Finite Group Databasebeta

← #29730685

Subgroups — #29730685

Order 15616.

1012 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840154C211yesmaximal, characteristic, complemented
2C2×#16839981C211yesmaximal, characteristic, complemented
3C2×#16839977C211yesmaximal, characteristic
4C2×#16839974C211yesmaximal, characteristic
5#21448888C211yesmaximal, characteristic, complemented
6#21447141C211yesmaximal, characteristic, complemented
7#21447134C211yesmaximal, characteristic, complemented
8#21446913C211yesmaximal, characteristic, complemented
9#21446896C211yesmaximal, characteristic
10#21446743C211yesmaximal, characteristic, complemented
11#21446543C211yesmaximal, characteristic, complemented
12#21446163C211yesmaximal, characteristic, complemented
13#21446156C211yesmaximal, characteristic, complemented
14#21445644C211yesmaximal, characteristic, complemented
15C61×#2547C211yesmaximal, characteristic, complemented
16C22×#11758202C2211yescharacteristic
17C22×#11758202C2211yescharacteristic
18C22×#11758200C2211yescharacteristic
19C22×#11758201C2211yescharacteristic
20C22×#11758201C2211yescharacteristic
21C22×#11758199C2211yescharacteristic
22C2×#14519765C2211yescharacteristic
23C2×C4×Dic122C2211yescharacteristic
24C2×C4×D244C2211yescharacteristic
25#16840154—24no—
26#16839981—24no—
27#16839977—24no—
28#16839974—24no—
29C2×C4⋊#92418C2211yescharacteristic
30C2×C4⋊#92418C2211yescharacteristic
31C2×C4⋊#92418C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×#14519700C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×#14519697C2211yescharacteristic
40C2×#14519688C2211yescharacteristic
41#16839668C2211yescharacteristic
42#16839664C2211yescharacteristic
43#16839652—21no—
44#16839651—21no—
45#16839633—21no—
46C4×C4⋊Dic61C2211yescharacteristic
47#16839609—21no—
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52C2×C4⋊Q8×C61C2211yescharacteristic
53C2×#124×C61C2211yescharacteristic
54C2×#124×C61C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic
56C61×#397—21no—
57C61×#397—21no—
58C61×#391C2211yescharacteristic
59C61×#391C2211yescharacteristic
60C61×#380—21no—
61C61×#380—21no—
62C4×C4⋊C4×C61C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C22×D244C2311yescharacteristic
65C22×C4×D61—21no—
66C2×#11758202—22no—
67C2×#11758202—22no—
68C2×#11758202—22no—
69C2×#11758202—22no—
70C2×#11758202—41no—
71C2×#11758202—41no—
72C2×#11758200—22no—
73C2×#11758200—22no—
74C2×#11758200—41no—
75C2×#11758201—22no—
76C2×#11758201—22no—
77C2×#11758201—22no—
78C2×#11758201—22no—
79C2×#11758201—41no—
80C2×#11758201—41no—
81C2×#11758199—22no—
82C2×#11758199—22no—
83C2×#11758199—41no—
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86C22×#92418C2311yescharacteristic
87C22×#92418C2311yescharacteristic
88#14519765—22no—
89#14519765D414yes—
90C4×Dic122—22no—
91C4×Dic122—41no—
92C4×D244—22no—
93C4×D244—41no—
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×#11758196—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×C4×Dic61—21no—
103C2×C4×Dic61—21no—
104C4⋊#92418—22no—
105C4⋊#92418—22no—
106C4⋊#92418—22no—
107#14519701—22no—
108#14519701—22no—
109#14519701—41no—
110#14519701—41no—
111#14519700—22no—
112#14519698—22no—
113#14519698D414yes—
114#14519697—22no—
115#14519688—22no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119C22×Q8×C61C2311yescharacteristic
120C22×Q8×C61C2311yescharacteristic
121C22×D4×C61C2311yescharacteristic
122C23×C4×C61—21no—
123C4⋊Q8×C61—22no—
124C4⋊Q8×C61—22no—
125#124×C61—22no—
126#124×C61—22no—
127#124×C61—41no—
128#124×C61—41no—
129C4×D4×C61—22no—
130C4×D4×C61—22no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61D411yescharacteristic
134C2×C4⋊C4×C61D411yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C42×C61C2311yescharacteristic
142C2×C42×C61C2311yescharacteristic
143C2×C42×C61C2311yescharacteristic
144#95×C61—21no—
145#95×C61—21no—
146#95×C61—21no—
147#95×C61—21no—
148#95×C61D411yescharacteristic
149#95×C61D411yescharacteristic
150C24×C61—21no—
151C23×D61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61C2×D412yes—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—42no—
174C22×C4×C61—42no—
175C22×C4×C61—42no—
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2411yescharacteristic
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186C2×D244—21no—
187C2×D244—21no—
188C2×D244—21no—
189C2×D244—21no—
190C2×D244—21no—
191C2×D244C2×D412yes—
192C2×C4×D61—42no—
193C2×C4×D61—42no—
194C2×C4×D61—81no—
195C2×Dic122—21no—
196C2×Dic122—21no—
197C2×Dic122—21no—
198C2×Dic122—21no—
199C2×Dic122—21no—
200C2×Dic122C2×D412yes—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—41no—
204C4⋊C4×C61—41no—
205C4⋊C4×C61—42no—
206C4⋊C4×C61—42no—
207C22⋊C4×C61—42no—
208C22⋊C4×C61—42no—
209C22⋊C4×C61—42no—
210C22⋊C4×C61—42no—
211C22⋊C4×C61—42no—
212C42×C61—21no—
213C42×C61—21no—
214C42×C61—21no—
215C42×C61—21no—
216C42×C61C2×D412yes—
217C42×C61#4112yes—
218#11758202—44no—
219#11758202—44no—
220#11758201—44no—
221#11758201—44no—
222#11758200—44no—
223#11758199—44no—
224#11758198—24no—
225#11758198—24no—
226#11758198—42no—
227#11758198—42no—
228#11758198—81no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61C2×D412yes—
233#11758196—42no—
234C4×Dic61—42no—
235C4×Dic61—81no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418C2×D412yes—
247C2×#92418#4112yes—
248C23×C61—22no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61C22×D411yescharacteristic
256C22×D61—22no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61—41no—
263Q8×C61—41no—
264Q8×C61—41no—
265Q8×C61—41no—
266Q8×C61—41no—
267Q8×C61—41no—
268Q8×C61—41no—
269Q8×C61—41no—
270Q8×C61—41no—
271D4×C61—22no—
272D4×C61—22no—
273D4×C61—41no—
274D4×C61—41no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
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—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—84no—
301C2×C4×C61#12112yes—
302C2×C4×C61#12112yes—
303C2×C4×C61C22×D411yescharacteristic
304C2×C4×C61C22×D411yescharacteristic
305C2×C4×C61C2×#4111yescharacteristic
306C2×C4×C61C2×#4111yescharacteristic
307C2×C4×C61H(5,𝔽2)11yescharacteristic
308C2×C4×C61H(5,𝔽2)11yescharacteristic
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318D244—22no—
319D244—22no—
320D244—41no—
321D244—41no—
322C4×D61—84no—
323Dic122—22no—
324Dic122—22no—
325Dic122—41no—
326Dic122—41no—
327#92418—22no—
328#92418—22no—
329#92418—41no—
330#92418—41no—
331#25381—611nomaximal, Sylow
332C22×C61—42no—
333C22×C61—42no—
334C22×C61—42no—
335C22×C61—81no—
336C22×C61—81no—
337C22×C61—81no—
338C22×C61—81no—
339C22×C61C2×#12111yescharacteristic
340C22×C61D4211yescharacteristic
341C22×C61#55011yescharacteristic
342C22×C61#57511yescharacteristic
343C22×C61#57511yescharacteristic
344C22×C61#57711yescharacteristic
345C22×C61#57811yescharacteristic
346C2×D61—42no—
347C2×D61—42no—
348C2×D61—42no—
349C2×D61—81no—
350C2×D61—81no—
351C2×D61—81no—
352C2×D61—81no—
353C4×C61—22no—
354C4×C61—22no—
355C4×C61—41no—
356C4×C61—41no—
357C4×C61—41no—
358C4×C61—41no—
359C4×C61—81no—
360C4×C61—81no—
361C4×C61—81no—
362C4×C61#53211yescharacteristic
363C4×C61#54011yescharacteristic
364C4×C61D4211yescharacteristic
365C4×C61#54611yescharacteristic
366Dic61—42no—
367Dic61—42no—
368Dic61—81no—
369C2×#497—611no—
370C2×#464—611no—
371C2×#463—611no—
372C2×#463—611no—
373#2547D6111yescharacteristic, complemented
374#2367—611no—
375#2056—611no—
376#2055—611no—
377#2015—611no—
378#2012—611no—
379#1981—611no—
380#1940—611no—
381#1878—611no—
382#1877—611no—
383#1762—611no—
384C2×C61—82no—
385C2×C61#242811yescharacteristic
386C2×C61#304011yescharacteristic
387C2×C61#304611yescharacteristic
388C2×C61#326711yescharacteristic
389C2×C61#326911yescharacteristic
390C2×C61#340111yescharacteristic
391C2×C61#340211yescharacteristic
392D61—82no—
393C22×Q16—611no—
394C22×Q16—611no—
395C22×SD16—611no—
396C22×SD16—611no—
397C22×SD16—611no—
398C22×D8—611no—
399C2×C4⋊Q8C2×D6111yescharacteristic
400C2×#124—611no—
401C2×#124C2×D6111yescharacteristic
402C2×#124C2×D6111yescharacteristic
403C2×C4×Q8—611no—
404C2×C4×D4—611no—
405C2×C4×D4C2×D6111yescharacteristic
406#497—1224no—
407#464—1224no—
408#463—1224no—
409#463—1224no—
410C2×C4⋊C8—611no—
411C2×C4⋊C8—611no—
412C2×C4⋊C8—611no—
413C2×#103—611no—
414C2×#103—611no—
415C2×#103—611no—
416C2×#103—611no—
417C2×#103—611no—
418C2×#102—611no—
419C2×#102—611no—
420C2×#102—611no—
421C2×#97—611no—
422#397—21no—
423#397—21no—
424#391—611no—
425#391C2×D6111yescharacteristic
426#391C2×D6111yescharacteristic
427#390—611no—
428#388—1221no—
429#388—1221no—
430#385—1221no—
431#380—21no—
432#380—21no—
433C4×C4⋊C4—611no—
434C4×C4⋊C4C2×D6111yescharacteristic
435C4×C22⋊C4—1221no—
436#340—611no—
437#340—611no—
438#336—611no—
439#336—611no—
440C61#2538111yescharacteristic, complemented, Sylow
441C22×Q8—611no—
442C22×Q8C22×D6111yescharacteristic
443C22×Q8C22×D6111yescharacteristic
444C22×D4—611no—
445C22×D4C22×D6111yescharacteristic
446C23×C4—21no—
447C23×C4—1221no—
448C2×Q16—1222no—
449C2×Q16—1222no—
450C2×Q16—1222no—
451C2×Q16—1222no—
452C2×Q16—2441no—
453C2×Q16—2441no—
454C2×SD16—1222no—
455C2×SD16—1222no—
456C2×SD16—1222no—
457C2×SD16—1222no—
458C2×SD16—1222no—
459C2×SD16—1222no—
460C2×SD16—2441no—
461C2×SD16—2441no—
462C2×SD16—2441no—
463C2×D8—1222no—
464C2×D8—1222no—
465C2×D8—2441no—
466C22×C8—611no—
467C22×C8—611no—
468C22×C8—611no—
469C22×C8—611no—
470C4⋊Q8—22no—
471C4⋊Q8—22no—
472#124—22no—
473#124—22no—
474#124—41no—
475#124—41no—
476#124—614no—
477#124—1222no—
478C4×Q8—1222no—
479C4×Q8—2441no—
480C4×D4—22no—
481C4×D4—22no—
482C4×D4—1222no—
483C4×D4—2441no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—611no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4C22⋊D6111yescharacteristic
490C2×C4⋊C4C22⋊D6111yescharacteristic
491C2×C4⋊C4C22×D6111yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—1221no—
498C2×C22⋊C4—1221no—
499C2×C22⋊C4—1221no—
500C2×C22⋊C4—1221no—
501C2×C22⋊C4—1221no—
502C2×C42—1221no—
503C2×C42—1221no—
504C2×C42C22×D6111yescharacteristic
505C2×C42C22×D6111yescharacteristic
506C2×C42C22×D6111yescharacteristic
507C4⋊C8—1222no—
508C4⋊C8—1222no—
509C4⋊C8—1222no—
510#103—1222no—
511#103—1222no—
512#103—1222no—
513#103—2441no—
514#103—2441no—
515#102—614no—
516#102—1222no—
517#102—1222no—
518#97—1222no—
519#95—21no—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—1221no—
524#95—1221no—
525#95—1221no—
526#95C22⋊D6111yescharacteristic
527#95C22⋊D6111yescharacteristic
528C24—21no—
529C24—1221no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—612no—
543C2×Q8—1221no—
544C2×Q8—1221no—
545C2×Q8—1221no—
546C2×Q8—1221no—
547C2×Q8—1221no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—612no—
554C2×D4—1221no—
555C2×D4—1221no—
556C2×D4—1221no—
557C2×D4—1221no—
558C2×D4—1221no—
559C2×D4D4×D6112yes—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—4881no—
570C22×C4—2442no—
571C22×C4—2442no—
572C22×C4C2×C22⋊D6111yescharacteristic
573C22×C4C2×C22⋊D6111yescharacteristic
574C22×C4C2×C22⋊D6111yescharacteristic
575C22×C4C2×C22⋊D6111yescharacteristic
576C22×C4C2×C22⋊D6111yescharacteristic
577C22×C4C2×C22⋊D6111yescharacteristic
578C22×C4C23×D6111yescharacteristic
579Q16—2444no—
580Q16—2444no—
581SD16—2444no—
582SD16—2444no—
583SD16—2444no—
584D8—2444no—
585C2×C8—612no—
586C2×C8—612no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8—1221no—
591C2×C8—1221no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8—1221no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—41no—
600C4⋊C4—41no—
601C4⋊C4—42no—
602C4⋊C4—42no—
603C4⋊C4—612no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—1221no—
607C4⋊C4—2442no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—42no—
613C22⋊C4—1224no—
614C22⋊C4—1224no—
615C22⋊C4—4881no—
616C22⋊C4—2442no—
617C22⋊C4—2442no—
618C42—21no—
619C42—21no—
620C42—21no—
621C42—21no—
622C42—4881no—
623C42—2442no—
624C42D4×D6112yes—
625C42#1175822412yes—
626C23—22no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—1222no—
634C23—2441no—
635C23—2441no—
636C23—2441no—
637C23—2441no—
638C23—2441no—
639C23—2441no—
640C23C22×C22⋊D6111yescharacteristic
641Q8—41no—
642Q8—41no—
643Q8—41no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8—41no—
649Q8—1222no—
650Q8—1222no—
651Q8—2441no—
652Q8—2441no—
653D4—22no—
654D4—22no—
655D4—41no—
656D4—41no—
657D4—1222no—
658D4—1222no—
659D4—2441no—
660D4—2441no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—84no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—4884no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4#1451974812yes—
698C2×C4#1451974812yes—
699C2×C4C2×D4×D6111yescharacteristic
700C2×C4C2×D4×D6111yescharacteristic
701C2×C4#41×D6111yescharacteristic
702C2×C4C2×#1175822411yescharacteristic
703C2×C4#1451982211yescharacteristic
704C2×C4#1451982311yescharacteristic
705C8—1222no—
706C8—1222no—
707C8—2441no—
708C8—2441no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—4881no—
717C22—4881no—
718C22—4881no—
719C22—4881no—
720C22—2442no—
721C22—2442no—
722C22—2442no—
723C22C2×#1451974811yescharacteristic
724C22D4×C22⋊D6111yescharacteristic
725C22#1684043111yescharacteristic
726C22#1684056011yescharacteristic
727C22#1684056011yescharacteristic
728C22#1684057011yescharacteristic
729C22#1684057711yescharacteristic
730C4—22no—
731C4—22no—
732C4—41no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—81no—
737C4—81no—
738C4—81no—
739C4—4881no—
740C4—2442no—
741C4—2442no—
742C4#1684030711yescharacteristic
743C4#1684036511yescharacteristic
744C4#1684039611yescharacteristic
745C4#1684040911yescharacteristic
746C2—82no—
747C2—4882no—
748C2#2144940311yescharacteristic
749C2#2145530911yescharacteristic
750C2#2145536511yescharacteristic
751C2#2145734511yescharacteristic
752C2#2145737011yescharacteristic
753C2#2145888511yescharacteristic
754C2#2145889411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2547C2
socleC23×C61C22×D4
prime radicalC22×#11758199C22
hypercenter#2547D61
hypocenterC61#25381
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2547

Complements

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

NH ≅ G/Ntype
1. C2×#16840154C2semidirect
2. C2×#16839981C2semidirect
5. #21448888C2semidirect
6. #21447141C2semidirect
7. #21447134C2semidirect
8. #21446913C2semidirect
10. #21446743C2semidirect
11. #21446543C2semidirect
12. #21446163C2semidirect
13. #21446156C2semidirect
14. #21445644C2semidirect
15. C61×#2547C2semidirect
373. #2547D61semidirect
440. C61#25381semidirect

Maximal subgroups

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

subgroupindex
C2×#168401542
C2×#168399812
C2×#168399772
C2×#168399742
#214488882
#214471412
#214471342
#214469132
#214468962
#214467432
#214465432
#214461632
#214461562
#214456442
C61×#25472
#2538161