Finite Group Databasebeta

← #29718770

Subgroups — #29718770

Order 15616.

1038 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839905C211yesmaximal, characteristic
2C2×#16839819C211yesmaximal, characteristic, complemented
3#21448309C211yesmaximal, characteristic, complemented
4#21447204C211yesmaximal, characteristic, complemented
5#21447197C211yesmaximal, characteristic, complemented
6#21447136C211yesmaximal, characteristic, complemented
7#21447129C211yesmaximal, characteristic, complemented
8#21446699C211yesmaximal, characteristic, complemented
9#21446694C211yesmaximal, characteristic, complemented
10#21446515C211yesmaximal, characteristic, complemented
11#21446508C211yesmaximal, characteristic, complemented
12#21446142C211yesmaximal, characteristic, complemented
13#21446016C211yesmaximal, characteristic, complemented
14#21445757C211yesmaximal, characteristic, complemented
15C61×#2854C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C2×#14519736C2211yescharacteristic
20#16839905—24no—
21#16839819—24no—
22C2×#14519710C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×C4⋊#92418C2211yescharacteristic
25C2×C4⋊#92418C2211yescharacteristic
26C2×#14519700C2211yescharacteristic
27C2×#14519700C2211yescharacteristic
28C2×#14519700C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519697C2211yescharacteristic
32C2×#14519697C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×C22⋊#92418C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×#14519688C2211yescharacteristic
37C2×#14519688C2211yescharacteristic
38#16839668C2211yescharacteristic
39#16839668C2211yescharacteristic
40#16839664C2211yescharacteristic
41#16839664C2211yescharacteristic
42#16839641—21no—
43#16839641—21no—
44C4×#11758198—21no—
45C4×#11758198—21no—
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50C2×#123×C61—21no—
51C2×#121×C61C2211yescharacteristic
52C22×C42×C61C2211yescharacteristic
53C61×#390C2211yescharacteristic
54C61×#390C2211yescharacteristic
55C61×#389C2211yescharacteristic
56C61×#389C2211yescharacteristic
57C61×#388—21no—
58C61×#388—21no—
59C61×#386—21no—
60C61×#380C2211yescharacteristic
61C2×#11758222—22no—
62C2×#11758222—22no—
63C2×#11758222—22no—
64C2×#11758222—22no—
65C2×#11758222—41no—
66C2×#11758222—41no—
67C22×Dic122C2311yescharacteristic
68C22×D244C2311yescharacteristic
69C22×C22⋊D61—21no—
70C22×C4×D61—21no—
71C2×#11758200—22no—
72C2×#11758200—22no—
73C2×#11758200—41no—
74C2×#11758199—22no—
75C2×#11758199—22no—
76C2×#11758199—41no—
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81#14519736—41no—
82#14519736—41no—
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C22⋊Dic61—21no—
86C2×#11758198—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×C4×Dic61—21no—
91#14519710—41no—
92#14519708—41no—
93C4⋊#92418—22no—
94C4⋊#92418—22no—
95#14519700—22no—
96#14519700—22no—
97#14519700—41no—
98#14519698—41no—
99#14519698—41no—
100#14519697—22no—
101#14519697—22no—
102#14519697—41no—
103C22⋊#92418—22no—
104C22⋊#92418D414yes—
105#14519688—22no—
106#14519688—22no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111C22×D4×C61—21no—
112C22×D4×C61C2311yescharacteristic
113C23×C4×C61D411yescharacteristic
114C23×C4×C61D411yescharacteristic
115C23×C4×C61C2311yescharacteristic
116#123×C61—44no—
117#121×C61—22no—
118#121×C61—22no—
119C2×C4⋊C4×C61—21no—
120C2×C4⋊C4×C61—21no—
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61—21no—
130C2×C42×C61—22no—
131C2×C42×C61—22no—
132C2×C42×C61D411yescharacteristic
133C2×C42×C61D411yescharacteristic
134C2×C42×C61C2311yescharacteristic
135C2×C42×C61C2311yescharacteristic
136#95×C61—21no—
137#95×C61—21no—
138#95×C61—21no—
139C24×C61—21no—
140C24×C61C2×D411yescharacteristic
141C23×D61—21no—
142C2×D4×C61—21no—
143C2×D4×C61—21no—
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61—42no—
149C2×D4×C61—42no—
150C2×D4×C61—42no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—22no—
156C22×C4×C61—22no—
157C22×C4×C61—22no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—41no—
162C22×C4×C61—41no—
163C22×C4×C61—41no—
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D412yes—
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61#4112yes—
171C22×C4×C61C2411yescharacteristic
172C2×C22⋊D61—24no—
173C2×C22⋊D61—42no—
174C2×C22⋊D61—42no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178#11758222—44no—
179#11758222—44no—
180#11758222—44no—
181#11758222—44no—
182C2×D244—21no—
183C2×D244—21no—
184C2×D244—21no—
185C2×D244—21no—
186C2×D244—21no—
187C2×D244#4112yes—
188C2×C4×D61—24no—
189C2×C4×D61—42no—
190C2×C4×D61—42no—
191C2×Dic122—21no—
192C2×Dic122—21no—
193C2×Dic122—21no—
194C2×Dic122—21no—
195C2×Dic122—21no—
196C2×Dic122#4112yes—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—42no—
204C4⋊C4×C61—42no—
205C22⋊C4×C61—42no—
206C22⋊C4×C61—42no—
207C22⋊C4×C61—42no—
208C22⋊C4×C61—42no—
209C22⋊C4×C61—42no—
210C22⋊C4×C61—42no—
211C42×C61—22no—
212C42×C61—22no—
213C42×C61—21no—
214C42×C61—21no—
215C42×C61—21no—
216C42×C61—21no—
217C22⋊Dic61—42no—
218#11758200—44no—
219#11758199—44no—
220#11758198—42no—
221#11758198—42no—
222#11758198—42no—
223#11758198—42no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4×Dic61—42no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418C2×D412yes—
240C2×#92418C2×D412yes—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61#12112yes—
255C23×C61C22×D411yescharacteristic
256C22×D61—22no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61—41no—
263D4×C61—41no—
264D4×C61—41no—
265D4×C61—41no—
266D4×C61—41no—
267D4×C61—84no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
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—44no—
286C2×C4×C61—44no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61#12112yes—
297C2×C4×C61AGL(1,ℤ/8)12yes—
298C2×C4×C61C22×D411yescharacteristic
299C2×C4×C61C2×#4111yescharacteristic
300C2×C4×C61C2×#4111yescharacteristic
301C2×C4×C61C2×#4111yescharacteristic
302C2×C4×C61H(5,𝔽2)11yescharacteristic
303C2×C4×C61H(5,𝔽2)11yescharacteristic
304C22⋊D61—48no—
305C2×Dic61—22no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314D244—22no—
315D244—22no—
316D244—41no—
317D244—41no—
318C4×D61—48no—
319Dic122—22no—
320Dic122—22no—
321Dic122—41no—
322Dic122—41no—
323#92418—22no—
324#92418—22no—
325#92418—41no—
326#92418—41no—
327#24510—611nomaximal, Sylow
328C22×C61—22no—
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—41no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—81no—
336C22×C61—81no—
337C22×C61—81no—
338C22×C61—81no—
339C22×C61—81no—
340C22×C61—81no—
341C22×C61—81no—
342C22×C61C2×#12111yescharacteristic
343C22×C61#52511yescharacteristic
344C22×C61#53511yescharacteristic
345C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
346C22×C61#57511yescharacteristic
347C22×C61#57511yescharacteristic
348C22×C61#57511yescharacteristic
349C2×D61—42no—
350C2×D61—42no—
351C2×D61—42no—
352C2×D61—81no—
353C2×D61—81no—
354C2×D61—81no—
355C2×D61—81no—
356C4×C61—22no—
357C4×C61—22no—
358C4×C61—41no—
359C4×C61—41no—
360C4×C61—41no—
361C4×C61—81no—
362C4×C61—81no—
363C4×C61—81no—
364C4×C61#54611yescharacteristic
365C4×C61#54611yescharacteristic
366C4×C61#55111yescharacteristic
367C4×C61#55111yescharacteristic
368Dic61—42no—
369Dic61—81no—
370Dic61—81no—
371C2×#449—611no—
372C2×#432—611no—
373#2854D6111yescharacteristic, complemented
374#2297—611no—
375#2067—611no—
376#2066—611no—
377#2055—611no—
378#2054—611no—
379#1973—611no—
380#1972—611no—
381#1936—611no—
382#1935—611no—
383#1875—611no—
384#1854—611no—
385#1788—611no—
386C2×C61—42no—
387C2×C61—161no—
388C2×C61#241111yescharacteristic
389C2×C61#305411yescharacteristic
390C2×C61#305511yescharacteristic
391C2×C61#311111yescharacteristic
392C2×C61#311511yescharacteristic
393C2×C61#321411yescharacteristic
394C2×C61#321911yescharacteristic
395D61—82no—
396C22×#41—611no—
397C22×SD16—611no—
398C22×D8—611no—
399C2×#123—21no—
400C2×#121C2×D6111yescharacteristic
401C2×#117—611no—
402C22×C42C2×D6111yescharacteristic
403#449—1224no—
404#432—1224no—
405C2×#107—611no—
406C2×#106—611no—
407C2×C4⋊C8—611no—
408C2×C4⋊C8—611no—
409C2×#103—611no—
410C2×#103—611no—
411C2×#103—611no—
412C2×#102—611no—
413C2×#102—611no—
414C2×#102—611no—
415C2×#102—611no—
416C2×#102—611no—
417C2×C22⋊C8—611no—
418C2×C22⋊C8—611no—
419C2×#97—611no—
420C2×#97—611no—
421#391—611no—
422#391—611no—
423#390—611no—
424#390—611no—
425#390C2×D6111yescharacteristic
426#390C2×D6111yescharacteristic
427#389C2×D6111yescharacteristic
428#389C2×D6111yescharacteristic
429#388—21no—
430#388—21no—
431#386—21no—
432#386—1221no—
433#386—1221no—
434#380C2×D6111yescharacteristic
435C4×C22⋊C4—1221no—
436C4×C22⋊C4—1221no—
437#340—611no—
438#340—611no—
439#340—611no—
440#340—611no—
441C61#2451011yescharacteristic, complemented, Sylow
442C2×#41—1222no—
443C2×#41—1222no—
444C2×#41—1222no—
445C2×#41—1222no—
446C2×#41—2441no—
447C2×#41—2441no—
448C22×Q8—611no—
449C22×D4—21no—
450C22×D4—611no—
451C22×D4—1221no—
452C22×D4C22×D6111yescharacteristic
453C23×C4—1221no—
454C23×C4C22⋊D6111yescharacteristic
455C23×C4C22⋊D6111yescharacteristic
456C23×C4C22×D6111yescharacteristic
457C2×SD16—1222no—
458C2×SD16—1222no—
459C2×SD16—2441no—
460C2×D8—1222no—
461C2×D8—1222no—
462C2×D8—2441no—
463C22×C8—611no—
464C22×C8—611no—
465C22×C8—611no—
466C22×C8—611no—
467#123—44no—
468#121—22no—
469#121—22no—
470#117—2441no—
471#117—2441no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4—611no—
476C2×C4⋊C4C22×D6111yescharacteristic
477C2×C4⋊C4C22×D6111yescharacteristic
478C2×C4⋊C4C22×D6111yescharacteristic
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—1221no—
486C2×C22⋊C4—1221no—
487C2×C22⋊C4—1221no—
488C2×C22⋊C4—1221no—
489C2×C22⋊C4—1221no—
490C2×C42—22no—
491C2×C42—22no—
492C2×C42—1221no—
493C2×C42C22⋊D6111yescharacteristic
494C2×C42C22⋊D6111yescharacteristic
495C2×C42C22×D6111yescharacteristic
496C2×C42C22×D6111yescharacteristic
497#107—2441no—
498#106—2441no—
499C4⋊C8—1222no—
500C4⋊C8—1222no—
501#103—1222no—
502#103—1222no—
503#103—2441no—
504#102—1222no—
505#102—1222no—
506#102—2441no—
507#102—2441no—
508#102—2441no—
509C22⋊C8—614no—
510C22⋊C8—1222no—
511#97—1222no—
512#97—1222no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—1221no—
517#95—1221no—
518#95—1221no—
519#95—1221no—
520C24—21no—
521C24—1221no—
522C24C2×C22⋊D6111yescharacteristic
523#41—2444no—
524#41—2444no—
525#41—2444no—
526#41—2444no—
527C2×Q8—612no—
528C2×Q8—1221no—
529C2×Q8—1221no—
530C2×Q8—1221no—
531C2×Q8—1221no—
532C2×Q8—1221no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—612no—
543C2×D4—1224no—
544C2×D4—1221no—
545C2×D4—1221no—
546C2×D4—1221no—
547C2×D4—1221no—
548C2×D4—1221no—
549C2×D4—2442no—
550C2×D4—2442no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—1224no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—2442no—
569C22×C4—2442no—
570C22×C4D4×D6112yes—
571C22×C4#1175822412yes—
572C22×C4C2×C22⋊D6111yescharacteristic
573C22×C4C2×C22⋊D6111yescharacteristic
574C22×C4C2×C22⋊D6111yescharacteristic
575C22×C4C2×C22⋊D6111yescharacteristic
576C22×C4C2×C22⋊D6111yescharacteristic
577C22×C4C23×D6111yescharacteristic
578SD16—2444no—
579D8—2444no—
580C2×C8—612no—
581C2×C8—612no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8—1221no—
591C2×C8—1221no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—1221no—
601C4⋊C4—1221no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—2442no—
611C22⋊C4—2442no—
612C22⋊C4—2442no—
613C22⋊C4—2442no—
614C22⋊C4—2442no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—22no—
620C42—22no—
621C42—2442no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—1222no—
636C23—2441no—
637C23—2441no—
638C23—2441no—
639C23—2441no—
640C23—2441no—
641C23—2441no—
642C23#1451974912yes—
643C23C22×C22⋊D6111yescharacteristic
644Q8—1222no—
645Q8—1222no—
646Q8—2441no—
647Q8—2441no—
648D4—41no—
649D4—41no—
650D4—41no—
651D4—41no—
652D4—84no—
653D4—1222no—
654D4—1222no—
655D4—2448no—
656D4—2441no—
657D4—2441no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
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—44no—
676C2×C4—44no—
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—1222no—
687C2×C4—2448no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4#1451974912yes—
697C2×C4#1451980312yes—
698C2×C4C2×D4×D6111yescharacteristic
699C2×C4#41×D6111yescharacteristic
700C2×C4#41×D6111yescharacteristic
701C2×C4C2×#1175822411yescharacteristic
702C2×C4#1451982311yescharacteristic
703C2×C4#1451982311yescharacteristic
704C8—1222no—
705C8—1222no—
706C8—2441no—
707C8—2441no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—4881no—
723C22—4881no—
724C22—4881no—
725C22—4881no—
726C22—2442no—
727C22—2442no—
728C22—2442no—
729C22C2×#1451974911yescharacteristic
730C22#1684026911yescharacteristic
731C22#1684032611yescharacteristic
732C22C2×#1451980311yescharacteristic
733C22#1684056011yescharacteristic
734C22#1684056011yescharacteristic
735C22#1684056011yescharacteristic
736C4—22no—
737C4—22no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4—81no—
742C4—81no—
743C4—81no—
744C4—4881no—
745C4—4881no—
746C4—2442no—
747C4#1684040411yescharacteristic
748C4#1684040411yescharacteristic
749C4#1684043511yescharacteristic
750C4#1684043511yescharacteristic
751C2—42no—
752C2—161no—
753C2—4882no—
754C2#2144920511yescharacteristic
755C2#2145542511yescharacteristic
756C2#2145543411yescharacteristic
757C2#2145592211yescharacteristic
758C2#2145596411yescharacteristic
759C2#2145681011yescharacteristic
760C2#2145685211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2854C2
socleC23×C61C22×D4
prime radicalC2×#16839905C2
hypercenter#2854D61
hypocenterC61#24510
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2854

Complements

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

NH ≅ G/Ntype
2. C2×#16839819C2semidirect
3. #21448309C2semidirect
4. #21447204C2semidirect
5. #21447197C2semidirect
6. #21447136C2semidirect
7. #21447129C2semidirect
8. #21446699C2semidirect
9. #21446694C2semidirect
10. #21446515C2semidirect
11. #21446508C2semidirect
12. #21446142C2semidirect
13. #21446016C2semidirect
14. #21445757C2semidirect
15. C61×#2854C2semidirect
373. #2854D61semidirect
441. C61#24510semidirect

Maximal subgroups

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

subgroupindex
C2×#168399052
C2×#168398192
#214483092
#214472042
#214471972
#214471362
#214471292
#214466992
#214466942
#214465152
#214465082
#214461422
#214460162
#214457572
C61×#28542
#2451061