Finite Group Databasebeta

← #29610675

Subgroups — #29610675

Order 15616.

1910 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839665C211yesmaximal, characteristic, complemented
2C2×#16839655C211yesmaximal, characteristic, complemented
3#21444076C211yesmaximal, characteristic, complemented
4#21444068C212yesmaximal, complemented
5#21444064C212yesmaximal, complemented
6#21444064C211yesmaximal, characteristic, complemented
7#21444060C212yesmaximal, complemented
8#21444060C212yesmaximal, complemented
9#21444060C211yesmaximal, characteristic, complemented
10#21444044C211yesmaximal, characteristic, complemented
11C2×C61×#392C211yesmaximal, characteristic
12C22×C4⋊Dic61C2211yescharacteristic
13C22×C4⋊Dic61C2211yescharacteristic
14C22×C22⋊Dic61C2211yescharacteristic
15C22×C22⋊Dic61C2211yescharacteristic
16C22×C22⋊Dic61C2212yes—
17C22×C22⋊Dic61C2212yes—
18C22×C22⋊Dic61C2212yes—
19C22×C22⋊Dic61C2212yes—
20C22×C22⋊Dic61C2212yes—
21C22×C4×Dic61C2211yescharacteristic
22#16839665—24no—
23#16839655—24no—
24C2×#14519684C2211yescharacteristic
25C2×#14519684C2211yescharacteristic
26C2×#14519684C2211yescharacteristic
27C2×#14519684C2212yes—
28C2×#14519684C2212yes—
29C2×#14519684C2212yes—
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C23×D4×C61C2211yescharacteristic
33C23×D4×C61C2212yes—
34C22×C22⋊C4×C61C2211yescharacteristic
35C22×C22⋊C4×C61C2212yes—
36C61×#392C418yescomplemented
37C2×#95×C61C2211yescharacteristic
38C23×Dic61C2311yescharacteristic
39C23×Dic61C2312yes—
40C23×Dic61C2311yescharacteristic
41C23×Dic61C2312yes—
42C23×Dic61C2311yescharacteristic
43C23×Dic61C2311yescharacteristic
44C2×C4⋊Dic61—22no—
45C2×C4⋊Dic61—22no—
46C2×C4⋊Dic61—42no—
47C2×C4⋊Dic61—42no—
48C2×C22⋊Dic61—22no—
49C2×C22⋊Dic61—22no—
50C2×C22⋊Dic61—24no—
51C2×C22⋊Dic61—24no—
52C2×C22⋊Dic61—42no—
53C2×C22⋊Dic61—42no—
54C2×C22⋊Dic61—42no—
55C2×C22⋊Dic61—42no—
56C2×C22⋊Dic61—42no—
57C2×C22⋊Dic61—42no—
58C2×C22⋊Dic61—42no—
59C2×C22⋊Dic61—42no—
60C2×C22⋊Dic61—42no—
61C2×C22⋊Dic61—42no—
62C2×C22⋊Dic61—42no—
63C2×C22⋊Dic61—42no—
64C2×C22⋊Dic61—42no—
65C2×C22⋊Dic61—42no—
66C2×C22⋊Dic61—42no—
67C2×C4×Dic61—42no—
68C2×C4×Dic61D414yescomplemented
69#14519684—22no—
70#14519684—22no—
71#14519684—22no—
72#14519684—42no—
73#14519684—42no—
74#14519684—42no—
75#14519684—42no—
76#14519684—42no—
77C25×C61C2311yescharacteristic
78C25×C61C2312yes—
79C22×D4×C61—22no—
80C22×D4×C61—22no—
81C22×D4×C61—42no—
82C22×D4×C61—42no—
83C22×D4×C61—42no—
84C22×D4×C61—42no—
85C22×D4×C61—42no—
86C22×D4×C61—42no—
87C22×D4×C61—42no—
88C22×D4×C61—42no—
89C22×D4×C61C2×C414yes—
90C22×D4×C61C2×C418yes—
91C23×C4×C61C2311yescharacteristic
92C23×C4×C61C2312yes—
93C23×C4×C61C2311yescharacteristic
94C2×C22⋊C4×C61—22no—
95C2×C22⋊C4×C61—22no—
96C2×C22⋊C4×C61—42no—
97C2×C22⋊C4×C61—42no—
98C2×C22⋊C4×C61C2×C414yes—
99C2×C22⋊C4×C61C2×C418yes—
100#95×C61C2×C414yes—
101C24×C61—21no—
102C24×C61—22no—
103C24×C61—21no—
104C24×C61—22no—
105C24×C61—22no—
106C24×C61—22no—
107C24×C61—22no—
108C24×C61—22no—
109C24×C61—21no—
110C24×C61—21no—
111C24×C61—22no—
112C24×C61—22no—
113C24×C61—22no—
114C24×C61—22no—
115C24×C61—22no—
116C24×C61—22no—
117C24×C61—22no—
118C24×C61—22no—
119C24×C61—22no—
120C24×C61—22no—
121C24×C61—22no—
122C24×C61—21no—
123C24×C61—21no—
124C24×C61—22no—
125C24×C61C22×C412yes—
126C24×C61C22×C414yes—
127C24×C61C2411yescharacteristic
128C2×D4×C61—28no—
129C2×D4×C61—48no—
130C2×D4×C61—48no—
131C2×D4×C61—48no—
132C2×D4×C61—48no—
133C2×D4×C61—44no—
134C2×D4×C61—44no—
135C2×D4×C61—48no—
136C2×D4×C61—48no—
137C2×D4×C61—48no—
138C2×D4×C61—48no—
139C2×D4×C61—48no—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—22no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61C22×C414yes—
153C22×C4×C61C22×C412yes—
154C22×C4×C61C22×C412yes—
155C22×C4×C61C2×D412yes—
156C22×C4×C61#4112yes—
157C22×Dic61—21no—
158C22×Dic61—22no—
159C22×Dic61—22no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—22no—
163C22×Dic61—22no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—22no—
168C22×Dic61—22no—
169C22×Dic61—21no—
170C22×Dic61—22no—
171C22×Dic61—22no—
172C22×Dic61—22no—
173C22×Dic61—22no—
174C22×Dic61—22no—
175C22×Dic61—22no—
176C22×Dic61—22no—
177C22×Dic61—22no—
178C22×Dic61—22no—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—22no—
188C22×Dic61—21no—
189C22×Dic61C2×D412yes—
190C22×Dic61C2×D412yes—
191C22⋊C4×C61—28no—
192C22⋊C4×C61—48no—
193C22⋊Dic61—44no—
194C22⋊Dic61—44no—
195C22⋊Dic61—48no—
196C22⋊Dic61—48no—
197C22⋊Dic61—48no—
198C22⋊Dic61—48no—
199C22⋊Dic61—48no—
200C4⋊Dic61—44no—
201C4⋊Dic61—44no—
202C4×Dic61—44no—
203C23×C61—22no—
204C23×C61—24no—
205C23×C61—24no—
206C23×C61—24no—
207C23×C61—22no—
208C23×C61—24no—
209C23×C61—24no—
210C23×C61—24no—
211C23×C61—24no—
212C23×C61—24no—
213C23×C61—22no—
214C23×C61—24no—
215C23×C61—41no—
216C23×C61—42no—
217C23×C61—42no—
218C23×C61—42no—
219C23×C61—41no—
220C23×C61—42no—
221C23×C61—41no—
222C23×C61—41no—
223C23×C61—41no—
224C23×C61—42no—
225C23×C61—41no—
226C23×C61—42no—
227C23×C61—42no—
228C23×C61—42no—
229C23×C61—42no—
230C23×C61—41no—
231C23×C61—42no—
232C23×C61—42no—
233C23×C61—42no—
234C23×C61—42no—
235C23×C61—41no—
236C23×C61—42no—
237C23×C61—42no—
238C23×C61—42no—
239C23×C61—42no—
240C23×C61—42no—
241C23×C61—42no—
242C23×C61—42no—
243C23×C61—42no—
244C23×C61—42no—
245C23×C61—42no—
246C23×C61—42no—
247C23×C61—42no—
248C23×C61—42no—
249C23×C61—42no—
250C23×C61—42no—
251C23×C61—42no—
252C23×C61—42no—
253C23×C61—42no—
254C23×C61—42no—
255C23×C61—42no—
256C23×C61—42no—
257C23×C61—42no—
258C23×C61—42no—
259C23×C61—42no—
260C23×C61—42no—
261C23×C61C23×C411yescharacteristic
262C23×C61C22×D411yescharacteristic
263C23×C61C2×#4111yescharacteristic
264C23×C61H(5,𝔽2)12yes—
265C23×C61H(5,𝔽2)12yes—
266C23×C61H(5,𝔽2)12yes—
267C23×C61H(5,𝔽2)12yes—
268C23×C61H(5,𝔽2)11yescharacteristic
269C23×C61H(5,𝔽2)11yescharacteristic
270C23×C61H(5,𝔽2)11yescharacteristic
271C23×C612−1+411yescharacteristic
272D4×C61—416no—
273D4×C61—432no—
274C2×C4×C61—24no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—24no—
278C2×C4×C61—22no—
279C2×C4×C61—24no—
280C2×C4×C61—24no—
281C2×C4×C61—24no—
282C2×C4×C61—24no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—42no—
286C2×C4×C61—42no—
287C2×C4×C61—42no—
288C2×C4×C61—42no—
289C2×C4×C61—42no—
290C2×C4×C61C4×D414yes—
291C2×Dic61—22no—
292C2×Dic61—22no—
293C2×Dic61—22no—
294C2×Dic61—22no—
295C2×Dic61—22no—
296C2×Dic61—22no—
297C2×Dic61—42no—
298C2×Dic61—42no—
299C2×Dic61—42no—
300C2×Dic61—42no—
301C2×Dic61—41no—
302C2×Dic61—42no—
303C2×Dic61—41no—
304C2×Dic61—42no—
305C2×Dic61—42no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—42no—
311C2×Dic61—42no—
312C2×Dic61—42no—
313C2×Dic61—42no—
314C2×Dic61—42no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317C2×Dic61—42no—
318C2×Dic61—42no—
319C2×Dic61—42no—
320C2×Dic61—42no—
321C2×Dic61—42no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324C2×Dic61—42no—
325#14623—611nomaximal, Sylow
326C22×C61—44no—
327C22×C61—42no—
328C22×C61—42no—
329C22×C61—44no—
330C22×C61—42no—
331C22×C61—44no—
332C22×C61—44no—
333C22×C61—44no—
334C22×C61—44no—
335C22×C61—44no—
336C22×C61—44no—
337C22×C61—44no—
338C22×C61—82no—
339C22×C61—81no—
340C22×C61—81no—
341C22×C61—82no—
342C22×C61—82no—
343C22×C61—82no—
344C22×C61—82no—
345C22×C61—82no—
346C22×C61—82no—
347C22×C61—82no—
348C22×C61—81no—
349C22×C61—82no—
350C22×C61—81no—
351C22×C61—82no—
352C22×C61C2×C4×D411yescharacteristic
353C22×C61#51812yes—
354C22×C61#51811yescharacteristic
355C22×C61#51812yes—
356C22×C61#52011yescharacteristic
357C22×C61#53411yescharacteristic
358C22×C61#53511yescharacteristic
359C22×C61#53511yescharacteristic
360C22×C61#53511yescharacteristic
361C22×C61#53511yescharacteristic
362C22×C61#53711yescharacteristic
363C22×C61#53812yes—
364C22×C61#54011yescharacteristic
365C22×C61#54012yes—
366C22×C61#54211yescharacteristic
367C22×C61#56012yes—
368C22×C61#56012yes—
369C22×C61#56012yes—
370C22×C61#56012yes—
371C22×C61#56012yes—
372C22×C61H(3,𝔽4)12yes—
373C22×C61#56212yes—
374C22×C61#56212yes—
375C4×C61—24no—
376C4×C61—42no—
377C4×C61—44no—
378Dic61—42no—
379Dic61—42no—
380Dic61—82no—
381Dic61—81no—
382Dic61—82no—
383Dic61—81no—
384C2×#392D6111yescharacteristic
385C2×#390—611no—
386C2×#388—611no—
387#1442—611no—
388#1440—612no—
389#1439—612no—
390#1439—611no—
391#1438—612no—
392#1438—612no—
393#1438—611no—
394#1434—611no—
395C2×C61—84no—
396C2×C61—82no—
397C2×C61#232111yescharacteristic
398C2×C61#232411yescharacteristic
399C2×C61#232811yescharacteristic
400C2×C61#237512yes—
401C2×C61#237712yes—
402C2×C61#281311yescharacteristic
403C2×C61#281511yescharacteristic
404C2×C61#281811yescharacteristic
405C2×C61#281911yescharacteristic
406C2×C61#282812yes—
407C2×C61#282912yes—
408C23×D4C2×D6111yescharacteristic
409C23×D4C2×D6112yes—
410C22×C4⋊C4—611no—
411C22×C4⋊C4—611no—
412C22×C22⋊C4—611no—
413C22×C22⋊C4—611no—
414C22×C22⋊C4—612no—
415C22×C22⋊C4—612no—
416C22×C22⋊C4—612no—
417C22×C22⋊C4—612no—
418C22×C22⋊C4—612no—
419C22×C22⋊C4C2×D6111yescharacteristic
420C22×C22⋊C4C2×D6112yes—
421C22×C42—611no—
422#392Dic6118yescomplemented
423#390—1224no—
424#388—1224no—
425C2×#95—611no—
426C2×#95—611no—
427C2×#95—611no—
428C2×#95—612no—
429C2×#95—612no—
430C2×#95—612no—
431C2×#95—612no—
432C2×#95—612no—
433C2×#95C2×D6111yescharacteristic
434C61#1462311yescharacteristic, complemented, Sylow
435C25C22×D6111yescharacteristic
436C25C22×D6112yes—
437C22×D4—22no—
438C22×D4—22no—
439C22×D4—42no—
440C22×D4—42no—
441C22×D4—42no—
442C22×D4—42no—
443C22×D4—42no—
444C22×D4—42no—
445C22×D4—42no—
446C22×D4—42no—
447C22×D4C2×Dic6114yes—
448C22×D4C2×Dic6118yes—
449C23×C4—611no—
450C23×C4—611no—
451C23×C4—611no—
452C23×C4—612no—
453C23×C4—611no—
454C23×C4—612no—
455C23×C4C22×D6111yescharacteristic
456C23×C4C22×D6112yes—
457C23×C4C22×D6111yescharacteristic
458C2×C4⋊C4—1222no—
459C2×C4⋊C4—1222no—
460C2×C4⋊C4—2442no—
461C2×C4⋊C4—2442no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—42no—
465C2×C22⋊C4—42no—
466C2×C22⋊C4—1222no—
467C2×C22⋊C4—1222no—
468C2×C22⋊C4—1224no—
469C2×C22⋊C4—1224no—
470C2×C22⋊C4—2442no—
471C2×C22⋊C4—2442no—
472C2×C22⋊C4—2442no—
473C2×C22⋊C4—2442no—
474C2×C22⋊C4—2442no—
475C2×C22⋊C4—2442no—
476C2×C22⋊C4—2442no—
477C2×C22⋊C4—2442no—
478C2×C22⋊C4—2442no—
479C2×C22⋊C4—2442no—
480C2×C22⋊C4—2442no—
481C2×C22⋊C4—2442no—
482C2×C22⋊C4—2442no—
483C2×C22⋊C4—2442no—
484C2×C22⋊C4—2442no—
485C2×C22⋊C4C2×Dic6114yes—
486C2×C22⋊C4C2×Dic6118yes—
487C2×C42—614no—
488C2×C42—2442no—
489#95—1222no—
490#95—1222no—
491#95—1222no—
492#95—2442no—
493#95—2442no—
494#95—2442no—
495#95—2442no—
496#95—2442no—
497#95C2×Dic6114yes—
498C24—21no—
499C24—22no—
500C24—21no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—21no—
517C24—21no—
518C24—21no—
519C24—22no—
520C24—22no—
521C24—21no—
522C24C22×Dic6112yes—
523C24C22×Dic6114yes—
524C24C23×D6111yescharacteristic
525C2×D4—28no—
526C2×D4—48no—
527C2×D4—48no—
528C2×D4—48no—
529C2×D4—48no—
530C2×D4—44no—
531C2×D4—44no—
532C2×D4—48no—
533C2×D4—48no—
534C2×D4—48no—
535C2×D4—48no—
536C2×D4—48no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—612no—
550C22×C4—612no—
551C22×C4—1221no—
552C22×C4—1222no—
553C22×C4—1222no—
554C22×C4—1222no—
555C22×C4—1221no—
556C22×C4—1222no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1222no—
562C22×C4—1222no—
563C22×C4—1221no—
564C22×C4—1222no—
565C22×C4—1222no—
566C22×C4—1222no—
567C22×C4—1222no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—1222no—
571C22×C4—1222no—
572C22×C4—1222no—
573C22×C4—1222no—
574C22×C4—1222no—
575C22×C4—1221no—
576C22×C4—1222no—
577C22×C4—1222no—
578C22×C4—1222no—
579C22×C4—1221no—
580C22×C4—1222no—
581C22×C4—1222no—
582C22×C4—1221no—
583C22×C4D4×D6112yes—
584C22×C4#1175822412yes—
585C22×C4C22×Dic6114yes—
586C22×C4C22×Dic6112yes—
587C22×C4C22×Dic6112yes—
588C4⋊C4—2444no—
589C4⋊C4—2444no—
590C22⋊C4—28no—
591C22⋊C4—48no—
592C22⋊C4—2444no—
593C22⋊C4—2448no—
594C22⋊C4—2444no—
595C22⋊C4—2448no—
596C22⋊C4—2448no—
597C22⋊C4—2448no—
598C22⋊C4—2448no—
599C42—2444no—
600C23—22no—
601C23—24no—
602C23—24no—
603C23—22no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—22no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—41no—
637C23—42no—
638C23—41no—
639C23—42no—
640C23—42no—
641C23—41no—
642C23—42no—
643C23—41no—
644C23—42no—
645C23—41no—
646C23—41no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—41no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—41no—
657C23—42no—
658C23C23×Dic6111yescharacteristic
659C23C2×D4×D6111yescharacteristic
660C23C2×#1175822411yescharacteristic
661C23#1451982212yes—
662C23#1451982212yes—
663C23#1451982212yes—
664C23#1451982212yes—
665C23#1451982211yescharacteristic
666C23#1451982211yescharacteristic
667C23#1451982311yescharacteristic
668C23#1451982411yescharacteristic
669D4—416no—
670D4—432no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—1222no—
690C2×C4—1222no—
691C2×C4—1222no—
692C2×C4—1222no—
693C2×C4—2442no—
694C2×C4—2442no—
695C2×C4—2442no—
696C2×C4—2442no—
697C2×C4—2442no—
698C2×C4—2442no—
699C2×C4—2442no—
700C2×C4—2442no—
701C2×C4—2442no—
702C2×C4—2442no—
703C2×C4—2442no—
704C2×C4—2442no—
705C2×C4—2441no—
706C2×C4—2442no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2442no—
710C2×C4—2441no—
711C2×C4—2442no—
712C2×C4—2441no—
713C2×C4—2441no—
714C2×C4—2442no—
715C2×C4—2442no—
716C2×C4—2442no—
717C2×C4—2442no—
718C2×C4—2442no—
719C2×C4—2442no—
720C2×C4—2442no—
721C2×C4D4×Dic6114yes—
722C22—44no—
723C22—44no—
724C22—44no—
725C22—44no—
726C22—44no—
727C22—44no—
728C22—44no—
729C22—42no—
730C22—42no—
731C22—44no—
732C22—42no—
733C22—44no—
734C22—82no—
735C22—81no—
736C22—81no—
737C22—82no—
738C22—82no—
739C22—81no—
740C22—82no—
741C22—82no—
742C22—82no—
743C22—82no—
744C22—82no—
745C22—82no—
746C22—81no—
747C22—82no—
748C22C2×D4×Dic6111yescharacteristic
749C22#1684023711yescharacteristic
750C22#1684023712yes—
751C22#1684023712yes—
752C22#1684024511yescharacteristic
753C22#1684032211yescharacteristic
754C22#1684032511yescharacteristic
755C22#1684032511yescharacteristic
756C22#1684032711yescharacteristic
757C22#1684032811yescharacteristic
758C22#1684034111yescharacteristic
759C22#1684034712yes—
760C22#1684036511yescharacteristic
761C22#1684036612yes—
762C22#1684037911yescharacteristic
763C22#1684050012yes—
764C22#1684050012yes—
765C22#1684050112yes—
766C22#1684050112yes—
767C22#1684050112yes—
768C22#1684050512yes—
769C22#1684050712yes—
770C22#1684050712yes—
771C4—24no—
772C4—44no—
773C4—42no—
774C4—4881no—
775C4—4882no—
776C4—4881no—
777C4—4882no—
778C4—2442no—
779C4—2442no—
780C2—82no—
781C2—84no—
782C2#2144848011yescharacteristic
783C2#2144851411yescharacteristic
784C2#2144854511yescharacteristic
785C2#2144896012yes—
786C2#2144897612yes—
787C2#2145381811yescharacteristic
788C2#2145384011yescharacteristic
789C2#2145385811yescharacteristic
790C2#2145386611yescharacteristic
791C2#2145394112yes—
792C2#2145395112yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
Fitting, prime radicalC2×C61×#392C2
socle, cosocleC24×C61C24
hypercenterC2×#392D61
hypocenterC61#14623
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C2×#16839665C2semidirect
2. C2×#16839655C2semidirect
3. #21444076C2semidirect
4. #21444068C2semidirect
5. #21444064C2semidirect
6. #21444064C2semidirect
7. #21444060C2semidirect
8. #21444060C2semidirect
9. #21444060C2semidirect
10. #21444044C2semidirect
36. C61×#392C4semidirect
68. C2×C4×Dic61D4semidirect
422. #392Dic61semidirect
434. C61#14623semidirect

Maximal subgroups

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

subgroupindex
C2×#168396652
C2×#168396552
#214440762
#214440682
#214440642
#214440602
#214440442
C2×C61×#3922
#1462361