14273701C2211yescharacteristic
36#14273699—21no—
37C4×Dic118C2211yescharacteristic
38(C22⋊D59)⋊C4—21no—
39#14273658C2211yescharacteristic
40C4⋊(C59⋊C8)C2211yescharacteristic
41#14273651C2211yescharacteristic
42#14273651C2211yescharacteristic
43#14273651C2211yescharacteristic
44#14273650C2211yescharacteristic
45#14273650C2211yescharacteristic
46#14273647C2211yescharacteristic
47C22⋊(C59⋊C8)C2211yescharacteristic
48C22⋊(C59⋊C8)C2211yescharacteristic
49#14273638C2211yescharacteristic
50C22×Q8×C59C2211yescharacteristic
51C22×Q8×C59C2211yescharacteristic
52C4⋊Q8×C59—21no—
53C4⋊Q8×C59C2211yescharacteristic
54C22⋊Q8×C59—21no—
55C22⋊Q8×C59—21no—
56C22⋊Q8×C59C2211yescharacteristic
57C22⋊Q8×C59C2211yescharacteristic
58C4×Q8×C59C2211yescharacteristic
59C4×D4×C59—21no—
60C4×D4×C59C2211yescharacteristic
61C2×Q8×C59—21no—
62C2×Q8×C59—21no—
63C2×Q8×C59—22no—
64C2×Q8×C59—22no—
65C2×Q8×C59—41no—
66C2×Q8×C59—41no—
67C2×Q8×C59C2311yescharacteristic
68C2×Q8×C59C2311yescharacteristic
69C2×Q8×C59C2311yescharacteristic
70C2×D4×C59D411yescharacteristic
71C22×C4×C59—21no—
72C22×C4×C59—21no—
73C22×C4×C59C2311yescharacteristic
74C22×C4×C59C2311yescharacteristic
75C2×C22⋊D59—21no—
76C2×C22⋊D59—21no—
77C22×Dic59—21no—
78#11745685—22no—
79#11745685—41no—
80C2×D236C2311yescharacteristic
81C2×C4×D59—21no—
82C2×Dic118—22no—
83C2×Dic118—21no—
84C2×Dic118—41no—
85C2×Dic118C2311yescharacteristic
86C2×Dic118C2311yescharacteristic
87C4⋊C4×C59—21no—
88C4⋊C4×C59—21no—
89C4⋊C4×C59—21no—
90C4⋊C4×C59—21no—
91C4⋊C4×C59—21no—
92C4⋊C4×C59D411yescharacteristic
93C4⋊C4×C59C2311yescharacteristic
94C22⋊C4×C59—21no—
95C22⋊C4×C59—21no—
96C22⋊C4×C59D411yescharacteristic
97C22⋊C4×C59D411yescharacteristic
98C42×C59—21no—
99C42×C59C2311yescharacteristic
100C22⋊Dic59—21no—
101#11745672—22no—
102#11745672—22no—
103#11745672—22no—
104#11745672—22no—
105#11745672—41no—
106#11745672D414yescomplemented
107#11745671—22no—
108#11745671—22no—
109#11745671—41no—
110(C2×D59)⋊C4—21no—
111(C2×D59)⋊C4—21no—
112(C2×D59)⋊C4—21no—
113C4⋊Dic59C2311yescharacteristic
114Dic59⋊C4—21no—
115Dic59⋊C4—21no—
116C4×Dic59—21no—
117#11745664—22no—
118C2×C59⋊C8—22no—
119C2×C59⋊C8C2311yescharacteristic
120C2×C59⋊C8C2311yescharacteristic
121C2×C59⋊C8C2311yescharacteristic
122C2×C59⋊C8C2311yescharacteristic
123C23×C59C2×D411yescharacteristic
124C23×C59C2×D411yescharacteristic
125C22×D59—21no—
126Q8×C59—21no—
127Q8×C59—21no—
128Q8×C59—21no—
129Q8×C59—21no—
130Q8×C59—21no—
131Q8×C59—42no—
132Q8×C59—42no—
133Q8×C59C2×D412yes—
134D4×C59—22no—
135C2×C4×C59—21no—
136C2×C4×C59—21no—
137C2×C4×C59—21no—
138C2×C4×C59—21no—
139C2×C4×C59—21no—
140C2×C4×C59—21no—
141C2×C4×C59—21no—
142C2×C4×C59—21no—
143C2×C4×C59—42no—
144C2×C4×C59—42no—
145C2×C4×C59C2×D411yescharacteristic
146C2×C4×C59C2×D411yescharacteristic
147C2×C4×C59C2×D411yescharacteristic
148C2×C4×C59C2×D411yescharacteristic
149C2×C4×C59C2411yescharacteristic
150C22⋊D59—42no—
151C22⋊D59—42no—
152C2×Dic59—21no—
153C2×Dic59—21no—
154C2×Dic59—21no—
155C2×Dic59—42no—
156D236—21no—
157D236—21no—
158C4×D59—42no—
159Dic118—21no—
160Dic118—21no—
161Dic118—21no—
162Dic118—42no—
163Dic118C2×D412yes—
164C59⋊C8—21no—
165C59⋊C8—21no—
166C59⋊C8—21no—
167C59⋊C8C2×D412yes—
168C22×C59—21no—
169C22×C59—21no—
170C22×C59—21no—
171C22×C59—21no—
172C22×C59—21no—
173C22×C59#13712yescomplemented
174C22×C59C22×D411yescharacteristic
175C2×D59—41no—
176C2×D59—41no—
177C2×D59—41no—
178C4×C59—21no—
179C4×C59—21no—
180C4×C59—22no—
181C4×C59—21no—
182C4×C59—21no—
183C4×C59—41no—
184C4×C59—41no—
185C4×C59—41no—
186C4×C59C22×D411yescharacteristic
187C4×C59H(5,𝔽2)11yescharacteristic
188Dic59—22no—
189Dic59—41no—
190Dic59—41no—
191#3270—591nomaximal, Sylow
192C2×C59—22no—
193C2×C59—41no—
194C2×C59D4211yescharacteristic
195C2×C59C2×#13711yescharacteristic
196C2×C59#57811yescharacteristic
197D59—81no—
198C2×#137—591no—
199C22×Q16—591no—
200D4×Q8D5911yescharacteristic, complemented
201#548—591no—
202#497—591no—
203#470—591no—
204#465—591no—
205#464—591no—
206#462—591no—
207#452—591no—
208#451—591no—
209#451—591no—
210#448—591no—
211#441—591no—
212#435—591no—
213C59#327011yescharacteristic, complemented, Sylow
214C2×#41—591no—
215C22×Q8—591no—
216C22×Q8C2×D5911yescharacteristic
217C22×Q8C2×D5911yescharacteristic
218#137—1184no—
219C2×Q16—591no—
220C2×Q16—591no—
221C2×Q16—591no—
222C2×Q16—591no—
223C2×Q16—591no—
224C2×Q16—591no—
225C2×Q16—1184no—
226C2×SD16—591no—
227C2×SD16—591no—
228C2×SD16—591no—
229C2×M16—591no—
230C22×C8—591no—
231C4⋊Q8—21no—
232C4⋊Q8C2×D5911yescharacteristic
233#124—591no—
234#124—1181no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237C22⋊Q8—591no—
238C22⋊Q8—1181no—
239C22⋊Q8C2×D5911yescharacteristic
240C22⋊Q8C2×D5911yescharacteristic
241#121—591no—
242#121—1181no—
243C4×Q8—591no—
244C4×Q8C2×D5911yescharacteristic
245C4×D4—21no—
246C4×D4—1181no—
247C4×D4C2×D5911yescharacteristic
248#106—591no—
249C4⋊C8—591no—
250#103—591no—
251#103—591no—
252#103—591no—
253#103—591no—
254#103—591no—
255#102—591no—
256C22⋊C8—591no—
257C22⋊C8—591no—
258#97—591no—
259#41—1182no—
260#41—2361no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—22no—
264C2×Q8—22no—
265C2×Q8—41no—
266C2×Q8—41no—
267C2×Q8—591no—
268C2×Q8—591no—
269C2×Q8—1182no—
270C2×Q8—1181no—
271C2×Q8—2361no—
272C2×Q8C22×D5911yescharacteristic
273C2×Q8C22×D5911yescharacteristic
274C2×Q8C22×D5911yescharacteristic
275C2×D4—591no—
276C2×D4—1181no—
277C2×D4—1181no—
278C2×D4C22⋊D5911yescharacteristic
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—1181no—
282C22×C4—1181no—
283C22×C4C22×D5911yescharacteristic
284C22×C4C22×D5911yescharacteristic
285Q16—594no—
286Q16—1182no—
287Q16—1182no—
288Q16—1182no—
289Q16—1182no—
290Q16—2361no—
291SD16—1182no—
292SD16—1182no—
293SD16—2361no—
294M16—1182no—
295C2×C8—591no—
296C2×C8—591no—
297C2×C8—591no—
298C2×C8—591no—
299C2×C8—1182no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—591no—
306C4⋊C4—1181no—
307C4⋊C4—1181no—
308C4⋊C4C22⋊D5911yescharacteristic
309C4⋊C4C22×D5911yescharacteristic
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—1181no—
313C22⋊C4—1181no—
314C22⋊C4—1181no—
315C22⋊C4—1181no—
316C22⋊C4C22⋊D5911yescharacteristic
317C22⋊C4C22⋊D5911yescharacteristic
318C42—21no—
319C42—1181no—
320C42C22×D5911yescharacteristic
321C23—1181no—
322C23C2×C22⋊D5911yescharacteristic
323C23C2×C22⋊D5911yescharacteristic
324Q8—21no—
325Q8—21no—
326Q8—21no—
327Q8—21no—
328Q8—21no—
329Q8—42no—
330Q8—42no—
331Q8—592no—
332Q8—1181no—
333Q8—1181no—
334Q8—1181no—
335Q8—2362no—
336Q8D4×D5912yes—
337D4—22no—
338D4—1181no—
339D4—1181no—
340D4—2362no—
341D4—2362no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—1181no—
353C2×C4—1181no—
354C2×C4—1181no—
355C2×C4—2362no—
356C2×C4—2362no—
357C2×C4C2×C22⋊D5911yescharacteristic
358C2×C4C2×C22⋊D5911yescharacteristic
359C2×C4C2×C22⋊D5911yescharacteristic
360C2×C4C2×C22⋊D5911yescharacteristic
361C2×C4C23×D5911yescharacteristic
362C8—592no—
363C8—1181no—
364C8—1181no—
365C8—1181no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—2361no—
372C22—2361no—
373C22—2361no—
374C22#1427375812yescomplemented
375C22C22×C22⋊D5911yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—22no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—1182no—
385C4—2361no—
386C4—2361no—
387C4C2×D4×D5911yescharacteristic
388C4#1427377211yescharacteristic
389C2—22no—
390C2—41no—
391C2—4721no—
392C2D4×C22⋊D5911yescharacteristic
393C2C2×#1427375811yescharacteristic
394C2#1683821711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingD4×Q8×C59C2
socleC22×C59C22×D4
hypercenterD4×Q8D59
hypocenterC59#3270
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#14273758C2semidirect
2. C22×#11745672C2semidirect
4. #16837794C2semidirect
5. #16837658C2semidirect
6. #16837633C2semidirect
7. #16837624C2semidirect
8. #16837609C2semidirect
9. #16837562C2semidirect
10. #16837558C2semidirect
11. #16837557C2semidirect
12. #16837541C2semidirect
13. #16837507C2semidirect
14. #16837474C2semidirect
15. D4×Q8×C59C2semidirect
106. #11745672D4semidirect
173. C22×C59#137semidirect
200. D4×Q8D59semidirect
213. C59#3270semidirect
374. C22#14273758semidirect