Finite Group Databasebeta

← #29459432

Subgroups — #29459432

Order 15104.

2686 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837913C211yesmaximal, characteristic, complemented
2#21434910C214yesmaximal, complemented
3#21434902C212yesmaximal, complemented
4#21434893C212yesmaximal, complemented
5#21434861C214yesmaximal, complemented
6#21434853C212yesmaximal, complemented
7#21434844C212yesmaximal, complemented
8#21434032C212yesmaximal, complemented
9#21434019C212yesmaximal, complemented
10#21433711C214yesmaximal, complemented
11#21433346C212yesmaximal, complemented
12#21433323C212yesmaximal, complemented
13C2×#16837366C211yesmaximal, characteristic, complemented
14C22×#121×C59C211yesmaximal, characteristic, complemented
15C22×#11745685C2211yescharacteristic, complemented
16C2×#14273753C2214yescomplemented
17C22×#11745664C2212yescomplemented
18#16837913—21no—
19#16837913—21no—
20#16837913—21no—
21#16837913—21no—
22#16837913C2212yes—
23#16837913C2212yescomplemented
24#16837913C2212yescomplemented
25#16837913C2212yescomplemented
26C2×#14273710—21no—
27C2×#14273706C2211yescharacteristic, complemented
28C2×#14273706C2211yescharacteristic, complemented
29C2×#14273701C2211yescharacteristic, complemented
30C2×#14273701C2211yescharacteristic, complemented
31C2×#14273696—21no—
32C2×C4×C22⋊D59—21no—
33C2×C4×C22⋊D59—21no—
34C2×#14273686C2211yescharacteristic, complemented
35#16837737C2214yescomplemented
36#16837732C2214yescomplemented
37#16837723C2218yescomplemented
38#16837720C2214yescomplemented
39#16837718C2214yescomplemented
40#16837715C2214yescomplemented
41#16837713C2214yescomplemented
42#16837653C2218yescomplemented
43#16837646C2218yescomplemented
44#16837636C2218yescomplemented
45#16837629C2218yescomplemented
46#16837553C2214yescomplemented
47#16837553C2214yescomplemented
48#16837545C2218yescomplemented
49#16837540C2214yescomplemented
50#16837536C2214yescomplemented
51#16837536C2214yescomplemented
52#16837535C2214yescomplemented
53#16837442C2214yescomplemented
54#16837407C2214yescomplemented
55#16837401C2214yescomplemented
56#16837366C2212yescomplemented
57#16837366C2212yescomplemented
58#16837366C2212yescomplemented
59#16837366C2212yescomplemented
60C2×C22⋊(C59⋊C8)C2212yescomplemented
61C2×C22⋊(C59⋊C8)C2212yescomplemented
62C23×D4×C59—21no—
63C23×D4×C59C2211yescharacteristic, complemented
64C24×C4×C59C2211yescharacteristic
65C2×#121×C59—21no—
66C2×#121×C59—21no—
67C2×#121×C59—21no—
68C2×#121×C59—21no—
69C2×#121×C59—21no—
70C2×#121×C59—21no—
71C2×#121×C59C2212yes—
72C2×#121×C59C2212yes—
73C2×#121×C59C2212yes—
74C2×#121×C59C2212yescomplemented
75C2×#121×C59C2212yescomplemented
76C2×#121×C59C2212yescomplemented
77C22×C4⋊C4×C59C2211yescharacteristic, complemented
78C22×C22⋊C4×C59—21no—
79C2×#11745685—21no—
80C2×#11745685—21no—
81C2×#11745685—44no—
82C2×#11745685C2312yes—
83C2×#11745685C2312yescomplemented
84C22×Dic118C2311yescharacteristic, complemented
85C22×D236C2311yescharacteristic, complemented
86C22×C22⋊D59—21no—
87C22×C22⋊D59—21no—
88C22×C22⋊D59—21no—
89C22×C4×D59—21no—
90#14273753—48no—
91C2×#11745670C2318yescomplemented
92C2×#11745669C2318yescomplemented
93C2×#11745664—44no—
94C2×#11745664C2314yes—
95C2×#11745664C2314yescomplemented
96C22×C59⋊C8C2314yescomplemented
97#14273710—22no—
98#14273710—22no—
99#14273710—22no—
100#14273710—22no—
101#14273706—21no—
102#14273706—21no—
103#14273706—21no—
104#14273706—21no—
105#14273706C2312yes—
106#14273706C2312yes—
107#14273706C2312yescomplemented
108#14273706C2312yescomplemented
109#14273701—21no—
110#14273701—21no—
111#14273701—21no—
112#14273701—21no—
113#14273701C2312yes—
114#14273701C2312yes—
115#14273701C2312yescomplemented
116#14273701C2312yescomplemented
117#14273696—22no—
118#14273696—22no—
119#14273696—22no—
120#14273696—22no—
121C4×C22⋊D59—22no—
122C4×C22⋊D59—22no—
123C4×C22⋊D59—22no—
124C4×C22⋊D59—22no—
125C4×C22⋊D59—22no—
126C4×C22⋊D59—22no—
127C4×C22⋊D59—22no—
128C4×C22⋊D59—22no—
129#14273686—21no—
130#14273686—21no—
131#14273686C2312yes—
132#14273686C2312yescomplemented
133C2×C4⋊Dic59C2311yescharacteristic, complemented
134C2×C4⋊Dic59C2311yescharacteristic, complemented
135C2×Dic59⋊C4—21no—
136C2×Dic59⋊C4—21no—
137C2×C22⋊Dic59—21no—
138C2×C22⋊Dic59—21no—
139C2×C22⋊Dic59—21no—
140C2×(C2×D59)⋊C4—21no—
141C2×(C2×D59)⋊C4—21no—
142C2×C4×Dic59—21no—
143#14273660C2318yescomplemented
144#14273658C2318yescomplemented
145#14273650C2318yescomplemented
146#14273648C2318yescomplemented
147#14273648C2318yescomplemented
148#14273647C2318yescomplemented
149C22⋊(C59⋊C8)C2314yes—
150C22⋊(C59⋊C8)C2314yes—
151C22⋊(C59⋊C8)C2314yescomplemented
152C22⋊(C59⋊C8)C2314yescomplemented
153C25×C59—21no—
154C25×C59D411yescharacteristic
155C22×D4×C59—22no—
156C22×D4×C59—22no—
157C22×D4×C59—22no—
158C22×D4×C59—22no—
159C22×D4×C59—22no—
160C22×D4×C59—22no—
161C22×D4×C59—21no—
162C22×D4×C59—21no—
163C22×D4×C59—21no—
164C22×D4×C59—44no—
165C22×D4×C59—48no—
166C22×D4×C59C2312yes—
167C22×D4×C59C2312yes—
168C22×D4×C59C2312yes—
169C23×C4×C59—21no—
170C23×C4×C59—44no—
171C23×C4×C59D411yescharacteristic
172C23×C4×C59D411yescharacteristic
173C23×C4×C59D411yescharacteristic
174C23×C4×C59D411yescharacteristic
175C23×C4×C59D411yescharacteristic
176C23×C4×C59D411yescharacteristic
177C23×C4×C59D411yescharacteristic
178C23×C4×C59C2311yescharacteristic
179C23×C4×C59C2311yescharacteristic
180C23×C4×C59C2311yescharacteristic
181C23×C4×C59C2311yescharacteristic
182C23×C4×C59C2311yescharacteristic
183C23×C4×C59C2311yescharacteristic
184C23×C4×C59C2311yescharacteristic
185#121×C59—22no—
186#121×C59—22no—
187#121×C59—22no—
188#121×C59—22no—
189#121×C59—22no—
190#121×C59—22no—
191#121×C59—22no—
192#121×C59—22no—
193#121×C59—22no—
194#121×C59—22no—
195#121×C59—22no—
196#121×C59—22no—
197#121×C59C2314yes—
198#121×C59C2314yes—
199#121×C59C2314yes—
200#121×C59C2314yes—
201C2×C4⋊C4×C59—21no—
202C2×C4⋊C4×C59—21no—
203C2×C4⋊C4×C59—21no—
204C2×C4⋊C4×C59C2312yes—
205C2×C4⋊C4×C59C2312yes—
206C2×C4⋊C4×C59C2312yes—
207C2×C22⋊C4×C59—22no—
208C2×C22⋊C4×C59—22no—
209C2×C22⋊C4×C59—22no—
210C2×C22⋊C4×C59—22no—
211C2×C22⋊C4×C59—22no—
212C2×C22⋊C4×C59—22no—
213C24×C59—24no—
214C24×C59—22no—
215C24×C59—22no—
216C24×C59—22no—
217C24×C59—42no—
218C24×C59—42no—
219C24×C59—44no—
220C24×C59—44no—
221C24×C59—44no—
222C24×C59C2×D411yescharacteristic
223C24×C59C2×D411yescharacteristic
224C24×C59C2×D411yescharacteristic
225C24×C59C2×D411yescharacteristic
226C24×C59C2×D411yescharacteristic
227C24×C59C2×D411yescharacteristic
228C24×C59C2×D411yescharacteristic
229C23×D59—21no—
230C2×D4×C59—24no—
231C2×D4×C59—24no—
232C2×D4×C59—24no—
233C2×D4×C59—24no—
234C2×D4×C59—22no—
235C2×D4×C59—22no—
236C2×D4×C59—22no—
237C2×D4×C59—28no—
238C2×D4×C59—44no—
239C2×D4×C59—44no—
240C2×D4×C59—44no—
241C2×D4×C59—44no—
242C2×D4×C59—44no—
243C2×D4×C59—48no—
244C2×D4×C59—48no—
245C2×D4×C59—48no—
246C2×D4×C59—48no—
247C2×D4×C59—48no—
248C2×D4×C59—48no—
249C2×D4×C59C2414yes—
250C22×C4×C59—24no—
251C22×C4×C59—24no—
252C22×C4×C59—24no—
253C22×C4×C59—22no—
254C22×C4×C59—22no—
255C22×C4×C59—22no—
256C22×C4×C59—42no—
257C22×C4×C59—42no—
258C22×C4×C59—42no—
259C22×C4×C59—42no—
260C22×C4×C59—42no—
261C22×C4×C59—42no—
262C22×C4×C59—42no—
263C22×C4×C59—42no—
264C22×C4×C59—42no—
265C22×C4×C59—42no—
266C22×C4×C59—42no—
267C22×C4×C59—44no—
268C22×C4×C59C2×D411yescharacteristic
269C22×C4×C59C2×D411yescharacteristic
270C22×C4×C59C2×D411yescharacteristic
271C22×C4×C59C2×D411yescharacteristic
272C22×C4×C59C2×D411yescharacteristic
273C22×C4×C59C2×D411yescharacteristic
274C22×C4×C59C2×D411yescharacteristic
275C22×C4×C59C2×D411yescharacteristic
276C22×C4×C59C2×D411yescharacteristic
277C22×C4×C59C2×D411yescharacteristic
278C22×C4×C59C2×D411yescharacteristic
279C22×C4×C59C2×D411yescharacteristic
280C22×C4×C59C2×D411yescharacteristic
281C22×C4×C59C2×D411yescharacteristic
282C22×C4×C59C2×D411yescharacteristic
283C22×C4×C59C2×D411yescharacteristic
284C22×C4×C59C2×D411yescharacteristic
285C22×C4×C59C2×D411yescharacteristic
286C22×C4×C59C2×D411yescharacteristic
287C22×C4×C59C2×D411yescharacteristic
288C22×C4×C59C2×D411yescharacteristic
289C22×C4×C59C2411yescharacteristic
290C22×C4×C59C2411yescharacteristic
291C22×C4×C59C2411yescharacteristic
292C22×C4×C59C2411yescharacteristic
293C22×C4×C59C2411yescharacteristic
294C22×C4×C59C2411yescharacteristic
295C22×C4×C59C2411yescharacteristic
296C2×C22⋊D59—22no—
297C2×C22⋊D59—22no—
298C2×C22⋊D59—22no—
299C2×C22⋊D59—22no—
300C2×C22⋊D59—22no—
301C2×C22⋊D59—22no—
302C2×C22⋊D59—44no—
303C2×C22⋊D59—44no—
304C2×C22⋊D59—44no—
305C22×Dic59—21no—
306C22×Dic59—21no—
307C22×Dic59—21no—
308#11745685—28no—
309#11745685—44no—
310#11745685—44no—
311#11745685—44no—
312C2×D236—21no—
313C2×D236—42no—
314C2×D236C2412yes—
315C2×C4×D59—22no—
316C2×C4×D59—22no—
317C2×C4×D59—44no—
318C2×Dic118—21no—
319C2×Dic118—42no—
320C2×Dic118C2412yes—
321C4⋊C4×C59—22no—
322C4⋊C4×C59—22no—
323C4⋊C4×C59—22no—
324C4⋊C4×C59C2414yes—
325C22⋊C4×C59—24no—
326C22⋊C4×C59—24no—
327C22⋊C4×C59—24no—
328C22⋊C4×C59—24no—
329C22⋊Dic59—22no—
330C22⋊Dic59—22no—
331C22⋊Dic59—22no—
332C22⋊Dic59—22no—
333C22⋊Dic59—22no—
334C22⋊Dic59—22no—
335#11745670—48no—
336#11745669—48no—
337(C2×D59)⋊C4—22no—
338(C2×D59)⋊C4—22no—
339(C2×D59)⋊C4—22no—
340(C2×D59)⋊C4—22no—
341C4⋊Dic59—21no—
342C4⋊Dic59—21no—
343C4⋊Dic59C2412yes—
344C4⋊Dic59C2412yes—
345Dic59⋊C4—22no—
346Dic59⋊C4—22no—
347Dic59⋊C4—22no—
348Dic59⋊C4—22no—
349C4×Dic59—22no—
350C4×Dic59—22no—
351#11745664—28no—
352#11745664—44no—
353C2×C59⋊C8—44no—
354C2×C59⋊C8C2418yes—
355C23×C59—22no—
356C23×C59—22no—
357C23×C59—22no—
358C23×C59—22no—
359C23×C59—22no—
360C23×C59—22no—
361C23×C59—22no—
362C23×C59—22no—
363C23×C59—22no—
364C23×C59—22no—
365C23×C59—22no—
366C23×C59—22no—
367C23×C59—24no—
368C23×C59—41no—
369C23×C59—41no—
370C23×C59—41no—
371C23×C59—41no—
372C23×C59—41no—
373C23×C59—41no—
374C23×C59—41no—
375C23×C59—41no—
376C23×C59—416no—
377C23×C59—44no—
378C23×C59—44no—
379C23×C59—44no—
380C23×C59—44no—
381C23×C59—44no—
382C23×C59—44no—
383C23×C59—44no—
384C23×C59—44no—
385C23×C59—44no—
386C23×C59—816no—
387C23×C59AGL(1,ℤ/8)14yescomplemented
388C23×C59C22×D411yescharacteristic
389C23×C59C22×D411yescharacteristic
390C23×C59C22×D411yescharacteristic
391C23×C59C22×D411yescharacteristic
392C23×C59C22×D411yescharacteristic
393C23×C59C22×D411yescharacteristic
394C23×C59C22×D411yescharacteristic
395C22×D59—22no—
396C22×D59—42no—
397C22×D59—42no—
398C22×D59—42no—
399D4×C59—28no—
400D4×C59—44no—
401D4×C59—44no—
402D4×C59—48no—
403D4×C59—48no—
404D4×C59—48no—
405D4×C59—48no—
406D4×C59—44no—
407C2×C4×C59—22no—
408C2×C4×C59—22no—
409C2×C4×C59—22no—
410C2×C4×C59—22no—
411C2×C4×C59—22no—
412C2×C4×C59—22no—
413C2×C4×C59—22no—
414C2×C4×C59—22no—
415C2×C4×C59—22no—
416C2×C4×C59—22no—
417C2×C4×C59—22no—
418C2×C4×C59—22no—
419C2×C4×C59—22no—
420C2×C4×C59—22no—
421C2×C4×C59—22no—
422C2×C4×C59—24no—
423C2×C4×C59—41no—
424C2×C4×C59—41no—
425C2×C4×C59—41no—
426C2×C4×C59—41no—
427C2×C4×C59—41no—
428C2×C4×C59—41no—
429C2×C4×C59—41no—
430C2×C4×C59—41no—
431C2×C4×C59—41no—
432C2×C4×C59—41no—
433C2×C4×C59—41no—
434C2×C4×C59—41no—
435C2×C4×C59—44no—
436C2×C4×C59—44no—
437C2×C4×C59—44no—
438C2×C4×C59C22×D411yescharacteristic
439C2×C4×C59C22×D411yescharacteristic
440C2×C4×C59C22×D411yescharacteristic
441C2×C4×C59C22×D411yescharacteristic
442C2×C4×C59C22×D411yescharacteristic
443C2×C4×C59C22×D411yescharacteristic
444C2×C4×C59C22×D411yescharacteristic
445C2×C4×C59H(5,𝔽2)14yes—
446C2×C4×C59C2511yescharacteristic
447C22⋊D59—44no—
448C22⋊D59—44no—
449C22⋊D59—44no—
450C22⋊D59—44no—
451C22⋊D59—44no—
452C22⋊D59—44no—
453C2×Dic59—22no—
454C2×Dic59—22no—
455C2×Dic59—22no—
456C2×Dic59—42no—
457C2×Dic59—42no—
458C2×Dic59—42no—
459D236—24no—
460D236—42no—
461C4×D59—44no—
462C4×D59—44no—
463Dic118—24no—
464Dic118—42no—
465C59⋊C8—28no—
466#60750—591nomaximal, Sylow
467C22×C59—28no—
468C22×C59—21no—
469C22×C59—21no—
470C22×C59—21no—
471C22×C59—21no—
472C22×C59—21no—
473C22×C59—21no—
474C22×C59—21no—
475C22×C59—21no—
476C22×C59—21no—
477C22×C59—21no—
478C22×C59—21no—
479C22×C59—21no—
480C22×C59—21no—
481C22×C59—21no—
482C22×C59—21no—
483C22×C59—21no—
484C22×C59—44no—
485C22×C59—44no—
486C22×C59—44no—
487C22×C59—44no—
488C22×C59—44no—
489C22×C59—44no—
490C22×C59—44no—
491C22×C59—44no—
492C22×C59—44no—
493C22×C59—88no—
494C22×C59—88no—
495C22×C59—88no—
496C22×C59#53412yes—
497C22×C59C2×AGL(1,ℤ/8)12yes—
498C22×C59C2×AGL(1,ℤ/8)12yes—
499C22×C59C2×AGL(1,ℤ/8)12yes—
500C22×C59#57512yes—
501C22×C59C23×D411yescharacteristic
502C2×D59—42no—
503C2×D59—42no—
504C2×D59—42no—
505C2×D59—84no—
506C4×C59—21no—
507C4×C59—21no—
508C4×C59—21no—
509C4×C59—21no—
510C4×C59—21no—
511C4×C59—21no—
512C4×C59—44no—
513C4×C59#53412yes—
514C4×C59C2×H(5,𝔽2)12yes—
515Dic59—42no—
516Dic59—42no—
517Dic59—42no—
518C2×#525—591no—
519C22×#121D5911yescharacteristic, complemented
520#3194—594no—
521#3193—592no—
522#3192—592no—
523#3188—594no—
524#3187—592no—
525#3186—592no—
526#3094—592no—
527#3092—592no—
528#3055—594no—
529#3006—592no—
530#3003—592no—
531C2×#407—591no—
532C2×C59—22no—
533C2×C59—22no—
534C2×C59—22no—
535C2×C59—22no—
536C2×C59—22no—
537C2×C59—41no—
538C2×C59—41no—
539C2×C59—84no—
540C2×C59C2×#53411yescharacteristic
541C2×C59C22×AGL(1,ℤ/8)11yescharacteristic
542C2×C59C2×#57511yescharacteristic
543D59—82no—
544C22×#41—591no—
545C23×D4—21no—
546C23×D4C2×D5911yescharacteristic, complemented
547C24×C4C2×D5911yescharacteristic
548C2×AGL(1,ℤ/8)—594no—
549C22×M16—592no—
550#525—592no—
551#525—592no—
552#525—592no—
553#525—592no—
554#525—1181no—
555#525—1181no—
556#525—1181no—
557#525—1181no—
558C2×#123—1181no—
559C2×C22⋊Q8—591no—
560C2×C22⋊Q8—591no—
561C2×#121—21no—
562C2×#121—21no—
563C2×#121—21no—
564C2×#121—21no—
565C2×#121—21no—
566C2×#121—21no—
567C2×#121—591no—
568C2×#121—591no—
569C2×#121C2×D5912yes—
570C2×#121C2×D5912yes—
571C2×#121C2×D5912yes—
572C2×#121C2×D5912yescomplemented
573C2×#121C2×D5912yescomplemented
574C2×#121C2×D5912yescomplemented
575C2×#120—1181no—
576C2×C4×D4—1181no—
577C2×C4×D4—1181no—
578C2×#117—591no—
579C22×C4⋊C4C2×D5911yescharacteristic, complemented
580C22×C22⋊C4—21no—
581#484—594no—
582#483—594no—
583#482—598no—
584#481—594no—
585#481—594no—
586#480—594no—
587#480—594no—
588#469—598no—
589#468—598no—
590#466—598no—
591#465—598no—
592#450—594no—
593#450—594no—
594#449—598no—
595#448—594no—
596#447—594no—
597#447—594no—
598#447—594no—
599#428—594no—
600#418—594no—
601#417—594no—
602#407—592no—
603#407—592no—
604#407—592no—
605#407—592no—
606C2×C22⋊C8—592no—
607C2×C22⋊C8—592no—
608C59#6075011yescharacteristic, complemented, Sylow
609C25—21no—
610C25C22⋊D5911yescharacteristic
611C2×#41—592no—
612C2×#41—592no—
613C2×#41—1181no—
614C2×#41—1181no—
615C2×#41—2364no—
616C22×Q8—591no—
617C22×D4—22no—
618C22×D4—22no—
619C22×D4—22no—
620C22×D4—22no—
621C22×D4—22no—
622C22×D4—22no—
623C22×D4—21no—
624C22×D4—21no—
625C22×D4—21no—
626C22×D4—44no—
627C22×D4—48no—
628C22×D4—591no—
629C22×D4—1181no—
630C22×D4—1181no—
631C22×D4—1181no—
632C22×D4C22×D5912yes—
633C22×D4C22×D5912yes—
634C22×D4C22×D5912yes—
635C23×C4—21no—
636C23×C4—44no—
637C23×C4—1181no—
638C23×C4C22⋊D5911yescharacteristic
639C23×C4C22⋊D5911yescharacteristic
640C23×C4C22⋊D5911yescharacteristic
641C23×C4C22⋊D5911yescharacteristic
642C23×C4C22⋊D5911yescharacteristic
643C23×C4C22⋊D5911yescharacteristic
644C23×C4C22⋊D5911yescharacteristic
645C23×C4C22×D5911yescharacteristic
646C23×C4C22×D5911yescharacteristic
647C23×C4C22×D5911yescharacteristic
648C23×C4C22×D5911yescharacteristic
649C23×C4C22×D5911yescharacteristic
650C23×C4C22×D5911yescharacteristic
651C23×C4C22×D5911yescharacteristic
652AGL(1,ℤ/8)—2368no—
653C2×SD16—598no—
654C2×D8—598no—
655C2×M16—594no—
656C2×M16—594no—
657C2×M16—2364no—
658C22×C8—594no—
659#123—1182no—
660#123—1182no—
661#123—1182no—
662#123—1182no—
663C22⋊Q8—592no—
664C22⋊Q8—592no—
665C22⋊Q8—592no—
666C22⋊Q8—592no—
667C22⋊Q8—1181no—
668C22⋊Q8—1181no—
669C22⋊Q8—1181no—
670C22⋊Q8—1181no—
671#121—22no—
672#121—22no—
673#121—22no—
674#121—22no—
675#121—22no—
676#121—22no—
677#121—22no—
678#121—22no—
679#121—22no—
680#121—22no—
681#121—22no—
682#121—22no—
683#121—592no—
684#121—592no—
685#121—592no—
686#121—592no—
687#121—1181no—
688#121—1181no—
689#121—1181no—
690#121—1181no—
691#121C22×D5914yes—
692#121C22×D5914yes—
693#121C22×D5914yes—
694#121C22×D5914yes—
695#120—1182no—
696#120—1182no—
697#120—1182no—
698#120—1182no—
699C4×D4—1182no—
700C4×D4—1182no—
701C4×D4—1182no—
702C4×D4—1182no—
703C4×D4—1182no—
704C4×D4—1182no—
705C4×D4—1182no—
706C4×D4—1182no—
707#117—592no—
708#117—592no—
709#117—1181no—
710#117—1181no—
711C2×C4⋊C4—21no—
712C2×C4⋊C4—21no—
713C2×C4⋊C4—21no—
714C2×C4⋊C4—591no—
715C2×C4⋊C4—591no—
716C2×C4⋊C4—1181no—
717C2×C4⋊C4—1181no—
718C2×C4⋊C4C22×D5912yes—
719C2×C4⋊C4C22×D5912yes—
720C2×C4⋊C4C22×D5912yes—
721C2×C22⋊C4—22no—
722C2×C22⋊C4—22no—
723C2×C22⋊C4—22no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—1181no—
728C2×C22⋊C4—1181no—
729C2×C22⋊C4—1181no—
730C2×C22⋊C4—1181no—
731C2×C22⋊C4—1181no—
732C2×C42—1181no—
733#107—598no—
734#106—598no—
735#103—598no—
736#102—598no—
737#102—598no—
738#102—598no—
739C22⋊C8—594no—
740C22⋊C8—594no—
741C22⋊C8—594no—
742C22⋊C8—594no—
743C24—24no—
744C24—22no—
745C24—22no—
746C24—22no—
747C24—42no—
748C24—42no—
749C24—44no—
750C24—44no—
751C24—44no—
752C24—1181no—
753C24C2×C22⋊D5911yescharacteristic
754C24C2×C22⋊D5911yescharacteristic
755C24C2×C22⋊D5911yescharacteristic
756C24C2×C22⋊D5911yescharacteristic
757C24C2×C22⋊D5911yescharacteristic
758C24C2×C22⋊D5911yescharacteristic
759C24C2×C22⋊D5911yescharacteristic
760#41—1188no—
761#41—2364no—
762#41—2364no—
763#41—2364no—
764C2×Q8—592no—
765C2×Q8—1181no—
766C2×Q8—2362no—
767C2×D4—24no—
768C2×D4—24no—
769C2×D4—24no—
770C2×D4—24no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—22no—
774C2×D4—28no—
775C2×D4—44no—
776C2×D4—44no—
777C2×D4—44no—
778C2×D4—44no—
779C2×D4—44no—
780C2×D4—48no—
781C2×D4—48no—
782C2×D4—48no—
783C2×D4—48no—
784C2×D4—48no—
785C2×D4—48no—
786C2×D4—592no—
787C2×D4—1182no—
788C2×D4—1182no—
789C2×D4—1182no—
790C2×D4—1182no—
791C2×D4—1182no—
792C2×D4—1182no—
793C2×D4—1181no—
794C2×D4—2362no—
795C2×D4—2364no—
796C2×D4—2364no—
797C2×D4—2364no—
798C2×D4C23×D5914yes—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—42no—
806C22×C4—42no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—44no—
817C22×C4—1181no—
818C22×C4—1181no—
819C22×C4—1181no—
820C22×C4—1182no—
821C22×C4—1182no—
822C22×C4—2364no—
823C22×C4C2×C22⋊D5911yescharacteristic
824C22×C4C2×C22⋊D5911yescharacteristic
825C22×C4C2×C22⋊D5911yescharacteristic
826C22×C4C2×C22⋊D5911yescharacteristic
827C22×C4C2×C22⋊D5911yescharacteristic
828C22×C4C2×C22⋊D5911yescharacteristic
829C22×C4C2×C22⋊D5911yescharacteristic
830C22×C4C2×C22⋊D5911yescharacteristic
831C22×C4C2×C22⋊D5911yescharacteristic
832C22×C4C2×C22⋊D5911yescharacteristic
833C22×C4C2×C22⋊D5911yescharacteristic
834C22×C4C2×C22⋊D5911yescharacteristic
835C22×C4C2×C22⋊D5911yescharacteristic
836C22×C4C2×C22⋊D5911yescharacteristic
837C22×C4C2×C22⋊D5911yescharacteristic
838C22×C4C2×C22⋊D5911yescharacteristic
839C22×C4C2×C22⋊D5911yescharacteristic
840C22×C4C2×C22⋊D5911yescharacteristic
841C22×C4C2×C22⋊D5911yescharacteristic
842C22×C4C2×C22⋊D5911yescharacteristic
843C22×C4C2×C22⋊D5911yescharacteristic
844C22×C4C23×D5911yescharacteristic
845C22×C4C23×D5911yescharacteristic
846C22×C4C23×D5911yescharacteristic
847C22×C4C23×D5911yescharacteristic
848C22×C4C23×D5911yescharacteristic
849C22×C4C23×D5911yescharacteristic
850C22×C4C23×D5911yescharacteristic
851SD16—2368no—
852D8—2368no—
853M16—1188no—
854M16—2364no—
855C2×C8—598no—
856C2×C8—2364no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—592no—
861C4⋊C4—592no—
862C4⋊C4—1181no—
863C4⋊C4—1181no—
864C4⋊C4—1182no—
865C4⋊C4—1182no—
866C4⋊C4—1182no—
867C4⋊C4—1182no—
868C4⋊C4C23×D5914yes—
869C22⋊C4—24no—
870C22⋊C4—24no—
871C22⋊C4—24no—
872C22⋊C4—24no—
873C22⋊C4—1182no—
874C22⋊C4—1182no—
875C22⋊C4—1182no—
876C22⋊C4—1182no—
877C22⋊C4—1182no—
878C22⋊C4—1182no—
879C22⋊C4—1182no—
880C22⋊C4—1182no—
881C22⋊C4—1182no—
882C22⋊C4—1182no—
883C42—1182no—
884C42—1182no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—24no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—416no—
907C23—44no—
908C23—44no—
909C23—44no—
910C23—44no—
911C23—44no—
912C23—44no—
913C23—44no—
914C23—44no—
915C23—44no—
916C23—816no—
917C23—1182no—
918C23—2362no—
919C23—2362no—
920C23—2362no—
921C23#1427375314yescomplemented
922C23C22×C22⋊D5911yescharacteristic
923C23C22×C22⋊D5911yescharacteristic
924C23C22×C22⋊D5911yescharacteristic
925C23C22×C22⋊D5911yescharacteristic
926C23C22×C22⋊D5911yescharacteristic
927C23C22×C22⋊D5911yescharacteristic
928C23C22×C22⋊D5911yescharacteristic
929Q8—1184no—
930Q8—2362no—
931D4—28no—
932D4—44no—
933D4—44no—
934D4—48no—
935D4—48no—
936D4—48no—
937D4—48no—
938D4—44no—
939D4—1184no—
940D4—2362no—
941D4—2364no—
942D4—2364no—
943D4—2364no—
944D4—2364no—
945D4—2364no—
946D4—2364no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—24no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—44no—
976C2×C4—44no—
977C2×C4—44no—
978C2×C4—1182no—
979C2×C4—1182no—
980C2×C4—1182no—
981C2×C4—2364no—
982C2×C4—2362no—
983C2×C4—2362no—
984C2×C4—2362no—
985C2×C4—2364no—
986C2×C4C22×C22⋊D5911yescharacteristic
987C2×C4C22×C22⋊D5911yescharacteristic
988C2×C4C22×C22⋊D5911yescharacteristic
989C2×C4C22×C22⋊D5911yescharacteristic
990C2×C4C22×C22⋊D5911yescharacteristic
991C2×C4C22×C22⋊D5911yescharacteristic
992C2×C4C22×C22⋊D5911yescharacteristic
993C2×C4#1427377214yes—
994C2×C4C24×D5911yescharacteristic
995C8—1188no—
996C22—28no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—44no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22—44no—
1019C22—44no—
1020C22—44no—
1021C22—44no—
1022C22—88no—
1023C22—88no—
1024C22—88no—
1025C22—4724no—
1026C22—2362no—
1027C22—2362no—
1028C22—2362no—
1029C22#1683796112yes—
1030C22C2×#1427375312yes—
1031C22C2×#1427375312yes—
1032C22C2×#1427375312yes—
1033C22#1683820012yes—
1034C22C23×C22⋊D5911yescharacteristic
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—21no—
1041C4—44no—
1042C4—2362no—
1043C4—2362no—
1044C4—2362no—
1045C4#1683796112yes—
1046C4C2×#1427377212yes—
1047C2—22no—
1048C2—22no—
1049C2—22no—
1050C2—22no—
1051C2—22no—
1052C2—41no—
1053C2—41no—
1054C2—84no—
1055C2—4722no—
1056C2C2×#1683796111yescharacteristic
1057C2C22×#1427375311yescharacteristic
1058C2C2×#1683820011yescharacteristic
subgroupG/H
centerC22C23×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC22×#121×C59C2
socleC22×C59C23×D4
hypercenterC22×#121D59
hypocenterC59#60750
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C24×C4 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C2×#16837913C2semidirect
2. #21434910C2semidirect
3. #21434902C2semidirect
4. #21434893C2semidirect
5. #21434861C2semidirect
6. #21434853C2semidirect
7. #21434844C2semidirect
8. #21434032C2semidirect
9. #21434019C2semidirect
10. #21433711C2semidirect
11. #21433346C2semidirect
12. #21433323C2semidirect
13. C2×#16837366C2semidirect
14. C22×#121×C59C2semidirect
15. C22×#11745685C22semidirect
16. C2×#14273753C22semidirect
17. C22×#11745664C22semidirect
23. #16837913C22semidirect
24. #16837913C22semidirect
25. #16837913C22semidirect
27. C2×#14273706C22semidirect
28. C2×#14273706C22semidirect
29. C2×#14273701C22semidirect
30. C2×#14273701C22semidirect
34. C2×#14273686C22semidirect
35. #16837737C22semidirect
36. #16837732C22semidirect
37. #16837723C22semidirect
38. #16837720C22semidirect
39. #16837718C22semidirect
40. #16837715C22semidirect
41. #16837713C22semidirect
42. #16837653C22semidirect
43. #16837646C22semidirect
44. #16837636C22semidirect
45. #16837629C22semidirect
46. #16837553C22semidirect
47. #16837553C22semidirect
48. #16837545C22semidirect
49. #16837540C22semidirect
50. #16837536C22semidirect
51. #16837536C22semidirect
52. #16837535C22semidirect
53. #16837442C22semidirect
54. #16837407C22semidirect
55. #16837401C22semidirect
56. #16837366C22semidirect
57. #16837366C22semidirect
58. #16837366C22semidirect
59. #16837366C22semidirect
60. C2×C22⋊(C59⋊C8)C22semidirect
61. C2×C22⋊(C59⋊C8)C22semidirect
63. C23×D4×C59C22semidirect
74. C2×#121×C59C22semidirect
75. C2×#121×C59C22semidirect
76. C2×#121×C59C22semidirect
77. C22×C4⋊C4×C59C22semidirect
83. C2×#11745685C23semidirect
84. C22×Dic118C23semidirect
85. C22×D236C23semidirect
91. C2×#11745670C23semidirect
92. C2×#11745669C23semidirect
95. C2×#11745664C23semidirect
96. C22×C59⋊C8C23semidirect
107. #14273706C23semidirect
108. #14273706C23semidirect
115. #14273701C23semidirect
116. #14273701C23semidirect
132. #14273686C23semidirect
133. C2×C4⋊Dic59C23semidirect
134. C2×C4⋊Dic59C23semidirect
143. #14273660C23semidirect
144. #14273658C23semidirect
145. #14273650C23semidirect
146. #14273648C23semidirect
147. #14273648C23semidirect
148. #14273647C23semidirect
151. C22⋊(C59⋊C8)C23semidirect
152. C22⋊(C59⋊C8)C23semidirect
387. C23×C59AGL(1,ℤ/8)semidirect
519. C22×#121D59semidirect
546. C23×D4C2×D59semidirect
572. C2×#121C2×D59semidirect
573. C2×#121C2×D59semidirect
574. C2×#121C2×D59semidirect
579. C22×C4⋊C4C2×D59semidirect
608. C59#60750semidirect
921. C23#14273753semidirect

Maximal subgroups

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

subgroupindex
C2×#168379132
#214349102
#214349022
#214348932
#214348612
#214348532
#214348442
#214340322
#214340192
#214337112
#214333462
#214333232
C2×#168373662
C22×#121×C592
#6075059