Finite Group Databasebeta

← #28556177

Subgroups — #28556177

Order 15104.

1510 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837913C211yesmaximal, characteristic
2C2×#16837366C211yesmaximal, characteristic, complemented
3#21422667C212yesmaximal, complemented
4#21422663C212yesmaximal, complemented
5#21422637C214yesmaximal, complemented
6#21422598C214yesmaximal, complemented
7C2×C59×#380C211yesmaximal, characteristic, complemented
8C22×#11745685C411yescharacteristic, complemented
9C22×#11745664—21no—
10#16837913—21no—
11#16837913—21no—
12#16837913—21no—
13#16837913—21no—
14#16837913C412yescomplemented
15#16837913C412yescomplemented
16#16837913C2212yes—
17#16837913C2212yes—
18C2×#14273710—21no—
19C2×#14273706C411yescharacteristic, complemented
20C2×#14273706C2211yescharacteristic
21C2×#14273701C411yescharacteristic, complemented
22C2×#14273701C2211yescharacteristic
23C2×#14273696—21no—
24C2×C4×C22⋊D59—21no—
25C2×C4×C22⋊D59—21no—
26C2×#14273686C411yescharacteristic, complemented
27#16837366—21no—
28#16837366—21no—
29#16837366C2212yescomplemented
30#16837366C2212yescomplemented
31C2×C22⋊(C59⋊C8)—21no—
32C2×C22⋊(C59⋊C8)C2212yes—
33#16837138C2218yescomplemented
34#16837135C2218yescomplemented
35C24×C4×C59C2211yescharacteristic
36C22×C4⋊C4×C59—21no—
37C22×C22⋊C4×C59—21no—
38C59×#380—21no—
39C59×#380—21no—
40C59×#380C2212yes—
41C59×#380C2212yescomplemented
42C2×#95×C59C2212yescomplemented
43C2×#11745685—21no—
44C2×#11745685—21no—
45C2×#11745685—44no—
46C2×#11745685C2×C412yes—
47C2×#11745685C2×C412yescomplemented
48C22×Dic118C2×C411yescharacteristic, complemented
49C22×D236C2×C411yescharacteristic, complemented
50C22×C22⋊D59—21no—
51C22×C22⋊D59—21no—
52C22×C22⋊D59—21no—
53C22×C4×D59—21no—
54C2×#11745664—22no—
55C2×#11745664—22no—
56C2×#11745664—44no—
57C22×C59⋊C8—22no—
58#14273710—22no—
59#14273710—22no—
60#14273710—22no—
61#14273710—22no—
62#14273706—21no—
63#14273706—21no—
64#14273706—21no—
65#14273706—21no—
66#14273706C2×C412yes—
67#14273706C2×C412yescomplemented
68#14273706C2×C412yescomplemented
69#14273706C2312yes—
70#14273701—21no—
71#14273701—21no—
72#14273701—21no—
73#14273701—21no—
74#14273701C2×C412yes—
75#14273701C2×C412yescomplemented
76#14273701C2×C412yescomplemented
77#14273701C2312yes—
78#14273696—22no—
79#14273696—22no—
80#14273696—22no—
81#14273696—22no—
82C4×C22⋊D59—22no—
83C4×C22⋊D59—22no—
84C4×C22⋊D59—22no—
85C4×C22⋊D59—22no—
86C4×C22⋊D59—22no—
87C4×C22⋊D59—22no—
88C4×C22⋊D59—22no—
89C4×C22⋊D59—22no—
90#14273686—21no—
91#14273686—21no—
92#14273686C2×C412yes—
93#14273686C2×C412yescomplemented
94C2×C4⋊Dic59C2×C411yescharacteristic, complemented
95C2×C4⋊Dic59C2×C411yescharacteristic, complemented
96C2×Dic59⋊C4—21no—
97C2×Dic59⋊C4—21no—
98C2×C22⋊Dic59—21no—
99C2×C22⋊Dic59—21no—
100C2×C22⋊Dic59—21no—
101C2×(C2×D59)⋊C4—21no—
102C2×(C2×D59)⋊C4—21no—
103C2×C4×Dic59—21no—
104C22⋊(C59⋊C8)—22no—
105C22⋊(C59⋊C8)—22no—
106C22⋊(C59⋊C8)—22no—
107C22⋊(C59⋊C8)C2314yes—
108C25×C59D411yescharacteristic
109C23×C4×C59—22no—
110C23×C4×C59—44no—
111C23×C4×C59C2×C411yescharacteristic
112C23×C4×C59C2×C411yescharacteristic
113C23×C4×C59C2×C411yescharacteristic
114C23×C4×C59C2×C411yescharacteristic
115C23×C4×C59D411yescharacteristic
116C23×C4×C59D411yescharacteristic
117C23×C4×C59D411yescharacteristic
118C23×C4×C59D411yescharacteristic
119C23×C4×C59D411yescharacteristic
120C23×C4×C59D411yescharacteristic
121C23×C4×C59D411yescharacteristic
122C23×C4×C59C2311yescharacteristic
123C23×C4×C59C2311yescharacteristic
124C23×C4×C59C2311yescharacteristic
125C2×C4⋊C4×C59—22no—
126C2×C4⋊C4×C59—22no—
127C2×C4⋊C4×C59—44no—
128C2×C22⋊C4×C59—22no—
129C2×C22⋊C4×C59—22no—
130C2×C22⋊C4×C59—44no—
131#95×C59—22no—
132#95×C59C2314yes—
133C24×C59—22no—
134C24×C59—22no—
135C24×C59—42no—
136C24×C59—42no—
137C24×C59C22⋊C411yescharacteristic
138C24×C59C22⋊C411yescharacteristic
139C24×C59C22⋊C411yescharacteristic
140C24×C59C22⋊C411yescharacteristic
141C24×C59C2×D411yescharacteristic
142C24×C59C2×D411yescharacteristic
143C24×C59C2×D411yescharacteristic
144C23×D59—21no—
145C22×C4×C59—24no—
146C22×C4×C59—24no—
147C22×C4×C59—24no—
148C22×C4×C59—24no—
149C22×C4×C59—42no—
150C22×C4×C59—42no—
151C22×C4×C59—42no—
152C22×C4×C59—42no—
153C22×C4×C59—42no—
154C22×C4×C59—42no—
155C22×C4×C59—42no—
156C22×C4×C59—42no—
157C22×C4×C59—42no—
158C22×C4×C59—42no—
159C22×C4×C59—42no—
160C22×C4×C59—44no—
161C22×C4×C59—44no—
162C22×C4×C59—44no—
163C22×C4×C59C22⋊C411yescharacteristic
164C22×C4×C59C22⋊C411yescharacteristic
165C22×C4×C59C22⋊C411yescharacteristic
166C22×C4×C59C22⋊C411yescharacteristic
167C22×C4×C59C22⋊C411yescharacteristic
168C22×C4×C59C22⋊C411yescharacteristic
169C22×C4×C59C22⋊C411yescharacteristic
170C22×C4×C59C22⋊C411yescharacteristic
171C22×C4×C59C22⋊C411yescharacteristic
172C22×C4×C59C22⋊C411yescharacteristic
173C22×C4×C59C22⋊C411yescharacteristic
174C22×C4×C59C22⋊C411yescharacteristic
175C22×C4×C59C22×C411yescharacteristic
176C22×C4×C59C22×C411yescharacteristic
177C22×C4×C59C22×C411yescharacteristic
178C22×C4×C59C22×C411yescharacteristic
179C22×C4×C59C22×C411yescharacteristic
180C22×C4×C59C22×C411yescharacteristic
181C22×C4×C59C2×D411yescharacteristic
182C22×C4×C59C2×D411yescharacteristic
183C22×C4×C59C2×D411yescharacteristic
184C22×C4×C59C2×D411yescharacteristic
185C22×C4×C59C2×D411yescharacteristic
186C22×C4×C59C2×D411yescharacteristic
187C22×C4×C59C2×D411yescharacteristic
188C22×C4×C59C2×D411yescharacteristic
189C22×C4×C59C2×D411yescharacteristic
190C22×C4×C59C2411yescharacteristic
191C2×C22⋊D59—22no—
192C2×C22⋊D59—22no—
193C2×C22⋊D59—22no—
194C2×C22⋊D59—22no—
195C2×C22⋊D59—22no—
196C2×C22⋊D59—22no—
197C2×C22⋊D59—44no—
198C2×C22⋊D59—44no—
199C2×C22⋊D59—42no—
200C2×C22⋊D59—42no—
201C22×Dic59—21no—
202C22×Dic59—21no—
203C22×Dic59—21no—
204#11745685—44no—
205#11745685—44no—
206#11745685—44no—
207#11745685—44no—
208C2×D236—21no—
209C2×D236—42no—
210C2×D236C22×C412yes—
211C2×C4×D59—22no—
212C2×C4×D59—22no—
213C2×C4×D59—44no—
214C2×Dic118—21no—
215C2×Dic118—42no—
216C2×Dic118C22×C412yes—
217C4⋊C4×C59—44no—
218C4⋊C4×C59—44no—
219C22⋊C4×C59—44no—
220C22⋊C4×C59—44no—
221C22⋊Dic59—22no—
222C22⋊Dic59—22no—
223C22⋊Dic59—22no—
224C22⋊Dic59—22no—
225C22⋊Dic59—22no—
226C22⋊Dic59—22no—
227(C2×D59)⋊C4—22no—
228(C2×D59)⋊C4—22no—
229(C2×D59)⋊C4—22no—
230(C2×D59)⋊C4—22no—
231C4⋊Dic59—21no—
232C4⋊Dic59—21no—
233C4⋊Dic59C22×C412yes—
234C4⋊Dic59C22×C412yes—
235Dic59⋊C4—22no—
236Dic59⋊C4—22no—
237Dic59⋊C4—22no—
238Dic59⋊C4—22no—
239C4×Dic59—22no—
240C4×Dic59—22no—
241#11745664—44no—
242#11745664—44no—
243C2×C59⋊C8—24no—
244C2×C59⋊C8—44no—
245C23×C59—21no—
246C23×C59—21no—
247C23×C59—22no—
248C23×C59—22no—
249C23×C59—21no—
250C23×C59—21no—
251C23×C59—22no—
252C23×C59—22no—
253C23×C59—22no—
254C23×C59—22no—
255C23×C59—22no—
256C23×C59—22no—
257C23×C59—22no—
258C23×C59—22no—
259C23×C59—41no—
260C23×C59—41no—
261C23×C59—41no—
262C23×C59—41no—
263C23×C59—41no—
264C23×C59—41no—
265C23×C59—41no—
266C23×C59—41no—
267C23×C59—48no—
268C23×C59—48no—
269C23×C59C2×C22⋊C411yescharacteristic
270C23×C59C2×C22⋊C411yescharacteristic
271C23×C59C2×C22⋊C411yescharacteristic
272C23×C59C2×C22⋊C411yescharacteristic
273C23×C59C2×C22⋊C411yescharacteristic
274C23×C59C2×C22⋊C411yescharacteristic
275C23×C59AGL(1,ℤ/8)12yes—
276C23×C59#13712yes—
277C23×C59C22×D411yescharacteristic
278C22×D59—22no—
279C22×D59—42no—
280C22×D59—42no—
281C22×D59—42no—
282C2×C4×C59—22no—
283C2×C4×C59—22no—
284C2×C4×C59—22no—
285C2×C4×C59—22no—
286C2×C4×C59—22no—
287C2×C4×C59—22no—
288C2×C4×C59—22no—
289C2×C4×C59—22no—
290C2×C4×C59—22no—
291C2×C4×C59—22no—
292C2×C4×C59—22no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—41no—
298C2×C4×C59—41no—
299C2×C4×C59—41no—
300C2×C4×C59—41no—
301C2×C4×C59—41no—
302C2×C4×C59—41no—
303C2×C4×C59—41no—
304C2×C4×C59—41no—
305C2×C4×C59—41no—
306C2×C4×C59—41no—
307C2×C4×C59—41no—
308C2×C4×C59—41no—
309C2×C4×C59—44no—
310C2×C4×C59—44no—
311C2×C4×C59—44no—
312C2×C4×C59—88no—
313C2×C4×C59#9914yes—
314C2×C4×C59C2×C22⋊C411yescharacteristic
315C2×C4×C59C2×C22⋊C411yescharacteristic
316C2×C4×C59C2×C22⋊C411yescharacteristic
317C2×C4×C59C2×C22⋊C411yescharacteristic
318C2×C4×C59C2×C22⋊C411yescharacteristic
319C2×C4×C59C2×C22⋊C411yescharacteristic
320C2×C4×C59C23×C411yescharacteristic
321C2×C4×C59C22×D411yescharacteristic
322C22⋊D59—44no—
323C22⋊D59—44no—
324C22⋊D59—42no—
325C22⋊D59—42no—
326C22⋊D59—44no—
327C22⋊D59—44no—
328C22⋊D59—44no—
329C2×Dic59—22no—
330C2×Dic59—22no—
331C2×Dic59—22no—
332C2×Dic59—42no—
333C2×Dic59—42no—
334C2×Dic59—42no—
335D236—42no—
336D236—42no—
337C4×D59—44no—
338C4×D59—44no—
339Dic118—42no—
340Dic118—42no—
341C59⋊C8—44no—
342#17592—591nomaximal, Sylow
343C22×C59—24no—
344C22×C59—24no—
345C22×C59—21no—
346C22×C59—21no—
347C22×C59—21no—
348C22×C59—21no—
349C22×C59—21no—
350C22×C59—21no—
351C22×C59—21no—
352C22×C59—21no—
353C22×C59—21no—
354C22×C59—21no—
355C22×C59—21no—
356C22×C59—21no—
357C22×C59—21no—
358C22×C59—21no—
359C22×C59—21no—
360C22×C59—21no—
361C22×C59—42no—
362C22×C59—42no—
363C22×C59—44no—
364C22×C59—44no—
365C22×C59—44no—
366C22×C59—44no—
367C22×C59—42no—
368C22×C59—42no—
369C22×C59C2×#9912yes—
370C22×C59#41712yes—
371C22×C59#41712yes—
372C22×C59#42112yes—
373C22×C59C22×C22⋊C411yescharacteristic
374C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
375C22×C59C2×#13711yescharacteristic
376C2×D59—42no—
377C2×D59—42no—
378C2×D59—42no—
379C2×D59—84no—
380C4×C59—21no—
381C4×C59—21no—
382C4×C59—21no—
383C4×C59—21no—
384C4×C59—21no—
385C4×C59—21no—
386C4×C59—84no—
387C4×C59C2×#9912yes—
388C4×C59C2×#9912yes—
389Dic59—42no—
390Dic59—42no—
391Dic59—42no—
392C2×#525—591no—
393C2×#407—591no—
394C2×#380D5911yescharacteristic, complemented
395#1520—592no—
396#1519—592no—
397#1513—594no—
398#1504—594no—
399C2×C59—21no—
400C2×C59—22no—
401C2×C59—21no—
402C2×C59—22no—
403C2×C59—22no—
404C2×C59—22no—
405C2×C59—41no—
406C2×C59—41no—
407C2×C59C22×#9911yescharacteristic
408C2×C59C2×#41711yescharacteristic
409C2×C59C2×#42111yescharacteristic
410D59—82no—
411C22×#41—591no—
412C24×C4C2×D5911yescharacteristic
413C22×M16—1181no—
414#525—592no—
415#525—592no—
416#525—592no—
417#525—592no—
418#525—1181no—
419#525—1181no—
420#525—1181no—
421#525—1181no—
422C2×#123—1181no—
423C2×C22⋊Q8—591no—
424C2×C22⋊Q8—591no—
425C2×#121—591no—
426C2×#121—591no—
427C2×#120—1181no—
428C2×C4×D4—1181no—
429C2×C4×D4—1181no—
430C2×#117—591no—
431C22×C4⋊C4—21no—
432C22×C22⋊C4—21no—
433#407—592no—
434#407—592no—
435#407—1181no—
436#407—1181no—
437C2×C22⋊C8—592no—
438C2×C22⋊C8—1181no—
439#380—21no—
440#380—21no—
441#380C2×D5912yes—
442#380C2×D5912yescomplemented
443C2×#95C2×D5912yescomplemented
444#328—598no—
445#327—598no—
446C59#1759211yescharacteristic, complemented, Sylow
447C25C22⋊D5911yescharacteristic
448C2×#41—592no—
449C2×#41—592no—
450C2×#41—1181no—
451C2×#41—1181no—
452C2×#41—2364no—
453C22×Q8—591no—
454C22×D4—591no—
455C22×D4—1181no—
456C22×D4—1181no—
457C22×D4—1181no—
458C23×C4—22no—
459C23×C4—44no—
460C23×C4—1181no—
461C23×C4C4×D5911yescharacteristic
462C23×C4C4×D5911yescharacteristic
463C23×C4C4×D5911yescharacteristic
464C23×C4C4×D5911yescharacteristic
465C23×C4D23611yescharacteristic
466C23×C4D23611yescharacteristic
467C23×C4D23611yescharacteristic
468C23×C4D23611yescharacteristic
469C23×C4C22⋊D5911yescharacteristic
470C23×C4C22⋊D5911yescharacteristic
471C23×C4C22⋊D5911yescharacteristic
472C23×C4C22×D5911yescharacteristic
473C23×C4C22×D5911yescharacteristic
474C23×C4C22×D5911yescharacteristic
475C2×M16—1182no—
476C2×M16—1182no—
477C2×M16—2364no—
478C22×C8—1182no—
479#123—1182no—
480#123—1182no—
481#123—1182no—
482#123—1182no—
483C22⋊Q8—592no—
484C22⋊Q8—592no—
485C22⋊Q8—592no—
486C22⋊Q8—592no—
487C22⋊Q8—1181no—
488C22⋊Q8—1181no—
489C22⋊Q8—1181no—
490C22⋊Q8—1181no—
491#121—592no—
492#121—592no—
493#121—592no—
494#121—592no—
495#121—1181no—
496#121—1181no—
497#121—1181no—
498#121—1181no—
499#120—1182no—
500#120—1182no—
501#120—1182no—
502#120—1182no—
503C4×D4—1182no—
504C4×D4—1182no—
505C4×D4—1182no—
506C4×D4—1182no—
507C4×D4—1182no—
508C4×D4—1182no—
509C4×D4—1182no—
510C4×D4—1182no—
511#117—592no—
512#117—592no—
513#117—1181no—
514#117—1181no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4—44no—
518C2×C4⋊C4—591no—
519C2×C4⋊C4—591no—
520C2×C4⋊C4—1181no—
521C2×C4⋊C4—1181no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—44no—
525C2×C22⋊C4—1181no—
526C2×C22⋊C4—1181no—
527C2×C22⋊C4—1181no—
528C2×C22⋊C4—1181no—
529C2×C22⋊C4—1181no—
530C2×C42—1181no—
531C22⋊C8—594no—
532C22⋊C8—1182no—
533C22⋊C8—1182no—
534C22⋊C8—1182no—
535#95—22no—
536#95C22×D5914yes—
537C24—22no—
538C24—22no—
539C24—42no—
540C24—42no—
541C24—1181no—
542C24(C2×D59)⋊C411yescharacteristic
543C24(C2×D59)⋊C411yescharacteristic
544C24(C2×D59)⋊C411yescharacteristic
545C24(C2×D59)⋊C411yescharacteristic
546C24C2×C22⋊D5911yescharacteristic
547C24C2×C22⋊D5911yescharacteristic
548C24C2×C22⋊D5911yescharacteristic
549#41—2364no—
550#41—2364no—
551#41—2364no—
552#41—2364no—
553C2×Q8—592no—
554C2×Q8—1181no—
555C2×Q8—2362no—
556C2×D4—592no—
557C2×D4—1182no—
558C2×D4—1182no—
559C2×D4—1182no—
560C2×D4—1182no—
561C2×D4—1182no—
562C2×D4—1182no—
563C2×D4—1181no—
564C2×D4—2362no—
565C2×D4—2364no—
566C2×D4—2364no—
567C2×D4—2362no—
568C2×D4—2362no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—1181no—
588C22×C4—1181no—
589C22×C4—1181no—
590C22×C4—1182no—
591C22×C4—1182no—
592C22×C4—2364no—
593C22×C4(C2×D59)⋊C411yescharacteristic
594C22×C4(C2×D59)⋊C411yescharacteristic
595C22×C4(C2×D59)⋊C411yescharacteristic
596C22×C4(C2×D59)⋊C411yescharacteristic
597C22×C4(C2×D59)⋊C411yescharacteristic
598C22×C4(C2×D59)⋊C411yescharacteristic
599C22×C4(C2×D59)⋊C411yescharacteristic
600C22×C4(C2×D59)⋊C411yescharacteristic
601C22×C4(C2×D59)⋊C411yescharacteristic
602C22×C4(C2×D59)⋊C411yescharacteristic
603C22×C4(C2×D59)⋊C411yescharacteristic
604C22×C4(C2×D59)⋊C411yescharacteristic
605C22×C4C2×C4×D5911yescharacteristic
606C22×C4C2×C4×D5911yescharacteristic
607C22×C4C2×C4×D5911yescharacteristic
608C22×C4C2×C4×D5911yescharacteristic
609C22×C4C2×C4×D5911yescharacteristic
610C22×C4C2×C4×D5911yescharacteristic
611C22×C4C2×D23611yescharacteristic
612C22×C4C2×D23611yescharacteristic
613C22×C4C2×D23611yescharacteristic
614C22×C4C2×D23611yescharacteristic
615C22×C4C2×D23611yescharacteristic
616C22×C4C2×D23611yescharacteristic
617C22×C4C2×C22⋊D5911yescharacteristic
618C22×C4C2×C22⋊D5911yescharacteristic
619C22×C4C2×C22⋊D5911yescharacteristic
620C22×C4C23×D5911yescharacteristic
621M16—2364no—
622M16—2364no—
623C2×C8—1184no—
624C2×C8—2364no—
625C4⋊C4—44no—
626C4⋊C4—44no—
627C4⋊C4—592no—
628C4⋊C4—592no—
629C4⋊C4—1181no—
630C4⋊C4—1181no—
631C4⋊C4—1182no—
632C4⋊C4—1182no—
633C4⋊C4—1182no—
634C4⋊C4—1182no—
635C22⋊C4—44no—
636C22⋊C4—44no—
637C22⋊C4—1182no—
638C22⋊C4—1182no—
639C22⋊C4—1182no—
640C22⋊C4—1182no—
641C22⋊C4—1182no—
642C22⋊C4—1182no—
643C22⋊C4—1182no—
644C22⋊C4—1182no—
645C22⋊C4—1182no—
646C22⋊C4—1182no—
647C42—1182no—
648C42—1182no—
649C23—22no—
650C23—21no—
651C23—21no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—21no—
660C23—21no—
661C23—22no—
662C23—22no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—48no—
672C23—48no—
673C23—1182no—
674C23—2362no—
675C23—2362no—
676C23—2362no—
677C23C2×(C2×D59)⋊C411yescharacteristic
678C23C2×(C2×D59)⋊C411yescharacteristic
679C23C2×(C2×D59)⋊C411yescharacteristic
680C23C2×(C2×D59)⋊C411yescharacteristic
681C23C2×(C2×D59)⋊C411yescharacteristic
682C23C2×(C2×D59)⋊C411yescharacteristic
683C23#1427375312yes—
684C23#1427375812yes—
685C23C22×C22⋊D5911yescharacteristic
686Q8—2362no—
687Q8—2362no—
688D4—2362no—
689D4—2364no—
690D4—2364no—
691D4—2364no—
692D4—2364no—
693D4—2362no—
694D4—2362no—
695D4—2364no—
696D4—2362no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—88no—
728C2×C4—1182no—
729C2×C4—1182no—
730C2×C4—1182no—
731C2×C4—2364no—
732C2×C4—2362no—
733C2×C4—2362no—
734C2×C4—2362no—
735C2×C4—2364no—
736C2×C4#1427364114yes—
737C2×C4C2×(C2×D59)⋊C411yescharacteristic
738C2×C4C2×(C2×D59)⋊C411yescharacteristic
739C2×C4C2×(C2×D59)⋊C411yescharacteristic
740C2×C4C2×(C2×D59)⋊C411yescharacteristic
741C2×C4C2×(C2×D59)⋊C411yescharacteristic
742C2×C4C2×(C2×D59)⋊C411yescharacteristic
743C2×C4C22×C4×D5911yescharacteristic
744C2×C4C22×D23611yescharacteristic
745C8—2364no—
746C22—24no—
747C22—24no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—42no—
765C22—42no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—42no—
771C22—42no—
772C22—4724no—
773C22—2362no—
774C22—2362no—
775C22—2362no—
776C22C2×#1427364112yes—
777C22#1683740112yes—
778C22#1683740112yes—
779C22#1683742012yes—
780C22C22×(C2×D59)⋊C411yescharacteristic
781C22C2×#1427375311yescharacteristic
782C22C2×#1427375811yescharacteristic
783C4—21no—
784C4—21no—
785C4—21no—
786C4—21no—
787C4—21no—
788C4—21no—
789C4—84no—
790C4—2362no—
791C4—2362no—
792C4—2362no—
793C4C2×#1427364112yes—
794C4C2×#1427364112yes—
795C2—21no—
796C2—22no—
797C2—21no—
798C2—22no—
799C2—22no—
800C2—22no—
801C2—41no—
802C2—41no—
803C2—4722no—
804C2C22×#1427364111yescharacteristic
805C2C2×#1683740111yescharacteristic
806C2C2×#1683742011yescharacteristic
subgroupG/H
centerC22C22×(C2×D59)⋊C4
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC2×C59×#380C2
socleC22×C59C22×C22⋊C4
prime radicalC2×#16837913C2
cosocleC22×C4×C59C24
hypercenterC2×#380D59
hypocenterC59#17592
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×#16837366C2semidirect
3. #21422667C2semidirect
4. #21422663C2semidirect
5. #21422637C2semidirect
6. #21422598C2semidirect
7. C2×C59×#380C2semidirect
8. C22×#11745685C4semidirect
14. #16837913C4semidirect
15. #16837913C4semidirect
19. C2×#14273706C4semidirect
21. C2×#14273701C4semidirect
26. C2×#14273686C4semidirect
29. #16837366C22semidirect
30. #16837366C22semidirect
33. #16837138C22semidirect
34. #16837135C22semidirect
41. C59×#380C22semidirect
42. C2×#95×C59C22semidirect
47. C2×#11745685C2×C4semidirect
48. C22×Dic118C2×C4semidirect
49. C22×D236C2×C4semidirect
67. #14273706C2×C4semidirect
68. #14273706C2×C4semidirect
75. #14273701C2×C4semidirect
76. #14273701C2×C4semidirect
93. #14273686C2×C4semidirect
94. C2×C4⋊Dic59C2×C4semidirect
95. C2×C4⋊Dic59C2×C4semidirect
394. C2×#380D59semidirect
442. #380C2×D59semidirect
443. C2×#95C2×D59semidirect
446. C59#17592semidirect

Maximal subgroups

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

subgroupindex
C2×#168379132
C2×#168373662
#214226672
#214226632
#214226372
#214225982
C2×C59×#3802
#1759259