Finite Group Databasebeta

← #28609142

Subgroups — #28609142

Order 15104.

1106 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837562C211yesmaximal, characteristic
2C2×#16837507C211yesmaximal, characteristic, complemented
3C2×#16837401C211yesmaximal, characteristic
4#21426936C211yesmaximal, characteristic
5#21424953C211yesmaximal, characteristic, complemented
6#21424792C211yesmaximal, characteristic, complemented
7#21424723C211yesmaximal, characteristic, complemented
8#21424530C211yesmaximal, characteristic, complemented
9#21424451C211yesmaximal, characteristic, complemented
10#21424440C211yesmaximal, characteristic, complemented
11#21424363C211yesmaximal, characteristic, complemented
12#21424289C211yesmaximal, characteristic, complemented
13C4×#14273650C211yesmaximal, characteristic, complemented
14#21423880C211yesmaximal, characteristic, complemented
15C59×#2360C211yesmaximal, characteristic, complemented
16C22×#11745685C2211yescharacteristic
17C22×#11745672C2211yescharacteristic
18C22×#11745671C2211yescharacteristic
19C22×#11745664C2211yescharacteristic
20C2×C4×Dic118C2211yescharacteristic
21C2×C4×Dic118C2211yescharacteristic
22#16837562C418yescomplemented
23#16837507—24no—
24C2×#14273658C2211yescharacteristic
25C2×#14273658C2211yescharacteristic
26#16837401—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×C4×C59⋊C8C2211yescharacteristic
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
53C22×C4⋊C4×C59C2211yescharacteristic
54C59×#391C2211yescharacteristic
55C59×#389—21no—
56C59×#389C2211yescharacteristic
57C59×#387—21no—
58C59×#385—21no—
59C4×C4⋊C4×C59C2211yescharacteristic
60C4×C22⋊C4×C59—21no—
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×C414yescomplemented
75C2×#11745671—41no—
76C2×#11745671—41no—
77C2×#11745671C2×C414yescomplemented
78C2×#11745664—22no—
79C2×#11745664—22no—
80C2×#11745664—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#14273658—22no—
101#14273658—41no—
102#14273651—22no—
103#14273651—41no—
104#14273650—22no—
105#14273650C2×C414yescomplemented
106#14273650D414yes—
107#14273647—22no—
108#14273647—22no—
109#14273647C2×C414yescomplemented
110C22⋊(C59⋊C8)C2×C414yes—
111#14273638—22no—
112C4×C59⋊C8—41no—
113C59⋊#95—21no—
114C22×Q8×C59C2311yescharacteristic
115C23×C4×C59—21no—
116C23×C4×C59C2311yescharacteristic
117C22⋊Q8×C59—22no—
118C22⋊Q8×C59C2×C414yes—
119C4×Q8×C59—22no—
120C4×Q8×C59—41no—
121C2×C4⋊C4×C59—21no—
122C2×C4⋊C4×C59—22no—
123C2×C4⋊C4×C59—21no—
124C2×C4⋊C4×C59—21no—
125C2×C4⋊C4×C59—21no—
126C2×C4⋊C4×C59—41no—
127C2×C4⋊C4×C59C2311yescharacteristic
128C2×C4⋊C4×C59C2311yescharacteristic
129C2×C4⋊C4×C59C2311yescharacteristic
130C2×C22⋊C4×C59—21no—
131C2×C22⋊C4×C59D411yescharacteristic
132C2×C22⋊C4×C59D411yescharacteristic
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×C59—42no—
160C22×C4×C59—42no—
161C22×C4×C59—81no—
162C22×C4×C59C22×C412yes—
163C22×C4×C59C2×D411yescharacteristic
164C22×C4×C59C2×D411yescharacteristic
165C22×C4×C59C2×D411yescharacteristic
166C22×C4×C59C2×D411yescharacteristic
167C22×C4×C59C2×D411yescharacteristic
168C22×C4×C59#4112yes—
169C22×C4×C59C2411yescharacteristic
170C2×C22⋊D59—24no—
171C2×C22⋊D59—42no—
172C2×C22⋊D59—42no—
173C22×Dic59—21no—
174C22×Dic59—21no—
175C22×Dic59—21no—
176#11745685—28no—
177#11745685—44no—
178#11745685—44no—
179#11745685—44no—
180C2×D236—21no—
181C2×D236—21no—
182C2×D236—21no—
183C2×D236—21no—
184C2×D236—21no—
185C2×D236C22×C412yes—
186C2×C4×D59—24no—
187C2×C4×D59—42no—
188C2×C4×D59—42no—
189C2×Dic118—21no—
190C2×Dic118—21no—
191C2×Dic118—21no—
192C2×Dic118C22×C412yes—
193C2×Dic118C2×D412yes—
194C2×Dic118#4112yes—
195C4⋊C4×C59—24no—
196C4⋊C4×C59—21no—
197C4⋊C4×C59—21no—
198C4⋊C4×C59—21no—
199C4⋊C4×C59—21no—
200C4⋊C4×C59—42no—
201C4⋊C4×C59—42no—
202C4⋊C4×C59—81no—
203C4⋊C4×C59C22×C412yes—
204C4⋊C4×C59C2×D412yes—
205C22⋊C4×C59—24no—
206C22⋊C4×C59—22no—
207C22⋊C4×C59—41no—
208C42×C59—21no—
209C42×C59—21no—
210C42×C59—21no—
211C42×C59—21no—
212C42×C59—42no—
213C42×C59—81no—
214C22⋊Dic59—81no—
215#11745672—28no—
216#11745671—44no—
217(C2×D59)⋊C4—42no—
218(C2×D59)⋊C4—42no—
219(C2×D59)⋊C4—81no—
220(C2×D59)⋊C4—81no—
221C4⋊Dic59—21no—
222C4⋊Dic59—21no—
223C4⋊Dic59—21no—
224C4⋊Dic59—21no—
225Dic59⋊C4—42no—
226Dic59⋊C4—42no—
227C4×Dic59—42no—
228C4×Dic59—42no—
229#11745664—44no—
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—21no—
237C2×C59⋊C8—21no—
238C2×C59⋊C8—21no—
239C2×C59⋊C8C22×C412yes—
240C2×C59⋊C8C22×C412yes—
241C2×C59⋊C8C2×D412yes—
242C23×C59—21no—
243C23×C59—21no—
244C23×C59—21no—
245C23×C59—21no—
246C23×C59—21no—
247C23×C59—21no—
248C23×C59C4×D412yes—
249C23×C59C22×D411yescharacteristic
250C22×D59—22no—
251C22×D59—41no—
252C22×D59—41no—
253C22×D59—41no—
254C22×D59—41no—
255C22×D59—41no—
256C22×D59—41no—
257Q8×C59—22no—
258Q8×C59—22no—
259Q8×C59—41no—
260Q8×C59—41no—
261C2×C4×C59—21no—
262C2×C4×C59—21no—
263C2×C4×C59—21no—
264C2×C4×C59—21no—
265C2×C4×C59—22no—
266C2×C4×C59—22no—
267C2×C4×C59—22no—
268C2×C4×C59—22no—
269C2×C4×C59—22no—
270C2×C4×C59—22no—
271C2×C4×C59—21no—
272C2×C4×C59—21no—
273C2×C4×C59—22no—
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—21no—
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×C59—41no—
290C2×C4×C59—84no—
291C2×C4×C59C4×D412yes—
292C2×C4×C59#13712yes—
293C2×C4×C59C23×C411yescharacteristic
294C2×C4×C59C22×D411yescharacteristic
295C2×C4×C59C2×#4111yescharacteristic
296C2×C4×C59C2×#4111yescharacteristic
297C2×C4×C59H(5,𝔽2)11yescharacteristic
298C2×C4×C59H(5,𝔽2)11yescharacteristic
299C22⋊D59—48no—
300C2×Dic59—22no—
301C2×Dic59—22no—
302C2×Dic59—22no—
303C2×Dic59—41no—
304C2×Dic59—41no—
305C2×Dic59—41no—
306C2×Dic59—41no—
307C2×Dic59—41no—
308C2×Dic59—41no—
309D236—22no—
310D236—22no—
311D236—41no—
312D236—41no—
313C4×D59—48no—
314Dic118—22no—
315Dic118—22no—
316Dic118—22no—
317Dic118C4×D414yes—
318C59⋊C8—22no—
319C59⋊C8—22no—
320C59⋊C8—22no—
321C59⋊C8—41no—
322#22867—591nomaximal, Sylow
323C22×C59—22no—
324C22×C59—22no—
325C22×C59—22no—
326C22×C59—41no—
327C22×C59—41no—
328C22×C59—41no—
329C22×C59—41no—
330C22×C59C2×C4×D411yescharacteristic
331C22×C59D4211yescharacteristic
332C22×C59#54611yescharacteristic
333C22×C59C2×#13711yescharacteristic
334C22×C59#57511yescharacteristic
335C22×C59#57711yescharacteristic
336C22×C59#57711yescharacteristic
337C2×D59—42no—
338C2×D59—42no—
339C2×D59—42no—
340C2×D59—81no—
341C2×D59—81no—
342C2×D59—81no—
343C2×D59—81no—
344C4×C59—22no—
345C4×C59—22no—
346C4×C59—42no—
347C4×C59—42no—
348C4×C59—41no—
349C4×C59—42no—
350C4×C59—41no—
351C4×C59—41no—
352C4×C59—81no—
353C4×C59C2×C4×D411yescharacteristic
354C4×C59#51811yescharacteristic
355C4×C59#54611yescharacteristic
356C4×C59#55111yescharacteristic
357Dic59—24no—
358Dic59—81no—
359Dic59—81no—
360C2×#452—591no—
361C2×#441—591no—
362C2×#417—591no—
363#2360D5911yescharacteristic, complemented
364#2341—591no—
365#1968—591no—
366#1936—591no—
367#1926—591no—
368#1894—591no—
369#1880—591no—
370#1878—591no—
371#1865—591no—
372#1853—591no—
373C4×#103—591no—
374#1753—591no—
375C2×C59—42no—
376C2×C59#235811yescharacteristic
377C2×C59C4×#13711yescharacteristic
378C2×C59#295211yescharacteristic
379C2×C59#327511yescharacteristic
380C2×C59#327811yescharacteristic
381C2×C59#331611yescharacteristic
382C2×C59#331711yescharacteristic
383D59—82no—
384C22×#41—591no—
385C22×Q16—591no—
386C22×SD16—591no—
387C22×M16—591no—
388C2×C22⋊Q8C2×D5911yescharacteristic
389C2×C4×Q8—591no—
390C2×C4×Q8—591no—
391C2×C4×Q8C2×D5911yescharacteristic
392C22×C4⋊C4C2×D5911yescharacteristic
393#452—598no—
394#441—1184no—
395C2×#106—591no—
396C2×#106—591no—
397#417—1184no—
398C2×#103—591no—
399C2×#103—591no—
400C2×#103—591no—
401C2×#103—591no—
402C2×#103—591no—
403C2×#102—591no—
404C2×#102—591no—
405C2×#102—591no—
406C2×C22⋊C8—591no—
407C2×#97—591no—
408C2×C4×C8—591no—
409#391C2×D5911yescharacteristic
410#390—591no—
411#390—591no—
412#390—1181no—
413#390—1181no—
414#389—21no—
415#389C2×D5911yescharacteristic
416#387—21no—
417#385—21no—
418#380—591no—
419#380—1181no—
420C4×C4⋊C4C2×D5911yescharacteristic
421C4×C22⋊C4—21no—
422C4×C22⋊C4—1181no—
423C4×C22⋊C4C2×D5911yescharacteristic
424#340—591no—
425#340—591no—
426#340—591no—
427#340—591no—
428#336—591no—
429#336—591no—
430C59#2286711yescharacteristic, complemented, Sylow
431C2×#41—594no—
432C2×#41—1182no—
433C2×#41—1182no—
434C2×#41—1182no—
435C2×#41—2361no—
436C2×#41—2361no—
437C22×Q8—591no—
438C22×Q8C22×D5911yescharacteristic
439C22×D4—591no—
440C22×D4—1181no—
441C23×C4—21no—
442C23×C4—1181no—
443C23×C4C22×D5911yescharacteristic
444C2×Q16—594no—
445C2×Q16—1182no—
446C2×Q16—1182no—
447C2×SD16—594no—
448C2×SD16—2361no—
449C2×SD16—2361no—
450C2×M16—1182no—
451C2×M16—1182no—
452C2×M16—2361no—
453C22×C8—591no—
454C22×C8—591no—
455C22×C8—591no—
456C22×C8—591no—
457C22⋊Q8—22no—
458C22⋊Q8C4×D5914yes—
459C4×Q8—22no—
460C4×Q8—41no—
461C4×Q8—1182no—
462C4×Q8—1182no—
463C4×Q8—2361no—
464C4×Q8—2361no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—41no—
471C2×C4⋊C4—591no—
472C2×C4⋊C4—591no—
473C2×C4⋊C4—1181no—
474C2×C4⋊C4—1181no—
475C2×C4⋊C4C22×D5911yescharacteristic
476C2×C4⋊C4C22×D5911yescharacteristic
477C2×C4⋊C4C22×D5911yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—1181no—
480C2×C22⋊C4—1181no—
481C2×C22⋊C4—1181no—
482C2×C22⋊C4—1181no—
483C2×C22⋊C4—1181no—
484C2×C22⋊C4C22⋊D5911yescharacteristic
485C2×C22⋊C4C22⋊D5911yescharacteristic
486C2×C42—21no—
487C2×C42—21no—
488C2×C42—1181no—
489C2×C42—1181no—
490C2×C42C22×D5911yescharacteristic
491C2×C42C22×D5911yescharacteristic
492#106—1182no—
493#106—2361no—
494#103—594no—
495#103—594no—
496#103—1182no—
497#103—1182no—
498#103—2361no—
499#102—594no—
500#102—1182no—
501#102—1182no—
502C22⋊C8—594no—
503#97—1182no—
504C4×C8—2361no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95—1181no—
510#95C22⋊D5911yescharacteristic
511#95C22⋊D5911yescharacteristic
512C24—1181no—
513C24C2×C22⋊D5911yescharacteristic
514#41—1188no—
515#41—2364no—
516#41—2364no—
517#41—2364no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—592no—
524C2×Q8—592no—
525C2×Q8—592no—
526C2×Q8—1181no—
527C2×Q8—1181no—
528C2×Q8—1181no—
529C2×Q8C2×C4×D5912yes—
530C2×D4—592no—
531C2×D4—1184no—
532C2×D4—1181no—
533C2×D4—1181no—
534C2×D4—1181no—
535C2×D4—1181no—
536C2×D4—1181no—
537C2×D4—2362no—
538C2×D4—2362no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—81no—
550C22×C4—1181no—
551C22×C4—1184no—
552C22×C4—1181no—
553C22×C4—1181no—
554C22×C4—2362no—
555C22×C4—2362no—
556C22×C4C2×C4×D5912yes—
557C22×C4#1174568512yes—
558C22×C4C2×C22⋊D5911yescharacteristic
559C22×C4C2×C22⋊D5911yescharacteristic
560C22×C4C2×C22⋊D5911yescharacteristic
561C22×C4C2×C22⋊D5911yescharacteristic
562C22×C4C2×C22⋊D5911yescharacteristic
563C22×C4C23×D5911yescharacteristic
564Q16—1188no—
565SD16—2364no—
566M16—2364no—
567C2×C8—592no—
568C2×C8—592no—
569C2×C8—592no—
570C2×C8—1181no—
571C2×C8—1181no—
572C2×C8—1181no—
573C2×C8—1181no—
574C2×C8—1181no—
575C2×C8—1181no—
576C2×C8—1181no—
577C2×C8—1181no—
578C2×C8—1181no—
579C4⋊C4—24no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—81no—
587C4⋊C4—1181no—
588C4⋊C4—1181no—
589C4⋊C4—1181no—
590C4⋊C4—1181no—
591C4⋊C4—2362no—
592C4⋊C4—2362no—
593C4⋊C4C2×C4×D5912yes—
594C4⋊C4D4×D5912yes—
595C22⋊C4—24no—
596C22⋊C4—22no—
597C22⋊C4—41no—
598C22⋊C4—4721no—
599C22⋊C4—4721no—
600C22⋊C4—4721no—
601C22⋊C4—2362no—
602C22⋊C4—2362no—
603C42—21no—
604C42—21no—
605C42—21no—
606C42—21no—
607C42—42no—
608C42—81no—
609C42—2362no—
610C42—2362no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—1182no—
618C23—2361no—
619C23—2361no—
620C23—2361no—
621C23—2361no—
622C23—2361no—
623C23—2361no—
624C23C4×C22⋊D5912yes—
625C23C22×C22⋊D5911yescharacteristic
626Q8—22no—
627Q8—22no—
628Q8—41no—
629Q8—41no—
630Q8—594no—
631Q8—1182no—
632Q8—1182no—
633Q8—1182no—
634D4—1182no—
635D4—1182no—
636D4—2368no—
637D4—2361no—
638D4—2361no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—84no—
669C2×C4—1182no—
670C2×C4—1182no—
671C2×C4—1182no—
672C2×C4—2368no—
673C2×C4—2361no—
674C2×C4—2361no—
675C2×C4—2361no—
676C2×C4—2361no—
677C2×C4—2361no—
678C2×C4—2361no—
679C2×C4C4×C22⋊D5912yes—
680C2×C4#1427375812yes—
681C2×C4C22×C4×D5911yescharacteristic
682C2×C4C2×D4×D5911yescharacteristic
683C2×C4#41×D5911yescharacteristic
684C2×C4C2×#1174568511yescharacteristic
685C2×C4#1427377211yescharacteristic
686C2×C4#1427377311yescharacteristic
687C8—1182no—
688C8—1182no—
689C8—1182no—
690C8—2361no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—4721no—
699C22—4721no—
700C22—4721no—
701C22—4721no—
702C22—2362no—
703C22—2362no—
704C22—2362no—
705C22C2×C4×C22⋊D5911yescharacteristic
706C22D4×C22⋊D5911yescharacteristic
707C22#1683804011yescharacteristic
708C22C2×#1427375811yescharacteristic
709C22#1683820011yescharacteristic
710C22#1683821011yescharacteristic
711C22#1683821311yescharacteristic
712C4—22no—
713C4—22no—
714C4—41no—
715C4—41no—
716C4—42no—
717C4—41no—
718C4—42no—
719C4—42no—
720C4—81no—
721C4—1184no—
722C4—4721no—
723C4—4721no—
724C4C4×D4×D5911yescharacteristic
725C4#1683787411yescharacteristic
726C4#1683804811yescharacteristic
727C4#1683808111yescharacteristic
728C2—42no—
729C2—4722no—
730C2#2142707311yescharacteristic
731C2C4×#1427375811yescharacteristic
732C2#2143297711yescharacteristic
733C2#2143572311yescharacteristic
734C2#2143575811yescharacteristic
735C2#2143620111yescharacteristic
736C2#2143621611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2360C2
socleC23×C59C22×D4
prime radicalC22×#11745685C22
cosocleC22×C4×C59C24
hypercenter#2360D59
hypocenterC59#22867
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2360

Complements

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

NH ≅ G/Ntype
2. C2×#16837507C2semidirect
5. #21424953C2semidirect
6. #21424792C2semidirect
7. #21424723C2semidirect
8. #21424530C2semidirect
9. #21424451C2semidirect
10. #21424440C2semidirect
11. #21424363C2semidirect
12. #21424289C2semidirect
13. C4×#14273650C2semidirect
14. #21423880C2semidirect
15. C59×#2360C2semidirect
22. #16837562C4semidirect
74. C2×#11745672C2×C4semidirect
77. C2×#11745671C2×C4semidirect
105. #14273650C2×C4semidirect
109. #14273647C2×C4semidirect
363. #2360D59semidirect
430. C59#22867semidirect

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×#168374012
#214269362
#214249532
#214247922
#214247232
#214245302
#214244512
#214244402
#214243632
#214242892
C4×#142736502
#214238802
C59×#23602
#2286759