Finite Group Databasebeta

← #29737227

Subgroups — #29737227

Order 15616.

1162 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840061C211yesmaximal, characteristic, complemented
2C22×#14519699C211yesmaximal, characteristic
3#21449544C211yesmaximal, characteristic, complemented
4#21448639C211yesmaximal, characteristic
5#21447341C211yesmaximal, characteristic, complemented
6#21447208C211yesmaximal, characteristic, complemented
7#21447188C211yesmaximal, characteristic, complemented
8#21446964C211yesmaximal, characteristic, complemented
9#21446077C211yesmaximal, characteristic, complemented
10#21446067C211yesmaximal, characteristic, complemented
11#21446006C211yesmaximal, characteristic, complemented
12#21445997C211yesmaximal, characteristic, complemented
13#21445828C211yesmaximal, characteristic, complemented
14#21445749C211yesmaximal, characteristic
15C61×#1807C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C2×#14519768C2211yescharacteristic, complemented
18C2×#14519739C2211yescharacteristic
19C2×#14519739C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic
21C2×C22⋊C4×D61—21no—
22#16840061—24no—
23C2×#14519710C2211yescharacteristic, complemented
24C2×#14519710C2211yescharacteristic, complemented
25C2×#14519706C2211yescharacteristic, complemented
26C2×#14519706C2211yescharacteristic, complemented
27C2×#14519699—24no—
28C2×#14519699C2211yescharacteristic
29C2×#14519699C2211yescharacteristic
30C2×#14519699C2211yescharacteristic
31C2×#14519699C2211yescharacteristic
32C2×#14519697C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×#14519697C2211yescharacteristic
36C2×C22⋊#92418C2211yescharacteristic
37#16839704—21no—
38#16839694—21no—
39#16839663C2211yescharacteristic
40#16839663C2211yescharacteristic
41#16839661C2211yescharacteristic, complemented
42#16839658C2211yescharacteristic, complemented
43#16839640—21no—
44#16839640—21no—
45#16839637—21no—
46#16839627C2211yescharacteristic, complemented
47#16839620—21no—
48#16839617—21no—
49C4×C22⋊Dic61C2211yescharacteristic
50#16839524C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839516C2211yescharacteristic, complemented
53#16839516C2211yescharacteristic, complemented
54C23×C8×C61C2211yescharacteristic
55C2×#106×C61C2211yescharacteristic, complemented
56C2×#106×C61C2211yescharacteristic, complemented
57C61×#380C2211yescharacteristic
58C61×#380C2211yescharacteristic
59C61×#340C2211yescharacteristic, complemented
60C61×#340C2211yescharacteristic, complemented
61C24×D61—21no—
62C22×D244—22no—
63C22×D244—22no—
64C22×D244—21no—
65C22×D244—22no—
66C22×D244—41no—
67C22×D244—41no—
68C22×D244Q814yes—
69C22×D244C2311yescharacteristic
70C22×D244C2311yescharacteristic
71C23×Dic61—21no—
72C22×C4×D61—21no—
73C22×C4×D61—21no—
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76#14519768—22no—
77#14519768—41no—
78#14519739—22no—
79#14519739—22no—
80#14519739—41no—
81#14519739—41no—
82C2×C4⋊Dic61—22no—
83C2×C4⋊Dic61—21no—
84C2×C4⋊Dic61—21no—
85C2×C4⋊Dic61—21no—
86C2×C4⋊Dic61—41no—
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×#11758196—21no—
90C2×#11758196—21no—
91C2×C22⋊Dic61D411yescharacteristic
92C2×C22⋊Dic61D411yescharacteristic
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C22⋊C4×D61—44no—
100C2×C4×Dic61C2311yescharacteristic
101C2×C4×Dic61C2311yescharacteristic
102#14519710—22no—
103#14519710—41no—
104#14519706—22no—
105#14519706—41no—
106#14519699—22no—
107#14519699—22no—
108#14519699—22no—
109#14519699D414yes—
110#14519697—22no—
111#14519697—22no—
112#14519697—41no—
113#14519697—41no—
114C22⋊#92418—22no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119#14519684D411yescharacteristic
120#14519684D411yescharacteristic
121C23×C4×C61C2311yescharacteristic
122C22×C8×C61—22no—
123C22×C8×C61—22no—
124C22×C8×C61—41no—
125C22×C8×C61C2311yescharacteristic
126C22×C8×C61C2311yescharacteristic
127C2×C4⋊C4×C61C2311yescharacteristic
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C4⋊C4×C61C2311yescharacteristic
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—21no—
133#106×C61—22no—
134#106×C61—41no—
135#95×C61—21no—
136#95×C61—21no—
137C24×C61C2×D411yescharacteristic
138C23×D61—21no—
139C23×D61—21no—
140C23×D61—24no—
141C23×D61—42no—
142C23×D61—42no—
143C23×D61—42no—
144C23×D61—42no—
145C23×D61—81no—
146C23×D61—81no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×Q812yes—
157C22×C4×C61#4112yes—
158C22×C4×C61C2411yescharacteristic
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—42no—
162C22×Dic61—42no—
163C22×Dic61—81no—
164C22×Dic61C2×D411yescharacteristic
165C22×Dic61C2×D411yescharacteristic
166C22×Dic61C2×D411yescharacteristic
167C22×Dic61C2×D411yescharacteristic
168C2×D244—21no—
169C2×D244—21no—
170C2×D244—21no—
171C2×D244—21no—
172C2×D244—21no—
173C2×D244—21no—
174C2×D244—21no—
175C2×D244—28no—
176C2×D244—24no—
177C2×D244—21no—
178C2×D244—44no—
179C2×D244—44no—
180C2×D244—44no—
181C2×D244—42no—
182C2×D244—42no—
183C2×D244C2×D412yes—
184C2×D244C2×Q812yes—
185C2×D244C2×Q812yes—
186C2×D244#4112yes—
187C2×C4×D61—42no—
188C2×C4×D61—42no—
189C2×C4×D61—42no—
190C2×C4×D61—42no—
191C2×C4×D61—81no—
192C2×C4×D61—81no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—44no—
199C2×C8×C61C2×D412yes—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C22⋊C4×C61—42no—
209C22⋊C4×C61—42no—
210C22⋊Dic61—22no—
211C22⋊Dic61—22no—
212#11758198—42no—
213#11758198—42no—
214#11758198—42no—
215#11758198—42no—
216#11758198—81no—
217#11758198—81no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—42no—
222C4⋊Dic61—42no—
223C4⋊Dic61—81no—
224C4⋊Dic61C2×D412yes—
225#11758196—42no—
226#11758196—81no—
227C4×Dic61—21no—
228C4×Dic61—21no—
229C4×Dic61—21no—
230C4×Dic61—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61C22⋊Q812yes—
242C23×C61#13512yes—
243C23×C61AGL(1,ℤ/8)12yes—
244C23×C61C22×D411yescharacteristic
245C22×D61—22no—
246C22×D61—22no—
247C22×D61—22no—
248C22×D61—22no—
249C22×D61—48no—
250C22×D61—41no—
251C22×D61—41no—
252C22×D61—41no—
253C22×D61—41no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—48no—
261C22×D61—84no—
262C22×D61—84no—
263C22×D61—84no—
264C22×D61—84no—
265C22×D61—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—41no—
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×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61C22⋊Q812yes—
285C2×C4×C61C22×D411yescharacteristic
286C2×C4×C61C22×Q811yescharacteristic
287C2×C4×C61C2×#4111yescharacteristic
288C2×C4×C61C2×#4111yescharacteristic
289C2×C4×C61H(5,𝔽2)11yescharacteristic
290C2×C4×C61H(5,𝔽2)11yescharacteristic
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61—22no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—84no—
310D244—22no—
311D244—22no—
312D244—22no—
313D244—22no—
314D244—22no—
315D244—48no—
316D244—41no—
317D244—41no—
318D244C22⋊Q814yes—
319C4×D61—84no—
320C4×D61—84no—
321C8×C61—22no—
322C8×C61—41no—
323#92418—41no—
324#92418—41no—
325#25960—611nomaximal, Sylow
326C22×C61—22no—
327C22×C61—22no—
328C22×C61—22no—
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—22no—
332C22×C61#47814yescomplemented
333C22×C61C2×C22⋊Q811yescharacteristic
334C22×C61D4211yescharacteristic
335C22×C61#54611yescharacteristic
336C22×C61C2×#13511yescharacteristic
337C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
338C22×C61#57611yescharacteristic
339C22×C61#57711yescharacteristic
340C2×D61—24no—
341C2×D61—42no—
342C2×D61—42no—
343C2×D61—42no—
344C2×D61—42no—
345C2×D61—42no—
346C2×D61—42no—
347C2×D61—42no—
348C2×D61—42no—
349C2×D61—42no—
350C2×D61—816no—
351C2×D61—81no—
352C2×D61—81no—
353C2×D61—81no—
354C2×D61—81no—
355C4×C61—22no—
356C4×C61—81no—
357C4×C61—81no—
358C4×C61—81no—
359C4×C61—81no—
360C4×C61C2×C22⋊Q811yescharacteristic
361C4×C61#54311yescharacteristic
362C4×C61#54611yescharacteristic
363C4×C61#55111yescharacteristic
364Dic61—41no—
365Dic61—42no—
366Dic61—41no—
367Dic61—41no—
368Dic61—41no—
369Dic61—81no—
370C2×#478—611no—
371C22×#102—611no—
372#2442—611no—
373D4×C22⋊C4—611no—
374#2092—611no—
375#2067—611no—
376#2065—611no—
377#2025—611no—
378#1864—611no—
379#1862—611no—
380#1852—611no—
381#1850—611no—
382#1807D6111yescharacteristic, complemented
383#1804—611no—
384#1786—611no—
385C2×C61—24no—
386C2×C61#243711yescharacteristic
387C2×C61C2×#47811yescharacteristic
388C2×C61#308111yescharacteristic
389C2×C61#326411yescharacteristic
390C2×C61#328211yescharacteristic
391C2×C61#329711yescharacteristic
392C2×C61#331011yescharacteristic
393D61—44no—
394D61—82no—
395C23×D4—611no—
396C23×C8C2×D6111yescharacteristic
397C2×#125—611no—
398C2×C4×D4—611no—
399C2×C4×D4—611no—
400C22×C4⋊C4—611no—
401C22×C22⋊C4—1221no—
402#478—1224no—
403C2×#107—611no—
404C2×#107—611no—
405C2×#106C2×D6111yescharacteristic, complemented
406C2×#106C2×D6111yescharacteristic, complemented
407C2×C4⋊C8—611no—
408C2×C4⋊C8—611no—
409C2×#102—611no—
410C2×#102—611no—
411C2×#102—611no—
412C2×#102—611no—
413C2×#102—611no—
414C2×#102—611no—
415C2×#102—611no—
416C2×#102—611no—
417C2×#102—1224no—
418C2×C22⋊C8—611no—
419#400—1221no—
420#398—1221no—
421#390—611no—
422#390—611no—
423#389—611no—
424#389—611no—
425#386—1221no—
426#386—1221no—
427#385—1221no—
428#382—611no—
429#380—1221no—
430#380C2×D6111yescharacteristic
431#380C2×D6111yescharacteristic
432#379—1221no—
433C4×C22⋊C4—611no—
434#340—611no—
435#340—611no—
436#340C2×D6111yescharacteristic, complemented
437#340C2×D6111yescharacteristic, complemented
438#336—611no—
439#336—611no—
440C61#2596011yescharacteristic, complemented, Sylow
441C25—1221no—
442C22×D4—614no—
443C22×D4—611no—
444C22×D4—611no—
445C22×D4—1222no—
446C22×D4—1222no—
447C22×D4—1222no—
448C22×D4—1221no—
449C22×D4—2441no—
450C22×D4—2441no—
451C23×C4—1221no—
452C23×C4—1221no—
453C23×C4—1221no—
454C23×C4C22×D6111yescharacteristic
455C22×C8—22no—
456C22×C8—22no—
457C22×C8—41no—
458C22×C8—611no—
459C22×C8—611no—
460C22×C8C22×D6111yescharacteristic
461C22×C8C22×D6111yescharacteristic
462#125—1222no—
463#125—2441no—
464C4×D4—1222no—
465C4×D4—1222no—
466C4×D4—2441no—
467C4×D4—2441no—
468C2×C4⋊C4—611no—
469C2×C4⋊C4—611no—
470C2×C4⋊C4—1222no—
471C2×C4⋊C4—1221no—
472C2×C4⋊C4—1221no—
473C2×C4⋊C4—1221no—
474C2×C4⋊C4—1221no—
475C2×C4⋊C4—1221no—
476C2×C4⋊C4—2441no—
477C2×C4⋊C4C22×D6111yescharacteristic
478C2×C4⋊C4C22×D6111yescharacteristic
479C2×C4⋊C4C22×D6111yescharacteristic
480C2×C4⋊C4C22×D6111yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—611no—
484C2×C22⋊C4—611no—
485C2×C22⋊C4—1221no—
486C2×C22⋊C4—1221no—
487C2×C22⋊C4—1221no—
488C2×C22⋊C4—1221no—
489C2×C22⋊C4—1221no—
490C2×C22⋊C4—1221no—
491C2×C22⋊C4—2444no—
492C2×C42—611no—
493C2×C42—611no—
494#107—1222no—
495#107—2441no—
496#106—22no—
497#106—41no—
498C4⋊C8—1222no—
499C4⋊C8—2441no—
500#102—614no—
501#102—1222no—
502#102—1222no—
503#102—1222no—
504#102—1222no—
505#102—1222no—
506#102—2441no—
507#102—2441no—
508C22⋊C8—1222no—
509#95—21no—
510#95—21no—
511#95—611no—
512#95—611no—
513#95—1221no—
514#95—1221no—
515#95—1221no—
516#95—1221no—
517C24—1221no—
518C24—1224no—
519C24—1221no—
520C24—4881no—
521C24—4881no—
522C24—2442no—
523C24—2442no—
524C24—2442no—
525C24—2442no—
526C24D4×D6111yescharacteristic
527C2×D4—612no—
528C2×D4—612no—
529C2×D4—612no—
530C2×D4—612no—
531C2×D4—1228no—
532C2×D4—1221no—
533C2×D4—1221no—
534C2×D4—1221no—
535C2×D4—1221no—
536C2×D4—1221no—
537C2×D4—1221no—
538C2×D4—1221no—
539C2×D4—1221no—
540C2×D4—1224no—
541C2×D4—2444no—
542C2×D4—2444no—
543C2×D4—2444no—
544C2×D4—2442no—
545C2×D4—2442no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—611no—
555C22×C4—611no—
556C22×C4—611no—
557C22×C4—611no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—4881no—
561C22×C4—4881no—
562C22×C4—4881no—
563C22×C4—2442no—
564C22×C4—2442no—
565C22×C4—2442no—
566C22×C4—2442no—
567C22×C4—2442no—
568C22×C4—2442no—
569C22×C4#1175822212yes—
570C22×C4D4×D6111yescharacteristic
571C22×C4Q8×D6112yes—
572C22×C4C23×D6111yescharacteristic
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—44no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8—1221no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8D4×D6112yes—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—612no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—1221no—
598C4⋊C4—4881no—
599C4⋊C4—4881no—
600C4⋊C4—2442no—
601C4⋊C4—2442no—
602C4⋊C4—2442no—
603C22⋊C4—42no—
604C22⋊C4—42no—
605C22⋊C4—1222no—
606C22⋊C4—1222no—
607C22⋊C4—4881no—
608C22⋊C4—4881no—
609C22⋊C4—2442no—
610C22⋊C4—2442no—
611C22⋊C4—2442no—
612C22⋊C4—2442no—
613C42—1221no—
614C42—1221no—
615C42—1221no—
616C42—1221no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—1222no—
622C23—1222no—
623C23—1222no—
624C23—1222no—
625C23—4884no—
626C23—4884no—
627C23—4884no—
628C23—4884no—
629C23—4884no—
630C23—2448no—
631C23—2441no—
632C23—2441no—
633C23—2441no—
634C23—2441no—
635C23—2448no—
636C23—2441no—
637C23—2441no—
638C23—2441no—
639C23—2441no—
640C23—2441no—
641C23—2441no—
642C23#1451975512yes—
643C23#1451979812yes—
644C23#1451980412yes—
645C23C2×D4×D6111yescharacteristic
646D4—614no—
647D4—1222no—
648D4—1222no—
649D4—1222no—
650D4—1222no—
651D4—1222no—
652D4—2448no—
653D4—2441no—
654D4—2441no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—1221no—
674C2×C4—1221no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1222no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—4884no—
687C2×C4—4884no—
688C2×C4—4884no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4#1451975512yes—
695C2×C4C2×D4×D6111yescharacteristic
696C2×C4C2×Q8×D6111yescharacteristic
697C2×C4#41×D6111yescharacteristic
698C2×C4C2×#1175822211yescharacteristic
699C2×C4#1451982211yescharacteristic
700C2×C4#1451982311yescharacteristic
701C8—22no—
702C8—41no—
703C8—2441no—
704C8—2441no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—1224no—
712C22—48816no—
713C22—4881no—
714C22—4881no—
715C22—4881no—
716C22—4881no—
717C22—2442no—
718C22—2442no—
719C22—2442no—
720C22—2442no—
721C22—2442no—
722C22—2442no—
723C22—2442no—
724C22—2442no—
725C22—2442no—
726C22#1684006114yescomplemented
727C22C2×#1451975511yescharacteristic
728C22#1684039611yescharacteristic
729C22#1684040111yescharacteristic
730C22C2×#1451979811yescharacteristic
731C22C2×#1451980411yescharacteristic
732C22#1684056411yescharacteristic
733C22#1684056911yescharacteristic
734C4—22no—
735C4—81no—
736C4—81no—
737C4—81no—
738C4—81no—
739C4—4881no—
740C4—2441no—
741C4—2441no—
742C4—2441no—
743C4—2442no—
744C4—2441no—
745C4C22⋊Q8×D6111yescharacteristic
746C4#1684038711yescharacteristic
747C4#1684040211yescharacteristic
748C4#1684043611yescharacteristic
749C2—24no—
750C2—4882no—
751C2—2444no—
752C2#2144948711yescharacteristic
753C2C2×#1684006111yescharacteristic
754C2#2145565311yescharacteristic
755C2#2145729611yescharacteristic
756C2#2145752311yescharacteristic
757C2#2145767511yescharacteristic
758C2#2145784611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1807C2
socleC23×C61C22×D4
prime radicalC23×D244C22
hypercenter#1807D61
hypocenterC61#25960
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1807

Complements

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

NH ≅ G/Ntype
1. C2×#16840061C2semidirect
3. #21449544C2semidirect
5. #21447341C2semidirect
6. #21447208C2semidirect
7. #21447188C2semidirect
8. #21446964C2semidirect
9. #21446077C2semidirect
10. #21446067C2semidirect
11. #21446006C2semidirect
12. #21445997C2semidirect
13. #21445828C2semidirect
15. C61×#1807C2semidirect
17. C2×#14519768C22semidirect
23. C2×#14519710C22semidirect
24. C2×#14519710C22semidirect
25. C2×#14519706C22semidirect
26. C2×#14519706C22semidirect
41. #16839661C22semidirect
42. #16839658C22semidirect
46. #16839627C22semidirect
50. #16839524C22semidirect
51. #16839524C22semidirect
52. #16839516C22semidirect
53. #16839516C22semidirect
55. C2×#106×C61C22semidirect
56. C2×#106×C61C22semidirect
59. C61×#340C22semidirect
60. C61×#340C22semidirect
332. C22×C61#478semidirect
382. #1807D61semidirect
405. C2×#106C2×D61semidirect
406. C2×#106C2×D61semidirect
436. #340C2×D61semidirect
437. #340C2×D61semidirect
440. C61#25960semidirect
726. C22#16840061semidirect

Maximal subgroups

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

subgroupindex
C2×#168400612
C22×#145196992
#214495442
#214486392
#214473412
#214472082
#214471882
#214469642
#214460772
#214460672
#214460062
#214459972
#214458282
#214457492
C61×#18072
#2596061