Finite Group Databasebeta

← #29460172

Subgroups — #29460172

Order 15104.

2444 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837952C211yesmaximal, characteristic, complemented
2C2×#16837952C211yesmaximal, characteristic, complemented
3#21435093C214yesmaximal, complemented
4#21435085C214yesmaximal, complemented
5#21435031C214yesmaximal, complemented
6#21435023C212yesmaximal, complemented
7#21435016C212yesmaximal, complemented
8#21434548C212yesmaximal, complemented
9#21434490C212yesmaximal, complemented
10#21433562C214yesmaximal, complemented
11#21433350C214yesmaximal, complemented
12C59×#2920C211yesmaximal, characteristic, complemented
13C22×#11745685—21no—
14C22×#11745685C2212yes—
15C2×#14273755C2218yescomplemented
16#16837952—21no—
17#16837952—21no—
18#16837952—21no—
19#16837952—21no—
20#16837952—21no—
21#16837952—21no—
22#16837952—21no—
23#16837952—21no—
24#16837952C2212yes—
25#16837952C2212yes—
26#16837952C2212yes—
27#16837952C2212yes—
28#16837952C2212yescomplemented
29#16837952C2212yescomplemented
30#16837952C2212yescomplemented
31#16837952C2212yescomplemented
32C2×#14273727C2211yescharacteristic, complemented
33C2×#14273727C2211yescharacteristic, complemented
34C2×#14273724C2211yescharacteristic, complemented
35C2×#14273724C2211yescharacteristic, complemented
36C2×#14273715—21no—
37C2×#14273715C2212yescomplemented
38C2×#14273701—21no—
39C2×#14273701—21no—
40C2×#14273701—21no—
41C2×#14273701C2212yes—
42C2×C4×D236—21no—
43C2×C4×D236—21no—
44C2×C4×D236—21no—
45C2×C4×D236C2212yescomplemented
46#16837791C2218yescomplemented
47#16837779C2214yescomplemented
48#16837775C2214yescomplemented
49#16837762C2218yescomplemented
50#16837753C2214yescomplemented
51#16837749C2214yescomplemented
52#16837618C22116yescomplemented
53#16837608C2218yescomplemented
54#16837598C2218yescomplemented
55#16837549C22116yescomplemented
56#16837543C2218yescomplemented
57#16837538C2218yescomplemented
58#16837404C2218yescomplemented
59C22×C42×C59C2211yescharacteristic
60C59×#432C2212yescomplemented
61C59×#432C2212yescomplemented
62C59×#431C2212yescomplemented
63C59×#431C2212yescomplemented
64C59×#423C2212yescomplemented
65C59×#407C2212yes—
66C4×M16×C59C2212yescomplemented
67C2×#11745685—22no—
68C2×#11745685—22no—
69C2×#11745685—22no—
70C2×#11745685—22no—
71C2×#11745685—22no—
72C2×#11745685—22no—
73C2×#11745685—48no—
74C2×#11745685—48no—
75C2×#11745685C2314yes—
76C2×#11745685C2314yes—
77C22×Dic118—21no—
78C22×Dic118C2312yes—
79C22×D236—21no—
80C22×D236—21no—
81C22×D236—21no—
82C22×D236—21no—
83C22×D236C2312yes—
84C22×D236C2312yes—
85C22×C22⋊D59—22no—
86C22×C22⋊D59—22no—
87C22×C4×D59—22no—
88C22×C4×D59—22no—
89#14273755—416no—
90C2×#11745660C23116yes—
91C2×D472C23116yes—
92#14273727—21no—
93#14273727—21no—
94#14273727—21no—
95#14273727—21no—
96#14273727C2312yes—
97#14273727C2312yes—
98#14273727C2312yes—
99#14273727C2312yes—
100#14273724—21no—
101#14273724—21no—
102#14273724—21no—
103#14273724—21no—
104#14273724C2312yes—
105#14273724C2312yes—
106#14273724C2312yes—
107#14273724C2312yes—
108#14273715—22no—
109#14273715—22no—
110#14273715—22no—
111#14273715—22no—
112#14273715—22no—
113#14273715—22no—
114#14273715C2314yes—
115#14273715C2314yes—
116#14273701—22no—
117#14273701—22no—
118#14273701—22no—
119#14273701—22no—
120#14273701—22no—
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#14273701C2314yes—
131#14273701C2314yes—
132C4×D236—22no—
133C4×D236—22no—
134C4×D236—22no—
135C4×D236—22no—
136C4×D236—22no—
137C4×D236—22no—
138C4×D236—22no—
139C4×D236—22no—
140C4×D236—22no—
141C4×D236—22no—
142C4×D236—22no—
143C4×D236—22no—
144C4×D236—22no—
145C4×D236—22no—
146C4×D236C2314yes—
147C4×D236C2314yes—
148C2×C4⋊Dic59—21no—
149C2×C4⋊Dic59—21no—
150C2×C4⋊Dic59—21no—
151C2×C4⋊Dic59C2312yes—
152C2×(C2×D59)⋊C4—22no—
153C2×(C2×D59)⋊C4—22no—
154C2×(C2×D59)⋊C4—22no—
155C2×(C2×D59)⋊C4—22no—
156#14273652C23116yes—
157#14273649C23116yes—
158C23×C4×C59D411yescharacteristic
159C23×C4×C59D411yescharacteristic
160C23×C4×C59C2311yescharacteristic
161C2×M16×C59C2314yes—
162C2×C42×C59D411yescharacteristic
163C2×C42×C59D411yescharacteristic
164C2×C42×C59D411yescharacteristic
165C2×C42×C59D411yescharacteristic
166C2×C42×C59D411yescharacteristic
167C2×C42×C59D411yescharacteristic
168C2×C42×C59C2311yescharacteristic
169C2×C42×C59C2311yescharacteristic
170C2×C42×C59C2311yescharacteristic
171C2×C42×C59C2311yescharacteristic
172C2×C42×C59C2311yescharacteristic
173C2×C42×C59C2311yescharacteristic
174C4⋊C8×C59C2314yes—
175C4⋊C8×C59C2314yes—
176C22⋊C8×C59C2314yes—
177C22⋊C8×C59C2314yes—
178#97×C59C2314yes—
179C4×C8×C59C2314yes—
180C24×C59C2×D411yescharacteristic
181C23×D59—22no—
182C23×D59—22no—
183C22×C4×C59—24no—
184C22×C4×C59—24no—
185C22×C4×C59—42no—
186C22×C4×C59C2×D411yescharacteristic
187C22×C4×C59C2×D411yescharacteristic
188C22×C4×C59C2×D411yescharacteristic
189C22×C4×C59C2×D411yescharacteristic
190C22×C4×C59C2×D411yescharacteristic
191C22×C4×C59C2×D411yescharacteristic
192C22×C4×C59C2×D411yescharacteristic
193C22×C4×C59C2×D411yescharacteristic
194C22×C4×C59C2×D411yescharacteristic
195C22×C4×C59C2×D411yescharacteristic
196C22×C4×C59C2×D411yescharacteristic
197C22×C4×C59C2×D411yescharacteristic
198C22×C4×C59C2×D411yescharacteristic
199C22×C4×C59C2×D411yescharacteristic
200C22×C4×C59C2×D411yescharacteristic
201C22×C4×C59C2411yescharacteristic
202C22×C4×C59C2411yescharacteristic
203C22×C4×C59C2411yescharacteristic
204C2×C22⋊D59—24no—
205C2×C22⋊D59—24no—
206C2×C22⋊D59—24no—
207C2×C22⋊D59—24no—
208C2×C22⋊D59—48no—
209C2×C22⋊D59—48no—
210C22×Dic59—22no—
211C22×Dic59—22no—
212#11745685—216no—
213#11745685—48no—
214#11745685—48no—
215#11745685—48no—
216#11745685—48no—
217#11745685—48no—
218#11745685—48no—
219#11745685—48no—
220C2×D236—28no—
221C2×D236—22no—
222C2×D236—22no—
223C2×D236—22no—
224C2×D236—22no—
225C2×D236—22no—
226C2×D236—22no—
227C2×D236—22no—
228C2×D236—22no—
229C2×D236—22no—
230C2×D236—22no—
231C2×D236—44no—
232C2×D236—44no—
233C2×D236—44no—
234C2×D236—44no—
235C2×D236—44no—
236C2×D236C2414yes—
237C2×D236C2414yes—
238C2×C4×D59—24no—
239C2×C4×D59—24no—
240C2×C4×D59—24no—
241C2×C4×D59—24no—
242C2×C4×D59—48no—
243C2×C4×D59—48no—
244C2×Dic118—22no—
245C2×Dic118—22no—
246C2×Dic118—22no—
247C2×Dic118—44no—
248C2×Dic118—44no—
249C2×Dic118C2414yes—
250M16×C59—28no—
251C2×C8×C59C2418yes—
252C42×C59C2×D411yescharacteristic
253C42×C59C2×D411yescharacteristic
254C42×C59C2×D411yescharacteristic
255C42×C59C2×D411yescharacteristic
256C42×C59C2×D411yescharacteristic
257C42×C59C2×D411yescharacteristic
258C42×C59C2×D411yescharacteristic
259C42×C59C2×D411yescharacteristic
260C42×C59C2×D411yescharacteristic
261C42×C59C2×D411yescharacteristic
262C42×C59C2×D411yescharacteristic
263C42×C59C2×D411yescharacteristic
264C42×C59C2411yescharacteristic
265C42×C59C2411yescharacteristic
266C42×C59C2411yescharacteristic
267C42×C59C2411yescharacteristic
268(C2×D59)⋊C4—24no—
269(C2×D59)⋊C4—24no—
270(C2×D59)⋊C4—24no—
271(C2×D59)⋊C4—24no—
272(C2×D59)⋊C4—24no—
273(C2×D59)⋊C4—24no—
274(C2×D59)⋊C4—24no—
275(C2×D59)⋊C4—24no—
276C4⋊Dic59—22no—
277C4⋊Dic59—22no—
278C4⋊Dic59—22no—
279C4⋊Dic59—22no—
280C4⋊Dic59—22no—
281C4⋊Dic59—22no—
282C4⋊Dic59—22no—
283C4⋊Dic59C2414yes—
284D472—416no—
285#11745660—416no—
286C23×C59—22no—
287C23×C59—22no—
288C23×C59—41no—
289C23×C59C22×D411yescharacteristic
290C23×C59C22×D411yescharacteristic
291C23×C59C22×D411yescharacteristic
292C22×D59—24no—
293C22×D59—24no—
294C22×D59—44no—
295C22×D59—44no—
296C22×D59—44no—
297C22×D59—44no—
298C22×D59—44no—
299C22×D59—44no—
300C2×C4×C59—22no—
301C2×C4×C59—22no—
302C2×C4×C59—22no—
303C2×C4×C59—22no—
304C2×C4×C59—22no—
305C2×C4×C59—22no—
306C2×C4×C59—22no—
307C2×C4×C59—22no—
308C2×C4×C59—22no—
309C2×C4×C59—22no—
310C2×C4×C59—22no—
311C2×C4×C59—22no—
312C2×C4×C59—22no—
313C2×C4×C59—41no—
314C2×C4×C59—41no—
315C2×C4×C59—41no—
316C2×C4×C59AGL(1,ℤ/8)14yescomplemented
317C2×C4×C59C22×D411yescharacteristic
318C2×C4×C59C22×D411yescharacteristic
319C2×C4×C59C22×D411yescharacteristic
320C2×C4×C59C22×D411yescharacteristic
321C2×C4×C59C22×D411yescharacteristic
322C2×C4×C59C22×D411yescharacteristic
323C2×C4×C59C22×D411yescharacteristic
324C2×C4×C59C22×D411yescharacteristic
325C2×C4×C59C22×D411yescharacteristic
326C2×C4×C59C22×D411yescharacteristic
327C2×C4×C59C22×D411yescharacteristic
328C2×C4×C59H(5,𝔽2)14yes—
329C2×C4×C59C2511yescharacteristic
330C22⋊D59—48no—
331C22⋊D59—48no—
332C22⋊D59—48no—
333C22⋊D59—48no—
334C2×Dic59—24no—
335C2×Dic59—24no—
336C2×Dic59—44no—
337C2×Dic59—44no—
338D236—28no—
339D236—28no—
340D236—44no—
341D236—44no—
342D236—44no—
343D236—44no—
344D236—44no—
345D236—44no—
346D236—44no—
347D236—44no—
348D236—44no—
349D236—44no—
350C4×D59—48no—
351C4×D59—48no—
352C4×D59—48no—
353C4×D59—48no—
354Dic118—28no—
355Dic118—44no—
356Dic118—44no—
357Dic118—44no—
358C8×C59—28no—
359#60803—591nomaximal, Sylow
360C22×C59—21no—
361C22×C59—21no—
362C22×C59—21no—
363C22×C59—21no—
364C22×C59—21no—
365C22×C59—21no—
366C22×C59—21no—
367C22×C59—44no—
368C22×C59#53512yes—
369C22×C59C2×AGL(1,ℤ/8)12yes—
370C22×C59C23×D411yescharacteristic
371C2×D59—44no—
372C2×D59—44no—
373C2×D59—44no—
374C2×D59—44no—
375C2×D59—44no—
376C2×D59—44no—
377C2×D59—88no—
378C2×D59—88no—
379C4×C59—21no—
380C4×C59—21no—
381C4×C59—21no—
382C4×C59—21no—
383C4×C59—21no—
384C4×C59—21no—
385C4×C59—21no—
386C4×C59#53512yes—
387C4×C59C2×AGL(1,ℤ/8)12yes—
388C4×C59C2×AGL(1,ℤ/8)12yes—
389C4×C59#57512yes—
390C4×C59C2×H(5,𝔽2)12yes—
391Dic59—44no—
392Dic59—44no—
393C2×#532—591no—
394C2×#532—591no—
395#3214—594no—
396#3213—594no—
397#3207—594no—
398#3206—592no—
399#3205—592no—
400#3151—592no—
401#3141—592no—
402#3036—594no—
403#3006—594no—
404#2920D5911yescharacteristic, complemented
405C2×C59—22no—
406C2×C59—22no—
407C2×C59—41no—
408C2×C59C2×#53511yescharacteristic
409C2×C59C22×AGL(1,ℤ/8)11yescharacteristic
410C2×C59C2×#57511yescharacteristic
411D59—84no—
412D59—84no—
413C22×#41—592no—
414C22×#41—1181no—
415C2×AGL(1,ℤ/8)—598no—
416#532—592no—
417#532—592no—
418#532—592no—
419#532—592no—
420#532—592no—
421#532—592no—
422#532—592no—
423#532—592no—
424#532—1181no—
425#532—1181no—
426#532—1181no—
427#532—1181no—
428#532—1181no—
429#532—1181no—
430#532—1181no—
431#532—1181no—
432C2×C4⋊Q8—591no—
433C2×C4⋊Q8—591no—
434C2×#127—591no—
435C2×#127—591no—
436C2×#124—592no—
437C2×#124—1181no—
438C2×#121—592no—
439C2×#121—1181no—
440C2×#121—1181no—
441C2×#121—1181no—
442C2×C4×D4—592no—
443C2×C4×D4—1181no—
444C2×C4×D4—1181no—
445C2×C4×D4—1181no—
446C22×C42C2×D5911yescharacteristic
447#496—598no—
448#493—594no—
449#492—594no—
450#489—598no—
451#487—594no—
452#486—594no—
453#463—5916no—
454#461—598no—
455#459—598no—
456#449—5916no—
457#448—598no—
458#447—598no—
459#432C2×D5912yescomplemented
460#432C2×D5912yescomplemented
461#431C2×D5912yescomplemented
462#431C2×D5912yescomplemented
463#423C2×D5912yescomplemented
464#417—598no—
465#407C2×D5912yes—
466C4×M16C2×D5912yescomplemented
467C59#6080311yescharacteristic, complemented, Sylow
468C2×#41—594no—
469C2×#41—594no—
470C2×#41—1182no—
471C2×#41—1182no—
472C2×#41—1182no—
473C2×#41—1182no—
474C2×#41—1182no—
475C2×#41—1182no—
476C2×#41—2368no—
477C2×#41—2368no—
478C22×Q8—592no—
479C22×Q8—1181no—
480C22×D4—592no—
481C22×D4—592no—
482C22×D4—1182no—
483C22×D4—1182no—
484C22×D4—1181no—
485C22×D4—1181no—
486C22×D4—1181no—
487C22×D4—1181no—
488C23×C4—1182no—
489C23×C4—1182no—
490C23×C4D23611yescharacteristic
491C23×C4D23611yescharacteristic
492C23×C4C22×D5911yescharacteristic
493AGL(1,ℤ/8)—23616no—
494C2×SD16—5916no—
495C2×D8—5916no—
496C2×M16C22×D5914yes—
497C4⋊Q8—592no—
498C4⋊Q8—592no—
499C4⋊Q8—592no—
500C4⋊Q8—592no—
501C4⋊Q8—1181no—
502C4⋊Q8—1181no—
503C4⋊Q8—1181no—
504C4⋊Q8—1181no—
505#127—592no—
506#127—592no—
507#127—592no—
508#127—592no—
509#127—1181no—
510#127—1181no—
511#127—1181no—
512#127—1181no—
513#124—594no—
514#124—594no—
515#124—1182no—
516#124—1182no—
517#124—1182no—
518#124—1182no—
519#124—1182no—
520#124—1182no—
521#121—594no—
522#121—594no—
523#121—1182no—
524#121—1182no—
525#121—1182no—
526#121—1182no—
527#121—1182no—
528#121—1182no—
529#121—1182no—
530#121—1182no—
531#121—1182no—
532#121—1182no—
533#121—1182no—
534#121—1182no—
535#121—1182no—
536#121—1182no—
537C4×D4—594no—
538C4×D4—594no—
539C4×D4—1182no—
540C4×D4—1182no—
541C4×D4—1182no—
542C4×D4—1182no—
543C4×D4—1182no—
544C4×D4—1182no—
545C4×D4—1182no—
546C4×D4—1182no—
547C4×D4—1182no—
548C4×D4—1182no—
549C4×D4—1182no—
550C4×D4—1182no—
551C4×D4—1182no—
552C4×D4—1182no—
553C2×C4⋊C4—592no—
554C2×C4⋊C4—1181no—
555C2×C4⋊C4—1181no—
556C2×C4⋊C4—1181no—
557C2×C22⋊C4—1182no—
558C2×C22⋊C4—1182no—
559C2×C22⋊C4—1182no—
560C2×C22⋊C4—1182no—
561C2×C42D23611yescharacteristic
562C2×C42D23611yescharacteristic
563C2×C42D23611yescharacteristic
564C2×C42D23611yescharacteristic
565C2×C42D23611yescharacteristic
566C2×C42D23611yescharacteristic
567C2×C42C22×D5911yescharacteristic
568C2×C42C22×D5911yescharacteristic
569C2×C42C22×D5911yescharacteristic
570C2×C42C22×D5911yescharacteristic
571C2×C42C22×D5911yescharacteristic
572C2×C42C22×D5911yescharacteristic
573C4⋊C8C22×D5914yes—
574C4⋊C8C22×D5914yes—
575#103—5916no—
576#102—5916no—
577C22⋊C8C22×D5914yes—
578C22⋊C8C22×D5914yes—
579#97C22×D5914yes—
580C4×C8C22×D5914yes—
581C24—1182no—
582C24—1182no—
583C24C2×D23611yescharacteristic
584#41—11816no—
585#41—2368no—
586#41—2368no—
587#41—2368no—
588#41—2368no—
589#41—2368no—
590#41—2368no—
591#41—2368no—
592C2×Q8—594no—
593C2×Q8—1182no—
594C2×Q8—1182no—
595C2×Q8—1182no—
596C2×Q8—2364no—
597C2×Q8—2364no—
598C2×D4—594no—
599C2×D4—594no—
600C2×D4—1184no—
601C2×D4—1184no—
602C2×D4—1184no—
603C2×D4—1184no—
604C2×D4—1182no—
605C2×D4—1182no—
606C2×D4—1182no—
607C2×D4—1182no—
608C2×D4—1182no—
609C2×D4—1182no—
610C2×D4—1182no—
611C2×D4—1182no—
612C2×D4—1182no—
613C2×D4—1182no—
614C2×D4—1188no—
615C2×D4—2364no—
616C2×D4—2364no—
617C2×D4—2364no—
618C2×D4—2364no—
619C2×D4—2368no—
620C2×D4—2368no—
621C2×D4—2364no—
622C22×C4—24no—
623C22×C4—24no—
624C22×C4—42no—
625C22×C4—1182no—
626C22×C4—1182no—
627C22×C4—1184no—
628C22×C4—1184no—
629C22×C4—1184no—
630C22×C4—1184no—
631C22×C4—2368no—
632C22×C4—2368no—
633C22×C4C2×D23611yescharacteristic
634C22×C4C2×D23611yescharacteristic
635C22×C4C2×D23611yescharacteristic
636C22×C4C2×D23611yescharacteristic
637C22×C4C2×D23611yescharacteristic
638C22×C4C2×D23611yescharacteristic
639C22×C4C2×D23611yescharacteristic
640C22×C4C2×D23611yescharacteristic
641C22×C4C2×D23611yescharacteristic
642C22×C4C2×D23611yescharacteristic
643C22×C4C2×D23611yescharacteristic
644C22×C4C2×D23611yescharacteristic
645C22×C4C2×D23611yescharacteristic
646C22×C4C2×D23611yescharacteristic
647C22×C4C2×D23611yescharacteristic
648C22×C4C23×D5911yescharacteristic
649C22×C4C23×D5911yescharacteristic
650C22×C4C23×D5911yescharacteristic
651SD16—23616no—
652D8—23616no—
653M16—28no—
654C2×C8C23×D5918yes—
655C4⋊C4—594no—
656C4⋊C4—1182no—
657C4⋊C4—1182no—
658C4⋊C4—1182no—
659C4⋊C4—1182no—
660C4⋊C4—1182no—
661C4⋊C4—1182no—
662C4⋊C4—1182no—
663C22⋊C4—1184no—
664C22⋊C4—1184no—
665C22⋊C4—1184no—
666C22⋊C4—1184no—
667C22⋊C4—1184no—
668C22⋊C4—1184no—
669C22⋊C4—1184no—
670C22⋊C4—1184no—
671C42C2×D23611yescharacteristic
672C42C2×D23611yescharacteristic
673C42C2×D23611yescharacteristic
674C42C2×D23611yescharacteristic
675C42C2×D23611yescharacteristic
676C42C2×D23611yescharacteristic
677C42C2×D23611yescharacteristic
678C42C2×D23611yescharacteristic
679C42C2×D23611yescharacteristic
680C42C2×D23611yescharacteristic
681C42C2×D23611yescharacteristic
682C42C2×D23611yescharacteristic
683C42C23×D5911yescharacteristic
684C42C23×D5911yescharacteristic
685C42C23×D5911yescharacteristic
686C42C23×D5911yescharacteristic
687C23—22no—
688C23—22no—
689C23—41no—
690C23—1184no—
691C23—1184no—
692C23—2364no—
693C23—2364no—
694C23—2364no—
695C23—2364no—
696C23—2364no—
697C23—2364no—
698C23C22×D23611yescharacteristic
699C23C22×D23611yescharacteristic
700C23C22×D23611yescharacteristic
701Q8—1188no—
702Q8—2364no—
703Q8—2364no—
704Q8—2364no—
705D4—1188no—
706D4—1188no—
707D4—2364no—
708D4—2364no—
709D4—2364no—
710D4—2364no—
711D4—2368no—
712D4—2368no—
713D4—2368no—
714D4—2368no—
715D4—2364no—
716D4—2364no—
717D4—2364no—
718D4—2364no—
719D4—2364no—
720D4—2364no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—1184no—
738C2×C4—1184no—
739C2×C4—2368no—
740C2×C4—2368no—
741C2×C4—2364no—
742C2×C4—2364no—
743C2×C4—2368no—
744C2×C4—2368no—
745C2×C4#1427375514yescomplemented
746C2×C4C22×D23611yescharacteristic
747C2×C4C22×D23611yescharacteristic
748C2×C4C22×D23611yescharacteristic
749C2×C4C22×D23611yescharacteristic
750C2×C4C22×D23611yescharacteristic
751C2×C4C22×D23611yescharacteristic
752C2×C4C22×D23611yescharacteristic
753C2×C4C22×D23611yescharacteristic
754C2×C4C22×D23611yescharacteristic
755C2×C4C22×D23611yescharacteristic
756C2×C4C22×D23611yescharacteristic
757C2×C4#1427377314yes—
758C2×C4C24×D5911yescharacteristic
759C8—28no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—44no—
768C22—4728no—
769C22—4728no—
770C22—2364no—
771C22—2364no—
772C22—2364no—
773C22—2364no—
774C22—2364no—
775C22—2364no—
776C22#1683797112yes—
777C22C2×#1427375512yes—
778C22C23×D23611yescharacteristic
779C4—21no—
780C4—21no—
781C4—21no—
782C4—21no—
783C4—21no—
784C4—21no—
785C4—21no—
786C4—2364no—
787C4—2364no—
788C4#1683797112yes—
789C4C2×#1427375512yes—
790C4C2×#1427375512yes—
791C4#1683820212yes—
792C4C2×#1427377312yes—
793C2—22no—
794C2—22no—
795C2—41no—
796C2—4724no—
797C2—4724no—
798C2C2×#1683797111yescharacteristic
799C2C22×#1427375511yescharacteristic
800C2C2×#1683820211yescharacteristic
subgroupG/H
centerC22C23×D236
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC59×#2920C2
socleC22×C59C23×D4
hypercenter#2920D59
hypocenterC59#60803
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C42 ◁ #2920

Complements

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

NH ≅ G/Ntype
1. C2×#16837952C2semidirect
2. C2×#16837952C2semidirect
3. #21435093C2semidirect
4. #21435085C2semidirect
5. #21435031C2semidirect
6. #21435023C2semidirect
7. #21435016C2semidirect
8. #21434548C2semidirect
9. #21434490C2semidirect
10. #21433562C2semidirect
11. #21433350C2semidirect
12. C59×#2920C2semidirect
15. C2×#14273755C22semidirect
28. #16837952C22semidirect
29. #16837952C22semidirect
30. #16837952C22semidirect
31. #16837952C22semidirect
32. C2×#14273727C22semidirect
33. C2×#14273727C22semidirect
34. C2×#14273724C22semidirect
35. C2×#14273724C22semidirect
37. C2×#14273715C22semidirect
45. C2×C4×D236C22semidirect
46. #16837791C22semidirect
47. #16837779C22semidirect
48. #16837775C22semidirect
49. #16837762C22semidirect
50. #16837753C22semidirect
51. #16837749C22semidirect
52. #16837618C22semidirect
53. #16837608C22semidirect
54. #16837598C22semidirect
55. #16837549C22semidirect
56. #16837543C22semidirect
57. #16837538C22semidirect
58. #16837404C22semidirect
60. C59×#432C22semidirect
61. C59×#432C22semidirect
62. C59×#431C22semidirect
63. C59×#431C22semidirect
64. C59×#423C22semidirect
66. C4×M16×C59C22semidirect
316. C2×C4×C59AGL(1,ℤ/8)semidirect
404. #2920D59semidirect
459. #432C2×D59semidirect
460. #432C2×D59semidirect
461. #431C2×D59semidirect
462. #431C2×D59semidirect
463. #423C2×D59semidirect
466. C4×M16C2×D59semidirect
467. C59#60803semidirect
745. C2×C4#14273755semidirect

Maximal subgroups

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

subgroupindex
C2×#168379522
#214350932
#214350852
#214350312
#214350232
#214350162
#214345482
#214344902
#214335622
#214333502
C59×#29202
#6080359