Finite Group Databasebeta

← #29455637

Subgroups — #29455637

Order 15104.

2714 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838200C211yesmaximal, characteristic, complemented
2#21437425C211yesmaximal, characteristic, complemented
3#21437299C211yesmaximal, characteristic, complemented
4#21433644C214yesmaximal, complemented
5#21433633C214yesmaximal, complemented
6#21433623C212yesmaximal, complemented
7#21433614C212yesmaximal, complemented
8#21433605C212yesmaximal, complemented
9#21433596C212yesmaximal, complemented
10#21433547C218yesmaximal, complemented
11C2×#16837428C211yesmaximal, characteristic, complemented
12#21432615C211yesmaximal, characteristic, complemented
13C2×#16837399C211yesmaximal, characteristic, complemented
14C22×#135×C59C211yesmaximal, characteristic, complemented
15C22×#11745685C2211yescharacteristic
16#16838200—28no—
17C2×#14273758C2212yes—
18C2×#14273757C2212yescomplemented
19C2×#14273753C2212yes—
20C2×#14273752C2212yescomplemented
21C2×#14273747C2214yescomplemented
22C22×#11745664C2211yescharacteristic
23#16837980—22no—
24#16837976C2212yes—
25#16837973C2212yescomplemented
26#16837969C2212yes—
27#16837966C2212yescomplemented
28#16837961—22no—
29#16837948C2214yescomplemented
30#16837913—22no—
31#16837909—22no—
32#16837885—22no—
33#16837885C2214yescomplemented
34#16837880C2212yescomplemented
35#16837877—22no—
36#16837877C2212yescomplemented
37#41×Dic59—22no—
38#41×Dic59C2214yescomplemented
39C2×#14273686—22no—
40C2×#14273686C2211yescharacteristic
41C2×#14273686C2211yescharacteristic
42#16837626C2218yescomplemented
43#16837622C2218yescomplemented
44#16837619C2218yescomplemented
45#16837615C2218yescomplemented
46#16837610C2218yescomplemented
47#16837605C2218yescomplemented
48#16837600C2218yescomplemented
49#16837595C2218yescomplemented
50#16837428C2212yescomplemented
51#16837428C2212yescomplemented
52#16837428C2214yescomplemented
53C2×Dic59⋊C8C2214yescomplemented
54#16837411C2212yescomplemented
55#16837407C2212yescomplemented
56#16837403C2214yescomplemented
57#16837399C2212yes—
58#16837399C2212yes—
59#16837399C2214yescomplemented
60#16837398C2214yescomplemented
61C2×#14273652C2212yescomplemented
62C2×#14273649C2212yescomplemented
63C22×#41×C59C2211yescharacteristic
64C22×#41×C59C2211yescharacteristic
65C2×#135×C59—28no—
66C2×#135×C59C2214yes—
67C2×#135×C59C2214yescomplemented
68C22×Q16×C59C2211yescharacteristic, complemented
69C22×SD16×C59C2211yescharacteristic, complemented
70C22×SD16×C59C2211yescharacteristic, complemented
71C22×D8×C59C2211yescharacteristic, complemented
72C23×C8×C59C2211yescharacteristic
73C2×#11745685—21no—
74C2×#11745685—21no—
75C2×#11745685—24no—
76C2×#11745685—24no—
77C2×#11745685C2312yes—
78C2×#11745685C2312yes—
79C22×Dic118C2311yescharacteristic
80C22×D236C2311yescharacteristic
81C22×C22⋊D59—21no—
82C22×C4×D59—21no—
83#14273758—28no—
84#14273757—28no—
85#14273753—28no—
86#14273752—28no—
87#14273747—216no—
88C2×#11745672C2314yes—
89C2×#11745670C2314yes—
90C2×#11745671C2314yes—
91C2×#11745669C2314yes—
92C2×#11745664—24no—
93C2×#11745664C2312yes—
94C2×#11745664C2312yes—
95C22×C59⋊C8C2312yes—
96#14273725C2314yes—
97#14273723C2314yes—
98#14273716C2314yes—
99#14273714C2314yes—
100#14273710—24no—
101#14273708—24no—
102#14273706—24no—
103#14273703—24no—
104#14273701—24no—
105#14273699—28no—
106#14273698—24no—
107#14273696—24no—
108#14273695—24no—
109Q8×Dic59—24no—
110Q8×Dic59C2318yes—
111D4×Dic59—28no—
112D4×Dic59—28no—
113D4×Dic59—24no—
114D4×Dic59C2318yes—
115C4×C22⋊D59—28no—
116#14273686—21no—
117#14273686—21no—
118#14273686—24no—
119#14273686—24no—
120#14273686—24no—
121#14273686D412yes—
122#14273686D412yes—
123#14273686C2312yes—
124#14273686C2312yes—
125#14273686C2312yes—
126#14273686C2312yes—
127C2×C4⋊Dic59—24no—
128C2×C4⋊Dic59D412yes—
129C2×C4⋊Dic59C2312yes—
130C2×C22⋊Dic59—21no—
131C2×C22⋊Dic59—24no—
132C2×C22⋊Dic59D412yes—
133C2×C4×Dic59—21no—
134C2×C4×Dic59—24no—
135C2×C4×Dic59C2312yes—
136Dic59⋊C8C2318yes—
137Dic59⋊C8C2318yes—
138#14273652C2314yes—
139#14273652C2314yes—
140#14273651C2318yes—
141#14273649C2314yes—
142#14273649C2314yes—
143#14273648C2318yes—
144C2×#41×C59—21no—
145C2×#41×C59—21no—
146C2×#41×C59—21no—
147C2×#41×C59—21no—
148C2×#41×C59—24no—
149C2×#41×C59—24no—
150C2×#41×C59—24no—
151C2×#41×C59D418yescomplemented
152C2×#41×C59C2312yes—
153C2×#41×C59C2312yes—
154C2×#41×C59C2312yes—
155C2×#41×C59C2312yes—
156C22×Q8×C59C2311yescharacteristic
157C22×Q8×C59C2311yescharacteristic
158C22×D4×C59—21no—
159C22×D4×C59—21no—
160C22×D4×C59C2311yescharacteristic
161C22×D4×C59C2311yescharacteristic
162C23×C4×C59—21no—
163C23×C4×C59—21no—
164C23×C4×C59C2311yescharacteristic
165#135×C59—216no—
166#135×C59—216no—
167C2×Q16×C59—24no—
168C2×Q16×C59C2314yes—
169C2×SD16×C59—24no—
170C2×SD16×C59—24no—
171C2×SD16×C59C2314yes—
172C2×SD16×C59C2314yes—
173C2×D8×C59—24no—
174C2×D8×C59C2314yes—
175C22×C8×C59—24no—
176C22×C8×C59C2312yes—
177C22×C8×C59C2311yescharacteristic
178C22×C8×C59C2311yescharacteristic
179C22×C8×C59C2312yes—
180C24×C59—21no—
181C24×C59—21no—
182C24×C59C2×D411yescharacteristic
183C23×D59—21no—
184#41×C59—28no—
185#41×C59—28no—
186#41×C59—24no—
187#41×C59—24no—
188#41×C59—24no—
189#41×C59—24no—
190#41×C59—24no—
191#41×C59—24no—
192#41×C59—44no—
193#41×C59—44no—
194#41×C59C2×D418yes—
195#41×C59C2×D418yes—
196C2×Q8×C59—21no—
197C2×Q8×C59—21no—
198C2×Q8×C59—22no—
199C2×Q8×C59—22no—
200C2×Q8×C59—22no—
201C2×Q8×C59C2×D414yes—
202C2×Q8×C59C2412yes—
203C2×Q8×C59C2412yes—
204C2×D4×C59—28no—
205C2×D4×C59—22no—
206C2×D4×C59—22no—
207C2×D4×C59—22no—
208C2×D4×C59—22no—
209C2×D4×C59—21no—
210C2×D4×C59—22no—
211C2×D4×C59—21no—
212C2×D4×C59—22no—
213C2×D4×C59—22no—
214C2×D4×C59—44no—
215C2×D4×C59C2×D414yes—
216C2×D4×C59C2412yes—
217C2×D4×C59C2412yes—
218C22×C4×C59—21no—
219C22×C4×C59—28no—
220C22×C4×C59—22no—
221C22×C4×C59—22no—
222C22×C4×C59—21no—
223C22×C4×C59—22no—
224C22×C4×C59—22no—
225C22×C4×C59—44no—
226C22×C4×C59C2×D411yescharacteristic
227C22×C4×C59C2×D411yescharacteristic
228C22×C4×C59C2×D411yescharacteristic
229C22×C4×C59C2×D414yes—
230C22×C4×C59#4114yes—
231C22×C4×C59C2411yescharacteristic
232C22×C4×C59C2411yescharacteristic
233C22×C4×C59C2411yescharacteristic
234C2×C22⋊D59—22no—
235C2×C22⋊D59—22no—
236C2×C22⋊D59—28no—
237C2×C22⋊D59—44no—
238C22×Dic59—21no—
239C22×Dic59—22no—
240C22×Dic59—28no—
241C22×Dic59C2×D414yes—
242#11745685—24no—
243#11745685—24no—
244#11745685—24no—
245#11745685—24no—
246#11745685—44no—
247#11745685—44no—
248C2×D236—22no—
249C2×D236—22no—
250C2×D236—21no—
251C2×D236C2412yes—
252C2×C4×D59—22no—
253C2×C4×D59—22no—
254C2×C4×D59—44no—
255C2×Dic118—22no—
256C2×Dic118—22no—
257C2×Dic118—21no—
258C2×Dic118C2412yes—
259Q16×C59—28no—
260SD16×C59—28no—
261SD16×C59—28no—
262D8×C59—28no—
263C2×C8×C59—22no—
264C2×C8×C59—22no—
265C2×C8×C59—24no—
266C2×C8×C59—24no—
267C2×C8×C59C2412yes—
268C2×C8×C59C2412yes—
269C22⋊Dic59—22no—
270C22⋊Dic59—22no—
271C22⋊Dic59—28no—
272C22⋊Dic59—28no—
273C22⋊Dic59C2×D414yes—
274C22⋊Dic59C2×D414yes—
275#11745672—28no—
276#11745671—28no—
277#11745670—28no—
278#11745669—28no—
279(C2×D59)⋊C4—28no—
280C4⋊Dic59—22no—
281C4⋊Dic59—28no—
282C4⋊Dic59C2×D414yes—
283C4⋊Dic59C2×D414yes—
284C4⋊Dic59C2414yes—
285Dic59⋊C4—28no—
286C4×Dic59—22no—
287C4×Dic59—22no—
288C4×Dic59—28no—
289C4×Dic59C2×D414yes—
290C4×Dic59C2414yes—
291#11745664—24no—
292#11745664—24no—
293C2×C59⋊C8—24no—
294C2×C59⋊C8C2414yes—
295C23×C59—22no—
296C23×C59—24no—
297C23×C59—22no—
298C23×C59—42no—
299C23×C59—42no—
300C23×C59—82no—
301C23×C59—82no—
302C23×C59#12114yes—
303C23×C59C22×D411yescharacteristic
304C23×C59C22×D411yescharacteristic
305C23×C59C22×D411yescharacteristic
306C22×D59—22no—
307C22×D59—42no—
308C22×D59—82no—
309Q8×C59—24no—
310Q8×C59—22no—
311Q8×C59—22no—
312Q8×C59—22no—
313Q8×C59—42no—
314Q8×C59C22×D414yes—
315D4×C59—28no—
316D4×C59—28no—
317D4×C59—24no—
318D4×C59—22no—
319D4×C59—22no—
320D4×C59—22no—
321D4×C59—44no—
322D4×C59—44no—
323D4×C59—42no—
324D4×C59C22×D414yes—
325C2×C4×C59—24no—
326C2×C4×C59—22no—
327C2×C4×C59—28no—
328C2×C4×C59—28no—
329C2×C4×C59—22no—
330C2×C4×C59—42no—
331C2×C4×C59—44no—
332C2×C4×C59—44no—
333C2×C4×C59#12114yes—
334C2×C4×C59#12114yes—
335C2×C4×C59#12114yes—
336C2×C4×C59C22×D411yescharacteristic
337C2×C4×C59C22×D411yescharacteristic
338C2×C4×C59C22×D411yescharacteristic
339C2×C4×C59C22×D412yes—
340C2×C4×C59C22×D412yes—
341C2×C4×C59C22×D412yes—
342C2×C4×C59C2×#4112yes—
343C2×C4×C59C2×#4112yes—
344C2×C4×C59C2×#4112yes—
345C2×C4×C59C2511yescharacteristic
346C22⋊D59—44no—
347C22⋊D59—44no—
348C22⋊D59—88no—
349C2×Dic59—24no—
350C2×Dic59—22no—
351C2×Dic59—44no—
352C2×Dic59—42no—
353C2×Dic59—88no—
354C2×Dic59—82no—
355C2×Dic59C22×D418yes—
356D236—22no—
357D236—22no—
358D236—42no—
359C4×D59—44no—
360C4×D59—44no—
361Dic118—22no—
362Dic118—22no—
363Dic118—42no—
364C8×C59—22no—
365C8×C59—22no—
366C59⋊C8—24no—
367#60422—591nomaximal, Sylow
368C22×C59—22no—
369C22×C59—22no—
370C22×C59—22no—
371C22×C59—24no—
372C22×C59—44no—
373C22×C59—44no—
374C22×C59—44no—
375C22×C59—42no—
376C22×C59—84no—
377C22×C59—84no—
378C22×C59C2×#12112yes—
379C22×C59C2×#12112yes—
380C22×C59C2×#12112yes—
381C22×C59C23×D411yescharacteristic
382C2×D59—44no—
383C2×D59—42no—
384C2×D59—84no—
385C4×C59—24no—
386C4×C59—42no—
387C4×C59C2×#12112yes—
388C4×C59C2×#12112yes—
389C4×C59C2×#12112yes—
390C4×C59C23×D411yescharacteristic
391C4×C59C22×#4111yescharacteristic
392Dic59—28no—
393Dic59—44no—
394Dic59—42no—
395C2×#575—591no—
396C22×#135D5911yescharacteristic, complemented
397#3449—591no—
398#3428—591no—
399#3046—594no—
400#3045—594no—
401#3044—592no—
402#3043—592no—
403#3042—592no—
404#3041—592no—
405#3035—598no—
406C2×#424—591no—
407#2896—591no—
408C2×#416—591no—
409C2×C59—22no—
410C2×C59—22no—
411C2×C59—22no—
412C2×C59—44no—
413C2×C59—82no—
414C2×C59C22×#12111yescharacteristic
415C2×C59#358412yes—
416D59—82no—
417C22×#41—591no—
418C22×#41C2×D5911yescharacteristic
419C22×#41C2×D5911yescharacteristic
420#575—1188no—
421C2×#137—592no—
422C2×#137—592no—
423C2×AGL(1,ℤ/8)—592no—
424C2×AGL(1,ℤ/8)—592no—
425C2×#135—28no—
426C2×#135—594no—
427C2×#135C2×D5914yes—
428C2×#135C2×D5914yescomplemented
429C22×Q16C2×D5911yescharacteristic, complemented
430C22×SD16C2×D5911yescharacteristic, complemented
431C22×SD16C2×D5911yescharacteristic, complemented
432C22×D8C2×D5911yescharacteristic, complemented
433C22×M16—591no—
434C23×C8C2×D5911yescharacteristic
435#537—1182no—
436#536—592no—
437#536—592no—
438#535—592no—
439#535—592no—
440#534—1182no—
441#532—594no—
442#525—1182no—
443#525—1182no—
444#520—594no—
445#520—1182no—
446#519—592no—
447#518—592no—
448#518—1182no—
449C4×#41—594no—
450C4×#41—1182no—
451C2×#117—591no—
452C2×#117—591no—
453C2×#117—1182no—
454#464—598no—
455#464—598no—
456#463—598no—
457#463—598no—
458#462—598no—
459#461—598no—
460#460—598no—
461#459—598no—
462#424—592no—
463#424—592no—
464#424—594no—
465C2×C4⋊C8—594no—
466#419—592no—
467#418—592no—
468#417—594no—
469#416—594no—
470#416—592no—
471#416—592no—
472#416—594no—
473C2×#103—592no—
474C2×#102—592no—
475C59#6042211yescharacteristic, complemented, Sylow
476C2×#41—21no—
477C2×#41—21no—
478C2×#41—21no—
479C2×#41—21no—
480C2×#41—24no—
481C2×#41—24no—
482C2×#41—24no—
483C2×#41—592no—
484C2×#41—592no—
485C2×#41—1181no—
486C2×#41—1181no—
487C2×#41—1184no—
488C2×#41—1184no—
489C2×#41C22⋊D5918yescomplemented
490C2×#41C22×D5912yes—
491C2×#41C22×D5912yes—
492C2×#41C22×D5912yes—
493C2×#41C22×D5912yes—
494C22×Q8—591no—
495C22×Q8C22×D5911yescharacteristic
496C22×Q8C22×D5911yescharacteristic
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—591no—
500C22×D4—1181no—
501C22×D4C22×D5911yescharacteristic
502C22×D4C22×D5911yescharacteristic
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—1181no—
506C23×C4C22×D5911yescharacteristic
507#137—1188no—
508#137—1188no—
509AGL(1,ℤ/8)—1188no—
510AGL(1,ℤ/8)—1188no—
511#135—216no—
512#135—216no—
513#135—11816no—
514C2×Q16—24no—
515C2×Q16—594no—
516C2×Q16C22×D5914yes—
517C2×SD16—24no—
518C2×SD16—24no—
519C2×SD16—594no—
520C2×SD16—594no—
521C2×SD16C22×D5914yes—
522C2×SD16C22×D5914yes—
523C2×D8—24no—
524C2×D8—594no—
525C2×D8C22×D5914yes—
526C2×M16—592no—
527C2×M16—592no—
528C2×M16—1184no—
529C22×C8—24no—
530C22×C8—592no—
531C22×C8C22×D5911yescharacteristic
532C22×C8C22×D5911yescharacteristic
533C22×C8C22×D5912yes—
534C22×C8C22×D5912yes—
535C4⋊Q8—594no—
536#127—594no—
537#124—594no—
538#124—594no—
539#123—1184no—
540#123—1184no—
541C22⋊Q8—1184no—
542C22⋊Q8—1184no—
543#121—1184no—
544#121—1184no—
545#121—1188no—
546#120—1184no—
547#120—1184no—
548C4×Q8—598no—
549C4×Q8—1184no—
550C4×D4—598no—
551C4×D4—1188no—
552C4×D4—1188no—
553C4×D4—1184no—
554C4×D4—1188no—
555#117—592no—
556#117—592no—
557#117—592no—
558#117—592no—
559#117—592no—
560#117—592no—
561#117—1184no—
562#117—1184no—
563#117—1184no—
564#117—1181no—
565#117—1181no—
566C2×C4⋊C4—592no—
567C2×C4⋊C4—592no—
568C2×C4⋊C4—1184no—
569C2×C22⋊C4—592no—
570C2×C22⋊C4—1184no—
571C2×C22⋊C4—1181no—
572C2×C42—592no—
573C2×C42—1184no—
574C2×C42—1181no—
575C4⋊C8—598no—
576C4⋊C8—598no—
577#103—598no—
578#103—594no—
579#103—594no—
580#102—598no—
581#102—594no—
582#102—594no—
583C24—21no—
584C24—21no—
585C24—1181no—
586C24D4×D5911yescharacteristic
587#41—28no—
588#41—28no—
589#41—24no—
590#41—24no—
591#41—24no—
592#41—24no—
593#41—24no—
594#41—24no—
595#41—44no—
596#41—44no—
597#41—1184no—
598#41—1184no—
599#41—1184no—
600#41—1184no—
601#41—2364no—
602#41—2364no—
603#41C2×C22⋊D5918yes—
604#41C2×C22⋊D5918yes—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—22no—
608C2×Q8—22no—
609C2×Q8—22no—
610C2×Q8—592no—
611C2×Q8—1181no—
612C2×Q8—1182no—
613C2×Q8—1182no—
614C2×Q8C2×C22⋊D5914yes—
615C2×Q8C23×D5912yes—
616C2×Q8C23×D5912yes—
617C2×D4—28no—
618C2×D4—22no—
619C2×D4—22no—
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—44no—
628C2×D4—592no—
629C2×D4—1188no—
630C2×D4—1182no—
631C2×D4—1182no—
632C2×D4—1181no—
633C2×D4—1182no—
634C2×D4—1182no—
635C2×D4—2364no—
636C2×D4C2×C22⋊D5914yes—
637C2×D4C23×D5912yes—
638C2×D4C23×D5912yes—
639C22×C4—21no—
640C22×C4—28no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—21no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—44no—
647C22×C4—594no—
648C22×C4—1188no—
649C22×C4—1182no—
650C22×C4—1181no—
651C22×C4—1182no—
652C22×C4—1182no—
653C22×C4—2364no—
654C22×C4D4×D5911yescharacteristic
655C22×C4D4×D5911yescharacteristic
656C22×C4D4×D5911yescharacteristic
657C22×C4#1174568714yes—
658C22×C4C2×C22⋊D5914yes—
659C22×C4C23×D5911yescharacteristic
660C22×C4C23×D5911yescharacteristic
661C22×C4C23×D5911yescharacteristic
662Q16—28no—
663Q16—1188no—
664SD16—28no—
665SD16—28no—
666SD16—1188no—
667SD16—1188no—
668D8—28no—
669D8—1188no—
670M16—1184no—
671M16—1184no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—24no—
675C2×C8—24no—
676C2×C8—594no—
677C2×C8—1184no—
678C2×C8C23×D5912yes—
679C2×C8C23×D5912yes—
680C4⋊C4—594no—
681C4⋊C4—594no—
682C4⋊C4—594no—
683C4⋊C4—1188no—
684C4⋊C4—1188no—
685C4⋊C4—1182no—
686C22⋊C4—594no—
687C22⋊C4—594no—
688C22⋊C4—1188no—
689C22⋊C4—1188no—
690C22⋊C4—1188no—
691C22⋊C4—1182no—
692C22⋊C4—1182no—
693C42—594no—
694C42—594no—
695C42—1188no—
696C42—1182no—
697C42—1182no—
698C23—22no—
699C23—24no—
700C23—22no—
701C23—42no—
702C23—42no—
703C23—82no—
704C23—82no—
705C23—1182no—
706C23—4722no—
707C23—2362no—
708C23#1427369914yes—
709C23C2×D4×D5911yescharacteristic
710C23C2×D4×D5911yescharacteristic
711C23C2×D4×D5911yescharacteristic
712Q8—24no—
713Q8—22no—
714Q8—22no—
715Q8—22no—
716Q8—42no—
717Q8—1182no—
718Q8—1182no—
719Q8—2362no—
720Q8C22×C22⋊D5914yes—
721D4—28no—
722D4—28no—
723D4—24no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4—44no—
728D4—44no—
729D4—42no—
730D4—1182no—
731D4—1182no—
732D4—4728no—
733D4—2364no—
734D4—2364no—
735D4—2362no—
736D4C22×C22⋊D5914yes—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—28no—
740C2×C4—28no—
741C2×C4—22no—
742C2×C4—42no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—598no—
746C2×C4—1184no—
747C2×C4—1182no—
748C2×C4—4728no—
749C2×C4—4722no—
750C2×C4—2364no—
751C2×C4—2362no—
752C2×C4—2364no—
753C2×C4—2364no—
754C2×C4#1427369914yes—
755C2×C4#1427369914yes—
756C2×C4#1427369914yes—
757C2×C4C2×D4×D5911yescharacteristic
758C2×C4C2×D4×D5911yescharacteristic
759C2×C4C2×D4×D5911yescharacteristic
760C2×C4C22×C22⋊D5912yes—
761C2×C4C22×C22⋊D5912yes—
762C2×C4C22×C22⋊D5912yes—
763C2×C4C2×#1174568712yes—
764C2×C4C2×#1174568712yes—
765C2×C4C2×#1174568712yes—
766C2×C4C24×D5911yescharacteristic
767C8—22no—
768C8—22no—
769C8—1184no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—24no—
774C22—44no—
775C22—44no—
776C22—42no—
777C22—44no—
778C22—84no—
779C22—84no—
780C22—4724no—
781C22—2362no—
782C22—2364no—
783C22C2×#1427369912yes—
784C22C2×#1427369912yes—
785C22C2×#1427369912yes—
786C22C22×D4×D5911yescharacteristic
787C4—24no—
788C4—42no—
789C4—1188no—
790C4—2362no—
791C4—2364no—
792C4C2×#1427369912yes—
793C4C2×#1427369912yes—
794C4C2×#1427369912yes—
795C4C23×C22⋊D5911yescharacteristic
796C4C22×#1174568711yescharacteristic
797C2—22no—
798C2—22no—
799C2—22no—
800C2—44no—
801C2—82no—
802C2—4722no—
803C2C22×#1427369911yescharacteristic
804C2#2143886512yes—
subgroupG/H
centerC2×C4C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC22×#135×C59C2
socleC22×C59C23×D4
hypercenterC22×#135D59
hypocenterC59#60422
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#135

Complements

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

NH ≅ G/Ntype
1. C2×#16838200C2semidirect
2. #21437425C2semidirect
3. #21437299C2semidirect
4. #21433644C2semidirect
5. #21433633C2semidirect
6. #21433623C2semidirect
7. #21433614C2semidirect
8. #21433605C2semidirect
9. #21433596C2semidirect
10. #21433547C2semidirect
11. C2×#16837428C2semidirect
12. #21432615C2semidirect
13. C2×#16837399C2semidirect
14. C22×#135×C59C2semidirect
18. C2×#14273757C22semidirect
20. C2×#14273752C22semidirect
21. C2×#14273747C22semidirect
25. #16837973C22semidirect
27. #16837966C22semidirect
29. #16837948C22semidirect
33. #16837885C22semidirect
34. #16837880C22semidirect
36. #16837877C22semidirect
38. #41×Dic59C22semidirect
42. #16837626C22semidirect
43. #16837622C22semidirect
44. #16837619C22semidirect
45. #16837615C22semidirect
46. #16837610C22semidirect
47. #16837605C22semidirect
48. #16837600C22semidirect
49. #16837595C22semidirect
50. #16837428C22semidirect
51. #16837428C22semidirect
52. #16837428C22semidirect
53. C2×Dic59⋊C8C22semidirect
54. #16837411C22semidirect
55. #16837407C22semidirect
56. #16837403C22semidirect
59. #16837399C22semidirect
60. #16837398C22semidirect
61. C2×#14273652C22semidirect
62. C2×#14273649C22semidirect
67. C2×#135×C59C22semidirect
68. C22×Q16×C59C22semidirect
69. C22×SD16×C59C22semidirect
70. C22×SD16×C59C22semidirect
71. C22×D8×C59C22semidirect
151. C2×#41×C59D4semidirect
396. C22×#135D59semidirect
428. C2×#135C2×D59semidirect
429. C22×Q16C2×D59semidirect
430. C22×SD16C2×D59semidirect
431. C22×SD16C2×D59semidirect
432. C22×D8C2×D59semidirect
475. C59#60422semidirect
489. C2×#41C22⋊D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168382002
#214374252
#214372992
#214336442
#214336332
#214336232
#214336142
#214336052
#214335962
#214335472
C2×#168374282
#214326152
C2×#168373992
C22×#135×C592
#6042259