Finite Group Databasebeta

← #28595366

Subgroups — #28595366

Order 15104.

1066 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×#16837653C211yesmaximal, characteristic
2C2×C4×#11745669C211yesmaximal, characteristic, complemented
3C2×#16837358C211yesmaximal, characteristic, complemented
4#21426789C211yesmaximal, characteristic, complemented
5#21424971C211yesmaximal, characteristic, complemented
6#21424836C211yesmaximal, characteristic, complemented
7#21424782C211yesmaximal, characteristic, complemented
8#21424778C211yesmaximal, characteristic, complemented
9#21424525C211yesmaximal, characteristic, complemented
10#21424522C211yesmaximal, characteristic, complemented
11#21424127C211yesmaximal, characteristic, complemented
12C4×#14273658C211yesmaximal, characteristic, complemented
13#21423924C211yesmaximal, characteristic, complemented
14#21423921C211yesmaximal, characteristic, complemented
15C59×#2324C211yesmaximal, characteristic, complemented
16C22×#11745669C2211yescharacteristic
17C22×#11745664C2211yescharacteristic
18C23×C59⋊C8C2211yescharacteristic
19C2×#14273701C2211yescharacteristic
20C2×C4×D236C2211yescharacteristic
21#16837653C418yescomplemented
22C4×#11745669—24no—
23C2×#14273660C2211yescharacteristic
24C2×#14273658C2211yescharacteristic
25C2×#14273658C2211yescharacteristic
26C2×#14273648C2211yescharacteristic
27C2×#14273648C2211yescharacteristic
28C2×#14273648C2211yescharacteristic
29C2×#14273647C2211yescharacteristic
30C2×#14273647C2211yescharacteristic
31C2×#14273647C2211yescharacteristic
32#16837358—24no—
33C2×#14273638C2211yescharacteristic
34C2×#14273638C2211yescharacteristic
35C2×C4×C59⋊C8C2211yescharacteristic
36C2×C4×C59⋊C8C2211yescharacteristic
37#16837304C2211yescharacteristic
38#16837302—21no—
39#16837300C2211yescharacteristic
40#16837292—21no—
41#16837278—21no—
42#16837273—21no—
43#16837262C2211yescharacteristic
44C4×C4⋊Dic59C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837164C2211yescharacteristic
50#16837164C2211yescharacteristic
51C2×#121×C59C2211yescharacteristic
52C2×C4×D4×C59C2211yescharacteristic
53C2×#117×C59C2211yescharacteristic
54C59×#390—21no—
55C59×#390C2211yescharacteristic
56C59×#389C2211yescharacteristic
57C59×#388—21no—
58C59×#386—21no—
59C59×#385—21no—
60C59×#380C2211yescharacteristic
61C4×C4⋊C4×C59C2211yescharacteristic
62C22×D236C2311yescharacteristic
63C22×C22⋊D59—21no—
64C22×C4×D59—21no—
65C2×#11745669—22no—
66C2×#11745669—22no—
67C2×#11745669C2×C414yes—
68C2×#11745664—22no—
69C2×#11745664—22no—
70C2×#11745664C2×C414yescomplemented
71C22×C59⋊C8—22no—
72C22×C59⋊C8—22no—
73C22×C59⋊C8—22no—
74C22×C59⋊C8C2311yescharacteristic
75C22×C59⋊C8C2311yescharacteristic
76C22×C59⋊C8C2311yescharacteristic
77C22×C59⋊C8C2311yescharacteristic
78#14273701—22no—
79#14273701C2×C414yescomplemented
80C4×D236—22no—
81C4×D236—22no—
82C2×C4⋊Dic59C2311yescharacteristic
83C2×C4⋊Dic59C2311yescharacteristic
84C2×C4⋊Dic59C2311yescharacteristic
85C2×Dic59⋊C4—21no—
86C2×C22⋊Dic59—21no—
87C2×(C2×D59)⋊C4—21no—
88C2×(C2×D59)⋊C4—21no—
89C2×(C2×D59)⋊C4—21no—
90C2×(C2×D59)⋊C4—21no—
91C2×C4×Dic59—21no—
92#14273660—22no—
93#14273658—22no—
94#14273658C2×C414yescomplemented
95#14273648—22no—
96#14273648—22no—
97#14273648C2×C414yescomplemented
98#14273647—22no—
99#14273647—22no—
100#14273647C2×C414yescomplemented
101#14273638—22no—
102#14273638—22no—
103C4×C59⋊C8—22no—
104C4×C59⋊C8D414yescomplemented
105C59⋊#95—21no—
106C59⋊#95—21no—
107C59⋊#95—21no—
108C22×D4×C59—21no—
109C22×D4×C59C2311yescharacteristic
110C23×C4×C59—21no—
111C23×C4×C59C2311yescharacteristic
112#121×C59—22no—
113#121×C59C2×C414yescomplemented
114C4×D4×C59—22no—
115C4×D4×C59—22no—
116#117×C59—22no—
117#117×C59—22no—
118C2×C4⋊C4×C59—21no—
119C2×C4⋊C4×C59D411yescharacteristic
120C2×C4⋊C4×C59D411yescharacteristic
121C2×C4⋊C4×C59C2311yescharacteristic
122C2×C4⋊C4×C59C2311yescharacteristic
123C2×C4⋊C4×C59C2311yescharacteristic
124C2×C22⋊C4×C59—21no—
125C2×C22⋊C4×C59—21no—
126C2×C22⋊C4×C59—21no—
127C2×C22⋊C4×C59—21no—
128C2×C22⋊C4×C59—21no—
129C2×C22⋊C4×C59D411yescharacteristic
130C2×C22⋊C4×C59D411yescharacteristic
131C2×C42×C59—21no—
132C2×C42×C59C2311yescharacteristic
133C2×C42×C59C2311yescharacteristic
134#95×C59—21no—
135#95×C59—21no—
136#95×C59—21no—
137C24×C59—21no—
138C24×C59C2×D411yescharacteristic
139C23×D59—21no—
140C2×D4×C59—24no—
141C2×D4×C59—21no—
142C2×D4×C59—21no—
143C2×D4×C59—21no—
144C2×D4×C59—21no—
145C2×D4×C59—21no—
146C2×D4×C59—81no—
147C2×D4×C59—81no—
148C2×D4×C59C22×C412yes—
149C22×C4×C59—21no—
150C22×C4×C59—21no—
151C22×C4×C59—21no—
152C22×C4×C59—21no—
153C22×C4×C59—21no—
154C22×C4×C59—21no—
155C22×C4×C59—21no—
156C22×C4×C59—42no—
157C22×C4×C59—81no—
158C22×C4×C59—81no—
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—81no—
169C2×C22⋊D59—81no—
170C22×Dic59—21no—
171C22×Dic59—21no—
172C22×Dic59—21no—
173C2×D236—21no—
174C2×D236—21no—
175C2×D236—21no—
176C2×D236—21no—
177C2×D236—21no—
178C2×D236C22×C412yes—
179C2×C4×D59—42no—
180C2×C4×D59—81no—
181C2×C4×D59—81no—
182C4⋊C4×C59—22no—
183C4⋊C4×C59—22no—
184C4⋊C4×C59—21no—
185C4⋊C4×C59—21no—
186C4⋊C4×C59—21no—
187C4⋊C4×C59—21no—
188C4⋊C4×C59—21no—
189C4⋊C4×C59—81no—
190C4⋊C4×C59C22×C412yes—
191C22⋊C4×C59—24no—
192C22⋊C4×C59—22no—
193C22⋊C4×C59—22no—
194C22⋊C4×C59—42no—
195C22⋊C4×C59—81no—
196C22⋊C4×C59—81no—
197C22⋊C4×C59—81no—
198C42×C59—21no—
199C42×C59—21no—
200C42×C59—81no—
201C42×C59C2×D412yes—
202C42×C59#4112yes—
203C22⋊Dic59—81no—
204#11745669—28no—
205(C2×D59)⋊C4—24no—
206(C2×D59)⋊C4—42no—
207(C2×D59)⋊C4—81no—
208(C2×D59)⋊C4—81no—
209C4⋊Dic59—21no—
210C4⋊Dic59—21no—
211C4⋊Dic59—21no—
212C4⋊Dic59—21no—
213C4⋊Dic59—21no—
214C4⋊Dic59C22×C412yes—
215Dic59⋊C4—81no—
216C4×Dic59—81no—
217#11745664—28no—
218C2×C59⋊C8—28no—
219C2×C59⋊C8—21no—
220C2×C59⋊C8—21no—
221C2×C59⋊C8—21no—
222C2×C59⋊C8—21no—
223C2×C59⋊C8—21no—
224C2×C59⋊C8—21no—
225C2×C59⋊C8C22×C412yes—
226C2×C59⋊C8C22×C412yes—
227C2×C59⋊C8C2×D412yes—
228C2×C59⋊C8C2×D412yes—
229C2×C59⋊C8#4112yes—
230C2×C59⋊C8#4112yes—
231C23×C59—21no—
232C23×C59—21no—
233C23×C59—21no—
234C23×C59—21no—
235C23×C59—21no—
236C23×C59—21no—
237C23×C59—22no—
238C23×C59—41no—
239C23×C59—41no—
240C23×C59—41no—
241C23×C59—41no—
242C23×C59—41no—
243C23×C59—41no—
244C23×C59C4×D412yes—
245C23×C59C22×D411yescharacteristic
246C22×D59—22no—
247C22×D59—41no—
248C22×D59—41no—
249C22×D59—41no—
250C22×D59—41no—
251C22×D59—41no—
252C22×D59—41no—
253D4×C59—22no—
254D4×C59—22no—
255D4×C59—41no—
256D4×C59—41no—
257D4×C59—84no—
258C2×C4×C59—21no—
259C2×C4×C59—21no—
260C2×C4×C59—21no—
261C2×C4×C59—21no—
262C2×C4×C59—21no—
263C2×C4×C59—21no—
264C2×C4×C59—22no—
265C2×C4×C59—22no—
266C2×C4×C59—22no—
267C2×C4×C59—22no—
268C2×C4×C59—22no—
269C2×C4×C59—21no—
270C2×C4×C59—21no—
271C2×C4×C59—21no—
272C2×C4×C59—21no—
273C2×C4×C59—21no—
274C2×C4×C59—21no—
275C2×C4×C59—41no—
276C2×C4×C59—41no—
277C2×C4×C59—41no—
278C2×C4×C59—41no—
279C2×C4×C59—41no—
280C2×C4×C59—41no—
281C2×C4×C59—41no—
282C2×C4×C59—41no—
283C2×C4×C59—84no—
284C2×C4×C59C4×D412yes—
285C2×C4×C59#12112yes—
286C2×C4×C59#12112yes—
287C2×C4×C59C23×C411yescharacteristic
288C2×C4×C59C22×D411yescharacteristic
289C2×C4×C59C2×#4111yescharacteristic
290C2×C4×C59C2×#4111yescharacteristic
291C2×C4×C59C2×#4111yescharacteristic
292C2×C4×C59C2×#4111yescharacteristic
293C22⋊D59—84no—
294C2×Dic59—22no—
295C2×Dic59—41no—
296C2×Dic59—41no—
297C2×Dic59—41no—
298C2×Dic59—41no—
299C2×Dic59—41no—
300C2×Dic59—41no—
301C2×Dic59—41no—
302C2×Dic59—41no—
303D236—22no—
304D236—22no—
305D236—41no—
306D236—41no—
307C4×D59—84no—
308C59⋊C8—22no—
309C59⋊C8—22no—
310C59⋊C8—22no—
311C59⋊C8C4×D414yes—
312#21536—591nomaximal, Sylow
313C22×C59—22no—
314C22×C59—22no—
315C22×C59—22no—
316C22×C59—41no—
317C22×C59—41no—
318C22×C59—41no—
319C22×C59—41no—
320C22×C59—42no—
321C22×C59—42no—
322C22×C59—42no—
323C22×C59—81no—
324C22×C59—81no—
325C22×C59—81no—
326C22×C59—81no—
327C22×C59C2×C4×D411yescharacteristic
328C22×C59C2×#12111yescharacteristic
329C22×C59#53211yescharacteristic
330C22×C59#57611yescharacteristic
331C22×C59#57611yescharacteristic
332C22×C59#57711yescharacteristic
333C22×C59#57711yescharacteristic
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—22no—
343C4×C59—22no—
344C4×C59—42no—
345C4×C59—41no—
346C4×C59—41no—
347C4×C59—81no—
348C4×C59—81no—
349C4×C59C2×C4×D411yescharacteristic
350C4×C59C4×#4111yescharacteristic
351C4×C59#52511yescharacteristic
352C4×C59#52911yescharacteristic
353Dic59—42no—
354Dic59—81no—
355Dic59—81no—
356C2×#469—591no—
357C2×C4×D8—591no—
358C2×#405—591no—
359#2324—591no—
360#2324D5911yescharacteristic, complemented
361#1972—591no—
362#1944—591no—
363#1934—591no—
364#1934—591no—
365#1893—591no—
366#1893—591no—
367#1809—591no—
368C4×#106—591no—
369#1762—591no—
370#1762—591no—
371C2×C59—42no—
372C2×C59—82no—
373C2×C59C4×#12111yescharacteristic
374C2×C59#294611yescharacteristic
375C2×C59#294611yescharacteristic
376C2×C59#305811yescharacteristic
377C2×C59#306011yescharacteristic
378C2×C59#317911yescharacteristic
379C2×C59#317911yescharacteristic
380D59—82no—
381C22×D8—591no—
382C22×M16—591no—
383C23×C8—591no—
384C2×#121—591no—
385C2×#121C2×D5911yescharacteristic
386C2×C4×D4—591no—
387C2×C4×D4C2×D5911yescharacteristic
388C2×#117C2×D5911yescharacteristic
389#469—598no—
390C4×D8—1184no—
391C2×#107—591no—
392C2×#106—591no—
393C2×#106—591no—
394C2×#102—591no—
395C2×#102—591no—
396C2×#102—591no—
397C2×#102—591no—
398C2×#102—591no—
399C2×#102—591no—
400#405—1184no—
401C2×#97—591no—
402C2×#97—591no—
403C2×C4×C8—591no—
404C2×C4×C8—591no—
405#390—21no—
406#390—591no—
407#390—1181no—
408#390C2×D5911yescharacteristic
409#389—591no—
410#389C2×D5911yescharacteristic
411#388—21no—
412#388—1181no—
413#386—21no—
414#386—1181no—
415#385—21no—
416#385—1181no—
417#380—591no—
418#380C2×D5911yescharacteristic
419C4×C4⋊C4—591no—
420C4×C4⋊C4C2×D5911yescharacteristic
421#340—591no—
422#340—591no—
423#340—591no—
424#340—591no—
425#340—591no—
426#340—591no—
427C59#2153611yescharacteristic, complemented, Sylow
428C22×D4—21no—
429C22×D4—591no—
430C22×D4—1181no—
431C22×D4C22×D5911yescharacteristic
432C23×C4—21no—
433C23×C4—1181no—
434C23×C4C22×D5911yescharacteristic
435C2×D8—594no—
436C2×D8—1182no—
437C2×D8—1182no—
438C2×M16—594no—
439C2×M16—1182no—
440C2×M16—1182no—
441C22×C8—591no—
442C22×C8—591no—
443C22×C8—591no—
444C22×C8—591no—
445C22×C8—1182no—
446C22×C8—1182no—
447C22×C8—1182no—
448#121—22no—
449#121—594no—
450#121—1182no—
451#121C4×D5914yescomplemented
452C4×D4—22no—
453C4×D4—22no—
454C4×D4—1182no—
455C4×D4—1182no—
456#117—22no—
457#117—22no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—591no—
460C2×C4⋊C4—591no—
461C2×C4⋊C4—591no—
462C2×C4⋊C4—1181no—
463C2×C4⋊C4C22⋊D5911yescharacteristic
464C2×C4⋊C4C22⋊D5911yescharacteristic
465C2×C4⋊C4C22×D5911yescharacteristic
466C2×C4⋊C4C22×D5911yescharacteristic
467C2×C4⋊C4C22×D5911yescharacteristic
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—1181no—
474C2×C22⋊C4—1181no—
475C2×C22⋊C4—1181no—
476C2×C22⋊C4—1181no—
477C2×C22⋊C4—1181no—
478C2×C22⋊C4C22⋊D5911yescharacteristic
479C2×C22⋊C4C22⋊D5911yescharacteristic
480C2×C42—21no—
481C2×C42—1181no—
482C2×C42C22×D5911yescharacteristic
483C2×C42C22×D5911yescharacteristic
484#107—1182no—
485#106—594no—
486#106—1182no—
487#102—594no—
488#102—594no—
489#102—1182no—
490#102—1182no—
491#102—1182no—
492#102—1182no—
493#97—1182no—
494#97—1182no—
495C4×C8—594no—
496C4×C8—1182no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95—1181no—
501#95—1181no—
502#95—1181no—
503C24—21no—
504C24—1181no—
505C24C2×C22⋊D5911yescharacteristic
506C2×D4—24no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—81no—
513C2×D4—81no—
514C2×D4—592no—
515C2×D4—1184no—
516C2×D4—1181no—
517C2×D4—1181no—
518C2×D4—1181no—
519C2×D4—1181no—
520C2×D4—1181no—
521C2×D4—4721no—
522C2×D4—4721no—
523C2×D4C2×C4×D5912yes—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—42no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4—1181no—
535C22×C4—1181no—
536C22×C4—1181no—
537C22×C4—4721no—
538C22×C4—4721no—
539C22×C4—2362no—
540C22×C4C2×C4×D5912yes—
541C22×C4#1174568512yes—
542C22×C4C2×C22⋊D5911yescharacteristic
543C22×C4C2×C22⋊D5911yescharacteristic
544C22×C4C2×C22⋊D5911yescharacteristic
545C22×C4C2×C22⋊D5911yescharacteristic
546C22×C4C2×C22⋊D5911yescharacteristic
547C22×C4C23×D5911yescharacteristic
548D8—1188no—
549M16—1188no—
550C2×C8—592no—
551C2×C8—592no—
552C2×C8—592no—
553C2×C8—592no—
554C2×C8—592no—
555C2×C8—592no—
556C2×C8—1188no—
557C2×C8—1181no—
558C2×C8—1181no—
559C2×C8—1181no—
560C2×C8—1181no—
561C2×C8—1181no—
562C2×C8—1181no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—81no—
571C4⋊C4—592no—
572C4⋊C4—1181no—
573C4⋊C4—1181no—
574C4⋊C4—1181no—
575C4⋊C4—1181no—
576C4⋊C4—1181no—
577C4⋊C4—4721no—
578C4⋊C4C2×C4×D5912yes—
579C22⋊C4—24no—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—42no—
583C22⋊C4—81no—
584C22⋊C4—81no—
585C22⋊C4—81no—
586C22⋊C4—1184no—
587C22⋊C4—4721no—
588C22⋊C4—4721no—
589C22⋊C4—4721no—
590C22⋊C4—2362no—
591C42—21no—
592C42—21no—
593C42—81no—
594C42—4721no—
595C42D4×D5912yes—
596C42#1174568712yes—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—22no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—1182no—
611C23—2361no—
612C23—2361no—
613C23—2361no—
614C23—2361no—
615C23—2361no—
616C23—2361no—
617C23C4×C22⋊D5912yes—
618C23C22×C22⋊D5911yescharacteristic
619D4—22no—
620D4—22no—
621D4—41no—
622D4—41no—
623D4—84no—
624D4—1182no—
625D4—1182no—
626D4—4724no—
627D4—2361no—
628D4—2361no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—84no—
655C2×C4—1182no—
656C2×C4—4724no—
657C2×C4—2361no—
658C2×C4—2361no—
659C2×C4—2361no—
660C2×C4—2361no—
661C2×C4—2361no—
662C2×C4—2361no—
663C2×C4—2361no—
664C2×C4—2361no—
665C2×C4C4×C22⋊D5912yes—
666C2×C4#1427369912yes—
667C2×C4#1427369912yes—
668C2×C4C22×C4×D5911yescharacteristic
669C2×C4C2×D4×D5911yescharacteristic
670C2×C4#41×D5911yescharacteristic
671C2×C4#41×D5911yescharacteristic
672C2×C4C2×#1174568711yescharacteristic
673C2×C4C2×#1174568511yescharacteristic
674C8—594no—
675C8—1182no—
676C8—1182no—
677C8—1182no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—42no—
686C22—42no—
687C22—42no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—4721no—
693C22—4721no—
694C22—4721no—
695C22—4721no—
696C22—2362no—
697C22—2362no—
698C22—2362no—
699C22C2×C4×C22⋊D5911yescharacteristic
700C22C2×#1427369911yescharacteristic
701C22#1683794811yescharacteristic
702C22#1683820511yescharacteristic
703C22#1683820511yescharacteristic
704C22#1683821011yescharacteristic
705C22#1683821311yescharacteristic
706C4—22no—
707C4—22no—
708C4—22no—
709C4—42no—
710C4—41no—
711C4—41no—
712C4—81no—
713C4—81no—
714C4—4721no—
715C4—4721no—
716C4—2362no—
717C4C4×D4×D5911yescharacteristic
718C4C4×#1174568711yescharacteristic
719C4#1683791111yescharacteristic
720C4#1683793211yescharacteristic
721C2—42no—
722C2—82no—
723C2—4722no—
724C2C4×#1427369911yescharacteristic
725C2#2143292411yescharacteristic
726C2#2143292811yescharacteristic
727C2#2143374111yescharacteristic
728C2#2143375511yescharacteristic
729C2#2143477311yescharacteristic
730C2#2143478111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2324C2
socleC23×C59C22×D4
prime radicalC2×#16837653C2
cosocleC22×C4×C59C24
hypercenter#2324D59
hypocenterC59#21536
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2324

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11745669C2semidirect
3. C2×#16837358C2semidirect
4. #21426789C2semidirect
5. #21424971C2semidirect
6. #21424836C2semidirect
7. #21424782C2semidirect
8. #21424778C2semidirect
9. #21424525C2semidirect
10. #21424522C2semidirect
11. #21424127C2semidirect
12. C4×#14273658C2semidirect
13. #21423924C2semidirect
14. #21423921C2semidirect
15. C59×#2324C2semidirect
21. #16837653C4semidirect
70. C2×#11745664C2×C4semidirect
79. #14273701C2×C4semidirect
94. #14273658C2×C4semidirect
97. #14273648C2×C4semidirect
100. #14273647C2×C4semidirect
104. C4×C59⋊C8D4semidirect
113. #121×C59C2×C4semidirect
360. #2324D59semidirect
427. C59#21536semidirect
451. #121C4×D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168376532
C2×C4×#117456692
C2×#168373582
#214267892
#214249712
#214248362
#214247822
#214247782
#214245252
#214245222
#214241272
C4×#142736582
#214239242
#214239212
C59×#23242
#2153659