Finite Group Databasebeta

← #28600039

Subgroups — #28600039

Order 15104.

968 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837562C211yesmaximal, characteristic
2#21426684C211yesmaximal, characteristic
3#21424980C211yesmaximal, characteristic, complemented
4#21424956C211yesmaximal, characteristic, complemented
5#21424785C211yesmaximal, characteristic, complemented
6#21424778C211yesmaximal, characteristic, complemented
7#21424737C211yesmaximal, characteristic, complemented
8#21424716C211yesmaximal, characteristic, complemented
9#21424451C211yesmaximal, characteristic, complemented
10#21424437C211yesmaximal, characteristic, complemented
11#21424404C211yesmaximal, characteristic, complemented
12#21424283C211yesmaximal, characteristic, complemented
13#21424034C211yesmaximal, characteristic
14#21423862C211yesmaximal, characteristic, complemented
15C59×#2323C211yesmaximal, characteristic, complemented
16C22×#11745685C2211yescharacteristic
17C22×#11745672C2211yescharacteristic
18C22×#11745671C2211yescharacteristic
19C22×C4⋊Dic59C2211yescharacteristic
20#16837562C418yescomplemented
21C2×#14273660C2211yescharacteristic
22C2×#14273660C2211yescharacteristic
23C2×#14273651C2211yescharacteristic
24C2×#14273651C2211yescharacteristic
25C2×#14273650C2211yescharacteristic
26C2×#14273650C2211yescharacteristic
27C2×#14273650C2211yescharacteristic
28C2×#14273647C2211yescharacteristic
29C2×#14273647C2211yescharacteristic
30C2×#14273647C2211yescharacteristic
31C2×C22⋊(C59⋊C8)C2211yescharacteristic
32C2×C22⋊(C59⋊C8)C2211yescharacteristic
33C2×#14273638C2211yescharacteristic
34C2×C4×C59⋊C8C2211yescharacteristic
35#16837308C2211yescharacteristic
36#16837308C2211yescharacteristic
37#16837304C2211yescharacteristic
38#16837304C2211yescharacteristic
39#16837279—21no—
40#16837279—21no—
41#16837259—21no—
42#16837259—21no—
43#16837164C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837157C2211yescharacteristic
48#16837157C2211yescharacteristic
49C2×C22⋊Q8×C59C2211yescharacteristic
50C2×C4×Q8×C59C2211yescharacteristic
51C2×#117×C59C2211yescharacteristic
52C59×#391C2211yescharacteristic
53C59×#389—21no—
54C59×#389C2211yescharacteristic
55C59×#388—21no—
56C59×#388—21no—
57C59×#387—21no—
58C59×#380C2211yescharacteristic
59C4×C4⋊C4×C59C2211yescharacteristic
60C2×#11745685—22no—
61C2×#11745685—41no—
62C2×#11745685—41no—
63C2×#11745685—41no—
64C2×#11745685—41no—
65C2×#11745685C2×C414yes—
66C22×Dic118C2311yescharacteristic
67C22×D236C2311yescharacteristic
68C22×C22⋊D59—21no—
69C23×Dic59—21no—
70C22×C4×D59—21no—
71C2×#11745672—41no—
72C2×#11745672—41no—
73C2×#11745672C2×C414yescomplemented
74C2×#11745671—41no—
75C2×#11745671—41no—
76C2×#11745671C2×C414yescomplemented
77C22×C59⋊C8C2311yescharacteristic
78C22×C59⋊C8C2311yescharacteristic
79C22×C59⋊C8C2311yescharacteristic
80C22×C59⋊C8C2311yescharacteristic
81C2×C4⋊Dic59—21no—
82C2×C4⋊Dic59—41no—
83C2×C4⋊Dic59—41no—
84C2×C4⋊Dic59C2311yescharacteristic
85C2×C4⋊Dic59C2311yescharacteristic
86C2×(C2×D59)⋊C4—21no—
87C2×(C2×D59)⋊C4—21no—
88C2×(C2×D59)⋊C4—21no—
89C2×(C2×D59)⋊C4—21no—
90#14273660—41no—
91#14273660—41no—
92#14273651—41no—
93#14273651—41no—
94#14273650—41no—
95#14273650—41no—
96#14273650C2×C414yescomplemented
97#14273647—41no—
98#14273647—41no—
99#14273647C2×C414yescomplemented
100C22⋊(C59⋊C8)—22no—
101C22⋊(C59⋊C8)C2×C414yes—
102#14273638—41no—
103C4×C59⋊C8—41no—
104C59⋊#95—21no—
105C59⋊#95—21no—
106C59⋊#95—21no—
107C59⋊#95—21no—
108C22×Q8×C59C2311yescharacteristic
109C23×C4×C59C2311yescharacteristic
110C22⋊Q8×C59—22no—
111C22⋊Q8×C59C2×C414yes—
112C4×Q8×C59—41no—
113C4×Q8×C59—41no—
114#117×C59—41no—
115#117×C59—41no—
116C2×C4⋊C4×C59—21no—
117C2×C4⋊C4×C59—21no—
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×C59D411yescharacteristic
127C2×C22⋊C4×C59D411yescharacteristic
128C2×C42×C59—21no—
129C2×C42×C59—21no—
130C2×C42×C59C2311yescharacteristic
131C2×C42×C59C2311yescharacteristic
132#95×C59—21no—
133#95×C59—21no—
134#95×C59—21no—
135#95×C59—21no—
136#95×C59—21no—
137C24×C59C2×D411yescharacteristic
138C23×D59—21no—
139C2×Q8×C59—21no—
140C2×Q8×C59—21no—
141C2×Q8×C59—21no—
142C2×Q8×C59—21no—
143C2×Q8×C59—21no—
144C2×Q8×C59C22×C412yes—
145C22×C4×C59—21no—
146C22×C4×C59—21no—
147C22×C4×C59—21no—
148C22×C4×C59—21no—
149C22×C4×C59—21no—
150C22×C4×C59—21no—
151C22×C4×C59—21no—
152C22×C4×C59—21no—
153C22×C4×C59C22×C412yes—
154C22×C4×C59C2×D411yescharacteristic
155C22×C4×C59C2×D411yescharacteristic
156C22×C4×C59C2×D411yescharacteristic
157C22×C4×C59C2×D411yescharacteristic
158C22×C4×C59C2×D411yescharacteristic
159C22×C4×C59#4112yes—
160C22×C4×C59C2411yescharacteristic
161C2×C22⋊D59—24no—
162C2×C22⋊D59—42no—
163C2×C22⋊D59—42no—
164C22×Dic59—21no—
165C22×Dic59—21no—
166C22×Dic59—21no—
167C22×Dic59—42no—
168C22×Dic59—81no—
169C22×Dic59—81no—
170#11745685—44no—
171#11745685—44no—
172#11745685—44no—
173#11745685—44no—
174C2×D236—21no—
175C2×D236—21no—
176C2×D236—21no—
177C2×D236—21no—
178C2×D236—21no—
179C2×D236C22×C412yes—
180C2×C4×D59—24no—
181C2×C4×D59—42no—
182C2×C4×D59—42no—
183C2×Dic118—21no—
184C2×Dic118—21no—
185C2×Dic118—21no—
186C2×Dic118—21no—
187C2×Dic118—21no—
188C2×Dic118C22×C412yes—
189C4⋊C4×C59—24no—
190C4⋊C4×C59—21no—
191C4⋊C4×C59—21no—
192C4⋊C4×C59—21no—
193C4⋊C4×C59—21no—
194C4⋊C4×C59—21no—
195C4⋊C4×C59—41no—
196C4⋊C4×C59—41no—
197C4⋊C4×C59—42no—
198C4⋊C4×C59—81no—
199C4⋊C4×C59C22×C412yes—
200C22⋊C4×C59—24no—
201C22⋊C4×C59—41no—
202C22⋊C4×C59—41no—
203C22⋊C4×C59—81no—
204C42×C59—21no—
205C42×C59—21no—
206C42×C59—21no—
207C42×C59—21no—
208C42×C59—42no—
209C42×C59—81no—
210#11745672—44no—
211#11745671—44no—
212(C2×D59)⋊C4—81no—
213(C2×D59)⋊C4—81no—
214(C2×D59)⋊C4—81no—
215(C2×D59)⋊C4—81no—
216C4⋊Dic59—21no—
217C4⋊Dic59—21no—
218C4⋊Dic59—21no—
219C4⋊Dic59—21no—
220C4⋊Dic59—42no—
221C2×C59⋊C8—21no—
222C2×C59⋊C8—21no—
223C2×C59⋊C8—21no—
224C2×C59⋊C8—21no—
225C2×C59⋊C8—21no—
226C2×C59⋊C8—21no—
227C2×C59⋊C8—21no—
228C2×C59⋊C8—21no—
229C2×C59⋊C8—21no—
230C2×C59⋊C8—21no—
231C2×C59⋊C8C22×C412yes—
232C2×C59⋊C8C22×C412yes—
233C23×C59—21no—
234C23×C59—21no—
235C23×C59—21no—
236C23×C59—21no—
237C23×C59—21no—
238C23×C59—21no—
239C23×C59C4×D412yes—
240C23×C59C22×D411yescharacteristic
241C22×D59—22no—
242C22×D59—41no—
243C22×D59—41no—
244C22×D59—41no—
245C22×D59—41no—
246C22×D59—41no—
247C22×D59—41no—
248Q8×C59—22no—
249Q8×C59—22no—
250Q8×C59—41no—
251Q8×C59—41no—
252C2×C4×C59—21no—
253C2×C4×C59—21no—
254C2×C4×C59—22no—
255C2×C4×C59—22no—
256C2×C4×C59—22no—
257C2×C4×C59—22no—
258C2×C4×C59—22no—
259C2×C4×C59—22no—
260C2×C4×C59—21no—
261C2×C4×C59—21no—
262C2×C4×C59—21no—
263C2×C4×C59—21no—
264C2×C4×C59—21no—
265C2×C4×C59—21no—
266C2×C4×C59—21no—
267C2×C4×C59—21no—
268C2×C4×C59—21no—
269C2×C4×C59—21no—
270C2×C4×C59—21no—
271C2×C4×C59—21no—
272C2×C4×C59—41no—
273C2×C4×C59—41no—
274C2×C4×C59—41no—
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×C59C4×D412yes—
283C2×C4×C59C23×C411yescharacteristic
284C2×C4×C59C2×#4111yescharacteristic
285C2×C4×C59H(5,𝔽2)11yescharacteristic
286C2×C4×C59H(5,𝔽2)11yescharacteristic
287C2×C4×C59H(5,𝔽2)11yescharacteristic
288C2×C4×C59H(5,𝔽2)11yescharacteristic
289C22⋊D59—48no—
290C2×Dic59—22no—
291C2×Dic59—41no—
292C2×Dic59—41no—
293C2×Dic59—41no—
294C2×Dic59—41no—
295C2×Dic59—41no—
296C2×Dic59—41no—
297C2×Dic59—41no—
298C2×Dic59—41no—
299C2×Dic59—84no—
300D236—22no—
301D236—22no—
302D236—41no—
303D236—41no—
304C4×D59—48no—
305Dic118—22no—
306Dic118—22no—
307Dic118—41no—
308Dic118—41no—
309C59⋊C8—22no—
310C59⋊C8—22no—
311C59⋊C8—41no—
312C59⋊C8—41no—
313#22057—591nomaximal, Sylow
314C22×C59—22no—
315C22×C59—22no—
316C22×C59—22no—
317C22×C59—41no—
318C22×C59—41no—
319C22×C59—41no—
320C22×C59—41no—
321C22×C59C2×C4×D411yescharacteristic
322C22×C59#53411yescharacteristic
323C22×C59#53511yescharacteristic
324C22×C59#57611yescharacteristic
325C22×C59#57711yescharacteristic
326C22×C59#57811yescharacteristic
327C22×C59#57811yescharacteristic
328C2×D59—42no—
329C2×D59—42no—
330C2×D59—42no—
331C2×D59—81no—
332C2×D59—81no—
333C2×D59—81no—
334C2×D59—81no—
335C4×C59—22no—
336C4×C59—42no—
337C4×C59—41no—
338C4×C59—41no—
339C4×C59—41no—
340C4×C59—41no—
341C4×C59—42no—
342C4×C59—81no—
343C4×C59—81no—
344C4×C59#51811yescharacteristic
345C4×C59#51811yescharacteristic
346C4×C59#53811yescharacteristic
347C4×C59#53811yescharacteristic
348Dic59—42no—
349Dic59—81no—
350Dic59—81no—
351C2×#452—591no—
352#2323D5911yescharacteristic, complemented
353#2311—591no—
354#1973—591no—
355#1969—591no—
356#1935—591no—
357#1934—591no—
358#1928—591no—
359#1925—591no—
360#1880—591no—
361#1878—591no—
362#1872—591no—
363#1852—591no—
364#1788—591no—
365#1750—591no—
366C2×C59—42no—
367C2×C59#232111yescharacteristic
368C2×C59#294711yescharacteristic
369C2×C59#295111yescharacteristic
370C2×C59#320111yescharacteristic
371C2×C59#320311yescharacteristic
372C2×C59#322311yescharacteristic
373C2×C59#322411yescharacteristic
374D59—82no—
375C22×#41—591no—
376C22×Q16—591no—
377C22×SD16—591no—
378C2×C22⋊Q8C2×D5911yescharacteristic
379C2×C4×Q8C2×D5911yescharacteristic
380C2×#117C2×D5911yescharacteristic
381C22×C4⋊C4—591no—
382#452—598no—
383C2×#107—591no—
384C2×#107—591no—
385C2×#103—591no—
386C2×#103—591no—
387C2×#103—591no—
388C2×#103—591no—
389C2×#103—591no—
390C2×#102—591no—
391C2×#102—591no—
392C2×#102—591no—
393C2×C22⋊C8—591no—
394C2×C22⋊C8—591no—
395C2×#97—591no—
396C2×C4×C8—591no—
397#391—591no—
398#391—591no—
399#391C2×D5911yescharacteristic
400#390—591no—
401#390—591no—
402#389—21no—
403#389C2×D5911yescharacteristic
404#388—21no—
405#388—21no—
406#387—21no—
407#386—1181no—
408#386—1181no—
409#380—1181no—
410#380—1181no—
411#380C2×D5911yescharacteristic
412C4×C4⋊C4C2×D5911yescharacteristic
413#340—591no—
414#340—591no—
415#340—591no—
416#340—591no—
417#336—591no—
418#336—591no—
419C59#2205711yescharacteristic, complemented, Sylow
420C2×#41—594no—
421C2×#41—1182no—
422C2×#41—2361no—
423C2×#41—2361no—
424C2×#41—2361no—
425C2×#41—2361no—
426C22×Q8—591no—
427C22×Q8C22×D5911yescharacteristic
428C22×D4—591no—
429C22×D4—1181no—
430C23×C4—1181no—
431C23×C4—1181no—
432C23×C4C22×D5911yescharacteristic
433C2×Q16—594no—
434C2×Q16—2361no—
435C2×Q16—2361no—
436C2×SD16—594no—
437C2×SD16—2361no—
438C2×SD16—2361no—
439C22×C8—591no—
440C22×C8—591no—
441C22×C8—591no—
442C22×C8—591no—
443C22⋊Q8—22no—
444C22⋊Q8C4×D5914yes—
445C4×Q8—41no—
446C4×Q8—41no—
447#117—41no—
448#117—41no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—591no—
453C2×C4⋊C4—591no—
454C2×C4⋊C4—1181no—
455C2×C4⋊C4—2361no—
456C2×C4⋊C4—2361no—
457C2×C4⋊C4C22⋊D5911yescharacteristic
458C2×C4⋊C4C22⋊D5911yescharacteristic
459C2×C4⋊C4C22×D5911yescharacteristic
460C2×C4⋊C4C22×D5911yescharacteristic
461C2×C4⋊C4C22×D5911yescharacteristic
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—1181no—
465C2×C22⋊C4—1181no—
466C2×C22⋊C4—1181no—
467C2×C22⋊C4—1181no—
468C2×C22⋊C4C22⋊D5911yescharacteristic
469C2×C22⋊C4C22⋊D5911yescharacteristic
470C2×C42—21no—
471C2×C42—21no—
472C2×C42C22×D5911yescharacteristic
473C2×C42C22×D5911yescharacteristic
474#107—2361no—
475#107—2361no—
476#103—594no—
477#103—2361no—
478#103—2361no—
479#103—2361no—
480#103—2361no—
481#102—594no—
482#102—2361no—
483#102—2361no—
484C22⋊C8—594no—
485C22⋊C8—1182no—
486#97—2361no—
487C4×C8—2361no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—1181no—
494#95—1181no—
495#95—1181no—
496#95—1181no—
497C24—1181no—
498C24C2×C22⋊D5911yescharacteristic
499#41—2364no—
500#41—2364no—
501#41—2364no—
502#41—2364no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—592no—
509C2×Q8—1181no—
510C2×Q8—1181no—
511C2×Q8—1181no—
512C2×Q8—1181no—
513C2×Q8—1181no—
514C2×Q8C2×C4×D5912yes—
515C2×D4—592no—
516C2×D4—1184no—
517C2×D4—1181no—
518C2×D4—1181no—
519C2×D4—1181no—
520C2×D4—1181no—
521C2×D4—1181no—
522C2×D4—2362no—
523C2×D4—2362no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—1181no—
533C22×C4—1184no—
534C22×C4—1181no—
535C22×C4—1181no—
536C22×C4—4721no—
537C22×C4—4721no—
538C22×C4—2362no—
539C22×C4—2362no—
540C22×C4—2362no—
541C22×C4C2×C4×D5912yes—
542C22×C4#1174568512yes—
543C22×C4C2×C22⋊D5911yescharacteristic
544C22×C4C2×C22⋊D5911yescharacteristic
545C22×C4C2×C22⋊D5911yescharacteristic
546C22×C4C2×C22⋊D5911yescharacteristic
547C22×C4C2×C22⋊D5911yescharacteristic
548C22×C4C23×D5911yescharacteristic
549Q16—2364no—
550SD16—2364no—
551C2×C8—592no—
552C2×C8—592no—
553C2×C8—1181no—
554C2×C8—1181no—
555C2×C8—1181no—
556C2×C8—1181no—
557C2×C8—1181no—
558C2×C8—1181no—
559C2×C8—1181no—
560C2×C8—1181no—
561C2×C8—1181no—
562C2×C8—1181no—
563C4⋊C4—24no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—41no—
570C4⋊C4—41no—
571C4⋊C4—42no—
572C4⋊C4—81no—
573C4⋊C4—1181no—
574C4⋊C4—1181no—
575C4⋊C4—1181no—
576C4⋊C4—1181no—
577C4⋊C4—2362no—
578C4⋊C4C2×C4×D5912yes—
579C22⋊C4—24no—
580C22⋊C4—41no—
581C22⋊C4—41no—
582C22⋊C4—81no—
583C22⋊C4—4721no—
584C22⋊C4—4721no—
585C22⋊C4—4721no—
586C22⋊C4—4721no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—42no—
592C42—81no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—1182no—
600C23—2361no—
601C23—2361no—
602C23—2361no—
603C23—2361no—
604C23—2361no—
605C23—2361no—
606C23C4×C22⋊D5912yes—
607C23C22×C22⋊D5911yescharacteristic
608Q8—22no—
609Q8—22no—
610Q8—41no—
611Q8—41no—
612Q8—1182no—
613Q8—1182no—
614Q8—2361no—
615Q8—2361no—
616D4—1182no—
617D4—1182no—
618D4—2368no—
619D4—2361no—
620D4—2361no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—1182no—
652C2×C4—4724no—
653C2×C4—2368no—
654C2×C4—2361no—
655C2×C4—2361no—
656C2×C4—2361no—
657C2×C4—2361no—
658C2×C4—2361no—
659C2×C4—2361no—
660C2×C4—2361no—
661C2×C4—2361no—
662C2×C4C4×C22⋊D5912yes—
663C2×C4C22×C4×D5911yescharacteristic
664C2×C4C2×#1174568511yescharacteristic
665C2×C4#1427377211yescharacteristic
666C2×C4#1427377211yescharacteristic
667C2×C4#1427377311yescharacteristic
668C2×C4#1427377311yescharacteristic
669C8—1182no—
670C8—1182no—
671C8—2361no—
672C8—2361no—
673C22—22no—
674C22—22no—
675C22—22no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—4721no—
681C22—4721no—
682C22—4721no—
683C22—4721no—
684C22—2362no—
685C22—2362no—
686C22—2362no—
687C22C2×C4×C22⋊D5911yescharacteristic
688C22#1683796111yescharacteristic
689C22#1683796611yescharacteristic
690C22#1683820511yescharacteristic
691C22#1683821011yescharacteristic
692C22#1683821711yescharacteristic
693C22#1683821711yescharacteristic
694C4—22no—
695C4—42no—
696C4—41no—
697C4—41no—
698C4—41no—
699C4—41no—
700C4—42no—
701C4—81no—
702C4—81no—
703C4—4721no—
704C4—4721no—
705C4—2362no—
706C4#1683787411yescharacteristic
707C4#1683787411yescharacteristic
708C4#1683798511yescharacteristic
709C4#1683798511yescharacteristic
710C2—42no—
711C2—4722no—
712C2#2142675011yescharacteristic
713C2#2143293911yescharacteristic
714C2#2143296911yescharacteristic
715C2#2143497811yescharacteristic
716C2#2143499311yescharacteristic
717C2#2143517311yescharacteristic
718C2#2143518411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2323C2
socleC23×C59C22×D4
prime radicalC22×#11745685C22
cosocleC22×C4×C59C24
hypercenter#2323D59
hypocenterC59#22057
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2323

Complements

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

NH ≅ G/Ntype
3. #21424980C2semidirect
4. #21424956C2semidirect
5. #21424785C2semidirect
6. #21424778C2semidirect
7. #21424737C2semidirect
8. #21424716C2semidirect
9. #21424451C2semidirect
10. #21424437C2semidirect
11. #21424404C2semidirect
12. #21424283C2semidirect
14. #21423862C2semidirect
15. C59×#2323C2semidirect
20. #16837562C4semidirect
73. C2×#11745672C2×C4semidirect
76. C2×#11745671C2×C4semidirect
96. #14273650C2×C4semidirect
99. #14273647C2×C4semidirect
352. #2323D59semidirect
419. C59#22057semidirect

Maximal subgroups

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

subgroupindex
C2×#168375622
#214266842
#214249802
#214249562
#214247852
#214247782
#214247372
#214247162
#214244512
#214244372
#214244042
#214242832
#214240342
#214238622
C59×#23232
#2205759