Finite Group Databasebeta

← #28608987

Subgroups — #28608987

Order 15104.

1146 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837547C211yesmaximal, characteristic
2C2×#16837500C211yesmaximal, characteristic, complemented
3C2×#16837398C211yesmaximal, characteristic, complemented
4#21427132C211yesmaximal, characteristic, complemented
5#21424971C211yesmaximal, characteristic, complemented
6#21424796C211yesmaximal, characteristic, complemented
7#21424713C211yesmaximal, characteristic, complemented
8#21424522C211yesmaximal, characteristic, complemented
9#21424451C211yesmaximal, characteristic, complemented
10#21424447C211yesmaximal, characteristic, complemented
11#21424364C211yesmaximal, characteristic, complemented
12#21424293C211yesmaximal, characteristic, complemented
13#21423926C211yesmaximal, characteristic, complemented
14#21423874C211yesmaximal, characteristic, complemented
15C59×#2341C211yesmaximal, characteristic, complemented
16C22×#11745671C2211yescharacteristic
17C22×#11745669C2211yescharacteristic
18C23×C59⋊C8C2211yescharacteristic
19C2×#14273701C2211yescharacteristic
20C2×C4×D236C2211yescharacteristic
21C2×#14273686C2211yescharacteristic
22#16837547C418yescomplemented
23#16837500—24no—
24C2×#14273660C2211yescharacteristic
25C2×#14273658C2211yescharacteristic
26#16837398—24no—
27C2×#14273651C2211yescharacteristic
28C2×#14273651C2211yescharacteristic
29C2×#14273651C2211yescharacteristic
30C2×#14273648C2211yescharacteristic
31C2×#14273648C2211yescharacteristic
32C2×#14273648C2211yescharacteristic
33C2×#14273647C2211yescharacteristic
34C2×#14273647C2211yescharacteristic
35C2×C22⋊(C59⋊C8)C2211yescharacteristic
36C2×#14273638C2211yescharacteristic
37C2×#14273638C2211yescharacteristic
38#16837304C2211yescharacteristic
39#16837302—21no—
40#16837300C2211yescharacteristic
41#16837291—21no—
42#16837278—21no—
43C4×C4⋊Dic59C2211yescharacteristic
44#16837249—21no—
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837157C2211yescharacteristic
50#16837157C2211yescharacteristic
51C22×#41×C59C2211yescharacteristic
52C2×C4×Q8×C59C2211yescharacteristic
53C2×C4×Q8×C59C2211yescharacteristic
54C59×#390—21no—
55C59×#390—21no—
56C59×#390C2211yescharacteristic
57C59×#390C2211yescharacteristic
58C59×#380—21no—
59C59×#380C2211yescharacteristic
60C4×C22⋊C4×C59—21no—
61C4×C22⋊C4×C59C2211yescharacteristic
62C22×D236C2311yescharacteristic
63C22×C22⋊D59—21no—
64C22×C4×D59—21no—
65C2×#11745671—22no—
66C2×#11745671—22no—
67C2×#11745671C2×C414yes—
68C2×#11745669—41no—
69C2×#11745669—41no—
70C2×#11745669C2×C414yes—
71C22×C59⋊C8—22no—
72C22×C59⋊C8—22no—
73C22×C59⋊C8—41no—
74C22×C59⋊C8C2311yescharacteristic
75C22×C59⋊C8C2311yescharacteristic
76C22×C59⋊C8C2311yescharacteristic
77C22×C59⋊C8C2311yescharacteristic
78#14273701—22no—
79#14273701C2×C414yes—
80C4×D236—22no—
81C4×D236—41no—
82#14273686—22no—
83#14273686—41no—
84C2×C4⋊Dic59C2311yescharacteristic
85C2×C4⋊Dic59C2311yescharacteristic
86C2×C4⋊Dic59C2311yescharacteristic
87C2×Dic59⋊C4—21no—
88C2×C22⋊Dic59—21no—
89C2×(C2×D59)⋊C4—21no—
90C2×(C2×D59)⋊C4—21no—
91C2×(C2×D59)⋊C4—21no—
92C2×(C2×D59)⋊C4—21no—
93C2×C4×Dic59—21no—
94C2×C4×Dic59—21no—
95#14273660—22no—
96#14273658—41no—
97#14273651—22no—
98#14273651C2×C414yescomplemented
99#14273651D414yescomplemented
100#14273648—22no—
101#14273648—22no—
102#14273648C2×C414yescomplemented
103#14273647—22no—
104#14273647—41no—
105C22⋊(C59⋊C8)C2×C414yescomplemented
106#14273638—22no—
107#14273638—41no—
108C59⋊#95—21no—
109C59⋊#95—21no—
110C2×#41×C59—22no—
111C2×#41×C59—22no—
112C2×#41×C59—22no—
113C2×#41×C59—41no—
114C2×#41×C59—41no—
115C2×#41×C59C2×C414yescomplemented
116C22×Q8×C59C2311yescharacteristic
117C22×D4×C59—21no—
118C22×D4×C59C2311yescharacteristic
119C23×C4×C59—21no—
120C23×C4×C59C2311yescharacteristic
121C4×Q8×C59—22no—
122C4×Q8×C59—22no—
123C4×Q8×C59—41no—
124C4×Q8×C59—41no—
125C2×C4⋊C4×C59—21no—
126C2×C4⋊C4×C59—21no—
127C2×C4⋊C4×C59C2311yescharacteristic
128C2×C4⋊C4×C59C2311yescharacteristic
129C2×C22⋊C4×C59—21no—
130C2×C22⋊C4×C59—21no—
131C2×C22⋊C4×C59—21no—
132C2×C22⋊C4×C59—21no—
133C2×C22⋊C4×C59—21no—
134C2×C22⋊C4×C59D411yescharacteristic
135C2×C22⋊C4×C59D411yescharacteristic
136C2×C42×C59—21no—
137C2×C42×C59—21no—
138C2×C42×C59C2311yescharacteristic
139C2×C42×C59C2311yescharacteristic
140#95×C59—21no—
141#95×C59D411yescharacteristic
142#95×C59D411yescharacteristic
143C24×C59—21no—
144C24×C59C2×D411yescharacteristic
145C23×D59—21no—
146#41×C59—28no—
147#41×C59—44no—
148#41×C59—44no—
149#41×C59—44no—
150C2×Q8×C59—21no—
151C2×Q8×C59—21no—
152C2×Q8×C59—21no—
153C2×Q8×C59C22×C412yes—
154C2×Q8×C59C2×D412yes—
155C2×Q8×C59#4112yes—
156C2×D4×C59—24no—
157C2×D4×C59—21no—
158C2×D4×C59—21no—
159C2×D4×C59—21no—
160C2×D4×C59—21no—
161C2×D4×C59—21no—
162C2×D4×C59—42no—
163C2×D4×C59—42no—
164C2×D4×C59C22×C412yes—
165C22×C4×C59—21no—
166C22×C4×C59—21no—
167C22×C4×C59—21no—
168C22×C4×C59—21no—
169C22×C4×C59—21no—
170C22×C4×C59—24no—
171C22×C4×C59—21no—
172C22×C4×C59—21no—
173C22×C4×C59—42no—
174C22×C4×C59—42no—
175C22×C4×C59C22×C412yes—
176C22×C4×C59C2×D411yescharacteristic
177C22×C4×C59C2×D411yescharacteristic
178C22×C4×C59C2×D411yescharacteristic
179C22×C4×C59C2×D411yescharacteristic
180C22×C4×C59C2×D411yescharacteristic
181C22×C4×C59#4112yes—
182C22×C4×C59C2411yescharacteristic
183C2×C22⋊D59—24no—
184C2×C22⋊D59—81no—
185C2×C22⋊D59—81no—
186C22×Dic59—21no—
187C22×Dic59—21no—
188C22×Dic59—21no—
189C2×D236—21no—
190C2×D236—21no—
191C2×D236—21no—
192C2×D236—21no—
193C2×D236—21no—
194C2×D236C22×C412yes—
195C2×C4×D59—42no—
196C2×C4×D59—42no—
197C2×C4×D59—81no—
198C4⋊C4×C59—21no—
199C4⋊C4×C59—21no—
200C4⋊C4×C59—21no—
201C4⋊C4×C59—21no—
202C4⋊C4×C59—42no—
203C4⋊C4×C59—42no—
204C22⋊C4×C59—41no—
205C22⋊C4×C59—41no—
206C22⋊C4×C59—42no—
207C22⋊C4×C59—42no—
208C22⋊C4×C59—81no—
209C22⋊C4×C59—81no—
210C22⋊C4×C59—81no—
211C42×C59—21no—
212C42×C59—21no—
213C42×C59—21no—
214C42×C59—21no—
215C42×C59—42no—
216C42×C59—42no—
217C22⋊Dic59—42no—
218#11745671—28no—
219#11745669—44no—
220(C2×D59)⋊C4—24no—
221(C2×D59)⋊C4—42no—
222(C2×D59)⋊C4—42no—
223(C2×D59)⋊C4—81no—
224C4⋊Dic59—21no—
225C4⋊Dic59—21no—
226C4⋊Dic59—21no—
227C4⋊Dic59—21no—
228C4⋊Dic59C22×C412yes—
229C4⋊Dic59C2×D412yes—
230Dic59⋊C4—81no—
231C4×Dic59—42no—
232C4×Dic59—81no—
233C2×C59⋊C8—21no—
234C2×C59⋊C8—21no—
235C2×C59⋊C8—21no—
236C2×C59⋊C8—21no—
237C2×C59⋊C8—21no—
238C2×C59⋊C8—21no—
239C2×C59⋊C8—21no—
240C2×C59⋊C8—21no—
241C2×C59⋊C8—21no—
242C2×C59⋊C8—44no—
243C2×C59⋊C8C22×C412yes—
244C2×C59⋊C8C22×C412yes—
245C2×C59⋊C8C2×D412yes—
246C23×C59—21no—
247C23×C59—21no—
248C23×C59—21no—
249C23×C59—21no—
250C23×C59—21no—
251C23×C59—21no—
252C23×C59—22no—
253C23×C59—41no—
254C23×C59—41no—
255C23×C59—41no—
256C23×C59—41no—
257C23×C59—41no—
258C23×C59—41no—
259C23×C59C4×D412yes—
260C23×C59C22×D411yescharacteristic
261C22×D59—22no—
262C22×D59—41no—
263C22×D59—41no—
264C22×D59—41no—
265C22×D59—41no—
266C22×D59—41no—
267C22×D59—41no—
268Q8×C59—22no—
269Q8×C59—22no—
270Q8×C59—22no—
271Q8×C59C4×D414yes—
272D4×C59—22no—
273D4×C59—22no—
274D4×C59—48no—
275D4×C59—41no—
276D4×C59—41no—
277C2×C4×C59—22no—
278C2×C4×C59—21no—
279C2×C4×C59—22no—
280C2×C4×C59—22no—
281C2×C4×C59—21no—
282C2×C4×C59—22no—
283C2×C4×C59—22no—
284C2×C4×C59—22no—
285C2×C4×C59—22no—
286C2×C4×C59—21no—
287C2×C4×C59—21no—
288C2×C4×C59—21no—
289C2×C4×C59—21no—
290C2×C4×C59—21no—
291C2×C4×C59—21no—
292C2×C4×C59—21no—
293C2×C4×C59—21no—
294C2×C4×C59—21no—
295C2×C4×C59—21no—
296C2×C4×C59—21no—
297C2×C4×C59—21no—
298C2×C4×C59—48no—
299C2×C4×C59—41no—
300C2×C4×C59—41no—
301C2×C4×C59—41no—
302C2×C4×C59—41no—
303C2×C4×C59—41no—
304C2×C4×C59—41no—
305C2×C4×C59C4×D412yes—
306C2×C4×C59C23×C411yescharacteristic
307C2×C4×C59C22×D411yescharacteristic
308C2×C4×C59C2×#4111yescharacteristic
309C2×C4×C59C2×#4111yescharacteristic
310C2×C4×C59H(5,𝔽2)11yescharacteristic
311C2×C4×C59H(5,𝔽2)11yescharacteristic
312C22⋊D59—84no—
313C2×Dic59—22no—
314C2×Dic59—22no—
315C2×Dic59—41no—
316C2×Dic59—41no—
317C2×Dic59—41no—
318C2×Dic59—41no—
319C2×Dic59—41no—
320C2×Dic59—41no—
321C2×Dic59—41no—
322D236—22no—
323D236—22no—
324D236—41no—
325D236—41no—
326C4×D59—84no—
327C59⋊C8—22no—
328C59⋊C8—22no—
329C59⋊C8—22no—
330C59⋊C8—41no—
331#22857—591nomaximal, Sylow
332C22×C59—22no—
333C22×C59—22no—
334C22×C59—22no—
335C22×C59—41no—
336C22×C59—41no—
337C22×C59—41no—
338C22×C59—41no—
339C22×C59—42no—
340C22×C59—42no—
341C22×C59—42no—
342C22×C59—81no—
343C22×C59—81no—
344C22×C59—81no—
345C22×C59—81no—
346C22×C59C2×C4×D411yescharacteristic
347C22×C59D4211yescharacteristic
348C22×C59#54611yescharacteristic
349C22×C59#57511yescharacteristic
350C22×C59#57511yescharacteristic
351C22×C59#57611yescharacteristic
352C22×C59#57711yescharacteristic
353C2×D59—42no—
354C2×D59—42no—
355C2×D59—42no—
356C2×D59—81no—
357C2×D59—81no—
358C2×D59—81no—
359C2×D59—81no—
360C4×C59—22no—
361C4×C59—24no—
362C4×C59—41no—
363C4×C59—41no—
364C4×C59—41no—
365C4×C59—41no—
366C4×C59—81no—
367C4×C59—81no—
368C4×C59C2×C4×D411yescharacteristic
369C4×C59#51811yescharacteristic
370C4×C59#54611yescharacteristic
371C4×C59#55111yescharacteristic
372Dic59—42no—
373Dic59—42no—
374Dic59—81no—
375C2×#449—591no—
376C2×#440—591no—
377C2×#416—591no—
378#2363—591no—
379#2341D5911yescharacteristic, complemented
380#1972—591no—
381#1936—591no—
382#1925—591no—
383#1893—591no—
384#1880—591no—
385#1879—591no—
386#1865—591no—
387#1854—591no—
388#1763—591no—
389#1752—591no—
390C2×C59—42no—
391C2×C59—82no—
392C2×C59#235811yescharacteristic
393C2×C59#294311yescharacteristic
394C2×C59#294611yescharacteristic
395C2×C59#326811yescharacteristic
396C2×C59#327111yescharacteristic
397C2×C59#330911yescharacteristic
398C2×C59#332111yescharacteristic
399D59—82no—
400C22×#41C2×D5911yescharacteristic
401C22×SD16—591no—
402C22×D8—591no—
403C23×C8—591no—
404C2×#121—591no—
405C2×C4×Q8C2×D5911yescharacteristic
406C2×C4×Q8C2×D5911yescharacteristic
407C2×C4×D4—591no—
408C2×#117—591no—
409#449—598no—
410#440—1184no—
411C2×#107—591no—
412C2×#106—591no—
413#416—1184no—
414C2×#103—591no—
415C2×#103—591no—
416C2×#103—591no—
417C2×#102—591no—
418C2×#102—591no—
419C2×#102—591no—
420C2×#102—591no—
421C2×#102—591no—
422C2×C22⋊C8—591no—
423C2×#97—591no—
424C2×#97—591no—
425#390—21no—
426#390—21no—
427#390—591no—
428#390—1181no—
429#390C2×D5911yescharacteristic
430#390C2×D5911yescharacteristic
431#389—591no—
432#388—1181no—
433#386—1181no—
434#380—21no—
435#380C2×D5911yescharacteristic
436C4×C4⋊C4—591no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4—1181no—
439C4×C22⋊C4C2×D5911yescharacteristic
440#340—591no—
441#340—591no—
442#340—591no—
443#340—591no—
444#336—591no—
445#336—591no—
446C59#2285711yescharacteristic, complemented, Sylow
447C2×#41—22no—
448C2×#41—22no—
449C2×#41—22no—
450C2×#41—41no—
451C2×#41—41no—
452C2×#41C4×D5914yescomplemented
453C22×Q8C22×D5911yescharacteristic
454C22×D4—21no—
455C22×D4—591no—
456C22×D4—1181no—
457C22×D4C22×D5911yescharacteristic
458C23×C4—21no—
459C23×C4—1181no—
460C23×C4C22×D5911yescharacteristic
461C2×SD16—594no—
462C2×SD16—1182no—
463C2×SD16—1182no—
464C2×D8—594no—
465C2×D8—2361no—
466C2×D8—2361no—
467C22×C8—591no—
468C22×C8—591no—
469C22×C8—591no—
470C22×C8—591no—
471C22×C8—1182no—
472C22×C8—1182no—
473C22×C8—2361no—
474#121—594no—
475#121—1182no—
476C4×Q8—22no—
477C4×Q8—22no—
478C4×Q8—41no—
479C4×Q8—41no—
480C4×D4—1182no—
481C4×D4—2361no—
482#117—1182no—
483#117—2361no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—591no—
487C2×C4⋊C4—591no—
488C2×C4⋊C4—591no—
489C2×C4⋊C4—1181no—
490C2×C4⋊C4C22×D5911yescharacteristic
491C2×C4⋊C4C22×D5911yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—1181no—
498C2×C22⋊C4—1181no—
499C2×C22⋊C4—1181no—
500C2×C22⋊C4—1181no—
501C2×C22⋊C4—1181no—
502C2×C22⋊C4C22⋊D5911yescharacteristic
503C2×C22⋊C4C22⋊D5911yescharacteristic
504C2×C42—21no—
505C2×C42—21no—
506C2×C42—1181no—
507C2×C42—1181no—
508C2×C42C22×D5911yescharacteristic
509C2×C42C22×D5911yescharacteristic
510#107—1182no—
511#106—2361no—
512#103—594no—
513#103—594no—
514#103—1182no—
515#102—594no—
516#102—1182no—
517#102—1182no—
518#102—1182no—
519#102—2361no—
520C22⋊C8—594no—
521#97—1182no—
522#97—2361no—
523#95—21no—
524#95—1181no—
525#95—1181no—
526#95C22⋊D5911yescharacteristic
527#95C22⋊D5911yescharacteristic
528C24—21no—
529C24—1181no—
530C24C2×C22⋊D5911yescharacteristic
531#41—28no—
532#41—44no—
533#41—44no—
534#41—44no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8C2×C4×D5912yes—
539C2×Q8D4×D5912yes—
540C2×Q8#1174568712yes—
541C2×D4—24no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—592no—
550C2×D4—1184no—
551C2×D4—1181no—
552C2×D4—1181no—
553C2×D4—1181no—
554C2×D4—1181no—
555C2×D4—1181no—
556C2×D4—4721no—
557C2×D4—4721no—
558C2×D4C2×C4×D5912yes—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—24no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—1181no—
570C22×C4—1181no—
571C22×C4—1181no—
572C22×C4—4721no—
573C22×C4—2362no—
574C22×C4—2362no—
575C22×C4C2×C4×D5912yes—
576C22×C4#1174568512yes—
577C22×C4C2×C22⋊D5911yescharacteristic
578C22×C4C2×C22⋊D5911yescharacteristic
579C22×C4C2×C22⋊D5911yescharacteristic
580C22×C4C2×C22⋊D5911yescharacteristic
581C22×C4C2×C22⋊D5911yescharacteristic
582C22×C4C23×D5911yescharacteristic
583SD16—1188no—
584D8—2364no—
585C2×C8—592no—
586C2×C8—592no—
587C2×C8—592no—
588C2×C8—1181no—
589C2×C8—1181no—
590C2×C8—1181no—
591C2×C8—1181no—
592C2×C8—1181no—
593C2×C8—1181no—
594C2×C8—1181no—
595C2×C8—1181no—
596C2×C8—1181no—
597C2×C8—2364no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4—592no—
605C4⋊C4—592no—
606C4⋊C4—1181no—
607C4⋊C4—1181no—
608C4⋊C4—1181no—
609C4⋊C4—1181no—
610C4⋊C4—4721no—
611C22⋊C4—41no—
612C22⋊C4—41no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—81no—
616C22⋊C4—81no—
617C22⋊C4—81no—
618C22⋊C4—1184no—
619C22⋊C4—4721no—
620C22⋊C4—2362no—
621C22⋊C4—2362no—
622C22⋊C4—2362no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—42no—
628C42—42no—
629C42—4721no—
630C42—2362no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—22no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—1182no—
645C23—2361no—
646C23—2361no—
647C23—2361no—
648C23—2361no—
649C23—2361no—
650C23—2361no—
651C23C4×C22⋊D5912yes—
652C23C22×C22⋊D5911yescharacteristic
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8(C22⋊D59)⋊C414yes—
657D4—22no—
658D4—22no—
659D4—48no—
660D4—41no—
661D4—41no—
662D4—1182no—
663D4—1182no—
664D4—4724no—
665D4—2361no—
666D4—2361no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—48no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—1182no—
696C2×C4—1182no—
697C2×C4—4724no—
698C2×C4—2361no—
699C2×C4—2361no—
700C2×C4—2361no—
701C2×C4—2361no—
702C2×C4—2361no—
703C2×C4—2361no—
704C2×C4—2361no—
705C2×C4C4×C22⋊D5912yes—
706C2×C4C22×C4×D5911yescharacteristic
707C2×C4C2×D4×D5911yescharacteristic
708C2×C4C2×#1174568711yescharacteristic
709C2×C4C2×#1174568511yescharacteristic
710C2×C4#1427377211yescharacteristic
711C2×C4#1427377211yescharacteristic
712C8—1182no—
713C8—1182no—
714C8—1182no—
715C8—2361no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—4721no—
731C22—4721no—
732C22—4721no—
733C22—4721no—
734C22—2362no—
735C22—2362no—
736C22—2362no—
737C22C2×C4×C22⋊D5911yescharacteristic
738C22D4×C22⋊D5911yescharacteristic
739C22#1683804611yescharacteristic
740C22#1683820011yescharacteristic
741C22#1683820011yescharacteristic
742C22#1683820511yescharacteristic
743C22#1683821011yescharacteristic
744C4—22no—
745C4—24no—
746C4—41no—
747C4—41no—
748C4—41no—
749C4—41no—
750C4—81no—
751C4—81no—
752C4—4721no—
753C4—2362no—
754C4—2362no—
755C4C2×(C22⋊D59)⋊C411yescharacteristic
756C4#1683787511yescharacteristic
757C4#1683804211yescharacteristic
758C4#1683807811yescharacteristic
759C2—42no—
760C2—82no—
761C2—4722no—
762C2#2142707511yescharacteristic
763C2#2143289411yescharacteristic
764C2#2143292411yescharacteristic
765C2#2143563711yescharacteristic
766C2#2143568211yescharacteristic
767C2#2143610211yescharacteristic
768C2#2143628211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2341C2
socleC23×C59C22×D4
prime radicalC2×#16837547C2
cosocleC22×C4×C59C24
hypercenter#2341D59
hypocenterC59#22857
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2341

Complements

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

NH ≅ G/Ntype
2. C2×#16837500C2semidirect
3. C2×#16837398C2semidirect
4. #21427132C2semidirect
5. #21424971C2semidirect
6. #21424796C2semidirect
7. #21424713C2semidirect
8. #21424522C2semidirect
9. #21424451C2semidirect
10. #21424447C2semidirect
11. #21424364C2semidirect
12. #21424293C2semidirect
13. #21423926C2semidirect
14. #21423874C2semidirect
15. C59×#2341C2semidirect
22. #16837547C4semidirect
98. #14273651C2×C4semidirect
99. #14273651D4semidirect
102. #14273648C2×C4semidirect
105. C22⋊(C59⋊C8)C2×C4semidirect
115. C2×#41×C59C2×C4semidirect
379. #2341D59semidirect
446. C59#22857semidirect
452. C2×#41C4×D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168375472
C2×#168375002
C2×#168373982
#214271322
#214249712
#214247962
#214247132
#214245222
#214244512
#214244472
#214243642
#214242932
#214239262
#214238742
C59×#23412
#2285759