Finite Group Databasebeta

← #29459464

Subgroups — #29459464

Order 15104.

2362 conjugacy classes of subgroups.

The subgroup lattice has 1182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837913C211yesmaximal, characteristic, complemented
2C2×#16837913C211yesmaximal, characteristic, complemented
3#21434938C214yesmaximal, complemented
4#21434928C212yesmaximal, complemented
5#21434912C212yesmaximal, complemented
6#21434889C214yesmaximal, complemented
7#21434879C212yesmaximal, complemented
8#21434863C212yesmaximal, complemented
9#21434045C211yesmaximal, characteristic, complemented
10#21434037C211yesmaximal, characteristic, complemented
11#21434029C212yesmaximal, complemented
12#21433726C212yesmaximal, complemented
13#21433715C212yesmaximal, complemented
14#21433358C211yesmaximal, characteristic, complemented
15#21433350C211yesmaximal, characteristic, complemented
16#21433341C212yesmaximal, complemented
17C2×C59×#407C211yesmaximal, characteristic, complemented
18C22×#11745685C2211yescharacteristic
19C22×#11745685C2211yescharacteristic, complemented
20C2×#14273760C2212yescomplemented
21C2×#14273755C2212yescomplemented
22#16837913—21no—
23#16837913—21no—
24#16837913—21no—
25#16837913—21no—
26#16837913—21no—
27#16837913—21no—
28#16837913—21no—
29#16837913—21no—
30#16837913C2212yes—
31#16837913C2212yes—
32#16837913C2212yes—
33#16837913C2212yes—
34#16837913C2212yescomplemented
35#16837913C2212yescomplemented
36#16837913C2212yescomplemented
37#16837913C2212yescomplemented
38C2×#14273710—21no—
39C2×#14273710—21no—
40C2×#14273706C2211yescharacteristic
41C2×#14273706C2211yescharacteristic, complemented
42C2×#14273706C2211yescharacteristic, complemented
43C2×#14273706C2211yescharacteristic, complemented
44C2×#14273701C2211yescharacteristic
45C2×#14273701C2211yescharacteristic, complemented
46C2×#14273701C2211yescharacteristic, complemented
47C2×#14273701C2211yescharacteristic, complemented
48C2×#14273696—21no—
49C2×#14273696—21no—
50C2×C4×C22⋊D59—21no—
51C2×C4×C22⋊D59—21no—
52C2×C4×C22⋊D59—21no—
53C2×C4×C22⋊D59—21no—
54C2×#14273686C2211yescharacteristic
55C2×#14273686C2211yescharacteristic, complemented
56#16837744C2214yescomplemented
57#16837744C2214yescomplemented
58#16837744C2214yescomplemented
59#16837738C2212yescomplemented
60#16837733C2212yescomplemented
61#16837727C2214yescomplemented
62#16837727C2214yescomplemented
63#16837727C2214yescomplemented
64#16837721C2212yescomplemented
65#16837716C2212yescomplemented
66#16837660C2214yescomplemented
67#16837655C2214yescomplemented
68#16837648C2214yescomplemented
69#16837648C2214yescomplemented
70#16837643C2214yescomplemented
71#16837638C2214yescomplemented
72#16837631C2214yescomplemented
73#16837631C2214yescomplemented
74#16837566C2214yescomplemented
75#16837566C2214yescomplemented
76#16837566C2214yescomplemented
77#16837560C2212yescomplemented
78#16837555C2212yescomplemented
79#16837549C2214yescomplemented
80#16837549C2214yescomplemented
81#16837549C2214yescomplemented
82#16837543C2212yescomplemented
83#16837538C2212yescomplemented
84#16837444C2212yescomplemented
85#16837444C2212yescomplemented
86#16837412C2212yescomplemented
87#16837408C2212yescomplemented
88#16837404C2212yescomplemented
89#16837404C2212yescomplemented
90C24×C4×C59C2211yescharacteristic
91C22×M16×C59C2212yescomplemented
92C59×#407C2211yescharacteristic
93C59×#407C2211yescharacteristic
94C59×#407C2212yescomplemented
95C59×#407C2212yescomplemented
96C59×#407C2212yescomplemented
97C2×C22⋊C8×C59C2212yescomplemented
98C2×C22⋊C8×C59C2212yescomplemented
99C2×#11745685—21no—
100C2×#11745685—21no—
101C2×#11745685—21no—
102C2×#11745685—21no—
103C2×#11745685—44no—
104C2×#11745685—44no—
105C2×#11745685C2312yes—
106C2×#11745685C2312yes—
107C2×#11745685C2312yes—
108C2×#11745685C2312yes—
109C22×Dic118C2311yescharacteristic
110C22×Dic118C2311yescharacteristic
111C22×D236C2311yescharacteristic
112C22×D236C2311yescharacteristic
113C22×C22⋊D59—21no—
114C22×C22⋊D59—21no—
115C22×C22⋊D59—21no—
116C22×C22⋊D59—21no—
117C22×C22⋊D59—21no—
118C22×C22⋊D59—21no—
119C22×C4×D59—21no—
120C22×C4×D59—21no—
121#14273760—44no—
122#14273755—44no—
123C2×Dic236C2314yescomplemented
124C2×#11745660C2314yescomplemented
125C2×#11745660C2314yescomplemented
126C2×D472C2314yescomplemented
127#14273710—22no—
128#14273710—22no—
129#14273710—22no—
130#14273710—22no—
131#14273710—22no—
132#14273710—22no—
133#14273710—22no—
134#14273710—22no—
135#14273706—21no—
136#14273706—21no—
137#14273706—21no—
138#14273706—21no—
139#14273706—21no—
140#14273706—21no—
141#14273706—21no—
142#14273706—21no—
143#14273706C2312yes—
144#14273706C2312yes—
145#14273706C2312yes—
146#14273706C2312yes—
147#14273706C2312yes—
148#14273706C2312yes—
149#14273706C2312yes—
150#14273706C2312yes—
151#14273701—21no—
152#14273701—21no—
153#14273701—21no—
154#14273701—21no—
155#14273701—21no—
156#14273701—21no—
157#14273701—21no—
158#14273701—21no—
159#14273701C2312yes—
160#14273701C2312yes—
161#14273701C2312yes—
162#14273701C2312yes—
163#14273701C2312yes—
164#14273701C2312yes—
165#14273701C2312yes—
166#14273701C2312yes—
167#14273696—22no—
168#14273696—22no—
169#14273696—22no—
170#14273696—22no—
171#14273696—22no—
172#14273696—22no—
173#14273696—22no—
174#14273696—22no—
175C4×C22⋊D59—22no—
176C4×C22⋊D59—22no—
177C4×C22⋊D59—22no—
178C4×C22⋊D59—22no—
179C4×C22⋊D59—22no—
180C4×C22⋊D59—22no—
181C4×C22⋊D59—22no—
182C4×C22⋊D59—22no—
183C4×C22⋊D59—22no—
184C4×C22⋊D59—22no—
185C4×C22⋊D59—22no—
186C4×C22⋊D59—22no—
187C4×C22⋊D59—22no—
188C4×C22⋊D59—22no—
189C4×C22⋊D59—22no—
190C4×C22⋊D59—22no—
191#14273686—21no—
192#14273686—21no—
193#14273686—21no—
194#14273686—21no—
195#14273686C2312yes—
196#14273686C2312yes—
197#14273686C2312yes—
198#14273686C2312yes—
199C2×C4⋊Dic59C2311yescharacteristic
200C2×C4⋊Dic59C2311yescharacteristic
201C2×C4⋊Dic59C2311yescharacteristic
202C2×C4⋊Dic59C2311yescharacteristic
203C2×Dic59⋊C4—21no—
204C2×Dic59⋊C4—21no—
205C2×Dic59⋊C4—21no—
206C2×Dic59⋊C4—21no—
207C2×C22⋊Dic59—21no—
208C2×C22⋊Dic59—21no—
209C2×C22⋊Dic59—21no—
210C2×C22⋊Dic59—21no—
211C2×C22⋊Dic59—21no—
212C2×C22⋊Dic59—21no—
213C2×(C2×D59)⋊C4—21no—
214C2×(C2×D59)⋊C4—21no—
215C2×(C2×D59)⋊C4—21no—
216C2×(C2×D59)⋊C4—21no—
217C2×C4×Dic59—21no—
218C2×C4×Dic59—21no—
219#14273661C2314yescomplemented
220#14273661C2314yescomplemented
221#14273659C2314yescomplemented
222#14273659C2314yescomplemented
223#14273652C2314yescomplemented
224#14273652C2314yescomplemented
225#14273652C2314yescomplemented
226#14273652C2314yescomplemented
227#14273649C2314yescomplemented
228#14273649C2314yescomplemented
229#14273649C2314yescomplemented
230#14273649C2314yescomplemented
231C25×C59D411yescharacteristic
232C23×C4×C59—44no—
233C23×C4×C59D411yescharacteristic
234C23×C4×C59D411yescharacteristic
235C23×C4×C59D411yescharacteristic
236C23×C4×C59D411yescharacteristic
237C23×C4×C59D411yescharacteristic
238C23×C4×C59D411yescharacteristic
239C23×C4×C59D411yescharacteristic
240C23×C4×C59C2311yescharacteristic
241C23×C4×C59C2311yescharacteristic
242C23×C4×C59C2311yescharacteristic
243C23×C4×C59C2311yescharacteristic
244C23×C4×C59C2311yescharacteristic
245C23×C4×C59C2311yescharacteristic
246C23×C4×C59C2311yescharacteristic
247C2×M16×C59—44no—
248C2×M16×C59C2312yes—
249C2×M16×C59C2312yes—
250C2×M16×C59C2314yes—
251C22×C8×C59C2314yes—
252C22⋊C8×C59C2312yes—
253C22⋊C8×C59C2312yes—
254C22⋊C8×C59C2312yes—
255C22⋊C8×C59C2312yes—
256C22⋊C8×C59C2314yes—
257C22⋊C8×C59C2314yes—
258C24×C59—42no—
259C24×C59—42no—
260C24×C59—42no—
261C24×C59C2×D411yescharacteristic
262C24×C59C2×D411yescharacteristic
263C24×C59C2×D411yescharacteristic
264C24×C59C2×D411yescharacteristic
265C24×C59C2×D411yescharacteristic
266C24×C59C2×D411yescharacteristic
267C24×C59C2×D411yescharacteristic
268C23×D59—21no—
269C23×D59—21no—
270C22×C4×C59—24no—
271C22×C4×C59—24no—
272C22×C4×C59—24no—
273C22×C4×C59—42no—
274C22×C4×C59—42no—
275C22×C4×C59—42no—
276C22×C4×C59—42no—
277C22×C4×C59—42no—
278C22×C4×C59—42no—
279C22×C4×C59—42no—
280C22×C4×C59—42no—
281C22×C4×C59—42no—
282C22×C4×C59—42no—
283C22×C4×C59—42no—
284C22×C4×C59C2×D411yescharacteristic
285C22×C4×C59C2×D411yescharacteristic
286C22×C4×C59C2×D411yescharacteristic
287C22×C4×C59C2×D411yescharacteristic
288C22×C4×C59C2×D411yescharacteristic
289C22×C4×C59C2×D411yescharacteristic
290C22×C4×C59C2×D411yescharacteristic
291C22×C4×C59C2×D411yescharacteristic
292C22×C4×C59C2×D411yescharacteristic
293C22×C4×C59C2×D411yescharacteristic
294C22×C4×C59C2×D411yescharacteristic
295C22×C4×C59C2×D411yescharacteristic
296C22×C4×C59C2×D411yescharacteristic
297C22×C4×C59C2×D411yescharacteristic
298C22×C4×C59C2×D411yescharacteristic
299C22×C4×C59C2×D411yescharacteristic
300C22×C4×C59C2×D411yescharacteristic
301C22×C4×C59C2×D411yescharacteristic
302C22×C4×C59C2×D411yescharacteristic
303C22×C4×C59C2×D411yescharacteristic
304C22×C4×C59C2×D411yescharacteristic
305C22×C4×C59C2411yescharacteristic
306C22×C4×C59C2411yescharacteristic
307C22×C4×C59C2411yescharacteristic
308C22×C4×C59C2411yescharacteristic
309C22×C4×C59C2411yescharacteristic
310C22×C4×C59C2411yescharacteristic
311C22×C4×C59C2411yescharacteristic
312C2×C22⋊D59—22no—
313C2×C22⋊D59—22no—
314C2×C22⋊D59—22no—
315C2×C22⋊D59—22no—
316C2×C22⋊D59—22no—
317C2×C22⋊D59—22no—
318C2×C22⋊D59—22no—
319C2×C22⋊D59—22no—
320C2×C22⋊D59—22no—
321C2×C22⋊D59—22no—
322C2×C22⋊D59—22no—
323C2×C22⋊D59—22no—
324C2×C22⋊D59—44no—
325C2×C22⋊D59—44no—
326C2×C22⋊D59—44no—
327C2×C22⋊D59—44no—
328C2×C22⋊D59—44no—
329C2×C22⋊D59—44no—
330C22×Dic59—21no—
331C22×Dic59—21no—
332C22×Dic59—21no—
333C22×Dic59—21no—
334C22×Dic59—21no—
335C22×Dic59—21no—
336#11745685—24no—
337#11745685—24no—
338#11745685—42no—
339#11745685—44no—
340#11745685—44no—
341#11745685—42no—
342#11745685—44no—
343#11745685—44no—
344#11745685—44no—
345#11745685—44no—
346C2×D236—24no—
347C2×D236—21no—
348C2×D236—21no—
349C2×D236—42no—
350C2×D236C2412yes—
351C2×D236C2412yes—
352C2×C4×D59—22no—
353C2×C4×D59—22no—
354C2×C4×D59—22no—
355C2×C4×D59—22no—
356C2×C4×D59—44no—
357C2×C4×D59—44no—
358C2×Dic118—24no—
359C2×Dic118—21no—
360C2×Dic118—21no—
361C2×Dic118—42no—
362C2×Dic118C2412yes—
363C2×Dic118C2412yes—
364M16×C59—24no—
365M16×C59—24no—
366M16×C59—44no—
367C2×C8×C59—44no—
368C2×C8×C59C2414yes—
369C2×C8×C59C2414yes—
370C22⋊Dic59—22no—
371C22⋊Dic59—22no—
372C22⋊Dic59—22no—
373C22⋊Dic59—22no—
374C22⋊Dic59—22no—
375C22⋊Dic59—22no—
376C22⋊Dic59—22no—
377C22⋊Dic59—22no—
378C22⋊Dic59—22no—
379C22⋊Dic59—22no—
380C22⋊Dic59—22no—
381C22⋊Dic59—22no—
382(C2×D59)⋊C4—22no—
383(C2×D59)⋊C4—22no—
384(C2×D59)⋊C4—22no—
385(C2×D59)⋊C4—22no—
386(C2×D59)⋊C4—22no—
387(C2×D59)⋊C4—22no—
388(C2×D59)⋊C4—22no—
389(C2×D59)⋊C4—22no—
390C4⋊Dic59—21no—
391C4⋊Dic59—21no—
392C4⋊Dic59—21no—
393C4⋊Dic59—21no—
394C4⋊Dic59C2412yes—
395C4⋊Dic59C2412yes—
396C4⋊Dic59C2412yes—
397C4⋊Dic59C2412yes—
398Dic59⋊C4—22no—
399Dic59⋊C4—22no—
400Dic59⋊C4—22no—
401Dic59⋊C4—22no—
402Dic59⋊C4—22no—
403Dic59⋊C4—22no—
404Dic59⋊C4—22no—
405Dic59⋊C4—22no—
406C4×Dic59—22no—
407C4×Dic59—22no—
408C4×Dic59—22no—
409C4×Dic59—22no—
410Dic236—44no—
411D472—44no—
412#11745660—44no—
413#11745660—44no—
414C23×C59—22no—
415C23×C59—22no—
416C23×C59—22no—
417C23×C59—22no—
418C23×C59—22no—
419C23×C59—22no—
420C23×C59—22no—
421C23×C59—22no—
422C23×C59—22no—
423C23×C59—41no—
424C23×C59—41no—
425C23×C59—41no—
426C23×C59—41no—
427C23×C59—41no—
428C23×C59—41no—
429C23×C59—41no—
430C23×C59—41no—
431C23×C59—41no—
432C23×C59—41no—
433C23×C59—41no—
434C23×C59—41no—
435C23×C59—416no—
436C23×C59C22×D411yescharacteristic
437C23×C59C22×D411yescharacteristic
438C23×C59C22×D411yescharacteristic
439C23×C59C22×D411yescharacteristic
440C23×C59C22×D411yescharacteristic
441C23×C59C22×D411yescharacteristic
442C23×C59C22×D411yescharacteristic
443C22×D59—22no—
444C22×D59—22no—
445C22×D59—42no—
446C22×D59—42no—
447C22×D59—42no—
448C22×D59—42no—
449C22×D59—42no—
450C22×D59—42no—
451C2×C4×C59—22no—
452C2×C4×C59—22no—
453C2×C4×C59—22no—
454C2×C4×C59—22no—
455C2×C4×C59—22no—
456C2×C4×C59—22no—
457C2×C4×C59—22no—
458C2×C4×C59—22no—
459C2×C4×C59—22no—
460C2×C4×C59—22no—
461C2×C4×C59—22no—
462C2×C4×C59—22no—
463C2×C4×C59—22no—
464C2×C4×C59—22no—
465C2×C4×C59—22no—
466C2×C4×C59—41no—
467C2×C4×C59—41no—
468C2×C4×C59—41no—
469C2×C4×C59—41no—
470C2×C4×C59—41no—
471C2×C4×C59—41no—
472C2×C4×C59—41no—
473C2×C4×C59—41no—
474C2×C4×C59—41no—
475C2×C4×C59—41no—
476C2×C4×C59—41no—
477C2×C4×C59—41no—
478C2×C4×C59C22×D411yescharacteristic
479C2×C4×C59C22×D411yescharacteristic
480C2×C4×C59C22×D411yescharacteristic
481C2×C4×C59C22×D411yescharacteristic
482C2×C4×C59C22×D411yescharacteristic
483C2×C4×C59C22×D411yescharacteristic
484C2×C4×C59C22×D411yescharacteristic
485C2×C4×C59H(5,𝔽2)14yes—
486C2×C4×C59C2511yescharacteristic
487C22⋊D59—44no—
488C22⋊D59—44no—
489C22⋊D59—44no—
490C22⋊D59—44no—
491C22⋊D59—44no—
492C22⋊D59—44no—
493C22⋊D59—44no—
494C22⋊D59—44no—
495C22⋊D59—44no—
496C22⋊D59—44no—
497C22⋊D59—44no—
498C22⋊D59—44no—
499C2×Dic59—22no—
500C2×Dic59—22no—
501C2×Dic59—22no—
502C2×Dic59—22no—
503C2×Dic59—22no—
504C2×Dic59—22no—
505C2×Dic59—42no—
506C2×Dic59—42no—
507C2×Dic59—42no—
508C2×Dic59—42no—
509C2×Dic59—42no—
510C2×Dic59—42no—
511D236—22no—
512D236—24no—
513D236—22no—
514D236—42no—
515D236—42no—
516C4×D59—44no—
517C4×D59—44no—
518C4×D59—44no—
519C4×D59—44no—
520Dic118—22no—
521Dic118—24no—
522Dic118—22no—
523Dic118—42no—
524Dic118—42no—
525C8×C59—24no—
526C8×C59—24no—
527#60752—591nomaximal, Sylow
528C22×C59—21no—
529C22×C59—21no—
530C22×C59—21no—
531C22×C59—21no—
532C22×C59—21no—
533C22×C59—21no—
534C22×C59—21no—
535C22×C59—21no—
536C22×C59—21no—
537C22×C59—21no—
538C22×C59—21no—
539C22×C59—21no—
540C22×C59—21no—
541C22×C59—21no—
542C22×C59—21no—
543C22×C59—21no—
544C22×C59—21no—
545C22×C59—21no—
546C22×C59—44no—
547C22×C59—44no—
548C22×C59—44no—
549C22×C59—44no—
550C22×C59—44no—
551C22×C59—44no—
552C22×C59—44no—
553C22×C59#53412yes—
554C22×C59#57512yes—
555C22×C59#57512yes—
556C22×C59C23×D411yescharacteristic
557C2×D59—42no—
558C2×D59—42no—
559C2×D59—42no—
560C2×D59—42no—
561C2×D59—42no—
562C2×D59—42no—
563C2×D59—84no—
564C2×D59—84no—
565C4×C59—21no—
566C4×C59—21no—
567C4×C59—21no—
568C4×C59—21no—
569C4×C59—21no—
570C4×C59—21no—
571C4×C59#53412yes—
572C4×C59C2×H(5,𝔽2)12yes—
573Dic59—42no—
574Dic59—42no—
575Dic59—42no—
576Dic59—42no—
577Dic59—42no—
578Dic59—42no—
579C2×#525—591no—
580C2×#525—591no—
581#3197—594no—
582#3196—592no—
583#3194—592no—
584#3191—594no—
585#3190—592no—
586#3188—592no—
587#3095—591no—
588#3094—591no—
589#3093—592no—
590#3056—592no—
591#3055—592no—
592#3007—591no—
593#3006—591no—
594#3005—592no—
595C2×#407D5911yescharacteristic, complemented
596C2×C59—22no—
597C2×C59—22no—
598C2×C59—22no—
599C2×C59—41no—
600C2×C59—41no—
601C2×C59—41no—
602C2×C59—41no—
603C2×C59C2×#53411yescharacteristic
604C2×C59C2×#57511yescharacteristic
605C2×C59C2×#57511yescharacteristic
606D59—82no—
607D59—82no—
608C22×#41—591no—
609C22×#41—591no—
610C24×C4C2×D5911yescharacteristic
611C2×#137—592no—
612C2×AGL(1,ℤ/8)—592no—
613C22×M16C2×D5912yescomplemented
614#525—592no—
615#525—592no—
616#525—592no—
617#525—592no—
618#525—592no—
619#525—592no—
620#525—592no—
621#525—592no—
622#525—1181no—
623#525—1181no—
624#525—1181no—
625#525—1181no—
626#525—1181no—
627#525—1181no—
628#525—1181no—
629#525—1181no—
630C2×#123—1181no—
631C2×#123—1181no—
632C2×C22⋊Q8—591no—
633C2×C22⋊Q8—591no—
634C2×C22⋊Q8—591no—
635C2×C22⋊Q8—591no—
636C2×#121—591no—
637C2×#121—591no—
638C2×#121—591no—
639C2×#121—591no—
640C2×#120—1181no—
641C2×#120—1181no—
642C2×C4×D4—1181no—
643C2×C4×D4—1181no—
644C2×C4×D4—1181no—
645C2×C4×D4—1181no—
646C2×#117—591no—
647C2×#117—591no—
648#485—594no—
649#485—594no—
650#485—594no—
651#484—592no—
652#483—592no—
653#482—594no—
654#482—594no—
655#482—594no—
656#481—592no—
657#480—592no—
658#470—594no—
659#469—594no—
660#468—594no—
661#468—594no—
662#467—594no—
663#466—594no—
664#465—594no—
665#465—594no—
666#452—594no—
667#452—594no—
668#452—594no—
669#451—592no—
670#450—592no—
671#449—594no—
672#449—594no—
673#449—594no—
674#448—592no—
675#447—592no—
676#428—592no—
677#428—592no—
678#419—592no—
679#418—592no—
680#417—592no—
681#417—592no—
682#407C2×D5911yescharacteristic
683#407C2×D5911yescharacteristic
684#407C2×D5912yescomplemented
685#407C2×D5912yescomplemented
686#407C2×D5912yescomplemented
687C2×C22⋊C8C2×D5912yescomplemented
688C2×C22⋊C8C2×D5912yescomplemented
689C59#6075211yescharacteristic, complemented, Sylow
690C25D23611yescharacteristic
691C2×#41—592no—
692C2×#41—592no—
693C2×#41—592no—
694C2×#41—592no—
695C2×#41—1181no—
696C2×#41—1181no—
697C2×#41—1181no—
698C2×#41—1181no—
699C2×#41—2364no—
700C2×#41—2364no—
701C22×Q8—591no—
702C22×Q8—591no—
703C22×D4—591no—
704C22×D4—591no—
705C22×D4—1181no—
706C22×D4—1181no—
707C22×D4—1181no—
708C22×D4—1181no—
709C22×D4—1181no—
710C22×D4—1181no—
711C23×C4—44no—
712C23×C4—1181no—
713C23×C4—1181no—
714C23×C4D23611yescharacteristic
715C23×C4D23611yescharacteristic
716C23×C4D23611yescharacteristic
717C23×C4D23611yescharacteristic
718C23×C4D23611yescharacteristic
719C23×C4D23611yescharacteristic
720C23×C4D23611yescharacteristic
721C23×C4C22×D5911yescharacteristic
722C23×C4C22×D5911yescharacteristic
723C23×C4C22×D5911yescharacteristic
724C23×C4C22×D5911yescharacteristic
725C23×C4C22×D5911yescharacteristic
726C23×C4C22×D5911yescharacteristic
727C23×C4C22×D5911yescharacteristic
728#137—2364no—
729AGL(1,ℤ/8)—2364no—
730C2×Q16—594no—
731C2×SD16—594no—
732C2×SD16—594no—
733C2×D8—594no—
734C2×M16—44no—
735C2×M16C22×D5912yes—
736C2×M16C22×D5912yes—
737C2×M16C22×D5914yes—
738C22×C8C22×D5914yes—
739#123—1182no—
740#123—1182no—
741#123—1182no—
742#123—1182no—
743#123—1182no—
744#123—1182no—
745#123—1182no—
746#123—1182no—
747C22⋊Q8—592no—
748C22⋊Q8—592no—
749C22⋊Q8—592no—
750C22⋊Q8—592no—
751C22⋊Q8—592no—
752C22⋊Q8—592no—
753C22⋊Q8—592no—
754C22⋊Q8—592no—
755C22⋊Q8—1181no—
756C22⋊Q8—1181no—
757C22⋊Q8—1181no—
758C22⋊Q8—1181no—
759C22⋊Q8—1181no—
760C22⋊Q8—1181no—
761C22⋊Q8—1181no—
762C22⋊Q8—1181no—
763#121—592no—
764#121—592no—
765#121—592no—
766#121—592no—
767#121—592no—
768#121—592no—
769#121—592no—
770#121—592no—
771#121—1181no—
772#121—1181no—
773#121—1181no—
774#121—1181no—
775#121—1181no—
776#121—1181no—
777#121—1181no—
778#121—1181no—
779#120—1182no—
780#120—1182no—
781#120—1182no—
782#120—1182no—
783#120—1182no—
784#120—1182no—
785#120—1182no—
786#120—1182no—
787C4×D4—1182no—
788C4×D4—1182no—
789C4×D4—1182no—
790C4×D4—1182no—
791C4×D4—1182no—
792C4×D4—1182no—
793C4×D4—1182no—
794C4×D4—1182no—
795C4×D4—1182no—
796C4×D4—1182no—
797C4×D4—1182no—
798C4×D4—1182no—
799C4×D4—1182no—
800C4×D4—1182no—
801C4×D4—1182no—
802C4×D4—1182no—
803#117—592no—
804#117—592no—
805#117—592no—
806#117—592no—
807#117—1181no—
808#117—1181no—
809#117—1181no—
810#117—1181no—
811C2×C4⋊C4—591no—
812C2×C4⋊C4—591no—
813C2×C4⋊C4—591no—
814C2×C4⋊C4—591no—
815C2×C4⋊C4—1181no—
816C2×C4⋊C4—1181no—
817C2×C4⋊C4—1181no—
818C2×C4⋊C4—1181no—
819C2×C22⋊C4—1181no—
820C2×C22⋊C4—1181no—
821C2×C22⋊C4—1181no—
822C2×C22⋊C4—1181no—
823C2×C22⋊C4—1181no—
824C2×C22⋊C4—1181no—
825C2×C22⋊C4—1181no—
826C2×C22⋊C4—1181no—
827C2×C22⋊C4—1181no—
828C2×C22⋊C4—1181no—
829C2×C42—1181no—
830C2×C42—1181no—
831#107—594no—
832#107—594no—
833#106—594no—
834#106—594no—
835#103—594no—
836#103—594no—
837#103—594no—
838#103—594no—
839#102—594no—
840#102—594no—
841#102—594no—
842#102—594no—
843C22⋊C8C22×D5912yes—
844C22⋊C8C22×D5912yes—
845C22⋊C8C22×D5912yes—
846C22⋊C8C22×D5912yes—
847C22⋊C8C22×D5914yes—
848C22⋊C8C22×D5914yes—
849C24—42no—
850C24—42no—
851C24—42no—
852C24—1181no—
853C24—1181no—
854C24C2×D23611yescharacteristic
855C24C2×D23611yescharacteristic
856C24C2×D23611yescharacteristic
857C24C2×D23611yescharacteristic
858C24C2×D23611yescharacteristic
859C24C2×D23611yescharacteristic
860C24C2×D23611yescharacteristic
861#41—1184no—
862#41—1184no—
863#41—2362no—
864#41—2364no—
865#41—2364no—
866#41—2362no—
867#41—2364no—
868#41—2364no—
869#41—2364no—
870#41—2364no—
871C2×Q8—592no—
872C2×Q8—592no—
873C2×Q8—1181no—
874C2×Q8—1181no—
875C2×Q8—1184no—
876C2×Q8—2362no—
877C2×D4—592no—
878C2×D4—592no—
879C2×D4—1182no—
880C2×D4—1182no—
881C2×D4—1182no—
882C2×D4—1182no—
883C2×D4—1182no—
884C2×D4—1182no—
885C2×D4—1182no—
886C2×D4—1182no—
887C2×D4—1182no—
888C2×D4—1182no—
889C2×D4—1182no—
890C2×D4—1182no—
891C2×D4—1181no—
892C2×D4—1181no—
893C2×D4—1184no—
894C2×D4—2362no—
895C2×D4—2364no—
896C2×D4—2364no—
897C2×D4—2364no—
898C2×D4—2364no—
899C2×D4—2364no—
900C2×D4—2364no—
901C22×C4—24no—
902C22×C4—24no—
903C22×C4—24no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—1181no—
916C22×C4—1181no—
917C22×C4—1181no—
918C22×C4—1181no—
919C22×C4—1181no—
920C22×C4—1181no—
921C22×C4—1182no—
922C22×C4—1182no—
923C22×C4—1182no—
924C22×C4—1182no—
925C22×C4—2364no—
926C22×C4—2364no—
927C22×C4C2×D23611yescharacteristic
928C22×C4C2×D23611yescharacteristic
929C22×C4C2×D23611yescharacteristic
930C22×C4C2×D23611yescharacteristic
931C22×C4C2×D23611yescharacteristic
932C22×C4C2×D23611yescharacteristic
933C22×C4C2×D23611yescharacteristic
934C22×C4C2×D23611yescharacteristic
935C22×C4C2×D23611yescharacteristic
936C22×C4C2×D23611yescharacteristic
937C22×C4C2×D23611yescharacteristic
938C22×C4C2×D23611yescharacteristic
939C22×C4C2×D23611yescharacteristic
940C22×C4C2×D23611yescharacteristic
941C22×C4C2×D23611yescharacteristic
942C22×C4C2×D23611yescharacteristic
943C22×C4C2×D23611yescharacteristic
944C22×C4C2×D23611yescharacteristic
945C22×C4C2×D23611yescharacteristic
946C22×C4C2×D23611yescharacteristic
947C22×C4C2×D23611yescharacteristic
948C22×C4C23×D5911yescharacteristic
949C22×C4C23×D5911yescharacteristic
950C22×C4C23×D5911yescharacteristic
951C22×C4C23×D5911yescharacteristic
952C22×C4C23×D5911yescharacteristic
953C22×C4C23×D5911yescharacteristic
954C22×C4C23×D5911yescharacteristic
955Q16—2364no—
956SD16—2364no—
957SD16—2364no—
958D8—2364no—
959M16—24no—
960M16—24no—
961M16—44no—
962C2×C8—44no—
963C2×C8C23×D5914yes—
964C2×C8C23×D5914yes—
965C4⋊C4—592no—
966C4⋊C4—592no—
967C4⋊C4—592no—
968C4⋊C4—592no—
969C4⋊C4—1181no—
970C4⋊C4—1181no—
971C4⋊C4—1181no—
972C4⋊C4—1181no—
973C4⋊C4—1182no—
974C4⋊C4—1182no—
975C4⋊C4—1182no—
976C4⋊C4—1182no—
977C4⋊C4—1182no—
978C4⋊C4—1182no—
979C4⋊C4—1182no—
980C4⋊C4—1182no—
981C22⋊C4—1182no—
982C22⋊C4—1182no—
983C22⋊C4—1182no—
984C22⋊C4—1182no—
985C22⋊C4—1182no—
986C22⋊C4—1182no—
987C22⋊C4—1182no—
988C22⋊C4—1182no—
989C22⋊C4—1182no—
990C22⋊C4—1182no—
991C22⋊C4—1182no—
992C22⋊C4—1182no—
993C22⋊C4—1182no—
994C22⋊C4—1182no—
995C22⋊C4—1182no—
996C22⋊C4—1182no—
997C22⋊C4—1182no—
998C22⋊C4—1182no—
999C22⋊C4—1182no—
1000C22⋊C4—1182no—
1001C42—1182no—
1002C42—1182no—
1003C42—1182no—
1004C42—1182no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—416no—
1027C23—1182no—
1028C23—1182no—
1029C23—2362no—
1030C23—2362no—
1031C23—2362no—
1032C23—2362no—
1033C23—2362no—
1034C23—2362no—
1035C23C22×D23611yescharacteristic
1036C23C22×D23611yescharacteristic
1037C23C22×D23611yescharacteristic
1038C23C22×D23611yescharacteristic
1039C23C22×D23611yescharacteristic
1040C23C22×D23611yescharacteristic
1041C23C22×D23611yescharacteristic
1042Q8—1182no—
1043Q8—1184no—
1044Q8—1182no—
1045Q8—2362no—
1046Q8—2362no—
1047D4—1182no—
1048D4—1184no—
1049D4—1182no—
1050D4—2362no—
1051D4—2364no—
1052D4—2364no—
1053D4—2364no—
1054D4—2364no—
1055D4—2364no—
1056D4—2364no—
1057D4—2364no—
1058D4—2364no—
1059D4—2364no—
1060D4—2364no—
1061D4—2364no—
1062D4—2364no—
1063D4—2362no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—1182no—
1092C2×C4—1182no—
1093C2×C4—1182no—
1094C2×C4—1182no—
1095C2×C4—1182no—
1096C2×C4—1182no—
1097C2×C4—2364no—
1098C2×C4—2364no—
1099C2×C4—2364no—
1100C2×C4—2362no—
1101C2×C4—2362no—
1102C2×C4—2362no—
1103C2×C4—2362no—
1104C2×C4—2362no—
1105C2×C4—2362no—
1106C2×C4—2364no—
1107C2×C4C22×D23611yescharacteristic
1108C2×C4C22×D23611yescharacteristic
1109C2×C4C22×D23611yescharacteristic
1110C2×C4C22×D23611yescharacteristic
1111C2×C4C22×D23611yescharacteristic
1112C2×C4C22×D23611yescharacteristic
1113C2×C4C22×D23611yescharacteristic
1114C2×C4#1427377214yes—
1115C2×C4C24×D5911yescharacteristic
1116C8—24no—
1117C8—24no—
1118C22—21no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—21no—
1124C22—21no—
1125C22—21no—
1126C22—21no—
1127C22—21no—
1128C22—21no—
1129C22—21no—
1130C22—21no—
1131C22—21no—
1132C22—21no—
1133C22—21no—
1134C22—21no—
1135C22—21no—
1136C22—44no—
1137C22—44no—
1138C22—44no—
1139C22—44no—
1140C22—44no—
1141C22—44no—
1142C22—44no—
1143C22—4724no—
1144C22—4724no—
1145C22—2362no—
1146C22—2362no—
1147C22—2362no—
1148C22—2362no—
1149C22—2362no—
1150C22—2362no—
1151C22#1683796412yes—
1152C22#1683820212yes—
1153C22#1683820212yes—
1154C22C23×D23611yescharacteristic
1155C4—21no—
1156C4—21no—
1157C4—21no—
1158C4—21no—
1159C4—21no—
1160C4—21no—
1161C4—2362no—
1162C4—2362no—
1163C4—2362no—
1164C4—2362no—
1165C4—2362no—
1166C4—2362no—
1167C4#1683796412yes—
1168C4C2×#1427377212yes—
1169C2—22no—
1170C2—22no—
1171C2—22no—
1172C2—41no—
1173C2—41no—
1174C2—41no—
1175C2—41no—
1176C2—4722no—
1177C2—4722no—
1178C2C2×#1683796411yescharacteristic
1179C2C2×#1683820211yescharacteristic
1180C2C2×#1683820211yescharacteristic
subgroupG/H
centerC22C23×D236
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#407C2
socleC22×C59C23×D4
hypercenterC2×#407D59
hypocenterC59#60752
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. C2×#16837913C2semidirect
3. #21434938C2semidirect
4. #21434928C2semidirect
5. #21434912C2semidirect
6. #21434889C2semidirect
7. #21434879C2semidirect
8. #21434863C2semidirect
9. #21434045C2semidirect
10. #21434037C2semidirect
11. #21434029C2semidirect
12. #21433726C2semidirect
13. #21433715C2semidirect
14. #21433358C2semidirect
15. #21433350C2semidirect
16. #21433341C2semidirect
17. C2×C59×#407C2semidirect
19. C22×#11745685C22semidirect
20. C2×#14273760C22semidirect
21. C2×#14273755C22semidirect
34. #16837913C22semidirect
35. #16837913C22semidirect
36. #16837913C22semidirect
37. #16837913C22semidirect
41. C2×#14273706C22semidirect
42. C2×#14273706C22semidirect
43. C2×#14273706C22semidirect
45. C2×#14273701C22semidirect
46. C2×#14273701C22semidirect
47. C2×#14273701C22semidirect
55. C2×#14273686C22semidirect
56. #16837744C22semidirect
57. #16837744C22semidirect
58. #16837744C22semidirect
59. #16837738C22semidirect
60. #16837733C22semidirect
61. #16837727C22semidirect
62. #16837727C22semidirect
63. #16837727C22semidirect
64. #16837721C22semidirect
65. #16837716C22semidirect
66. #16837660C22semidirect
67. #16837655C22semidirect
68. #16837648C22semidirect
69. #16837648C22semidirect
70. #16837643C22semidirect
71. #16837638C22semidirect
72. #16837631C22semidirect
73. #16837631C22semidirect
74. #16837566C22semidirect
75. #16837566C22semidirect
76. #16837566C22semidirect
77. #16837560C22semidirect
78. #16837555C22semidirect
79. #16837549C22semidirect
80. #16837549C22semidirect
81. #16837549C22semidirect
82. #16837543C22semidirect
83. #16837538C22semidirect
84. #16837444C22semidirect
85. #16837444C22semidirect
86. #16837412C22semidirect
87. #16837408C22semidirect
88. #16837404C22semidirect
89. #16837404C22semidirect
91. C22×M16×C59C22semidirect
94. C59×#407C22semidirect
95. C59×#407C22semidirect
96. C59×#407C22semidirect
97. C2×C22⋊C8×C59C22semidirect
98. C2×C22⋊C8×C59C22semidirect
123. C2×Dic236C23semidirect
124. C2×#11745660C23semidirect
125. C2×#11745660C23semidirect
126. C2×D472C23semidirect
219. #14273661C23semidirect
220. #14273661C23semidirect
221. #14273659C23semidirect
222. #14273659C23semidirect
223. #14273652C23semidirect
224. #14273652C23semidirect
225. #14273652C23semidirect
226. #14273652C23semidirect
227. #14273649C23semidirect
228. #14273649C23semidirect
229. #14273649C23semidirect
230. #14273649C23semidirect
595. C2×#407D59semidirect
613. C22×M16C2×D59semidirect
684. #407C2×D59semidirect
685. #407C2×D59semidirect
686. #407C2×D59semidirect
687. C2×C22⋊C8C2×D59semidirect
688. C2×C22⋊C8C2×D59semidirect
689. C59#60752semidirect

Maximal subgroups

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

subgroupindex
C2×#168379132
#214349382
#214349282
#214349122
#214348892
#214348792
#214348632
#214340452
#214340372
#214340292
#214337262
#214337152
#214333582
#214333502
#214333412
C2×C59×#4072
#6075259