Finite Group Databasebeta

← #28749504

Subgroups — #28749504

Order 15104.

2682 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273714C211yesmaximal, characteristic
2#21427205C214yesmaximal, complemented
3#21427169C212yesmaximal, complemented
4#21427166C212yesmaximal, complemented
5#21426947C212yesmaximal, complemented
6#21426941C212yesmaximal, complemented
7C22⋊C4×Dic118C211yesmaximal, characteristic, complemented
8#21426928C211yesmaximal, characteristic, complemented
9D4×C22⋊Dic59C211yesmaximal, characteristic
10#21426905C214yesmaximal, complemented
11#21426692C212yesmaximal, complemented
12#21426643C212yesmaximal, complemented
13C4×#14273714C212yesmaximal, complemented
14#21426491C211yesmaximal, characteristic, complemented
15#21426449C212yesmaximal, complemented
16C4×#14273683C211yesmaximal, characteristic, complemented
17D4×C22⋊C4×C59C211yesmaximal, characteristic
18C23×Dic118C2211yescharacteristic
19C2×#14273714C4116yescomplemented
20C2×#14273714C2212yes—
21C2×#14273714C2211yescharacteristic
22C2×#14273714C2211yescharacteristic
23C2×#14273714C2212yes—
24C2×#14273714C2211yescharacteristic
25C2×#14273714C2211yescharacteristic
26C2×C4×Dic118C2212yescomplemented
27C2×#14273692C2212yescomplemented
28C2×D4×Dic59C2212yes—
29C2×#14273683C2211yescharacteristic
30C2×#14273683C2211yescharacteristic
31C22×C22⋊Dic59C2212yes—
32C22×C22⋊Dic59C2212yes—
33C22×C22⋊Dic59C2212yes—
34C22×C4×Dic59C2211yescharacteristic
35#16837308C2212yescomplemented
36#16837307C2212yescomplemented
37#16837306C2214yescomplemented
38#16837306C2214yescomplemented
39#16837305C2212yes—
40#16837296C2214yescomplemented
41#16837296C2214yescomplemented
42#16837296C2214yescomplemented
43#16837296C2214yescomplemented
44#16837290C2214yescomplemented
45#16837290C2214yescomplemented
46#16837290C2214yescomplemented
47#16837290C2214yescomplemented
48#16837282C2214yes—
49#16837275C2214yescomplemented
50#16837274C2214yescomplemented
51#16837269C2212yescomplemented
52#16837267C2212yescomplemented
53#16837263C2212yes—
54#16837262C2211yescharacteristic
55#16837260C2212yes—
56#16837260C2212yes—
57#16837258C2212yes—
58C4⋊C4×Dic59C2212yescomplemented
59C4×Dic59⋊C4C2212yescomplemented
60#16837253C2212yescomplemented
61C22⋊C4×Dic59C2211yescharacteristic
62C22⋊C4×Dic59C2211yescharacteristic
63C22⋊C4×Dic59C2212yes—
64C22⋊C4×Dic59C2212yes—
65C22⋊C4×Dic59C2212yes—
66C22⋊C4×Dic59C2214yescomplemented
67C22⋊C4×Dic59C2214yescomplemented
68C22⋊C4×Dic59C2214yescomplemented
69C4×C22⋊Dic59C2211yescharacteristic
70C4×C22⋊Dic59C2214yescomplemented
71C4×C22⋊Dic59C2214yescomplemented
72C4×C22⋊Dic59C2214yescomplemented
73#16837247C2212yescomplemented
74#16837247C2212yescomplemented
75C42×Dic59C2212yescomplemented
76C23×D4×C59C2211yescharacteristic
77C2×C4×D4×C59C2212yes—
78C22×C22⋊C4×C59C2212yes—
79C59×#390C2212yes—
80C59×#386C2214yes—
81C59×#380C2211yescharacteristic
82C59×#379C2212yes—
83C4×C22⋊C4×C59C2211yescharacteristic
84C22×Dic118—44no—
85C22×Dic118C2×C418yescomplemented
86C22×Dic118C2311yescharacteristic
87C22×Dic118C2311yescharacteristic
88C22×Dic118C2312yes—
89C23×Dic59C2311yescharacteristic
90C23×Dic59C2314yes—
91C23×Dic59C2312yes—
92C23×Dic59C2311yescharacteristic
93#14273714C2×C418yescomplemented
94#14273714C2×C418yescomplemented
95#14273714C2×C418yescomplemented
96#14273714C2×C418yescomplemented
97#14273714C2×C4116yescomplemented
98#14273714C2×C4116yescomplemented
99C4×Dic118—44no—
100#14273692—44no—
101D4×Dic59—44no—
102#14273683—24no—
103#14273683—24no—
104C2×C4⋊Dic59C2312yes—
105C2×Dic59⋊C4C2312yes—
106C2×Dic59⋊C4C2312yes—
107C2×Dic59⋊C4C2314yes—
108C2×Dic59⋊C4C2314yes—
109C2×C22⋊Dic59—28no—
110C2×C22⋊Dic59C2×C4116yescomplemented
111C2×C22⋊Dic59C2×C4116yescomplemented
112C2×C22⋊Dic59C2311yescharacteristic
113C2×C22⋊Dic59C2314yes—
114C2×C22⋊Dic59C2312yes—
115C2×C22⋊Dic59C2314yes—
116C2×C22⋊Dic59C2314yes—
117C2×C22⋊Dic59C2312yes—
118C2×C22⋊Dic59C2312yes—
119C2×C22⋊Dic59C2312yes—
120C2×C22⋊Dic59C2312yes—
121C2×C22⋊Dic59C2312yes—
122C2×C22⋊Dic59C2312yes—
123C2×C22⋊Dic59C2312yes—
124C2×C22⋊Dic59C2312yes—
125C2×C22⋊Dic59C2311yescharacteristic
126C2×C4×Dic59C2×C418yescomplemented
127C2×C4×Dic59C2312yes—
128C2×C4×Dic59C2312yes—
129C2×C4×Dic59C2312yes—
130C2×C4×Dic59C2312yes—
131C2×C4×Dic59C2312yes—
132C2×C4×Dic59C2314yes—
133C2×C4×Dic59C2314yes—
134C2×C4×Dic59C2314yes—
135C2×C4×Dic59C2311yescharacteristic
136C2×C4×Dic59C2311yescharacteristic
137C2×C4×Dic59C2311yescharacteristic
138C2×C4×Dic59C2311yescharacteristic
139C59⋊#95C2312yes—
140C59⋊#95C2312yes—
141C59⋊#95C2314yes—
142C59⋊#95C2312yes—
143C59⋊#95C2312yes—
144C59⋊#95C2314yes—
145C59⋊#95C2314yes—
146C59⋊#95C2314yes—
147C59⋊#95C2314yes—
148C59⋊#95C2314yes—
149C59⋊#95C2314yes—
150C25×C59C2312yes—
151C22×D4×C59—44no—
152C22×D4×C59C2×C418yes—
153C22×D4×C59C2311yescharacteristic
154C22×D4×C59C2311yescharacteristic
155C22×D4×C59C2312yes—
156C23×C4×C59C2311yescharacteristic
157C23×C4×C59C2314yes—
158C4×D4×C59—44no—
159C2×C4⋊C4×C59C2312yes—
160C2×C22⋊C4×C59—28no—
161C2×C22⋊C4×C59C2311yescharacteristic
162C2×C22⋊C4×C59C2312yes—
163C2×C22⋊C4×C59C2314yes—
164C2×C22⋊C4×C59C2314yes—
165C2×C22⋊C4×C59C2314yes—
166C2×C22⋊C4×C59C2311yescharacteristic
167C2×C42×C59C2312yes—
168#95×C59C2312yes—
169#95×C59C2312yes—
170C24×C59—24no—
171C24×C59—24no—
172C24×C59—44no—
173C24×C59—44no—
174C24×C59C22×C418yes—
175C24×C59C2412yes—
176C24×C59C2412yes—
177C24×C59C2411yescharacteristic
178C2×D4×C59—24no—
179C2×D4×C59—24no—
180C2×D4×C59—416no—
181C2×D4×C59—44no—
182C2×D4×C59C22×C414yes—
183C2×D4×C59C22×C414yes—
184C2×D4×C59C22×C418yes—
185C22×C4×C59—24no—
186C22×C4×C59—28no—
187C22×C4×C59—44no—
188C22×C4×C59—44no—
189C22×C4×C59C22×C414yes—
190C22×C4×C59C2412yes—
191C22×C4×C59C2414yes—
192C22×C4×C59C2411yescharacteristic
193C22×C4×C59C2412yes—
194C22×C4×C59C2411yescharacteristic
195C22×Dic59—22no—
196C22×Dic59—22no—
197C22×Dic59—28no—
198C22×Dic59—42no—
199C22×Dic59—44no—
200C22×Dic59—44no—
201C22×Dic59—44no—
202C22×Dic59C22×C414yes—
203C22×Dic59C22×C414yes—
204C22×Dic59C22×C418yes—
205C22×Dic59C2414yes—
206C22×Dic59C2412yes—
207C22×Dic59C2411yescharacteristic
208C22×Dic59C2411yescharacteristic
209C22×Dic59C2411yescharacteristic
210C22×Dic59C2411yescharacteristic
211C22×Dic59C2412yes—
212C22×Dic59C2412yes—
213C22×Dic59C2412yes—
214C2×Dic118—24no—
215C2×Dic118—24no—
216C2×Dic118—416no—
217C2×Dic118—44no—
218C2×Dic118C22×C414yes—
219C2×Dic118C22×C414yes—
220C2×Dic118C22×C418yes—
221C4⋊C4×C59—24no—
222C22⋊C4×C59—24no—
223C22⋊C4×C59—22no—
224C22⋊C4×C59—28no—
225C22⋊C4×C59—44no—
226C22⋊C4×C59—44no—
227C22⋊C4×C59#4114yes—
228C42×C59—24no—
229C22⋊Dic59—24no—
230C22⋊Dic59—22no—
231C22⋊Dic59—28no—
232C22⋊Dic59—44no—
233C22⋊Dic59—44no—
234C22⋊Dic59C22×C418yes—
235C22⋊Dic59C22×C418yes—
236C22⋊Dic59C22×C418yes—
237C22⋊Dic59C22×C418yes—
238C22⋊Dic59C22×C418yes—
239C22⋊Dic59C22×C418yes—
240C22⋊Dic59C22×C418yes—
241C22⋊Dic59C22×C418yes—
242C22⋊Dic59#4114yes—
243C4⋊Dic59—24no—
244Dic59⋊C4—24no—
245Dic59⋊C4—24no—
246Dic59⋊C4—44no—
247Dic59⋊C4—44no—
248C4×Dic59—24no—
249C4×Dic59—24no—
250C4×Dic59—24no—
251C4×Dic59—42no—
252C4×Dic59—42no—
253C4×Dic59—44no—
254C4×Dic59—44no—
255C4×Dic59—44no—
256C4×Dic59C22×C414yes—
257C4×Dic59C22×C414yes—
258C4×Dic59C22×C414yes—
259C4×Dic59C22×C414yes—
260C23×C59—22no—
261C23×C59—22no—
262C23×C59—22no—
263C23×C59—22no—
264C23×C59—22no—
265C23×C59—22no—
266C23×C59—24no—
267C23×C59—24no—
268C23×C59—24no—
269C23×C59—24no—
270C23×C59—216no—
271C23×C59—48no—
272C23×C59—48no—
273C23×C59—88no—
274C23×C59—88no—
275C23×C59C23×C414yes—
276C23×C59C23×C414yes—
277C23×C59C23×C412yes—
278C23×C59C2×#4112yes—
279C23×C59C2×#4112yes—
280C23×C59C2511yescharacteristic
281D4×C59—28no—
282D4×C59—28no—
283D4×C59—48no—
284C2×C4×C59—22no—
285C2×C4×C59—22no—
286C2×C4×C59—22no—
287C2×C4×C59—28no—
288C2×C4×C59—22no—
289C2×C4×C59—24no—
290C2×C4×C59—24no—
291C2×C4×C59—22no—
292C2×C4×C59—22no—
293C2×C4×C59—24no—
294C2×C4×C59—88no—
295C2×C4×C59C23×C412yes—
296C2×C4×C59C23×C412yes—
297C2×C4×C59C2×#4114yes—
298C2×C4×C59H(5,𝔽2)14yes—
299C2×Dic59—28no—
300C2×Dic59—21no—
301C2×Dic59—21no—
302C2×Dic59—21no—
303C2×Dic59—21no—
304C2×Dic59—22no—
305C2×Dic59—24no—
306C2×Dic59—24no—
307C2×Dic59—22no—
308C2×Dic59—22no—
309C2×Dic59—22no—
310C2×Dic59—22no—
311C2×Dic59—24no—
312C2×Dic59—22no—
313C2×Dic59—24no—
314C2×Dic59—22no—
315C2×Dic59—24no—
316C2×Dic59—48no—
317C2×Dic59—44no—
318C2×Dic59—88no—
319C2×Dic59C23×C412yes—
320C2×Dic59C23×C412yes—
321C2×Dic59C23×C412yes—
322C2×Dic59C23×C412yes—
323C2×Dic59C23×C414yes—
324C2×Dic59C23×C414yes—
325C2×Dic59C2×#4114yes—
326Dic118—28no—
327Dic118—28no—
328Dic118—48no—
329#34240—591nomaximal, Sylow
330C22×C59—22no—
331C22×C59—22no—
332C22×C59—24no—
333C22×C59—24no—
334C22×C59—24no—
335C22×C59—24no—
336C22×C59—24no—
337C22×C59—24no—
338C22×C59—24no—
339C22×C59—24no—
340C22×C59—44no—
341C22×C59—44no—
342C22×C59—44no—
343C22×C59—44no—
344C22×C59—816no—
345C22×C59C4×#4114yes—
346C22×C59C24×C411yescharacteristic
347C22×C59C22×#4111yescharacteristic
348C22×C59C22×#4111yescharacteristic
349C22×C59C2×H(5,𝔽2)12yes—
350C22×C59#58512yes—
351C4×C59—22no—
352C4×C59—24no—
353C4×C59—42no—
354C4×C59—44no—
355C4×C59#51814yes—
356Dic59—22no—
357Dic59—22no—
358Dic59—24no—
359Dic59—24no—
360Dic59—22no—
361Dic59—22no—
362Dic59—24no—
363Dic59—42no—
364Dic59—44no—
365C22×#124—591no—
366#2372—594no—
367#2367—592no—
368#2367—592no—
369#2342—592no—
370#2342—592no—
371Q8×C22⋊C4—591no—
372Q8×C22⋊C4—591no—
373D4×C22⋊C4—591no—
374D4×C22⋊C4D5911yescharacteristic
375#2337—594no—
376#2312—592no—
377C4×#124—592no—
378C4×#124—592no—
379#2283—591no—
380#2273—592no—
381C4×#117—591no—
382C2×C59—24no—
383C2×C59—44no—
384C2×C59—44no—
385C2×C59C2×C4×#4111yescharacteristic
386C2×C59C2×#51811yescharacteristic
387C2×C59#342811yescharacteristic
388C2×C59#351412yes—
389C2×C59#351412yes—
390C23×Q8—591no—
391C23×D4C2×D5911yescharacteristic
392C2×#124—5916no—
393C2×#124—592no—
394C2×#124—591no—
395C2×#124—591no—
396C2×#124—592no—
397C2×#124—591no—
398C2×#124—591no—
399C2×C4×Q8—592no—
400C2×C4×Q8—592no—
401C2×C4×D4—592no—
402C2×C4×D4C2×D5912yes—
403C2×#117—591no—
404C2×#117—591no—
405C22×C22⋊C4—592no—
406C22×C22⋊C4—592no—
407C22×C22⋊C4—592no—
408C22×C22⋊C4C2×D5912yes—
409C22×C42—591no—
410#391—592no—
411#391—592no—
412#391—594no—
413#391—594no—
414#390—592no—
415#390C2×D5912yes—
416#388—594no—
417#388—594no—
418#388—594no—
419#388—594no—
420#388—594no—
421#388—594no—
422#388—594no—
423#388—594no—
424#386—594no—
425#386C2×D5914yes—
426#385—594no—
427#385—594no—
428#383—592no—
429#382—592no—
430#381—592no—
431#380—591no—
432#380—592no—
433#380—592no—
434#380C2×D5911yescharacteristic
435#379—592no—
436#379C2×D5912yes—
437C4×C4⋊C4—592no—
438C4×C4⋊C4—592no—
439C4×C4⋊C4—592no—
440C4×C22⋊C4—594no—
441C4×C22⋊C4—591no—
442C4×C22⋊C4—594no—
443C4×C22⋊C4—594no—
444C4×C22⋊C4—591no—
445C4×C22⋊C4—592no—
446C4×C22⋊C4—594no—
447C4×C22⋊C4—592no—
448C4×C22⋊C4—592no—
449C4×C22⋊C4—594no—
450C4×C22⋊C4—594no—
451C4×C22⋊C4—591no—
452C4×C22⋊C4C2×D5911yescharacteristic
453#376—592no—
454#376—592no—
455C43—592no—
456C59#3424011yescharacteristic, complemented, Sylow
457C25C22×D5912yes—
458C22×Q8—598no—
459C22×Q8—591no—
460C22×Q8—591no—
461C22×Q8—592no—
462C22×Q8—2364no—
463C22×D4—44no—
464C22×D4C4×D5918yes—
465C22×D4C22×D5911yescharacteristic
466C22×D4C22×D5911yescharacteristic
467C22×D4C22×D5912yes—
468C23×C4—591no—
469C23×C4—592no—
470C23×C4—591no—
471C23×C4—594no—
472C23×C4C22×D5911yescharacteristic
473C23×C4C22×D5914yes—
474#124—598no—
475#124—598no—
476#124—598no—
477#124—598no—
478#124—5916no—
479#124—5916no—
480C4×Q8—2364no—
481C4×Q8—2364no—
482C4×D4—44no—
483C4×D4—2364no—
484#117—1184no—
485#117—1184no—
486C2×C4⋊C4—592no—
487C2×C4⋊C4—592no—
488C2×C4⋊C4—592no—
489C2×C4⋊C4—594no—
490C2×C4⋊C4—594no—
491C2×C4⋊C4C22×D5912yes—
492C2×C22⋊C4—28no—
493C2×C22⋊C4—5916no—
494C2×C22⋊C4—5916no—
495C2×C22⋊C4—591no—
496C2×C22⋊C4—592no—
497C2×C22⋊C4—592no—
498C2×C22⋊C4—592no—
499C2×C22⋊C4—592no—
500C2×C22⋊C4—592no—
501C2×C22⋊C4—592no—
502C2×C22⋊C4—592no—
503C2×C22⋊C4—592no—
504C2×C22⋊C4—592no—
505C2×C22⋊C4—594no—
506C2×C22⋊C4—591no—
507C2×C22⋊C4—594no—
508C2×C22⋊C4—594no—
509C2×C22⋊C4—1188no—
510C2×C22⋊C4C22×D5912yes—
511C2×C22⋊C4C22×D5914yes—
512C2×C22⋊C4C22×D5911yescharacteristic
513C2×C22⋊C4C22×D5914yes—
514C2×C22⋊C4C22×D5914yes—
515C2×C22⋊C4C22×D5911yescharacteristic
516C2×C42—598no—
517C2×C42—591no—
518C2×C42—591no—
519C2×C42—591no—
520C2×C42—591no—
521C2×C42—592no—
522C2×C42—592no—
523C2×C42—592no—
524C2×C42—594no—
525C2×C42—594no—
526C2×C42—592no—
527C2×C42—592no—
528C2×C42—594no—
529C2×C42C22×D5912yes—
530#95—592no—
531#95—594no—
532#95—592no—
533#95—592no—
534#95—592no—
535#95—594no—
536#95—594no—
537#95—594no—
538#95—594no—
539#95—594no—
540#95—594no—
541#95C22×D5912yes—
542#95C22×D5912yes—
543C24—24no—
544C24—24no—
545C24—44no—
546C24—44no—
547C24C2×C4×D5918yes—
548C24C23×D5912yes—
549C24C23×D5912yes—
550C24C23×D5911yescharacteristic
551C2×Q8—594no—
552C2×Q8—594no—
553C2×Q8—598no—
554C2×Q8—1184no—
555C2×Q8—1184no—
556C2×Q8—2364no—
557C2×Q8—23616no—
558C2×D4—24no—
559C2×D4—24no—
560C2×D4—416no—
561C2×D4—44no—
562C2×D4C2×C4×D5914yes—
563C2×D4C2×C4×D5914yes—
564C2×D4C2×C4×D5918yes—
565C22×C4—24no—
566C22×C4—28no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—594no—
570C22×C4—591no—
571C22×C4—591no—
572C22×C4—591no—
573C22×C4—592no—
574C22×C4—591no—
575C22×C4—592no—
576C22×C4—592no—
577C22×C4—594no—
578C22×C4—598no—
579C22×C4—594no—
580C22×C4—592no—
581C22×C4—1188no—
582C22×C4—1182no—
583C22×C4—1182no—
584C22×C4—2364no—
585C22×C4—2364no—
586C22×C4—2364no—
587C22×C4—2362no—
588C22×C4C2×C4×D5914yes—
589C22×C4C23×D5914yes—
590C22×C4C23×D5912yes—
591C22×C4C23×D5911yescharacteristic
592C22×C4C23×D5912yes—
593C22×C4C23×D5911yescharacteristic
594C4⋊C4—24no—
595C4⋊C4—1184no—
596C4⋊C4—1184no—
597C4⋊C4—1184no—
598C4⋊C4—2364no—
599C4⋊C4—2364no—
600C22⋊C4—22no—
601C22⋊C4—24no—
602C22⋊C4—28no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C22⋊C4—598no—
606C22⋊C4—598no—
607C22⋊C4—598no—
608C22⋊C4—598no—
609C22⋊C4—598no—
610C22⋊C4—598no—
611C22⋊C4—598no—
612C22⋊C4—598no—
613C22⋊C4—594no—
614C22⋊C4—1188no—
615C22⋊C4—1184no—
616C22⋊C4—1182no—
617C22⋊C4—2364no—
618C22⋊C4—2364no—
619C22⋊C4#1174568714yes—
620C42—24no—
621C42—594no—
622C42—594no—
623C42—594no—
624C42—594no—
625C42—1184no—
626C42—1184no—
627C42—1184no—
628C42—2364no—
629C42—2364no—
630C42—2362no—
631C42—2362no—
632C42—2364no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—216no—
644C23—48no—
645C23—48no—
646C23—88no—
647C23—88no—
648C23C22×C4×D5914yes—
649C23C22×C4×D5914yes—
650C23C22×C4×D5912yes—
651C23#41×D5912yes—
652C23C2×#1174568712yes—
653C23C24×D5911yescharacteristic
654Q8—1188no—
655Q8—1188no—
656Q8—2368no—
657D4—28no—
658D4—28no—
659D4—48no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—28no—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—88no—
671C2×C4—592no—
672C2×C4—592no—
673C2×C4—592no—
674C2×C4—592no—
675C2×C4—594no—
676C2×C4—594no—
677C2×C4—594no—
678C2×C4—1181no—
679C2×C4—1181no—
680C2×C4—1181no—
681C2×C4—1181no—
682C2×C4—1182no—
683C2×C4—1184no—
684C2×C4—1184no—
685C2×C4—1182no—
686C2×C4—1182no—
687C2×C4—1182no—
688C2×C4—1188no—
689C2×C4—1184no—
690C2×C4—1182no—
691C2×C4—1182no—
692C2×C4—1184no—
693C2×C4—1182no—
694C2×C4—1184no—
695C2×C4—4728no—
696C2×C4—2364no—
697C2×C4—2368no—
698C2×C4C22×C4×D5912yes—
699C2×C4C22×C4×D5912yes—
700C2×C4C2×#1174568714yes—
701C2×C4#1427377214yes—
702C22—24no—
703C22—22no—
704C22—24no—
705C22—22no—
706C22—24no—
707C22—24no—
708C22—24no—
709C22—24no—
710C22—24no—
711C22—24no—
712C22—44no—
713C22—44no—
714C22—44no—
715C22—44no—
716C22—816no—
717C22C4×#1174568714yes—
718C22C23×C4×D5911yescharacteristic
719C22C2×#41×D5911yescharacteristic
720C22C22×#1174568711yescharacteristic
721C22C2×#1427377212yes—
722C22#1683823712yes—
723C4—24no—
724C4—22no—
725C4—44no—
726C4—42no—
727C4—1182no—
728C4—1182no—
729C4—1184no—
730C4—1184no—
731C4—1184no—
732C4—1182no—
733C4—1182no—
734C4—2362no—
735C4—2364no—
736C4#1683787514yes—
737C2—24no—
738C2—44no—
739C2—44no—
740C2C2×C4×#1174568711yescharacteristic
741C2C2×#1683787511yescharacteristic
742C2#2143729411yescharacteristic
743C2#2143804812yes—
744C2#2143805412yes—
subgroupG/H
center, FrattiniC23C24×D59
commutatorC22×C59C24×C4
FittingD4×C22⋊C4×C59C2
socle, cosocleC23×C59C25
prime radicalC23×D4×C59C22
hypercenterD4×C22⋊C4D59
hypocenterC59#34240
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #21427205C2semidirect
3. #21427169C2semidirect
4. #21427166C2semidirect
5. #21426947C2semidirect
6. #21426941C2semidirect
7. C22⋊C4×Dic118C2semidirect
8. #21426928C2semidirect
10. #21426905C2semidirect
11. #21426692C2semidirect
12. #21426643C2semidirect
13. C4×#14273714C2semidirect
14. #21426491C2semidirect
15. #21426449C2semidirect
16. C4×#14273683C2semidirect
19. C2×#14273714C4semidirect
26. C2×C4×Dic118C22semidirect
27. C2×#14273692C22semidirect
35. #16837308C22semidirect
36. #16837307C22semidirect
37. #16837306C22semidirect
38. #16837306C22semidirect
40. #16837296C22semidirect
41. #16837296C22semidirect
42. #16837296C22semidirect
43. #16837296C22semidirect
44. #16837290C22semidirect
45. #16837290C22semidirect
46. #16837290C22semidirect
47. #16837290C22semidirect
49. #16837275C22semidirect
50. #16837274C22semidirect
51. #16837269C22semidirect
52. #16837267C22semidirect
58. C4⋊C4×Dic59C22semidirect
59. C4×Dic59⋊C4C22semidirect
60. #16837253C22semidirect
66. C22⋊C4×Dic59C22semidirect
67. C22⋊C4×Dic59C22semidirect
68. C22⋊C4×Dic59C22semidirect
70. C4×C22⋊Dic59C22semidirect
71. C4×C22⋊Dic59C22semidirect
72. C4×C22⋊Dic59C22semidirect
73. #16837247C22semidirect
74. #16837247C22semidirect
75. C42×Dic59C22semidirect
85. C22×Dic118C2×C4semidirect
93. #14273714C2×C4semidirect
94. #14273714C2×C4semidirect
95. #14273714C2×C4semidirect
96. #14273714C2×C4semidirect
97. #14273714C2×C4semidirect
98. #14273714C2×C4semidirect
110. C2×C22⋊Dic59C2×C4semidirect
111. C2×C22⋊Dic59C2×C4semidirect
126. C2×C4×Dic59C2×C4semidirect
456. C59#34240semidirect

Maximal subgroups

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

subgroupindex
C22×#142737142
#214272052
#214271692
#214271662
#214269472
#214269412
C22⋊C4×Dic1182
#214269282
D4×C22⋊Dic592
#214269052
#214266922
#214266432
C4×#142737142
#214264912
#214264492
C4×#142736832
D4×C22⋊C4×C592
#3424059