Finite Group Databasebeta

← #21433636

Subgroups — #21433636

Order 7552.

504 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×#14273751C211yesmaximal, characteristic, complemented
2C2×#14273748C211yesmaximal, characteristic, complemented
3#16837970C211yesmaximal, characteristic, complemented
4#16837881C211yesmaximal, characteristic, complemented
5#16837627C211yesmaximal, characteristic, complemented
6#16837621C211yesmaximal, characteristic, complemented
7#16837619C211yesmaximal, characteristic, complemented
8#16837603C211yesmaximal, characteristic, complemented
9#16837601C211yesmaximal, characteristic, complemented
10#16837597C211yesmaximal, characteristic, complemented
11#16837595C211yesmaximal, characteristic, complemented
12#16837427C211yesmaximal, characteristic, complemented
13#16837402C211yesmaximal, characteristic, complemented
14#102×D59C211yesmaximal, characteristic, complemented
15C59×#463C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic
17C2×#11745687C2211yescharacteristic
18C2×D4×D59C2211yescharacteristic
19#14273751—24no—
20#14273748—24no—
21C2×#11745672C2211yescharacteristic, complemented
22C2×#11745660C2211yescharacteristic
23C2×#11745660C2211yescharacteristic, complemented
24C2×#11745670C2211yescharacteristic
25C2×#11745669C2211yescharacteristic
26C2×#11745669C2211yescharacteristic, complemented
27C2×#11745659C2211yescharacteristic
28C2×C8×D59C2211yescharacteristic
29#14273724C2211yescharacteristic
30#14273723C2211yescharacteristic
31#14273716C2211yescharacteristic
32#14273700—21no—
33#14273700—21no—
34#14273697—21no—
35#14273697—21no—
36C4×Dic118C2211yescharacteristic, complemented
37#14273692C2211yescharacteristic, complemented
38D4×Dic59C2211yescharacteristic, complemented
39C4×C22⋊D59—21no—
40(C22⋊D59)⋊C4—21no—
41#14273684C2211yescharacteristic
42#14273683—21no—
43C2×Dic59⋊C4—21no—
44C4⋊C4×D59C2211yescharacteristic
45C4⋊(C59⋊C8)C2211yescharacteristic, complemented
46Dic59⋊C8C2211yescharacteristic, complemented
47Dic59⋊C8C2211yescharacteristic, complemented
48#14273651C2211yescharacteristic, complemented
49#14273649C2211yescharacteristic
50#14273649C2211yescharacteristic, complemented
51#14273648C2211yescharacteristic
52#14273647C2211yescharacteristic
53#14273647C2211yescharacteristic, complemented
54C2×SD16×C59C2211yescharacteristic, complemented
55C2×D8×C59C2211yescharacteristic
56#124×C59C2211yescharacteristic
57C4×D4×C59C2211yescharacteristic, complemented
58C4⋊C8×C59C2211yescharacteristic, complemented
59#103×C59C2211yescharacteristic, complemented
60#102×C59C2211yescharacteristic
61C23×D59—21no—
62C2×Q8×C59C2311yescharacteristic
63C2×D4×C59C2311yescharacteristic
64C2×D4×C59C2311yescharacteristic
65C22×C4×C59—21no—
66C2×C22⋊D59—21no—
67C2×C22⋊D59—21no—
68C2×C22⋊D59—21no—
69C2×C22⋊D59—21no—
70C22×Dic59—21no—
71C22×Dic59—21no—
72#11745689—22no—
73#11745689—22no—
74#11745687—22no—
75#11745687D414yescomplemented
76D4×D59—22no—
77D4×D59—22no—
78C2×D236—21no—
79C2×D236—21no—
80C2×D236—21no—
81C2×D236C2311yescharacteristic
82C2×D236C2311yescharacteristic
83C2×C4×D59—21no—
84C2×C4×D59—21no—
85C2×C4×D59C2311yescharacteristic
86C2×Dic118C2311yescharacteristic
87SD16×C59—22no—
88D8×C59—22no—
89C2×C8×C59C2311yescharacteristic
90C2×C8×C59C2311yescharacteristic
91C4⋊C4×C59C2311yescharacteristic
92C22⋊C4×C59—21no—
93C22⋊C4×C59—21no—
94C22⋊C4×C59—21no—
95C42×C59C2311yescharacteristic
96C22⋊Dic59—21no—
97#11745672—22no—
98#11745670—22no—
99#11745669—22no—
100#11745669—22no—
101(C2×D59)⋊C4—21no—
102(C2×D59)⋊C4—21no—
103(C2×D59)⋊C4D411yescharacteristic
104(C2×D59)⋊C4D411yescharacteristic
105C4⋊Dic59C2311yescharacteristic
106Dic59⋊C4—21no—
107Dic59⋊C4—21no—
108Dic59⋊C4—21no—
109Dic59⋊C4D411yescharacteristic
110Dic59⋊C4D411yescharacteristic
111C4×Dic59—21no—
112C4×Dic59—21no—
113C4×Dic59C2311yescharacteristic
114C2×C59⋊C8C2311yescharacteristic
115C2×C59⋊C8C2311yescharacteristic
116#11745660—22no—
117#11745660—22no—
118#11745659—22no—
119C8×D59—22no—
120C23×C59—21no—
121C23×C59—21no—
122C22×D59—21no—
123C22×D59—21no—
124C22×D59—42no—
125C22×D59—81no—
126C22×D59—81no—
127C22×D59C2×D411yescharacteristic
128Q8×C59—21no—
129Q8×C59—21no—
130D4×C59—21no—
131D4×C59—21no—
132D4×C59—21no—
133D4×C59C2×D412yes—
134C2×C4×C59—21no—
135C2×C4×C59—21no—
136C2×C4×C59—81no—
137C2×C4×C59C2×D411yescharacteristic
138C2×C4×C59C2×D411yescharacteristic
139C2×C4×C59C2411yescharacteristic
140C22⋊D59—24no—
141C22⋊D59—42no—
142C22⋊D59—81no—
143C22⋊D59—81no—
144C2×Dic59—21no—
145C2×Dic59—24no—
146C2×Dic59—21no—
147C2×Dic59—81no—
148C2×Dic59C2×D411yescharacteristic
149C2×Dic59C2×D411yescharacteristic
150C2×Dic59C2×D411yescharacteristic
151D236—21no—
152D236—21no—
153D236—21no—
154D236—21no—
155D236—42no—
156D236—81no—
157D236—81no—
158C4×D59—42no—
159C4×D59—81no—
160C4×D59C2×D412yes—
161C4×D59#4112yes—
162Dic118—21no—
163Dic118C2×D412yes—
164C8×C59—21no—
165C8×C59—21no—
166C59⋊C8—21no—
167C59⋊C8—21no—
168C22×C59—22no—
169C22×C59—41no—
170C22×C59—41no—
171C22×C59—41no—
172C22×C59—41no—
173C22×C59—41no—
174C22×C59C22×D411yescharacteristic
175C2×D59—21no—
176C2×D59—21no—
177C2×D59—41no—
178C2×D59—41no—
179C2×D59—41no—
180C2×D59—41no—
181C2×D59—41no—
182C2×D59—41no—
183C2×D59—84no—
184C2×D59#12112yes—
185C4×C59—21no—
186C4×C59—21no—
187C4×C59—41no—
188C4×C59—41no—
189C4×C59C22×D411yescharacteristic
190C4×C59C2×#4111yescharacteristic
191Dic59—22no—
192Dic59—21no—
193Dic59—21no—
194Dic59—41no—
195Dic59#12112yes—
196#3045—591nomaximal, Sylow
197C2×C59—42no—
198C2×C59—81no—
199C2×C59C2×#12111yescharacteristic
200C2×C59#57611yescharacteristic
201C2×C59#57711yescharacteristic
202D59—22no—
203D59—81no—
204D59—81no—
205C2×AGL(1,ℤ/8)—591no—
206C2×#135—591no—
207#535—591no—
208#520—591no—
209#464—591no—
210#464—591no—
211#463—591no—
212#463D5911yescharacteristic, complemented
213#460—591no—
214#460—591no—
215#459—591no—
216#459—591no—
217#424—591no—
218#417—591no—
219C2×#102—591no—
220C59#304511yescharacteristic, complemented, Sylow
221C2×#41—591no—
222C2×#41—591no—
223C22×D4—591no—
224AGL(1,ℤ/8)—1184no—
225#135—1184no—
226C2×Q16—591no—
227C2×SD16—591no—
228C2×SD16—591no—
229C2×SD16—591no—
230C2×SD16C2×D5911yescharacteristic, complemented
231C2×D8—591no—
232C2×D8—591no—
233C2×D8C2×D5911yescharacteristic
234C2×M16—591no—
235C22×C8—591no—
236#127—591no—
237#127—591no—
238#124—591no—
239#124C2×D5911yescharacteristic
240#121—1181no—
241#121—1181no—
242#120—1181no—
243#120—1181no—
244C4×Q8—591no—
245C4×Q8—591no—
246C4×D4—591no—
247C4×D4—1181no—
248C4×D4—1181no—
249C4×D4C2×D5911yescharacteristic, complemented
250#117—591no—
251#117—1181no—
252C2×C4⋊C4—591no—
253C2×C4⋊C4—1181no—
254C4⋊C8—591no—
255C4⋊C8—591no—
256C4⋊C8—591no—
257C4⋊C8C2×D5911yescharacteristic, complemented
258#103—591no—
259#103C2×D5911yescharacteristic, complemented
260#102—591no—
261#102—591no—
262#102—591no—
263#102—591no—
264#102—591no—
265#102C2×D5911yescharacteristic
266C24—1181no—
267#41—594no—
268#41—1182no—
269#41—1182no—
270#41—1182no—
271C2×Q8—591no—
272C2×Q8C22×D5911yescharacteristic
273C2×D4—591no—
274C2×D4—591no—
275C2×D4—1181no—
276C2×D4—1182no—
277C2×D4—1182no—
278C2×D4—1181no—
279C2×D4—1181no—
280C2×D4—1181no—
281C2×D4—1181no—
282C2×D4—1181no—
283C2×D4—1181no—
284C2×D4C22×D5911yescharacteristic
285C2×D4C22×D5911yescharacteristic
286C22×C4—21no—
287C22×C4—591no—
288C22×C4—1181no—
289C22×C4—1181no—
290C22×C4—1181no—
291C22×C4—1181no—
292Q16—1182no—
293SD16—22no—
294SD16—1182no—
295SD16—1182no—
296SD16—1182no—
297D8—22no—
298D8—1182no—
299D8—1182no—
300M16—1182no—
301C2×C8—591no—
302C2×C8—591no—
303C2×C8—1182no—
304C2×C8C22×D5911yescharacteristic
305C2×C8C22×D5911yescharacteristic
306C4⋊C4—591no—
307C4⋊C4—591no—
308C4⋊C4—591no—
309C4⋊C4—1181no—
310C4⋊C4—1181no—
311C4⋊C4—1181no—
312C4⋊C4C22×D5911yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—591no—
317C22⋊C4—591no—
318C22⋊C4—1181no—
319C22⋊C4—1181no—
320C22⋊C4—1181no—
321C42—591no—
322C42—1181no—
323C42—1181no—
324C42C22×D5911yescharacteristic
325C23—21no—
326C23—21no—
327C23—591no—
328C23—1181no—
329C23—1181no—
330C23—4721no—
331C23—4721no—
332C23—2362no—
333Q8—21no—
334Q8—21no—
335Q8—592no—
336Q8—1181no—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—1184no—
341D4—1181no—
342D4—1181no—
343D4—1181no—
344D4—1181no—
345D4—4721no—
346D4—4721no—
347D4—4721no—
348D4—4721no—
349D4—2362no—
350D4—2362no—
351D4D4×D5912yes—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—81no—
355C2×C4—591no—
356C2×C4—592no—
357C2×C4—592no—
358C2×C4—591no—
359C2×C4—591no—
360C2×C4—1184no—
361C2×C4—1181no—
362C2×C4—1181no—
363C2×C4—4721no—
364C2×C4—4721no—
365C2×C4—2362no—
366C2×C4D4×D5911yescharacteristic
367C2×C4D4×D5911yescharacteristic
368C2×C4C23×D5911yescharacteristic
369C8—21no—
370C8—21no—
371C8—1181no—
372C8—1181no—
373C22—22no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—592no—
380C22—1181no—
381C22—1181no—
382C22—4724no—
383C22—2361no—
384C22—2361no—
385C22—2361no—
386C22—2361no—
387C22—2361no—
388C22—2361no—
389C22C2×D4×D5911yescharacteristic
390C4—21no—
391C4—21no—
392C4—41no—
393C4—41no—
394C4—592no—
395C4—1182no—
396C4—1181no—
397C4—1181no—
398C4—2361no—
399C4C2×D4×D5911yescharacteristic
400C4#41×D5911yescharacteristic
401C2—42no—
402C2—81no—
403C2—1182no—
404C2—4721no—
405C2—4721no—
406C2#121×D5911yescharacteristic
407C2#1683820611yescharacteristic
408C2#1683820911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#463C2
socleC22×C59C22×D4
hypercenter#463D59
hypocenterC59#3045
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#14273751C2semidirect
2. C2×#14273748C2semidirect
3. #16837970C2semidirect
4. #16837881C2semidirect
5. #16837627C2semidirect
6. #16837621C2semidirect
7. #16837619C2semidirect
8. #16837603C2semidirect
9. #16837601C2semidirect
10. #16837597C2semidirect
11. #16837595C2semidirect
12. #16837427C2semidirect
13. #16837402C2semidirect
14. #102×D59C2semidirect
15. C59×#463C2semidirect
21. C2×#11745672C22semidirect
23. C2×#11745660C22semidirect
26. C2×#11745669C22semidirect
36. C4×Dic118C22semidirect
37. #14273692C22semidirect
38. D4×Dic59C22semidirect
45. C4⋊(C59⋊C8)C22semidirect
46. Dic59⋊C8C22semidirect
47. Dic59⋊C8C22semidirect
48. #14273651C22semidirect
50. #14273649C22semidirect
53. #14273647C22semidirect
54. C2×SD16×C59C22semidirect
57. C4×D4×C59C22semidirect
58. C4⋊C8×C59C22semidirect
59. #103×C59C22semidirect
75. #11745687D4semidirect
212. #463D59semidirect
220. C59#3045semidirect
230. C2×SD16C2×D59semidirect
249. C4×D4C2×D59semidirect
257. C4⋊C8C2×D59semidirect
259. #103C2×D59semidirect