Finite Group Databasebeta

← #29723720

Subgroups — #29723720

Order 15616.

1006 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×#16839762C211yesmaximal, characteristic, complemented
2#21449166C211yesmaximal, characteristic
3#21448749C211yesmaximal, characteristic, complemented
4#21447337C211yesmaximal, characteristic, complemented
5#21447240C211yesmaximal, characteristic, complemented
6#21447012C211yesmaximal, characteristic, complemented
7#21447009C211yesmaximal, characteristic, complemented
8#21446455C211yesmaximal, characteristic, complemented
9#21446445C211yesmaximal, characteristic, complemented
10#21446141C211yesmaximal, characteristic, complemented
11#21446113C211yesmaximal, characteristic, complemented
12#21446010C211yesmaximal, characteristic, complemented
13#21445853C211yesmaximal, characteristic, complemented
14#21445758C211yesmaximal, characteristic, complemented
15C2×C61×#485C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C2×#14519751C2211yescharacteristic
19C2×C4×C22⋊D61C2211yescharacteristic
20C2×C4⋊C4×D61C2211yescharacteristic
21C2×#14519709C2211yescharacteristic
22C2×#14519708C2211yescharacteristic
23#16839762—24no—
24C2×#14519701C2211yescharacteristic
25C2×#14519701C2211yescharacteristic
26C2×#14519699C2211yescharacteristic
27C2×#14519699C2211yescharacteristic
28C2×#14519697C2211yescharacteristic
29C2×#14519697C2211yescharacteristic
30C2×C22⋊#92418C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32#16839679—21no—
33#16839671—21no—
34#16839669C2211yescharacteristic
35#16839663C2211yescharacteristic
36#16839656—21no—
37#16839646—21no—
38#16839638—21no—
39#16839638—21no—
40#16839633—21no—
41#16839627C2211yescharacteristic
42#16839622C2211yescharacteristic
43#16839619C2211yescharacteristic
44#16839619C2211yescharacteristic
45C4⋊C4×Dic61C2211yescharacteristic
46C4×#11758198—21no—
47#16839525C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53C2×C22⋊Q8×C61C2211yescharacteristic
54C2×#117×C61C2211yescharacteristic
55C61×#485—24no—
56C2×#107×C61C2211yescharacteristic
57C2×#106×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C2×#11758226—22no—
62C2×#11758226—22no—
63C2×#11758226—22no—
64C2×#11758226—22no—
65C2×#11758226—41no—
66C2×#11758226—41no—
67C22×D244—21no—
68C22×D244C2311yescharacteristic
69C22×C22⋊D61—21no—
70C22×C22⋊D61D411yescharacteristic
71C22×C4×D61—21no—
72C22×C4×D61—21no—
73C22×C4×D61C2311yescharacteristic
74C2×#11758189—22no—
75C2×#11758189—22no—
76C2×#11758189—41no—
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79#14519751—22no—
80#14519751—41no—
81C4×C22⋊D61—22no—
82C4×C22⋊D61—22no—
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×#11758196—21no—
87C2×#11758196D411yescharacteristic
88C4⋊C4×D61—22no—
89C4⋊C4×D61—41no—
90C2×C22⋊Dic61—21no—
91C2×C22⋊Dic61D411yescharacteristic
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×#11758198D411yescharacteristic
98C2×C4×Dic61—21no—
99C2×C4×Dic61C2311yescharacteristic
100#14519709—41no—
101#14519708—41no—
102#14519701—22no—
103#14519701—41no—
104#14519699—22no—
105#14519699—22no—
106#14519697—22no—
107#14519697—41no—
108C22⋊#92418—41no—
109#14519689—22no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118C22×Q8×C61C2311yescharacteristic
119C23×C4×C61C2311yescharacteristic
120C22×C8×C61C2311yescharacteristic
121C22×C8×C61C2311yescharacteristic
122C22⋊Q8×C61—22no—
123C22⋊Q8×C61—41no—
124#117×C61—22no—
125#117×C61—41no—
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61C2311yescharacteristic
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—21no—
132C2×C42×C61—21no—
133#107×C61—22no—
134#106×C61—22no—
135#103×C61—22no—
136#103×C61D414yescomplemented
137C22⋊C8×C61—22no—
138C24×C61C2×D411yescharacteristic
139C23×D61—21no—
140C23×D61C2×D411yescharacteristic
141C2×Q8×C61—21no—
142C2×Q8×C61—21no—
143C2×Q8×C61—21no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61C2×D412yes—
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×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2411yescharacteristic
159C2×C22⋊D61—22no—
160C2×C22⋊D61—41no—
161C2×C22⋊D61—41no—
162C2×C22⋊D61—42no—
163C2×C22⋊D61—42no—
164C2×C22⋊D61—81no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61C2×D411yescharacteristic
169C22×Dic61C2×D411yescharacteristic
170C22×Dic61C2×D411yescharacteristic
171#11758226—28no—
172#11758226—44no—
173#11758226—44no—
174#11758226—44no—
175C2×D244—21no—
176C2×D244—21no—
177C2×D244—21no—
178C2×D244—21no—
179C2×D244—21no—
180C2×D244—42no—
181C2×D244—42no—
182C2×D244—42no—
183C2×D244#4112yes—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—21no—
187C2×C4×D61—21no—
188C2×C4×D61—42no—
189C2×C4×D61—42no—
190C2×C4×D61—42no—
191C2×C4×D61—42no—
192C2×C4×D61—42no—
193C2×C4×D61—81no—
194C2×C4×D61#4112yes—
195C2×C4×D61#4112yes—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61C2×D412yes—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—42no—
208C4⋊C4×C61C2×D412yes—
209C22⋊C4×C61—42no—
210C22⋊C4×C61—42no—
211C42×C61—42no—
212C22⋊Dic61—22no—
213C22⋊Dic61—81no—
214#11758198—22no—
215#11758198—42no—
216#11758198—42no—
217#11758198—42no—
218#11758198—81no—
219#11758198—81no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226#11758196—22no—
227#11758196—42no—
228C4×Dic61—21no—
229C4×Dic61—21no—
230C4×Dic61—81no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237#11758189—44no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61C22×D411yescharacteristic
246C22×D61—21no—
247C22×D61—21no—
248C22×D61—21no—
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—22no—
253C22×D61—41no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61#12312yes—
260Q8×C61—22no—
261Q8×C61—22no—
262Q8×C61—41no—
263Q8×C61—41no—
264C2×C4×C61—21no—
265C2×C4×C61—22no—
266C2×C4×C61—21no—
267C2×C4×C61—22no—
268C2×C4×C61—21no—
269C2×C4×C61—41no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
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×C61C22×D411yescharacteristic
284C2×C4×C61C2×#4111yescharacteristic
285C2×C4×C61C2×#4111yescharacteristic
286C2×C4×C61C2×#4111yescharacteristic
287C2×C4×C61H(5,𝔽2)11yescharacteristic
288C2×C4×C61H(5,𝔽2)11yescharacteristic
289C22⋊D61—44no—
290C22⋊D61—84no—
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61#12312yes—
309D244—22no—
310D244—22no—
311D244—48no—
312D244—41no—
313D244—41no—
314C4×D61—22no—
315C4×D61—22no—
316C4×D61—22no—
317C4×D61—22no—
318C4×D61—48no—
319C4×D61—84no—
320C8×C61—22no—
321C8×C61—41no—
322#92418—41no—
323#92418—41no—
324#24891—611nomaximal, Sylow
325C22×C61—41no—
326C22×C61—41no—
327C22×C61—41no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—41no—
332C22×C61C2×#12311yescharacteristic
333C22×C61D4211yescharacteristic
334C22×C61#54611yescharacteristic
335C22×C61#57511yescharacteristic
336C22×C61#57511yescharacteristic
337C22×C61#57711yescharacteristic
338C22×C61#57711yescharacteristic
339C2×D61—22no—
340C2×D61—22no—
341C2×D61—22no—
342C2×D61—41no—
343C2×D61—41no—
344C2×D61—41no—
345C2×D61—41no—
346C2×D61—42no—
347C2×D61—42no—
348C2×D61—42no—
349C2×D61—81no—
350C2×D61—81no—
351C2×D61—81no—
352C2×D61—81no—
353C4×C61—42no—
354C4×C61—41no—
355C4×C61—42no—
356C4×C61—81no—
357C4×C61—81no—
358C4×C61#52511yescharacteristic
359C4×C61#53811yescharacteristic
360C4×C61#54611yescharacteristic
361C4×C61#55111yescharacteristic
362Dic61—22no—
363Dic61—41no—
364Dic61—41no—
365Dic61—81no—
366Dic61—81no—
367Dic61—81no—
368C2×#485D6111yescharacteristic, complemented
369C2×#417—611no—
370#2407—611no—
371#2352—611no—
372#2092—611no—
373#2074—611no—
374#2035—611no—
375#2034—611no—
376#1927—611no—
377#1926—611no—
378#1875—611no—
379#1870—611no—
380#1853—611no—
381#1809—611no—
382#1788—611no—
383C2×C61—81no—
384C2×C61#241811yescharacteristic
385C2×C61#309311yescharacteristic
386C2×C61#309911yescharacteristic
387C2×C61#327111yescharacteristic
388C2×C61#327511yescharacteristic
389C2×C61#330711yescharacteristic
390C2×C61#332311yescharacteristic
391D61—42no—
392D61—82no—
393C22×#41—611no—
394C22×M16—611no—
395C2×C22⋊Q8C2×D6111yescharacteristic
396C2×#121—611no—
397C2×C4×D4—611no—
398C2×#117C2×D6111yescharacteristic
399C22×C4⋊C4—611no—
400#485—24no—
401C2×#107C2×D6111yescharacteristic
402C2×#106—611no—
403C2×#106—611no—
404C2×#106C2×D6111yescharacteristic
405#417—1224no—
406C2×#103—611no—
407C2×#103—611no—
408C2×#103C2×D6111yescharacteristic
409C2×#103C2×D6111yescharacteristic
410C2×#102—611no—
411C2×#102—611no—
412C2×#102—611no—
413C2×#102—611no—
414C2×C22⋊C8—611no—
415C2×C22⋊C8—611no—
416C2×C22⋊C8C2×D6111yescharacteristic
417#394—1221no—
418#392—1221no—
419#391—611no—
420#390—611no—
421#388—1221no—
422#387—1221no—
423#386—1221no—
424#386—1221no—
425#385—1221no—
426#382—611no—
427#380—611no—
428#380—611no—
429#380—611no—
430C4×C4⋊C4—611no—
431C4×C22⋊C4—1221no—
432#340—611no—
433#340—611no—
434#340—611no—
435#340—611no—
436#336—611no—
437#336—611no—
438C61#2489111yescharacteristic, complemented, Sylow
439C2×#41—1222no—
440C2×#41—1222no—
441C2×#41—1222no—
442C2×#41—1222no—
443C2×#41—2441no—
444C2×#41—2441no—
445C22×Q8C22×D6111yescharacteristic
446C22×D4—611no—
447C22×D4—611no—
448C22×D4—1221no—
449C22×D4—1221no—
450C23×C4—611no—
451C23×C4—1221no—
452C23×C4—1221no—
453C23×C4C22×D6111yescharacteristic
454C2×M16—1222no—
455C2×M16—1222no—
456C2×M16—2441no—
457C22×C8—611no—
458C22×C8—611no—
459C22×C8C22×D6111yescharacteristic
460C22×C8C22×D6111yescharacteristic
461C22⋊Q8—22no—
462C22⋊Q8—41no—
463#121—1222no—
464#121—2441no—
465C4×D4—1222no—
466C4×D4—1222no—
467#117—22no—
468#117—41no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—611no—
471C2×C4⋊C4—611no—
472C2×C4⋊C4—611no—
473C2×C4⋊C4—611no—
474C2×C4⋊C4—1222no—
475C2×C4⋊C4—1221no—
476C2×C4⋊C4—2441no—
477C2×C4⋊C4C22×D6111yescharacteristic
478C2×C4⋊C4C22×D6111yescharacteristic
479C2×C4⋊C4C22×D6111yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—611no—
483C2×C22⋊C4—611no—
484C2×C22⋊C4—1221no—
485C2×C22⋊C4—1221no—
486C2×C22⋊C4—1221no—
487C2×C22⋊C4—1221no—
488C2×C22⋊C4—1221no—
489C2×C22⋊C4—1221no—
490C2×C42—21no—
491C2×C42—611no—
492C2×C42—1221no—
493#107—22no—
494#106—22no—
495#106—2441no—
496#106—2441no—
497#103—22no—
498#103—1222no—
499#103—2441no—
500#103C22⋊D6114yescomplemented
501#102—1222no—
502#102—1222no—
503#102—1222no—
504#102—2441no—
505C22⋊C8—22no—
506C22⋊C8—1222no—
507C22⋊C8—2441no—
508#95—1221no—
509#95—1221no—
510#95—1221no—
511#95—1221no—
512#95—1221no—
513#95—1221no—
514#95—1221no—
515#95—1221no—
516C24—611no—
517C24—1221no—
518C24D4×D6111yescharacteristic
519#41—1228no—
520#41—2444no—
521#41—2444no—
522#41—2444no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8C2×C22⋊D6112yes—
529C2×D4—612no—
530C2×D4—1222no—
531C2×D4—1221no—
532C2×D4—1221no—
533C2×D4—1221no—
534C2×D4—1221no—
535C2×D4—1221no—
536C2×D4—4881no—
537C2×D4—2442no—
538C2×D4—2442no—
539C2×D4—2442no—
540C2×D4—2441no—
541C2×D4—2441no—
542C2×D4—2442no—
543C2×D4—2442no—
544C22×C4—21no—
545C22×C4—21no—
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—612no—
556C22×C4—612no—
557C22×C4—611no—
558C22×C4—611no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—4881no—
567C22×C4—2442no—
568C22×C4—2442no—
569C22×C4—2442no—
570C22×C4—2442no—
571C22×C4—2442no—
572C22×C4D4×D6111yescharacteristic
573C22×C4C23×D6111yescharacteristic
574M16—2444no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—1221no—
581C2×C8—1221no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8C2×C22⋊D6112yes—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—42no—
593C4⋊C4—1222no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—1221no—
598C4⋊C4—1221no—
599C4⋊C4—1221no—
600C4⋊C4—2442no—
601C4⋊C4C2×C22⋊D6112yes—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C22⋊C4—1222no—
605C22⋊C4—1222no—
606C22⋊C4—4881no—
607C22⋊C4—4881no—
608C22⋊C4—4881no—
609C22⋊C4—2442no—
610C22⋊C4—2442no—
611C22⋊C4—2442no—
612C42—42no—
613C42—1221no—
614C42—1221no—
615C42—4881no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—612no—
624C23—1221no—
625C23—1221no—
626C23—1221no—
627C23—1221no—
628C23—1221no—
629C23—1221no—
630C23—1222no—
631C23—2441no—
632C23—2441no—
633C23—2441no—
634C23—2441no—
635C23—2441no—
636C23—2441no—
637C23C2×D4×D6111yescharacteristic
638Q8—22no—
639Q8—22no—
640Q8—41no—
641Q8—41no—
642D4—1222no—
643D4—1222no—
644D4—4884no—
645D4—2448no—
646D4—2444no—
647D4—2441no—
648D4—2441no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—612no—
669C2×C4—1221no—
670C2×C4—1221no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1222no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—4884no—
682C2×C4—2448no—
683C2×C4—2441no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4C22×C22⋊D6111yescharacteristic
693C2×C4#41×D6111yescharacteristic
694C2×C4#41×D6111yescharacteristic
695C2×C4#41×D6111yescharacteristic
696C2×C4#1451982211yescharacteristic
697C2×C4#1451982311yescharacteristic
698C8—22no—
699C8—41no—
700C8—2441no—
701C8—2441no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—1222no—
710C22—1222no—
711C22—1222no—
712C22—4881no—
713C22—4881no—
714C22—4881no—
715C22—4881no—
716C22—2442no—
717C22—2442no—
718C22—2442no—
719C22—2441no—
720C22—2441no—
721C22—2441no—
722C22—2441no—
723C22#123×D6111yescharacteristic
724C22D4×C22⋊D6111yescharacteristic
725C22#1684040411yescharacteristic
726C22#1684055911yescharacteristic
727C22#1684056111yescharacteristic
728C22#1684056911yescharacteristic
729C22#1684057111yescharacteristic
730C4—42no—
731C4—41no—
732C4—42no—
733C4—81no—
734C4—81no—
735C4—1222no—
736C4—4881no—
737C4—4881no—
738C4—4881no—
739C4—2441no—
740C4—2441no—
741C4#1684026911yescharacteristic
742C4#1684034811yescharacteristic
743C4#1684040011yescharacteristic
744C4#1684044011yescharacteristic
745C2—81no—
746C2—4882no—
747C2—2442no—
748C2#2144927811yescharacteristic
749C2#2145575111yescharacteristic
750C2#2145580511yescharacteristic
751C2#2145740411yescharacteristic
752C2#2145744411yescharacteristic
753C2#2145779311yescharacteristic
754C2#2145803311yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#485C2
socleC23×C61C22×D4
prime radical#21449166C2
hypercenterC2×#485D61
hypocenterC61#24891
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
1. C2×#16839762C2semidirect
3. #21448749C2semidirect
4. #21447337C2semidirect
5. #21447240C2semidirect
6. #21447012C2semidirect
7. #21447009C2semidirect
8. #21446455C2semidirect
9. #21446445C2semidirect
10. #21446141C2semidirect
11. #21446113C2semidirect
12. #21446010C2semidirect
13. #21445853C2semidirect
14. #21445758C2semidirect
15. C2×C61×#485C2semidirect
136. #103×C61D4semidirect
368. C2×#485D61semidirect
438. C61#24891semidirect
500. #103C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168397622
#214491662
#214487492
#214473372
#214472402
#214470122
#214470092
#214464552
#214464452
#214461412
#214461132
#214460102
#214458532
#214457582
C2×C61×#4852
#2489161