Finite Group Databasebeta

← #28604901

Subgroups — #28604901

Order 15104.

1474 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838052C211yesmaximal, characteristic
2C2×(C22⋊D59)⋊C8C211yesmaximal, characteristic, complemented
3C4⋊C4×C22⋊D59C211yesmaximal, characteristic, complemented
4#21425055C211yesmaximal, characteristic, complemented
5#21425046C211yesmaximal, characteristic, complemented
6#21424525C211yesmaximal, characteristic, complemented
7#21424521C211yesmaximal, characteristic, complemented
8#21424410C211yesmaximal, characteristic, complemented
9#21424183C211yesmaximal, characteristic, complemented
10#21424181C211yesmaximal, characteristic, complemented
11#21424094C211yesmaximal, characteristic, complemented
12#102×Dic59C211yesmaximal, characteristic, complemented
13C2×#16837164C211yesmaximal, characteristic, complemented
14#340×D59C211yesmaximal, characteristic, complemented
15C59×#1874C211yesmaximal, characteristic, complemented
16C22×#11745687—21no—
17C23×C59⋊C8C2211yescharacteristic
18C22×C8×D59C2211yescharacteristic
19#16838052—24no—
20#16838052C418yescomplemented
21C2×#14273726C2211yescharacteristic
22C2×#14273709—21no—
23C2×#14273708—21no—
24C2×#14273704—21no—
25C2×#14273698C2211yescharacteristic
26C2×D4×Dic59C2211yescharacteristic
27C2×C4×C22⋊D59—21no—
28C2×C4×C22⋊D59C2211yescharacteristic
29C22×C4⋊Dic59C2211yescharacteristic
30C2×C4⋊C4×D59C2211yescharacteristic
31C2×C4⋊C4×D59C2211yescharacteristic
32(C22⋊D59)⋊C8—24no—
33C2×Dic59⋊C8C2211yescharacteristic
34C2×#14273648C2211yescharacteristic
35C2×#14273648C2211yescharacteristic
36C2×(C2×D59)⋊C8C2211yescharacteristic
37C2×C8×Dic59C2211yescharacteristic
38#16837297—21no—
39#16837275—21no—
40#16837273—21no—
41#16837271C2211yescharacteristic
42#16837262C2211yescharacteristic
43#16837259C2211yescharacteristic
44C4⋊C4×Dic59C2211yescharacteristic
45#16837165C2211yescharacteristic
46#16837165C2211yescharacteristic
47#16837165C2211yescharacteristic
48#16837165C2211yescharacteristic
49#16837164C2211yescharacteristic
50#16837164C2211yescharacteristic
51#16837164C2211yescharacteristic
52#16837164C2211yescharacteristic
53#16837164C2211yescharacteristic
54#16837164C2211yescharacteristic
55C2×#121×C59C2211yescharacteristic
56C22×C4⋊C4×C59C2211yescharacteristic
57C2×#102×C59C2211yescharacteristic
58C2×#102×C59C2211yescharacteristic
59C2×C22⋊C8×C59C2211yescharacteristic
60C59×#340C2211yescharacteristic
61C59×#340C2211yescharacteristic
62C2×#11745687—28no—
63C2×#11745687—44no—
64C2×#11745687—44no—
65C22×Dic118—21no—
66C22×C22⋊D59—21no—
67C22×C22⋊D59D411yescharacteristic
68C23×Dic59—21no—
69C23×Dic59—21no—
70C22×C4×D59—21no—
71C22×C4×D59—21no—
72C22×C4×D59C2311yescharacteristic
73C22×C59⋊C8—22no—
74C22×C59⋊C8—22no—
75C22×C59⋊C8—41no—
76C22×C59⋊C8C2311yescharacteristic
77C22×C59⋊C8C2311yescharacteristic
78C2×C8×D59—22no—
79C2×C8×D59—22no—
80C2×C8×D59—41no—
81#14273726—22no—
82#14273726C2×C414yescomplemented
83#14273709—28no—
84#14273708—28no—
85#14273704—28no—
86#14273698—22no—
87#14273698C2×C414yescomplemented
88D4×Dic59—22no—
89D4×Dic59C2×C414yescomplemented
90C4×C22⋊D59—44no—
91C4×C22⋊D59C2×C414yes—
92C4×C22⋊D59D414yes—
93C2×C4⋊Dic59—21no—
94C2×C4⋊Dic59—22no—
95C2×C4⋊Dic59C2×C414yescomplemented
96C2×C4⋊Dic59C2311yescharacteristic
97C2×C4⋊Dic59C2311yescharacteristic
98C2×C4⋊Dic59C2311yescharacteristic
99C2×C4⋊Dic59C2311yescharacteristic
100C2×Dic59⋊C4—21no—
101C2×Dic59⋊C4—21no—
102C2×Dic59⋊C4—21no—
103C2×Dic59⋊C4—21no—
104C2×Dic59⋊C4—21no—
105C2×Dic59⋊C4D411yescharacteristic
106C4⋊C4×D59—22no—
107C4⋊C4×D59—22no—
108C4⋊C4×D59—41no—
109C4⋊C4×D59C2×C414yescomplemented
110C2×C22⋊Dic59—21no—
111C2×C22⋊Dic59—21no—
112C2×C22⋊Dic59—21no—
113C2×C22⋊Dic59D411yescharacteristic
114C2×(C2×D59)⋊C4—21no—
115C2×(C2×D59)⋊C4D411yescharacteristic
116C2×C4×Dic59—21no—
117C2×C4×Dic59C2311yescharacteristic
118Dic59⋊C8—22no—
119#14273648—22no—
120#14273648—41no—
121(C2×D59)⋊C8—22no—
122C8×Dic59—22no—
123C59⋊#95—21no—
124C59⋊#95—21no—
125C59⋊#95—21no—
126C22×D4×C59—21no—
127C22×D4×C59C2311yescharacteristic
128C23×C4×C59—21no—
129C23×C4×C59C2311yescharacteristic
130C22×C8×C59C2311yescharacteristic
131C22×C8×C59C2311yescharacteristic
132#121×C59—22no—
133#121×C59C2×C414yescomplemented
134C2×C4⋊C4×C59—22no—
135C2×C4⋊C4×C59—21no—
136C2×C4⋊C4×C59—41no—
137C2×C4⋊C4×C59C2311yescharacteristic
138C2×C4⋊C4×C59C2311yescharacteristic
139C2×C4⋊C4×C59C2311yescharacteristic
140C2×C22⋊C4×C59—21no—
141#102×C59—22no—
142#102×C59—41no—
143C22⋊C8×C59—22no—
144C24×C59—21no—
145C24×C59C2×D411yescharacteristic
146C23×D59C2×D411yescharacteristic
147C2×D4×C59—24no—
148C2×D4×C59—21no—
149C2×D4×C59—21no—
150C2×D4×C59—21no—
151C2×D4×C59—21no—
152C2×D4×C59—21no—
153C2×D4×C59—42no—
154C2×D4×C59—42no—
155C2×D4×C59C22×C412yes—
156C22×C4×C59—21no—
157C22×C4×C59—21no—
158C22×C4×C59—21no—
159C22×C4×C59—21no—
160C22×C4×C59—21no—
161C22×C4×C59—21no—
162C22×C4×C59—21no—
163C22×C4×C59—42no—
164C22×C4×C59—42no—
165C22×C4×C59—81no—
166C22×C4×C59C22×C412yes—
167C22×C4×C59C2×D411yescharacteristic
168C22×C4×C59C2×D412yes—
169C22×C4×C59C2411yescharacteristic
170C2×C22⋊D59—24no—
171C2×C22⋊D59—42no—
172C2×C22⋊D59—42no—
173C2×C22⋊D59C22⋊C414yes—
174C2×C22⋊D59D814yes—
175C2×C22⋊D59SD1614yes—
176C22×Dic59—24no—
177C22×Dic59—21no—
178C22×Dic59—21no—
179C22×Dic59—24no—
180C22×Dic59—21no—
181C22×Dic59—21no—
182C22×Dic59—42no—
183C22×Dic59—42no—
184C22×Dic59—42no—
185C22×Dic59—42no—
186C22×Dic59C2×D411yescharacteristic
187C22×Dic59C2×D411yescharacteristic
188C22×Dic59C2×D411yescharacteristic
189#11745687—432no—
190C2×C4×D59—21no—
191C2×C4×D59—21no—
192C2×C4×D59—21no—
193C2×C4×D59—21no—
194C2×C4×D59—24no—
195C2×C4×D59—42no—
196C2×C4×D59—42no—
197C2×C4×D59—42no—
198C2×C4×D59—42no—
199C2×C4×D59—81no—
200C2×C4×D59C22×C412yes—
201C2×C4×D59C2×D412yes—
202C2×Dic118—24no—
203C2×Dic118—42no—
204C2×Dic118—42no—
205C2×C8×C59—21no—
206C2×C8×C59—21no—
207C2×C8×C59—21no—
208C2×C8×C59—21no—
209C2×C8×C59—21no—
210C2×C8×C59—21no—
211C4⋊C4×C59—21no—
212C4⋊C4×C59—21no—
213C4⋊C4×C59—21no—
214C4⋊C4×C59—21no—
215C4⋊C4×C59—42no—
216C4⋊C4×C59C22×C412yes—
217C4⋊C4×C59#4112yescomplemented
218C22⋊C4×C59—24no—
219C22⋊Dic59—24no—
220C22⋊Dic59—24no—
221C22⋊Dic59—42no—
222C22⋊Dic59C22⋊C414yes—
223(C2×D59)⋊C4—42no—
224(C2×D59)⋊C4C22⋊C414yes—
225C4⋊Dic59—24no—
226C4⋊Dic59—21no—
227C4⋊Dic59—21no—
228C4⋊Dic59—21no—
229C4⋊Dic59—21no—
230C4⋊Dic59—21no—
231C4⋊Dic59—21no—
232C4⋊Dic59C22×C412yes—
233C4⋊Dic59C22×C412yes—
234Dic59⋊C4—24no—
235Dic59⋊C4—24no—
236Dic59⋊C4—42no—
237Dic59⋊C4—42no—
238Dic59⋊C4—81no—
239Dic59⋊C4C22⋊C414yes—
240C4×Dic59—42no—
241C4×Dic59C22×C412yes—
242C4×Dic59C2×D412yes—
243C2×C59⋊C8—21no—
244C2×C59⋊C8—21no—
245C2×C59⋊C8—21no—
246C2×C59⋊C8—21no—
247C2×C59⋊C8—21no—
248C2×C59⋊C8—44no—
249C2×C59⋊C8#4112yescomplemented
250C8×D59—44no—
251C23×C59—21no—
252C23×C59—21no—
253C23×C59—21no—
254C23×C59—21no—
255C23×C59—22no—
256C23×C59—41no—
257C23×C59—41no—
258C23×C59—41no—
259C23×C59—41no—
260C23×C59—41no—
261C23×C59—41no—
262C23×C59C2×C22⋊C412yes—
263C23×C59C2×D812yes—
264C23×C59C2×SD1612yes—
265C23×C59C22×D411yescharacteristic
266C22×D59—21no—
267C22×D59—21no—
268C22×D59—21no—
269C22×D59—21no—
270C22×D59C2×C22⋊C412yes—
271C22×D59C2×D812yes—
272C22×D59C2×SD1612yes—
273D4×C59—22no—
274D4×C59—22no—
275D4×C59—48no—
276D4×C59—41no—
277D4×C59—41no—
278C2×C4×C59—21no—
279C2×C4×C59—21no—
280C2×C4×C59—22no—
281C2×C4×C59—22no—
282C2×C4×C59—22no—
283C2×C4×C59—22no—
284C2×C4×C59—22no—
285C2×C4×C59—22no—
286C2×C4×C59—41no—
287C2×C4×C59—41no—
288C2×C4×C59—41no—
289C2×C4×C59—41no—
290C2×C4×C59—41no—
291C2×C4×C59—41no—
292C2×C4×C59—41no—
293C2×C4×C59—84no—
294C2×C4×C59C2×C22⋊C412yes—
295C2×C4×C59C23×C411yescharacteristic
296C2×C4×C59C22×D411yescharacteristic
297C2×C4×C59C2×#4111yescharacteristic
298C2×C4×C59C2×#4111yescharacteristic
299C2×C4×C59H(5,𝔽2)11yescharacteristic
300C2×C4×C592−1+411yescharacteristic
301C22⋊D59—48no—
302C22⋊D59#102116yescomplemented
303C2×Dic59—21no—
304C2×Dic59—21no—
305C2×Dic59—21no—
306C2×Dic59—21no—
307C2×Dic59—22no—
308C2×Dic59—22no—
309C2×Dic59—41no—
310C2×Dic59—41no—
311C2×Dic59—41no—
312C2×Dic59—41no—
313C2×Dic59—48no—
314C2×Dic59—48no—
315C2×Dic59—41no—
316C2×Dic59—41no—
317C2×Dic59—41no—
318C2×Dic59—41no—
319C2×Dic59—41no—
320C2×Dic59—41no—
321C2×Dic59C2×C22⋊C412yes—
322C2×Dic59C2×C22⋊C412yes—
323C2×Dic59C2×C22⋊C412yes—
324C2×Dic59C2×D812yes—
325C2×Dic59C2×SD1612yes—
326C4×D59—22no—
327C4×D59—22no—
328C4×D59—22no—
329C4×D59—22no—
330C4×D59—48no—
331C4×D59—84no—
332Dic118—48no—
333C8×C59—41no—
334C8×C59—41no—
335C59⋊C8—22no—
336C59⋊C8—41no—
337#22485—591nomaximal, Sylow
338C22×C59—22no—
339C22×C59—22no—
340C22×C59—22no—
341C22×C59—22no—
342C22×C59—22no—
343C22×C59—22no—
344C22×C59—42no—
345C22×C59—42no—
346C22×C59—42no—
347C22×C59—81no—
348C22×C59—81no—
349C22×C59—81no—
350C22×C59—81no—
351C22×C59C2×#10214yes—
352C22×C59C22×C22⋊C411yescharacteristic
353C22×C59#54611yescharacteristic
354C22×C59#54711yescharacteristic
355C22×C59C22×D811yescharacteristic
356C22×C59C22×SD1611yescharacteristic
357C22×C59#57711yescharacteristic
358C22×C59#57811yescharacteristic
359C2×D59—22no—
360C2×D59—22no—
361C2×D59—22no—
362C2×D59—22no—
363C2×D59—22no—
364C2×D59—22no—
365C2×D59C2×#10214yes—
366C4×C59—22no—
367C4×C59—42no—
368C4×C59—42no—
369C4×C59—81no—
370C4×C59C4×#4111yescharacteristic
371C4×C59#52011yescharacteristic
372C4×C59#54611yescharacteristic
373C4×C59#54711yescharacteristic
374Dic59—22no—
375Dic59—22no—
376Dic59—42no—
377Dic59—42no—
378Dic59—81no—
379Dic59—81no—
380Dic59C2×#10214yes—
381C2×#547—591no—
382C2×C8×D4—591no—
383D4×C4⋊C4—591no—
384#1990—591no—
385#1988—591no—
386#1893—591no—
387#1893—591no—
388#1874—591no—
389#1874D5911yescharacteristic, complemented
390#1823—591no—
391#1823—591no—
392#1802—591no—
393C4×#102—591no—
394C2×#340—591no—
395C2×#340—591no—
396C2×C59—24no—
397C2×C59—82no—
398C2×C59#233911yescharacteristic
399C2×C59C22×#10211yescharacteristic
400C2×C59#289811yescharacteristic
401C2×C59#329411yescharacteristic
402C2×C59#329811yescharacteristic
403C2×C59#333411yescharacteristic
404C2×C59#333511yescharacteristic
405D59—24no—
406C22×#41—1181no—
407C23×C8—591no—
408C23×C8—591no—
409#547—598no—
410#547—1184no—
411C2×C4⋊Q8—591no—
412C2×#123—1181no—
413C2×#123—1181no—
414C2×C22⋊Q8—1181no—
415C2×#121—591no—
416C2×#121C2×D5911yescharacteristic
417C2×C4×D4—591no—
418C2×C4×D4—591no—
419C2×C4×D4—1181no—
420C22×C4⋊C4—591no—
421C22×C4⋊C4—591no—
422C22×C4⋊C4—591no—
423C22×C4⋊C4C2×D5911yescharacteristic
424C8×D4—1184no—
425C2×C4⋊C8—591no—
426C2×#102—591no—
427C2×#102—591no—
428C2×#102C2×D5911yescharacteristic
429C2×#102C2×D5911yescharacteristic
430C2×C22⋊C8—591no—
431C2×C22⋊C8C2×D5911yescharacteristic
432C2×C4×C8—591no—
433#389—1181no—
434#385—1181no—
435#385—1181no—
436#384—591no—
437#380—591no—
438#380—591no—
439C4×C4⋊C4—591no—
440#340—591no—
441#340—591no—
442#340—591no—
443#340—591no—
444#340—591no—
445#340—591no—
446#340—591no—
447#340—591no—
448#340—591no—
449#340—591no—
450#340C2×D5911yescharacteristic
451#340C2×D5911yescharacteristic
452C59#2248511yescharacteristic, complemented, Sylow
453C2×#41—1188no—
454C2×#41—2364no—
455C2×#41—2364no—
456C22×Q8—1181no—
457C22×D4—21no—
458C22×D4—591no—
459C22×D4—1181no—
460C22×D4C22×D5911yescharacteristic
461C23×C4—21no—
462C23×C4—591no—
463C23×C4—1181no—
464C23×C4—1181no—
465C23×C4—1181no—
466C23×C4—1181no—
467C23×C4C22×D5911yescharacteristic
468C22×C8—591no—
469C22×C8—591no—
470C22×C8—1182no—
471C22×C8—1182no—
472C22×C8—1182no—
473C22×C8—1182no—
474C22×C8—2361no—
475C22×C8—2361no—
476C22×C8C22×D5911yescharacteristic
477C22×C8C22×D5911yescharacteristic
478C4⋊Q8—594no—
479C4⋊Q8—1182no—
480#123—1188no—
481#123—1188no—
482C22⋊Q8—1188no—
483#121—22no—
484#121—594no—
485#121—1182no—
486#121C4×D5914yescomplemented
487C4×D4—594no—
488C4×D4—594no—
489C4×D4—594no—
490C4×D4—1182no—
491C4×D4—2364no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—41no—
495C2×C4⋊C4—591no—
496C2×C4⋊C4—594no—
497C2×C4⋊C4—591no—
498C2×C4⋊C4—591no—
499C2×C4⋊C4—594no—
500C2×C4⋊C4—591no—
501C2×C4⋊C4—591no—
502C2×C4⋊C4—1182no—
503C2×C4⋊C4—1181no—
504C2×C4⋊C4—1181no—
505C2×C4⋊C4—1181no—
506C2×C4⋊C4—1182no—
507C2×C4⋊C4—1182no—
508C2×C4⋊C4—1181no—
509C2×C4⋊C4—1181no—
510C2×C4⋊C4—1181no—
511C2×C4⋊C4—2361no—
512C2×C4⋊C4C22×D5911yescharacteristic
513C2×C4⋊C4C22×D5911yescharacteristic
514C2×C4⋊C4C22×D5911yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—591no—
517C2×C22⋊C4—591no—
518C2×C22⋊C4—1181no—
519C2×C22⋊C4—1181no—
520C2×C22⋊C4—1181no—
521C2×C22⋊C4—1181no—
522C2×C42—591no—
523C2×C42—1181no—
524C4⋊C8—1182no—
525#102—22no—
526#102—41no—
527#102—1182no—
528#102—2361no—
529C22⋊C8—22no—
530C22⋊C8—1182no—
531C4×C8—1182no—
532#95—1181no—
533#95—1181no—
534#95—1181no—
535C24—21no—
536C24—591no—
537C24D4×D5911yescharacteristic
538#41—23632no—
539C2×Q8—1184no—
540C2×Q8—2362no—
541C2×Q8—2362no—
542C2×D4—24no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4—594no—
551C2×D4—594no—
552C2×D4—594no—
553C2×D4—1184no—
554C2×D4—2362no—
555C2×D4—2362no—
556C2×D4C2×C4×D5912yes—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—81no—
567C22×C4—591no—
568C22×C4—591no—
569C22×C4—591no—
570C22×C4—592no—
571C22×C4—592no—
572C22×C4—1184no—
573C22×C4—1184no—
574C22×C4—1181no—
575C22×C4—1181no—
576C22×C4—1181no—
577C22×C4—1181no—
578C22×C4—1184no—
579C22×C4—1181no—
580C22×C4—1181no—
581C22×C4—1181no—
582C22×C4—1181no—
583C22×C4—4721no—
584C22×C4—2362no—
585C22×C4—2362no—
586C22×C4—2362no—
587C22×C4—2362no—
588C22×C4—2362no—
589C22×C4—2362no—
590C22×C4—2362no—
591C22×C4—2362no—
592C22×C4C2×C4×D5912yes—
593C22×C4D4×D5911yescharacteristic
594C22×C4D4×D5912yes—
595C22×C4C23×D5911yescharacteristic
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—592no—
603C2×C8—1181no—
604C2×C8—1181no—
605C2×C8—1181no—
606C2×C8—1181no—
607C2×C8—1181no—
608C2×C8—2364no—
609C2×C8—2364no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—42no—
615C4⋊C4—594no—
616C4⋊C4—592no—
617C4⋊C4—592no—
618C4⋊C4—1184no—
619C4⋊C4—1184no—
620C4⋊C4—1184no—
621C4⋊C4—1181no—
622C4⋊C4—1181no—
623C4⋊C4—1181no—
624C4⋊C4—1181no—
625C4⋊C4—1181no—
626C4⋊C4—1181no—
627C4⋊C4—4721no—
628C4⋊C4—2362no—
629C4⋊C4—2362no—
630C4⋊C4C2×C4×D5912yes—
631C4⋊C4#1174568712yescomplemented
632C22⋊C4—24no—
633C22⋊C4—594no—
634C22⋊C4—594no—
635C22⋊C4—1184no—
636C22⋊C4—1184no—
637C22⋊C4—2362no—
638C22⋊C4—2362no—
639C42—592no—
640C42—592no—
641C42—2362no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—22no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—592no—
654C23—592no—
655C23—592no—
656C23—1181no—
657C23—1181no—
658C23—1181no—
659C23—1181no—
660C23C22⋊C4×D5912yes—
661C23D8×D5912yes—
662C23SD16×D5912yes—
663C23C2×D4×D5911yescharacteristic
664Q8—2368no—
665D4—22no—
666D4—22no—
667D4—48no—
668D4—41no—
669D4—41no—
670D4—5916no—
671D4—2368no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—84no—
688C2×C4—592no—
689C2×C4—592no—
690C2×C4—592no—
691C2×C4—592no—
692C2×C4—592no—
693C2×C4—1181no—
694C2×C4—1181no—
695C2×C4—1181no—
696C2×C4—1181no—
697C2×C4—1182no—
698C2×C4—1182no—
699C2×C4—1182no—
700C2×C4—1182no—
701C2×C4—1182no—
702C2×C4—1182no—
703C2×C4—4724no—
704C2×C4—2368no—
705C2×C4—2368no—
706C2×C4—2361no—
707C2×C4—2361no—
708C2×C4—2361no—
709C2×C4—2361no—
710C2×C4—2361no—
711C2×C4—2361no—
712C2×C4—2368no—
713C2×C4—2361no—
714C2×C4—2361no—
715C2×C4—2361no—
716C2×C4—2361no—
717C2×C4C22⋊C4×D5912yes—
718C2×C4C22×C4×D5911yescharacteristic
719C2×C4C2×D4×D5911yescharacteristic
720C2×C4#41×D5911yescharacteristic
721C2×C4C2×#1174568711yescharacteristic
722C2×C4#1427377211yescharacteristic
723C2×C4#1427377411yescharacteristic
724C8—41no—
725C8—41no—
726C8—1182no—
727C8—2361no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—594no—
742C22—1182no—
743C22—1182no—
744C22—1182no—
745C22—1182no—
746C22—1182no—
747C22—1182no—
748C22#102×D5914yes—
749C22C2×C22⋊C4×D5911yescharacteristic
750C22#1683803911yescharacteristic
751C22#1683805011yescharacteristic
752C22C2×D8×D5911yescharacteristic
753C22C2×SD16×D5911yescharacteristic
754C22#1683821211yescharacteristic
755C22#1683821811yescharacteristic
756C4—22no—
757C4—42no—
758C4—42no—
759C4—81no—
760C4—594no—
761C4—1182no—
762C4—1182no—
763C4—4721no—
764C4—4721no—
765C4—2362no—
766C4—2362no—
767C4C4×#1174568711yescharacteristic
768C4#1683788111yescharacteristic
769C4#1683804111yescharacteristic
770C4#1683805211yescharacteristic
771C2—24no—
772C2—82no—
773C2—1184no—
774C2#2142692211yescharacteristic
775C2C2×#102×D5911yescharacteristic
776C2#2143262711yescharacteristic
777C2#2143590211yescharacteristic
778C2#2143595411yescharacteristic
779C2#2143643811yescharacteristic
780C2#2143645111yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#1874C2
socleC23×C59C22×D4
prime radicalC2×#16838052C2
cosocleC22×C4×C59C24
hypercenter#1874D59
hypocenterC59#22485
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
2. C2×(C22⋊D59)⋊C8C2semidirect
3. C4⋊C4×C22⋊D59C2semidirect
4. #21425055C2semidirect
5. #21425046C2semidirect
6. #21424525C2semidirect
7. #21424521C2semidirect
8. #21424410C2semidirect
9. #21424183C2semidirect
10. #21424181C2semidirect
11. #21424094C2semidirect
12. #102×Dic59C2semidirect
13. C2×#16837164C2semidirect
14. #340×D59C2semidirect
15. C59×#1874C2semidirect
20. #16838052C4semidirect
82. #14273726C2×C4semidirect
87. #14273698C2×C4semidirect
89. D4×Dic59C2×C4semidirect
95. C2×C4⋊Dic59C2×C4semidirect
109. C4⋊C4×D59C2×C4semidirect
133. #121×C59C2×C4semidirect
217. C4⋊C4×C59#41semidirect
249. C2×C59⋊C8#41semidirect
302. C22⋊D59#102semidirect
389. #1874D59semidirect
452. C59#22485semidirect
486. #121C4×D59semidirect
631. C4⋊C4#11745687semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168380522
C2×(C22⋊D59)⋊C82
C4⋊C4×C22⋊D592
#214250552
#214250462
#214245252
#214245212
#214244102
#214241832
#214241812
#214240942
#102×Dic592
C2×#168371642
#340×D592
C59×#18742
#2248559