Finite Group Databasebeta

← #28556147

Subgroups — #28556147

Order 15104.

1466 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837913C211yesmaximal, characteristic
2C2×#16837265C211yesmaximal, characteristic, complemented
3#21422653C214yesmaximal, complemented
4#21422630C212yesmaximal, complemented
5#21422626C212yesmaximal, complemented
6#21422601C214yesmaximal, complemented
7C2×C59×#407C211yesmaximal, characteristic, complemented
8C22×#11745685C411yescharacteristic, complemented
9#16837913—21no—
10#16837913—21no—
11#16837913—21no—
12#16837913—21no—
13#16837913C412yescomplemented
14#16837913C412yescomplemented
15#16837913C2212yes—
16#16837913C2212yes—
17C2×#14273710—21no—
18C2×#14273706C411yescharacteristic, complemented
19C2×#14273706C2211yescharacteristic
20C2×#14273701C411yescharacteristic, complemented
21C2×#14273701C2211yescharacteristic
22C2×#14273696—21no—
23C2×C4×C22⋊D59—21no—
24C2×C4×C22⋊D59—21no—
25C2×#14273686C411yescharacteristic, complemented
26C22×C22⋊Dic59—21no—
27#16837265—21no—
28#16837265—21no—
29#16837265C2212yes—
30#16837265C2212yescomplemented
31C2×C59⋊#95—21no—
32C2×C59⋊#95C2212yescomplemented
33#16837140C2218yescomplemented
34#16837137C2218yescomplemented
35C24×C4×C59C2211yescharacteristic
36C22×M16×C59—21no—
37C59×#407—21no—
38C59×#407—21no—
39C59×#407C2212yes—
40C59×#407C2212yescomplemented
41C2×C22⋊C8×C59—21no—
42C2×C22⋊C8×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—
53C23×Dic59—22no—
54C22×C4×D59—21no—
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#14273706C2×C412yes—
64#14273706C2×C412yescomplemented
65#14273706C2×C412yescomplemented
66#14273706C2312yes—
67#14273701—21no—
68#14273701—21no—
69#14273701—21no—
70#14273701—21no—
71#14273701C2×C412yes—
72#14273701C2×C412yescomplemented
73#14273701C2×C412yescomplemented
74#14273701C2312yes—
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#14273686C2×C412yes—
90#14273686C2×C412yescomplemented
91C2×C4⋊Dic59C2×C411yescharacteristic, complemented
92C2×C4⋊Dic59C2×C411yescharacteristic, complemented
93C2×Dic59⋊C4—21no—
94C2×Dic59⋊C4—21no—
95C2×C22⋊Dic59—21no—
96C2×C22⋊Dic59—21no—
97C2×C22⋊Dic59—21no—
98C2×C22⋊Dic59—22no—
99C2×C22⋊Dic59—22no—
100C2×C22⋊Dic59—44no—
101C2×(C2×D59)⋊C4—21no—
102C2×(C2×D59)⋊C4—21no—
103C2×C4×Dic59—21no—
104C59⋊#95—22no—
105C59⋊#95—22no—
106C59⋊#95—22no—
107C59⋊#95C2314yes—
108C25×C59D411yescharacteristic
109C23×C4×C59—44no—
110C23×C4×C59C2×C411yescharacteristic
111C23×C4×C59C2×C411yescharacteristic
112C23×C4×C59C2×C411yescharacteristic
113C23×C4×C59C2×C411yescharacteristic
114C23×C4×C59D411yescharacteristic
115C23×C4×C59D411yescharacteristic
116C23×C4×C59D411yescharacteristic
117C23×C4×C59D411yescharacteristic
118C23×C4×C59D411yescharacteristic
119C23×C4×C59D411yescharacteristic
120C23×C4×C59D411yescharacteristic
121C23×C4×C59C2311yescharacteristic
122C23×C4×C59C2311yescharacteristic
123C23×C4×C59C2311yescharacteristic
124C2×M16×C59—22no—
125C2×M16×C59—22no—
126C2×M16×C59—44no—
127C22×C8×C59—22no—
128C22⋊C8×C59—22no—
129C22⋊C8×C59—22no—
130C22⋊C8×C59—22no—
131C22⋊C8×C59C2314yes—
132C24×C59—24no—
133C24×C59—42no—
134C24×C59—42no—
135C24×C59C22⋊C411yescharacteristic
136C24×C59C22⋊C411yescharacteristic
137C24×C59C22⋊C411yescharacteristic
138C24×C59C22⋊C411yescharacteristic
139C24×C59C2×D411yescharacteristic
140C24×C59C2×D411yescharacteristic
141C24×C59C2×D411yescharacteristic
142C23×D59—21no—
143C22×C4×C59—24no—
144C22×C4×C59—24no—
145C22×C4×C59—42no—
146C22×C4×C59—42no—
147C22×C4×C59—42no—
148C22×C4×C59—42no—
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×C59C22⋊C411yescharacteristic
158C22×C4×C59C22⋊C411yescharacteristic
159C22×C4×C59C22⋊C411yescharacteristic
160C22×C4×C59C22⋊C411yescharacteristic
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×C59C2×D411yescharacteristic
176C22×C4×C59C2×D411yescharacteristic
177C22×C4×C59C2×D411yescharacteristic
178C22×C4×C59C2×D411yescharacteristic
179C22×C4×C59C2×D411yescharacteristic
180C22×C4×C59C2×D411yescharacteristic
181C22×C4×C59C2×D411yescharacteristic
182C22×C4×C59C2×D411yescharacteristic
183C22×C4×C59C2×D411yescharacteristic
184C22×C4×C59C2411yescharacteristic
185C2×C22⋊D59—22no—
186C2×C22⋊D59—22no—
187C2×C22⋊D59—22no—
188C2×C22⋊D59—22no—
189C2×C22⋊D59—22no—
190C2×C22⋊D59—22no—
191C2×C22⋊D59—44no—
192C2×C22⋊D59—44no—
193C2×C22⋊D59—44no—
194C22×Dic59—21no—
195C22×Dic59—21no—
196C22×Dic59—21no—
197C22×Dic59—24no—
198C22×Dic59—44no—
199C22×Dic59—44no—
200C22×Dic59—44no—
201#11745685—44no—
202#11745685—44no—
203#11745685—44no—
204#11745685—44no—
205C2×D236—21no—
206C2×D236—42no—
207C2×D236C22×C412yes—
208C2×C4×D59—22no—
209C2×C4×D59—22no—
210C2×C4×D59—44no—
211C2×Dic118—21no—
212C2×Dic118—42no—
213C2×Dic118C22×C412yes—
214M16×C59—44no—
215M16×C59—44no—
216C2×C8×C59—24no—
217C2×C8×C59—44no—
218C22⋊Dic59—22no—
219C22⋊Dic59—22no—
220C22⋊Dic59—22no—
221C22⋊Dic59—22no—
222C22⋊Dic59—22no—
223C22⋊Dic59—22no—
224C22⋊Dic59—44no—
225C22⋊Dic59—44no—
226(C2×D59)⋊C4—22no—
227(C2×D59)⋊C4—22no—
228(C2×D59)⋊C4—22no—
229(C2×D59)⋊C4—22no—
230C4⋊Dic59—21no—
231C4⋊Dic59—21no—
232C4⋊Dic59C22×C412yes—
233C4⋊Dic59C22×C412yes—
234Dic59⋊C4—22no—
235Dic59⋊C4—22no—
236Dic59⋊C4—22no—
237Dic59⋊C4—22no—
238C4×Dic59—22no—
239C4×Dic59—22no—
240C23×C59—22no—
241C23×C59—22no—
242C23×C59—22no—
243C23×C59—22no—
244C23×C59—22no—
245C23×C59—22no—
246C23×C59—22no—
247C23×C59—22no—
248C23×C59—22no—
249C23×C59—22no—
250C23×C59—22no—
251C23×C59—22no—
252C23×C59—41no—
253C23×C59—41no—
254C23×C59—41no—
255C23×C59—41no—
256C23×C59—41no—
257C23×C59—41no—
258C23×C59—41no—
259C23×C59—41no—
260C23×C59—416no—
261C23×C59#9914yes—
262C23×C59C2×C22⋊C411yescharacteristic
263C23×C59C2×C22⋊C411yescharacteristic
264C23×C59C2×C22⋊C411yescharacteristic
265C23×C59C2×C22⋊C411yescharacteristic
266C23×C59C2×C22⋊C411yescharacteristic
267C23×C59C2×C22⋊C411yescharacteristic
268C23×C59C22×D411yescharacteristic
269C22×D59—22no—
270C22×D59—42no—
271C22×D59—42no—
272C22×D59—42no—
273C2×C4×C59—22no—
274C2×C4×C59—22no—
275C2×C4×C59—22no—
276C2×C4×C59—22no—
277C2×C4×C59—22no—
278C2×C4×C59—22no—
279C2×C4×C59—22no—
280C2×C4×C59—22no—
281C2×C4×C59—22no—
282C2×C4×C59—22no—
283C2×C4×C59—22no—
284C2×C4×C59—22no—
285C2×C4×C59—41no—
286C2×C4×C59—41no—
287C2×C4×C59—41no—
288C2×C4×C59—41no—
289C2×C4×C59—41no—
290C2×C4×C59—41no—
291C2×C4×C59—41no—
292C2×C4×C59—41no—
293C2×C4×C59—41no—
294C2×C4×C59—41no—
295C2×C4×C59—41no—
296C2×C4×C59—41no—
297C2×C4×C59—41no—
298C2×C4×C59—41no—
299C2×C4×C59—41no—
300C2×C4×C59—41no—
301C2×C4×C59C2×C22⋊C411yescharacteristic
302C2×C4×C59C2×C22⋊C411yescharacteristic
303C2×C4×C59C2×C22⋊C411yescharacteristic
304C2×C4×C59C2×C22⋊C411yescharacteristic
305C2×C4×C59C2×C22⋊C411yescharacteristic
306C2×C4×C59C2×C22⋊C411yescharacteristic
307C2×C4×C59C23×C411yescharacteristic
308C2×C4×C59C22×D411yescharacteristic
309C22⋊D59—44no—
310C22⋊D59—44no—
311C22⋊D59—44no—
312C22⋊D59—44no—
313C22⋊D59—44no—
314C22⋊D59—44no—
315C2×Dic59—22no—
316C2×Dic59—22no—
317C2×Dic59—22no—
318C2×Dic59—42no—
319C2×Dic59—42no—
320C2×Dic59—42no—
321C2×Dic59—44no—
322C2×Dic59—44no—
323C2×Dic59—44no—
324C2×Dic59—88no—
325D236—42no—
326D236—42no—
327C4×D59—44no—
328C4×D59—44no—
329Dic118—42no—
330Dic118—42no—
331C8×C59—44no—
332#17587—591nomaximal, Sylow
333C22×C59—28no—
334C22×C59—21no—
335C22×C59—21no—
336C22×C59—21no—
337C22×C59—21no—
338C22×C59—21no—
339C22×C59—21no—
340C22×C59—21no—
341C22×C59—21no—
342C22×C59—21no—
343C22×C59—21no—
344C22×C59—21no—
345C22×C59—21no—
346C22×C59—21no—
347C22×C59—21no—
348C22×C59—21no—
349C22×C59—21no—
350C22×C59—44no—
351C22×C59—44no—
352C22×C59—44no—
353C22×C59—44no—
354C22×C59—44no—
355C22×C59—44no—
356C22×C59C2×#9912yes—
357C22×C59C2×#9912yes—
358C22×C59C2×#9912yes—
359C22×C59#42112yes—
360C22×C59C22×C22⋊C411yescharacteristic
361C22×C59#57512yes—
362C2×D59—42no—
363C2×D59—42no—
364C2×D59—42no—
365C2×D59—84no—
366C4×C59—21no—
367C4×C59—21no—
368C4×C59—21no—
369C4×C59—21no—
370C4×C59—21no—
371C4×C59—21no—
372C4×C59—21no—
373C4×C59—21no—
374Dic59—42no—
375Dic59—42no—
376Dic59—42no—
377Dic59—84no—
378C2×#525—591no—
379C2×#407D5911yescharacteristic, complemented
380C2×#381—591no—
381#1516—594no—
382#1511—592no—
383#1510—592no—
384#1504—594no—
385C2×C59—22no—
386C2×C59—22no—
387C2×C59—22no—
388C2×C59—22no—
389C2×C59—22no—
390C2×C59—41no—
391C2×C59—41no—
392C2×C59C22×#9911yescharacteristic
393C2×C59#289611yescharacteristic
394C2×C59C2×#42111yescharacteristic
395D59—82no—
396C22×#41—591no—
397C24×C4C2×D5911yescharacteristic
398C22×M16—21no—
399#525—592no—
400#525—592no—
401#525—592no—
402#525—592no—
403#525—1181no—
404#525—1181no—
405#525—1181no—
406#525—1181no—
407C2×#123—1181no—
408C2×C22⋊Q8—591no—
409C2×C22⋊Q8—591no—
410C2×#121—591no—
411C2×#121—591no—
412C2×#120—1181no—
413C2×C4×D4—1181no—
414C2×C4×D4—1181no—
415C2×#117—591no—
416C22×C22⋊C4—1181no—
417#407—21no—
418#407—21no—
419#407C2×D5912yes—
420#407C2×D5912yescomplemented
421C2×C22⋊C8—21no—
422C2×C22⋊C8C2×D5912yescomplemented
423#381—592no—
424#381—592no—
425#381—1181no—
426#381—1181no—
427C2×#95—592no—
428C2×#95—1181no—
429#328—598no—
430#327—598no—
431C59#1758711yescharacteristic, complemented, Sylow
432C25D23611yescharacteristic
433C2×#41—592no—
434C2×#41—592no—
435C2×#41—1181no—
436C2×#41—1181no—
437C2×#41—2364no—
438C22×Q8—591no—
439C22×D4—591no—
440C22×D4—1181no—
441C22×D4—1181no—
442C22×D4—1181no—
443C23×C4—44no—
444C23×C4—1181no—
445C23×C4—1182no—
446C23×C4C4×D5911yescharacteristic
447C23×C4C4×D5911yescharacteristic
448C23×C4C4×D5911yescharacteristic
449C23×C4C4×D5911yescharacteristic
450C23×C4D23611yescharacteristic
451C23×C4D23611yescharacteristic
452C23×C4D23611yescharacteristic
453C23×C4C22⋊D5911yescharacteristic
454C23×C4C22⋊D5911yescharacteristic
455C23×C4C22⋊D5911yescharacteristic
456C23×C4C22⋊D5911yescharacteristic
457C23×C4C22×D5911yescharacteristic
458C23×C4C22×D5911yescharacteristic
459C23×C4C22×D5911yescharacteristic
460C2×M16—22no—
461C2×M16—22no—
462C2×M16—44no—
463C22×C8—22no—
464#123—1182no—
465#123—1182no—
466#123—1182no—
467#123—1182no—
468C22⋊Q8—592no—
469C22⋊Q8—592no—
470C22⋊Q8—592no—
471C22⋊Q8—592no—
472C22⋊Q8—1181no—
473C22⋊Q8—1181no—
474C22⋊Q8—1181no—
475C22⋊Q8—1181no—
476#121—592no—
477#121—592no—
478#121—592no—
479#121—592no—
480#121—1181no—
481#121—1181no—
482#121—1181no—
483#121—1181no—
484#120—1182no—
485#120—1182no—
486#120—1182no—
487#120—1182no—
488C4×D4—1182no—
489C4×D4—1182no—
490C4×D4—1182no—
491C4×D4—1182no—
492C4×D4—1182no—
493C4×D4—1182no—
494C4×D4—1182no—
495C4×D4—1182no—
496#117—592no—
497#117—592no—
498#117—1181no—
499#117—1181no—
500C2×C4⋊C4—591no—
501C2×C4⋊C4—591no—
502C2×C4⋊C4—1181no—
503C2×C4⋊C4—1181no—
504C2×C22⋊C4—1181no—
505C2×C22⋊C4—1181no—
506C2×C22⋊C4—1181no—
507C2×C22⋊C4—1181no—
508C2×C22⋊C4—1181no—
509C2×C22⋊C4—1182no—
510C2×C22⋊C4—1182no—
511C2×C22⋊C4—2364no—
512C2×C42—1181no—
513C22⋊C8—22no—
514C22⋊C8—22no—
515C22⋊C8—22no—
516C22⋊C8C22×D5914yes—
517#95—594no—
518#95—1182no—
519#95—1182no—
520#95—1182no—
521C24—24no—
522C24—42no—
523C24—42no—
524C24—1181no—
525C24(C2×D59)⋊C411yescharacteristic
526C24(C2×D59)⋊C411yescharacteristic
527C24(C2×D59)⋊C411yescharacteristic
528C24(C2×D59)⋊C411yescharacteristic
529C24C2×D23611yescharacteristic
530C24C2×D23611yescharacteristic
531C24C2×D23611yescharacteristic
532#41—2364no—
533#41—2364no—
534#41—2364no—
535#41—2364no—
536C2×Q8—592no—
537C2×Q8—1181no—
538C2×Q8—2362no—
539C2×D4—592no—
540C2×D4—1182no—
541C2×D4—1182no—
542C2×D4—1182no—
543C2×D4—1182no—
544C2×D4—1182no—
545C2×D4—1182no—
546C2×D4—1181no—
547C2×D4—2362no—
548C2×D4—2364no—
549C2×D4—2364no—
550C2×D4—2364no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—1181no—
566C22×C4—1181no—
567C22×C4—1181no—
568C22×C4—1182no—
569C22×C4—1182no—
570C22×C4—1184no—
571C22×C4—2364no—
572C22×C4—2364no—
573C22×C4—2364no—
574C22×C4—2364no—
575C22×C4(C2×D59)⋊C411yescharacteristic
576C22×C4(C2×D59)⋊C411yescharacteristic
577C22×C4(C2×D59)⋊C411yescharacteristic
578C22×C4(C2×D59)⋊C411yescharacteristic
579C22×C4(C2×D59)⋊C411yescharacteristic
580C22×C4(C2×D59)⋊C411yescharacteristic
581C22×C4(C2×D59)⋊C411yescharacteristic
582C22×C4(C2×D59)⋊C411yescharacteristic
583C22×C4(C2×D59)⋊C411yescharacteristic
584C22×C4(C2×D59)⋊C411yescharacteristic
585C22×C4(C2×D59)⋊C411yescharacteristic
586C22×C4(C2×D59)⋊C411yescharacteristic
587C22×C4C2×C4×D5911yescharacteristic
588C22×C4C2×C4×D5911yescharacteristic
589C22×C4C2×C4×D5911yescharacteristic
590C22×C4C2×C4×D5911yescharacteristic
591C22×C4C2×C4×D5911yescharacteristic
592C22×C4C2×C4×D5911yescharacteristic
593C22×C4C2×D23611yescharacteristic
594C22×C4C2×D23611yescharacteristic
595C22×C4C2×D23611yescharacteristic
596C22×C4C2×C22⋊D5911yescharacteristic
597C22×C4C2×C22⋊D5911yescharacteristic
598C22×C4C2×C22⋊D5911yescharacteristic
599C22×C4C2×C22⋊D5911yescharacteristic
600C22×C4C2×C22⋊D5911yescharacteristic
601C22×C4C2×C22⋊D5911yescharacteristic
602C22×C4C23×D5911yescharacteristic
603M16—44no—
604M16—44no—
605C2×C8—24no—
606C2×C8—44no—
607C4⋊C4—592no—
608C4⋊C4—592no—
609C4⋊C4—1181no—
610C4⋊C4—1181no—
611C4⋊C4—1182no—
612C4⋊C4—1182no—
613C4⋊C4—1182no—
614C4⋊C4—1182no—
615C22⋊C4—1182no—
616C22⋊C4—1182no—
617C22⋊C4—1182no—
618C22⋊C4—1182no—
619C22⋊C4—1182no—
620C22⋊C4—1182no—
621C22⋊C4—1182no—
622C22⋊C4—1182no—
623C22⋊C4—1182no—
624C22⋊C4—1182no—
625C22⋊C4—2364no—
626C22⋊C4—2364no—
627C42—1182no—
628C42—1182no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—416no—
650C23—1182no—
651C23—2362no—
652C23—2362no—
653C23—2362no—
654C23#1427364114yes—
655C23C2×(C2×D59)⋊C411yescharacteristic
656C23C2×(C2×D59)⋊C411yescharacteristic
657C23C2×(C2×D59)⋊C411yescharacteristic
658C23C2×(C2×D59)⋊C411yescharacteristic
659C23C2×(C2×D59)⋊C411yescharacteristic
660C23C2×(C2×D59)⋊C411yescharacteristic
661C23C22×D23611yescharacteristic
662Q8—2362no—
663Q8—2362no—
664D4—2362no—
665D4—2362no—
666D4—2364no—
667D4—2364no—
668D4—2364no—
669D4—2364no—
670D4—2364no—
671D4—2364no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—1182no—
701C2×C4—1182no—
702C2×C4—1182no—
703C2×C4—4728no—
704C2×C4—2364no—
705C2×C4—2364no—
706C2×C4—2364no—
707C2×C4—2364no—
708C2×C4—2364no—
709C2×C4—2362no—
710C2×C4—2362no—
711C2×C4—2362no—
712C2×C4C2×(C2×D59)⋊C411yescharacteristic
713C2×C4C2×(C2×D59)⋊C411yescharacteristic
714C2×C4C2×(C2×D59)⋊C411yescharacteristic
715C2×C4C2×(C2×D59)⋊C411yescharacteristic
716C2×C4C2×(C2×D59)⋊C411yescharacteristic
717C2×C4C2×(C2×D59)⋊C411yescharacteristic
718C2×C4C22×C4×D5911yescharacteristic
719C2×C4C22×C22⋊D5911yescharacteristic
720C8—44no—
721C22—28no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—4724no—
745C22—2362no—
746C22—2362no—
747C22—2362no—
748C22C2×#1427364112yes—
749C22C2×#1427364112yes—
750C22C2×#1427364112yes—
751C22#1683741812yes—
752C22C22×(C2×D59)⋊C411yescharacteristic
753C22#1683820212yes—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—21no—
760C4—21no—
761C4—21no—
762C4—4724no—
763C4—2362no—
764C4—2362no—
765C4—2362no—
766C2—22no—
767C2—22no—
768C2—22no—
769C2—22no—
770C2—22no—
771C2—41no—
772C2—41no—
773C2—4722no—
774C2C22×#1427364111yescharacteristic
775C2#2143261611yescharacteristic
776C2C2×#1683741811yescharacteristic
subgroupG/H
centerC22C22×(C2×D59)⋊C4
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC2×C59×#407C2
socleC22×C59C22×C22⋊C4
prime radicalC2×#16837913C2
cosocleC22×C4×C59C24
hypercenterC2×#407D59
hypocenterC59#17587
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C2×#16837265C2semidirect
3. #21422653C2semidirect
4. #21422630C2semidirect
5. #21422626C2semidirect
6. #21422601C2semidirect
7. C2×C59×#407C2semidirect
8. C22×#11745685C4semidirect
13. #16837913C4semidirect
14. #16837913C4semidirect
18. C2×#14273706C4semidirect
20. C2×#14273701C4semidirect
25. C2×#14273686C4semidirect
30. #16837265C22semidirect
32. C2×C59⋊#95C22semidirect
33. #16837140C22semidirect
34. #16837137C22semidirect
40. C59×#407C22semidirect
42. C2×C22⋊C8×C59C22semidirect
47. C2×#11745685C2×C4semidirect
48. C22×Dic118C2×C4semidirect
49. C22×D236C2×C4semidirect
64. #14273706C2×C4semidirect
65. #14273706C2×C4semidirect
72. #14273701C2×C4semidirect
73. #14273701C2×C4semidirect
90. #14273686C2×C4semidirect
91. C2×C4⋊Dic59C2×C4semidirect
92. C2×C4⋊Dic59C2×C4semidirect
379. C2×#407D59semidirect
420. #407C2×D59semidirect
422. C2×C22⋊C8C2×D59semidirect
431. C59#17587semidirect

Maximal subgroups

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

subgroupindex
C2×#168379132
C2×#168372652
#214226532
#214226302
#214226262
#214226012
C2×C59×#4072
#1758759