Finite Group Databasebeta

← #29474760

Subgroups — #29474760

Order 15104.

2282 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21438323C211yesmaximal, characteristic, complemented
2#21436177C212yesmaximal, complemented
3#21436057C212yesmaximal, complemented
4#21435920C212yesmaximal, complemented
5#21435909C212yesmaximal, complemented
6#21435799C212yesmaximal, complemented
7#21435777C212yesmaximal, complemented
8#21435587C212yesmaximal, complemented
9#21435572C212yesmaximal, complemented
10#21435190C212yesmaximal, complemented
11#21434948C212yesmaximal, complemented
12#21434873C211yesmaximal, characteristic, complemented
13#21434857C211yesmaximal, characteristic, complemented
14#21434280C212yesmaximal, complemented
15#21433400C212yesmaximal, complemented
16C2×#16837553C211yesmaximal, characteristic, complemented
17C2×#16837536C211yesmaximal, characteristic, complemented
18#21433152C211yesmaximal, characteristic, complemented
19C59×#3484C211yesmaximal, characteristic, complemented
20C2×#14273753C2212yescomplemented
21C2×#14273747C2212yescomplemented
22C22×#11745670C2212yescomplemented
23C22×#11745669C2212yescomplemented
24#16838149—22no—
25#16838109C2212yescomplemented
26#16838061C2212yescomplemented
27#16838056C2212yescomplemented
28#16838048C2212yescomplemented
29#16838039—22no—
30#16838027—21no—
31#16838023C2212yescomplemented
32#16838001—21no—
33#16837989—21no—
34#16837980C2212yescomplemented
35#16837979—21no—
36C2×#14273706C2211yescharacteristic, complemented
37C2×#14273701C2211yescharacteristic, complemented
38#16837789C2212yescomplemented
39#16837784C2212yescomplemented
40#16837761C2212yescomplemented
41#16837748C2212yescomplemented
42#16837743C2212yescomplemented
43#16837735C2211yescharacteristic, complemented
44#16837730C2211yescharacteristic, complemented
45#16837726C2212yescomplemented
46#16837718C2211yescharacteristic, complemented
47#16837718C2212yescomplemented
48#16837713C2211yescharacteristic, complemented
49#16837713C2212yescomplemented
50#16837692C2212yescomplemented
51#16837682C2212yescomplemented
52#16837653C2212yescomplemented
53#16837646C2212yescomplemented
54#16837641C2212yescomplemented
55#16837636C2212yescomplemented
56#16837636C2212yescomplemented
57#16837633C2212yescomplemented
58#16837629C2212yescomplemented
59#16837629C2212yescomplemented
60#16837621C2212yescomplemented
61#16837617C2212yescomplemented
62#16837617C2212yescomplemented
63#16837614C2212yescomplemented
64#16837599C2212yescomplemented
65#16837594C2212yescomplemented
66#16837564C2212yescomplemented
67#16837564C2212yescomplemented
68#16837557C2211yescharacteristic, complemented
69#16837553C2212yescomplemented
70#16837553C2212yescomplemented
71#16837553C2212yescomplemented
72#16837553C2212yescomplemented
73#16837553C2212yescomplemented
74#16837552C2211yescharacteristic, complemented
75#16837547C2212yescomplemented
76#16837547C2212yescomplemented
77#16837545C2212yescomplemented
78#16837545C2212yescomplemented
79#16837540C2211yescharacteristic, complemented
80#16837536C2212yes—
81#16837536C2212yescomplemented
82#16837536C2212yescomplemented
83#16837536C2212yescomplemented
84#16837536C2212yescomplemented
85#16837535C2211yescharacteristic, complemented
86#16837512C2212yescomplemented
87#16837502C2212yescomplemented
88C4×#11745670C2212yescomplemented
89C4×#11745669C2212yescomplemented
90#16837474C2212yescomplemented
91#16837474C2212yescomplemented
92D4×C59⋊C8C2212yescomplemented
93D4×C59⋊C8C2212yescomplemented
94#16837463C2212yescomplemented
95#16837403C2212yescomplemented
96C2×#14273648C2212yescomplemented
97C2×#14273648C2212yescomplemented
98C2×#14273648C2212yescomplemented
99#16837369C2212yescomplemented
100C2×C22⋊(C59⋊C8)C2211yescharacteristic, complemented
101C2×C22⋊(C59⋊C8)C2211yescharacteristic, complemented
102C2×H(5,𝔽2)×C59C2211yescharacteristic, complemented
103C23×D4×C59C2211yescharacteristic
104C59×#546—21no—
105C59×#546—21no—
106C59×#546C2212yes—
107C59×#546C2212yescomplemented
108D42×C59—21no—
109D42×C59—21no—
110D42×C59C2212yes—
111D42×C59C2212yescomplemented
112C59×#535C2211yescharacteristic, complemented
113C59×#535C2211yescharacteristic, complemented
114C59×#534—22no—
115C59×#525C2211yescharacteristic
116C59×#525C2211yescharacteristic
117C2×#120×C59—22no—
118C59×#518C2211yescharacteristic, complemented
119C2×#11745685C2312yescomplemented
120C2×#11745687—22no—
121C22×Dic118C2311yescharacteristic
122C22×D236C2311yescharacteristic
123C22×C22⋊D59—21no—
124#14273753—44no—
125#14273747—44no—
126C2×#11745672C2312yescomplemented
127C2×#11745670—44no—
128C2×#11745670C2312yes—
129C2×#11745670C2312yes—
130C2×#11745670C2312yes—
131C2×#11745670C2312yes—
132C2×#11745670C2312yescomplemented
133C2×#11745671C2312yescomplemented
134C2×#11745669—44no—
135C2×#11745669C2312yes—
136C2×#11745669C2312yes—
137C2×#11745669C2312yes—
138C2×#11745669C2312yes—
139C2×#11745669C2312yescomplemented
140C2×#11745664C2312yescomplemented
141C22×C59⋊C8C2312yes—
142C22×C59⋊C8C2312yes—
143C22×C59⋊C8C2312yescomplemented
144#14273727C2312yescomplemented
145#14273722—22no—
146#14273718—22no—
147#14273715C2312yescomplemented
148#14273713—22no—
149#14273713—22no—
150#14273712—22no—
151#14273711—22no—
152#14273711—22no—
153#14273709—22no—
154#14273707—22no—
155#14273706—21no—
156#14273706—21no—
157#14273706C2312yes—
158#14273706C2312yes—
159#14273706C2312yescomplemented
160#14273705—22no—
161#14273705—22no—
162#14273704—22no—
163#14273704—22no—
164#14273703—22no—
165#14273701—21no—
166#14273701—21no—
167#14273701C2312yes—
168#14273701C2312yes—
169#14273701C2312yescomplemented
170#14273700—22no—
171#14273699—22no—
172#14273699—22no—
173#14273699—22no—
174#14273698—22no—
175#14273695—22no—
176C4×Dic118C2312yescomplemented
177C4×D236C2312yescomplemented
178D4×Dic59—22no—
179(C22⋊D59)⋊C4—22no—
180C2×C4⋊Dic59C2311yescharacteristic
181C2×C4⋊Dic59C2311yescharacteristic
182C2×C4⋊Dic59C2312yescomplemented
183C2×Dic59⋊C4—21no—
184C2×C22⋊Dic59—21no—
185C2×(C2×D59)⋊C4—21no—
186C22⋊C4×D59—22no—
187#14273660C2312yescomplemented
188#14273660C2312yescomplemented
189#14273658C2312yescomplemented
190#14273658C2312yescomplemented
191C4⋊(C59⋊C8)C2312yescomplemented
192C4⋊(C59⋊C8)C2312yescomplemented
193#14273651C2312yescomplemented
194#14273651C2312yescomplemented
195#14273650C2312yescomplemented
196#14273650C2312yescomplemented
197#14273648C2312yes—
198#14273648C2312yes—
199#14273648C2312yes—
200#14273648C2312yes—
201#14273648C2312yes—
202#14273648C2312yes—
203#14273648C2312yes—
204#14273648C2312yes—
205#14273648C2312yescomplemented
206#14273648C2312yescomplemented
207#14273647C2312yescomplemented
208#14273647C2312yescomplemented
209C22⋊(C59⋊C8)C2311yescharacteristic
210C22⋊(C59⋊C8)C2311yescharacteristic
211C22⋊(C59⋊C8)C2312yes—
212C22⋊(C59⋊C8)C2312yes—
213C22⋊(C59⋊C8)C2311yescharacteristic
214C22⋊(C59⋊C8)C2311yescharacteristic
215C22⋊(C59⋊C8)C2312yescomplemented
216C22⋊(C59⋊C8)C2312yescomplemented
217#14273638C2312yescomplemented
218C4×C59⋊C8C2312yescomplemented
219C25×C59—21no—
220H(5,𝔽2)×C59—44no—
221C2×#41×C59—21no—
222C2×#41×C59C2312yes—
223C2×#41×C59C2311yescharacteristic
224C2×#41×C59C2311yescharacteristic
225C22×D4×C59—22no—
226C22×D4×C59—21no—
227C22×D4×C59—22no—
228C22×D4×C59—22no—
229C22×D4×C59—21no—
230C22×D4×C59—21no—
231C22×D4×C59—21no—
232C22×D4×C59—44no—
233C22×D4×C59C2311yescharacteristic
234C22×D4×C59C2312yes—
235C22×D4×C59C2312yes—
236C22×D4×C59C2312yes—
237C22×D4×C59C2311yescharacteristic
238C23×C4×C59C2311yescharacteristic
239#127×C59—21no—
240#127×C59C2312yes—
241#124×C59—21no—
242#124×C59C2312yes—
243#123×C59—21no—
244#123×C59—22no—
245#123×C59—22no—
246#123×C59D412yes—
247C22⋊Q8×C59D411yescharacteristic
248C22⋊Q8×C59D411yescharacteristic
249C22⋊Q8×C59C2311yescharacteristic
250C22⋊Q8×C59C2311yescharacteristic
251#121×C59—22no—
252#121×C59—22no—
253#121×C59—21no—
254#121×C59—21no—
255#121×C59—22no—
256#121×C59—22no—
257#121×C59D411yescharacteristic
258#121×C59D411yescharacteristic
259#121×C59C2311yescharacteristic
260#121×C59C2312yes—
261#121×C59C2312yes—
262#121×C59C2311yescharacteristic
263#120×C59—21no—
264#120×C59—22no—
265#120×C59—22no—
266#120×C59—22no—
267#120×C59—22no—
268#120×C59—22no—
269#120×C59—22no—
270#120×C59—22no—
271#120×C59—22no—
272#120×C59D412yes—
273C4×D4×C59—21no—
274C4×D4×C59—21no—
275C4×D4×C59—21no—
276C4×D4×C59—21no—
277C4×D4×C59C2312yes—
278C4×D4×C59C2312yes—
279C4×D4×C59C2312yes—
280C4×D4×C59C2312yes—
281#117×C59C2311yescharacteristic
282#117×C59C2311yescharacteristic
283C2×C22⋊C4×C59—22no—
284C2×C22⋊C4×C59—22no—
285C2×C22⋊C4×C59—22no—
286C24×C59—21no—
287C24×C59—22no—
288C24×C59—22no—
289C24×C59—21no—
290C24×C59—22no—
291C24×C59—44no—
292C24×C59—82no—
293C24×C59—82no—
294C24×C59C2×D411yescharacteristic
295C23×D59—21no—
296#41×C59—24no—
297#41×C59—42no—
298#41×C59—42no—
299#41×C59—42no—
300#41×C59—44no—
301C2×Q8×C59C2×D411yescharacteristic
302C2×Q8×C59C2411yescharacteristic
303C2×D4×C59—24no—
304C2×D4×C59—24no—
305C2×D4×C59—24no—
306C2×D4×C59—24no—
307C2×D4×C59—21no—
308C2×D4×C59—21no—
309C2×D4×C59—21no—
310C2×D4×C59—22no—
311C2×D4×C59—22no—
312C2×D4×C59—22no—
313C2×D4×C59—21no—
314C2×D4×C59—22no—
315C2×D4×C59—22no—
316C2×D4×C59—22no—
317C2×D4×C59—21no—
318C2×D4×C59—22no—
319C2×D4×C59—22no—
320C2×D4×C59—42no—
321C2×D4×C59—42no—
322C2×D4×C59—42no—
323C2×D4×C59—42no—
324C2×D4×C59—44no—
325C2×D4×C59—44no—
326C2×D4×C59—44no—
327C2×D4×C59—44no—
328C2×D4×C59—48no—
329C2×D4×C59—84no—
330C2×D4×C59—84no—
331C2×D4×C59C2×D412yes—
332C2×D4×C59C2×D412yes—
333C2×D4×C59C2×D412yes—
334C2×D4×C59C2×D411yescharacteristic
335C2×D4×C59C2412yes—
336C2×D4×C59C2411yescharacteristic
337C2×D4×C59C2412yes—
338C22×C4×C59—22no—
339C22×C4×C59—21no—
340C22×C4×C59—22no—
341C22×C4×C59—22no—
342C22×C4×C59—42no—
343C22×C4×C59C2×D411yescharacteristic
344C22×C4×C59C2×D411yescharacteristic
345C22×C4×C59C2×D411yescharacteristic
346C22×C4×C59C2411yescharacteristic
347C22×C4×C59C2412yes—
348C22×C4×C59C2411yescharacteristic
349C22×C4×C59C2411yescharacteristic
350C2×C22⋊D59—22no—
351C2×C22⋊D59—22no—
352C2×C22⋊D59—22no—
353C2×C22⋊D59—22no—
354C2×C22⋊D59—82no—
355C22×Dic59—21no—
356C22×Dic59—21no—
357C22×Dic59—21no—
358C22×Dic59—22no—
359#11745687—84no—
360#11745685—42no—
361#11745685—42no—
362C2×D236—21no—
363C2×D236—42no—
364C2×D236C2412yes—
365C2×C4×D59—22no—
366C2×C4×D59—22no—
367C2×Dic118—22no—
368C2×Dic118—21no—
369C2×Dic118—42no—
370C2×Dic118C2412yes—
371C4⋊C4×C59—21no—
372C4⋊C4×C59—21no—
373C4⋊C4×C59C2×D411yescharacteristic
374C4⋊C4×C59C2×D411yescharacteristic
375C4⋊C4×C59C2×D412yes—
376C4⋊C4×C59C2×D412yes—
377C4⋊C4×C59C2411yescharacteristic
378C4⋊C4×C59C2411yescharacteristic
379C22⋊C4×C59—21no—
380C22⋊C4×C59—21no—
381C22⋊C4×C59—21no—
382C22⋊C4×C59—22no—
383C22⋊C4×C59—22no—
384C22⋊C4×C59—22no—
385C22⋊C4×C59—22no—
386C22⋊C4×C59—22no—
387C22⋊C4×C59—22no—
388C22⋊C4×C59—21no—
389C22⋊C4×C59—21no—
390C22⋊C4×C59C2×D412yes—
391C22⋊C4×C59C2×D412yes—
392C22⋊C4×C59C2×D412yes—
393C22⋊C4×C59C2×D412yes—
394C22⋊C4×C59C2×D412yes—
395C42×C59—21no—
396C42×C59C2412yes—
397C22⋊Dic59—22no—
398C22⋊Dic59—22no—
399C22⋊Dic59—22no—
400#11745672—42no—
401#11745671—42no—
402#11745670—24no—
403#11745670—24no—
404#11745670—42no—
405#11745670—42no—
406#11745670—42no—
407#11745669—24no—
408#11745669—24no—
409#11745669—42no—
410#11745669—42no—
411#11745669—42no—
412(C2×D59)⋊C4—22no—
413(C2×D59)⋊C4—22no—
414(C2×D59)⋊C4—22no—
415(C2×D59)⋊C4—22no—
416(C2×D59)⋊C4—22no—
417(C2×D59)⋊C4—22no—
418C4⋊Dic59—21no—
419C4⋊Dic59—21no—
420C4⋊Dic59—22no—
421C4⋊Dic59—22no—
422C4⋊Dic59C2412yes—
423C4⋊Dic59C2412yes—
424Dic59⋊C4—22no—
425Dic59⋊C4—22no—
426Dic59⋊C4—22no—
427Dic59⋊C4—22no—
428C4×Dic59—22no—
429#11745664—42no—
430C2×C59⋊C8—42no—
431C2×C59⋊C8—42no—
432C2×C59⋊C8—42no—
433C2×C59⋊C8C2412yes—
434C2×C59⋊C8C2412yes—
435C2×C59⋊C8C2412yes—
436C2×C59⋊C8C2412yes—
437C23×C59—24no—
438C23×C59—22no—
439C23×C59—22no—
440C23×C59—22no—
441C23×C59—22no—
442C23×C59—21no—
443C23×C59—41no—
444C23×C59—44no—
445C23×C59—44no—
446C23×C59—44no—
447C23×C59—42no—
448C23×C59—44no—
449C23×C59—44no—
450C23×C59—82no—
451C23×C59—82no—
452C23×C59—81no—
453C23×C59—81no—
454C23×C59—81no—
455C23×C59—81no—
456C23×C59—82no—
457C23×C59—82no—
458C23×C59—816no—
459C23×C59C22×D411yescharacteristic
460C23×C59C22×D412yes—
461C23×C59C22×D411yescharacteristic
462C23×C59C22×D411yescharacteristic
463C22×D59—22no—
464C22×D59—42no—
465C22×D59—81no—
466C22×D59—81no—
467Q8×C59—22no—
468Q8×C59—41no—
469D4×C59—24no—
470D4×C59—24no—
471D4×C59—24no—
472D4×C59—22no—
473D4×C59—22no—
474D4×C59—22no—
475D4×C59—22no—
476D4×C59—42no—
477D4×C59—41no—
478D4×C59—44no—
479D4×C59—44no—
480D4×C59—44no—
481D4×C59—42no—
482D4×C59—44no—
483D4×C59—42no—
484D4×C59—42no—
485D4×C59—42no—
486D4×C59—82no—
487D4×C59—82no—
488D4×C59—82no—
489D4×C59—82no—
490D4×C59H(5,𝔽2)14yes—
491C2×C4×C59—22no—
492C2×C4×C59—22no—
493C2×C4×C59—22no—
494C2×C4×C59—22no—
495C2×C4×C59—22no—
496C2×C4×C59—21no—
497C2×C4×C59—21no—
498C2×C4×C59—21no—
499C2×C4×C59—41no—
500C2×C4×C59—41no—
501C2×C4×C59—41no—
502C2×C4×C59—44no—
503C2×C4×C59—42no—
504C2×C4×C59—82no—
505C2×C4×C59—82no—
506C2×C4×C59C22×D412yes—
507C2×C4×C59C22×D411yescharacteristic
508C2×C4×C59C22×D411yescharacteristic
509C2×C4×C59C22×D412yes—
510C2×C4×C59C22×D412yes—
511C2×C4×C59C22×D411yescharacteristic
512C2×C4×C59C2511yescharacteristic
513C22⋊D59—44no—
514C22⋊D59—82no—
515C22⋊D59—82no—
516C22⋊D59—82no—
517C2×Dic59—22no—
518C2×Dic59—22no—
519C2×Dic59—22no—
520C2×Dic59—42no—
521C2×Dic59—81no—
522C2×Dic59—82no—
523C2×Dic59—81no—
524D236—22no—
525D236—22no—
526D236—81no—
527C4×D59—82no—
528C4×D59—82no—
529Dic118—22no—
530Dic118—22no—
531Dic118—81no—
532Dic118—82no—
533C59⋊C8—22no—
534C59⋊C8—22no—
535C59⋊C8—22no—
536C59⋊C8—22no—
537#61629—591nomaximal, Sylow
538C22×C59—21no—
539C22×C59—21no—
540C22×C59—21no—
541C22×C59—21no—
542C22×C59—22no—
543C22×C59—21no—
544C22×C59—24no—
545C22×C59—22no—
546C22×C59—21no—
547C22×C59—22no—
548C22×C59—21no—
549C22×C59—44no—
550C22×C59—42no—
551C22×C59—42no—
552C22×C59—41no—
553C22×C59—42no—
554C22×C59—41no—
555C22×C59—42no—
556C22×C59—41no—
557C22×C59—42no—
558C22×C59—88no—
559C22×C59—88no—
560C22×C59—84no—
561C22×C59—84no—
562C22×C59—164no—
563C22×C59#57612yes—
564C22×C59#57712yes—
565C22×C59C23×D411yescharacteristic
566C2×D59—42no—
567C2×D59—42no—
568C2×D59—42no—
569C2×D59—162no—
570C4×C59—21no—
571C4×C59—22no—
572C4×C59—21no—
573C4×C59—21no—
574C4×C59—22no—
575C4×C59—22no—
576C4×C59—41no—
577C4×C59—41no—
578C4×C59—41no—
579C4×C59C2×H(5,𝔽2)12yes—
580Dic59—42no—
581Dic59—42no—
582Dic59—42no—
583#3536—591no—
584#3484D5911yescharacteristic, complemented
585#3314—592no—
586#3306—592no—
587#3295—592no—
588#3294—592no—
589#3282—592no—
590#3280—592no—
591#3265—592no—
592#3264—592no—
593#3224—592no—
594#3198—592no—
595#3190—591no—
596#3188—591no—
597#3118—592no—
598#3012—592no—
599C2×#450—591no—
600C2×#447—591no—
601#2977—591no—
602C2×C59—22no—
603C2×C59—22no—
604C2×C59—41no—
605C2×C59—42no—
606C2×C59—44no—
607C2×C59—82no—
608C2×C59—81no—
609C2×C59#348411yescharacteristic
610C2×C59C2×#57611yescharacteristic
611C2×C59C2×#57711yescharacteristic
612D59—82no—
613C2×H(5,𝔽2)C2×D5911yescharacteristic, complemented
614C23×D4C2×D5911yescharacteristic
615C2×AGL(1,ℤ/8)—592no—
616C2×#135—592no—
617C22×SD16—592no—
618C22×D8—592no—
619#562—1182no—
620#554—592no—
621#548—592no—
622#547—592no—
623#546—21no—
624#546—21no—
625#546—592no—
626#546—1182no—
627#546C2×D5912yes—
628#546C2×D5912yescomplemented
629D42—21no—
630D42—21no—
631D42C2×D5912yes—
632D42C2×D5912yescomplemented
633#543—1181no—
634#542—592no—
635#539—1181no—
636#538—1181no—
637#537—592no—
638#537—1181no—
639#535C2×D5911yescharacteristic, complemented
640#535C2×D5911yescharacteristic, complemented
641#534—22no—
642#525C2×D5911yescharacteristic
643#525C2×D5911yescharacteristic
644C2×C22⋊Q8—591no—
645C2×#121—591no—
646C2×#120—22no—
647#518C2×D5911yescharacteristic, complemented
648#496—592no—
649#495—592no—
650#489—592no—
651#486—592no—
652#485—592no—
653#484—591no—
654#483—591no—
655#482—592no—
656#481—591no—
657#481—592no—
658#480—591no—
659#480—592no—
660#476—592no—
661#474—592no—
662#469—592no—
663#468—592no—
664#467—592no—
665#466—592no—
666#466—592no—
667#465—592no—
668#465—592no—
669#465—592no—
670#464—592no—
671#463—592no—
672#463—592no—
673#463—592no—
674#460—592no—
675#459—592no—
676#452—592no—
677#452—592no—
678#451—591no—
679#450—592no—
680#450—592no—
681#450—592no—
682#450—592no—
683#450—592no—
684#450—591no—
685#449—592no—
686#449—592no—
687#449—592no—
688#449—592no—
689#448—591no—
690#447—592no—
691#447—592no—
692#447—592no—
693#447—592no—
694#447—592no—
695#447—591no—
696#442—592no—
697#440—592no—
698C4×SD16—592no—
699C4×D8—592no—
700#435—592no—
701#435—592no—
702C8×D4—592no—
703C8×D4—592no—
704#433—592no—
705#417—592no—
706C2×#102—592no—
707C2×#102—592no—
708C2×#102—592no—
709#408—592no—
710C2×C22⋊C8—591no—
711C2×C22⋊C8—591no—
712C59#6162911yescharacteristic, complemented, Sylow
713C25—21no—
714H(5,𝔽2)—44no—
715C2×#41—21no—
716C2×#41—592no—
717C2×#41—1182no—
718C2×#41C22×D5912yes—
719C2×#41C22×D5911yescharacteristic
720C2×#41C22×D5911yescharacteristic
721C22×Q8—591no—
722C22×D4—22no—
723C22×D4—21no—
724C22×D4—22no—
725C22×D4—22no—
726C22×D4—21no—
727C22×D4—21no—
728C22×D4—21no—
729C22×D4—44no—
730C22×D4—591no—
731C22×D4—1181no—
732C22×D4C22×D5911yescharacteristic
733C22×D4C22×D5912yes—
734C22×D4C22×D5912yes—
735C22×D4C22×D5912yes—
736C22×D4C22×D5911yescharacteristic
737C23×C4C22×D5911yescharacteristic
738AGL(1,ℤ/8)—2364no—
739#135—2364no—
740C2×Q16—592no—
741C2×SD16—592no—
742C2×SD16—592no—
743C2×SD16—592no—
744C2×SD16—592no—
745C2×SD16—592no—
746C2×SD16—592no—
747C2×SD16—2364no—
748C2×D8—592no—
749C2×D8—592no—
750C2×D8—592no—
751C2×D8—592no—
752C2×D8—592no—
753C2×D8—2364no—
754C2×M16—592no—
755C22×C8—592no—
756C22×C8—592no—
757C22×C8—592no—
758C4⋊Q8—592no—
759#127—21no—
760#127C22×D5912yes—
761#126—1182no—
762#125—1182no—
763#124—21no—
764#124—592no—
765#124—1182no—
766#124—1182no—
767#124C22×D5912yes—
768#123—21no—
769#123—22no—
770#123—22no—
771#123—1182no—
772#123—1182no—
773#123—1182no—
774#123—1182no—
775#123C22⋊D5912yes—
776C22⋊Q8—592no—
777C22⋊Q8—592no—
778C22⋊Q8—592no—
779C22⋊Q8—1182no—
780C22⋊Q8—1181no—
781C22⋊Q8—1181no—
782C22⋊Q8—1182no—
783C22⋊Q8—1182no—
784C22⋊Q8—1182no—
785C22⋊Q8—1182no—
786C22⋊Q8—1182no—
787C22⋊Q8C22⋊D5911yescharacteristic
788C22⋊Q8C22⋊D5911yescharacteristic
789C22⋊Q8C22×D5911yescharacteristic
790C22⋊Q8C22×D5911yescharacteristic
791#121—22no—
792#121—22no—
793#121—21no—
794#121—21no—
795#121—22no—
796#121—22no—
797#121—592no—
798#121—592no—
799#121—592no—
800#121—1182no—
801#121—1182no—
802#121—1182no—
803#121—1182no—
804#121—1181no—
805#121—1181no—
806#121—1182no—
807#121C22⋊D5911yescharacteristic
808#121C22⋊D5911yescharacteristic
809#121C22×D5911yescharacteristic
810#121C22×D5911yescharacteristic
811#121C22×D5912yes—
812#121C22×D5912yes—
813#120—21no—
814#120—22no—
815#120—22no—
816#120—22no—
817#120—22no—
818#120—22no—
819#120—22no—
820#120—22no—
821#120—22no—
822#120—1182no—
823#120C22⋊D5912yes—
824C4×Q8—592no—
825C4×D4—21no—
826C4×D4—21no—
827C4×D4—21no—
828C4×D4—21no—
829C4×D4—592no—
830C4×D4—1182no—
831C4×D4—1182no—
832C4×D4C22×D5912yes—
833C4×D4C22×D5912yes—
834C4×D4C22×D5912yes—
835C4×D4C22×D5912yes—
836#117C22×D5911yescharacteristic
837#117C22×D5911yescharacteristic
838C2×C4⋊C4—591no—
839C2×C4⋊C4—591no—
840C2×C4⋊C4—592no—
841C2×C4⋊C4—1181no—
842C2×C22⋊C4—22no—
843C2×C22⋊C4—22no—
844C2×C22⋊C4—22no—
845C2×C22⋊C4—1181no—
846C2×C22⋊C4—1181no—
847C2×C22⋊C4—1182no—
848#107—592no—
849#107—592no—
850#106—592no—
851#106—592no—
852C4⋊C8—592no—
853C4⋊C8—592no—
854#103—592no—
855#103—592no—
856#103—592no—
857#103—592no—
858#102—592no—
859#102—592no—
860#102—592no—
861#102—592no—
862#102—592no—
863#102—592no—
864#102—592no—
865#102—592no—
866#102—592no—
867#102—592no—
868#102—592no—
869#102—592no—
870C22⋊C8—592no—
871C22⋊C8—592no—
872C22⋊C8—591no—
873C22⋊C8—591no—
874C22⋊C8—591no—
875C22⋊C8—591no—
876C22⋊C8—592no—
877C22⋊C8—592no—
878#97—592no—
879C4×C8—592no—
880C24—21no—
881C24—22no—
882C24—22no—
883C24—21no—
884C24—22no—
885C24—44no—
886C24—82no—
887C24—82no—
888C24—1181no—
889C24C2×C22⋊D5911yescharacteristic
890#41—24no—
891#41—42no—
892#41—42no—
893#41—42no—
894#41—44no—
895#41—4724no—
896#41—2362no—
897#41—2362no—
898C2×Q8—592no—
899C2×Q8—1181no—
900C2×Q8—1182no—
901C2×Q8—2362no—
902C2×Q8C2×C22⋊D5911yescharacteristic
903C2×Q8C23×D5911yescharacteristic
904C2×D4—24no—
905C2×D4—24no—
906C2×D4—24no—
907C2×D4—24no—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—21no—
911C2×D4—22no—
912C2×D4—22no—
913C2×D4—22no—
914C2×D4—21no—
915C2×D4—22no—
916C2×D4—22no—
917C2×D4—22no—
918C2×D4—21no—
919C2×D4—22no—
920C2×D4—22no—
921C2×D4—42no—
922C2×D4—42no—
923C2×D4—42no—
924C2×D4—42no—
925C2×D4—44no—
926C2×D4—44no—
927C2×D4—44no—
928C2×D4—44no—
929C2×D4—48no—
930C2×D4—84no—
931C2×D4—84no—
932C2×D4—592no—
933C2×D4—1182no—
934C2×D4—1182no—
935C2×D4—1182no—
936C2×D4—1182no—
937C2×D4—1181no—
938C2×D4—4722no—
939C2×D4—2362no—
940C2×D4C2×C22⋊D5912yes—
941C2×D4C2×C22⋊D5912yes—
942C2×D4C2×C22⋊D5912yes—
943C2×D4C2×C22⋊D5911yescharacteristic
944C2×D4C23×D5912yes—
945C2×D4C23×D5911yescharacteristic
946C2×D4C23×D5912yes—
947C22×C4—22no—
948C22×C4—21no—
949C22×C4—22no—
950C22×C4—22no—
951C22×C4—42no—
952C22×C4—1181no—
953C22×C4—1181no—
954C22×C4—1182no—
955C22×C4—1181no—
956C22×C4—1182no—
957C22×C4—1182no—
958C22×C4C2×C22⋊D5911yescharacteristic
959C22×C4C2×C22⋊D5911yescharacteristic
960C22×C4C2×C22⋊D5911yescharacteristic
961C22×C4C23×D5911yescharacteristic
962C22×C4C23×D5911yescharacteristic
963C22×C4C23×D5912yes—
964C22×C4C23×D5911yescharacteristic
965Q16—2362no—
966SD16—1184no—
967SD16—1184no—
968SD16—2362no—
969SD16—2362no—
970SD16—2362no—
971SD16—2362no—
972D8—1184no—
973D8—1184no—
974D8—2362no—
975D8—2362no—
976D8—2362no—
977M16—2362no—
978C2×C8—592no—
979C2×C8—592no—
980C2×C8—592no—
981C2×C8—592no—
982C2×C8—2362no—
983C2×C8—2362no—
984C2×C8—2362no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—592no—
988C4⋊C4—592no—
989C4⋊C4—1181no—
990C4⋊C4—1182no—
991C4⋊C4—1181no—
992C4⋊C4—1182no—
993C4⋊C4—1182no—
994C4⋊C4—1182no—
995C4⋊C4—1182no—
996C4⋊C4—1182no—
997C4⋊C4C2×C22⋊D5911yescharacteristic
998C4⋊C4C2×C22⋊D5911yescharacteristic
999C4⋊C4C2×C22⋊D5912yes—
1000C4⋊C4C2×C22⋊D5912yes—
1001C4⋊C4C23×D5911yescharacteristic
1002C4⋊C4C23×D5911yescharacteristic
1003C22⋊C4—21no—
1004C22⋊C4—21no—
1005C22⋊C4—21no—
1006C22⋊C4—22no—
1007C22⋊C4—22no—
1008C22⋊C4—22no—
1009C22⋊C4—22no—
1010C22⋊C4—22no—
1011C22⋊C4—22no—
1012C22⋊C4—21no—
1013C22⋊C4—21no—
1014C22⋊C4—1182no—
1015C22⋊C4—1182no—
1016C22⋊C4—1182no—
1017C22⋊C4—1182no—
1018C22⋊C4—1182no—
1019C22⋊C4—1182no—
1020C22⋊C4—1182no—
1021C22⋊C4—1182no—
1022C22⋊C4—1182no—
1023C22⋊C4C2×C22⋊D5912yes—
1024C22⋊C4C2×C22⋊D5912yes—
1025C22⋊C4C2×C22⋊D5912yes—
1026C22⋊C4C2×C22⋊D5912yes—
1027C22⋊C4C2×C22⋊D5912yes—
1028C42—21no—
1029C42—1182no—
1030C42C23×D5912yes—
1031C23—24no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—21no—
1037C23—41no—
1038C23—44no—
1039C23—44no—
1040C23—44no—
1041C23—42no—
1042C23—44no—
1043C23—44no—
1044C23—82no—
1045C23—82no—
1046C23—81no—
1047C23—81no—
1048C23—81no—
1049C23—81no—
1050C23—82no—
1051C23—82no—
1052C23—816no—
1053C23—1182no—
1054C23—4721no—
1055C23—4721no—
1056C23—2362no—
1057C23C22×C22⋊D5911yescharacteristic
1058C23C22×C22⋊D5912yes—
1059C23C22×C22⋊D5911yescharacteristic
1060C23C22×C22⋊D5911yescharacteristic
1061Q8—22no—
1062Q8—41no—
1063Q8—1182no—
1064Q8—1182no—
1065Q8—4721no—
1066Q8—4722no—
1067D4—24no—
1068D4—24no—
1069D4—24no—
1070D4—22no—
1071D4—22no—
1072D4—22no—
1073D4—22no—
1074D4—41no—
1075D4—42no—
1076D4—44no—
1077D4—44no—
1078D4—44no—
1079D4—42no—
1080D4—44no—
1081D4—42no—
1082D4—42no—
1083D4—42no—
1084D4—82no—
1085D4—82no—
1086D4—82no—
1087D4—82no—
1088D4—1182no—
1089D4—1182no—
1090D4—4721no—
1091D4—4722no—
1092D4—4722no—
1093D4—4722no—
1094D4—2364no—
1095D4#1427377214yes—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—44no—
1108C2×C4—42no—
1109C2×C4—82no—
1110C2×C4—82no—
1111C2×C4—1182no—
1112C2×C4—1182no—
1113C2×C4—1182no—
1114C2×C4—4722no—
1115C2×C4—4722no—
1116C2×C4—4721no—
1117C2×C4—4721no—
1118C2×C4—4722no—
1119C2×C4—2362no—
1120C2×C4C22×C22⋊D5911yescharacteristic
1121C2×C4C22×C22⋊D5912yes—
1122C2×C4C22×C22⋊D5912yes—
1123C2×C4C22×C22⋊D5912yes—
1124C2×C4C22×C22⋊D5911yescharacteristic
1125C2×C4C22×C22⋊D5911yescharacteristic
1126C2×C4C24×D5911yescharacteristic
1127C8—1182no—
1128C8—1182no—
1129C8—1182no—
1130C8—1182no—
1131C22—21no—
1132C22—21no—
1133C22—21no—
1134C22—21no—
1135C22—21no—
1136C22—22no—
1137C22—24no—
1138C22—22no—
1139C22—21no—
1140C22—22no—
1141C22—21no—
1142C22—44no—
1143C22—42no—
1144C22—42no—
1145C22—41no—
1146C22—42no—
1147C22—41no—
1148C22—42no—
1149C22—41no—
1150C22—42no—
1151C22—88no—
1152C22—88no—
1153C22—84no—
1154C22—84no—
1155C22—164no—
1156C22—9442no—
1157C22—2362no—
1158C22—2362no—
1159C22—2362no—
1160C22#1683820512yes—
1161C22#1683821312yes—
1162C22C23×C22⋊D5911yescharacteristic
1163C4—21no—
1164C4—22no—
1165C4—21no—
1166C4—21no—
1167C4—22no—
1168C4—22no—
1169C4—41no—
1170C4—41no—
1171C4—41no—
1172C4—2362no—
1173C4—2362no—
1174C4—2362no—
1175C4C2×#1427377212yes—
1176C2—22no—
1177C2—22no—
1178C2—41no—
1179C2—42no—
1180C2—44no—
1181C2—82no—
1182C2—81no—
1183C2—4722no—
1184C2#2143773111yescharacteristic
1185C2C2×#1683820511yescharacteristic
1186C2C2×#1683821311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC59×#3484C2
socleC22×C59C23×D4
hypercenter#3484D59
hypocenterC59#61629
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ #525 ◁ #3484

Complements

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

NH ≅ G/Ntype
1. #21438323C2semidirect
2. #21436177C2semidirect
3. #21436057C2semidirect
4. #21435920C2semidirect
5. #21435909C2semidirect
6. #21435799C2semidirect
7. #21435777C2semidirect
8. #21435587C2semidirect
9. #21435572C2semidirect
10. #21435190C2semidirect
11. #21434948C2semidirect
12. #21434873C2semidirect
13. #21434857C2semidirect
14. #21434280C2semidirect
15. #21433400C2semidirect
16. C2×#16837553C2semidirect
17. C2×#16837536C2semidirect
18. #21433152C2semidirect
19. C59×#3484C2semidirect
20. C2×#14273753C22semidirect
21. C2×#14273747C22semidirect
22. C22×#11745670C22semidirect
23. C22×#11745669C22semidirect
25. #16838109C22semidirect
26. #16838061C22semidirect
27. #16838056C22semidirect
28. #16838048C22semidirect
31. #16838023C22semidirect
34. #16837980C22semidirect
36. C2×#14273706C22semidirect
37. C2×#14273701C22semidirect
38. #16837789C22semidirect
39. #16837784C22semidirect
40. #16837761C22semidirect
41. #16837748C22semidirect
42. #16837743C22semidirect
43. #16837735C22semidirect
44. #16837730C22semidirect
45. #16837726C22semidirect
46. #16837718C22semidirect
47. #16837718C22semidirect
48. #16837713C22semidirect
49. #16837713C22semidirect
50. #16837692C22semidirect
51. #16837682C22semidirect
52. #16837653C22semidirect
53. #16837646C22semidirect
54. #16837641C22semidirect
55. #16837636C22semidirect
56. #16837636C22semidirect
57. #16837633C22semidirect
58. #16837629C22semidirect
59. #16837629C22semidirect
60. #16837621C22semidirect
61. #16837617C22semidirect
62. #16837617C22semidirect
63. #16837614C22semidirect
64. #16837599C22semidirect
65. #16837594C22semidirect
66. #16837564C22semidirect
67. #16837564C22semidirect
68. #16837557C22semidirect
69. #16837553C22semidirect
70. #16837553C22semidirect
71. #16837553C22semidirect
72. #16837553C22semidirect
73. #16837553C22semidirect
74. #16837552C22semidirect
75. #16837547C22semidirect
76. #16837547C22semidirect
77. #16837545C22semidirect
78. #16837545C22semidirect
79. #16837540C22semidirect
81. #16837536C22semidirect
82. #16837536C22semidirect
83. #16837536C22semidirect
84. #16837536C22semidirect
85. #16837535C22semidirect
86. #16837512C22semidirect
87. #16837502C22semidirect
88. C4×#11745670C22semidirect
89. C4×#11745669C22semidirect
90. #16837474C22semidirect
91. #16837474C22semidirect
92. D4×C59⋊C8C22semidirect
93. D4×C59⋊C8C22semidirect
94. #16837463C22semidirect
95. #16837403C22semidirect
96. C2×#14273648C22semidirect
97. C2×#14273648C22semidirect
98. C2×#14273648C22semidirect
99. #16837369C22semidirect
100. C2×C22⋊(C59⋊C8)C22semidirect
101. C2×C22⋊(C59⋊C8)C22semidirect
102. C2×H(5,𝔽2)×C59C22semidirect
107. C59×#546C22semidirect
111. D42×C59C22semidirect
112. C59×#535C22semidirect
113. C59×#535C22semidirect
118. C59×#518C22semidirect
119. C2×#11745685C23semidirect
126. C2×#11745672C23semidirect
132. C2×#11745670C23semidirect
133. C2×#11745671C23semidirect
139. C2×#11745669C23semidirect
140. C2×#11745664C23semidirect
143. C22×C59⋊C8C23semidirect
144. #14273727C23semidirect
147. #14273715C23semidirect
159. #14273706C23semidirect
169. #14273701C23semidirect
176. C4×Dic118C23semidirect
177. C4×D236C23semidirect
182. C2×C4⋊Dic59C23semidirect
187. #14273660C23semidirect
188. #14273660C23semidirect
189. #14273658C23semidirect
190. #14273658C23semidirect
191. C4⋊(C59⋊C8)C23semidirect
192. C4⋊(C59⋊C8)C23semidirect
193. #14273651C23semidirect
194. #14273651C23semidirect
195. #14273650C23semidirect
196. #14273650C23semidirect
205. #14273648C23semidirect
206. #14273648C23semidirect
207. #14273647C23semidirect
208. #14273647C23semidirect
215. C22⋊(C59⋊C8)C23semidirect
216. C22⋊(C59⋊C8)C23semidirect
217. #14273638C23semidirect
218. C4×C59⋊C8C23semidirect
584. #3484D59semidirect
613. C2×H(5,𝔽2)C2×D59semidirect
628. #546C2×D59semidirect
632. D42C2×D59semidirect
639. #535C2×D59semidirect
640. #535C2×D59semidirect
647. #518C2×D59semidirect
712. C59#61629semidirect

Maximal subgroups

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

subgroupindex
#214383232
#214361772
#214360572
#214359202
#214359092
#214357992
#214357772
#214355872
#214355722
#214351902
#214349482
#214348732
#214348572
#214342802
#214334002
C2×#168375532
C2×#168375362
#214331522
C59×#34842
#6162959