Finite Group Databasebeta

← #29459434

Subgroups — #29459434

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
2C22×#14273701C211yesmaximal, characteristic, complemented
3#21434912C214yesmaximal, complemented
4#21434903C212yesmaximal, complemented
5#21434896C212yesmaximal, complemented
6#21434863C214yesmaximal, complemented
7#21434854C212yesmaximal, complemented
8#21434847C212yesmaximal, complemented
9#21434037C212yesmaximal, complemented
10#21434021C212yesmaximal, complemented
11#21433715C214yesmaximal, complemented
12#21433350C212yesmaximal, complemented
13#21433326C212yesmaximal, complemented
14C2×C59×#407C211yesmaximal, characteristic, complemented
15C22×#11745685C2211yescharacteristic, complemented
16C23×D236C2211yescharacteristic, complemented
17C23×C22⋊D59—21no—
18C2×#14273755C2214yescomplemented
19#16837913—21no—
20#16837913—21no—
21#16837913—21no—
22#16837913—21no—
23#16837913C2212yes—
24#16837913C2212yescomplemented
25#16837913C2212yescomplemented
26#16837913C2212yescomplemented
27C2×#14273710—21no—
28C2×#14273706C2211yescharacteristic, complemented
29C2×#14273706C2211yescharacteristic, complemented
30C2×#14273701—21no—
31C2×#14273701—21no—
32C2×#14273701—21no—
33C2×#14273701—21no—
34C2×#14273701—21no—
35C2×#14273701—21no—
36C2×#14273701C2212yes—
37C2×#14273701C2212yes—
38C2×#14273701C2212yes—
39C2×#14273701C2212yescomplemented
40C2×#14273701C2212yescomplemented
41C2×#14273701C2212yescomplemented
42C2×#14273701C2211yescharacteristic, complemented
43C2×#14273701C2211yescharacteristic, complemented
44C2×#14273696—21no—
45C2×C4×C22⋊D59—21no—
46C2×C4×C22⋊D59—21no—
47C2×#14273686C2211yescharacteristic, complemented
48C22×C4⋊Dic59C2211yescharacteristic, complemented
49C22×(C2×D59)⋊C4—21no—
50#16837738C2214yescomplemented
51#16837733C2214yescomplemented
52#16837727C2218yescomplemented
53#16837721C2214yescomplemented
54#16837721C2214yescomplemented
55#16837716C2214yescomplemented
56#16837716C2214yescomplemented
57#16837655C2218yescomplemented
58#16837648C2218yescomplemented
59#16837638C2218yescomplemented
60#16837631C2218yescomplemented
61#16837555C2214yescomplemented
62#16837555C2214yescomplemented
63#16837549C2218yescomplemented
64#16837543C2214yescomplemented
65#16837538C2214yescomplemented
66#16837538C2214yescomplemented
67#16837538C2214yescomplemented
68#16837444C2214yescomplemented
69#16837408C2214yescomplemented
70#16837404C2214yescomplemented
71C24×C4×C59C2211yescharacteristic
72C22×M16×C59C2212yescomplemented
73C59×#407C2212yescomplemented
74C59×#407C2212yescomplemented
75C59×#407C2212yescomplemented
76C59×#407C2212yescomplemented
77C2×C22⋊C8×C59C2212yescomplemented
78C2×C22⋊C8×C59C2212yescomplemented
79C24×D59—21no—
80C2×#11745685—21no—
81C2×#11745685—21no—
82C2×#11745685—44no—
83C2×#11745685C2312yes—
84C2×#11745685C2312yescomplemented
85C22×Dic118C2311yescharacteristic, complemented
86C22×D236—21no—
87C22×D236—21no—
88C22×D236—21no—
89C22×D236—44no—
90C22×D236C2312yes—
91C22×D236C2312yes—
92C22×D236C2312yes—
93C22×D236C2311yescharacteristic, complemented
94C22×C22⋊D59—21no—
95C22×C22⋊D59—21no—
96C22×C22⋊D59—21no—
97C22×C22⋊D59—22no—
98C22×C22⋊D59—22no—
99C22×C22⋊D59—22no—
100C22×C22⋊D59—22no—
101C22×C22⋊D59—22no—
102C22×C22⋊D59—22no—
103C22×C22⋊D59—48no—
104C23×Dic59—21no—
105C22×C4×D59—21no—
106#14273755—48no—
107C2×#11745660C2318yescomplemented
108C2×D472C2318yescomplemented
109#14273710—22no—
110#14273710—22no—
111#14273710—22no—
112#14273710—22no—
113#14273706—21no—
114#14273706—21no—
115#14273706—21no—
116#14273706—21no—
117#14273706C2312yes—
118#14273706C2312yes—
119#14273706C2312yescomplemented
120#14273706C2312yescomplemented
121#14273701—22no—
122#14273701—22no—
123#14273701—22no—
124#14273701—22no—
125#14273701—22no—
126#14273701—22no—
127#14273701—22no—
128#14273701—22no—
129#14273701—22no—
130#14273701—22no—
131#14273701—22no—
132#14273701—22no—
133#14273701—21no—
134#14273701—21no—
135#14273701—21no—
136#14273701—21no—
137#14273701C2314yes—
138#14273701C2314yes—
139#14273701C2314yes—
140#14273701C2314yes—
141#14273701C2312yes—
142#14273701C2312yes—
143#14273701C2312yescomplemented
144#14273701C2312yescomplemented
145#14273696—22no—
146#14273696—22no—
147#14273696—22no—
148#14273696—22no—
149C4×C22⋊D59—22no—
150C4×C22⋊D59—22no—
151C4×C22⋊D59—22no—
152C4×C22⋊D59—22no—
153C4×C22⋊D59—22no—
154C4×C22⋊D59—22no—
155C4×C22⋊D59—22no—
156C4×C22⋊D59—22no—
157#14273686—21no—
158#14273686—21no—
159#14273686C2312yes—
160#14273686C2312yescomplemented
161C2×C4⋊Dic59—21no—
162C2×C4⋊Dic59—21no—
163C2×C4⋊Dic59—21no—
164C2×C4⋊Dic59C2312yes—
165C2×C4⋊Dic59C2312yes—
166C2×C4⋊Dic59C2312yes—
167C2×C4⋊Dic59C2311yescharacteristic, complemented
168C2×C4⋊Dic59C2311yescharacteristic, complemented
169C2×Dic59⋊C4—21no—
170C2×Dic59⋊C4—21no—
171C2×C22⋊Dic59—21no—
172C2×C22⋊Dic59—21no—
173C2×C22⋊Dic59—21no—
174C2×(C2×D59)⋊C4—22no—
175C2×(C2×D59)⋊C4—22no—
176C2×(C2×D59)⋊C4—22no—
177C2×(C2×D59)⋊C4—22no—
178C2×(C2×D59)⋊C4—22no—
179C2×(C2×D59)⋊C4—22no—
180C2×(C2×D59)⋊C4—21no—
181C2×(C2×D59)⋊C4—21no—
182C2×C4×Dic59—21no—
183#14273661C2318yescomplemented
184#14273659C2318yescomplemented
185#14273652C2318yescomplemented
186#14273649C2318yescomplemented
187#14273649C2318yescomplemented
188#14273649C2318yescomplemented
189C25×C59D411yescharacteristic
190C23×C4×C59—44no—
191C23×C4×C59D411yescharacteristic
192C23×C4×C59D411yescharacteristic
193C23×C4×C59D411yescharacteristic
194C23×C4×C59D411yescharacteristic
195C23×C4×C59D411yescharacteristic
196C23×C4×C59D411yescharacteristic
197C23×C4×C59D411yescharacteristic
198C23×C4×C59C2311yescharacteristic
199C23×C4×C59C2311yescharacteristic
200C23×C4×C59C2311yescharacteristic
201C23×C4×C59C2311yescharacteristic
202C23×C4×C59C2311yescharacteristic
203C23×C4×C59C2311yescharacteristic
204C23×C4×C59C2311yescharacteristic
205C2×M16×C59—44no—
206C2×M16×C59C2314yes—
207C2×M16×C59C2314yescomplemented
208C22×C8×C59C2314yescomplemented
209C22⋊C8×C59C2314yes—
210C22⋊C8×C59C2314yes—
211C22⋊C8×C59C2314yescomplemented
212C22⋊C8×C59C2314yescomplemented
213C24×C59—24no—
214C24×C59—42no—
215C24×C59—42no—
216C24×C59C2×D411yescharacteristic
217C24×C59C2×D411yescharacteristic
218C24×C59C2×D411yescharacteristic
219C24×C59C2×D411yescharacteristic
220C24×C59C2×D411yescharacteristic
221C24×C59C2×D411yescharacteristic
222C24×C59C2×D411yescharacteristic
223C23×D59—21no—
224C23×D59—22no—
225C23×D59—22no—
226C23×D59—22no—
227C23×D59—44no—
228C23×D59—44no—
229C23×D59—44no—
230C22×C4×C59—24no—
231C22×C4×C59—24no—
232C22×C4×C59—24no—
233C22×C4×C59—42no—
234C22×C4×C59—42no—
235C22×C4×C59—42no—
236C22×C4×C59—42no—
237C22×C4×C59—42no—
238C22×C4×C59—42no—
239C22×C4×C59—42no—
240C22×C4×C59—42no—
241C22×C4×C59—42no—
242C22×C4×C59—42no—
243C22×C4×C59—42no—
244C22×C4×C59C2×D411yescharacteristic
245C22×C4×C59C2×D411yescharacteristic
246C22×C4×C59C2×D411yescharacteristic
247C22×C4×C59C2×D411yescharacteristic
248C22×C4×C59C2×D411yescharacteristic
249C22×C4×C59C2×D411yescharacteristic
250C22×C4×C59C2×D411yescharacteristic
251C22×C4×C59C2×D411yescharacteristic
252C22×C4×C59C2×D411yescharacteristic
253C22×C4×C59C2×D411yescharacteristic
254C22×C4×C59C2×D411yescharacteristic
255C22×C4×C59C2×D411yescharacteristic
256C22×C4×C59C2×D411yescharacteristic
257C22×C4×C59C2×D411yescharacteristic
258C22×C4×C59C2×D411yescharacteristic
259C22×C4×C59C2×D411yescharacteristic
260C22×C4×C59C2×D411yescharacteristic
261C22×C4×C59C2×D411yescharacteristic
262C22×C4×C59C2×D411yescharacteristic
263C22×C4×C59C2×D411yescharacteristic
264C22×C4×C59C2×D411yescharacteristic
265C22×C4×C59C2411yescharacteristic
266C22×C4×C59C2411yescharacteristic
267C22×C4×C59C2411yescharacteristic
268C22×C4×C59C2411yescharacteristic
269C22×C4×C59C2411yescharacteristic
270C22×C4×C59C2411yescharacteristic
271C22×C4×C59C2411yescharacteristic
272C2×C22⋊D59—22no—
273C2×C22⋊D59—22no—
274C2×C22⋊D59—22no—
275C2×C22⋊D59—22no—
276C2×C22⋊D59—22no—
277C2×C22⋊D59—22no—
278C2×C22⋊D59—24no—
279C2×C22⋊D59—24no—
280C2×C22⋊D59—24no—
281C2×C22⋊D59—24no—
282C2×C22⋊D59—44no—
283C2×C22⋊D59—48no—
284C2×C22⋊D59—48no—
285C2×C22⋊D59—48no—
286C2×C22⋊D59—48no—
287C2×C22⋊D59—48no—
288C2×C22⋊D59—44no—
289C2×C22⋊D59—44no—
290C2×C22⋊D59—48no—
291C22×Dic59—21no—
292C22×Dic59—21no—
293C22×Dic59—22no—
294C22×Dic59—22no—
295C22×Dic59—22no—
296C22×Dic59—21no—
297C22×Dic59—44no—
298#11745685—28no—
299#11745685—44no—
300#11745685—44no—
301#11745685—44no—
302C2×D236—28no—
303C2×D236—22no—
304C2×D236—22no—
305C2×D236—22no—
306C2×D236—21no—
307C2×D236—44no—
308C2×D236—44no—
309C2×D236—42no—
310C2×D236—44no—
311C2×D236—44no—
312C2×D236—44no—
313C2×D236C2414yes—
314C2×D236C2412yes—
315C2×C4×D59—22no—
316C2×C4×D59—22no—
317C2×C4×D59—44no—
318C2×Dic118—21no—
319C2×Dic118—42no—
320C2×Dic118C2412yes—
321M16×C59—28no—
322M16×C59—44no—
323C2×C8×C59—44no—
324C2×C8×C59C2418yes—
325C22⋊Dic59—22no—
326C22⋊Dic59—22no—
327C22⋊Dic59—22no—
328C22⋊Dic59—22no—
329C22⋊Dic59—22no—
330C22⋊Dic59—22no—
331(C2×D59)⋊C4—24no—
332(C2×D59)⋊C4—24no—
333(C2×D59)⋊C4—24no—
334(C2×D59)⋊C4—24no—
335(C2×D59)⋊C4—22no—
336(C2×D59)⋊C4—22no—
337(C2×D59)⋊C4—22no—
338(C2×D59)⋊C4—22no—
339C4⋊Dic59—22no—
340C4⋊Dic59—22no—
341C4⋊Dic59—22no—
342C4⋊Dic59—21no—
343C4⋊Dic59—21no—
344C4⋊Dic59C2412yes—
345C4⋊Dic59C2412yes—
346C4⋊Dic59C2414yes—
347Dic59⋊C4—22no—
348Dic59⋊C4—22no—
349Dic59⋊C4—22no—
350Dic59⋊C4—22no—
351C4×Dic59—22no—
352C4×Dic59—22no—
353D472—48no—
354#11745660—48no—
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—41no—
368C23×C59—41no—
369C23×C59—41no—
370C23×C59—41no—
371C23×C59—41no—
372C23×C59—41no—
373C23×C59—41no—
374C23×C59—41no—
375C23×C59—416no—
376C23×C59AGL(1,ℤ/8)14yescomplemented
377C23×C59C22×D411yescharacteristic
378C23×C59C22×D411yescharacteristic
379C23×C59C22×D411yescharacteristic
380C23×C59C22×D411yescharacteristic
381C23×C59C22×D411yescharacteristic
382C23×C59C22×D411yescharacteristic
383C23×C59C22×D411yescharacteristic
384C22×D59—22no—
385C22×D59—24no—
386C22×D59—42no—
387C22×D59—44no—
388C22×D59—44no—
389C22×D59—44no—
390C22×D59—44no—
391C22×D59—42no—
392C22×D59—44no—
393C22×D59—44no—
394C22×D59—44no—
395C22×D59—44no—
396C22×D59—42no—
397C22×D59—44no—
398C22×D59—816no—
399C2×C4×C59—22no—
400C2×C4×C59—22no—
401C2×C4×C59—22no—
402C2×C4×C59—22no—
403C2×C4×C59—22no—
404C2×C4×C59—22no—
405C2×C4×C59—22no—
406C2×C4×C59—22no—
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—41no—
415C2×C4×C59—41no—
416C2×C4×C59—41no—
417C2×C4×C59—41no—
418C2×C4×C59—41no—
419C2×C4×C59—41no—
420C2×C4×C59—41no—
421C2×C4×C59—41no—
422C2×C4×C59—41no—
423C2×C4×C59—41no—
424C2×C4×C59—41no—
425C2×C4×C59—41no—
426C2×C4×C59C22×D411yescharacteristic
427C2×C4×C59C22×D411yescharacteristic
428C2×C4×C59C22×D411yescharacteristic
429C2×C4×C59C22×D411yescharacteristic
430C2×C4×C59C22×D411yescharacteristic
431C2×C4×C59C22×D411yescharacteristic
432C2×C4×C59C22×D411yescharacteristic
433C2×C4×C59H(5,𝔽2)14yes—
434C2×C4×C59C2511yescharacteristic
435C22⋊D59—44no—
436C22⋊D59—44no—
437C22⋊D59—48no—
438C22⋊D59—48no—
439C22⋊D59—44no—
440C22⋊D59—44no—
441C22⋊D59—44no—
442C22⋊D59—48no—
443C22⋊D59—48no—
444C22⋊D59—44no—
445C2×Dic59—22no—
446C2×Dic59—22no—
447C2×Dic59—22no—
448C2×Dic59—24no—
449C2×Dic59—42no—
450C2×Dic59—44no—
451C2×Dic59—44no—
452C2×Dic59—42no—
453C2×Dic59—44no—
454C2×Dic59—42no—
455D236—28no—
456D236—24no—
457D236—44no—
458D236—44no—
459D236—42no—
460D236—44no—
461C4×D59—44no—
462C4×D59—44no—
463Dic118—24no—
464Dic118—42no—
465C8×C59—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#53412yes—
491C22×C59C2×AGL(1,ℤ/8)12yes—
492C22×C59C2×AGL(1,ℤ/8)12yes—
493C22×C59C2×AGL(1,ℤ/8)12yes—
494C22×C59#57512yes—
495C22×C59C23×D411yescharacteristic
496C2×D59—42no—
497C2×D59—44no—
498C2×D59—44no—
499C2×D59—42no—
500C2×D59—42no—
501C2×D59—44no—
502C2×D59—84no—
503C2×D59—88no—
504C2×D59—88no—
505C2×D59—88no—
506C4×C59—21no—
507C4×C59—21no—
508C4×C59—21no—
509C4×C59—21no—
510C4×C59—21no—
511C4×C59—21no—
512C4×C59#53412yes—
513C4×C59C2×H(5,𝔽2)12yes—
514Dic59—42no—
515Dic59—44no—
516Dic59—42no—
517Dic59—42no—
518C2×#525—591no—
519C22×#121—591no—
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×#407D5911yescharacteristic, complemented
532C2×C59—22no—
533C2×C59—22no—
534C2×C59—22no—
535C2×C59—22no—
536C2×C59—22no—
537C2×C59—41no—
538C2×C59—41no—
539C2×C59C2×#53411yescharacteristic
540C2×C59C22×AGL(1,ℤ/8)11yescharacteristic
541C2×C59C2×#57511yescharacteristic
542D59—82no—
543D59—84no—
544C22×#41—591no—
545C23×D4—591no—
546C23×D4—1181no—
547C24×C4C2×D5911yescharacteristic
548C2×AGL(1,ℤ/8)—594no—
549C22×M16C2×D5912yescomplemented
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—592no—
562C2×#121—592no—
563C2×#121—592no—
564C2×#121—592no—
565C2×#121—592no—
566C2×#121—592no—
567C2×#121—591no—
568C2×#121—591no—
569C2×#121—1181no—
570C2×#121—1181no—
571C2×#121—1181no—
572C2×#121—1181no—
573C2×#121—1181no—
574C2×#121—1181no—
575C2×#120—1181no—
576C2×C4×D4—1181no—
577C2×C4×D4—1181no—
578C2×#117—591no—
579C22×C4⋊C4—591no—
580C22×C22⋊C4—1181no—
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#407C2×D5912yescomplemented
603#407C2×D5912yescomplemented
604#407C2×D5912yescomplemented
605#407C2×D5912yescomplemented
606C2×C22⋊C8C2×D5912yescomplemented
607C2×C22⋊C8C2×D5912yescomplemented
608C59#6075011yescharacteristic, complemented, Sylow
609C25—1181no—
610C25D23611yescharacteristic
611C2×#41—592no—
612C2×#41—592no—
613C2×#41—1181no—
614C2×#41—1181no—
615C2×#41—2364no—
616C22×Q8—591no—
617C22×D4—592no—
618C22×D4—592no—
619C22×D4—592no—
620C22×D4—591no—
621C22×D4—1181no—
622C22×D4—1181no—
623C22×D4—1181no—
624C22×D4—1182no—
625C22×D4—1182no—
626C22×D4—1182no—
627C22×D4—1182no—
628C22×D4—1182no—
629C22×D4—1182no—
630C22×D4—1181no—
631C22×D4—1181no—
632C22×D4—1181no—
633C22×D4—2364no—
634C22×D4—2368no—
635C23×C4—44no—
636C23×C4—1181no—
637C23×C4—1181no—
638C23×C4D23611yescharacteristic
639C23×C4D23611yescharacteristic
640C23×C4D23611yescharacteristic
641C23×C4D23611yescharacteristic
642C23×C4D23611yescharacteristic
643C23×C4D23611yescharacteristic
644C23×C4D23611yescharacteristic
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—44no—
656C2×M16C22×D5914yes—
657C2×M16C22×D5914yescomplemented
658C22×C8C22×D5914yescomplemented
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—594no—
672#121—594no—
673#121—594no—
674#121—594no—
675#121—592no—
676#121—592no—
677#121—592no—
678#121—592no—
679#121—1182no—
680#121—1182no—
681#121—1182no—
682#121—1182no—
683#121—1182no—
684#121—1182no—
685#121—1182no—
686#121—1182no—
687#121—1182no—
688#121—1182no—
689#121—1182no—
690#121—1182no—
691#121—1181no—
692#121—1181no—
693#121—1181no—
694#121—1181no—
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—592no—
712C2×C4⋊C4—592no—
713C2×C4⋊C4—592no—
714C2×C4⋊C4—591no—
715C2×C4⋊C4—591no—
716C2×C4⋊C4—1181no—
717C2×C4⋊C4—1181no—
718C2×C4⋊C4—1181no—
719C2×C4⋊C4—1181no—
720C2×C4⋊C4—1181no—
721C2×C22⋊C4—1181no—
722C2×C22⋊C4—1181no—
723C2×C22⋊C4—1181no—
724C2×C22⋊C4—1182no—
725C2×C22⋊C4—1182no—
726C2×C22⋊C4—1182no—
727C2×C22⋊C4—1182no—
728C2×C22⋊C4—1182no—
729C2×C22⋊C4—1182no—
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⋊C8C22×D5914yes—
740C22⋊C8C22×D5914yes—
741C22⋊C8C22×D5914yescomplemented
742C22⋊C8C22×D5914yescomplemented
743C24—24no—
744C24—42no—
745C24—42no—
746C24—1181no—
747C24—1182no—
748C24—1182no—
749C24—1182no—
750C24—2364no—
751C24—2364no—
752C24—2364no—
753C24C2×D23611yescharacteristic
754C24C2×D23611yescharacteristic
755C24C2×D23611yescharacteristic
756C24C2×D23611yescharacteristic
757C24C2×D23611yescharacteristic
758C24C2×D23611yescharacteristic
759C24C2×D23611yescharacteristic
760#41—1188no—
761#41—2364no—
762#41—2364no—
763#41—2364no—
764C2×Q8—592no—
765C2×Q8—1181no—
766C2×Q8—2362no—
767C2×D4—592no—
768C2×D4—594no—
769C2×D4—1182no—
770C2×D4—1182no—
771C2×D4—1182no—
772C2×D4—1182no—
773C2×D4—1182no—
774C2×D4—1182no—
775C2×D4—1184no—
776C2×D4—1184no—
777C2×D4—1184no—
778C2×D4—1184no—
779C2×D4—1182no—
780C2×D4—1182no—
781C2×D4—1182no—
782C2×D4—1181no—
783C2×D4—1188no—
784C2×D4—2364no—
785C2×D4—2364no—
786C2×D4—2362no—
787C2×D4—2364no—
788C2×D4—2364no—
789C2×D4—2364no—
790C2×D4—2368no—
791C2×D4—2368no—
792C2×D4—2368no—
793C2×D4—2368no—
794C2×D4—2368no—
795C2×D4—2364no—
796C2×D4—2364no—
797C2×D4—2368no—
798C2×D4—2364no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—42no—
803C22×C4—42no—
804C22×C4—42no—
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—1181no—
814C22×C4—1181no—
815C22×C4—1182no—
816C22×C4—1182no—
817C22×C4—1182no—
818C22×C4—1181no—
819C22×C4—1182no—
820C22×C4—1182no—
821C22×C4—2364no—
822C22×C4—2364no—
823C22×C4C2×D23611yescharacteristic
824C22×C4C2×D23611yescharacteristic
825C22×C4C2×D23611yescharacteristic
826C22×C4C2×D23611yescharacteristic
827C22×C4C2×D23611yescharacteristic
828C22×C4C2×D23611yescharacteristic
829C22×C4C2×D23611yescharacteristic
830C22×C4C2×D23611yescharacteristic
831C22×C4C2×D23611yescharacteristic
832C22×C4C2×D23611yescharacteristic
833C22×C4C2×D23611yescharacteristic
834C22×C4C2×D23611yescharacteristic
835C22×C4C2×D23611yescharacteristic
836C22×C4C2×D23611yescharacteristic
837C22×C4C2×D23611yescharacteristic
838C22×C4C2×D23611yescharacteristic
839C22×C4C2×D23611yescharacteristic
840C22×C4C2×D23611yescharacteristic
841C22×C4C2×D23611yescharacteristic
842C22×C4C2×D23611yescharacteristic
843C22×C4C2×D23611yescharacteristic
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—28no—
854M16—44no—
855C2×C8—44no—
856C2×C8C23×D5918yes—
857C4⋊C4—592no—
858C4⋊C4—592no—
859C4⋊C4—594no—
860C4⋊C4—1182no—
861C4⋊C4—1182no—
862C4⋊C4—1182no—
863C4⋊C4—1181no—
864C4⋊C4—1181no—
865C4⋊C4—1182no—
866C4⋊C4—1182no—
867C4⋊C4—1182no—
868C4⋊C4—1182no—
869C22⋊C4—1182no—
870C22⋊C4—1182no—
871C22⋊C4—1182no—
872C22⋊C4—1182no—
873C22⋊C4—1182no—
874C22⋊C4—1182no—
875C22⋊C4—1184no—
876C22⋊C4—1184no—
877C22⋊C4—1184no—
878C22⋊C4—1184no—
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—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—416no—
906C23—1182no—
907C23—1184no—
908C23—47216no—
909C23—2362no—
910C23—2364no—
911C23—2364no—
912C23—2364no—
913C23—2364no—
914C23—2362no—
915C23—2364no—
916C23—2364no—
917C23—2364no—
918C23—2362no—
919C23—2364no—
920C23—2364no—
921C23#1427375514yescomplemented
922C23C22×D23611yescharacteristic
923C23C22×D23611yescharacteristic
924C23C22×D23611yescharacteristic
925C23C22×D23611yescharacteristic
926C23C22×D23611yescharacteristic
927C23C22×D23611yescharacteristic
928C23C22×D23611yescharacteristic
929Q8—1184no—
930Q8—2362no—
931D4—1184no—
932D4—1188no—
933D4—2364no—
934D4—2364no—
935D4—2362no—
936D4—2364no—
937D4—2368no—
938D4—2368no—
939D4—2364no—
940D4—2364no—
941D4—2364no—
942D4—2368no—
943D4—2368no—
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—41no—
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—1182no—
975C2×C4—1182no—
976C2×C4—1184no—
977C2×C4—1182no—
978C2×C4—2364no—
979C2×C4—2364no—
980C2×C4—2364no—
981C2×C4—2362no—
982C2×C4—2362no—
983C2×C4—2364no—
984C2×C4—2362no—
985C2×C4—2364no—
986C2×C4C22×D23611yescharacteristic
987C2×C4C22×D23611yescharacteristic
988C2×C4C22×D23611yescharacteristic
989C2×C4C22×D23611yescharacteristic
990C2×C4C22×D23611yescharacteristic
991C2×C4C22×D23611yescharacteristic
992C2×C4C22×D23611yescharacteristic
993C2×C4#1427377214yes—
994C2×C4C24×D5911yescharacteristic
995C8—28no—
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—4728no—
1020C22—4728no—
1021C22—4728no—
1022C22—4724no—
1023C22—2364no—
1024C22—2362no—
1025C22—2362no—
1026C22—2364no—
1027C22—2362no—
1028C22—2364no—
1029C22#1683796412yes—
1030C22C2×#1427375512yes—
1031C22C2×#1427375512yes—
1032C22C2×#1427375512yes—
1033C22#1683820212yes—
1034C22C23×D23611yescharacteristic
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—21no—
1041C4—2364no—
1042C4—2362no—
1043C4—2362no—
1044C4—2362no—
1045C4#1683796412yes—
1046C4C2×#1427377212yes—
1047C2—22no—
1048C2—22no—
1049C2—22no—
1050C2—22no—
1051C2—22no—
1052C2—41no—
1053C2—41no—
1054C2—4724no—
1055C2—4722no—
1056C2C2×#1683796411yescharacteristic
1057C2C22×#1427375511yescharacteristic
1058C2C2×#1683820211yescharacteristic
subgroupG/H
centerC22C23×D236
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#407C2
socleC22×C59C23×D4
hypercenterC2×#407D59
hypocenterC59#60750
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
1. C2×#16837913C2semidirect
2. C22×#14273701C2semidirect
3. #21434912C2semidirect
4. #21434903C2semidirect
5. #21434896C2semidirect
6. #21434863C2semidirect
7. #21434854C2semidirect
8. #21434847C2semidirect
9. #21434037C2semidirect
10. #21434021C2semidirect
11. #21433715C2semidirect
12. #21433350C2semidirect
13. #21433326C2semidirect
14. C2×C59×#407C2semidirect
15. C22×#11745685C22semidirect
16. C23×D236C22semidirect
18. C2×#14273755C22semidirect
24. #16837913C22semidirect
25. #16837913C22semidirect
26. #16837913C22semidirect
28. C2×#14273706C22semidirect
29. C2×#14273706C22semidirect
39. C2×#14273701C22semidirect
40. C2×#14273701C22semidirect
41. C2×#14273701C22semidirect
42. C2×#14273701C22semidirect
43. C2×#14273701C22semidirect
47. C2×#14273686C22semidirect
48. C22×C4⋊Dic59C22semidirect
50. #16837738C22semidirect
51. #16837733C22semidirect
52. #16837727C22semidirect
53. #16837721C22semidirect
54. #16837721C22semidirect
55. #16837716C22semidirect
56. #16837716C22semidirect
57. #16837655C22semidirect
58. #16837648C22semidirect
59. #16837638C22semidirect
60. #16837631C22semidirect
61. #16837555C22semidirect
62. #16837555C22semidirect
63. #16837549C22semidirect
64. #16837543C22semidirect
65. #16837538C22semidirect
66. #16837538C22semidirect
67. #16837538C22semidirect
68. #16837444C22semidirect
69. #16837408C22semidirect
70. #16837404C22semidirect
72. C22×M16×C59C22semidirect
73. C59×#407C22semidirect
74. C59×#407C22semidirect
75. C59×#407C22semidirect
76. C59×#407C22semidirect
77. C2×C22⋊C8×C59C22semidirect
78. C2×C22⋊C8×C59C22semidirect
84. C2×#11745685C23semidirect
85. C22×Dic118C23semidirect
93. C22×D236C23semidirect
107. C2×#11745660C23semidirect
108. C2×D472C23semidirect
119. #14273706C23semidirect
120. #14273706C23semidirect
143. #14273701C23semidirect
144. #14273701C23semidirect
160. #14273686C23semidirect
167. C2×C4⋊Dic59C23semidirect
168. C2×C4⋊Dic59C23semidirect
183. #14273661C23semidirect
184. #14273659C23semidirect
185. #14273652C23semidirect
186. #14273649C23semidirect
187. #14273649C23semidirect
188. #14273649C23semidirect
207. C2×M16×C59C23semidirect
208. C22×C8×C59C23semidirect
211. C22⋊C8×C59C23semidirect
212. C22⋊C8×C59C23semidirect
376. C23×C59AGL(1,ℤ/8)semidirect
531. C2×#407D59semidirect
549. C22×M16C2×D59semidirect
602. #407C2×D59semidirect
603. #407C2×D59semidirect
604. #407C2×D59semidirect
605. #407C2×D59semidirect
606. C2×C22⋊C8C2×D59semidirect
607. C2×C22⋊C8C2×D59semidirect
608. C59#60750semidirect
657. C2×M16C22×D59semidirect
658. C22×C8C22×D59semidirect
741. C22⋊C8C22×D59semidirect
742. C22⋊C8C22×D59semidirect
921. C23#14273755semidirect

Maximal subgroups

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

subgroupindex
C2×#168379132
C22×#142737012
#214349122
#214349032
#214348962
#214348632
#214348542
#214348472
#214340372
#214340212
#214337152
#214333502
#214333262
C2×C59×#4072
#6075059