Finite Group Databasebeta

← #21435703

Subgroups — #21435703

Order 7552.

520 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273753C211yesmaximal, characteristic, complemented
2C2×#14273752C211yesmaximal, characteristic, complemented
3#16838048C211yesmaximal, characteristic, complemented
4#16837784C211yesmaximal, characteristic, complemented
5#16837650C211yesmaximal, characteristic, complemented
6#16837646C211yesmaximal, characteristic, complemented
7#16837617C211yesmaximal, characteristic, complemented
8#16837614C211yesmaximal, characteristic, complemented
9#16837564C211yesmaximal, characteristic, complemented
10#16837562C211yesmaximal, characteristic, complemented
11#16837536C211yesmaximal, characteristic, complemented
12#16837535C211yesmaximal, characteristic, complemented
13C4×#11745669C211yesmaximal, characteristic, complemented
14#16837480C211yesmaximal, characteristic, complemented
15C59×#546C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C22×D236C2211yescharacteristic, complemented
18#14273753—24no—
19#14273752—24no—
20C2×#11745672C2211yescharacteristic, complemented
21C2×#11745670C2211yescharacteristic, complemented
22C2×#11745670C2211yescharacteristic, complemented
23C2×#11745671C2211yescharacteristic, complemented
24C2×#11745671C2211yescharacteristic, complemented
25C2×#11745669C2211yescharacteristic
26C2×#11745669C2211yescharacteristic
27C2×#11745669C2211yescharacteristic
28C2×#11745669C2211yescharacteristic
29C2×#11745664C2211yescharacteristic, complemented
30C2×#11745664C2211yescharacteristic, complemented
31#14273715C2211yescharacteristic, complemented
32#14273712—21no—
33#14273706C2211yescharacteristic, complemented
34#14273701C2211yescharacteristic
35#14273700—21no—
36#14273695—21no—
37C4×D236C2211yescharacteristic, complemented
38C22⋊C4×D59—21no—
39#14273660C2211yescharacteristic, complemented
40C4⋊(C59⋊C8)C2211yescharacteristic, complemented
41#14273651C2211yescharacteristic, complemented
42#14273650C2211yescharacteristic, complemented
43#14273648C2211yescharacteristic, complemented
44#14273648C2211yescharacteristic, complemented
45#14273647C2211yescharacteristic, complemented
46#14273647C2211yescharacteristic, complemented
47C22⋊(C59⋊C8)C2211yescharacteristic, complemented
48C22⋊(C59⋊C8)C2211yescharacteristic, complemented
49C4×C59⋊C8C2211yescharacteristic, complemented
50C2×#41×C59C2211yescharacteristic
51C22×D4×C59C2211yescharacteristic, complemented
52#124×C59C2211yescharacteristic, complemented
53#123×C59—21no—
54C22⋊Q8×C59C2211yescharacteristic, complemented
55#121×C59—21no—
56#121×C59C2211yescharacteristic
57#120×C59—21no—
58C4×D4×C59C2211yescharacteristic
59C4×D4×C59C2211yescharacteristic, complemented
60C2×C22⋊C4×C59—21no—
61C24×C59—21no—
62C23×D59—21no—
63#41×C59—22no—
64#41×C59—41no—
65C2×Q8×C59C2311yescharacteristic
66C2×D4×C59—22no—
67C2×D4×C59—21no—
68C2×D4×C59—21no—
69C2×D4×C59—21no—
70C2×D4×C59—41no—
71C2×D4×C59D411yescharacteristic
72C2×D4×C59C2311yescharacteristic
73C2×D4×C59C2311yescharacteristic
74C22×C4×C59—21no—
75C22×C4×C59—21no—
76C22×C4×C59C2311yescharacteristic
77C22×C4×C59C2311yescharacteristic
78C2×C22⋊D59—21no—
79C2×C22⋊D59—21no—
80#11745685—22no—
81#11745685—41no—
82C2×D236—22no—
83C2×D236—21no—
84C2×D236—41no—
85C2×D236C2311yescharacteristic
86C2×D236C2311yescharacteristic
87C2×C4×D59—21no—
88C2×C4×D59—21no—
89C2×Dic118C2311yescharacteristic
90C4⋊C4×C59—21no—
91C4⋊C4×C59D411yescharacteristic
92C4⋊C4×C59C2311yescharacteristic
93C22⋊C4×C59—21no—
94C22⋊C4×C59—21no—
95C22⋊C4×C59—21no—
96C22⋊C4×C59—21no—
97C22⋊C4×C59—21no—
98C22⋊C4×C59D411yescharacteristic
99C22⋊C4×C59D411yescharacteristic
100C42×C59C2311yescharacteristic
101C22⋊Dic59—21no—
102#11745672—41no—
103#11745671—22no—
104#11745671—22no—
105#11745670—22no—
106#11745670—22no—
107#11745669—22no—
108#11745669—22no—
109#11745669—41no—
110#11745669D414yescomplemented
111(C2×D59)⋊C4—21no—
112(C2×D59)⋊C4—21no—
113(C2×D59)⋊C4—21no—
114(C2×D59)⋊C4—21no—
115C4⋊Dic59C2311yescharacteristic
116Dic59⋊C4—21no—
117#11745664—22no—
118#11745664—22no—
119C2×C59⋊C8C2311yescharacteristic
120C2×C59⋊C8C2311yescharacteristic
121C2×C59⋊C8C2311yescharacteristic
122C2×C59⋊C8C2311yescharacteristic
123C23×C59—21no—
124C23×C59—21no—
125C23×C59—42no—
126C23×C59—42no—
127C23×C59—81no—
128C23×C59C2×D411yescharacteristic
129C23×C59C2×D411yescharacteristic
130C22×D59—21no—
131C22×D59—21no—
132C22×D59—42no—
133C22×D59—42no—
134C22×D59—81no—
135Q8×C59—21no—
136Q8×C59—21no—
137D4×C59—21no—
138D4×C59—21no—
139D4×C59—21no—
140D4×C59—41no—
141D4×C59—42no—
142D4×C59—42no—
143D4×C59—81no—
144D4×C59C2×D412yes—
145C2×C4×C59—21no—
146C2×C4×C59—21no—
147C2×C4×C59—21no—
148C2×C4×C59—21no—
149C2×C4×C59—21no—
150C2×C4×C59—21no—
151C2×C4×C59—42no—
152C2×C4×C59—81no—
153C2×C4×C59C2×D411yescharacteristic
154C2×C4×C59C2×D411yescharacteristic
155C2×C4×C59C2×D411yescharacteristic
156C2×C4×C59C2×D411yescharacteristic
157C2×C4×C59C2411yescharacteristic
158C22⋊D59—42no—
159C22⋊D59—81no—
160C2×Dic59—21no—
161C2×Dic59—21no—
162D236—21no—
163D236—21no—
164D236—21no—
165D236—42no—
166D236C2×D412yes—
167C4×D59—42no—
168C4×D59—81no—
169Dic118—21no—
170Dic118—21no—
171C59⋊C8—21no—
172C59⋊C8—21no—
173C59⋊C8—21no—
174C59⋊C8C2×D412yes—
175C22×C59—21no—
176C22×C59—21no—
177C22×C59—22no—
178C22×C59—21no—
179C22×C59—21no—
180C22×C59—21no—
181C22×C59—21no—
182C22×C59—41no—
183C22×C59—41no—
184C22×C59—41no—
185C22×C59—41no—
186C22×C59—41no—
187C22×C59—84no—
188C22×C59C22×D411yescharacteristic
189C2×D59—22no—
190C2×D59—41no—
191C2×D59—41no—
192C2×D59—41no—
193C2×D59—41no—
194C2×D59—41no—
195C2×D59—84no—
196C4×C59—21no—
197C4×C59—21no—
198C4×C59—21no—
199C4×C59—21no—
200C4×C59—41no—
201C4×C59—41no—
202C4×C59C22×D411yescharacteristic
203C4×C59H(5,𝔽2)11yescharacteristic
204Dic59—41no—
205Dic59—41no—
206#3273—591nomaximal, Sylow
207C2×C59—41no—
208C2×C59—41no—
209C2×C59—42no—
210C2×C59—81no—
211C2×C59D4211yescharacteristic
212C2×C59#57511yescharacteristic
213C2×C59#57611yescharacteristic
214D59—42no—
215D59—81no—
216C2×AGL(1,ℤ/8)—591no—
217C2×AGL(1,ℤ/8)—591no—
218#546—591no—
219#546D5911yescharacteristic, complemented
220#495—591no—
221#468—591no—
222#468—591no—
223#463—591no—
224#463—591no—
225#452—591no—
226#452—591no—
227#447—591no—
228#447—591no—
229C4×D8—591no—
230#436—591no—
231C59#327311yescharacteristic, complemented, Sylow
232C2×#41—591no—
233C2×#41C2×D5911yescharacteristic
234C22×D4—591no—
235C22×D4C2×D5911yescharacteristic, complemented
236AGL(1,ℤ/8)—1184no—
237AGL(1,ℤ/8)—1184no—
238C2×Q16—591no—
239C2×SD16—591no—
240C2×SD16—591no—
241C2×SD16—591no—
242C2×SD16—591no—
243C2×D8—591no—
244C2×D8—591no—
245C2×D8—591no—
246C2×D8—591no—
247C2×M16—591no—
248C2×M16—591no—
249#124—591no—
250#124C2×D5911yescharacteristic, complemented
251#123—21no—
252#123—1181no—
253C22⋊Q8—591no—
254C22⋊Q8C2×D5911yescharacteristic, complemented
255#121—21no—
256#121—591no—
257#121—1181no—
258#121C2×D5911yescharacteristic
259#120—21no—
260#120—1181no—
261C4×D4—591no—
262C4×D4C2×D5911yescharacteristic
263C4×D4C2×D5911yescharacteristic, complemented
264C2×C22⋊C4—21no—
265C2×C22⋊C4—1181no—
266#107—591no—
267C4⋊C8—591no—
268#103—591no—
269#103—591no—
270#102—591no—
271#102—591no—
272#102—591no—
273#102—591no—
274C22⋊C8—591no—
275C22⋊C8—591no—
276C4×C8—591no—
277C24—21no—
278C24—1181no—
279#41—22no—
280#41—41no—
281#41—1182no—
282#41—2361no—
283C2×Q8—591no—
284C2×Q8C22×D5911yescharacteristic
285C2×D4—22no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—41no—
290C2×D4—591no—
291C2×D4—591no—
292C2×D4—1182no—
293C2×D4—1181no—
294C2×D4—1181no—
295C2×D4—1181no—
296C2×D4—2361no—
297C2×D4C22⋊D5911yescharacteristic
298C2×D4C22×D5911yescharacteristic
299C2×D4C22×D5911yescharacteristic
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—1181no—
303C22×C4—1181no—
304C22×C4C22×D5911yescharacteristic
305C22×C4C22×D5911yescharacteristic
306Q16—2361no—
307SD16—1182no—
308SD16—1182no—
309SD16—1182no—
310SD16—1182no—
311D8—594no—
312D8—1182no—
313D8—1182no—
314D8—2361no—
315M16—1182no—
316M16—1182no—
317C2×C8—591no—
318C2×C8—591no—
319C2×C8—591no—
320C2×C8—591no—
321C4⋊C4—21no—
322C4⋊C4—591no—
323C4⋊C4—1181no—
324C4⋊C4C22⋊D5911yescharacteristic
325C4⋊C4C22×D5911yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—21no—
330C22⋊C4—21no—
331C22⋊C4—1181no—
332C22⋊C4—1181no—
333C22⋊C4—1181no—
334C22⋊C4—1181no—
335C22⋊C4—1181no—
336C22⋊C4C22⋊D5911yescharacteristic
337C22⋊C4C22⋊D5911yescharacteristic
338C42C22×D5911yescharacteristic
339C23—21no—
340C23—21no—
341C23—42no—
342C23—42no—
343C23—81no—
344C23—1181no—
345C23—1181no—
346C23—4721no—
347C23—2362no—
348C23—2362no—
349C23C2×C22⋊D5911yescharacteristic
350C23C2×C22⋊D5911yescharacteristic
351Q8—21no—
352Q8—21no—
353Q8—1181no—
354Q8—1181no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—41no—
359D4—42no—
360D4—42no—
361D4—81no—
362D4—592no—
363D4—1181no—
364D4—1181no—
365D4—1181no—
366D4—4721no—
367D4—2362no—
368D4—2362no—
369D4D4×D5912yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—42no—
377C2×C4—81no—
378C2×C4—1181no—
379C2×C4—1181no—
380C2×C4—4721no—
381C2×C4—2362no—
382C2×C4C2×C22⋊D5911yescharacteristic
383C2×C4C2×C22⋊D5911yescharacteristic
384C2×C4C2×C22⋊D5911yescharacteristic
385C2×C4C2×C22⋊D5911yescharacteristic
386C2×C4C23×D5911yescharacteristic
387C8—592no—
388C8—1181no—
389C8—1181no—
390C8—1181no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—22no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—84no—
404C22—1182no—
405C22—4724no—
406C22—2361no—
407C22—2361no—
408C22—2361no—
409C22—2361no—
410C22—2361no—
411C22C22×C22⋊D5911yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—41no—
417C4—41no—
418C4—2361no—
419C4—2361no—
420C4C2×D4×D5911yescharacteristic
421C4#1427377211yescharacteristic
422C2—41no—
423C2—41no—
424C2—42no—
425C2—81no—
426C2—4721no—
427C2—2362no—
428C2D4×C22⋊D5911yescharacteristic
429C2#1683820011yescharacteristic
430C2#1683820511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#546C2
socleC22×C59C22×D4
hypercenter#546D59
hypocenterC59#3273
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C2×#14273753C2semidirect
2. C2×#14273752C2semidirect
3. #16838048C2semidirect
4. #16837784C2semidirect
5. #16837650C2semidirect
6. #16837646C2semidirect
7. #16837617C2semidirect
8. #16837614C2semidirect
9. #16837564C2semidirect
10. #16837562C2semidirect
11. #16837536C2semidirect
12. #16837535C2semidirect
13. C4×#11745669C2semidirect
14. #16837480C2semidirect
15. C59×#546C2semidirect
17. C22×D236C22semidirect
20. C2×#11745672C22semidirect
21. C2×#11745670C22semidirect
22. C2×#11745670C22semidirect
23. C2×#11745671C22semidirect
24. C2×#11745671C22semidirect
29. C2×#11745664C22semidirect
30. C2×#11745664C22semidirect
31. #14273715C22semidirect
33. #14273706C22semidirect
37. C4×D236C22semidirect
39. #14273660C22semidirect
40. C4⋊(C59⋊C8)C22semidirect
41. #14273651C22semidirect
42. #14273650C22semidirect
43. #14273648C22semidirect
44. #14273648C22semidirect
45. #14273647C22semidirect
46. #14273647C22semidirect
47. C22⋊(C59⋊C8)C22semidirect
48. C22⋊(C59⋊C8)C22semidirect
49. C4×C59⋊C8C22semidirect
51. C22×D4×C59C22semidirect
52. #124×C59C22semidirect
54. C22⋊Q8×C59C22semidirect
59. C4×D4×C59C22semidirect
110. #11745669D4semidirect
219. #546D59semidirect
231. C59#3273semidirect
235. C22×D4C2×D59semidirect
250. #124C2×D59semidirect
254. C22⋊Q8C2×D59semidirect
263. C4×D4C2×D59semidirect