Finite Group Databasebeta

← #29456111

Subgroups — #29456111

Order 15104.

2628 conjugacy classes of subgroups.

The subgroup lattice has 1084 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838200C211yesmaximal, characteristic, complemented
2C2×#16838200C211yesmaximal, characteristic, complemented
3C2×#16838169C211yesmaximal, characteristic, complemented
4#21433835C214yesmaximal, complemented
5#21433830C214yesmaximal, complemented
6#21433826C214yesmaximal, complemented
7#21433821C214yesmaximal, complemented
8#21433813C218yesmaximal, complemented
9C2×#16837450C211yesmaximal, characteristic, complemented
10C2×#16837386C211yesmaximal, characteristic, complemented
11C2×#16837384C211yesmaximal, characteristic, complemented
12C2×C59×#575C211yesmaximal, characteristic, complemented
13C22×#11745685C2211yescharacteristic
14#16838200—22no—
15#16838200—22no—
16#16838200—22no—
17#16838200—22no—
18#16838200—22no—
19#16838200—22no—
20#16838200C2214yes—
21#16838200C2214yescomplemented
22C2×#14273758—21no—
23C2×#14273758C2212yescomplemented
24C2×#14273757C2212yescomplemented
25C2×#14273757C2212yescomplemented
26C2×#14273753—21no—
27C2×#14273753C2212yescomplemented
28C2×#14273752C2212yescomplemented
29C2×#14273752C2212yescomplemented
30C2×#14273747—22no—
31C2×#14273747C2214yescomplemented
32#16838169—22no—
33#16838169—22no—
34#16838169C2214yescomplemented
35#16838169C2214yescomplemented
36C2×#14273734—22no—
37C2×#14273734C2214yescomplemented
38C22×#11745664—22no—
39C22×#11745664C2211yescharacteristic
40C22×#11745664C2211yescharacteristic
41C22×#11745664C2211yescharacteristic
42#16837675C22116yescomplemented
43#16837670C22116yescomplemented
44#16837667C22116yescomplemented
45#16837663C22116yescomplemented
46#16837450C2214yescomplemented
47#16837450C2214yescomplemented
48C2×#14273662C2214yescomplemented
49#16837386C2214yescomplemented
50#16837386C2214yescomplemented
51#16837384C2214yescomplemented
52#16837384C2214yescomplemented
53C2×#14273646C2212yescomplemented
54C2×#14273645C2212yescomplemented
55C2×#14273644C2212yescomplemented
56C2×#14273643C2212yescomplemented
57C22×#41×C59C2211yescharacteristic
58C22×#41×C59C2211yescharacteristic
59C59×#575—22no—
60C59×#575—22no—
61C59×#575C2214yes—
62C59×#575C2214yescomplemented
63C2×#137×C59—21no—
64C2×#137×C59C2212yescomplemented
65C2×AGL(1,ℤ/8)×C59—21no—
66C2×AGL(1,ℤ/8)×C59C2212yescomplemented
67C2×#135×C59—22no—
68C22×M16×C59C2211yescharacteristic
69C2×#11745685—21no—
70C2×#11745685—21no—
71C2×#11745685—21no—
72C2×#11745685—21no—
73C2×#11745685—21no—
74C2×#11745685—21no—
75C2×#11745685—21no—
76C2×#11745685—21no—
77C2×#11745685—21no—
78C2×#11745685—21no—
79C2×#11745685C2312yes—
80C2×#11745685C2312yes—
81C22×Dic118C2311yescharacteristic
82C22×D236C2311yescharacteristic
83C22×C22⋊D59—21no—
84C22×C4×D59—21no—
85#14273758—24no—
86#14273758—24no—
87#14273758—24no—
88#14273758—24no—
89#14273757—24no—
90#14273757—24no—
91#14273757—24no—
92#14273757C2318yes—
93#14273753—24no—
94#14273753—24no—
95#14273753—24no—
96#14273753—24no—
97#14273752—24no—
98#14273752—24no—
99#14273752—24no—
100#14273752C2318yes—
101#14273747—28no—
102#14273747—28no—
103#14273747—28no—
104#14273747—28no—
105C2×#11745672—22no—
106C2×#11745672C2314yescomplemented
107C2×#11745670—22no—
108C2×#11745670C2314yescomplemented
109C2×#11745671—22no—
110C2×#11745671C2314yescomplemented
111C2×#11745669—22no—
112C2×#11745669C2314yescomplemented
113#14273734—28no—
114#14273734—28no—
115#14273734—28no—
116#14273734C23116yes—
117C2×#11745664—21no—
118C2×#11745664—21no—
119C2×#11745664—21no—
120C2×#11745664—21no—
121C2×#11745664—21no—
122C2×#11745664—21no—
123C2×#11745664—28no—
124C2×#11745664—28no—
125C2×#11745664—24no—
126C2×#11745664D412yes—
127C2×#11745664D412yes—
128C2×#11745664D412yes—
129C2×#11745664D412yes—
130C2×#11745664C2312yes—
131C2×#11745664C2312yes—
132C2×#11745664C2312yes—
133C2×#11745664C2312yes—
134C2×#11745664C2312yes—
135C2×#11745664C2312yes—
136C2×#11745664C2312yes—
137C2×#11745664C2312yes—
138C22×C59⋊C8—21no—
139C22×C59⋊C8—21no—
140C22×C59⋊C8—24no—
141C22×C59⋊C8C2312yes—
142#14273662C23116yescomplemented
143#14273646C2318yescomplemented
144#14273645C2318yescomplemented
145#14273644C2318yescomplemented
146#14273643C2318yescomplemented
147C2×#41×C59—21no—
148C2×#41×C59—21no—
149C2×#41×C59—21no—
150C2×#41×C59—21no—
151C2×#41×C59—21no—
152C2×#41×C59—21no—
153C2×#41×C59—21no—
154C2×#41×C59—21no—
155C2×#41×C59—21no—
156C2×#41×C59—21no—
157C2×#41×C59—21no—
158C2×#41×C59—21no—
159C2×#41×C59—21no—
160C2×#41×C59—21no—
161C2×#41×C59—21no—
162C2×#41×C59—21no—
163C2×#41×C59D412yes—
164C2×#41×C59D412yes—
165C2×#41×C59D412yes—
166C2×#41×C59C2312yes—
167C2×#41×C59C2312yes—
168C2×#41×C59C2312yes—
169C2×#41×C59C2312yes—
170C2×#41×C59C2312yes—
171C22×Q8×C59D411yescharacteristic
172C22×Q8×C59C2311yescharacteristic
173C22×D4×C59—21no—
174C22×D4×C59—21no—
175C22×D4×C59D411yescharacteristic
176C22×D4×C59C2311yescharacteristic
177C23×C4×C59—21no—
178C23×C4×C59—21no—
179C23×C4×C59C2311yescharacteristic
180#137×C59—24no—
181#137×C59—24no—
182#137×C59—24no—
183#137×C59C2318yes—
184AGL(1,ℤ/8)×C59—24no—
185AGL(1,ℤ/8)×C59—24no—
186AGL(1,ℤ/8)×C59—24no—
187AGL(1,ℤ/8)×C59C2318yes—
188#135×C59—28no—
189#135×C59—28no—
190C2×Q16×C59—22no—
191C2×SD16×C59—22no—
192C2×SD16×C59—22no—
193C2×D8×C59—22no—
194C2×M16×C59—21no—
195C2×M16×C59—21no—
196C2×M16×C59—21no—
197C2×M16×C59C2312yes—
198C2×M16×C59C2312yes—
199C2×M16×C59C2312yes—
200C22×C8×C59—21no—
201C24×C59—21no—
202C24×C59—21no—
203C24×C59#4111yescharacteristic
204C23×D59—21no—
205#41×C59—22no—
206#41×C59—22no—
207#41×C59—22no—
208#41×C59—22no—
209#41×C59—22no—
210#41×C59—22no—
211#41×C59—22no—
212#41×C59—22no—
213#41×C59—22no—
214#41×C59—22no—
215#41×C59—22no—
216#41×C59—22no—
217#41×C59—22no—
218#41×C59—22no—
219#41×C59—22no—
220#41×C59—22no—
221#41×C59—22no—
222#41×C59—22no—
223#41×C59—22no—
224#41×C59—22no—
225#41×C59—41no—
226#41×C59—41no—
227#41×C59—41no—
228#41×C59—41no—
229#41×C59—41no—
230#41×C59—41no—
231#41×C59—41no—
232#41×C59—41no—
233#41×C59C2×D414yes—
234#41×C59C2×D414yes—
235#41×C59C2×D414yes—
236#41×C59C2414yes—
237C2×Q8×C59—21no—
238C2×Q8×C59—21no—
239C2×Q8×C59—21no—
240C2×Q8×C59—21no—
241C2×Q8×C59—21no—
242C2×Q8×C59—21no—
243C2×Q8×C59—21no—
244C2×Q8×C59—21no—
245C2×Q8×C59C2×D412yes—
246C2×Q8×C59C2×D412yes—
247C2×Q8×C59C2×D412yes—
248C2×Q8×C59C2412yes—
249C2×D4×C59—22no—
250C2×D4×C59—22no—
251C2×D4×C59—22no—
252C2×D4×C59—22no—
253C2×D4×C59—22no—
254C2×D4×C59—22no—
255C2×D4×C59—22no—
256C2×D4×C59—22no—
257C2×D4×C59—21no—
258C2×D4×C59—21no—
259C2×D4×C59—21no—
260C2×D4×C59—21no—
261C2×D4×C59—21no—
262C2×D4×C59—21no—
263C2×D4×C59—21no—
264C2×D4×C59—21no—
265C2×D4×C59—41no—
266C2×D4×C59—41no—
267C2×D4×C59—41no—
268C2×D4×C59—41no—
269C2×D4×C59C2×D412yes—
270C2×D4×C59C2×D412yes—
271C2×D4×C59C2×D412yes—
272C2×D4×C59C2412yes—
273C22×C4×C59—21no—
274C22×C4×C59—22no—
275C22×C4×C59—22no—
276C22×C4×C59—22no—
277C22×C4×C59—22no—
278C22×C4×C59—22no—
279C22×C4×C59—22no—
280C22×C4×C59—21no—
281C22×C4×C59—22no—
282C22×C4×C59—22no—
283C22×C4×C59—41no—
284C22×C4×C59—41no—
285C22×C4×C59—41no—
286C22×C4×C59—41no—
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×C59#4111yescharacteristic
296C22×C4×C59#4111yescharacteristic
297C22×C4×C59#4111yescharacteristic
298C22×C4×C59C2411yescharacteristic
299C22×C4×C59C2411yescharacteristic
300C22×C4×C59C2411yescharacteristic
301C2×C22⋊D59—22no—
302C2×C22⋊D59—22no—
303C2×C22⋊D59—41no—
304C2×C22⋊D59—41no—
305C2×C22⋊D59—41no—
306C2×C22⋊D59—41no—
307C22×Dic59—21no—
308#11745685—22no—
309#11745685—22no—
310#11745685—22no—
311#11745685—22no—
312#11745685—22no—
313#11745685—22no—
314#11745685—22no—
315#11745685—22no—
316#11745685—41no—
317#11745685—41no—
318#11745685—41no—
319#11745685—41no—
320#11745685—41no—
321#11745685—41no—
322#11745685—41no—
323#11745685—41no—
324C2×D236—21no—
325C2×D236—21no—
326C2×D236—21no—
327C2×D236—21no—
328C2×D236—21no—
329C2×D236C2412yes—
330C2×C4×D59—22no—
331C2×C4×D59—22no—
332C2×C4×D59—41no—
333C2×C4×D59—41no—
334C2×C4×D59—41no—
335C2×C4×D59—41no—
336C2×Dic118—21no—
337C2×Dic118—21no—
338C2×Dic118—21no—
339C2×Dic118—21no—
340C2×Dic118—21no—
341C2×Dic118C2412yes—
342Q16×C59—28no—
343SD16×C59—28no—
344SD16×C59—28no—
345D8×C59—28no—
346M16×C59—22no—
347M16×C59—22no—
348M16×C59—22no—
349M16×C59C2414yes—
350C2×C8×C59—22no—
351C2×C8×C59—22no—
352C2×C8×C59—22no—
353#11745672—28no—
354#11745672—28no—
355#11745671—28no—
356#11745671—28no—
357#11745670—28no—
358#11745670—28no—
359#11745669—28no—
360#11745669—28no—
361#11745664—22no—
362#11745664—22no—
363#11745664—22no—
364#11745664—22no—
365#11745664—22no—
366#11745664—22no—
367#11745664—216no—
368#11745664C2×D414yes—
369#11745664C2×D414yes—
370#11745664C2×D414yes—
371#11745664C2×D414yes—
372#11745664C2414yes—
373#11745664C2414yes—
374C2×C59⋊C8—22no—
375C2×C59⋊C8—22no—
376C2×C59⋊C8—22no—
377C2×C59⋊C8—22no—
378C2×C59⋊C8—22no—
379C2×C59⋊C8—22no—
380C2×C59⋊C8—216no—
381C2×C59⋊C8C2×D414yes—
382C2×C59⋊C8C2×D414yes—
383C2×C59⋊C8C2414yes—
384C23×C59—22no—
385C23×C59—22no—
386C23×C59—22no—
387C23×C59—22no—
388C23×C59—41no—
389C23×C59—41no—
390C23×C59—81no—
391C23×C59—82no—
392C23×C59—82no—
393C23×C59#12111yescharacteristic
394C23×C59#12111yescharacteristic
395C23×C59#12111yescharacteristic
396C23×C59#12111yescharacteristic
397C23×C59C2×#4111yescharacteristic
398C23×C59C2×#4111yescharacteristic
399C23×C59C2×#4111yescharacteristic
400C22×D59—22no—
401C22×D59—41no—
402C22×D59—41no—
403C22×D59—82no—
404Q8×C59—22no—
405Q8×C59—22no—
406Q8×C59—22no—
407Q8×C59—22no—
408Q8×C59—22no—
409Q8×C59—41no—
410Q8×C59—41no—
411Q8×C59C22×D414yes—
412D4×C59—24no—
413D4×C59—24no—
414D4×C59—24no—
415D4×C59—24no—
416D4×C59—22no—
417D4×C59—22no—
418D4×C59—22no—
419D4×C59—22no—
420D4×C59—22no—
421D4×C59—42no—
422D4×C59—42no—
423D4×C59—42no—
424D4×C59—42no—
425D4×C59—41no—
426D4×C59—41no—
427D4×C59C22×D414yes—
428C2×C4×C59—22no—
429C2×C4×C59—22no—
430C2×C4×C59—22no—
431C2×C4×C59—24no—
432C2×C4×C59—24no—
433C2×C4×C59—24no—
434C2×C4×C59—24no—
435C2×C4×C59—22no—
436C2×C4×C59—41no—
437C2×C4×C59—41no—
438C2×C4×C59—42no—
439C2×C4×C59—42no—
440C2×C4×C59—42no—
441C2×C4×C59—42no—
442C2×C4×C59#12111yescharacteristic
443C2×C4×C59#12111yescharacteristic
444C2×C4×C59#12111yescharacteristic
445C2×C4×C59#12111yescharacteristic
446C2×C4×C59#12111yescharacteristic
447C2×C4×C59#12111yescharacteristic
448C2×C4×C59#12111yescharacteristic
449C2×C4×C59#12111yescharacteristic
450C2×C4×C59#12111yescharacteristic
451C2×C4×C59#12111yescharacteristic
452C2×C4×C59#12111yescharacteristic
453C2×C4×C59#12111yescharacteristic
454C2×C4×C59C22×D411yescharacteristic
455C2×C4×C59C22×D411yescharacteristic
456C2×C4×C59C22×D411yescharacteristic
457C2×C4×C59C22×D411yescharacteristic
458C2×C4×C59C22×D411yescharacteristic
459C2×C4×C59C22×D411yescharacteristic
460C2×C4×C59C22×D411yescharacteristic
461C2×C4×C59C22×D411yescharacteristic
462C2×C4×C59C22×D411yescharacteristic
463C2×C4×C59C22×D411yescharacteristic
464C2×C4×C59C22×D411yescharacteristic
465C2×C4×C59C22×D411yescharacteristic
466C2×C4×C59C2×#4111yescharacteristic
467C2×C4×C59C2×#4111yescharacteristic
468C2×C4×C59C2×#4111yescharacteristic
469C2×C4×C59C2511yescharacteristic
470C22⋊D59—42no—
471C22⋊D59—42no—
472C22⋊D59—42no—
473C22⋊D59—42no—
474C2×Dic59—22no—
475C2×Dic59—41no—
476C2×Dic59—41no—
477D236—22no—
478D236—22no—
479D236—41no—
480D236—41no—
481C4×D59—42no—
482C4×D59—42no—
483C4×D59—42no—
484C4×D59—42no—
485Dic118—22no—
486Dic118—22no—
487Dic118—41no—
488Dic118—41no—
489C8×C59—24no—
490C59⋊C8—24no—
491C59⋊C8—24no—
492C59⋊C8C22×D418yes—
493#60469—591nomaximal, Sylow
494C22×C59—24no—
495C22×C59—41no—
496C22×C59—41no—
497C22×C59—41no—
498C22×C59—41no—
499C22×C59—41no—
500C22×C59—41no—
501C22×C59—41no—
502C22×C59—44no—
503C22×C59—42no—
504C22×C59—82no—
505C22×C59—82no—
506C22×C59—82no—
507C22×C59—82no—
508C22×C59—82no—
509C22×C59C2×#12111yescharacteristic
510C22×C59C2×#12111yescharacteristic
511C22×C59C2×#12111yescharacteristic
512C22×C59C2×#12111yescharacteristic
513C22×C59C2×#12111yescharacteristic
514C22×C59C2×#12111yescharacteristic
515C22×C59C22×#4111yescharacteristic
516C2×D59—42no—
517C2×D59—82no—
518C2×D59—82no—
519C2×D59—82no—
520C4×C59—24no—
521C4×C59—42no—
522C4×C59C2×#12111yescharacteristic
523C4×C59C2×#12111yescharacteristic
524C4×C59C2×#12111yescharacteristic
525C4×C59C2×#12111yescharacteristic
526C4×C59C2×#12111yescharacteristic
527C4×C59C2×#12111yescharacteristic
528C4×C59C23×D411yescharacteristic
529C4×C59C23×D411yescharacteristic
530Dic59—42no—
531C2×#575—591no—
532C2×#575—591no—
533C2×#575D5911yescharacteristic, complemented
534C2×#568—591no—
535#3069—594no—
536#3069—594no—
537#3068—594no—
538#3068—594no—
539#3067—598no—
540C2×#430—591no—
541C2×#413—591no—
542C2×#413—591no—
543C2×C59—21no—
544C2×C59—21no—
545C2×C59—21no—
546C2×C59—21no—
547C2×C59—21no—
548C2×C59—21no—
549C2×C59—21no—
550C2×C59—44no—
551C2×C59—82no—
552C2×C59C22×#12111yescharacteristic
553D59—82no—
554C22×#41—591no—
555C22×#41C2×D5911yescharacteristic
556C22×#41C2×D5911yescharacteristic
557#575—22no—
558#575—22no—
559#575—594no—
560#575—594no—
561#575—1182no—
562#575—1182no—
563#575—1182no—
564#575—1182no—
565#575—1182no—
566#575—1182no—
567#575C2×D5914yes—
568#575C2×D5914yescomplemented
569C2×#137—21no—
570C2×#137—592no—
571C2×#137—592no—
572C2×#137—592no—
573C2×#137—1181no—
574C2×#137C2×D5912yescomplemented
575C2×AGL(1,ℤ/8)—21no—
576C2×AGL(1,ℤ/8)—592no—
577C2×AGL(1,ℤ/8)—592no—
578C2×AGL(1,ℤ/8)—592no—
579C2×AGL(1,ℤ/8)—1181no—
580C2×AGL(1,ℤ/8)C2×D5912yescomplemented
581C2×#135—22no—
582C2×#135—594no—
583C2×#135—1182no—
584#568—594no—
585#568—594no—
586#568—1182no—
587#568—1182no—
588C2×#131—594no—
589C2×#131—1182no—
590C22×M16—591no—
591C22×M16—591no—
592C22×M16—591no—
593C22×M16—1182no—
594C22×M16C2×D5911yescharacteristic
595#473—5916no—
596#472—5916no—
597#471—5916no—
598#471—5916no—
599#430—594no—
600#430—594no—
601C2×#108—594no—
602#413—594no—
603#413—594no—
604#413—594no—
605#413—594no—
606C2×#101—592no—
607C2×#101—592no—
608C2×#100—592no—
609C2×#100—592no—
610C59#6046911yescharacteristic, complemented, Sylow
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—21no—
614C2×#41—21no—
615C2×#41—21no—
616C2×#41—21no—
617C2×#41—21no—
618C2×#41—21no—
619C2×#41—21no—
620C2×#41—21no—
621C2×#41—21no—
622C2×#41—21no—
623C2×#41—21no—
624C2×#41—21no—
625C2×#41—21no—
626C2×#41—21no—
627C2×#41—592no—
628C2×#41—592no—
629C2×#41—1181no—
630C2×#41—1181no—
631C2×#41—1181no—
632C2×#41—1181no—
633C2×#41—1181no—
634C2×#41—1181no—
635C2×#41—1181no—
636C2×#41—1181no—
637C2×#41—1181no—
638C2×#41—1181no—
639C2×#41C22⋊D5912yes—
640C2×#41C22⋊D5912yes—
641C2×#41C22⋊D5912yes—
642C2×#41C22×D5912yes—
643C2×#41C22×D5912yes—
644C2×#41C22×D5912yes—
645C2×#41C22×D5912yes—
646C2×#41C22×D5912yes—
647C22×Q8—591no—
648C22×Q8C22⋊D5911yescharacteristic
649C22×Q8C22×D5911yescharacteristic
650C22×D4—21no—
651C22×D4—21no—
652C22×D4—591no—
653C22×D4—1181no—
654C22×D4C22⋊D5911yescharacteristic
655C22×D4C22×D5911yescharacteristic
656C23×C4—21no—
657C23×C4—21no—
658C23×C4—1181no—
659C23×C4C22×D5911yescharacteristic
660#137—24no—
661#137—24no—
662#137—24no—
663#137—598no—
664#137—1184no—
665#137—1184no—
666#137—1184no—
667#137—1184no—
668#137—1184no—
669#137—1184no—
670#137—1184no—
671#137C22×D5918yes—
672AGL(1,ℤ/8)—24no—
673AGL(1,ℤ/8)—24no—
674AGL(1,ℤ/8)—24no—
675AGL(1,ℤ/8)—598no—
676AGL(1,ℤ/8)—1184no—
677AGL(1,ℤ/8)—1184no—
678AGL(1,ℤ/8)—1184no—
679AGL(1,ℤ/8)—1184no—
680AGL(1,ℤ/8)—1184no—
681AGL(1,ℤ/8)—1184no—
682AGL(1,ℤ/8)—1184no—
683AGL(1,ℤ/8)C22×D5918yes—
684#135—28no—
685#135—28no—
686#135—1188no—
687#135—1188no—
688#135—1188no—
689#135—1188no—
690C2×Q16—22no—
691C2×Q16—594no—
692C2×Q16—1182no—
693C2×SD16—22no—
694C2×SD16—22no—
695C2×SD16—594no—
696C2×SD16—594no—
697C2×SD16—1182no—
698C2×SD16—1182no—
699C2×D8—22no—
700C2×D8—594no—
701C2×D8—1182no—
702#131—5916no—
703#131—1188no—
704#131—1188no—
705#131—1188no—
706C2×M16—21no—
707C2×M16—21no—
708C2×M16—21no—
709C2×M16—592no—
710C2×M16—592no—
711C2×M16—592no—
712C2×M16—592no—
713C2×M16—592no—
714C2×M16—592no—
715C2×M16—592no—
716C2×M16—592no—
717C2×M16—592no—
718C2×M16—592no—
719C2×M16—592no—
720C2×M16—592no—
721C2×M16—1184no—
722C2×M16—1188no—
723C2×M16—1188no—
724C2×M16—1181no—
725C2×M16—1181no—
726C2×M16—1181no—
727C2×M16—1181no—
728C2×M16—1181no—
729C2×M16—1181no—
730C2×M16C22×D5912yes—
731C2×M16C22×D5912yes—
732C2×M16C22×D5912yes—
733C22×C8—21no—
734C22×C8—592no—
735C22×C8—1184no—
736C22×C8—1181no—
737C22×C8—1181no—
738#108—5916no—
739#101—598no—
740#101—598no—
741#100—598no—
742#100—598no—
743C24—21no—
744C24—21no—
745C24—1181no—
746C24#1174568711yescharacteristic
747#41—22no—
748#41—22no—
749#41—22no—
750#41—22no—
751#41—22no—
752#41—22no—
753#41—22no—
754#41—22no—
755#41—22no—
756#41—22no—
757#41—22no—
758#41—22no—
759#41—22no—
760#41—22no—
761#41—22no—
762#41—22no—
763#41—22no—
764#41—22no—
765#41—22no—
766#41—22no—
767#41—41no—
768#41—41no—
769#41—41no—
770#41—41no—
771#41—41no—
772#41—41no—
773#41—41no—
774#41—41no—
775#41—1182no—
776#41—1182no—
777#41—1182no—
778#41—1182no—
779#41—1182no—
780#41—1182no—
781#41—1182no—
782#41—1182no—
783#41—2361no—
784#41—2361no—
785#41—2361no—
786#41—2361no—
787#41—2361no—
788#41—2361no—
789#41—2361no—
790#41—2361no—
791#41C2×C22⋊D5914yes—
792#41C2×C22⋊D5914yes—
793#41C2×C22⋊D5914yes—
794#41C23×D5914yes—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—21no—
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—592no—
804C2×Q8—1181no—
805C2×Q8—1181no—
806C2×Q8—1181no—
807C2×Q8—1181no—
808C2×Q8—1181no—
809C2×Q8C2×C22⋊D5912yes—
810C2×Q8C2×C22⋊D5912yes—
811C2×Q8C2×C22⋊D5912yes—
812C2×Q8C23×D5912yes—
813C2×D4—22no—
814C2×D4—22no—
815C2×D4—22no—
816C2×D4—22no—
817C2×D4—22no—
818C2×D4—22no—
819C2×D4—22no—
820C2×D4—22no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—41no—
830C2×D4—41no—
831C2×D4—41no—
832C2×D4—41no—
833C2×D4—592no—
834C2×D4—1182no—
835C2×D4—1182no—
836C2×D4—1181no—
837C2×D4—1181no—
838C2×D4—1181no—
839C2×D4—1181no—
840C2×D4—1181no—
841C2×D4—2361no—
842C2×D4—2361no—
843C2×D4—2361no—
844C2×D4—2361no—
845C2×D4C2×C22⋊D5912yes—
846C2×D4C2×C22⋊D5912yes—
847C2×D4C2×C22⋊D5912yes—
848C2×D4C23×D5912yes—
849C22×C4—21no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—21no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—41no—
860C22×C4—41no—
861C22×C4—41no—
862C22×C4—41no—
863C22×C4—1181no—
864C22×C4—1182no—
865C22×C4—1182no—
866C22×C4—2361no—
867C22×C4—2361no—
868C22×C4—2361no—
869C22×C4—2361no—
870C22×C4D4×D5911yescharacteristic
871C22×C4D4×D5911yescharacteristic
872C22×C4D4×D5911yescharacteristic
873C22×C4D4×D5911yescharacteristic
874C22×C4#1174568711yescharacteristic
875C22×C4#1174568711yescharacteristic
876C22×C4#1174568711yescharacteristic
877C22×C4C2×C22⋊D5911yescharacteristic
878C22×C4C2×C22⋊D5911yescharacteristic
879C22×C4C2×C22⋊D5911yescharacteristic
880C22×C4C2×C22⋊D5911yescharacteristic
881C22×C4C23×D5911yescharacteristic
882C22×C4C23×D5911yescharacteristic
883C22×C4C23×D5911yescharacteristic
884Q16—28no—
885Q16—1188no—
886Q16—1188no—
887SD16—28no—
888SD16—28no—
889SD16—1188no—
890SD16—1188no—
891SD16—1188no—
892SD16—1188no—
893D8—28no—
894D8—1188no—
895D8—1188no—
896M16—22no—
897M16—22no—
898M16—22no—
899M16—594no—
900M16—594no—
901M16—594no—
902M16—594no—
903M16—594no—
904M16—594no—
905M16—11816no—
906M16—1182no—
907M16—1182no—
908M16—1182no—
909M16—1182no—
910M16—1182no—
911M16—1182no—
912M16C23×D5914yes—
913C2×C8—22no—
914C2×C8—22no—
915C2×C8—22no—
916C2×C8—594no—
917C2×C8—594no—
918C2×C8—594no—
919C2×C8—11816no—
920C2×C8—1182no—
921C2×C8—1182no—
922C2×C8—1182no—
923C2×C8—1182no—
924C2×C8—1182no—
925C2×C8—1182no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—41no—
931C23—41no—
932C23—81no—
933C23—82no—
934C23—82no—
935C23—1182no—
936C23—4722no—
937C23—2361no—
938C23—2361no—
939C23#1427369911yescharacteristic
940C23#1427369911yescharacteristic
941C23#1427369911yescharacteristic
942C23#1427369911yescharacteristic
943C23C2×#1174568711yescharacteristic
944C23C2×#1174568711yescharacteristic
945C23C2×#1174568711yescharacteristic
946Q8—22no—
947Q8—22no—
948Q8—22no—
949Q8—22no—
950Q8—22no—
951Q8—41no—
952Q8—41no—
953Q8—1182no—
954Q8—1182no—
955Q8—2361no—
956Q8—2361no—
957Q8C22×C22⋊D5914yes—
958D4—24no—
959D4—24no—
960D4—24no—
961D4—24no—
962D4—22no—
963D4—22no—
964D4—22no—
965D4—22no—
966D4—22no—
967D4—42no—
968D4—42no—
969D4—42no—
970D4—42no—
971D4—41no—
972D4—41no—
973D4—1182no—
974D4—1182no—
975D4—2362no—
976D4—2362no—
977D4—2362no—
978D4—2362no—
979D4—2361no—
980D4—2361no—
981D4C22×C22⋊D5914yes—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—22no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—42no—
995C2×C4—42no—
996C2×C4—1182no—
997C2×C4—2361no—
998C2×C4—2361no—
999C2×C4—2362no—
1000C2×C4—2362no—
1001C2×C4—2362no—
1002C2×C4—2362no—
1003C2×C4#1427369911yescharacteristic
1004C2×C4#1427369911yescharacteristic
1005C2×C4#1427369911yescharacteristic
1006C2×C4#1427369911yescharacteristic
1007C2×C4#1427369911yescharacteristic
1008C2×C4#1427369911yescharacteristic
1009C2×C4#1427369911yescharacteristic
1010C2×C4#1427369911yescharacteristic
1011C2×C4#1427369911yescharacteristic
1012C2×C4#1427369911yescharacteristic
1013C2×C4#1427369911yescharacteristic
1014C2×C4#1427369911yescharacteristic
1015C2×C4C2×D4×D5911yescharacteristic
1016C2×C4C2×D4×D5911yescharacteristic
1017C2×C4C2×D4×D5911yescharacteristic
1018C2×C4C2×D4×D5911yescharacteristic
1019C2×C4C2×D4×D5911yescharacteristic
1020C2×C4C2×D4×D5911yescharacteristic
1021C2×C4C22×C22⋊D5911yescharacteristic
1022C2×C4C22×C22⋊D5911yescharacteristic
1023C2×C4C22×C22⋊D5911yescharacteristic
1024C2×C4C22×C22⋊D5911yescharacteristic
1025C2×C4C22×C22⋊D5911yescharacteristic
1026C2×C4C22×C22⋊D5911yescharacteristic
1027C2×C4C2×#1174568711yescharacteristic
1028C2×C4C2×#1174568711yescharacteristic
1029C2×C4C2×#1174568711yescharacteristic
1030C2×C4C24×D5911yescharacteristic
1031C8—24no—
1032C8—598no—
1033C8—1184no—
1034C8—1184no—
1035C22—24no—
1036C22—41no—
1037C22—41no—
1038C22—41no—
1039C22—41no—
1040C22—41no—
1041C22—41no—
1042C22—41no—
1043C22—44no—
1044C22—42no—
1045C22—82no—
1046C22—82no—
1047C22—82no—
1048C22—82no—
1049C22—82no—
1050C22—4722no—
1051C22—4722no—
1052C22—4722no—
1053C22—2362no—
1054C22C2×#1427369911yescharacteristic
1055C22C2×#1427369911yescharacteristic
1056C22C2×#1427369911yescharacteristic
1057C22C2×#1427369911yescharacteristic
1058C22C2×#1427369911yescharacteristic
1059C22C2×#1427369911yescharacteristic
1060C22C22×#1174568711yescharacteristic
1061C4—24no—
1062C4—42no—
1063C4—2362no—
1064C4C2×#1427369911yescharacteristic
1065C4C2×#1427369911yescharacteristic
1066C4C2×#1427369911yescharacteristic
1067C4C2×#1427369911yescharacteristic
1068C4C2×#1427369911yescharacteristic
1069C4C2×#1427369911yescharacteristic
1070C4C22×D4×D5911yescharacteristic
1071C4C23×C22⋊D5911yescharacteristic
1072C2—21no—
1073C2—21no—
1074C2—21no—
1075C2—21no—
1076C2—21no—
1077C2—21no—
1078C2—21no—
1079C2—44no—
1080C2—82no—
1081C2—4722no—
1082C2C22×#1427369911yescharacteristic
subgroupG/H
centerC4C2×#14273699
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#575C2
socleC2×C59C22×#121
hypercenterC2×#575D59
hypocenterC59#60469
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. C2×#16838200C2semidirect
2. C2×#16838200C2semidirect
3. C2×#16838169C2semidirect
4. #21433835C2semidirect
5. #21433830C2semidirect
6. #21433826C2semidirect
7. #21433821C2semidirect
8. #21433813C2semidirect
9. C2×#16837450C2semidirect
10. C2×#16837386C2semidirect
11. C2×#16837384C2semidirect
12. C2×C59×#575C2semidirect
21. #16838200C22semidirect
23. C2×#14273758C22semidirect
24. C2×#14273757C22semidirect
25. C2×#14273757C22semidirect
27. C2×#14273753C22semidirect
28. C2×#14273752C22semidirect
29. C2×#14273752C22semidirect
31. C2×#14273747C22semidirect
34. #16838169C22semidirect
35. #16838169C22semidirect
37. C2×#14273734C22semidirect
42. #16837675C22semidirect
43. #16837670C22semidirect
44. #16837667C22semidirect
45. #16837663C22semidirect
46. #16837450C22semidirect
47. #16837450C22semidirect
48. C2×#14273662C22semidirect
49. #16837386C22semidirect
50. #16837386C22semidirect
51. #16837384C22semidirect
52. #16837384C22semidirect
53. C2×#14273646C22semidirect
54. C2×#14273645C22semidirect
55. C2×#14273644C22semidirect
56. C2×#14273643C22semidirect
62. C59×#575C22semidirect
64. C2×#137×C59C22semidirect
66. C2×AGL(1,ℤ/8)×C59C22semidirect
106. C2×#11745672C23semidirect
108. C2×#11745670C23semidirect
110. C2×#11745671C23semidirect
112. C2×#11745669C23semidirect
142. #14273662C23semidirect
143. #14273646C23semidirect
144. #14273645C23semidirect
145. #14273644C23semidirect
146. #14273643C23semidirect
533. C2×#575D59semidirect
568. #575C2×D59semidirect
574. C2×#137C2×D59semidirect
580. C2×AGL(1,ℤ/8)C2×D59semidirect
610. C59#60469semidirect

Maximal subgroups

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

subgroupindex
C2×#168382002
C2×#168381692
#214338352
#214338302
#214338262
#214338212
#214338132
C2×#168374502
C2×#168373862
C2×#168373842
C2×C59×#5752
#6046959