Finite Group Databasebeta

← #28751619

Subgroups — #28751619

Order 15104.

2630 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21427244C214yesmaximal, complemented
2#21427092C214yesmaximal, complemented
3#21426973C212yesmaximal, complemented
4#21426945C212yesmaximal, complemented
5#21426945C212yesmaximal, complemented
6D4×C22⋊Dic59C212yesmaximal
7#21426890C214yesmaximal, complemented
8#21426768C214yesmaximal, complemented
9#21426714C211yesmaximal, characteristic, complemented
10#21426710C211yesmaximal, characteristic, complemented
11#21426699C211yesmaximal, characteristic, complemented
12#21426694C211yesmaximal, characteristic, complemented
13#21426479C211yesmaximal, characteristic, complemented
14C2×#16837262C211yesmaximal, characteristic, complemented
15C22×#123×C59C211yesmaximal, characteristic
16C2×D4×Dic59C2214yes—
17C2×#14273686C2212yes—
18C2×#14273686C2212yescomplemented
19C22×C4⋊Dic59C2212yescomplemented
20C22×C22⋊Dic59C2212yes—
21C22×C22⋊Dic59C2212yes—
22#16837305C2214yes—
23#16837301C2214yescomplemented
24#16837301C2214yescomplemented
25#16837301C2214yescomplemented
26#16837295C2214yescomplemented
27#16837295C2214yescomplemented
28#16837295C2214yescomplemented
29#16837295C2214yescomplemented
30#16837295C2214yescomplemented
31#16837295C2214yescomplemented
32#16837288C2214yescomplemented
33#16837288C2214yescomplemented
34#16837288C2214yescomplemented
35#16837288C2214yescomplemented
36#16837282C2214yes—
37#16837282C2214yes—
38#16837277C2214yescomplemented
39#16837277C2214yescomplemented
40#16837277C2214yescomplemented
41#16837277C2214yescomplemented
42#16837265C2212yes—
43#16837265C2212yescomplemented
44#16837262C2212yes—
45#16837262C2212yes—
46#16837262C2211yescharacteristic
47#16837262C2211yescharacteristic
48#16837262C2211yescharacteristic
49#16837262C2211yescharacteristic
50#16837262C2212yes—
51#16837262C2212yescomplemented
52#16837262C2212yescomplemented
53#16837262C2212yescomplemented
54#16837258C2212yes—
55#16837258C2212yes—
56C4⋊C4×Dic59C2214yescomplemented
57C22⋊C4×Dic59C2214yescomplemented
58C22⋊C4×Dic59C2214yescomplemented
59C4×C22⋊Dic59C2212yes—
60C4×C22⋊Dic59C2212yes—
61C4×C22⋊Dic59C2212yes—
62C4×C22⋊Dic59C2212yescomplemented
63C2×C59⋊#95C2212yescomplemented
64C23×D4×C59C2211yescharacteristic
65C24×C4×C59C2211yescharacteristic
66C2×#123×C59C4116yescomplemented
67C2×#123×C59C2212yes—
68C2×#123×C59C2212yes—
69C2×#123×C59C2212yes—
70C2×#123×C59C2212yes—
71C22×C4⋊C4×C59C2211yescharacteristic
72C22×C4⋊C4×C59C2211yescharacteristic
73C22×C22⋊C4×C59C2211yescharacteristic
74C22×C22⋊C4×C59C2211yescharacteristic
75C22×C22⋊C4×C59C2211yescharacteristic
76C23×Dic59C2314yes—
77C23×Dic59C2314yes—
78D4×Dic59—48no—
79#14273686—44no—
80#14273686—44no—
81C2×C4⋊Dic59—44no—
82C2×C4⋊Dic59C2314yes—
83C2×C4⋊Dic59C2312yes—
84C2×C4⋊Dic59C2312yes—
85C2×C4⋊Dic59C2314yes—
86C2×C4⋊Dic59C2312yes—
87C2×C4⋊Dic59C2312yes—
88C2×C4⋊Dic59C2314yes—
89C2×C4⋊Dic59C2314yes—
90C2×C22⋊Dic59—44no—
91C2×C22⋊Dic59—44no—
92C2×C22⋊Dic59C2312yes—
93C2×C22⋊Dic59C2312yes—
94C2×C22⋊Dic59C2312yes—
95C2×C22⋊Dic59C2312yes—
96C2×C22⋊Dic59C2314yes—
97C2×C22⋊Dic59C2314yes—
98C2×C22⋊Dic59C2314yes—
99C2×C22⋊Dic59C2314yes—
100C2×C22⋊Dic59C2314yes—
101C2×C22⋊Dic59C2314yes—
102C2×C4×Dic59C2314yes—
103C2×C4×Dic59C2314yes—
104C2×C4×Dic59C2314yes—
105C2×C4×Dic59C2314yes—
106C59⋊#95C2314yes—
107C59⋊#95C2312yes—
108C59⋊#95C2312yes—
109C59⋊#95C2314yes—
110C59⋊#95C2314yes—
111C59⋊#95C2314yes—
112C59⋊#95C2312yes—
113C59⋊#95C2312yes—
114C59⋊#95C2314yes—
115C59⋊#95C2314yes—
116C59⋊#95C2314yes—
117C59⋊#95C2314yes—
118C25×C59C2311yescharacteristic
119C25×C59C2311yescharacteristic
120C22×D4×C59—44no—
121C22×D4×C59C2×C418yes—
122C22×D4×C59C2312yes—
123C22×D4×C59C2312yes—
124C23×C4×C59—44no—
125C23×C4×C59C2×C418yescomplemented
126C23×C4×C59C2311yescharacteristic
127C23×C4×C59C2311yescharacteristic
128C23×C4×C59C2311yescharacteristic
129C23×C4×C59C2311yescharacteristic
130C23×C4×C59C2311yescharacteristic
131C23×C4×C59C2311yescharacteristic
132C23×C4×C59C2311yescharacteristic
133C23×C4×C59C2311yescharacteristic
134C23×C4×C59C2311yescharacteristic
135#123×C59C2×C4116yescomplemented
136#123×C59C2×C4116yescomplemented
137#123×C59C2×C4116yescomplemented
138#123×C59C2×C4116yescomplemented
139C2×C4⋊C4×C59C2×C418yescomplemented
140C2×C4⋊C4×C59C2×C418yescomplemented
141C2×C4⋊C4×C59C2312yes—
142C2×C4⋊C4×C59C2312yes—
143C2×C4⋊C4×C59C2312yes—
144C2×C4⋊C4×C59C2312yes—
145C2×C22⋊C4×C59C2×C418yescomplemented
146C2×C22⋊C4×C59C2×C418yescomplemented
147C2×C22⋊C4×C59C2×C418yescomplemented
148C2×C22⋊C4×C59C2312yes—
149C2×C22⋊C4×C59C2312yes—
150C2×C22⋊C4×C59C2312yes—
151C2×C22⋊C4×C59C2312yes—
152C2×C22⋊C4×C59C2312yes—
153C2×C22⋊C4×C59C2312yes—
154C24×C59—24no—
155C24×C59—22no—
156C24×C59—22no—
157C24×C59—22no—
158C24×C59—22no—
159C24×C59—42no—
160C24×C59—42no—
161C24×C59—42no—
162C24×C59C22×C414yes—
163C24×C59C22×C414yes—
164C24×C59C2412yes—
165C24×C59C2411yescharacteristic
166C24×C59C2411yescharacteristic
167C24×C59C2411yescharacteristic
168C2×D4×C59—28no—
169C2×D4×C59—44no—
170C2×D4×C59—416no—
171C2×D4×C59C22×C418yes—
172C2×D4×C59C22×C418yes—
173C22×C4×C59—24no—
174C22×C4×C59—24no—
175C22×C4×C59—22no—
176C22×C4×C59—22no—
177C22×C4×C59—416no—
178C22×C4×C59—42no—
179C22×C4×C59—42no—
180C22×C4×C59—42no—
181C22×C4×C59—42no—
182C22×C4×C59—42no—
183C22×C4×C59—42no—
184C22×C4×C59C22×C414yes—
185C22×C4×C59C22×C414yes—
186C22×C4×C59C22×C414yes—
187C22×C4×C59C22×C414yes—
188C22×C4×C59C22×C414yes—
189C22×C4×C59C22×C414yes—
190C22×C4×C59C22×C414yes—
191C22×C4×C59C22×C414yes—
192C22×C4×C59C22×C414yes—
193C22×C4×C59C2412yes—
194C22×C4×C59C2412yes—
195C22×C4×C59C2411yescharacteristic
196C22×C4×C59C2411yescharacteristic
197C22×C4×C59C2411yescharacteristic
198C22×C4×C59C2411yescharacteristic
199C22×C4×C59C2412yes—
200C22×Dic59—28no—
201C22×Dic59—44no—
202C22×Dic59—44no—
203C22×Dic59—44no—
204C22×Dic59—44no—
205C22×Dic59—44no—
206C22×Dic59C2414yes—
207C22×Dic59C2414yes—
208C22×Dic59C2414yes—
209C22×Dic59C2414yes—
210C4⋊C4×C59C22×C418yes—
211C4⋊C4×C59C22×C418yes—
212C4⋊C4×C59C22×C418yes—
213C4⋊C4×C59C22×C418yes—
214C22⋊C4×C59C22×C418yes—
215C22⋊C4×C59C22×C418yes—
216C22⋊C4×C59C22×C418yes—
217C22⋊C4×C59C22×C418yes—
218C22⋊C4×C59C22×C418yes—
219C22⋊C4×C59C22×C418yes—
220C22⋊Dic59—24no—
221C22⋊Dic59—24no—
222C22⋊Dic59—24no—
223C22⋊Dic59—28no—
224C22⋊Dic59—24no—
225C22⋊Dic59—44no—
226C22⋊Dic59—44no—
227C22⋊Dic59—44no—
228C22⋊Dic59—44no—
229C22⋊Dic59—44no—
230C4⋊Dic59—42no—
231C4⋊Dic59—44no—
232C4⋊Dic59—42no—
233C4⋊Dic59—44no—
234C4⋊Dic59—42no—
235C4⋊Dic59—42no—
236C4⋊Dic59—44no—
237C4⋊Dic59—44no—
238C4×Dic59—44no—
239C4×Dic59—44no—
240C4×Dic59—44no—
241C4×Dic59—44no—
242C23×C59—21no—
243C23×C59—22no—
244C23×C59—21no—
245C23×C59—22no—
246C23×C59—22no—
247C23×C59—28no—
248C23×C59—28no—
249C23×C59—21no—
250C23×C59—22no—
251C23×C59—24no—
252C23×C59—22no—
253C23×C59—21no—
254C23×C59—22no—
255C23×C59—22no—
256C23×C59—24no—
257C23×C59—28no—
258C23×C59—44no—
259C23×C59—44no—
260C23×C59—44no—
261C23×C59—48no—
262C23×C59—48no—
263C23×C59—84no—
264C23×C59—84no—
265C23×C59C23×C414yes—
266C23×C59C23×C412yes—
267C23×C59C23×C412yes—
268C23×C59C23×C412yes—
269C23×C59H(5,𝔽2)14yes—
270C23×C59H(5,𝔽2)12yes—
271C23×C592−1+412yes—
272C23×C59C2511yescharacteristic
273D4×C59—216no—
274D4×C59—48no—
275C2×C4×C59—28no—
276C2×C4×C59—28no—
277C2×C4×C59—28no—
278C2×C4×C59—22no—
279C2×C4×C59—22no—
280C2×C4×C59—24no—
281C2×C4×C59—22no—
282C2×C4×C59—22no—
283C2×C4×C59—22no—
284C2×C4×C59—22no—
285C2×C4×C59—24no—
286C2×C4×C59—44no—
287C2×C4×C59—44no—
288C2×C4×C59—44no—
289C2×C4×C59—44no—
290C2×C4×C59—44no—
291C2×C4×C59—44no—
292C2×C4×C59C23×C414yes—
293C2×C4×C59C23×C414yes—
294C2×C4×C59C23×C412yes—
295C2×C4×C59C23×C412yes—
296C2×C4×C59C23×C412yes—
297C2×C4×C59C23×C412yes—
298C2×C4×C59C23×C414yes—
299C2×Dic59—24no—
300C2×Dic59—24no—
301C2×Dic59—24no—
302C2×Dic59—24no—
303C2×Dic59—24no—
304C2×Dic59—24no—
305C2×Dic59—24no—
306C2×Dic59—24no—
307C2×Dic59—24no—
308C2×Dic59—24no—
309C2×Dic59—24no—
310C2×Dic59—24no—
311C2×Dic59—88no—
312C2×Dic59—88no—
313#34376—591nomaximal, Sylow
314C22×C59—22no—
315C22×C59—22no—
316C22×C59—22no—
317C22×C59—22no—
318C22×C59—24no—
319C22×C59—24no—
320C22×C59—24no—
321C22×C59—24no—
322C22×C59—22no—
323C22×C59—24no—
324C22×C59—22no—
325C22×C59—24no—
326C22×C59—22no—
327C22×C59—24no—
328C22×C59—416no—
329C22×C59—44no—
330C22×C59—42no—
331C22×C59—42no—
332C22×C59—44no—
333C22×C59—88no—
334C22×C59#51814yes—
335C22×C59#52014yes—
336C22×C59C24×C411yescharacteristic
337C22×C59C2×H(5,𝔽2)12yes—
338C22×C59C2×H(5,𝔽2)11yescharacteristic
339C22×C59C2×2−1+411yescharacteristic
340C22×C59#58512yes—
341C4×C59—22no—
342C4×C59—22no—
343C4×C59—22no—
344C4×C59—22no—
345C4×C59—24no—
346C4×C59—24no—
347C4×C59—24no—
348Dic59—44no—
349Dic59—44no—
350Dic59—44no—
351Dic59—44no—
352C22×#123D5911yescharacteristic
353#2376—594no—
354#2359—594no—
355#2345—592no—
356#2342—592no—
357#2342—592no—
358D4×C22⋊C4—592no—
359#2335—594no—
360#2322—594no—
361#2316—591no—
362#2315—591no—
363#2313—591no—
364#2312—591no—
365#2280—591no—
366C2×#380—591no—
367C2×C59—24no—
368C2×C59—24no—
369C2×C59—42no—
370C2×C59—44no—
371C2×C59C2×#51811yescharacteristic
372C2×C59C2×#52011yescharacteristic
373C2×C59#342811yescharacteristic
374C2×C59#353412yes—
375C2×C59#353512yes—
376C23×D4C2×D5911yescharacteristic
377C24×C4C2×D5911yescharacteristic
378C2×#123Dic59116yescomplemented
379C2×#123C2×D5912yes—
380C2×#123C2×D5912yes—
381C2×#123C2×D5912yes—
382C2×#123C2×D5912yes—
383C2×C4×D4—594no—
384C2×#117—592no—
385C2×#117—592no—
386C22×C4⋊C4—592no—
387C22×C4⋊C4C2×D5911yescharacteristic
388C22×C4⋊C4C2×D5911yescharacteristic
389C22×C22⋊C4—592no—
390C22×C22⋊C4—592no—
391C22×C22⋊C4C2×D5911yescharacteristic
392C22×C22⋊C4C2×D5911yescharacteristic
393C22×C22⋊C4C2×D5911yescharacteristic
394#390—594no—
395#389—594no—
396#389—594no—
397#389—594no—
398#388—594no—
399#388—594no—
400#388—594no—
401#388—594no—
402#388—594no—
403#388—594no—
404#387—594no—
405#387—594no—
406#387—594no—
407#387—594no—
408#386—594no—
409#386—594no—
410#385—594no—
411#385—594no—
412#385—594no—
413#385—594no—
414#381—592no—
415#381—592no—
416#380—591no—
417#380—591no—
418#380—591no—
419#380—591no—
420#380—592no—
421#380—592no—
422#380—592no—
423#380—592no—
424#380—592no—
425#380—592no—
426#379—592no—
427#379—592no—
428C4×C4⋊C4—594no—
429C4×C22⋊C4—592no—
430C4×C22⋊C4—592no—
431C4×C22⋊C4—592no—
432C4×C22⋊C4—592no—
433C4×C22⋊C4—594no—
434C4×C22⋊C4—594no—
435C2×#95—592no—
436C59#3437611yescharacteristic, complemented, Sylow
437C25C22×D5911yescharacteristic
438C25C22×D5911yescharacteristic
439C22×D4—44no—
440C22×D4C2×Dic5918yes—
441C22×D4C22×D5912yes—
442C22×D4C22×D5912yes—
443C23×C4—44no—
444C23×C4—594no—
445C23×C4—594no—
446C23×C4C2×Dic5918yescomplemented
447C23×C4C22×D5911yescharacteristic
448C23×C4C22×D5911yescharacteristic
449C23×C4C22×D5911yescharacteristic
450C23×C4C22×D5911yescharacteristic
451C23×C4C22×D5911yescharacteristic
452C23×C4C22×D5911yescharacteristic
453C23×C4C22×D5911yescharacteristic
454C23×C4C22×D5911yescharacteristic
455C23×C4C22×D5911yescharacteristic
456#123C2×Dic59116yescomplemented
457#123C2×Dic59116yescomplemented
458#123C2×Dic59116yescomplemented
459#123C2×Dic59116yescomplemented
460C4×D4—2368no—
461#117—2364no—
462#117—2364no—
463C2×C4⋊C4—592no—
464C2×C4⋊C4—594no—
465C2×C4⋊C4—592no—
466C2×C4⋊C4—592no—
467C2×C4⋊C4—592no—
468C2×C4⋊C4—594no—
469C2×C4⋊C4—594no—
470C2×C4⋊C4—594no—
471C2×C4⋊C4—2364no—
472C2×C4⋊C4C2×Dic5918yescomplemented
473C2×C4⋊C4C2×Dic5918yescomplemented
474C2×C4⋊C4C22×D5912yes—
475C2×C4⋊C4C22×D5912yes—
476C2×C4⋊C4C22×D5912yes—
477C2×C4⋊C4C22×D5912yes—
478C2×C22⋊C4—592no—
479C2×C22⋊C4—592no—
480C2×C22⋊C4—592no—
481C2×C22⋊C4—594no—
482C2×C22⋊C4—592no—
483C2×C22⋊C4—594no—
484C2×C22⋊C4—594no—
485C2×C22⋊C4—594no—
486C2×C22⋊C4—594no—
487C2×C22⋊C4—594no—
488C2×C22⋊C4—2364no—
489C2×C22⋊C4—2364no—
490C2×C22⋊C4C2×Dic5918yescomplemented
491C2×C22⋊C4C2×Dic5918yescomplemented
492C2×C22⋊C4C2×Dic5918yescomplemented
493C2×C22⋊C4C22×D5912yes—
494C2×C22⋊C4C22×D5912yes—
495C2×C22⋊C4C22×D5912yes—
496C2×C22⋊C4C22×D5912yes—
497C2×C22⋊C4C22×D5912yes—
498C2×C22⋊C4C22×D5912yes—
499C2×C42—594no—
500C2×C42—594no—
501C2×C42—594no—
502C2×C42—594no—
503#95—594no—
504#95—592no—
505#95—592no—
506#95—592no—
507#95—594no—
508#95—592no—
509#95—594no—
510#95—594no—
511#95—594no—
512#95—594no—
513#95—594no—
514#95—594no—
515C24—24no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—42no—
521C24—42no—
522C24—42no—
523C24C22×Dic5914yes—
524C24C22×Dic5914yes—
525C24C23×D5911yescharacteristic
526C24C23×D5912yes—
527C24C23×D5911yescharacteristic
528C24C23×D5911yescharacteristic
529C2×D4—28no—
530C2×D4—44no—
531C2×D4—416no—
532C2×D4C22×Dic5918yes—
533C2×D4C22×Dic5918yes—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—416no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—594no—
546C22×C4—594no—
547C22×C4—594no—
548C22×C4—594no—
549C22×C4—1188no—
550C22×C4—2364no—
551C22×C4—2364no—
552C22×C4—2364no—
553C22×C4—2364no—
554C22×C4—2364no—
555C22×C4C22×Dic5914yes—
556C22×C4C22×Dic5914yes—
557C22×C4C22×Dic5914yes—
558C22×C4C22×Dic5914yes—
559C22×C4C22×Dic5914yes—
560C22×C4C22×Dic5914yes—
561C22×C4C22×Dic5914yes—
562C22×C4C22×Dic5914yes—
563C22×C4C22×Dic5914yes—
564C22×C4C23×D5911yescharacteristic
565C22×C4C23×D5912yes—
566C22×C4C23×D5912yes—
567C22×C4C23×D5912yes—
568C22×C4C23×D5911yescharacteristic
569C22×C4C23×D5911yescharacteristic
570C22×C4C23×D5911yescharacteristic
571C4⋊C4—2362no—
572C4⋊C4—2364no—
573C4⋊C4—2362no—
574C4⋊C4—2362no—
575C4⋊C4—2362no—
576C4⋊C4—2364no—
577C4⋊C4—2364no—
578C4⋊C4—2364no—
579C4⋊C4C22×Dic5918yes—
580C4⋊C4C22×Dic5918yes—
581C4⋊C4C22×Dic5918yes—
582C4⋊C4C22×Dic5918yes—
583C22⋊C4—1188no—
584C22⋊C4—1184no—
585C22⋊C4—1184no—
586C22⋊C4—1184no—
587C22⋊C4—1184no—
588C22⋊C4—2364no—
589C22⋊C4—2364no—
590C22⋊C4—2364no—
591C22⋊C4—2364no—
592C22⋊C4—2364no—
593C22⋊C4C22×Dic5918yes—
594C22⋊C4C22×Dic5918yes—
595C22⋊C4C22×Dic5918yes—
596C22⋊C4C22×Dic5918yes—
597C22⋊C4C22×Dic5918yes—
598C22⋊C4C22×Dic5918yes—
599C42—2364no—
600C42—2364no—
601C42—2364no—
602C42—2364no—
603C23—22no—
604C23—21no—
605C23—21no—
606C23—22no—
607C23—22no—
608C23—24no—
609C23—22no—
610C23—21no—
611C23—22no—
612C23—21no—
613C23—22no—
614C23—22no—
615C23—24no—
616C23—28no—
617C23—28no—
618C23—28no—
619C23—44no—
620C23—44no—
621C23—44no—
622C23—48no—
623C23—48no—
624C23—84no—
625C23—84no—
626C23C23×Dic5914yes—
627C23C23×Dic5912yes—
628C23C23×Dic5912yes—
629C23C23×Dic5912yes—
630C23#1427377214yes—
631C23#1427377312yes—
632C23#1427377412yes—
633C23C24×D5911yescharacteristic
634D4—216no—
635D4—48no—
636C2×C4—22no—
637C2×C4—24no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—24no—
644C2×C4—28no—
645C2×C4—28no—
646C2×C4—28no—
647C2×C4—44no—
648C2×C4—44no—
649C2×C4—44no—
650C2×C4—44no—
651C2×C4—44no—
652C2×C4—44no—
653C2×C4—1184no—
654C2×C4—1184no—
655C2×C4—1184no—
656C2×C4—1184no—
657C2×C4—1184no—
658C2×C4—1184no—
659C2×C4—1184no—
660C2×C4—1184no—
661C2×C4—1184no—
662C2×C4—1184no—
663C2×C4—1184no—
664C2×C4—1184no—
665C2×C4—4728no—
666C2×C4—4728no—
667C2×C4C23×Dic5914yes—
668C2×C4C23×Dic5914yes—
669C2×C4C23×Dic5912yes—
670C2×C4C23×Dic5912yes—
671C2×C4C23×Dic5912yes—
672C2×C4C23×Dic5912yes—
673C2×C4C23×Dic5914yes—
674C22—24no—
675C22—24no—
676C22—22no—
677C22—24no—
678C22—24no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—24no—
684C22—22no—
685C22—24no—
686C22—22no—
687C22—24no—
688C22—416no—
689C22—44no—
690C22—42no—
691C22—42no—
692C22—44no—
693C22—88no—
694C22#1683787714yes—
695C22#1683788514yes—
696C22C24×Dic5911yescharacteristic
697C22C2×#1427377212yes—
698C22C2×#1427377311yescharacteristic
699C22C2×#1427377411yescharacteristic
700C22#1683823812yes—
701C4—22no—
702C4—22no—
703C4—22no—
704C4—22no—
705C4—24no—
706C4—24no—
707C4—24no—
708C4—2364no—
709C4—2364no—
710C4—2364no—
711C4—2364no—
712C2—24no—
713C2—24no—
714C2—42no—
715C2—44no—
716C2C2×#1683787711yescharacteristic
717C2C2×#1683788511yescharacteristic
718C2#2143729911yescharacteristic
719C2#2143829012yes—
720C2#2143830912yes—
subgroupG/H
center, FrattiniC23C24×D59
commutatorC22×C59C24×C4
FittingC22×#123×C59C2
socle, cosocleC23×C59C25
prime radicalC23×D4×C59C22
hypercenterC22×#123D59
hypocenterC59#34376
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. #21427244C2semidirect
2. #21427092C2semidirect
3. #21426973C2semidirect
4. #21426945C2semidirect
5. #21426945C2semidirect
7. #21426890C2semidirect
8. #21426768C2semidirect
9. #21426714C2semidirect
10. #21426710C2semidirect
11. #21426699C2semidirect
12. #21426694C2semidirect
13. #21426479C2semidirect
14. C2×#16837262C2semidirect
18. C2×#14273686C22semidirect
19. C22×C4⋊Dic59C22semidirect
23. #16837301C22semidirect
24. #16837301C22semidirect
25. #16837301C22semidirect
26. #16837295C22semidirect
27. #16837295C22semidirect
28. #16837295C22semidirect
29. #16837295C22semidirect
30. #16837295C22semidirect
31. #16837295C22semidirect
32. #16837288C22semidirect
33. #16837288C22semidirect
34. #16837288C22semidirect
35. #16837288C22semidirect
38. #16837277C22semidirect
39. #16837277C22semidirect
40. #16837277C22semidirect
41. #16837277C22semidirect
43. #16837265C22semidirect
51. #16837262C22semidirect
52. #16837262C22semidirect
53. #16837262C22semidirect
56. C4⋊C4×Dic59C22semidirect
57. C22⋊C4×Dic59C22semidirect
58. C22⋊C4×Dic59C22semidirect
62. C4×C22⋊Dic59C22semidirect
63. C2×C59⋊#95C22semidirect
66. C2×#123×C59C4semidirect
125. C23×C4×C59C2×C4semidirect
135. #123×C59C2×C4semidirect
136. #123×C59C2×C4semidirect
137. #123×C59C2×C4semidirect
138. #123×C59C2×C4semidirect
139. C2×C4⋊C4×C59C2×C4semidirect
140. C2×C4⋊C4×C59C2×C4semidirect
145. C2×C22⋊C4×C59C2×C4semidirect
146. C2×C22⋊C4×C59C2×C4semidirect
147. C2×C22⋊C4×C59C2×C4semidirect
378. C2×#123Dic59semidirect
436. C59#34376semidirect
446. C23×C4C2×Dic59semidirect
456. #123C2×Dic59semidirect
457. #123C2×Dic59semidirect
458. #123C2×Dic59semidirect
459. #123C2×Dic59semidirect
472. C2×C4⋊C4C2×Dic59semidirect
473. C2×C4⋊C4C2×Dic59semidirect
490. C2×C22⋊C4C2×Dic59semidirect
491. C2×C22⋊C4C2×Dic59semidirect
492. C2×C22⋊C4C2×Dic59semidirect

Maximal subgroups

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

subgroupindex
#214272442
#214270922
#214269732
#214269452
D4×C22⋊Dic592
#214268902
#214267682
#214267142
#214267102
#214266992
#214266942
#214264792
C2×#168372622
C22×#123×C592
#3437659