Finite Group Databasebeta

← #28593826

Subgroups — #28593826

Order 15104.

1150 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838025C211yesmaximal, characteristic
2C2×#16837460C211yesmaximal, characteristic, complemented
3#21426453C211yesmaximal, characteristic, complemented
4#21425046C211yesmaximal, characteristic, complemented
5#21425042C211yesmaximal, characteristic, complemented
6#21425025C211yesmaximal, characteristic, complemented
7#21425025C211yesmaximal, characteristic, complemented
8#21424416C211yesmaximal, characteristic
9#21424413C211yesmaximal, characteristic
10#21424409C211yesmaximal, characteristic, complemented
11#21423928C211yesmaximal, characteristic, complemented
12#21423920C211yesmaximal, characteristic, complemented
13#103×Dic59C211yesmaximal, characteristic, complemented
14#21423910C211yesmaximal, characteristic, complemented
15C59×#1872C211yesmaximal, characteristic, complemented
16#16838025—24no—
17#16838025C418yescomplemented
18C2×#14273726C2211yescharacteristic
19C2×#14273722—21no—
20C2×#14273716C2211yescharacteristic
21C2×#14273713—21no—
22C2×#14273709—21no—
23C2×#14273707—21no—
24C2×#14273701C2211yescharacteristic
25C2×Q8×Dic59C2211yescharacteristic
26C2×#14273689C2211yescharacteristic
27C2×#14273686C2211yescharacteristic
28C2×#14273686C2211yescharacteristic
29#16837460—24no—
30C2×Dic59⋊C8C2211yescharacteristic
31C2×Dic59⋊C8C2211yescharacteristic
32C2×#14273651C2211yescharacteristic
33C2×#14273651C2211yescharacteristic
34C2×#14273649C2211yescharacteristic
35C2×#14273649C2211yescharacteristic
36C2×#14273647C2211yescharacteristic
37C2×#14273647C2211yescharacteristic
38C2×C22⋊(C59⋊C8)C2211yescharacteristic
39C2×#14273637C2211yescharacteristic
40C2×C8×Dic59C2211yescharacteristic
41C4⋊C4×Dic59—21no—
42C4⋊C4×Dic59—21no—
43C4⋊C4×Dic59C2211yescharacteristic
44C4⋊C4×Dic59C2211yescharacteristic
45C4⋊C4×Dic59C2211yescharacteristic
46C4⋊C4×Dic59C2211yescharacteristic
47C4×C22⋊Dic59—21no—
48C4×C22⋊Dic59—21no—
49#16837165C2211yescharacteristic
50#16837165C2211yescharacteristic
51#16837164C2211yescharacteristic
52#16837164C2211yescharacteristic
53#16837164C2211yescharacteristic
54#16837164C2211yescharacteristic
55C2×C22⋊Q8×C59C2211yescharacteristic
56C22×C4⋊C4×C59C2211yescharacteristic
57C2×#103×C59C2211yescharacteristic
58C2×#103×C59C2211yescharacteristic
59C2×C22⋊C8×C59C2211yescharacteristic
60C59×#340C2211yescharacteristic
61C59×#340C2211yescharacteristic
62C22×Dic118—21no—
63C22×D236C2311yescharacteristic
64C22×C22⋊D59—21no—
65C22×C4×D59—21no—
66C22×C59⋊C8C2311yescharacteristic
67C22×C59⋊C8C2311yescharacteristic
68#14273726—22no—
69#14273726C2×C414yescomplemented
70#14273722—28no—
71#14273716—22no—
72#14273716C2×C414yescomplemented
73#14273713—28no—
74#14273709—28no—
75#14273707—28no—
76#14273701—22no—
77#14273701C2×C414yes—
78Q8×Dic59—22no—
79Q8×Dic59C2×C414yescomplemented
80#14273689—22no—
81#14273689C2×C414yescomplemented
82#14273686—22no—
83#14273686—22no—
84#14273686C2×C414yes—
85#14273686D414yes—
86C2×C4⋊Dic59—21no—
87C2×C4⋊Dic59D411yescharacteristic
88C2×C4⋊Dic59D411yescharacteristic
89C2×C4⋊Dic59C2311yescharacteristic
90C2×C4⋊Dic59C2311yescharacteristic
91C2×C4⋊Dic59C2311yescharacteristic
92C2×Dic59⋊C4—21no—
93C2×C22⋊Dic59—21no—
94C2×C22⋊Dic59D411yescharacteristic
95C2×C22⋊Dic59D411yescharacteristic
96C2×(C2×D59)⋊C4—21no—
97C2×(C2×D59)⋊C4—21no—
98C2×(C2×D59)⋊C4—21no—
99C2×(C2×D59)⋊C4—21no—
100C2×C4×Dic59—21no—
101C2×C4×Dic59—21no—
102C2×C4×Dic59—21no—
103C2×C4×Dic59—21no—
104C2×C4×Dic59—21no—
105C2×C4×Dic59—21no—
106C2×C4×Dic59C2311yescharacteristic
107C2×C4×Dic59C2311yescharacteristic
108Dic59⋊C8—22no—
109Dic59⋊C8—22no—
110#14273651—22no—
111#14273651—22no—
112#14273649—22no—
113#14273649—22no—
114#14273647—22no—
115#14273647—22no—
116C22⋊(C59⋊C8)—22no—
117#14273637—22no—
118C8×Dic59—22no—
119C59⋊#95—21no—
120C59⋊#95—21no—
121C59⋊#95—21no—
122C59⋊#95—21no—
123C22×Q8×C59C2311yescharacteristic
124C23×C4×C59—21no—
125C23×C4×C59C2311yescharacteristic
126C22×C8×C59C2311yescharacteristic
127C22×C8×C59C2311yescharacteristic
128C22⋊Q8×C59—22no—
129C22⋊Q8×C59C2×C414yes—
130C2×C4⋊C4×C59—21no—
131C2×C4⋊C4×C59—21no—
132C2×C4⋊C4×C59—22no—
133C2×C4⋊C4×C59—22no—
134C2×C4⋊C4×C59C2311yescharacteristic
135C2×C4⋊C4×C59C2311yescharacteristic
136C2×C4⋊C4×C59C2311yescharacteristic
137C2×C22⋊C4×C59—21no—
138#103×C59—22no—
139#103×C59—22no—
140C22⋊C8×C59—22no—
141C24×C59C2×D411yescharacteristic
142C23×D59—21no—
143C2×Q8×C59—21no—
144C2×Q8×C59—21no—
145C2×Q8×C59—21no—
146C2×Q8×C59—21no—
147C2×Q8×C59—21no—
148C2×Q8×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—21no—
157C22×C4×C59—24no—
158C22×C4×C59—81no—
159C22×C4×C59—81no—
160C22×C4×C59C22×C412yes—
161C22×C4×C59C2×D411yescharacteristic
162C22×C4×C59C2×D412yes—
163C22×C4×C59C2411yescharacteristic
164C2×C22⋊D59—24no—
165C2×C22⋊D59—81no—
166C2×C22⋊D59—81no—
167C22×Dic59—21no—
168C22×Dic59—21no—
169C22×Dic59—21no—
170C22×Dic59C2×D411yescharacteristic
171C22×Dic59C2×D411yescharacteristic
172C22×Dic59C2×D411yescharacteristic
173C22×Dic59C2×D411yescharacteristic
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—81no—
182C2×C4×D59—81no—
183C2×Dic118—24no—
184C2×Dic118—81no—
185C2×Dic118—81no—
186C2×C8×C59—21no—
187C2×C8×C59—21no—
188C2×C8×C59—21no—
189C2×C8×C59—21no—
190C2×C8×C59—21no—
191C2×C8×C59—21no—
192C4⋊C4×C59—24no—
193C4⋊C4×C59—24no—
194C4⋊C4×C59—21no—
195C4⋊C4×C59—21no—
196C4⋊C4×C59—21no—
197C4⋊C4×C59C22×C412yes—
198C4⋊C4×C59#4112yes—
199C4⋊C4×C59#4112yes—
200C22⋊C4×C59—24no—
201C22⋊Dic59—24no—
202C22⋊Dic59C22⋊C414yes—
203C22⋊Dic59C22⋊C414yes—
204(C2×D59)⋊C4—24no—
205(C2×D59)⋊C4—24no—
206(C2×D59)⋊C4—24no—
207(C2×D59)⋊C4—24no—
208C4⋊Dic59—21no—
209C4⋊Dic59—21no—
210C4⋊Dic59—21no—
211C4⋊Dic59—24no—
212C4⋊Dic59C22⋊C414yes—
213C4⋊Dic59C22⋊C414yes—
214C4⋊Dic59C22×C412yes—
215C4⋊Dic59#4112yes—
216C4⋊Dic59#4112yes—
217Dic59⋊C4—24no—
218C4×Dic59—24no—
219C4×Dic59—24no—
220C4×Dic59—81no—
221C4×Dic59—81no—
222C4×Dic59—81no—
223C4×Dic59—81no—
224C4×Dic59C22×C412yes—
225C4×Dic59C22×C412yes—
226C4×Dic59C2×D412yes—
227C4×Dic59C2×D412yes—
228C2×C59⋊C8—21no—
229C2×C59⋊C8—21no—
230C2×C59⋊C8—21no—
231C2×C59⋊C8—21no—
232C2×C59⋊C8—21no—
233C2×C59⋊C8—21no—
234C23×C59—21no—
235C23×C59—21no—
236C23×C59—21no—
237C23×C59—21no—
238C23×C59—21no—
239C23×C59—21no—
240C23×C59C2×C22⋊C412yes—
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—22no—
250Q8×C59—22no—
251Q8×C59—41no—
252Q8×C59—41no—
253C2×C4×C59—21no—
254C2×C4×C59—21no—
255C2×C4×C59—22no—
256C2×C4×C59—22no—
257C2×C4×C59—22no—
258C2×C4×C59—22no—
259C2×C4×C59—22no—
260C2×C4×C59—22no—
261C2×C4×C59—22no—
262C2×C4×C59—22no—
263C2×C4×C59—41no—
264C2×C4×C59—41no—
265C2×C4×C59—41no—
266C2×C4×C59—41no—
267C2×C4×C59—41no—
268C2×C4×C59—41no—
269C2×C4×C59—41no—
270C2×C4×C59—41no—
271C2×C4×C59—84no—
272C2×C4×C59C2×C22⋊C412yes—
273C2×C4×C59C23×C411yescharacteristic
274C2×C4×C59C22×D411yescharacteristic
275C2×C4×C59C2×#4111yescharacteristic
276C2×C4×C59C2×#4111yescharacteristic
277C2×C4×C59C2×#4111yescharacteristic
278C2×C4×C59C2×#4111yescharacteristic
279C22⋊D59—84no—
280C2×Dic59—21no—
281C2×Dic59—21no—
282C2×Dic59—21no—
283C2×Dic59—21no—
284C2×Dic59—21no—
285C2×Dic59—21no—
286C2×Dic59—21no—
287C2×Dic59—21no—
288C2×Dic59—22no—
289C2×Dic59—22no—
290C2×Dic59—22no—
291C2×Dic59—41no—
292C2×Dic59—41no—
293C2×Dic59—41no—
294C2×Dic59—41no—
295C2×Dic59—41no—
296C2×Dic59—41no—
297C2×Dic59C2×C22⋊C412yes—
298C2×Dic59C2×C22⋊C412yes—
299C2×Dic59C2×C22⋊C412yes—
300C2×Dic59C2×C22⋊C412yes—
301D236—22no—
302D236—22no—
303D236—41no—
304D236—41no—
305C4×D59—84no—
306Dic118—84no—
307C8×C59—41no—
308C8×C59—41no—
309C59⋊C8—41no—
310C59⋊C8—41no—
311#21397—591nomaximal, Sylow
312C22×C59—22no—
313C22×C59—22no—
314C22×C59—22no—
315C22×C59—41no—
316C22×C59—41no—
317C22×C59—41no—
318C22×C59—41no—
319C22×C59C22×C22⋊C411yescharacteristic
320C22×C59#52511yescharacteristic
321C22×C59#52511yescharacteristic
322C22×C59#57611yescharacteristic
323C22×C59#57711yescharacteristic
324C22×C59#57711yescharacteristic
325C22×C59#57811yescharacteristic
326C2×D59—42no—
327C2×D59—42no—
328C2×D59—42no—
329C2×D59—81no—
330C2×D59—81no—
331C2×D59—81no—
332C2×D59—81no—
333C4×C59—22no—
334C4×C59—42no—
335C4×C59—42no—
336C4×C59—42no—
337C4×C59—42no—
338C4×C59C4×#4111yescharacteristic
339C4×C59C4×#4111yescharacteristic
340C4×C59#53211yescharacteristic
341C4×C59#53211yescharacteristic
342Dic59—22no—
343Dic59—22no—
344Dic59—22no—
345Dic59—22no—
346Dic59—42no—
347Dic59—42no—
348Dic59—42no—
349C2×#542—591no—
350C2×#433—591no—
351#2274—591no—
352#1988—591no—
353#1987—591no—
354#1983—591no—
355#1983—591no—
356#1875—591no—
357#1874—591no—
358#1873—591no—
359#1872D5911yescharacteristic, complemented
360#1763—591no—
361#1762—591no—
362C4×#103—591no—
363C4×#102—591no—
364C2×C59—42no—
365C2×C59#229711yescharacteristic
366C2×C59#289711yescharacteristic
367C2×C59#289811yescharacteristic
368C2×C59#311811yescharacteristic
369C2×C59#312111yescharacteristic
370C2×C59#312411yescharacteristic
371C2×C59#312511yescharacteristic
372D59—82no—
373#542—598no—
374#542—1184no—
375C2×C4⋊Q8—591no—
376C2×#126—1181no—
377C2×#124—591no—
378C2×#124—1181no—
379C2×#123—1181no—
380C2×C22⋊Q8—1181no—
381C2×C22⋊Q8C2×D5911yescharacteristic
382C2×#121—591no—
383C2×C4×Q8—591no—
384C2×C4×D4—591no—
385C2×#117—591no—
386C2×#117—591no—
387C22×C4⋊C4C2×D5911yescharacteristic
388#433—1184no—
389C2×C4⋊C8—591no—
390C2×C4⋊C8—591no—
391C2×#103—591no—
392C2×#103—591no—
393C2×#103C2×D5911yescharacteristic
394C2×#103C2×D5911yescharacteristic
395C2×#102—591no—
396C2×#102—591no—
397C2×#102—591no—
398C2×#102—591no—
399C2×C22⋊C8—591no—
400C2×C22⋊C8C2×D5911yescharacteristic
401C2×#97—591no—
402C2×C4×C8—591no—
403C4×C4⋊C4—591no—
404C4×C4⋊C4—591no—
405C4×C4⋊C4—591no—
406C4×C4⋊C4—591no—
407C4×C4⋊C4—1181no—
408C4×C4⋊C4—1181no—
409C4×C22⋊C4—1181no—
410C4×C22⋊C4—1181no—
411#340—591no—
412#340—591no—
413#340—591no—
414#340—591no—
415#340—591no—
416#340—591no—
417#340C2×D5911yescharacteristic
418#340C2×D5911yescharacteristic
419C59#2139711yescharacteristic, complemented, Sylow
420C22×Q8—1181no—
421C22×Q8C22×D5911yescharacteristic
422C22×D4—591no—
423C22×D4—1181no—
424C23×C4—21no—
425C23×C4—1181no—
426C23×C4C22×D5911yescharacteristic
427C22×C8—591no—
428C22×C8—591no—
429C22×C8C22×D5911yescharacteristic
430C22×C8C22×D5911yescharacteristic
431C4⋊Q8—594no—
432C4⋊Q8—1182no—
433#126—1188no—
434#124—594no—
435#124—1182no—
436#124—1188no—
437#123—1188no—
438C22⋊Q8—22no—
439C22⋊Q8—1188no—
440C22⋊Q8C4×D5914yes—
441#121—594no—
442#121—1182no—
443C4×Q8—594no—
444C4×Q8—1182no—
445C4×D4—594no—
446C4×D4—1182no—
447#117—594no—
448#117—594no—
449#117—1182no—
450#117—1182no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—591no—
456C2×C4⋊C4—591no—
457C2×C4⋊C4—591no—
458C2×C4⋊C4—591no—
459C2×C4⋊C4—591no—
460C2×C4⋊C4—1181no—
461C2×C4⋊C4—1181no—
462C2×C4⋊C4C22×D5911yescharacteristic
463C2×C4⋊C4C22×D5911yescharacteristic
464C2×C4⋊C4C22×D5911yescharacteristic
465C2×C22⋊C4—21no—
466C2×C22⋊C4—591no—
467C2×C22⋊C4—591no—
468C2×C22⋊C4—1181no—
469C2×C22⋊C4—1181no—
470C2×C22⋊C4—1181no—
471C2×C22⋊C4—1181no—
472C2×C22⋊C4—1181no—
473C2×C42—591no—
474C2×C42—591no—
475C2×C42—1181no—
476C2×C42—1181no—
477C2×C42—1181no—
478C2×C42—1181no—
479C2×C42—1181no—
480C2×C42—1181no—
481C4⋊C8—1182no—
482C4⋊C8—1182no—
483#103—22no—
484#103—22no—
485#103—1182no—
486#103—1182no—
487#102—1182no—
488#102—1182no—
489#102—1182no—
490#102—1182no—
491C22⋊C8—22no—
492C22⋊C8—1182no—
493#97—1182no—
494C4×C8—1182no—
495#95—1181no—
496#95—1181no—
497#95—1181no—
498#95—1181no—
499C24—1181no—
500C24D4×D5911yescharacteristic
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—1184no—
507C2×Q8—4721no—
508C2×Q8—4721no—
509C2×Q8C2×C4×D5912yes—
510C2×D4—592no—
511C2×D4—1184no—
512C2×D4—1181no—
513C2×D4—1181no—
514C2×D4—1181no—
515C2×D4—1181no—
516C2×D4—1181no—
517C2×D4—4721no—
518C2×D4—4721no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—24no—
528C22×C4—81no—
529C22×C4—81no—
530C22×C4—591no—
531C22×C4—591no—
532C22×C4—591no—
533C22×C4—591no—
534C22×C4—1184no—
535C22×C4—1181no—
536C22×C4—1181no—
537C22×C4—1181no—
538C22×C4—4721no—
539C22×C4—4721no—
540C22×C4C2×C4×D5912yes—
541C22×C4D4×D5911yescharacteristic
542C22×C4D4×D5912yes—
543C22×C4C23×D5911yescharacteristic
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—1181no—
551C2×C8—1181no—
552C2×C8—1181no—
553C2×C8—1181no—
554C2×C8—1181no—
555C2×C8—1181no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—594no—
562C4⋊C4—594no—
563C4⋊C4—592no—
564C4⋊C4—592no—
565C4⋊C4—592no—
566C4⋊C4—1184no—
567C4⋊C4—1184no—
568C4⋊C4—1181no—
569C4⋊C4—1181no—
570C4⋊C4—1181no—
571C4⋊C4C2×C4×D5912yes—
572C4⋊C4#1174568712yes—
573C4⋊C4#1174568712yes—
574C22⋊C4—24no—
575C22⋊C4—594no—
576C22⋊C4—594no—
577C22⋊C4—1184no—
578C22⋊C4—1184no—
579C22⋊C4—1184no—
580C22⋊C4—1184no—
581C22⋊C4—1184no—
582C42—592no—
583C42—592no—
584C42—592no—
585C42—592no—
586C42—1184no—
587C42—1184no—
588C42—4721no—
589C42—4721no—
590C42—4721no—
591C42—4721no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—1182no—
599C23—2361no—
600C23—2361no—
601C23—2361no—
602C23—2361no—
603C23—2361no—
604C23—2361no—
605C23C22⋊C4×D5912yes—
606C23C2×D4×D5911yescharacteristic
607Q8—22no—
608Q8—22no—
609Q8—41no—
610Q8—41no—
611Q8—4724no—
612D4—1182no—
613D4—1182no—
614D4—4724no—
615D4—2361no—
616D4—2361no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—84no—
636C2×C4—592no—
637C2×C4—592no—
638C2×C4—592no—
639C2×C4—592no—
640C2×C4—1181no—
641C2×C4—1181no—
642C2×C4—1181no—
643C2×C4—1181no—
644C2×C4—1181no—
645C2×C4—1181no—
646C2×C4—1181no—
647C2×C4—1181no—
648C2×C4—1182no—
649C2×C4—1182no—
650C2×C4—1182no—
651C2×C4—4724no—
652C2×C4—2361no—
653C2×C4—2361no—
654C2×C4—2361no—
655C2×C4—2361no—
656C2×C4—2361no—
657C2×C4—2361no—
658C2×C4C22⋊C4×D5912yes—
659C2×C4C22×C4×D5911yescharacteristic
660C2×C4C2×D4×D5911yescharacteristic
661C2×C4#41×D5911yescharacteristic
662C2×C4#41×D5911yescharacteristic
663C2×C4C2×#1174568711yescharacteristic
664C2×C4C2×#1174568711yescharacteristic
665C8—41no—
666C8—41no—
667C8—2361no—
668C8—2361no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—4721no—
677C22—4721no—
678C22—4721no—
679C22—4721no—
680C22—2362no—
681C22—2362no—
682C22—2362no—
683C22C2×C22⋊C4×D5911yescharacteristic
684C22#1683790811yescharacteristic
685C22#1683791011yescharacteristic
686C22#1683820611yescharacteristic
687C22#1683820811yescharacteristic
688C22#1683821111yescharacteristic
689C22#1683821511yescharacteristic
690C4—22no—
691C4—42no—
692C4—42no—
693C4—42no—
694C4—42no—
695C4—1182no—
696C4—1182no—
697C4—1182no—
698C4—1182no—
699C4—2362no—
700C4—2362no—
701C4—2362no—
702C4C4×#1174568711yescharacteristic
703C4C4×#1174568711yescharacteristic
704C4#1683794711yescharacteristic
705C4#1683794711yescharacteristic
706C2—42no—
707C2—4722no—
708C2#2142658111yescharacteristic
709C2#2143262011yescharacteristic
710C2#2143262411yescharacteristic
711C2#2143428111yescharacteristic
712C2#2143432611yescharacteristic
713C2#2143436111yescharacteristic
714C2#2143436811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#1872C2
socleC23×C59C22×D4
prime radicalC2×#14273701C22
cosocleC22×C4×C59C24
hypercenter#1872D59
hypocenterC59#21397
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
2. C2×#16837460C2semidirect
3. #21426453C2semidirect
4. #21425046C2semidirect
5. #21425042C2semidirect
6. #21425025C2semidirect
7. #21425025C2semidirect
10. #21424409C2semidirect
11. #21423928C2semidirect
12. #21423920C2semidirect
13. #103×Dic59C2semidirect
14. #21423910C2semidirect
15. C59×#1872C2semidirect
17. #16838025C4semidirect
69. #14273726C2×C4semidirect
72. #14273716C2×C4semidirect
79. Q8×Dic59C2×C4semidirect
81. #14273689C2×C4semidirect
359. #1872D59semidirect
419. C59#21397semidirect

Maximal subgroups

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

subgroupindex
C2×#168380252
C2×#168374602
#214264532
#214250462
#214250422
#214250252
#214244162
#214244132
#214244092
#214239282
#214239202
#103×Dic592
#214239102
C59×#18722
#2139759