Finite Group Databasebeta

← #29610671

Subgroups — #29610671

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×#16839671C211yesmaximal, characteristic
2C2×#16839664C211yesmaximal, characteristic, complemented
3#21444075C211yesmaximal, characteristic, complemented
4#21444067C212yesmaximal, complemented
5#21444064C211yesmaximal, characteristic, complemented
6#21444061C212yesmaximal, complemented
7#21444059C211yesmaximal, characteristic, complemented
8#21444058C212yesmaximal, complemented
9#21444058C212yesmaximal, complemented
10#21444046C211yesmaximal, characteristic, complemented
11C2×C61×#388C211yesmaximal, characteristic, complemented
12C23×D244C2211yescharacteristic
13C23×C22⋊D61C2212yes—
14C22×C4⋊Dic61C2211yescharacteristic
15C22×C22⋊Dic61C2212yes—
16C22×#11758198C2212yes—
17C22×#11758198C2212yes—
18C22×#11758198C2212yes—
19C22×#11758198C2212yes—
20C22×#11758198C2212yes—
21#16839671C418yescomplemented
22#16839664—24no—
23C2×#14519684C2211yescharacteristic
24C2×#14519684C2212yes—
25C2×#14519684C2212yes—
26C2×#14519684C2212yes—
27C2×#14519684C2212yes—
28C2×#14519684C2212yes—
29C2×#14519684C2211yescharacteristic
30C22×C4⋊C4×C61C2211yescharacteristic
31C22×C22⋊C4×C61C2211yescharacteristic
32C22×C22⋊C4×C61C2211yescharacteristic
33C22×C22⋊C4×C61C2211yescharacteristic
34C22×C42×C61C2211yescharacteristic
35C61×#388—24no—
36C2×#95×C61C2211yescharacteristic
37C2×#95×C61C2211yescharacteristic
38C24×D61C2312yes—
39C22×D244—22no—
40C22×D244—22no—
41C22×D244—42no—
42C22×D244—42no—
43C22×D244C2×C414yes—
44C22×C22⋊D61—42no—
45C22×C22⋊D61—42no—
46C22×C22⋊D61—42no—
47C22×C22⋊D61—42no—
48C22×C22⋊D61—42no—
49C22×C22⋊D61—42no—
50C22×C22⋊D61C2×C418yes—
51C23×Dic61C2312yes—
52C23×Dic61C2312yes—
53C23×Dic61C2312yes—
54C2×C4⋊Dic61—22no—
55C2×C4⋊Dic61—42no—
56C2×C22⋊Dic61—42no—
57C2×C22⋊Dic61—42no—
58C2×C22⋊Dic61—42no—
59C2×#11758198—24no—
60C2×#11758198—24no—
61C2×#11758198—42no—
62C2×#11758198—42no—
63C2×#11758198—42no—
64C2×#11758198—42no—
65C2×#11758198—42no—
66C2×#11758198—42no—
67C2×#11758198—42no—
68C2×#11758198—42no—
69C2×#11758198—42no—
70C2×#11758198—42no—
71C2×#11758198—42no—
72C2×#11758198—42no—
73C2×#11758198C2×C418yes—
74#14519684—22no—
75#14519684—42no—
76#14519684—42no—
77#14519684—42no—
78#14519684—42no—
79#14519684—42no—
80#14519684C2×C414yes—
81C25×C61C2311yescharacteristic
82C23×C4×C61C2311yescharacteristic
83C23×C4×C61C2311yescharacteristic
84C23×C4×C61C2311yescharacteristic
85C23×C4×C61C2311yescharacteristic
86C23×C4×C61C2311yescharacteristic
87C23×C4×C61C2311yescharacteristic
88C2×C4⋊C4×C61—22no—
89C2×C4⋊C4×C61—42no—
90C2×C22⋊C4×C61—22no—
91C2×C22⋊C4×C61—22no—
92C2×C22⋊C4×C61—22no—
93C2×C22⋊C4×C61—22no—
94C2×C22⋊C4×C61—42no—
95C2×C22⋊C4×C61—42no—
96C2×C22⋊C4×C61C2×C414yes—
97C2×C42×C61—42no—
98C2×C42×C61D414yescomplemented
99#95×C61—22no—
100#95×C61—22no—
101C24×C61—21no—
102C24×C61—21no—
103C24×C61—21no—
104C24×C61—21no—
105C24×C61—22no—
106C24×C61—22no—
107C24×C61—22no—
108C24×C61—22no—
109C24×C61—21no—
110C24×C61—21no—
111C24×C61C22×C412yes—
112C24×C61C2411yescharacteristic
113C23×D61—22no—
114C23×D61—22no—
115C23×D61—22no—
116C23×D61—22no—
117C23×D61—22no—
118C23×D61—22no—
119C23×D61—22no—
120C23×D61—22no—
121C23×D61—22no—
122C23×D61—22no—
123C23×D61—22no—
124C23×D61—22no—
125C23×D61—22no—
126C23×D61—22no—
127C23×D61C22×C414yes—
128C22×C4×C61—22no—
129C22×C4×C61—22no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—21no—
137C22×C4×C61—22no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—22no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—22no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—21no—
148C22×C4×C61—22no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61C22×C412yes—
153C22×C4×C61C22×C412yes—
154C22×C4×C61C2×D412yes—
155C22×C4×C61C2×D412yes—
156C22×C4×C61C2×D412yes—
157C22×C4×C61#4112yes—
158C2×C22⋊D61—48no—
159C2×C22⋊D61—48no—
160C2×C22⋊D61—48no—
161C2×C22⋊D61—48no—
162C2×C22⋊D61—48no—
163C2×C22⋊D61—48no—
164C2×C22⋊D61—48no—
165C22×Dic61—22no—
166C22×Dic61—22no—
167C22×Dic61—22no—
168C22×Dic61—22no—
169C22×Dic61—22no—
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—22no—
182C22×Dic61—22no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61C22×C414yes—
186C2×D244—28no—
187C2×D244—48no—
188C2×D244—44no—
189C2×D244—44no—
190C2×D244—48no—
191C4⋊C4×C61—44no—
192C22⋊C4×C61—28no—
193C22⋊C4×C61—44no—
194C22⋊C4×C61—44no—
195C42×C61—44no—
196C22⋊Dic61—48no—
197#11758198—48no—
198#11758198—48no—
199#11758198—48no—
200#11758198—48no—
201#11758198—48no—
202C4⋊Dic61—44no—
203C23×C61—22no—
204C23×C61—22no—
205C23×C61—24no—
206C23×C61—24no—
207C23×C61—22no—
208C23×C61—41no—
209C23×C61—41no—
210C23×C61—41no—
211C23×C61—41no—
212C23×C61—41no—
213C23×C61—41no—
214C23×C61—42no—
215C23×C61—41no—
216C23×C61—42no—
217C23×C61—41no—
218C23×C61—42no—
219C23×C61—42no—
220C23×C61—42no—
221C23×C61—42no—
222C23×C61—42no—
223C23×C61—42no—
224C23×C61—42no—
225C23×C61—42no—
226C23×C61C23×C411yescharacteristic
227C23×C61C22×D411yescharacteristic
228C23×C61C2×#4111yescharacteristic
229C23×C61H(5,𝔽2)12yes—
230C23×C61H(5,𝔽2)12yes—
231C23×C61H(5,𝔽2)12yes—
232C23×C61H(5,𝔽2)12yes—
233C23×C61H(5,𝔽2)11yescharacteristic
234C23×C61H(5,𝔽2)11yescharacteristic
235C23×C61H(5,𝔽2)11yescharacteristic
236C23×C612−1+411yescharacteristic
237C22×D61—24no—
238C22×D61—24no—
239C22×D61—24no—
240C22×D61—24no—
241C22×D61—24no—
242C22×D61—24no—
243C22×D61—24no—
244C22×D61—42no—
245C22×D61—42no—
246C22×D61—42no—
247C22×D61—42no—
248C22×D61—42no—
249C22×D61—42no—
250C22×D61—42no—
251C22×D61—42no—
252C22×D61—42no—
253C22×D61—42no—
254C22×D61—42no—
255C22×D61—42no—
256C22×D61—42no—
257C22×D61—42no—
258C22×D61—42no—
259C22×D61—42no—
260C22×D61—42no—
261C22×D61—42no—
262C22×D61—42no—
263C22×D61—42no—
264C22×D61—42no—
265C22×D61—42no—
266C22×D61—42no—
267C22×D61—42no—
268C22×D61—42no—
269C22×D61—42no—
270C22×D61—42no—
271C22×D61—42no—
272C2×C4×C61—24no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—24no—
276C2×C4×C61—22no—
277C2×C4×C61—24no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—42no—
287C2×C4×C61—42no—
288C2×C4×C61—42no—
289C2×C4×C61—42no—
290C2×C4×C61—42no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—42no—
298C2×C4×C61—42no—
299C2×C4×C61—42no—
300C2×C4×C61—42no—
301C2×C4×C61C4×D414yes—
302C22⋊D61—432no—
303C2×Dic61—24no—
304C2×Dic61—24no—
305C2×Dic61—24no—
306C2×Dic61—42no—
307C2×Dic61—42no—
308C2×Dic61—42no—
309C2×Dic61—42no—
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—
324D244—416no—
325#14623—611nomaximal, Sylow
326C22×C61—42no—
327C22×C61—42no—
328C22×C61—42no—
329C22×C61—44no—
330C22×C61—44no—
331C22×C61—81no—
332C22×C61—81no—
333C22×C61—82no—
334C22×C61—82no—
335C22×C61—81no—
336C22×C61—81no—
337C22×C61C2×C4×D411yescharacteristic
338C22×C61#51812yes—
339C22×C61#51812yes—
340C22×C61#51811yescharacteristic
341C22×C61#52011yescharacteristic
342C22×C61#53411yescharacteristic
343C22×C61#53511yescharacteristic
344C22×C61#53511yescharacteristic
345C22×C61#53511yescharacteristic
346C22×C61#53511yescharacteristic
347C22×C61#53711yescharacteristic
348C22×C61#53812yes—
349C22×C61#54012yes—
350C22×C61#54011yescharacteristic
351C22×C61#54211yescharacteristic
352C22×C61#56012yes—
353C22×C61#56012yes—
354C22×C61#56012yes—
355C22×C61#56012yes—
356C22×C61#56012yes—
357C22×C61H(3,𝔽4)12yes—
358C22×C61#56212yes—
359C22×C61#56212yes—
360C2×D61—44no—
361C2×D61—44no—
362C2×D61—44no—
363C2×D61—44no—
364C2×D61—44no—
365C2×D61—44no—
366C2×D61—44no—
367C2×D61—82no—
368C2×D61—82no—
369C2×D61—82no—
370C2×D61—82no—
371C2×D61—82no—
372C2×D61—82no—
373C2×D61—82no—
374C2×D61—82no—
375C4×C61—24no—
376C4×C61—42no—
377C4×C61—42no—
378C4×C61—42no—
379C4×C61—81no—
380C4×C61—81no—
381Dic61—44no—
382Dic61—82no—
383Dic61—82no—
384C2×#392—611no—
385C2×#390—611no—
386C2×#388D6111yescharacteristic, complemented
387#1442—611no—
388#1440—612no—
389#1439—612no—
390#1439—611no—
391#1438—611no—
392#1438—612no—
393#1438—612no—
394#1434—611no—
395C2×C61—82no—
396C2×C61#232111yescharacteristic
397C2×C61#232411yescharacteristic
398C2×C61#232811yescharacteristic
399C2×C61#237512yes—
400C2×C61#237712yes—
401C2×C61#281311yescharacteristic
402C2×C61#281511yescharacteristic
403C2×C61#281811yescharacteristic
404C2×C61#281911yescharacteristic
405C2×C61#282812yes—
406C2×C61#282912yes—
407D61—84no—
408C23×D4—612no—
409C23×D4—611no—
410C22×C4⋊C4—611no—
411C22×C4⋊C4C2×D6111yescharacteristic
412C22×C22⋊C4—612no—
413C22×C22⋊C4—612no—
414C22×C22⋊C4—612no—
415C22×C22⋊C4—612no—
416C22×C22⋊C4—612no—
417C22×C22⋊C4—612no—
418C22×C22⋊C4C2×D6111yescharacteristic
419C22×C22⋊C4C2×D6111yescharacteristic
420C22×C22⋊C4C2×D6111yescharacteristic
421C22×C42C2×D6111yescharacteristic
422#392—618no—
423#390—1224no—
424#388—24no—
425C2×#95—611no—
426C2×#95—611no—
427C2×#95—612no—
428C2×#95—612no—
429C2×#95—612no—
430C2×#95—612no—
431C2×#95—612no—
432C2×#95C2×D6111yescharacteristic
433C2×#95C2×D6111yescharacteristic
434C61#1462311yescharacteristic, complemented, Sylow
435C25—612no—
436C25C22×D6111yescharacteristic
437C22×D4—618no—
438C22×D4—614no—
439C22×D4—1222no—
440C22×D4—1222no—
441C22×D4—2442no—
442C22×D4—2442no—
443C22×D4—2442no—
444C22×D4—2442no—
445C22×D4—2442no—
446C22×D4—2442no—
447C22×D4—2442no—
448C22×D4—2442no—
449C23×C4—612no—
450C23×C4—612no—
451C23×C4—612no—
452C23×C4C22×D6111yescharacteristic
453C23×C4C22×D6111yescharacteristic
454C23×C4C22×D6111yescharacteristic
455C23×C4C22×D6111yescharacteristic
456C23×C4C22×D6111yescharacteristic
457C23×C4C22×D6111yescharacteristic
458C2×C4⋊C4—22no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4—1222no—
461C2×C4⋊C4—2442no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—42no—
467C2×C22⋊C4—42no—
468C2×C22⋊C4—618no—
469C2×C22⋊C4—1224no—
470C2×C22⋊C4—1224no—
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⋊C4—2442no—
486C2×C22⋊C4C4×D6114yes—
487C2×C42—42no—
488C2×C42C22⋊D6114yescomplemented
489#95—22no—
490#95—22no—
491#95—614no—
492#95—1222no—
493#95—2442no—
494#95—2442no—
495#95—2442no—
496#95—2442no—
497#95—2442no—
498C24—21no—
499C24—21no—
500C24—22no—
501C24—22no—
502C24—21no—
503C24—22no—
504C24—22no—
505C24—21no—
506C24—21no—
507C24—21no—
508C24—614no—
509C24—1222no—
510C24—1222no—
511C24—1222no—
512C24—1222no—
513C24—1222no—
514C24—1222no—
515C24—1222no—
516C24—1222no—
517C24—1222no—
518C24—1222no—
519C24—1222no—
520C24—1222no—
521C24—1222no—
522C24—1222no—
523C24C2×C4×D6112yes—
524C24C23×D6111yescharacteristic
525C2×D4—1228no—
526C2×D4—2448no—
527C2×D4—2444no—
528C2×D4—2444no—
529C2×D4—2448no—
530C2×D4—2448no—
531C2×D4—2448no—
532C2×D4—2448no—
533C2×D4—2448no—
534C2×D4—2448no—
535C2×D4—2448no—
536C2×D4—2448no—
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—21no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—614no—
562C22×C4—1222no—
563C22×C4—1222no—
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—1222no—
576C22×C4—1222no—
577C22×C4—1222no—
578C22×C4—1222no—
579C22×C4—1222no—
580C22×C4—1222no—
581C22×C4—1222no—
582C22×C4C2×C4×D6112yes—
583C22×C4C2×C4×D6112yes—
584C22×C4#1175822212yes—
585C22×C4C2×C22⋊D6112yes—
586C22×C4C2×C22⋊D6112yes—
587C22×C4C2×C22⋊D6112yes—
588C4⋊C4—44no—
589C4⋊C4—2444no—
590C22⋊C4—28no—
591C22⋊C4—44no—
592C22⋊C4—44no—
593C22⋊C4—2448no—
594C22⋊C4—2448no—
595C22⋊C4—2448no—
596C22⋊C4—2448no—
597C22⋊C4—2448no—
598C22⋊C4—2448no—
599C42—44no—
600C23—22no—
601C23—24no—
602C23—24no—
603C23—22no—
604C23—22no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—42no—
620C23—42no—
621C23—41no—
622C23—41no—
623C23—1224no—
624C23—1224no—
625C23—1224no—
626C23—1224no—
627C23—1224no—
628C23—1224no—
629C23—1224no—
630C23—2442no—
631C23—2442no—
632C23—2442no—
633C23—2442no—
634C23—2442no—
635C23—2442no—
636C23—2442no—
637C23—2442no—
638C23—2442no—
639C23—2442no—
640C23—2442no—
641C23—2442no—
642C23—2442no—
643C23—2442no—
644C23—2442no—
645C23—2442no—
646C23—2442no—
647C23—2442no—
648C23—2442no—
649C23—2442no—
650C23—2442no—
651C23—2442no—
652C23—2442no—
653C23—2442no—
654C23—2442no—
655C23—2442no—
656C23—2442no—
657C23—2442no—
658C23C22×C4×D6111yescharacteristic
659C23C22×C22⋊D6111yescharacteristic
660C23C2×#1175822211yescharacteristic
661C23#1451982212yes—
662C23#1451982212yes—
663C23#1451982312yes—
664C23#1451982312yes—
665C23#1451982311yescharacteristic
666C23#1451982311yescharacteristic
667C23#1451982311yescharacteristic
668C23#1451982411yescharacteristic
669D4—24416no—
670D4—24432no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—1224no—
701C2×C4—1224no—
702C2×C4—1224no—
703C2×C4—2442no—
704C2×C4—2442no—
705C2×C4—2442no—
706C2×C4—2442no—
707C2×C4—2442no—
708C2×C4—2442no—
709C2×C4—2442no—
710C2×C4—2442no—
711C2×C4—2442no—
712C2×C4—2442no—
713C2×C4—2442no—
714C2×C4—2442no—
715C2×C4—2442no—
716C2×C4—2442no—
717C2×C4—2442no—
718C2×C4—2442no—
719C2×C4—2442no—
720C2×C4—2442no—
721C2×C4C4×C22⋊D6114yes—
722C22—44no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—44no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—82no—
731C22—82no—
732C22—81no—
733C22—4882no—
734C22—4882no—
735C22—4882no—
736C22—4882no—
737C22—4882no—
738C22—4882no—
739C22—4882no—
740C22—4882no—
741C22—2444no—
742C22—2444no—
743C22—2444no—
744C22—2444no—
745C22—2444no—
746C22—2444no—
747C22—2444no—
748C22C2×C4×C22⋊D6111yescharacteristic
749C22#1684023412yes—
750C22#1684023412yes—
751C22#1684023611yescharacteristic
752C22#1684024211yescharacteristic
753C22#1684032111yescharacteristic
754C22#1684032611yescharacteristic
755C22#1684032611yescharacteristic
756C22#1684032611yescharacteristic
757C22#1684032911yescharacteristic
758C22#1684034011yescharacteristic
759C22#1684034512yes—
760C22#1684036312yes—
761C22#1684036711yescharacteristic
762C22#1684038311yescharacteristic
763C22#1684050012yes—
764C22#1684050012yes—
765C22#1684050212yes—
766C22#1684050312yes—
767C22#1684050312yes—
768C22#1684050412yes—
769C22#1684050612yes—
770C22#1684050912yes—
771C4—24no—
772C4—42no—
773C4—42no—
774C4—42no—
775C4—81no—
776C4—81no—
777C4—4882no—
778C4—4882no—
779C4—2444no—
780C2—82no—
781C2—4884no—
782C2#2144847311yescharacteristic
783C2#2144851211yescharacteristic
784C2#2144854111yescharacteristic
785C2#2144895912yes—
786C2#2144897212yes—
787C2#2145382111yescharacteristic
788C2#2145384111yescharacteristic
789C2#2145385911yescharacteristic
790C2#2145386411yescharacteristic
791C2#2145393612yes—
792C2#2145394512yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#388C2
socle, cosocleC24×C61C24
prime radicalC2×#16839671C2
hypercenterC2×#388D61
hypocenterC61#14623
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#16839664C2semidirect
3. #21444075C2semidirect
4. #21444067C2semidirect
5. #21444064C2semidirect
6. #21444061C2semidirect
7. #21444059C2semidirect
8. #21444058C2semidirect
9. #21444058C2semidirect
10. #21444046C2semidirect
11. C2×C61×#388C2semidirect
21. #16839671C4semidirect
98. C2×C42×C61D4semidirect
386. C2×#388D61semidirect
434. C61#14623semidirect
488. C2×C42C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396712
C2×#168396642
#214440752
#214440672
#214440642
#214440612
#214440592
#214440582
#214440462
C2×C61×#3882
#1462361