Finite Group Databasebeta

← #28609052

Subgroups — #28609052

Order 15104.

1090 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837562C211yesmaximal, characteristic
2C2×#16837507C211yesmaximal, characteristic, complemented
3C2×#16837396C211yesmaximal, characteristic
4#21426936C211yesmaximal, characteristic
5#21424980C211yesmaximal, characteristic, complemented
6#21424792C211yesmaximal, characteristic, complemented
7#21424723C211yesmaximal, characteristic, complemented
8#21424520C211yesmaximal, characteristic, complemented
9#21424451C211yesmaximal, characteristic, complemented
10#21424440C211yesmaximal, characteristic, complemented
11#21424349C211yesmaximal, characteristic, complemented
12#21424295C211yesmaximal, characteristic, complemented
13#21423929C211yesmaximal, characteristic, complemented
14#21423874C211yesmaximal, characteristic, complemented
15C59×#2362C211yesmaximal, characteristic, complemented
16C22×#11745685C2211yescharacteristic
17C22×#11745672C2211yescharacteristic
18C22×#11745671C2211yescharacteristic
19C23×C59⋊C8C2211yescharacteristic
20C2×C4×Dic118C2211yescharacteristic
21C2×C4×Dic118C2211yescharacteristic
22#16837562C418yescomplemented
23#16837507—24no—
24C2×#14273660C2211yescharacteristic
25C2×#14273658C2211yescharacteristic
26#16837396—24no—
27C2×#14273651C2211yescharacteristic
28C2×#14273651C2211yescharacteristic
29C2×#14273650C2211yescharacteristic
30C2×#14273650C2211yescharacteristic
31C2×#14273650C2211yescharacteristic
32C2×#14273647C2211yescharacteristic
33C2×#14273647C2211yescharacteristic
34C2×#14273647C2211yescharacteristic
35C2×C22⋊(C59⋊C8)C2211yescharacteristic
36C2×#14273638C2211yescharacteristic
37C2×#14273638C2211yescharacteristic
38#16837304C2211yescharacteristic
39#16837304C2211yescharacteristic
40#16837302—21no—
41#16837302—21no—
42#16837262C2211yescharacteristic
43#16837261—21no—
44#16837249—21no—
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837157C2211yescharacteristic
50#16837157C2211yescharacteristic
51C2×C22⋊Q8×C59C2211yescharacteristic
52C2×C4×Q8×C59C2211yescharacteristic
53C2×#117×C59C2211yescharacteristic
54C59×#391C2211yescharacteristic
55C59×#389C2211yescharacteristic
56C59×#388—21no—
57C59×#388—21no—
58C59×#387—21no—
59C4×C4⋊C4×C59—21no—
60C4×C4⋊C4×C59C2211yescharacteristic
61C4×C22⋊C4×C59C2211yescharacteristic
62C2×#11745685—22no—
63C2×#11745685—22no—
64C2×#11745685—22no—
65C2×#11745685—41no—
66C2×#11745685—41no—
67C2×#11745685C2×C414yes—
68C22×Dic118C2311yescharacteristic
69C22×D236C2311yescharacteristic
70C22×C22⋊D59—21no—
71C22×C4×D59—21no—
72C2×#11745672—22no—
73C2×#11745672—22no—
74C2×#11745672C2×C414yes—
75C2×#11745671—41no—
76C2×#11745671—41no—
77C2×#11745671C2×C414yes—
78C22×C59⋊C8—22no—
79C22×C59⋊C8—22no—
80C22×C59⋊C8—41no—
81C22×C59⋊C8C2311yescharacteristic
82C22×C59⋊C8C2311yescharacteristic
83C22×C59⋊C8C2311yescharacteristic
84C22×C59⋊C8C2311yescharacteristic
85C4×Dic118—22no—
86C4×Dic118—22no—
87C4×Dic118—41no—
88C4×Dic118—41no—
89C2×C4⋊Dic59C2311yescharacteristic
90C2×C4⋊Dic59C2311yescharacteristic
91C2×Dic59⋊C4—21no—
92C2×Dic59⋊C4—21no—
93C2×C22⋊Dic59—21no—
94C2×(C2×D59)⋊C4—21no—
95C2×(C2×D59)⋊C4—21no—
96C2×(C2×D59)⋊C4—21no—
97C2×(C2×D59)⋊C4—21no—
98C2×C4×Dic59—21no—
99C2×C4×Dic59—21no—
100#14273660—41no—
101#14273658—22no—
102#14273651—22no—
103#14273651—41no—
104#14273650—22no—
105#14273650C2×C414yes—
106#14273650D414yes—
107#14273647—22no—
108#14273647—22no—
109#14273647C2×C414yes—
110C22⋊(C59⋊C8)C2×C414yes—
111#14273638—22no—
112#14273638—41no—
113C59⋊#95—21no—
114C22×Q8×C59C2311yescharacteristic
115C23×C4×C59C2311yescharacteristic
116C22⋊Q8×C59—22no—
117C22⋊Q8×C59C2×C414yes—
118C4×Q8×C59—22no—
119C4×Q8×C59—41no—
120#117×C59—22no—
121#117×C59—41no—
122C2×C4⋊C4×C59—21no—
123C2×C4⋊C4×C59—21no—
124C2×C4⋊C4×C59—21no—
125C2×C4⋊C4×C59C2311yescharacteristic
126C2×C4⋊C4×C59C2311yescharacteristic
127C2×C4⋊C4×C59C2311yescharacteristic
128C2×C22⋊C4×C59—21no—
129C2×C22⋊C4×C59—21no—
130C2×C22⋊C4×C59D411yescharacteristic
131C2×C22⋊C4×C59D411yescharacteristic
132C2×C42×C59—21no—
133C2×C42×C59—21no—
134C2×C42×C59—21no—
135C2×C42×C59C2311yescharacteristic
136C2×C42×C59C2311yescharacteristic
137#95×C59—21no—
138#95×C59—21no—
139#95×C59—21no—
140#95×C59—21no—
141#95×C59D411yescharacteristic
142#95×C59D411yescharacteristic
143C24×C59C2×D411yescharacteristic
144C23×D59—21no—
145C2×Q8×C59—21no—
146C2×Q8×C59—21no—
147C2×Q8×C59—21no—
148C2×Q8×C59—21no—
149C2×Q8×C59—21no—
150C2×Q8×C59C22×C412yes—
151C22×C4×C59—21no—
152C22×C4×C59—21no—
153C22×C4×C59—21no—
154C22×C4×C59—21no—
155C22×C4×C59—21no—
156C22×C4×C59—21no—
157C22×C4×C59—21no—
158C22×C4×C59—21no—
159C22×C4×C59C22×C412yes—
160C22×C4×C59C2×D411yescharacteristic
161C22×C4×C59C2×D411yescharacteristic
162C22×C4×C59C2×D411yescharacteristic
163C22×C4×C59C2×D411yescharacteristic
164C22×C4×C59C2×D411yescharacteristic
165C22×C4×C59#4112yes—
166C22×C4×C59C2411yescharacteristic
167C2×C22⋊D59—24no—
168C2×C22⋊D59—42no—
169C2×C22⋊D59—42no—
170C22×Dic59—21no—
171C22×Dic59—21no—
172C22×Dic59—21no—
173#11745685—28no—
174#11745685—44no—
175#11745685—44no—
176#11745685—44no—
177C2×D236—21no—
178C2×D236—21no—
179C2×D236—21no—
180C2×D236—21no—
181C2×D236—21no—
182C2×D236C22×C412yes—
183C2×C4×D59—24no—
184C2×C4×D59—42no—
185C2×C4×D59—42no—
186C2×Dic118—21no—
187C2×Dic118—21no—
188C2×Dic118—21no—
189C2×Dic118C22×C412yes—
190C2×Dic118C2×D412yes—
191C2×Dic118#4112yes—
192C4⋊C4×C59—24no—
193C4⋊C4×C59—21no—
194C4⋊C4×C59—21no—
195C4⋊C4×C59—21no—
196C4⋊C4×C59—21no—
197C4⋊C4×C59—42no—
198C4⋊C4×C59—42no—
199C4⋊C4×C59C22×C412yes—
200C4⋊C4×C59C2×D412yes—
201C22⋊C4×C59—24no—
202C22⋊C4×C59—41no—
203C22⋊C4×C59—41no—
204C22⋊C4×C59—42no—
205C42×C59—21no—
206C42×C59—21no—
207C42×C59—21no—
208C42×C59—21no—
209C42×C59—42no—
210C42×C59—42no—
211C42×C59—42no—
212C22⋊Dic59—81no—
213#11745672—28no—
214#11745671—44no—
215(C2×D59)⋊C4—42no—
216(C2×D59)⋊C4—42no—
217(C2×D59)⋊C4—81no—
218(C2×D59)⋊C4—81no—
219C4⋊Dic59—21no—
220C4⋊Dic59—21no—
221C4⋊Dic59—21no—
222C4⋊Dic59—21no—
223Dic59⋊C4—42no—
224Dic59⋊C4—42no—
225C4×Dic59—42no—
226C4×Dic59—42no—
227C2×C59⋊C8—21no—
228C2×C59⋊C8—21no—
229C2×C59⋊C8—21no—
230C2×C59⋊C8—21no—
231C2×C59⋊C8—21no—
232C2×C59⋊C8—21no—
233C2×C59⋊C8—21no—
234C2×C59⋊C8—21no—
235C2×C59⋊C8—21no—
236C2×C59⋊C8—44no—
237C2×C59⋊C8C22×C412yes—
238C2×C59⋊C8C22×C412yes—
239C2×C59⋊C8C2×D412yes—
240C23×C59—21no—
241C23×C59—21no—
242C23×C59—21no—
243C23×C59—21no—
244C23×C59—21no—
245C23×C59—21no—
246C23×C59C4×D412yes—
247C23×C59C22×D411yescharacteristic
248C22×D59—22no—
249C22×D59—41no—
250C22×D59—41no—
251C22×D59—41no—
252C22×D59—41no—
253C22×D59—41no—
254C22×D59—41no—
255Q8×C59—22no—
256Q8×C59—22no—
257Q8×C59—41no—
258Q8×C59—41no—
259C2×C4×C59—21no—
260C2×C4×C59—21no—
261C2×C4×C59—22no—
262C2×C4×C59—22no—
263C2×C4×C59—22no—
264C2×C4×C59—22no—
265C2×C4×C59—22no—
266C2×C4×C59—22no—
267C2×C4×C59—21no—
268C2×C4×C59—21no—
269C2×C4×C59—22no—
270C2×C4×C59—21no—
271C2×C4×C59—21no—
272C2×C4×C59—21no—
273C2×C4×C59—21no—
274C2×C4×C59—21no—
275C2×C4×C59—21no—
276C2×C4×C59—21no—
277C2×C4×C59—21no—
278C2×C4×C59—21no—
279C2×C4×C59—21no—
280C2×C4×C59—41no—
281C2×C4×C59—41no—
282C2×C4×C59—41no—
283C2×C4×C59—41no—
284C2×C4×C59—41no—
285C2×C4×C59—41no—
286C2×C4×C59—41no—
287C2×C4×C59—41no—
288C2×C4×C59—41no—
289C2×C4×C59C4×D412yes—
290C2×C4×C59C23×C411yescharacteristic
291C2×C4×C59C22×D411yescharacteristic
292C2×C4×C59C2×#4111yescharacteristic
293C2×C4×C59C2×#4111yescharacteristic
294C2×C4×C59H(5,𝔽2)11yescharacteristic
295C2×C4×C59H(5,𝔽2)11yescharacteristic
296C22⋊D59—48no—
297C2×Dic59—22no—
298C2×Dic59—22no—
299C2×Dic59—22no—
300C2×Dic59—41no—
301C2×Dic59—41no—
302C2×Dic59—41no—
303C2×Dic59—41no—
304C2×Dic59—41no—
305C2×Dic59—41no—
306D236—22no—
307D236—22no—
308D236—41no—
309D236—41no—
310C4×D59—48no—
311Dic118—22no—
312Dic118—22no—
313Dic118—22no—
314Dic118C4×D414yes—
315C59⋊C8—22no—
316C59⋊C8—22no—
317C59⋊C8—22no—
318C59⋊C8—41no—
319#22861—591nomaximal, Sylow
320C22×C59—22no—
321C22×C59—22no—
322C22×C59—22no—
323C22×C59—41no—
324C22×C59—41no—
325C22×C59—41no—
326C22×C59—41no—
327C22×C59C2×C4×D411yescharacteristic
328C22×C59D4211yescharacteristic
329C22×C59#54611yescharacteristic
330C22×C59#57511yescharacteristic
331C22×C59#57511yescharacteristic
332C22×C59#57711yescharacteristic
333C22×C59#57811yescharacteristic
334C2×D59—42no—
335C2×D59—42no—
336C2×D59—42no—
337C2×D59—81no—
338C2×D59—81no—
339C2×D59—81no—
340C2×D59—81no—
341C4×C59—22no—
342C4×C59—42no—
343C4×C59—42no—
344C4×C59—41no—
345C4×C59—42no—
346C4×C59—41no—
347C4×C59—41no—
348C4×C59—41no—
349C4×C59—81no—
350C4×C59C2×C4×D411yescharacteristic
351C4×C59#51811yescharacteristic
352C4×C59#54611yescharacteristic
353C4×C59#55111yescharacteristic
354Dic59—24no—
355Dic59—81no—
356Dic59—81no—
357C2×#452—591no—
358C2×#441—591no—
359C2×#416—591no—
360#2362D5911yescharacteristic, complemented
361#2341—591no—
362#1973—591no—
363#1936—591no—
364#1926—591no—
365#1892—591no—
366#1880—591no—
367#1878—591no—
368#1863—591no—
369#1854—591no—
370#1763—591no—
371#1752—591no—
372C2×C59—42no—
373C2×C59#235811yescharacteristic
374C2×C59#294311yescharacteristic
375C2×C59#294711yescharacteristic
376C2×C59#326911yescharacteristic
377C2×C59#327111yescharacteristic
378C2×C59#331311yescharacteristic
379C2×C59#331711yescharacteristic
380D59—82no—
381C22×#41—591no—
382C22×Q16—591no—
383C22×SD16—591no—
384C23×C8—591no—
385C2×C22⋊Q8C2×D5911yescharacteristic
386C2×C4×Q8—591no—
387C2×C4×Q8—591no—
388C2×C4×Q8C2×D5911yescharacteristic
389C2×#117C2×D5911yescharacteristic
390#452—598no—
391#441—1184no—
392C2×#107—591no—
393C2×#106—591no—
394#416—1184no—
395C2×#103—591no—
396C2×#103—591no—
397C2×#103—591no—
398C2×#103—591no—
399C2×#103—591no—
400C2×#102—591no—
401C2×#102—591no—
402C2×#102—591no—
403C2×C22⋊C8—591no—
404C2×#97—591no—
405C2×#97—591no—
406#391C2×D5911yescharacteristic
407#390—591no—
408#390—591no—
409#390—1181no—
410#390—1181no—
411#389C2×D5911yescharacteristic
412#388—21no—
413#388—21no—
414#387—21no—
415#380—591no—
416#380—1181no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4C2×D5911yescharacteristic
419C4×C22⋊C4—1181no—
420C4×C22⋊C4C2×D5911yescharacteristic
421#340—591no—
422#340—591no—
423#340—591no—
424#340—591no—
425#336—591no—
426#336—591no—
427C59#2286111yescharacteristic, complemented, Sylow
428C2×#41—594no—
429C2×#41—1182no—
430C2×#41—1182no—
431C2×#41—1182no—
432C2×#41—2361no—
433C2×#41—2361no—
434C22×Q8—591no—
435C22×Q8C22×D5911yescharacteristic
436C22×D4—591no—
437C22×D4—1181no—
438C23×C4—1181no—
439C23×C4C22×D5911yescharacteristic
440C2×Q16—594no—
441C2×Q16—1182no—
442C2×Q16—1182no—
443C2×SD16—594no—
444C2×SD16—2361no—
445C2×SD16—2361no—
446C22×C8—591no—
447C22×C8—591no—
448C22×C8—591no—
449C22×C8—591no—
450C22×C8—1182no—
451C22×C8—1182no—
452C22×C8—2361no—
453C22⋊Q8—22no—
454C22⋊Q8C4×D5914yes—
455C4×Q8—22no—
456C4×Q8—41no—
457C4×Q8—1182no—
458C4×Q8—1182no—
459C4×Q8—2361no—
460C4×Q8—2361no—
461#117—22no—
462#117—41no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—591no—
467C2×C4⋊C4—591no—
468C2×C4⋊C4—1181no—
469C2×C4⋊C4—1181no—
470C2×C4⋊C4C22×D5911yescharacteristic
471C2×C4⋊C4C22×D5911yescharacteristic
472C2×C4⋊C4C22×D5911yescharacteristic
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—1181no—
476C2×C22⋊C4—1181no—
477C2×C22⋊C4—1181no—
478C2×C22⋊C4—1181no—
479C2×C22⋊C4—1181no—
480C2×C22⋊C4C22⋊D5911yescharacteristic
481C2×C22⋊C4C22⋊D5911yescharacteristic
482C2×C42—21no—
483C2×C42—21no—
484C2×C42—21no—
485C2×C42—1181no—
486C2×C42—1181no—
487C2×C42C22×D5911yescharacteristic
488C2×C42C22×D5911yescharacteristic
489#107—2361no—
490#106—1182no—
491#103—594no—
492#103—594no—
493#103—1182no—
494#103—1182no—
495#103—2361no—
496#102—594no—
497#102—1182no—
498#102—1182no—
499C22⋊C8—594no—
500#97—1182no—
501#97—2361no—
502#95—21no—
503#95—21no—
504#95—21no—
505#95—21no—
506#95—1181no—
507#95C22⋊D5911yescharacteristic
508#95C22⋊D5911yescharacteristic
509C24—1181no—
510C24C2×C22⋊D5911yescharacteristic
511#41—1188no—
512#41—2364no—
513#41—2364no—
514#41—2364no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—592no—
521C2×Q8—592no—
522C2×Q8—592no—
523C2×Q8—1181no—
524C2×Q8—1181no—
525C2×Q8—1181no—
526C2×Q8C2×C4×D5912yes—
527C2×D4—592no—
528C2×D4—1184no—
529C2×D4—1181no—
530C2×D4—1181no—
531C2×D4—1181no—
532C2×D4—1181no—
533C2×D4—1181no—
534C2×D4—2362no—
535C2×D4—2362no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—1181no—
545C22×C4—1184no—
546C22×C4—1181no—
547C22×C4—1181no—
548C22×C4—2362no—
549C22×C4—2362no—
550C22×C4C2×C4×D5912yes—
551C22×C4#1174568512yes—
552C22×C4C2×C22⋊D5911yescharacteristic
553C22×C4C2×C22⋊D5911yescharacteristic
554C22×C4C2×C22⋊D5911yescharacteristic
555C22×C4C2×C22⋊D5911yescharacteristic
556C22×C4C2×C22⋊D5911yescharacteristic
557C22×C4C23×D5911yescharacteristic
558Q16—1188no—
559SD16—2364no—
560C2×C8—592no—
561C2×C8—592no—
562C2×C8—592no—
563C2×C8—1181no—
564C2×C8—1181no—
565C2×C8—1181no—
566C2×C8—1181no—
567C2×C8—1181no—
568C2×C8—1181no—
569C2×C8—1181no—
570C2×C8—1181no—
571C2×C8—1181no—
572C2×C8—2364no—
573C4⋊C4—24no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—1181no—
581C4⋊C4—1181no—
582C4⋊C4—1181no—
583C4⋊C4—1181no—
584C4⋊C4—2362no—
585C4⋊C4—2362no—
586C4⋊C4C2×C4×D5912yes—
587C4⋊C4D4×D5912yes—
588C22⋊C4—24no—
589C22⋊C4—41no—
590C22⋊C4—41no—
591C22⋊C4—42no—
592C22⋊C4—4721no—
593C22⋊C4—4721no—
594C22⋊C4—4721no—
595C22⋊C4—2362no—
596C22⋊C4—2362no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—21no—
601C42—42no—
602C42—42no—
603C42—42no—
604C42—2362no—
605C42—2362no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—1182no—
613C23—2361no—
614C23—2361no—
615C23—2361no—
616C23—2361no—
617C23—2361no—
618C23—2361no—
619C23C4×C22⋊D5912yes—
620C23C22×C22⋊D5911yescharacteristic
621Q8—22no—
622Q8—22no—
623Q8—41no—
624Q8—41no—
625Q8—594no—
626Q8—1182no—
627Q8—1182no—
628Q8—1182no—
629D4—1182no—
630D4—1182no—
631D4—2368no—
632D4—2361no—
633D4—2361no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—1182no—
665C2×C4—1182no—
666C2×C4—1182no—
667C2×C4—2368no—
668C2×C4—2361no—
669C2×C4—2361no—
670C2×C4—2361no—
671C2×C4—2361no—
672C2×C4—2361no—
673C2×C4—2361no—
674C2×C4C4×C22⋊D5912yes—
675C2×C4C22×C4×D5911yescharacteristic
676C2×C4C2×D4×D5911yescharacteristic
677C2×C4#41×D5911yescharacteristic
678C2×C4C2×#1174568511yescharacteristic
679C2×C4#1427377211yescharacteristic
680C2×C4#1427377311yescharacteristic
681C8—1182no—
682C8—1182no—
683C8—1182no—
684C8—2361no—
685C22—22no—
686C22—22no—
687C22—22no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—4721no—
693C22—4721no—
694C22—4721no—
695C22—4721no—
696C22—2362no—
697C22—2362no—
698C22—2362no—
699C22C2×C4×C22⋊D5911yescharacteristic
700C22D4×C22⋊D5911yescharacteristic
701C22#1683804011yescharacteristic
702C22#1683820011yescharacteristic
703C22#1683820011yescharacteristic
704C22#1683821011yescharacteristic
705C22#1683821711yescharacteristic
706C4—22no—
707C4—41no—
708C4—41no—
709C4—42no—
710C4—42no—
711C4—41no—
712C4—41no—
713C4—42no—
714C4—81no—
715C4—1184no—
716C4—4721no—
717C4—4721no—
718C4C4×D4×D5911yescharacteristic
719C4#1683787411yescharacteristic
720C4#1683804811yescharacteristic
721C4#1683808111yescharacteristic
722C2—42no—
723C2—4722no—
724C2#2142707311yescharacteristic
725C2#2143289411yescharacteristic
726C2#2143293911yescharacteristic
727C2#2143564711yescharacteristic
728C2#2143568211yescharacteristic
729C2#2143615611yescharacteristic
730C2#2143621611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2362C2
socleC23×C59C22×D4
prime radicalC22×#11745685C22
cosocleC22×C4×C59C24
hypercenter#2362D59
hypocenterC59#22861
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2362

Complements

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

NH ≅ G/Ntype
2. C2×#16837507C2semidirect
5. #21424980C2semidirect
6. #21424792C2semidirect
7. #21424723C2semidirect
8. #21424520C2semidirect
9. #21424451C2semidirect
10. #21424440C2semidirect
11. #21424349C2semidirect
12. #21424295C2semidirect
13. #21423929C2semidirect
14. #21423874C2semidirect
15. C59×#2362C2semidirect
22. #16837562C4semidirect
360. #2362D59semidirect
427. C59#22861semidirect

Maximal subgroups

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

subgroupindex
C2×#168375622
C2×#168375072
C2×#168373962
#214269362
#214249802
#214247922
#214247232
#214245202
#214244512
#214244402
#214243492
#214242952
#214239292
#214238742
C59×#23622
#2286159