Finite Group Databasebeta

← #29452370

Subgroups — #29452370

Order 15104.

2694 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838168C211yesmaximal, characteristic
2#21437297C211yesmaximal, characteristic
3C2×#16837883C211yesmaximal, characteristic
4#21432695C214yesmaximal, complemented
5#21432692C214yesmaximal, complemented
6#21432690C214yesmaximal, complemented
7#21432687C214yesmaximal, complemented
8#21432686C211yesmaximal, characteristic, complemented
9#21432685C211yesmaximal, characteristic, complemented
10#21432683C214yesmaximal, complemented
11C2×#16837442C211yesmaximal, characteristic, complemented
12#428×D59C214yesmaximal, complemented
13C2×C59×#428C211yesmaximal, characteristic, complemented
14C22×#11745685C2211yescharacteristic
15#16838168C4116yescomplemented
16C2×#14273735C2214yes—
17C2×#14273733C2214yes—
18C22×#11745664C2211yescharacteristic
19C2×M16×D59C2214yes—
20#16837883—22no—
21#16837883—22no—
22#16837883C2214yes—
23#16837883C2214yes—
24#16837883C2212yes—
25#16837883C2212yes—
26#16837882C2212yes—
27#16837882C2212yes—
28#16837879—21no—
29#16837876—21no—
30#16837875—22no—
31C4×#11745685—22no—
32#16837870—22no—
33C2×#14273692—21no—
34C2×#14273689—21no—
35C2×C4×C22⋊D59—22no—
36C2×#14273686C2211yescharacteristic
37C2×#14273686C2211yescharacteristic
38C2×#14273685C2212yes—
39#117×D59C2214yes—
40C2×C4⋊C4×D59C2212yes—
41#16837445C2212yes—
42#16837445C2212yes—
43#16837444C2212yes—
44#16837444C2212yes—
45#16837444C2212yescomplemented
46#16837444C2212yescomplemented
47#16837443C2218yescomplemented
48#16837443C2218yescomplemented
49#16837442C2214yes—
50#16837442C2214yescomplemented
51#16837442C2212yescomplemented
52#16837442C2212yescomplemented
53#16837441C2218yescomplemented
54#16837441C2218yescomplemented
55#16837440C2214yescomplemented
56#16837439C2218yescomplemented
57#16837438C2214yescomplemented
58#16837437C2218yescomplemented
59C2×#14273660C2212yescomplemented
60#107×D59C2218yescomplemented
61C2×#14273658C2212yescomplemented
62#106×D59C2218yescomplemented
63C22×M16×C59C2211yescharacteristic
64C2×#117×C59C2211yescharacteristic
65C22×C4⋊C4×C59C2211yescharacteristic
66C59×#428C2214yes—
67C59×#428C2214yescomplemented
68C2×#107×C59C2212yescomplemented
69C2×#106×C59C2212yescomplemented
70C2×#11745685C2×C418yes—
71C2×#11745685D412yes—
72C2×#11745685D412yes—
73C2×#11745685Q818yes—
74C2×#11745685C2312yes—
75C2×#11745685C2312yes—
76C22×Dic118D411yescharacteristic
77C22×D236D411yescharacteristic
78C22×C22⋊D59D412yes—
79C22×C4×D59—22no—
80C22×C4×D59C2312yes—
81#14273735C2×C4132yescomplemented
82#14273733C2×C4132yescomplemented
83C2×#11745664C2×C418yescomplemented
84C2×#11745664C2312yes—
85C2×#11745664C2312yes—
86C2×#11745659C2318yes—
87M16×D59C2×C4132yescomplemented
88C22×C59⋊C8C2312yes—
89C2×C8×D59C2318yes—
90C4×Dic118—22no—
91C4×Dic118—22no—
92#14273692—24no—
93#14273692—24no—
94#14273692—22no—
95#14273692—22no—
96C4×D236—22no—
97C4×D236—22no—
98#14273689—24no—
99#14273689—24no—
100#14273689—22no—
101#14273689—22no—
102C4×C22⋊D59—28no—
103C4×C22⋊D59—28no—
104C4×C22⋊D59—24no—
105C4×C22⋊D59—24no—
106(C22⋊D59)⋊C4—24no—
107(C22⋊D59)⋊C4—24no—
108#14273686—21no—
109#14273686—21no—
110#14273686—21no—
111#14273686—21no—
112#14273686C2312yes—
113#14273686C2312yes—
114#14273686C2312yes—
115#14273686C2312yes—
116#14273685—24no—
117#14273685C2314yes—
118#14273685C2318yes—
119#14273685C2314yes—
120#14273684—24no—
121#14273683—24no—
122C2×C4⋊Dic59C2311yescharacteristic
123C2×C4⋊Dic59C2311yescharacteristic
124C2×C4⋊Dic59C2311yescharacteristic
125C2×C4⋊Dic59C2311yescharacteristic
126C2×Dic59⋊C4—22no—
127C4⋊C4×D59—24no—
128C4⋊C4×D59C2314yes—
129C4⋊C4×D59C2318yes—
130C4⋊C4×D59C2314yes—
131C2×C22⋊Dic59—21no—
132C2×C22⋊Dic59—21no—
133C2×(C2×D59)⋊C4—22no—
134C22⋊C4×D59—24no—
135C2×C4×Dic59—21no—
136C2×C4×Dic59—21no—
137C2×C4×Dic59—22no—
138C42×D59—24no—
139#14273661C2314yes—
140#14273661C2314yes—
141#14273660C2314yes—
142#14273660C2318yes—
143#14273660C2314yes—
144#14273659C2314yes—
145#14273659C2314yes—
146#14273658C2314yes—
147#14273658C2318yes—
148#14273658C2314yes—
149C23×C4×C59—21no—
150C23×C4×C59C2311yescharacteristic
151C2×M16×C59C2×C418yescomplemented
152C2×M16×C59C2312yes—
153C2×M16×C59C2312yes—
154C22×C8×C59C2312yes—
155#117×C59—21no—
156#117×C59—21no—
157#117×C59C2312yes—
158#117×C59C2312yes—
159C2×C4⋊C4×C59—21no—
160C2×C4⋊C4×C59—21no—
161C2×C4⋊C4×C59—21no—
162C2×C4⋊C4×C59C2312yes—
163C2×C4⋊C4×C59C2312yes—
164C2×C4⋊C4×C59C2311yescharacteristic
165C2×C4⋊C4×C59C2312yes—
166C2×C4⋊C4×C59C2311yescharacteristic
167C2×C22⋊C4×C59—21no—
168C2×C42×C59—21no—
169#107×C59C2318yes—
170#106×C59C2318yes—
171C24×C59C2×D411yescharacteristic
172C23×D59C2×D412yes—
173C22×C4×C59—22no—
174C22×C4×C59—21no—
175C22×C4×C59—21no—
176C22×C4×C59—22no—
177C22×C4×C59—22no—
178C22×C4×C59—82no—
179C22×C4×C59C22×C414yes—
180C22×C4×C59C2×D411yescharacteristic
181C22×C4×C59C2×D411yescharacteristic
182C22×C4×C59C2×D411yescharacteristic
183C22×C4×C59C2×Q814yes—
184C22×C4×C59C2411yescharacteristic
185C22×C4×C59C2411yescharacteristic
186C22×C4×C59C2411yescharacteristic
187C2×C22⋊D59C4⋊C4116yes—
188C2×C22⋊D59C2×D414yes—
189C2×C22⋊D59C2×D414yes—
190C22×Dic59—21no—
191C22×Dic59—21no—
192C22×Dic59—21no—
193C22×Dic59—21no—
194C22×Dic59C2×D412yes—
195#11745685C4⋊C4116yes—
196#11745685C4⋊C4116yes—
197#11745685C22×C418yes—
198#11745685C22×C418yes—
199#11745685C2×Q818yes—
200#11745685C2×Q818yes—
201C2×D236C4⋊C418yes—
202C2×D236C2×D412yes—
203C2×D236C2×D412yes—
204C2×C4×D59—24no—
205C2×C4×D59—24no—
206C2×C4×D59—28no—
207C2×C4×D59—84no—
208C2×C4×D59C22×C418yes—
209C2×C4×D59C2×D414yes—
210C2×C4×D59C2×Q818yes—
211C2×C4×D59C2414yes—
212C2×Dic118C4⋊C418yes—
213C2×Dic118C2×D412yes—
214C2×Dic118C2×D412yes—
215M16×C59C22×C418yes—
216M16×C59C22×C418yescomplemented
217C2×C8×C59C22×C418yescomplemented
218C2×C8×C59C2414yes—
219C4⋊C4×C59—22no—
220C4⋊C4×C59—22no—
221C4⋊C4×C59—22no—
222C4⋊C4×C59—21no—
223C4⋊C4×C59—21no—
224C4⋊C4×C59C2412yes—
225C4⋊C4×C59C2414yes—
226C4⋊C4×C59C2412yes—
227C22⋊C4×C59—22no—
228C22⋊C4×C59—22no—
229C42×C59—22no—
230C42×C59—22no—
231C22⋊Dic59—22no—
232C22⋊Dic59—22no—
233C22⋊Dic59—22no—
234C22⋊Dic59—22no—
235(C2×D59)⋊C4—24no—
236(C2×D59)⋊C4—24no—
237(C2×D59)⋊C4—28no—
238C4⋊Dic59—21no—
239C4⋊Dic59—21no—
240C4⋊Dic59—21no—
241C4⋊Dic59—21no—
242C4⋊Dic59C2412yes—
243C4⋊Dic59C2412yes—
244C4⋊Dic59C2412yes—
245C4⋊Dic59C2412yes—
246Dic59⋊C4—28no—
247Dic59⋊C4—24no—
248Dic59⋊C4—24no—
249C4×Dic59—22no—
250C4×Dic59—22no—
251C4×Dic59—22no—
252C4×Dic59—22no—
253C4×Dic59—24no—
254C4×Dic59—24no—
255C4×Dic59—28no—
256#11745664C22×C418yes—
257#11745664C22×C418yescomplemented
258C2×C59⋊C8C22×C418yescomplemented
259C2×C59⋊C8C2414yes—
260#11745659C22×C4132yescomplemented
261C8×D59C22×C4132yescomplemented
262C23×C59—41no—
263C23×C59—41no—
264C23×C59C2×C4⋊C414yes—
265C23×C59C22×D411yescharacteristic
266C23×C59C22×D411yescharacteristic
267C23×C59C22×D411yescharacteristic
268C22×D59—42no—
269C22×D59—42no—
270C22×D59C2×C4⋊C418yes—
271C22×D59C22×D414yes—
272C2×C4×C59—22no—
273C2×C4×C59—22no—
274C2×C4×C59—24no—
275C2×C4×C59—44no—
276C2×C4×C59—81no—
277C2×C4×C59—81no—
278C2×C4×C59—82no—
279C2×C4×C59—82no—
280C2×C4×C59C2×C4⋊C414yes—
281C2×C4×C59C2×C4⋊C414yes—
282C2×C4×C59C2×C4⋊C414yes—
283C2×C4×C59C23×C412yes—
284C2×C4×C59C23×C412yes—
285C2×C4×C59C23×C412yes—
286C2×C4×C59C22×D411yescharacteristic
287C2×C4×C59C22×D411yescharacteristic
288C2×C4×C59C22×D411yescharacteristic
289C2×C4×C59C22×Q812yes—
290C2×C4×C59C22×Q812yes—
291C2×C4×C59C22×Q812yes—
292C2×C4×C59C2511yescharacteristic
293C22⋊D59C2×C4⋊C4116yes—
294C22⋊D59C2×C4⋊C4116yes—
295C2×Dic59—22no—
296C2×Dic59—22no—
297C2×Dic59—22no—
298C2×Dic59—22no—
299C2×Dic59—42no—
300C2×Dic59—42no—
301C2×Dic59—81no—
302C2×Dic59—81no—
303C2×Dic59C2×C4⋊C418yes—
304C2×Dic59C22×D414yes—
305D236C2×C4⋊C418yes—
306D236C2×C4⋊C418yes—
307C4×D59—84no—
308C4×D59—84no—
309C4×D59—88no—
310C4×D59C2×C4⋊C4116yes—
311C4×D59C23×C418yes—
312C4×D59C22×Q818yes—
313Dic118C2×C4⋊C418yes—
314Dic118C2×C4⋊C418yes—
315C8×C59C23×C418yes—
316C59⋊C8C23×C418yes—
317#60109—591nomaximal, Sylow
318C22×C59—21no—
319C22×C59—21no—
320C22×C59—21no—
321C22×C59—21no—
322C22×C59—21no—
323C22×C59—21no—
324C22×C59—44no—
325C22×C59C22×C4⋊C412yes—
326C22×C59C22×C4⋊C412yes—
327C22×C59C22×C4⋊C412yes—
328C22×C59C23×D411yescharacteristic
329C2×D59—24no—
330C2×D59—24no—
331C2×D59—48no—
332C2×D59C22×C4⋊C418yes—
333C4×C59—44no—
334C4×C59—42no—
335C4×C59—42no—
336C4×C59C22×C4⋊C412yes—
337C4×C59C22×C4⋊C412yes—
338C4×C59C22×C4⋊C412yes—
339C4×C59C24×C411yescharacteristic
340C4×C59C23×Q811yescharacteristic
341Dic59—42no—
342Dic59—42no—
343Dic59—42no—
344Dic59—42no—
345Dic59C22×C4⋊C418yes—
346C2×#568—591no—
347#3428—591no—
348C2×#520—591no—
349#2913—594no—
350#2913—594no—
351#2912—594no—
352#2912—594no—
353#2911—594no—
354#2911—591no—
355#2911—591no—
356C2×#428—594no—
357C2×#428—591no—
358C2×#428D5911yescharacteristic, complemented
359C2×C59—22no—
360C2×C59—22no—
361C2×C59—22no—
362C2×C59C23×C4⋊C411yescharacteristic
363C2×C59#358511yescharacteristic
364C2×C59#358611yescharacteristic
365D59—28no—
366C22×#41—591no—
367#568—5916no—
368C2×#131—594no—
369C2×#131—594no—
370C22×M16—591no—
371C22×M16—594no—
372C22×M16C2×D5911yescharacteristic
373#520—592no—
374#520—592no—
375#520—592no—
376#520—594no—
377#520—594no—
378#520—592no—
379#520—1182no—
380#520—1182no—
381#519—1181no—
382#518—1182no—
383#518—1181no—
384C4×#41—1182no—
385C4×#41—1182no—
386C2×C4×Q8—1181no—
387C2×C4×D4—1181no—
388C2×C4×D4—1182no—
389C2×#117—591no—
390C2×#117—591no—
391C2×#117—594no—
392C2×#117—592no—
393C2×#117C2×D5911yescharacteristic
394C22×C4⋊C4—592no—
395C22×C4⋊C4C2×D5911yescharacteristic
396#428—592no—
397#428—592no—
398#428—592no—
399#428—592no—
400#428—592no—
401#428—592no—
402#428—594no—
403#428—594no—
404#428—592no—
405#428—592no—
406#428—598no—
407#428—598no—
408#428—598no—
409#428—598no—
410#428C2×D5914yes—
411#428C2×D5914yescomplemented
412#427—594no—
413#427—594no—
414#427—598no—
415#427—598no—
416C2×#107—592no—
417C2×#107—598no—
418C2×#107C2×D5912yescomplemented
419C2×#106—592no—
420C2×#106—598no—
421C2×#106C2×D5912yescomplemented
422C59#6010911yescharacteristic, complemented, Sylow
423C2×#41—598no—
424C2×#41—592no—
425C2×#41—592no—
426C2×#41—598no—
427C2×#41—592no—
428C2×#41—592no—
429C22×Q8—591no—
430C22×D4—592no—
431C22×D4—591no—
432C23×C4—21no—
433C23×C4—592no—
434C23×C4—1182no—
435C23×C4C22×D5911yescharacteristic
436#131—5932no—
437#131—5932no—
438C2×M16—598no—
439C2×M16—592no—
440C2×M16—592no—
441C2×M16—5932no—
442C2×M16—598no—
443C2×M16C4×D5918yescomplemented
444C2×M16C22×D5912yes—
445C2×M16C22×D5912yes—
446C22×C8—592no—
447C22×C8—598no—
448C22×C8C22×D5912yes—
449C4×Q8—1182no—
450C4×Q8—1182no—
451C4×Q8—1184no—
452C4×Q8—1184no—
453C4×Q8—1182no—
454C4×Q8—1182no—
455C4×D4—1182no—
456C4×D4—1182no—
457C4×D4—1184no—
458C4×D4—1184no—
459C4×D4—1184no—
460C4×D4—1184no—
461C4×D4—1182no—
462C4×D4—1182no—
463C4×D4—1188no—
464C4×D4—1188no—
465C4×D4—1184no—
466C4×D4—1184no—
467#117—21no—
468#117—21no—
469#117—592no—
470#117—592no—
471#117—592no—
472#117—592no—
473#117—594no—
474#117—598no—
475#117—594no—
476#117—1184no—
477#117—1184no—
478#117—1184no—
479#117—1181no—
480#117—1181no—
481#117—1181no—
482#117—1181no—
483#117C22×D5912yes—
484#117C22×D5912yes—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—591no—
489C2×C4⋊C4—591no—
490C2×C4⋊C4—591no—
491C2×C4⋊C4—591no—
492C2×C4⋊C4—598no—
493C2×C4⋊C4—594no—
494C2×C4⋊C4—594no—
495C2×C4⋊C4—1184no—
496C2×C4⋊C4—1182no—
497C2×C4⋊C4C22×D5912yes—
498C2×C4⋊C4C22×D5912yes—
499C2×C4⋊C4C22×D5912yes—
500C2×C4⋊C4C22×D5911yescharacteristic
501C2×C4⋊C4C22×D5911yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—1184no—
504C2×C22⋊C4—1182no—
505C2×C22⋊C4—1181no—
506C2×C22⋊C4—1181no—
507C2×C42—21no—
508C2×C42—1184no—
509C2×C42—1182no—
510C2×C42—1181no—
511C2×C42—1181no—
512#107—594no—
513#107—594no—
514#107—594no—
515#107—598no—
516#107—594no—
517#107C22×D5918yes—
518#106—594no—
519#106—594no—
520#106—598no—
521#106—594no—
522#106—594no—
523#106C22×D5918yes—
524C24—592no—
525C24D4×D5911yescharacteristic
526#41—5916no—
527#41—5916no—
528#41—598no—
529#41—598no—
530#41—598no—
531#41—598no—
532C2×Q8—598no—
533C2×Q8—592no—
534C2×Q8—592no—
535C2×D4—5916no—
536C2×D4—594no—
537C2×D4—594no—
538C2×D4—598no—
539C2×D4—592no—
540C2×D4—592no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—82no—
547C22×C4—592no—
548C22×C4—598no—
549C22×C4—594no—
550C22×C4—598no—
551C22×C4—594no—
552C22×C4—1184no—
553C22×C4—1184no—
554C22×C4—1188no—
555C22×C4—1181no—
556C22×C4—1181no—
557C22×C4—1181no—
558C22×C4—1181no—
559C22×C4—4724no—
560C22×C4C2×C4×D5914yes—
561C22×C4D4×D5911yescharacteristic
562C22×C4D4×D5911yescharacteristic
563C22×C4D4×D5911yescharacteristic
564C22×C4Q8×D5914yes—
565C22×C4C23×D5911yescharacteristic
566C22×C4C23×D5911yescharacteristic
567C22×C4C23×D5911yescharacteristic
568M16—598no—
569M16—598no—
570M16—5932no—
571M16C2×C4×D5918yes—
572M16C2×C4×D5918yescomplemented
573C2×C8—598no—
574C2×C8—594no—
575C2×C8—5932no—
576C2×C8C2×C4×D5918yescomplemented
577C2×C8C23×D5914yes—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—592no—
584C4⋊C4—592no—
585C4⋊C4—592no—
586C4⋊C4—592no—
587C4⋊C4—1188no—
588C4⋊C4—1184no—
589C4⋊C4—1184no—
590C4⋊C4—1181no—
591C4⋊C4—1181no—
592C4⋊C4—1181no—
593C4⋊C4—1181no—
594C4⋊C4C23×D5912yes—
595C4⋊C4C23×D5914yes—
596C4⋊C4C23×D5912yes—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—1184no—
600C22⋊C4—1184no—
601C22⋊C4—1188no—
602C22⋊C4—1182no—
603C22⋊C4—1182no—
604C22⋊C4—1182no—
605C22⋊C4—1182no—
606C42—22no—
607C42—22no—
608C42—1184no—
609C42—1184no—
610C42—1188no—
611C42—1182no—
612C42—1182no—
613C42—1182no—
614C42—1182no—
615C23—41no—
616C23—41no—
617C23—594no—
618C23—598no—
619C23—2362no—
620C23—2362no—
621C23C4⋊C4×D5914yes—
622C23C2×D4×D5911yescharacteristic
623C23C2×D4×D5911yescharacteristic
624C23C2×D4×D5911yescharacteristic
625Q8—598no—
626Q8—598no—
627D4—5916no—
628D4—5916no—
629D4—598no—
630D4—598no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—24no—
634C2×C4—44no—
635C2×C4—81no—
636C2×C4—81no—
637C2×C4—82no—
638C2×C4—82no—
639C2×C4—594no—
640C2×C4—598no—
641C2×C4—598no—
642C2×C4—598no—
643C2×C4—5916no—
644C2×C4—1182no—
645C2×C4—1182no—
646C2×C4—1182no—
647C2×C4—1182no—
648C2×C4—4724no—
649C2×C4—4724no—
650C2×C4—4728no—
651C2×C4—4721no—
652C2×C4—4721no—
653C2×C4—2362no—
654C2×C4—2362no—
655C2×C4C4⋊C4×D5914yes—
656C2×C4C4⋊C4×D5914yes—
657C2×C4C4⋊C4×D5914yes—
658C2×C4C22×C4×D5912yes—
659C2×C4C22×C4×D5912yes—
660C2×C4C22×C4×D5912yes—
661C2×C4C2×D4×D5911yescharacteristic
662C2×C4C2×D4×D5911yescharacteristic
663C2×C4C2×D4×D5911yescharacteristic
664C2×C4C2×Q8×D5912yes—
665C2×C4C2×Q8×D5912yes—
666C2×C4C2×Q8×D5912yes—
667C2×C4C24×D5911yescharacteristic
668C8—598no—
669C8C22×C4×D5918yes—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—21no—
676C22—44no—
677C22—598no—
678C22—1184no—
679C22—1184no—
680C22—2368no—
681C22C2×C4⋊C4×D5912yes—
682C22C2×C4⋊C4×D5912yes—
683C22C2×C4⋊C4×D5912yes—
684C22C22×D4×D5911yescharacteristic
685C4—44no—
686C4—42no—
687C4—42no—
688C4—598no—
689C4—2362no—
690C4—2362no—
691C4—2362no—
692C4—2362no—
693C4C2×C4⋊C4×D5912yes—
694C4C2×C4⋊C4×D5912yes—
695C4C2×C4⋊C4×D5912yes—
696C4C23×C4×D5911yescharacteristic
697C4C22×Q8×D5911yescharacteristic
698C2—22no—
699C2—22no—
700C2—22no—
701C2—1188no—
702C2C22×C4⋊C4×D5911yescharacteristic
703C2#2143887211yescharacteristic
704C2#2143887911yescharacteristic
subgroupG/H
centerC22C22×D4×D59
commutatorC4×C59C24×C4
FrattiniC2×C4C24×D59
FittingC2×C59×#428C2
socleC22×C59C23×D4
prime radicalC22×#11745685C22
cosocleC2×C4×C59C25
hypercenterC2×#428D59
hypocenterC59#60109
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
4. #21432695C2semidirect
5. #21432692C2semidirect
6. #21432690C2semidirect
7. #21432687C2semidirect
8. #21432686C2semidirect
9. #21432685C2semidirect
10. #21432683C2semidirect
11. C2×#16837442C2semidirect
12. #428×D59C2semidirect
13. C2×C59×#428C2semidirect
15. #16838168C4semidirect
45. #16837444C22semidirect
46. #16837444C22semidirect
47. #16837443C22semidirect
48. #16837443C22semidirect
50. #16837442C22semidirect
51. #16837442C22semidirect
52. #16837442C22semidirect
53. #16837441C22semidirect
54. #16837441C22semidirect
55. #16837440C22semidirect
56. #16837439C22semidirect
57. #16837438C22semidirect
58. #16837437C22semidirect
59. C2×#14273660C22semidirect
60. #107×D59C22semidirect
61. C2×#14273658C22semidirect
62. #106×D59C22semidirect
67. C59×#428C22semidirect
68. C2×#107×C59C22semidirect
69. C2×#106×C59C22semidirect
81. #14273735C2×C4semidirect
82. #14273733C2×C4semidirect
83. C2×#11745664C2×C4semidirect
87. M16×D59C2×C4semidirect
151. C2×M16×C59C2×C4semidirect
216. M16×C59C22×C4semidirect
217. C2×C8×C59C22×C4semidirect
257. #11745664C22×C4semidirect
258. C2×C59⋊C8C22×C4semidirect
260. #11745659C22×C4semidirect
261. C8×D59C22×C4semidirect
358. C2×#428D59semidirect
411. #428C2×D59semidirect
418. C2×#107C2×D59semidirect
421. C2×#106C2×D59semidirect
422. C59#60109semidirect
443. C2×M16C4×D59semidirect
572. M16C2×C4×D59semidirect
576. C2×C8C2×C4×D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168381682
#214372972
C2×#168378832
#214326952
#214326922
#214326902
#214326872
#214326862
#214326852
#214326832
C2×#168374422
#428×D592
C2×C59×#4282
#6010959