Finite Group Databasebeta

← #28598491

Subgroups — #28598491

Order 15104.

1598 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837913C211yesmaximal, characteristic
2C2×#16837262C211yesmaximal, characteristic, complemented
3#21425081C212yesmaximal, complemented
4#21424932C212yesmaximal, complemented
5#21424547C214yesmaximal, complemented
6#21424081C214yesmaximal, complemented
7C59×#2280C211yesmaximal, characteristic, complemented
8C22×#11745685C411yescharacteristic, complemented
9#16837913—21no—
10#16837913—21no—
11#16837913—21no—
12#16837913—21no—
13#16837913—21no—
14#16837913—21no—
15#16837913—21no—
16#16837913—21no—
17C2×#14273710C412yescomplemented
18C2×#14273706C411yescharacteristic, complemented
19C2×#14273706C2211yescharacteristic
20C2×#14273701C411yescharacteristic, complemented
21C2×#14273701C2211yescharacteristic
22C2×#14273696C2212yes—
23C2×C4×C22⋊D59C412yescomplemented
24C2×C4×C22⋊D59C2212yes—
25C2×#14273686C411yescharacteristic, complemented
26C22×C4⋊Dic59—21no—
27C22×C22⋊Dic59C2212yes—
28C2×#14273641C2218yes—
29#16837262—21no—
30#16837262—21no—
31#16837262C2212yes—
32#16837262C2212yes—
33C2×C59⋊#95—21no—
34#16837168C2218yes—
35C24×C4×C59C2211yescharacteristic
36C2×#117×C59—21no—
37C59×#381—21no—
38C59×#380—21no—
39C59×#380C2212yes—
40C59×#379C2212yes—
41C4×C22⋊C4×C59—21no—
42C4×C22⋊C4×C59C2212yes—
43C2×#11745685—21no—
44C2×#11745685—21no—
45C2×#11745685—21no—
46C2×#11745685—21no—
47C2×#11745685—44no—
48C22×Dic118C2×C411yescharacteristic, complemented
49C22×D236C2×C411yescharacteristic, complemented
50C22×C22⋊D59C2×C412yes—
51C22×C22⋊D59C2×C412yes—
52C22×C22⋊D59C2312yes—
53C23×Dic59—22no—
54C22×C4×D59C2×C412yescomplemented
55#14273710—22no—
56#14273710—22no—
57#14273710—22no—
58#14273710—22no—
59#14273706—21no—
60#14273706—21no—
61#14273706—21no—
62#14273706—21no—
63#14273706—21no—
64#14273706—21no—
65#14273706—21no—
66#14273706—21no—
67#14273701—21no—
68#14273701—21no—
69#14273701—21no—
70#14273701—21no—
71#14273701—21no—
72#14273701—21no—
73#14273701—21no—
74#14273701—21no—
75#14273696—22no—
76#14273696—22no—
77#14273696—22no—
78#14273696—22no—
79C4×C22⋊D59—22no—
80C4×C22⋊D59—22no—
81C4×C22⋊D59—22no—
82C4×C22⋊D59—22no—
83C4×C22⋊D59—22no—
84C4×C22⋊D59—22no—
85C4×C22⋊D59—22no—
86C4×C22⋊D59—22no—
87#14273686—21no—
88#14273686—21no—
89#14273686—21no—
90#14273686—21no—
91C2×C4⋊Dic59—22no—
92C2×C4⋊Dic59—22no—
93C2×C4⋊Dic59—44no—
94C2×C4⋊Dic59C2×C411yescharacteristic, complemented
95C2×C4⋊Dic59C2×C411yescharacteristic, complemented
96C2×Dic59⋊C4C2×C412yescomplemented
97C2×Dic59⋊C4C2×C412yescomplemented
98C2×C22⋊Dic59—22no—
99C2×C22⋊Dic59—44no—
100C2×C22⋊Dic59C2×C412yes—
101C2×C22⋊Dic59C2×C412yes—
102C2×C22⋊Dic59C2314yes—
103C2×C22⋊Dic59C2312yes—
104C2×(C2×D59)⋊C4C2×C412yescomplemented
105C2×(C2×D59)⋊C4C2×C412yescomplemented
106C2×C4×Dic59C2×C412yescomplemented
107#14273641—48no—
108C59⋊#95—22no—
109C59⋊#95—22no—
110C25×C59C2311yescharacteristic
111C23×C4×C59—44no—
112C23×C4×C59C2×C411yescharacteristic
113C23×C4×C59C2×C411yescharacteristic
114C23×C4×C59C2×C411yescharacteristic
115C23×C4×C59C2×C411yescharacteristic
116C23×C4×C59D411yescharacteristic
117C23×C4×C59D411yescharacteristic
118C23×C4×C59D411yescharacteristic
119C23×C4×C59D411yescharacteristic
120C23×C4×C59D411yescharacteristic
121C23×C4×C59D411yescharacteristic
122C23×C4×C59D411yescharacteristic
123C23×C4×C59D411yescharacteristic
124C23×C4×C59C2311yescharacteristic
125C23×C4×C59C2311yescharacteristic
126#117×C59—44no—
127C2×C4⋊C4×C59—22no—
128C2×C22⋊C4×C59—22no—
129C2×C22⋊C4×C59—22no—
130C2×C22⋊C4×C59C2314yes—
131C2×C42×C59—22no—
132#95×C59—22no—
133#95×C59—22no—
134C24×C59—22no—
135C24×C59—22no—
136C24×C59—42no—
137C24×C59—42no—
138C24×C59C22×C411yescharacteristic
139C24×C59C22×C411yescharacteristic
140C24×C59C2×D411yescharacteristic
141C24×C59C2×D411yescharacteristic
142C24×C59C2×D411yescharacteristic
143C24×C59C2×D411yescharacteristic
144C24×C59C2411yescharacteristic
145C23×D59C22×C412yes—
146C22×C4×C59—24no—
147C22×C4×C59—24no—
148C22×C4×C59—24no—
149C22×C4×C59—24no—
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—42no—
161C22×C4×C59C22⋊C411yescharacteristic
162C22×C4×C59C22⋊C411yescharacteristic
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
189C2×C22⋊D59—22no—
190C2×C22⋊D59—22no—
191C2×C22⋊D59—22no—
192C2×C22⋊D59—22no—
193C2×C22⋊D59—22no—
194C2×C22⋊D59—22no—
195C2×C22⋊D59—24no—
196C2×C22⋊D59—24no—
197C2×C22⋊D59—44no—
198C2×C22⋊D59—44no—
199C22×Dic59—24no—
200C22×Dic59—44no—
201C22×Dic59—44no—
202C22×Dic59—44no—
203C22×Dic59C22×C412yes—
204C22×Dic59C22×C412yes—
205C22×Dic59C22×C412yes—
206#11745685—44no—
207#11745685—44no—
208#11745685—44no—
209#11745685—44no—
210C2×D236—21no—
211C2×D236—21no—
212C2×D236—42no—
213C2×C4×D59—22no—
214C2×C4×D59—22no—
215C2×C4×D59—44no—
216C2×Dic118—21no—
217C2×Dic118—21no—
218C2×Dic118—42no—
219C4⋊C4×C59—44no—
220C22⋊C4×C59—24no—
221C22⋊C4×C59—24no—
222C22⋊C4×C59—44no—
223C22⋊C4×C59—44no—
224C42×C59—44no—
225C22⋊Dic59—22no—
226C22⋊Dic59—22no—
227C22⋊Dic59—22no—
228C22⋊Dic59—22no—
229C22⋊Dic59—22no—
230C22⋊Dic59—22no—
231C22⋊Dic59—28no—
232C22⋊Dic59—44no—
233(C2×D59)⋊C4—22no—
234(C2×D59)⋊C4—22no—
235(C2×D59)⋊C4—22no—
236(C2×D59)⋊C4—22no—
237C4⋊Dic59—21no—
238C4⋊Dic59—21no—
239C4⋊Dic59—21no—
240C4⋊Dic59—21no—
241C4⋊Dic59—44no—
242C4⋊Dic59—44no—
243Dic59⋊C4—22no—
244Dic59⋊C4—22no—
245Dic59⋊C4—22no—
246Dic59⋊C4—22no—
247C4×Dic59—22no—
248C4×Dic59—22no—
249C23×C59—21no—
250C23×C59—21no—
251C23×C59—22no—
252C23×C59—22no—
253C23×C59—22no—
254C23×C59—22no—
255C23×C59—21no—
256C23×C59—21no—
257C23×C59—22no—
258C23×C59—22no—
259C23×C59—22no—
260C23×C59—22no—
261C23×C59—22no—
262C23×C59—22no—
263C23×C59—41no—
264C23×C59—41no—
265C23×C59—41no—
266C23×C59—41no—
267C23×C59—41no—
268C23×C59—41no—
269C23×C59—41no—
270C23×C59—41no—
271C23×C59—48no—
272C23×C59—48no—
273C23×C59C2×C22⋊C411yescharacteristic
274C23×C59C2×C22⋊C411yescharacteristic
275C23×C59C2×C22⋊C411yescharacteristic
276C23×C59C2×C22⋊C411yescharacteristic
277C23×C59C23×C411yescharacteristic
278C23×C59C22×D411yescharacteristic
279C23×C59C22×D411yescharacteristic
280C23×C59H(5,𝔽2)12yes—
281C23×C592−1+412yes—
282C22×D59—22no—
283C22×D59—24no—
284C22×D59—42no—
285C22×D59—42no—
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—22no—
298C2×C4×C59—22no—
299C2×C4×C59—22no—
300C2×C4×C59—22no—
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—41no—
310C2×C4×C59—41no—
311C2×C4×C59—41no—
312C2×C4×C59—41no—
313C2×C4×C59—44no—
314C2×C4×C59—44no—
315C2×C4×C59—44no—
316C2×C4×C59#9914yescomplemented
317C2×C4×C59C2×C22⋊C411yescharacteristic
318C2×C4×C59C2×C22⋊C411yescharacteristic
319C2×C4×C59C2×C22⋊C411yescharacteristic
320C2×C4×C59C2×C22⋊C411yescharacteristic
321C2×C4×C59C2×C22⋊C411yescharacteristic
322C2×C4×C59C2×C22⋊C411yescharacteristic
323C2×C4×C59C2×C22⋊C411yescharacteristic
324C2×C4×C59C2×C22⋊C411yescharacteristic
325C22⋊D59—44no—
326C22⋊D59—44no—
327C22⋊D59—42no—
328C22⋊D59—42no—
329C22⋊D59—44no—
330C22⋊D59—44no—
331C22⋊D59—44no—
332C2×Dic59—22no—
333C2×Dic59—22no—
334C2×Dic59—22no—
335C2×Dic59—24no—
336C2×Dic59—42no—
337C2×Dic59—42no—
338C2×Dic59—44no—
339C2×Dic59—44no—
340C2×Dic59—44no—
341C2×Dic59—88no—
342D236—42no—
343D236—42no—
344C4×D59—44no—
345C4×D59—44no—
346Dic118—42no—
347Dic118—42no—
348#21874—591nomaximal, Sylow
349C22×C59—24no—
350C22×C59—24no—
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—21no—
362C22×C59—21no—
363C22×C59—21no—
364C22×C59—21no—
365C22×C59—21no—
366C22×C59—21no—
367C22×C59—42no—
368C22×C59—42no—
369C22×C59—44no—
370C22×C59—44no—
371C22×C59—44no—
372C22×C59—44no—
373C22×C59—42no—
374C22×C59—42no—
375C22×C59C2×#9912yes—
376C22×C59#41012yes—
377C22×C59C22×C22⋊C411yescharacteristic
378C22×C59#52012yes—
379C22×C59#53511yescharacteristic
380C22×C59#53611yescharacteristic
381C22×C59#53712yes—
382C2×D59—42no—
383C2×D59—42no—
384C2×D59—42no—
385C2×D59—84no—
386C4×C59—21no—
387C4×C59—21no—
388C4×C59—21no—
389C4×C59—21no—
390C4×C59—21no—
391C4×C59—21no—
392C4×C59—84no—
393C4×C59C2×#9912yes—
394C4×C59C2×#9912yes—
395Dic59—42no—
396Dic59—42no—
397Dic59—42no—
398Dic59—84no—
399C2×#525—591no—
400#2280D5911yescharacteristic, complemented
401C2×#380—591no—
402#1996—592no—
403#1964—592no—
404#1898—594no—
405#1799—594no—
406C2×C59—21no—
407C2×C59—22no—
408C2×C59—22no—
409C2×C59—21no—
410C2×C59—22no—
411C2×C59—22no—
412C2×C59—41no—
413C2×C59—41no—
414C2×C59#231111yescharacteristic
415C2×C59C22×#9911yescharacteristic
416C2×C59C2×#41011yescharacteristic
417D59—82no—
418C22×#41—591no—
419C24×C4C2×D5911yescharacteristic
420#525—1181no—
421#525—1181no—
422#525—1181no—
423#525—1181no—
424#525—1181no—
425#525—1181no—
426#525—1181no—
427#525—1181no—
428C2×#123—592no—
429C2×C22⋊Q8—591no—
430C2×C22⋊Q8—591no—
431C2×#121—591no—
432C2×#121—591no—
433C2×#120—592no—
434C2×C4×D4—592no—
435C2×C4×D4—592no—
436C2×#117—21no—
437C2×#117—591no—
438C22×C4⋊C4—1181no—
439C22×C22⋊C4—592no—
440C2×#99—598no—
441#381—21no—
442#380—21no—
443#380—592no—
444#380—592no—
445#380—1181no—
446#380—1181no—
447#380C2×D5912yes—
448#379C2×D5912yes—
449C4×C22⋊C4—21no—
450C4×C22⋊C4C2×D5912yes—
451C2×#95—1181no—
452#342—598no—
453C59#2187411yescharacteristic, complemented, Sylow
454C25C22×D5911yescharacteristic
455C2×#41—1181no—
456C2×#41—1181no—
457C2×#41—1181no—
458C2×#41—1181no—
459C2×#41—2364no—
460C22×Q8—591no—
461C22×D4—592no—
462C22×D4—592no—
463C22×D4—592no—
464C22×D4—591no—
465C23×C4—44no—
466C23×C4—592no—
467C23×C4—1182no—
468C23×C4C4×D5911yescharacteristic
469C23×C4C4×D5911yescharacteristic
470C23×C4C4×D5911yescharacteristic
471C23×C4C4×D5911yescharacteristic
472C23×C4D23611yescharacteristic
473C23×C4D23611yescharacteristic
474C23×C4D23611yescharacteristic
475C23×C4D23611yescharacteristic
476C23×C4C22⋊D5911yescharacteristic
477C23×C4C22⋊D5911yescharacteristic
478C23×C4C22⋊D5911yescharacteristic
479C23×C4C22⋊D5911yescharacteristic
480C23×C4C22×D5911yescharacteristic
481C23×C4C22×D5911yescharacteristic
482#123—1182no—
483#123—1182no—
484#123—1182no—
485#123—1182no—
486C22⋊Q8—1181no—
487C22⋊Q8—1181no—
488C22⋊Q8—1181no—
489C22⋊Q8—1181no—
490C22⋊Q8—1181no—
491C22⋊Q8—1181no—
492C22⋊Q8—1181no—
493C22⋊Q8—1181no—
494#121—1181no—
495#121—1181no—
496#121—1181no—
497#121—1181no—
498#121—1181no—
499#121—1181no—
500#121—1181no—
501#121—1181no—
502#120—1182no—
503#120—1182no—
504#120—1182no—
505#120—1182no—
506C4×D4—1182no—
507C4×D4—1182no—
508C4×D4—1182no—
509C4×D4—1182no—
510C4×D4—1182no—
511C4×D4—1182no—
512C4×D4—1182no—
513C4×D4—1182no—
514#117—44no—
515#117—1181no—
516#117—1181no—
517#117—1181no—
518#117—1181no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—591no—
521C2×C4⋊C4—591no—
522C2×C4⋊C4—592no—
523C2×C4⋊C4—592no—
524C2×C4⋊C4—1182no—
525C2×C4⋊C4—1182no—
526C2×C4⋊C4—2364no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—592no—
530C2×C22⋊C4—592no—
531C2×C22⋊C4—592no—
532C2×C22⋊C4—592no—
533C2×C22⋊C4—592no—
534C2×C22⋊C4—594no—
535C2×C22⋊C4—1182no—
536C2×C22⋊C4—2364no—
537C2×C22⋊C4C22×D5914yes—
538C2×C42—22no—
539C2×C42—592no—
540#99—2368no—
541#95—22no—
542#95—22no—
543#95—1182no—
544#95—1182no—
545C24—22no—
546C24—22no—
547C24—42no—
548C24—42no—
549C24—592no—
550C24C2×C4×D5911yescharacteristic
551C24C2×C4×D5911yescharacteristic
552C24C2×D23611yescharacteristic
553C24C2×D23611yescharacteristic
554C24C2×C22⋊D5911yescharacteristic
555C24C2×C22⋊D5911yescharacteristic
556C24C23×D5911yescharacteristic
557#41—2364no—
558#41—2364no—
559#41—2364no—
560#41—2364no—
561C2×Q8—1181no—
562C2×Q8—1181no—
563C2×Q8—2362no—
564C2×D4—1182no—
565C2×D4—1182no—
566C2×D4—1182no—
567C2×D4—1182no—
568C2×D4—1182no—
569C2×D4—1182no—
570C2×D4—1184no—
571C2×D4—1184no—
572C2×D4—1181no—
573C2×D4—1181no—
574C2×D4—2362no—
575C2×D4—2364no—
576C2×D4—2364no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—592no—
593C22×C4—592no—
594C22×C4—592no—
595C22×C4—1182no—
596C22×C4—1182no—
597C22×C4—1184no—
598C22×C4—2364no—
599C22×C4—2364no—
600C22×C4—2364no—
601C22×C4—2364no—
602C22×C4(C2×D59)⋊C411yescharacteristic
603C22×C4(C2×D59)⋊C411yescharacteristic
604C22×C4(C2×D59)⋊C411yescharacteristic
605C22×C4(C2×D59)⋊C411yescharacteristic
606C22×C4(C2×D59)⋊C411yescharacteristic
607C22×C4(C2×D59)⋊C411yescharacteristic
608C22×C4(C2×D59)⋊C411yescharacteristic
609C22×C4(C2×D59)⋊C411yescharacteristic
610C22×C4(C2×D59)⋊C411yescharacteristic
611C22×C4(C2×D59)⋊C411yescharacteristic
612C22×C4(C2×D59)⋊C411yescharacteristic
613C22×C4(C2×D59)⋊C411yescharacteristic
614C22×C4(C2×D59)⋊C411yescharacteristic
615C22×C4(C2×D59)⋊C411yescharacteristic
616C22×C4(C2×D59)⋊C411yescharacteristic
617C22×C4(C2×D59)⋊C411yescharacteristic
618C22×C4C2×C4×D5911yescharacteristic
619C22×C4C2×C4×D5911yescharacteristic
620C22×C4C2×C4×D5911yescharacteristic
621C22×C4C2×C4×D5911yescharacteristic
622C22×C4C2×D23611yescharacteristic
623C22×C4C2×D23611yescharacteristic
624C22×C4C2×D23611yescharacteristic
625C22×C4C2×D23611yescharacteristic
626C22×C4C2×C22⋊D5911yescharacteristic
627C22×C4C2×C22⋊D5911yescharacteristic
628C22×C4C2×C22⋊D5911yescharacteristic
629C22×C4C2×C22⋊D5911yescharacteristic
630C4⋊C4—44no—
631C4⋊C4—1181no—
632C4⋊C4—1181no—
633C4⋊C4—1181no—
634C4⋊C4—1181no—
635C4⋊C4—1182no—
636C4⋊C4—1182no—
637C4⋊C4—1182no—
638C4⋊C4—1182no—
639C4⋊C4—2364no—
640C4⋊C4—2364no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—44no—
644C22⋊C4—44no—
645C22⋊C4—1182no—
646C22⋊C4—1182no—
647C22⋊C4—1182no—
648C22⋊C4—1182no—
649C22⋊C4—1182no—
650C22⋊C4—1182no—
651C22⋊C4—1182no—
652C22⋊C4—1182no—
653C22⋊C4—1182no—
654C22⋊C4—1182no—
655C22⋊C4—1188no—
656C22⋊C4—2364no—
657C42—44no—
658C42—1182no—
659C42—1182no—
660C23—21no—
661C23—21no—
662C23—22no—
663C23—22no—
664C23—21no—
665C23—21no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—48no—
683C23—48no—
684C23—1184no—
685C23—1182no—
686C23—2362no—
687C23—2362no—
688C23C2×(C2×D59)⋊C411yescharacteristic
689C23C2×(C2×D59)⋊C411yescharacteristic
690C23C2×(C2×D59)⋊C411yescharacteristic
691C23C2×(C2×D59)⋊C411yescharacteristic
692C23C22×C4×D5911yescharacteristic
693C23C22×C22⋊D5911yescharacteristic
694C23C22×D23611yescharacteristic
695C23#1427377312yes—
696C23#1427377412yes—
697Q8—2362no—
698Q8—2362no—
699D4—2362no—
700D4—2364no—
701D4—2364no—
702D4—2362no—
703D4—2362no—
704D4—2364no—
705D4—2364no—
706D4—2364no—
707D4—2362no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—1182no—
739C2×C4—1182no—
740C2×C4—1182no—
741C2×C4—1184no—
742C2×C4—4728no—
743C2×C4—2364no—
744C2×C4—2364no—
745C2×C4—2364no—
746C2×C4—2364no—
747C2×C4—2364no—
748C2×C4—2362no—
749C2×C4—2362no—
750C2×C4#1427364114yescomplemented
751C2×C4C2×(C2×D59)⋊C411yescharacteristic
752C2×C4C2×(C2×D59)⋊C411yescharacteristic
753C2×C4C2×(C2×D59)⋊C411yescharacteristic
754C2×C4C2×(C2×D59)⋊C411yescharacteristic
755C2×C4C2×(C2×D59)⋊C411yescharacteristic
756C2×C4C2×(C2×D59)⋊C411yescharacteristic
757C2×C4C2×(C2×D59)⋊C411yescharacteristic
758C2×C4C2×(C2×D59)⋊C411yescharacteristic
759C22—24no—
760C22—24no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—42no—
784C22—42no—
785C22—4724no—
786C22—2362no—
787C22—2362no—
788C22—2362no—
789C22C2×#1427364112yes—
790C22#1683737512yes—
791C22C22×(C2×D59)⋊C411yescharacteristic
792C22#1683788212yes—
793C22#1683797111yescharacteristic
794C22#1683797811yescharacteristic
795C22#1683798012yes—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—84no—
803C4—4724no—
804C4—2362no—
805C4—2362no—
806C4—2362no—
807C4C2×#1427364112yes—
808C4C2×#1427364112yes—
809C2—22no—
810C2—21no—
811C2—21no—
812C2—22no—
813C2—22no—
814C2—22no—
815C2—41no—
816C2—41no—
817C2—4722no—
818C2#2142668411yescharacteristic
819C2C22×#1427364111yescharacteristic
820C2C2×#1683737511yescharacteristic
subgroupG/H
centerC22C22×(C2×D59)⋊C4
commutatorC23×C59C23×C4
FrattiniC24C23×D59
FittingC59×#2280C2
socleC22×C59C22×C22⋊C4
prime radicalC2×#16837913C2
cosocleC24×C59C24
hypercenter#2280D59
hypocenterC59#21874
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. C2×#16837262C2semidirect
3. #21425081C2semidirect
4. #21424932C2semidirect
5. #21424547C2semidirect
6. #21424081C2semidirect
7. C59×#2280C2semidirect
8. C22×#11745685C4semidirect
17. C2×#14273710C4semidirect
18. C2×#14273706C4semidirect
20. C2×#14273701C4semidirect
23. C2×C4×C22⋊D59C4semidirect
25. C2×#14273686C4semidirect
48. C22×Dic118C2×C4semidirect
49. C22×D236C2×C4semidirect
54. C22×C4×D59C2×C4semidirect
94. C2×C4⋊Dic59C2×C4semidirect
95. C2×C4⋊Dic59C2×C4semidirect
96. C2×Dic59⋊C4C2×C4semidirect
97. C2×Dic59⋊C4C2×C4semidirect
104. C2×(C2×D59)⋊C4C2×C4semidirect
105. C2×(C2×D59)⋊C4C2×C4semidirect
106. C2×C4×Dic59C2×C4semidirect
316. C2×C4×C59#99semidirect
400. #2280D59semidirect
453. C59#21874semidirect
750. C2×C4#14273641semidirect

Maximal subgroups

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

subgroupindex
C2×#168379132
C2×#168372622
#214250812
#214249322
#214245472
#214240812
C59×#22802
#2187459