Finite Group Databasebeta

← #29887028

Subgroups — #29887028

Order 15616.

2970 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840320C211yesmaximal, characteristic, complemented
2C22×#14519761C211yesmaximal, characteristic, complemented
3#21454099C212yesmaximal, complemented
4#21452506C214yesmaximal, complemented
5#21452502C214yesmaximal, complemented
6#21452139C214yesmaximal, complemented
7#21452137C214yesmaximal, complemented
8#21451565C212yesmaximal, complemented
9#21450750C211yesmaximal, characteristic, complemented
10#21450312C211yesmaximal, characteristic, complemented
11#21450311C211yesmaximal, characteristic, complemented
12#21449143C212yesmaximal, complemented
13#21449130C212yesmaximal, complemented
14#21448414C211yesmaximal, characteristic, complemented
15C61×#2539C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C22×D4×D61C2212yes—
18C24×Dic61C2211yescharacteristic, complemented
19#16840320—28no—
20C2×#14519762C2212yescomplemented
21C2×#14519761—28no—
22C2×#14519761C2214yescomplemented
23C2×#14519761C2214yescomplemented
24C2×#14519760C2212yescomplemented
25C2×#14519759C2212yescomplemented
26C2×#14519751C2211yescharacteristic
27C2×#14519749C2212yes—
28C2×#14519749C2214yescomplemented
29C2×#14519747C2212yescomplemented
30C2×#14519746C2212yescomplemented
31C2×#14519745C2212yescomplemented
32C2×#14519745C2214yescomplemented
33C22×C4⋊Dic61C2211yescharacteristic, complemented
34C22×C4⋊Dic61C2211yescharacteristic, complemented
35C22×#11758198C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37#16839698C2212yescomplemented
38#16839695C2214yescomplemented
39#16839689C2214yescomplemented
40#16839687C2214yescomplemented
41#16839685C2214yescomplemented
42#16839684C2214yescomplemented
43#16839679C2214yescomplemented
44#16839678C2214yescomplemented
45#16839677C2214yescomplemented
46#16839671C2214yes—
47#16839671C2212yescomplemented
48#16839670C2214yes—
49#16839665C2212yescomplemented
50#16839664C2212yescomplemented
51#16839662C2214yescomplemented
52#16839653C2214yescomplemented
53#16839651C2214yescomplemented
54#16839642C2212yescomplemented
55#16839642C2214yescomplemented
56#16839642C2212yescomplemented
57#16839639C2212yescomplemented
58#16839639C2214yescomplemented
59#16839639C2212yescomplemented
60#16839638C2214yescomplemented
61#16839633C2214yescomplemented
62#16839628C2212yescomplemented
63#16839627C2212yescomplemented
64#16839620C2212yescomplemented
65#16839620C2214yescomplemented
66#16839617C2212yes—
67#16839617C2214yescomplemented
68C4×C22⋊Dic61C2211yescharacteristic, complemented
69C2×#123×C61C2212yescomplemented
70C2×#121×C61C2211yescharacteristic
71C2×#120×C61C2212yescomplemented
72C22×C22⋊C4×C61C2211yescharacteristic, complemented
73C61×#399C2212yescomplemented
74C61×#392C2212yescomplemented
75C61×#390C2214yescomplemented
76C4×C22⋊C4×C61C2211yescharacteristic, complemented
77C24×D61C2311yescharacteristic
78C24×D61C2312yes—
79C22×D244C2311yescharacteristic
80C22×D244C2312yes—
81C22×C22⋊D61—24no—
82C22×C22⋊D61—44no—
83C22×C22⋊D61C2312yes—
84C22×C22⋊D61C2314yes—
85C22×C22⋊D61C2314yes—
86C22×C22⋊D61C2312yes—
87C22×C22⋊D61C2312yes—
88C2×D4×D61—28no—
89C2×D4×D61—44no—
90C2×D4×D61—44no—
91C23×Dic61—24no—
92C23×Dic61—44no—
93C23×Dic61C2314yes—
94C23×Dic61C2311yescharacteristic
95C23×Dic61C2311yescharacteristic
96C23×Dic61C2311yescharacteristic
97C22×C4×D61C2312yes—
98#14519762—28no—
99#14519761—216no—
100#14519761—216no—
101#14519760—44no—
102#14519759—28no—
103#14519751—24no—
104#14519749—28no—
105#14519749—48no—
106#14519747—28no—
107#14519746—44no—
108#14519745—28no—
109#14519745—48no—
110C2×C4⋊Dic61—24no—
111C2×C4⋊Dic61—24no—
112C2×C4⋊Dic61C2314yes—
113C2×C4⋊Dic61C2312yes—
114C2×C4⋊Dic61C2312yes—
115C2×C4⋊Dic61C2311yescharacteristic
116C2×#11758196C2312yes—
117C2×#11758196C2314yes—
118C2×#11758196C2314yes—
119C2×C22⋊Dic61C2312yes—
120C2×C22⋊Dic61C2312yes—
121C2×C22⋊Dic61C2314yes—
122C2×C22⋊Dic61C2314yes—
123C2×C22⋊Dic61C2314yes—
124C2×#11758198—24no—
125C2×#11758198D418yescomplemented
126C2×#11758198C2312yes—
127C2×#11758198C2312yes—
128C2×#11758198C2314yes—
129C2×#11758198C2314yes—
130C2×#11758198C2314yes—
131C2×#11758198C2314yes—
132C2×#11758198C2314yes—
133C2×#11758198C2314yes—
134C2×#11758198C2312yes—
135C2×#11758198C2312yes—
136C2×C4×Dic61C2312yes—
137#14519684C2314yes—
138#14519684C2314yes—
139#14519684C2312yes—
140#14519684C2314yes—
141#14519684C2314yes—
142#14519684C2314yes—
143C25×C61C2311yescharacteristic
144C22×D4×C61C2312yes—
145C22×D4×C61C2311yescharacteristic
146C22×D4×C61C2314yes—
147C23×C4×C61C2311yescharacteristic
148C23×C4×C61C2311yescharacteristic
149#123×C61—44no—
150#121×C61—24no—
151#120×C61—44no—
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C4⋊C4×C61C2314yes—
154C2×C22⋊C4×C61—24no—
155C2×C22⋊C4×C61C2312yes—
156C2×C22⋊C4×C61C2312yes—
157C2×C22⋊C4×C61C2312yes—
158C2×C22⋊C4×C61C2312yes—
159C2×C22⋊C4×C61C2314yes—
160C2×C22⋊C4×C61C2314yes—
161C2×C42×C61C2312yes—
162#95×C61C2312yes—
163C24×C61—22no—
164C24×C61—24no—
165C24×C61—24no—
166C24×C61—42no—
167C24×C61C2412yes—
168C24×C61C2412yes—
169C24×C61C2411yescharacteristic
170C23×D61—24no—
171C23×D61—24no—
172C23×D61—42no—
173C23×D61—42no—
174C23×D61—42no—
175C23×D61—42no—
176C23×D61—44no—
177C23×D61—44no—
178C23×D61C2×D414yes—
179C23×D61C2412yes—
180C23×D61C2412yes—
181C2×D4×C61—24no—
182C2×D4×C61—24no—
183C2×D4×C61—24no—
184C2×D4×C61—28no—
185C2×D4×C61—22no—
186C2×D4×C61—44no—
187C2×D4×C61—42no—
188C2×D4×C61—44no—
189C22×C4×C61—22no—
190C22×C4×C61—24no—
191C22×C4×C61—42no—
192C22×C4×C61C2×D414yes—
193C22×C4×C61C2412yes—
194C22×C4×C61C2414yes—
195C22×C4×C61C2412yes—
196C22×C4×C61C2411yescharacteristic
197C22×C4×C61C2411yescharacteristic
198C2×C22⋊D61—24no—
199C2×C22⋊D61—24no—
200C2×C22⋊D61—24no—
201C2×C22⋊D61—28no—
202C2×C22⋊D61—24no—
203C2×C22⋊D61—28no—
204C2×C22⋊D61—28no—
205C2×C22⋊D61—24no—
206C2×C22⋊D61—42no—
207C2×C22⋊D61—42no—
208C2×C22⋊D61—44no—
209C2×C22⋊D61—44no—
210C2×C22⋊D61—44no—
211C2×C22⋊D61—44no—
212C2×C22⋊D61—416no—
213C22×Dic61—22no—
214C22×Dic61—22no—
215C22×Dic61—28no—
216C22×Dic61—28no—
217C22×Dic61—42no—
218C22×Dic61—44no—
219C22×Dic61—42no—
220C22×Dic61—42no—
221C22×Dic61—416no—
222C22×Dic61C2×D414yes—
223C22×Dic61C2412yes—
224C22×Dic61C2412yes—
225C22×Dic61C2412yes—
226C22×Dic61C2414yes—
227C22×Dic61C2412yes—
228D4×D61—432no—
229C2×D244—24no—
230C2×D244—22no—
231C2×D244—42no—
232C2×D244—42no—
233C2×D244—42no—
234C2×C4×D61—24no—
235C2×C4×D61—42no—
236C2×C4×D61—42no—
237C4⋊C4×C61—22no—
238C4⋊C4×C61—44no—
239C22⋊C4×C61—24no—
240C22⋊C4×C61—24no—
241C22⋊C4×C61—24no—
242C22⋊C4×C61—24no—
243C22⋊C4×C61—44no—
244C22⋊C4×C61—44no—
245C42×C61—42no—
246C22⋊Dic61—24no—
247C22⋊Dic61—24no—
248C22⋊Dic61—44no—
249C22⋊Dic61—44no—
250C22⋊Dic61—44no—
251#11758198—28no—
252#11758198—24no—
253#11758198—24no—
254#11758198—44no—
255#11758198—44no—
256#11758198—44no—
257#11758198—44no—
258#11758198—44no—
259#11758198C2×D418yes—
260#11758198C2×D418yes—
261C4⋊Dic61—24no—
262C4⋊Dic61—24no—
263C4⋊Dic61—22no—
264C4⋊Dic61—28no—
265#11758196—24no—
266#11758196—44no—
267#11758196—44no—
268C4×Dic61—42no—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61—28no—
272C23×C61—22no—
273C23×C61—24no—
274C23×C61—22no—
275C23×C61—24no—
276C23×C61—22no—
277C23×C61—24no—
278C23×C61—22no—
279C23×C61—22no—
280C23×C61—24no—
281C23×C61—416no—
282C23×C61—44no—
283C23×C61—44no—
284C23×C61C22×D412yes—
285C23×C61H(5,𝔽2)14yes—
286C23×C61H(5,𝔽2)14yes—
287C23×C61C2511yescharacteristic
288C22×D61—24no—
289C22×D61—22no—
290C22×D61—22no—
291C22×D61—24no—
292C22×D61—28no—
293C22×D61—22no—
294C22×D61—22no—
295C22×D61—24no—
296C22×D61—22no—
297C22×D61—24no—
298C22×D61—44no—
299C22×D61—44no—
300C22×D61—48no—
301C22×D61—84no—
302C22×D61—84no—
303C22×D61—88no—
304C22×D61—88no—
305C22×D61—88no—
306C22×D61C22×D414yes—
307D4×C61—48no—
308D4×C61—82no—
309D4×C61—88no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—24no—
315C2×C4×C61—24no—
316C2×C4×C61—24no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—24no—
320C2×C4×C61—44no—
321C2×C4×C61—44no—
322C2×C4×C61C22×D412yes—
323C2×C4×C61C22×D412yes—
324C22⋊D61—416no—
325C22⋊D61—48no—
326C22⋊D61—48no—
327C22⋊D61—84no—
328C22⋊D61—88no—
329C2×Dic61—24no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—24no—
335C2×Dic61—24no—
336C2×Dic61—24no—
337C2×Dic61—24no—
338C2×Dic61—22no—
339C2×Dic61—24no—
340C2×Dic61—44no—
341C2×Dic61—416no—
342C2×Dic61—44no—
343C2×Dic61—44no—
344C2×Dic61C22×D414yes—
345D244—48no—
346D244—82no—
347C4×D61—48no—
348#36721—611nomaximal, Sylow
349C22×C61—22no—
350C22×C61—22no—
351C22×C61—28no—
352C22×C61—24no—
353C22×C61—28no—
354C22×C61—416no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61—44no—
358C22×C61—42no—
359C22×C61—42no—
360C22×C61—42no—
361C22×C61—44no—
362C22×C61—44no—
363C22×C61#53514yes—
364C22×C61C23×D411yescharacteristic
365C22×C61C2×H(5,𝔽2)12yes—
366C22×C61C2×H(5,𝔽2)12yes—
367C22×C61#58512yes—
368C2×D61—24no—
369C2×D61—24no—
370C2×D61—24no—
371C2×D61—44no—
372C2×D61—44no—
373C2×D61—42no—
374C2×D61—42no—
375C2×D61—42no—
376C2×D61—44no—
377C2×D61—44no—
378C2×D61—88no—
379C2×D61—816no—
380C4×C61—22no—
381C4×C61—22no—
382C4×C61—42no—
383C4×C61—42no—
384C4×C61—44no—
385Dic61—24no—
386Dic61—42no—
387Dic61—42no—
388Dic61—42no—
389Dic61—44no—
390C2×#534—611no—
391C22×#123—611no—
392#2847—612no—
393#2706—614no—
394#2706—614no—
395#2678—614no—
396#2678—614no—
397#2618—612no—
398#2539—611no—
399#2539D6111yescharacteristic, complemented
400#2504—611no—
401#2504—611no—
402#2405—612no—
403#2403—612no—
404#2312—611no—
405C2×C61—24no—
406C2×C61—44no—
407C2×C61—82no—
408C2×C61C2×#53511yescharacteristic
409C2×C61#348411yescharacteristic
410C2×C61#348511yescharacteristic
411C2×C61#353414yes—
412D61—44no—
413D61—82no—
414C23×D4—611no—
415C23×D4—612no—
416C24×C4—611no—
417#534—1228no—
418C2×#123—612no—
419C2×#123—612no—
420C2×#123—612no—
421C2×#123—614no—
422C2×#123—614no—
423C2×#123—1228no—
424C2×#123C2×D6112yescomplemented
425C2×#121—612no—
426C2×#121—611no—
427C2×#121—614no—
428C2×#121C2×D6111yescharacteristic
429C2×#120—612no—
430C2×#120—612no—
431C2×#120—614no—
432C2×#120—612no—
433C2×#120C2×D6112yescomplemented
434C22×C4⋊C4—611no—
435C22×C4⋊C4—611no—
436C22×C22⋊C4—611no—
437C22×C22⋊C4—611no—
438C22×C22⋊C4C2×D6111yescharacteristic, complemented
439#399—612no—
440#399C2×D6112yescomplemented
441#398—614no—
442#397—614no—
443#397—614no—
444#396—614no—
445#396—614no—
446#394—614no—
447#394—614no—
448#394—614no—
449#392—614no—
450#392—614no—
451#392—612no—
452#392C2×D6112yescomplemented
453#390—612no—
454#390—614no—
455#390—612no—
456#390C2×D6114yescomplemented
457#388—614no—
458#388—614no—
459#386—612no—
460#386—614no—
461#386—612no—
462#386—612no—
463#386—614no—
464#386—612no—
465#386—614no—
466#385—614no—
467#382—612no—
468#382—612no—
469#380—612no—
470#380—614no—
471#379—612no—
472#379—614no—
473C4×C22⋊C4—611no—
474C4×C22⋊C4C2×D6111yescharacteristic, complemented
475C61#3672111yescharacteristic, complemented, Sylow
476C25—611no—
477C25—612no—
478C25C22×D6111yescharacteristic
479C22×D4—612no—
480C22×D4—614no—
481C22×D4—612no—
482C22×D4—614no—
483C22×D4—612no—
484C22×D4—611no—
485C22×D4—612no—
486C22×D4—1228no—
487C22×D4—1224no—
488C22×D4—2444no—
489C22×D4—2444no—
490C22×D4—2444no—
491C22×D4C22×D6112yes—
492C22×D4C22×D6111yescharacteristic
493C22×D4C22×D6114yes—
494C23×C4—611no—
495C23×C4—614no—
496C23×C4—611no—
497C23×C4—611no—
498C23×C4—612no—
499C23×C4—1224no—
500C23×C4—2444no—
501C23×C4C22×D6111yescharacteristic
502C23×C4C22×D6111yescharacteristic
503#123—44no—
504#123—12216no—
505#123—12216no—
506#123—1228no—
507#123—1228no—
508#123—2444no—
509#121—24no—
510#121—1228no—
511#121—1224no—
512#121—2448no—
513#120—44no—
514#120—1228no—
515#120—1228no—
516#120—2444no—
517#120—2448no—
518C2×C4⋊C4—612no—
519C2×C4⋊C4—612no—
520C2×C4⋊C4—614no—
521C2×C4⋊C4—612no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—614no—
524C2×C4⋊C4—614no—
525C2×C4⋊C4—1224no—
526C2×C4⋊C4—1224no—
527C2×C4⋊C4C22×D6111yescharacteristic
528C2×C4⋊C4C22×D6114yes—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—618no—
531C2×C22⋊C4—612no—
532C2×C22⋊C4—612no—
533C2×C22⋊C4—612no—
534C2×C22⋊C4—612no—
535C2×C22⋊C4—614no—
536C2×C22⋊C4—612no—
537C2×C22⋊C4—612no—
538C2×C22⋊C4—614no—
539C2×C22⋊C4—614no—
540C2×C22⋊C4—614no—
541C2×C22⋊C4—614no—
542C2×C22⋊C4—614no—
543C2×C22⋊C4—614no—
544C2×C22⋊C4—614no—
545C2×C22⋊C4—614no—
546C2×C22⋊C4—1224no—
547C2×C22⋊C4C22×D6112yes—
548C2×C22⋊C4C22×D6112yes—
549C2×C22⋊C4C22×D6112yes—
550C2×C22⋊C4C22×D6112yes—
551C2×C22⋊C4C22×D6114yes—
552C2×C22⋊C4C22×D6114yes—
553C2×C42—612no—
554C2×C42C22×D6112yes—
555#95—612no—
556#95—614no—
557#95—614no—
558#95—614no—
559#95—614no—
560#95—614no—
561#95C22×D6112yes—
562C24—22no—
563C24—24no—
564C24—24no—
565C24—42no—
566C24—612no—
567C24—614no—
568C24—612no—
569C24—1224no—
570C24—1224no—
571C24—2444no—
572C24—2444no—
573C24—2442no—
574C24—2442no—
575C24—2442no—
576C24—2442no—
577C24C23×D6112yes—
578C24C23×D6112yes—
579C24C23×D6111yescharacteristic
580C2×D4—24no—
581C2×D4—24no—
582C2×D4—24no—
583C2×D4—28no—
584C2×D4—22no—
585C2×D4—44no—
586C2×D4—42no—
587C2×D4—44no—
588C2×D4—1224no—
589C2×D4—1224no—
590C2×D4—1228no—
591C2×D4—1224no—
592C2×D4—1228no—
593C2×D4—1224no—
594C2×D4—1224no—
595C2×D4—1224no—
596C2×D4—1228no—
597C2×D4—1222no—
598C2×D4—2442no—
599C2×D4—2442no—
600C2×D4—2442no—
601C2×D4—2444no—
602C2×D4—2444no—
603C2×D4—2444no—
604C2×D4—2442no—
605C2×D4—2442no—
606C2×D4—2444no—
607C2×D4—24432no—
608C2×D4—24416no—
609C22×C4—22no—
610C22×C4—24no—
611C22×C4—42no—
612C22×C4—612no—
613C22×C4—614no—
614C22×C4—614no—
615C22×C4—612no—
616C22×C4—612no—
617C22×C4—612no—
618C22×C4—1224no—
619C22×C4—1228no—
620C22×C4—1222no—
621C22×C4—1222no—
622C22×C4—1228no—
623C22×C4—2442no—
624C22×C4—2442no—
625C22×C4—2442no—
626C22×C4—2444no—
627C22×C4—2442no—
628C22×C4—2442no—
629C22×C4—24416no—
630C22×C4D4×D6114yes—
631C22×C4C23×D6112yes—
632C22×C4C23×D6114yes—
633C22×C4C23×D6112yes—
634C22×C4C23×D6111yescharacteristic
635C22×C4C23×D6111yescharacteristic
636C4⋊C4—22no—
637C4⋊C4—44no—
638C4⋊C4—1228no—
639C4⋊C4—1224no—
640C4⋊C4—1224no—
641C4⋊C4—1224no—
642C4⋊C4—1222no—
643C4⋊C4—2444no—
644C4⋊C4—2444no—
645C22⋊C4—24no—
646C22⋊C4—24no—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—44no—
650C22⋊C4—44no—
651C22⋊C4—618no—
652C22⋊C4—618no—
653C22⋊C4—1224no—
654C22⋊C4—1228no—
655C22⋊C4—1224no—
656C22⋊C4—1224no—
657C22⋊C4—1224no—
658C22⋊C4—2444no—
659C22⋊C4—2444no—
660C22⋊C4—2444no—
661C22⋊C4—2444no—
662C22⋊C4—2444no—
663C22⋊C4—2444no—
664C22⋊C4—2444no—
665C22⋊C4—2444no—
666C42—42no—
667C42—2442no—
668C23—22no—
669C23—22no—
670C23—28no—
671C23—22no—
672C23—24no—
673C23—22no—
674C23—24no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—24no—
679C23—24no—
680C23—416no—
681C23—44no—
682C23—44no—
683C23—614no—
684C23—1228no—
685C23—1222no—
686C23—1222no—
687C23—1224no—
688C23—1224no—
689C23—1222no—
690C23—1222no—
691C23—1222no—
692C23—1224no—
693C23—1224no—
694C23—4888no—
695C23—4884no—
696C23—4884no—
697C23—4888no—
698C23—4888no—
699C23—2444no—
700C23—2444no—
701C23—2448no—
702C23C2×D4×D6112yes—
703C23#1451982214yes—
704C23#1451982314yes—
705C23C24×D6111yescharacteristic
706D4—48no—
707D4—82no—
708D4—88no—
709D4—4882no—
710D4—4884no—
711D4—4888no—
712D4—2448no—
713D4—24416no—
714D4—2448no—
715D4—2448no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—614no—
729C2×C4—1224no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1224no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1224no—
737C2×C4—1224no—
738C2×C4—1224no—
739C2×C4—1224no—
740C2×C4—2448no—
741C2×C4—2444no—
742C2×C4—24416no—
743C2×C4—2444no—
744C2×C4—2444no—
745C2×C4C2×D4×D6112yes—
746C2×C4C2×D4×D6112yes—
747C22—22no—
748C22—28no—
749C22—22no—
750C22—28no—
751C22—24no—
752C22—416no—
753C22—42no—
754C22—44no—
755C22—42no—
756C22—42no—
757C22—44no—
758C22—44no—
759C22—42no—
760C22—42no—
761C22—1224no—
762C22—1224no—
763C22—1224no—
764C22—4888no—
765C22—48816no—
766C22—2442no—
767C22—2444no—
768C22—2444no—
769C22—2442no—
770C22—2442no—
771C22—2444no—
772C22—2444no—
773C22#1684032514yes—
774C22C22×D4×D6111yescharacteristic
775C22C2×#1451982212yes—
776C22C2×#1451982312yes—
777C22#1684059712yes—
778C4—22no—
779C4—22no—
780C4—44no—
781C4—42no—
782C4—42no—
783C4—1224no—
784C4—2444no—
785C4—2442no—
786C4—2442no—
787C4—2442no—
788C2—24no—
789C2—44no—
790C2—82no—
791C2—4882no—
792C2—2444no—
793C2C2×#1684032511yescharacteristic
794C2#2145945211yescharacteristic
795C2#2145946011yescharacteristic
796C2#2146000514yes—
subgroupG/H
center, FrattiniC23C24×D61
commutator, socle, cosocleC23×C61C25
FittingC61×#2539C2
hypercenter#2539D61
hypocenterC61#36721
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2539

Complements

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

NH ≅ G/Ntype
1. C2×#16840320C2semidirect
2. C22×#14519761C2semidirect
3. #21454099C2semidirect
4. #21452506C2semidirect
5. #21452502C2semidirect
6. #21452139C2semidirect
7. #21452137C2semidirect
8. #21451565C2semidirect
9. #21450750C2semidirect
10. #21450312C2semidirect
11. #21450311C2semidirect
12. #21449143C2semidirect
13. #21449130C2semidirect
14. #21448414C2semidirect
15. C61×#2539C2semidirect
18. C24×Dic61C22semidirect
20. C2×#14519762C22semidirect
22. C2×#14519761C22semidirect
23. C2×#14519761C22semidirect
24. C2×#14519760C22semidirect
25. C2×#14519759C22semidirect
28. C2×#14519749C22semidirect
29. C2×#14519747C22semidirect
30. C2×#14519746C22semidirect
31. C2×#14519745C22semidirect
32. C2×#14519745C22semidirect
33. C22×C4⋊Dic61C22semidirect
34. C22×C4⋊Dic61C22semidirect
37. #16839698C22semidirect
38. #16839695C22semidirect
39. #16839689C22semidirect
40. #16839687C22semidirect
41. #16839685C22semidirect
42. #16839684C22semidirect
43. #16839679C22semidirect
44. #16839678C22semidirect
45. #16839677C22semidirect
47. #16839671C22semidirect
49. #16839665C22semidirect
50. #16839664C22semidirect
51. #16839662C22semidirect
52. #16839653C22semidirect
53. #16839651C22semidirect
54. #16839642C22semidirect
55. #16839642C22semidirect
56. #16839642C22semidirect
57. #16839639C22semidirect
58. #16839639C22semidirect
59. #16839639C22semidirect
60. #16839638C22semidirect
61. #16839633C22semidirect
62. #16839628C22semidirect
63. #16839627C22semidirect
64. #16839620C22semidirect
65. #16839620C22semidirect
67. #16839617C22semidirect
68. C4×C22⋊Dic61C22semidirect
69. C2×#123×C61C22semidirect
71. C2×#120×C61C22semidirect
72. C22×C22⋊C4×C61C22semidirect
73. C61×#399C22semidirect
74. C61×#392C22semidirect
75. C61×#390C22semidirect
76. C4×C22⋊C4×C61C22semidirect
125. C2×#11758198D4semidirect
399. #2539D61semidirect
424. C2×#123C2×D61semidirect
433. C2×#120C2×D61semidirect
438. C22×C22⋊C4C2×D61semidirect
440. #399C2×D61semidirect
452. #392C2×D61semidirect
456. #390C2×D61semidirect
474. C4×C22⋊C4C2×D61semidirect
475. C61#36721semidirect

Maximal subgroups

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

subgroupindex
C2×#168403202
C22×#145197612
#214540992
#214525062
#214525022
#214521392
#214521372
#214515652
#214507502
#214503122
#214503112
#214491432
#214491302
#214484142
C61×#25392
#3672161