Finite Group Databasebeta

← #29696274

Subgroups — #29696274

Order 15616.

1206 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840476C211yesmaximal, characteristic
2C2×C8×C22⋊D61C211yesmaximal, characteristic, complemented
3#21448763C211yesmaximal, characteristic, complemented
4#21446778C211yesmaximal, characteristic, complemented
5#21446765C211yesmaximal, characteristic, complemented
6#21446244C211yesmaximal, characteristic, complemented
7#21446142C211yesmaximal, characteristic, complemented
8#21446138C211yesmaximal, characteristic, complemented
9#21445913C211yesmaximal, characteristic, complemented
10#21445911C211yesmaximal, characteristic, complemented
11#21445817C211yesmaximal, characteristic, complemented
12#102×Dic61C211yesmaximal, characteristic, complemented
13#21445536C211yesmaximal, characteristic, complemented
14#21445534C211yesmaximal, characteristic, complemented
15C61×#1893C211yesmaximal, characteristic, complemented
16C22×C8×D61C2211yescharacteristic
17#16840476—24no—
18#16840476C418yescomplemented
19C2×#14519776C2211yescharacteristic
20C2×#14519764—21no—
21C2×#14519763—21no—
22C2×#14519749—21no—
23C2×#14519748C2211yescharacteristic
24C2×D4×Dic61C2211yescharacteristic
25C2×C4×C22⋊D61C2211yescharacteristic
26C2×#14519736C2211yescharacteristic
27C2×#14519736C2211yescharacteristic
28C2×#14519735C2211yescharacteristic
29C2×#14519735C2211yescharacteristic
30C2×#14519733—21no—
31C8×C22⋊D61—24no—
32C2×#14519706C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×#14519689C2211yescharacteristic
37C2×C8×Dic61C2211yescharacteristic
38#16839662—21no—
39#16839656—21no—
40#16839651—21no—
41#16839631C2211yescharacteristic
42#16839619C2211yescharacteristic
43C4⋊C4×Dic61C2211yescharacteristic
44#16839613—21no—
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55C23×C8×C61C2211yescharacteristic
56C2×#121×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C61×#380C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C22×Dic122—21no—
63C22×C22⋊D61—21no—
64C22×C22⋊D61D411yescharacteristic
65C23×Dic61—21no—
66C22×C4×D61C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C2×C8×D61—22no—
70C2×C8×D61—22no—
71C2×C8×D61—41no—
72#14519776—22no—
73#14519776C2×C414yes—
74#14519764—28no—
75#14519763—28no—
76#14519749—28no—
77#14519748—22no—
78#14519748C2×C414yes—
79D4×Dic61—22no—
80D4×Dic61C2×C414yes—
81C4×C22⋊D61C2×C414yes—
82C4×C22⋊D61D414yes—
83#14519736—22no—
84#14519736—22no—
85#14519736—41no—
86#14519736C2×C414yes—
87#14519735—22no—
88#14519735—22no—
89#14519735—41no—
90#14519735C2×C414yes—
91#14519733—28no—
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×#11758196D411yescharacteristic
100C2×C22⋊Dic61—21no—
101C2×C22⋊Dic61—21no—
102C2×C22⋊Dic61—21no—
103C2×C22⋊Dic61—21no—
104C2×C22⋊Dic61D411yescharacteristic
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108C2×#11758198D411yescharacteristic
109C2×C4×Dic61—21no—
110C2×C4×Dic61—21no—
111C2×C4×Dic61—21no—
112C2×C4×Dic61—21no—
113C2×C4×Dic61—21no—
114C2×C4×Dic61C2311yescharacteristic
115#14519706—22no—
116#14519698—22no—
117#14519698—41no—
118C22⋊#92418—22no—
119#14519689—22no—
120C8×Dic61—22no—
121#14519684—21no—
122#14519684—21no—
123C22×D4×C61—21no—
124C22×D4×C61C2311yescharacteristic
125C23×C4×C61C2311yescharacteristic
126C22×C8×C61—22no—
127C22×C8×C61—22no—
128C22×C8×C61—41no—
129C22×C8×C61C2311yescharacteristic
130C22×C8×C61C2311yescharacteristic
131#121×C61—22no—
132#121×C61C2×C414yes—
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138#102×C61—22no—
139#102×C61—41no—
140#95×C61—21no—
141C24×C61—21no—
142C24×C61C2×D411yescharacteristic
143C23×D61C2×D411yescharacteristic
144C2×D4×C61—24no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—81no—
151C2×D4×C61—81no—
152C2×D4×C61C22×C412yes—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61C22×C412yes—
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×D412yes—
163C22×C4×C61C2411yescharacteristic
164C2×C22⋊D61—24no—
165C2×C22⋊D61—22no—
166C2×C22⋊D61—22no—
167C2×C22⋊D61—81no—
168C2×C22⋊D61—81no—
169C2×C22⋊D61C22⋊C414yes—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61—24no—
174C22×Dic61—21no—
175C22×Dic61—42no—
176C22×Dic61—42no—
177C22×Dic61C2×D411yescharacteristic
178C22×Dic61C2×D411yescharacteristic
179C22×Dic61C2×D411yescharacteristic
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61C22×C412yes—
185C2×C4×D61C2×D412yes—
186C2×Dic122—24no—
187C2×Dic122—81no—
188C2×Dic122—81no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—44no—
195C2×C8×C61#4112yes—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61C22×C412yes—
202C22⋊C4×C61—24no—
203C22⋊C4×C61—81no—
204C22⋊Dic61—24no—
205C22⋊Dic61—24no—
206C22⋊Dic61—24no—
207C22⋊Dic61—42no—
208C22⋊Dic61C22⋊C414yes—
209#11758198—24no—
210#11758198—42no—
211#11758198—81no—
212#11758198C22⋊C414yes—
213C4⋊Dic61—21no—
214C4⋊Dic61—21no—
215C4⋊Dic61—21no—
216C4⋊Dic61—21no—
217C4⋊Dic61—21no—
218C4⋊Dic61C22×C412yes—
219C4⋊Dic61C22×C412yes—
220C4⋊Dic61#4112yes—
221#11758196—24no—
222#11758196—42no—
223#11758196—81no—
224#11758196C22⋊C414yes—
225C4×Dic61—24no—
226C4×Dic61—24no—
227C4×Dic61—42no—
228C4×Dic61—42no—
229C4×Dic61—42no—
230C4×Dic61C22×C412yes—
231C4×Dic61C2×D412yes—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C8×D61—44no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—22no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61C2×C22⋊C412yes—
253C23×C61C22×D411yescharacteristic
254C22×D61—21no—
255C22×D61—21no—
256C22×D61—21no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61C2×C22⋊C412yes—
261D4×C61—22no—
262D4×C61—22no—
263D4×C61—41no—
264D4×C61—41no—
265D4×C61—84no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—41no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61C2×C22⋊C412yes—
282C2×C4×C61C23×C411yescharacteristic
283C2×C4×C61C22×D411yescharacteristic
284C2×C4×C61C2×#4111yescharacteristic
285C2×C4×C61C2×#4111yescharacteristic
286C2×C4×C61H(5,𝔽2)11yescharacteristic
287C2×C4×C612−1+411yescharacteristic
288C22⋊D61—28no—
289C22⋊D61—84no—
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61—22no—
295C2×Dic61—22no—
296C2×Dic61—22no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—48no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61C2×C22⋊C412yes—
308C2×Dic61C2×C22⋊C412yes—
309C2×Dic61C2×C22⋊C412yes—
310C2×Dic61#13512yes—
311C2×Dic61#13512yes—
312C4×D61—22no—
313C4×D61—22no—
314C4×D61—22no—
315C4×D61—22no—
316Dic122—84no—
317C8×C61—22no—
318C8×C61—41no—
319#92418—41no—
320#92418—41no—
321#22489—611nomaximal, Sylow
322C22×C61—22no—
323C22×C61—22no—
324C22×C61—22no—
325C22×C61—41no—
326C22×C61—41no—
327C22×C61—41no—
328C22×C61—41no—
329C22×C61—42no—
330C22×C61—42no—
331C22×C61—42no—
332C22×C61—81no—
333C22×C61—81no—
334C22×C61—81no—
335C22×C61—81no—
336C22×C61C22×C22⋊C411yescharacteristic
337C22×C61#54611yescharacteristic
338C22×C61#54711yescharacteristic
339C22×C61C2×#13511yescharacteristic
340C22×C61C2×#13511yescharacteristic
341C22×C61#57611yescharacteristic
342C22×C61#57711yescharacteristic
343C2×D61—22no—
344C2×D61—22no—
345C2×D61—22no—
346C2×D61—41no—
347C2×D61—41no—
348C2×D61—41no—
349C2×D61—41no—
350C4×C61—22no—
351C4×C61—42no—
352C4×C61—81no—
353C4×C61—81no—
354C4×C61C4×#4111yescharacteristic
355C4×C61#52011yescharacteristic
356C4×C61#54611yescharacteristic
357C4×C61#54711yescharacteristic
358Dic61—22no—
359Dic61—22no—
360Dic61—42no—
361Dic61—42no—
362Dic61—42no—
363Dic61—81no—
364Dic61#41614yes—
365C2×#555—611no—
366C2×C8×D4—611no—
367#2354—611no—
368#1990—611no—
369#1987—611no—
370#1893—611no—
371#1893D6111yescharacteristic, complemented
372#1875—611no—
373#1875—611no—
374#1825—611no—
375#1825—611no—
376#1802—611no—
377C4×#102—611no—
378#1735—611no—
379#1735—611no—
380C2×C61—42no—
381C2×C61—82no—
382C2×C61#233911yescharacteristic
383C2×C61C2×#41611yescharacteristic
384C2×C61#289711yescharacteristic
385C2×C61#330311yescharacteristic
386C2×C61#330511yescharacteristic
387C2×C61#334011yescharacteristic
388C2×C61#334111yescharacteristic
389D61—42no—
390C23×C8—611no—
391C23×C8C2×D6111yescharacteristic
392#555—618no—
393#555—1224no—
394C2×C4⋊Q8—611no—
395C2×#124—1221no—
396C2×#124—1221no—
397C2×#121—611no—
398C2×#121—1221no—
399C2×#121C2×D6111yescharacteristic
400C2×C4×D4—611no—
401C2×C4×D4—611no—
402C2×#117—611no—
403C2×#117—611no—
404C2×#117—611no—
405C2×#117—611no—
406C2×#117—1221no—
407C8×D4—1224no—
408C2×C4⋊C8—611no—
409C2×#102—611no—
410C2×#102—611no—
411C2×#102C2×D6111yescharacteristic
412C2×#102C2×D6111yescharacteristic
413C2×C22⋊C8—611no—
414C2×C22⋊C8—611no—
415C2×C4×C8—611no—
416#390—1221no—
417#388—1221no—
418#388—1221no—
419#384—611no—
420#380—611no—
421#380C2×D6111yescharacteristic
422C4×C4⋊C4—611no—
423C4×C4⋊C4—1221no—
424#340—611no—
425#340—611no—
426#340—611no—
427#340—611no—
428#340—611no—
429#340—611no—
430#340—611no—
431#340—611no—
432#340—611no—
433#340—611no—
434#340C2×D6111yescharacteristic
435#340C2×D6111yescharacteristic
436C61#2248911yescharacteristic, complemented, Sylow
437C22×Q8—1221no—
438C22×D4—21no—
439C22×D4—611no—
440C22×D4—1221no—
441C22×D4C22×D6111yescharacteristic
442C23×C4—611no—
443C23×C4—1221no—
444C23×C4C22×D6111yescharacteristic
445C22×C8—22no—
446C22×C8—22no—
447C22×C8—41no—
448C22×C8—611no—
449C22×C8—611no—
450C22×C8—1222no—
451C22×C8—1222no—
452C22×C8—2441no—
453C22×C8C22×D6111yescharacteristic
454C22×C8C22×D6111yescharacteristic
455C4⋊Q8—614no—
456C4⋊Q8—1222no—
457#124—1228no—
458#124—1228no—
459#121—22no—
460#121—614no—
461#121—1222no—
462#121—1228no—
463#121C4×D6114yes—
464C4×D4—614no—
465C4×D4—614no—
466C4×D4—614no—
467C4×D4—1222no—
468#117—614no—
469#117—614no—
470#117—1228no—
471#117—1222no—
472#117—1222no—
473#117—1222no—
474#117—1222no—
475#117—2441no—
476#117—2441no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—1221no—
483C2×C4⋊C4—1221no—
484C2×C4⋊C4—1221no—
485C2×C4⋊C4C22×D6111yescharacteristic
486C2×C4⋊C4C22×D6111yescharacteristic
487C2×C4⋊C4C22×D6111yescharacteristic
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—611no—
491C2×C22⋊C4—611no—
492C2×C22⋊C4—1221no—
493C2×C22⋊C4—1221no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C22⋊C4—1221no—
497C2×C22⋊C4—1221no—
498C2×C22⋊C4—1221no—
499C2×C42—611no—
500C2×C42—1221no—
501C2×C42—1221no—
502C2×C42—1221no—
503C2×C42—1221no—
504C2×C42—1221no—
505C4⋊C8—1222no—
506#102—22no—
507#102—41no—
508#102—1222no—
509#102—2441no—
510C22⋊C8—1222no—
511C22⋊C8—1222no—
512C4×C8—1222no—
513#95—21no—
514#95—1221no—
515#95—1221no—
516C24—21no—
517C24—611no—
518C24D4×D6111yescharacteristic
519C2×Q8—1224no—
520C2×Q8—4881no—
521C2×Q8—4881no—
522C2×D4—24no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—81no—
529C2×D4—81no—
530C2×D4—614no—
531C2×D4—1222no—
532C2×D4—1222no—
533C2×D4—1224no—
534C2×D4—4881no—
535C2×D4—4881no—
536C2×D4C2×C4×D6112yes—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—611no—
545C22×C4—611no—
546C22×C4—611no—
547C22×C4—612no—
548C22×C4—612no—
549C22×C4—1224no—
550C22×C4—1221no—
551C22×C4—1221no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—2442no—
559C22×C4—2442no—
560C22×C4C2×C4×D6112yes—
561C22×C4D4×D6112yes—
562C22×C4D4×D6111yescharacteristic
563C22×C4C23×D6111yescharacteristic
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—44no—
570C2×C8—1221no—
571C2×C8—1221no—
572C2×C8—1221no—
573C2×C8—1221no—
574C2×C8—1221no—
575C2×C8—1221no—
576C2×C8—2444no—
577C2×C8#1175822412yes—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—614no—
584C4⋊C4—612no—
585C4⋊C4—612no—
586C4⋊C4—612no—
587C4⋊C4—1224no—
588C4⋊C4—1221no—
589C4⋊C4—1221no—
590C4⋊C4—1221no—
591C4⋊C4—1221no—
592C4⋊C4—1221no—
593C4⋊C4—4881no—
594C4⋊C4—2442no—
595C4⋊C4C2×C4×D6112yes—
596C22⋊C4—24no—
597C22⋊C4—81no—
598C22⋊C4—614no—
599C22⋊C4—614no—
600C22⋊C4—1224no—
601C22⋊C4—1224no—
602C22⋊C4—1224no—
603C22⋊C4—1224no—
604C22⋊C4—4881no—
605C22⋊C4—2442no—
606C22⋊C4—2442no—
607C42—612no—
608C42—612no—
609C42—1224no—
610C42—1224no—
611C42—2442no—
612C42—2442no—
613C42—2442no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—22no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—612no—
628C23—1221no—
629C23—1221no—
630C23—1221no—
631C23—1221no—
632C23—1221no—
633C23—1221no—
634C23C22⋊C4×D6112yes—
635C23C2×D4×D6111yescharacteristic
636Q8—4884no—
637D4—22no—
638D4—22no—
639D4—41no—
640D4—41no—
641D4—84no—
642D4—1228no—
643D4—4884no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—612no—
660C2×C4—612no—
661C2×C4—612no—
662C2×C4—612no—
663C2×C4—612no—
664C2×C4—1221no—
665C2×C4—1221no—
666C2×C4—1221no—
667C2×C4—1221no—
668C2×C4—1222no—
669C2×C4—1222no—
670C2×C4—1222no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1222no—
675C2×C4—2448no—
676C2×C4—2441no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4—2441no—
684C2×C4—2441no—
685C2×C4C22⋊C4×D6112yes—
686C2×C4C22×C4×D6111yescharacteristic
687C2×C4C2×D4×D6111yescharacteristic
688C2×C4#41×D6111yescharacteristic
689C2×C4C2×#1175822411yescharacteristic
690C2×C4#1451982211yescharacteristic
691C2×C4#1451982411yescharacteristic
692C8—22no—
693C8—41no—
694C8—2441no—
695C8—2441no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—1222no—
711C22—1222no—
712C22—1222no—
713C22—2441no—
714C22—2441no—
715C22—2441no—
716C22—2441no—
717C22C2×C22⋊C4×D6111yescharacteristic
718C22#1684040111yescharacteristic
719C22#1684041211yescharacteristic
720C22#135×D6111yescharacteristic
721C22#135×D6111yescharacteristic
722C22#1684056311yescharacteristic
723C22#1684056811yescharacteristic
724C4—22no—
725C4—42no—
726C4—81no—
727C4—81no—
728C4—614no—
729C4—1222no—
730C4—1222no—
731C4—4881no—
732C4—2442no—
733C4—2442no—
734C4—2442no—
735C4C4×#1175822411yescharacteristic
736C4#1684024111yescharacteristic
737C4#1684039911yescharacteristic
738C4#1684041011yescharacteristic
739C2—42no—
740C2—82no—
741C2—2442no—
742C2#2144864511yescharacteristic
743C2#416×D6111yescharacteristic
744C2#2145434011yescharacteristic
745C2#2145774211yescharacteristic
746C2#2145776411yescharacteristic
747C2#2145822711yescharacteristic
748C2#2145823811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1893C2
socleC23×C61C22×D4
prime radicalC2×#16840476C2
cosocleC22×C4×C61C24
hypercenter#1893D61
hypocenterC61#22489
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1893

Complements

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

NH ≅ G/Ntype
2. C2×C8×C22⋊D61C2semidirect
3. #21448763C2semidirect
4. #21446778C2semidirect
5. #21446765C2semidirect
6. #21446244C2semidirect
7. #21446142C2semidirect
8. #21446138C2semidirect
9. #21445913C2semidirect
10. #21445911C2semidirect
11. #21445817C2semidirect
12. #102×Dic61C2semidirect
13. #21445536C2semidirect
14. #21445534C2semidirect
15. C61×#1893C2semidirect
18. #16840476C4semidirect
371. #1893D61semidirect
436. C61#22489semidirect

Maximal subgroups

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

subgroupindex
C2×#168404762
C2×C8×C22⋊D612
#214487632
#214467782
#214467652
#214462442
#214461422
#214461382
#214459132
#214459112
#214458172
#102×Dic612
#214455362
#214455342
C61×#18932
#2248961