Finite Group Databasebeta

← #28625157

Subgroups — #28625157

Order 15104.

1118 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837699C211yesmaximal, characteristic, complemented
2C2×C4×#11745669C211yesmaximal, characteristic
3#21429454C211yesmaximal, characteristic, complemented
4#21425431C211yesmaximal, characteristic, complemented
5#21425421C211yesmaximal, characteristic, complemented
6#21425239C211yesmaximal, characteristic, complemented
7#21425229C211yesmaximal, characteristic, complemented
8#21425062C211yesmaximal, characteristic, complemented
9#21425033C211yesmaximal, characteristic, complemented
10#21424444C211yesmaximal, characteristic
11#21424444C211yesmaximal, characteristic
12#21424357C211yesmaximal, characteristic, complemented
13#21424343C211yesmaximal, characteristic, complemented
14#21424106C211yesmaximal, characteristic, complemented
15C2×C59×#554C211yesmaximal, characteristic, complemented
16C22×#11745669C2211yescharacteristic
17C2×C4×D236C2211yescharacteristic
18#16837699—24no—
19C4×#11745669—24no—
20C2×#14273660C2211yescharacteristic
21C2×#14273660C2211yescharacteristic
22C2×#14273658C2211yescharacteristic
23C2×C4⋊(C59⋊C8)C2211yescharacteristic
24C2×#14273648C2211yescharacteristic
25C2×#14273648C2211yescharacteristic
26C2×#14273648C2211yescharacteristic
27C2×#14273647C2211yescharacteristic
28C2×#14273647C2211yescharacteristic
29C2×#14273647C2211yescharacteristic
30C2×C4×C59⋊C8C2211yescharacteristic
31#16837337—21no—
32#16837313—21no—
33#16837304C2211yescharacteristic
34#16837304C2211yescharacteristic
35#16837300C2211yescharacteristic
36#16837300C2211yescharacteristic
37#16837273—21no—
38#16837273—21no—
39#16837268C2211yescharacteristic
40#16837164C2211yescharacteristic
41#16837164C2211yescharacteristic
42#16837164C2211yescharacteristic
43#16837164C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837157C2211yescharacteristic
47#16837157C2211yescharacteristic
48#16837157C2211yescharacteristic
49#16837157C2211yescharacteristic
50C59×#554—24no—
51C59×#554—24no—
52C2×C4⋊Q8×C59C2211yescharacteristic
53C2×#125×C59C2211yescharacteristic
54C2×#125×C59C2211yescharacteristic
55C2×C22⋊Q8×C59—21no—
56C2×C22⋊Q8×C59—21no—
57C2×C22⋊Q8×C59—21no—
58C2×C4×Q8×C59C2211yescharacteristic
59C2×C4×D4×C59C2211yescharacteristic
60C2×C4×D4×C59C2211yescharacteristic
61C2×C4×D4×C59C2211yescharacteristic
62C22×C4⋊C4×C59—21no—
63C22×D236C2311yescharacteristic
64C22×C4×D59—21no—
65C2×#11745669—22no—
66C2×#11745669—22no—
67C2×#11745669Q814yescomplemented
68C22×C59⋊C8C2311yescharacteristic
69C22×C59⋊C8C2311yescharacteristic
70C22×C59⋊C8C2311yescharacteristic
71C22×C59⋊C8C2311yescharacteristic
72C4×D236—22no—
73C4×D236—22no—
74C2×C4⋊Dic59C2311yescharacteristic
75C2×C4⋊Dic59C2311yescharacteristic
76C2×C4⋊Dic59C2311yescharacteristic
77C2×Dic59⋊C4—21no—
78C2×Dic59⋊C4—21no—
79C2×(C2×D59)⋊C4—21no—
80C2×(C2×D59)⋊C4—21no—
81C2×(C2×D59)⋊C4—21no—
82C2×(C2×D59)⋊C4—21no—
83C2×(C2×D59)⋊C4—21no—
84#14273660—22no—
85#14273660—22no—
86#14273658—22no—
87C4⋊(C59⋊C8)—22no—
88#14273648—22no—
89#14273648—22no—
90#14273648—22no—
91#14273647—22no—
92#14273647—22no—
93#14273647—22no—
94C4×C59⋊C8—22no—
95C59⋊#95—21no—
96C59⋊#95—21no—
97C59⋊#95—21no—
98C59⋊#95—21no—
99C22×Q8×C59—21no—
100C22×Q8×C59D411yescharacteristic
101C22×D4×C59C2311yescharacteristic
102C23×C4×C59—21no—
103C23×C4×C59—21no—
104C23×C4×C59—21no—
105C4⋊Q8×C59—22no—
106C4⋊Q8×C59—22no—
107#125×C59—22no—
108#125×C59—22no—
109#125×C59—22no—
110#125×C59D414yes—
111C22⋊Q8×C59—28no—
112C22⋊Q8×C59—28no—
113C22⋊Q8×C59—28no—
114C4×Q8×C59—22no—
115C4×Q8×C59—22no—
116C4×D4×C59—22no—
117C4×D4×C59—22no—
118C4×D4×C59—22no—
119C4×D4×C59—22no—
120C4×D4×C59—22no—
121C4×D4×C59D414yes—
122C2×C4⋊C4×C59—28no—
123C2×C4⋊C4×C59—21no—
124C2×C4⋊C4×C59—21no—
125C2×C4⋊C4×C59—21no—
126C2×C4⋊C4×C59—21no—
127C2×C4⋊C4×C59—21no—
128C2×C4⋊C4×C59D411yescharacteristic
129C2×C4⋊C4×C59D411yescharacteristic
130C2×C4⋊C4×C59D411yescharacteristic
131C2×C4⋊C4×C59C2311yescharacteristic
132C2×C4⋊C4×C59C2311yescharacteristic
133C2×C4⋊C4×C59C2311yescharacteristic
134C2×C22⋊C4×C59—21no—
135C2×C22⋊C4×C59—21no—
136C2×C22⋊C4×C59—21no—
137C2×C42×C59C2311yescharacteristic
138C2×C42×C59C2311yescharacteristic
139C2×C42×C59C2311yescharacteristic
140C24×C59—21no—
141C23×D59—21no—
142C2×Q8×C59—24no—
143C2×Q8×C59—22no—
144C2×Q8×C59—22no—
145C2×Q8×C59—41no—
146C2×Q8×C59—81no—
147C2×Q8×C59—81no—
148C2×D4×C59—21no—
149C2×D4×C59—21no—
150C2×D4×C59—21no—
151C2×D4×C59C2×D412yes—
152C2×D4×C59C2×Q812yes—
153C2×D4×C59#4112yes—
154C22×C4×C59—24no—
155C22×C4×C59—21no—
156C22×C4×C59—21no—
157C22×C4×C59—21no—
158C22×C4×C59—24no—
159C22×C4×C59—24no—
160C22×C4×C59—42no—
161C22×C4×C59—42no—
162C22×C4×C59—81no—
163C22×C4×C59—81no—
164C22×C4×C59—81no—
165C22×C4×C59—81no—
166C22×C4×C59C2×D411yescharacteristic
167C22×C4×C59C2×D411yescharacteristic
168C22×C4×C59C2×D411yescharacteristic
169C22×C4×C59C2×D411yescharacteristic
170C22×C4×C59C2×D411yescharacteristic
171C22×C4×C59C2×D411yescharacteristic
172C22×C4×C59C2411yescharacteristic
173C22×Dic59—21no—
174C22×Dic59—21no—
175C22×Dic59—21no—
176C2×D236—21no—
177C2×D236—21no—
178C2×D236—21no—
179C2×D236—21no—
180C2×D236—21no—
181C2×D236C2×Q812yes—
182C2×C4×D59—42no—
183C2×C4×D59—81no—
184C2×C4×D59—81no—
185C4⋊C4×C59—24no—
186C4⋊C4×C59—24no—
187C4⋊C4×C59—24no—
188C4⋊C4×C59—22no—
189C4⋊C4×C59—24no—
190C4⋊C4×C59—24no—
191C4⋊C4×C59—22no—
192C4⋊C4×C59—22no—
193C4⋊C4×C59—21no—
194C4⋊C4×C59—21no—
195C4⋊C4×C59—21no—
196C4⋊C4×C59C2×D412yes—
197C4⋊C4×C59C2×D412yes—
198C4⋊C4×C59C2×D412yes—
199C22⋊C4×C59—24no—
200C22⋊C4×C59—24no—
201C22⋊C4×C59—24no—
202C42×C59—21no—
203C42×C59—21no—
204C42×C59—21no—
205C42×C59—21no—
206C42×C59C2×D412yes—
207C42×C59C2×D412yes—
208#11745669—28no—
209(C2×D59)⋊C4—42no—
210(C2×D59)⋊C4—42no—
211(C2×D59)⋊C4—42no—
212(C2×D59)⋊C4—81no—
213(C2×D59)⋊C4—81no—
214C4⋊Dic59—21no—
215C4⋊Dic59—21no—
216C4⋊Dic59—21no—
217C4⋊Dic59—21no—
218C4⋊Dic59—21no—
219C4⋊Dic59—21no—
220Dic59⋊C4—81no—
221Dic59⋊C4—81no—
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⋊C8—21no—
232C2×C59⋊C8—21no—
233C2×C59⋊C8C2×Q812yes—
234C23×C59—22no—
235C23×C59—22no—
236C23×C59—22no—
237C23×C59—41no—
238C23×C59—41no—
239C23×C59—41no—
240C23×C59—41no—
241C23×C59C22×D411yescharacteristic
242C22×D59—22no—
243C22×D59—41no—
244C22×D59—41no—
245C22×D59—41no—
246C22×D59—41no—
247C22×D59—41no—
248C22×D59—41no—
249Q8×C59—44no—
250Q8×C59—84no—
251D4×C59—22no—
252D4×C59—22no—
253D4×C59—22no—
254D4×C59C22⋊Q814yes—
255C2×C4×C59—21no—
256C2×C4×C59—21no—
257C2×C4×C59—21no—
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—21no—
268C2×C4×C59—21no—
269C2×C4×C59—21no—
270C2×C4×C59—21no—
271C2×C4×C59—21no—
272C2×C4×C59—21no—
273C2×C4×C59—48no—
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—84no—
281C2×C4×C59—84no—
282C2×C4×C59#12012yes—
283C2×C4×C59#12012yes—
284C2×C4×C59#13512yes—
285C2×C4×C59C22×D411yescharacteristic
286C2×C4×C59C22×D411yescharacteristic
287C2×C4×C59C22×Q811yescharacteristic
288C2×C4×C59C2×#4111yescharacteristic
289C2×C4×C592−1+411yescharacteristic
290C2×C4×C592−1+411yescharacteristic
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—41no—
300D236—22no—
301D236—22no—
302D236—41no—
303D236—41no—
304C4×D59—84no—
305C59⋊C8—22no—
306C59⋊C8—41no—
307C59⋊C8—41no—
308C59⋊C8—41no—
309#24335—591nomaximal, Sylow
310C22×C59—24no—
311C22×C59—42no—
312C22×C59—42no—
313C22×C59—42no—
314C22×C59—42no—
315C22×C59—42no—
316C22×C59—42no—
317C22×C59C2×#12011yescharacteristic
318C22×C59#54811yescharacteristic
319C22×C59D4×Q811yescharacteristic
320C22×C59C2×#13511yescharacteristic
321C22×C59#57511yescharacteristic
322C22×C59#57611yescharacteristic
323C22×C59#57611yescharacteristic
324C2×D59—42no—
325C2×D59—42no—
326C2×D59—42no—
327C2×D59—81no—
328C2×D59—81no—
329C2×D59—81no—
330C2×D59—81no—
331C4×C59—22no—
332C4×C59—22no—
333C4×C59—22no—
334C4×C59—41no—
335C4×C59—42no—
336C4×C59—41no—
337C4×C59—41no—
338C4×C59—42no—
339C4×C59—42no—
340C4×C59C2×C22⋊Q811yescharacteristic
341C4×C59#53611yescharacteristic
342C4×C59#54811yescharacteristic
343C4×C59D4×Q811yescharacteristic
344Dic59—81no—
345Dic59—81no—
346Dic59—81no—
347C2×#554D5911yescharacteristic, complemented
348C2×#478—591no—
349C2×C4×D8—591no—
350#2580—591no—
351#2059—591no—
352#2057—591no—
353#2025—591no—
354#2023—591no—
355#1991—591no—
356#1984—591no—
357#1879—591no—
358#1879—591no—
359#1864—591no—
360#1862—591no—
361#1804—591no—
362C2×C59—44no—
363C2×C59#240911yescharacteristic
364C2×C59#300211yescharacteristic
365C2×C59#300811yescharacteristic
366C2×C59#336111yescharacteristic
367C2×C59#337011yescharacteristic
368C2×C59#338011yescharacteristic
369C2×C59#338911yescharacteristic
370D59—82no—
371C22×D8—591no—
372#554—24no—
373#554—24no—
374C2×C4⋊Q8C2×D5911yescharacteristic
375C2×#125C2×D5911yescharacteristic
376C2×#125C2×D5911yescharacteristic
377C2×C22⋊Q8—21no—
378C2×C22⋊Q8—21no—
379C2×C22⋊Q8—21no—
380C2×C4×Q8C2×D5911yescharacteristic
381C2×C4×D4—591no—
382C2×C4×D4C2×D5911yescharacteristic
383C2×C4×D4C2×D5911yescharacteristic
384C2×C4×D4C2×D5911yescharacteristic
385C22×C4⋊C4—21no—
386#478—1184no—
387C4×D8—1184no—
388C2×#107—591no—
389C2×#107—591no—
390C2×#106—591no—
391C2×C4⋊C8—591no—
392C2×#102—591no—
393C2×#102—591no—
394C2×#102—591no—
395C2×#102—591no—
396C2×#102—591no—
397C2×#102—591no—
398C2×C4×C8—591no—
399#399—1181no—
400#393—1181no—
401#390—591no—
402#390—591no—
403#389—591no—
404#389—591no—
405#385—1181no—
406#385—1181no—
407#382—591no—
408#340—591no—
409#340—591no—
410#340—591no—
411#340—591no—
412#340—591no—
413#340—591no—
414#336—591no—
415#336—591no—
416#336—591no—
417#336—591no—
418C59#2433511yescharacteristic, complemented, Sylow
419C22×Q8—21no—
420C22×Q8C22⋊D5911yescharacteristic
421C22×D4—591no—
422C22×D4C22×D5911yescharacteristic
423C23×C4—21no—
424C23×C4—21no—
425C23×C4—21no—
426C23×C4—1181no—
427C2×D8—594no—
428C2×D8—1182no—
429C2×D8—1182no—
430C22×C8—591no—
431C22×C8—591no—
432C22×C8—591no—
433C22×C8—591no—
434C4⋊Q8—22no—
435C4⋊Q8—22no—
436#125—22no—
437#125—22no—
438#125—22no—
439#125C22⋊D5914yes—
440C22⋊Q8—28no—
441C22⋊Q8—28no—
442C22⋊Q8—28no—
443C4×Q8—22no—
444C4×Q8—22no—
445C4×D4—22no—
446C4×D4—22no—
447C4×D4—22no—
448C4×D4—22no—
449C4×D4—22no—
450C4×D4—1182no—
451C4×D4—1182no—
452C4×D4C22⋊D5914yes—
453C2×C4⋊C4—28no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—591no—
460C2×C4⋊C4—591no—
461C2×C4⋊C4—591no—
462C2×C4⋊C4—1181no—
463C2×C4⋊C4—1181no—
464C2×C4⋊C4C22⋊D5911yescharacteristic
465C2×C4⋊C4C22⋊D5911yescharacteristic
466C2×C4⋊C4C22⋊D5911yescharacteristic
467C2×C4⋊C4C22×D5911yescharacteristic
468C2×C4⋊C4C22×D5911yescharacteristic
469C2×C4⋊C4C22×D5911yescharacteristic
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×C42C22×D5911yescharacteristic
479C2×C42C22×D5911yescharacteristic
480C2×C42C22×D5911yescharacteristic
481#107—1182no—
482#107—1182no—
483#106—1182no—
484C4⋊C8—1182no—
485#102—1182no—
486#102—1182no—
487#102—1182no—
488#102—1182no—
489#102—1182no—
490#102—1182no—
491C4×C8—1182no—
492#95—1181no—
493#95—1181no—
494#95—1181no—
495#95—1181no—
496C24—21no—
497C24—1181no—
498C2×Q8—24no—
499C2×Q8—22no—
500C2×Q8—22no—
501C2×Q8—41no—
502C2×Q8—81no—
503C2×Q8—81no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—592no—
508C2×D4—1181no—
509C2×D4—1181no—
510C2×D4—1181no—
511C2×D4—1181no—
512C2×D4—1181no—
513C2×D4Q8×D5912yes—
514C2×D4#1174568912yes—
515C2×D4C2×C22⋊D5912yes—
516C22×C4—24no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—81no—
525C22×C4—81no—
526C22×C4—81no—
527C22×C4—81no—
528C22×C4—1181no—
529C22×C4—1181no—
530C22×C4—1181no—
531C22×C4—4721no—
532C22×C4—4721no—
533C22×C4—2362no—
534C22×C4C2×C22⋊D5911yescharacteristic
535C22×C4C2×C22⋊D5911yescharacteristic
536C22×C4C2×C22⋊D5911yescharacteristic
537C22×C4C2×C22⋊D5911yescharacteristic
538C22×C4C2×C22⋊D5911yescharacteristic
539C22×C4C2×C22⋊D5911yescharacteristic
540C22×C4C23×D5911yescharacteristic
541D8—1188no—
542C2×C8—592no—
543C2×C8—1181no—
544C2×C8—1181no—
545C2×C8—1181no—
546C2×C8—1181no—
547C2×C8—1181no—
548C2×C8—1181no—
549C2×C8—1181no—
550C2×C8—1181no—
551C2×C8—1181no—
552C2×C8—1181no—
553C2×C8—1181no—
554C4⋊C4—24no—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—22no—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—1181no—
566C4⋊C4—1181no—
567C4⋊C4—1181no—
568C4⋊C4—1181no—
569C4⋊C4—1181no—
570C4⋊C4—1181no—
571C4⋊C4—4721no—
572C4⋊C4—4721no—
573C4⋊C4C2×C22⋊D5912yes—
574C4⋊C4C2×C22⋊D5912yes—
575C4⋊C4C2×C22⋊D5912yes—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—24no—
579C22⋊C4—4721no—
580C22⋊C4—4721no—
581C22⋊C4—2362no—
582C22⋊C4—2362no—
583C22⋊C4—2362no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42C2×C22⋊D5912yes—
589C42C2×C22⋊D5912yes—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—1182no—
598C23—2361no—
599C23—2361no—
600C23—2361no—
601C23—2361no—
602C23—2361no—
603C23—2361no—
604C23C22×C22⋊D5911yescharacteristic
605Q8—44no—
606Q8—84no—
607D4—22no—
608D4—22no—
609D4—22no—
610D4—1182no—
611D4—1182no—
612D4—2361no—
613D4—2361no—
614D4#1427370314yes—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
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—48no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—84no—
641C2×C4—84no—
642C2×C4—4724no—
643C2×C4—2361no—
644C2×C4—2361no—
645C2×C4—2361no—
646C2×C4—2361no—
647C2×C4—2361no—
648C2×C4—2361no—
649C2×C4—2361no—
650C2×C4—2361no—
651C2×C4—2361no—
652C2×C4#1427369612yes—
653C2×C4#1427369612yes—
654C2×C4#1427374712yes—
655C2×C4C22×C22⋊D5911yescharacteristic
656C2×C4C22×C22⋊D5911yescharacteristic
657C2×C4C2×Q8×D5911yescharacteristic
658C2×C4C2×#1174568911yescharacteristic
659C2×C4#1427377511yescharacteristic
660C2×C4#1427377511yescharacteristic
661C8—1182no—
662C8—2361no—
663C8—2361no—
664C8—2361no—
665C22—24no—
666C22—42no—
667C22—42no—
668C22—42no—
669C22—42no—
670C22—42no—
671C22—42no—
672C22—4721no—
673C22—4721no—
674C22—4721no—
675C22—4721no—
676C22—2362no—
677C22—2362no—
678C22—2362no—
679C22C2×#1427369611yescharacteristic
680C22#1683806311yescharacteristic
681C22Q8×C22⋊D5911yescharacteristic
682C22C2×#1427374711yescharacteristic
683C22#1683820011yescharacteristic
684C22#1683820511yescharacteristic
685C22#1683820511yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—41no—
690C4—41no—
691C4—42no—
692C4—42no—
693C4—41no—
694C4—42no—
695C4—4721no—
696C4—4721no—
697C4—4721no—
698C4C2×#1427370311yescharacteristic
699C4#1683797611yescharacteristic
700C4#1683806311yescharacteristic
701C4Q8×C22⋊D5911yescharacteristic
702C2—44no—
703C2—4722no—
704C2#2142745511yescharacteristic
705C2#2143331411yescharacteristic
706C2#2143336411yescharacteristic
707C2#2143675611yescharacteristic
708C2#2143684911yescharacteristic
709C2#2143695911yescharacteristic
710C2#2143705011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC2×C59×#554C2
socleC23×C59C22×D4
prime radicalC22×#11745669C22
hypercenterC2×#554D59
hypocenterC59#24335
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#16837699C2semidirect
3. #21429454C2semidirect
4. #21425431C2semidirect
5. #21425421C2semidirect
6. #21425239C2semidirect
7. #21425229C2semidirect
8. #21425062C2semidirect
9. #21425033C2semidirect
12. #21424357C2semidirect
13. #21424343C2semidirect
14. #21424106C2semidirect
15. C2×C59×#554C2semidirect
67. C2×#11745669Q8semidirect
347. C2×#554D59semidirect
418. C59#24335semidirect

Maximal subgroups

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

subgroupindex
C2×#168376992
C2×C4×#117456692
#214294542
#214254312
#214254212
#214252392
#214252292
#214250622
#214250332
#214244442
#214243572
#214243432
#214241062
C2×C59×#5542
#2433559