Finite Group Databasebeta

← #30617072

Subgroups — #30617072

Order 15616.

998 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840805C211yesmaximal, characteristic, complemented
2#21462535C211yesmaximal, characteristic, complemented
3#21462533C211yesmaximal, characteristic, complemented
4C22×C8×#6923C211yesmaximal, characteristic, complemented
5#21461971C211yesmaximal, characteristic, complemented
6#21461926C211yesmaximal, characteristic, complemented
7#21461913C211yesmaximal, characteristic, complemented
8#21461912C211yesmaximal, characteristic, complemented
9#21461837C211yesmaximal, characteristic, complemented
10#21461836C211yesmaximal, characteristic, complemented
11#21461698C211yesmaximal, characteristic, complemented
12#21461622C211yesmaximal, characteristic, complemented
13#21461596C211yesmaximal, characteristic, complemented
14#21461594C211yesmaximal, characteristic, complemented
15#21455395C211yesmaximal, characteristic
16C2×#14519865C2211yescharacteristic
17C2×#14519864C2211yescharacteristic
18C22×D61⋊C8C2211yescharacteristic
19C22×C4×#6923C2211yescharacteristic
20#16840805—24no—
21#16840794—21no—
22#16840793—21no—
23#16840792—21no—
24#16840791—21no—
25#16840790—21no—
26#16840789—21no—
27#16840789—21no—
28D4×#92420—21no—
29C2×#14519847C2211yescharacteristic
30C2×#14519847C2211yescharacteristic
31#16840769C2211yescharacteristic
32#16840769C2211yescharacteristic
33C2×#14519842C2211yescharacteristic
34C2×#14519842C2211yescharacteristic
35C2×#14519841C2211yescharacteristic
36C2×#14519841C2211yescharacteristic
37#16840737C2211yescharacteristic
38#16840736C2211yescharacteristic
39#16840733C2211yescharacteristic
40#16840733C2211yescharacteristic
41#16840727C2211yescharacteristic
42#16840727C2211yescharacteristic
43C2×C8×#6923—24no—
44C2×C8×#6923C2211yescharacteristic
45C2×C8×#6923C2211yescharacteristic
46C2×C8×#6923C2211yescharacteristic
47C2×C8×#6923C2211yescharacteristic
48#16840638C2211yescharacteristic
49#16840638C2211yescharacteristic
50#16840632C2211yescharacteristic
51#16840632C2211yescharacteristic
52#16840632C2211yescharacteristic
53#16840632C2211yescharacteristic
54C2×#14519798C2211yescharacteristic
55C22×C8×D61C2211yescharacteristic
56#16840275C2211yescharacteristic
57#16840272C2211yescharacteristic
58#16840002C411yescharacteristic, complemented
59#16840001C411yescharacteristic, complemented
60#16839997C411yescharacteristic, complemented
61#16839996C411yescharacteristic, complemented
62#16839992C411yescharacteristic, complemented
63#16839991C411yescharacteristic, complemented
64#16839988C411yescharacteristic, complemented
65#16839797C2211yescharacteristic
66#16839757C2211yescharacteristic
67#16839755C2211yescharacteristic
68C61×#465C411yescharacteristic, complemented
69C23×#6923—21no—
70#14519865—22no—
71#14519865—22no—
72#14519864—22no—
73#14519864—22no—
74C2×#11758213—21no—
75C2×#11758213C2311yescharacteristic
76C2×#11758213C2311yescharacteristic
77C2×#11758213C2311yescharacteristic
78C2×#11758213C2311yescharacteristic
79C2×#11758217—21no—
80C2×D61⋊C8—22no—
81C2×D61⋊C8—22no—
82C2×D61⋊C8—21no—
83C2×D61⋊C8D411yescharacteristic
84C2×D61⋊C8D411yescharacteristic
85C2×D61⋊C8C2311yescharacteristic
86C2×D61⋊C8C2311yescharacteristic
87C22×#92420—21no—
88C22×#92420D411yescharacteristic
89C22×#92420D411yescharacteristic
90C2×C4×#6923—21no—
91C2×C4×#6923—22no—
92C2×C4×#6923—22no—
93C2×C4×#6923C2311yescharacteristic
94C2×C4×#6923C2311yescharacteristic
95#14519847—22no—
96#14519847—22no—
97#14519844—21no—
98#14519844—21no—
99C4⋊#92420—21no—
100C4⋊#92420—21no—
101#14519842—22no—
102#14519842—22no—
103#14519841—22no—
104#14519841—22no—
105#14519834—21no—
106#14519834—21no—
107#14519834—21no—
108#14519834—21no—
109C22⋊#92420—21no—
110C22⋊#92420—21no—
111C22⋊#92420—21no—
112C22⋊#92420—21no—
113#14519832—21no—
114#14519832—21no—
115C4×#92420—21no—
116C4×#92420—21no—
117C8×#6923—22no—
118C8×#6923—22no—
119C8×#6923—22no—
120C8×#6923D414yescomplemented
121C2×#11758226C2311yescharacteristic
122C2×#11758224C2311yescharacteristic
123C22×C4×D61C2311yescharacteristic
124#14519798—22no—
125#14519798—22no—
126C2×#11758202C2×C411yescharacteristic, complemented
127C2×#11758190C2×C411yescharacteristic, complemented
128C2×#11758199C2×C411yescharacteristic, complemented
129C22×#92418C2×C411yescharacteristic
130C2×C8×D61—22no—
131C2×C8×D61—22no—
132C2×C8×D61C2×C411yescharacteristic
133C2×C8×D61C2×C411yescharacteristic
134C2×C8×D61C2311yescharacteristic
135C2×C8×D61C2311yescharacteristic
136#14519762—21no—
137#14519759—21no—
138#14519757C2×C411yescharacteristic
139#14519756C2×C411yescharacteristic
140#14519753C2×C411yescharacteristic
141#14519752C2×C411yescharacteristic
142#14519751C2×C411yescharacteristic
143#14519748C2×C411yescharacteristic
144#14519747—21no—
145#14519745—21no—
146D4×Dic61—21no—
147#14519739—21no—
148#14519737—21no—
149#14519737—21no—
150#14519735C2311yescharacteristic
151#14519735C2311yescharacteristic
152#14519710C2×C411yescharacteristic, complemented
153#14519710C2×C411yescharacteristic, complemented
154#14519709C2×C411yescharacteristic, complemented
155#14519702C2×C411yescharacteristic, complemented
156#14519701C2×C411yescharacteristic, complemented
157#14519700C2×C411yescharacteristic, complemented
158#14519699C2×C411yescharacteristic, complemented
159#14519698C2×C411yescharacteristic, complemented
160#14519697C2×C411yescharacteristic, complemented
161C2×SD16×C61C2×C411yescharacteristic, complemented
162C22×C8×C61C2×C411yescharacteristic
163C22⋊Q8×C61C2×C411yescharacteristic
164#121×C61C2×C411yescharacteristic
165#106×C61C2×C411yescharacteristic, complemented
166#103×C61C2×C411yescharacteristic, complemented
167#102×C61C2×C411yescharacteristic, complemented
168C23×D61#4111yescharacteristic
169C22×#6923—24no—
170C22×#6923—24no—
171C22×#6923—24no—
172C22×#6923—21no—
173C22×#6923—21no—
174C2×Q8×C61C22×C411yescharacteristic
175C2×D4×C61—21no—
176C2×D4×C61C22×C411yescharacteristic
177C22×C4×C61C22×C411yescharacteristic
178C2×C22⋊D61—21no—
179C2×C22⋊D61—21no—
180C2×C22⋊D61—21no—
181C22×Dic61—21no—
182C22×Dic61C2×D411yescharacteristic
183#11758226—21no—
184#11758226—21no—
185#11758226—21no—
186#11758226—21no—
187#11758224—21no—
188#11758224—21no—
189#11758224—21no—
190#11758224—21no—
191C2×D244—21no—
192C2×D244—21no—
193C2×D244C22×C411yescharacteristic
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61C22×C411yescharacteristic
200C2×C4×D61C2×D411yescharacteristic
201C2×C4×D61#4111yescharacteristic
202C2×C4×D61C2411yescharacteristic
203C2×Dic122C22×C411yescharacteristic
204#11758217—42no—
205C2×#92420—22no—
206C2×#92420—22no—
207C2×#92420—21no—
208C2×#92420—21no—
209C2×#92420—21no—
210C2×#92420—21no—
211C2×#92420—42no—
212C2×#92420C2×D411yescharacteristic
213C2×#92420C2×D411yescharacteristic
214C2×#92420C2×D411yescharacteristic
215C2×#92420C2×D411yescharacteristic
216C4×#6923—24no—
217C4×#6923—21no—
218C4×#6923—21no—
219C4×#6923C2×D412yes—
220C4×#6923#4112yes—
221#11758213—21no—
222#11758213—21no—
223#11758213—21no—
224#11758213—21no—
225#11758213—21no—
226#11758213—21no—
227#11758213—21no—
228#11758213—21no—
229#11758213—42no—
230D61⋊C8—21no—
231D61⋊C8—21no—
232D61⋊C8—22no—
233D61⋊C8—22no—
234D61⋊C8—42no—
235D61⋊C8C2×D412yes—
236D61⋊C8#4112yes—
237SD16×C61—22no—
238C2×C8×C61—22no—
239C2×C8×C61C22×C411yescharacteristic
240C2×C8×C61C22×C411yescharacteristic
241C4⋊C4×C61—21no—
242C4⋊C4×C61C22×C411yescharacteristic
243C4⋊C4×C61C22×C411yescharacteristic
244C22⋊C4×C61—21no—
245C22⋊C4×C61—21no—
246C22⋊Dic61—21no—
247C22⋊Dic61—21no—
248#11758202—22no—
249#11758199—22no—
250#11758198—21no—
251#11758198—21no—
252#11758198—21no—
253#11758198—21no—
254#11758198—21no—
255#11758198—21no—
256C4⋊Dic61—21no—
257C4⋊Dic61C22×C411yescharacteristic
258C4⋊Dic61C22×C411yescharacteristic
259#11758196—21no—
260#11758196—21no—
261C4×Dic61—21no—
262C4×Dic61—21no—
263C2×#92418—22no—
264C2×#92418C22×C411yescharacteristic
265C2×#92418C22×C411yescharacteristic
266#11758190—22no—
267C8×D61—21no—
268C8×D61—21no—
269C8×D61—22no—
270C8×D61—22no—
271C8×D61C2×D412yes—
272C8×D61#4112yes—
273C23×C61—21no—
274C23×C61C4×D411yescharacteristic
275C22×D61—22no—
276C22×D61—21no—
277C22×D61—21no—
278C22×D61—22no—
279C22×D61—21no—
280C22×D61C4×D411yescharacteristic
281C22×D61C2×#4111yescharacteristic
282C2×#6923—216no—
283C2×#6923—22no—
284C2×#6923—22no—
285C2×#6923—22no—
286C2×#6923—22no—
287C2×#6923—22no—
288C2×#6923—22no—
289Q8×C61—21no—
290Q8×C61—21no—
291D4×C61—21no—
292D4×C61—21no—
293D4×C61—42no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61C4×D411yescharacteristic
300C2×C4×C61C23×C411yescharacteristic
301C22⋊D61—42no—
302C22⋊D61—41no—
303C22⋊D61—41no—
304C22⋊D61—42no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61C4×D411yescharacteristic
313C2×Dic61C22×D411yescharacteristic
314D244—21no—
315D244—21no—
316D244—41no—
317D244—41no—
318D244—42no—
319C4×D61—21no—
320C4×D61—21no—
321C4×D61—21no—
322C4×D61—21no—
323C4×D61—21no—
324C4×D61—21no—
325C4×D61—41no—
326C4×D61—41no—
327C4×D61C22×D411yescharacteristic
328C4×D61C2×#4111yescharacteristic
329C4×D61C2×#4111yescharacteristic
330C4×D61C2×#4111yescharacteristic
331Dic122—21no—
332Dic122—21no—
333#92420—21no—
334#92420—21no—
335#92420—41no—
336#92420—41no—
337#92420—41no—
338#92420—41no—
339#92420#12112yes—
340#92420#12112yes—
341C8×C61—21no—
342C8×C61C4×D412yes—
343#92418—21no—
344#92418C4×D412yes—
345#21544—611nomaximal, Sylow
346C22×C61—21no—
347C22×C61—21no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61#44312yescomplemented
352C22×C61C2×C4×D411yescharacteristic
353C2×D61—24no—
354C2×D61—24no—
355C2×D61—21no—
356C2×D61—21no—
357C2×D61—21no—
358C2×D61—21no—
359C2×D61—41no—
360C2×D61—41no—
361C2×D61—41no—
362C2×D61#44312yescomplemented
363C2×D61#52511yescharacteristic
364C2×D61#52911yescharacteristic
365#6923—24no—
366#6923—24no—
367C4×C61—21no—
368C4×C61—41no—
369C4×C61—41no—
370C4×C61—41no—
371C4×C61C2×C4×D411yescharacteristic
372C4×C61C4×#4111yescharacteristic
373Dic61—21no—
374Dic61—41no—
375Dic61—41no—
376Dic61—41no—
377Dic61C2×#12111yescharacteristic
378Dic61#53211yescharacteristic
379#3050—611no—
380C2×#443—611no—
381#2929—611no—
382#2929—611no—
383C22×C4×C8—611no—
384#1974—611no—
385#1945—611no—
386#1937—611no—
387#1937—611no—
388#1896—611no—
389#1896—611no—
390#1810—611no—
391#1772—611no—
392#1764—611no—
393#1764—611no—
394C2×C61—22no—
395C2×C61—81no—
396C2×C61C4×#12111yescharacteristic
397C2×C61C2×#44311yescharacteristic
398C2×C61C2×#44311yescharacteristic
399D61—21no—
400D61—21no—
401D61—22no—
402D61—81no—
403C2×#135—611no—
404C2×#131—611no—
405C2×#131—611no—
406C23×C8—611no—
407C23×C8—611no—
408#525—611no—
409#525—611no—
410C22×C42—611no—
411#467—611no—
412#467—611no—
413#466—611no—
414#466—611no—
415#465—611no—
416#465—611no—
417#465—611no—
418#465#692311yescharacteristic, complemented
419#443—1224no—
420#435—1221no—
421#435—1221no—
422#435—1221no—
423#435—1221no—
424C8×D4—1221no—
425C8×D4—1221no—
426C8×D4—1221no—
427C8×D4—1221no—
428C2×#108—611no—
429C2×#108—611no—
430#427—611no—
431#424—611no—
432#424—611no—
433C2×#104—611no—
434C2×#104—611no—
435C2×#104—611no—
436C2×#104—611no—
437#416—611no—
438#416—611no—
439#408—611no—
440#408—611no—
441#407—611no—
442#407—611no—
443#405—611no—
444#405—611no—
445C2×C4×C8—611no—
446C2×C4×C8—611no—
447C2×C4×C8—611no—
448C2×C4×C8—611no—
449C2×C4×C8—1224no—
450#341—611no—
451#341—611no—
452#339—611no—
453#339—611no—
454#339—611no—
455#339—611no—
456C61#2154411yescharacteristic, complemented, Sylow
457C2×#41—611no—
458C2×#41—611no—
459C23×C4—611no—
460C23×C4—1221no—
461#135—1222no—
462#135—1222no—
463C2×Q16—611no—
464C2×SD16—611no—
465C2×SD16C2×#692311yescharacteristic, complemented
466C2×D8—611no—
467#131—1222no—
468#131—1222no—
469#131—1222no—
470#131—1222no—
471C2×M16—611no—
472C2×M16—611no—
473C2×M16—611no—
474C2×M16—611no—
475C2×M16—1221no—
476C2×M16—1221no—
477C22×C8—611no—
478C22×C8—611no—
479C22×C8—611no—
480C22×C8—611no—
481C22×C8—611no—
482C22×C8—611no—
483C22×C8—611no—
484C22×C8—611no—
485C22×C8—611no—
486C22×C8—611no—
487C22×C8—611no—
488C22×C8—1222no—
489C22×C8—1222no—
490C22×C8—1222no—
491C22×C8—1222no—
492C22×C8—1221no—
493C22×C8—1221no—
494C22×C8C2×#692311yescharacteristic
495#123—1221no—
496#123—1221no—
497C22⋊Q8—611no—
498C22⋊Q8—611no—
499C22⋊Q8—611no—
500C22⋊Q8C2×#692311yescharacteristic
501#121—611no—
502#121—611no—
503#121—611no—
504#121C2×#692311yescharacteristic
505#120—1221no—
506#120—1221no—
507C4×D4—1221no—
508C4×D4—1221no—
509C4×D4—1221no—
510C4×D4—1221no—
511#117—611no—
512#117—611no—
513C2×C42—611no—
514C2×C42—611no—
515C2×C42—1222no—
516C2×C42—1222no—
517C2×C42—1221no—
518#108—1222no—
519#108—1222no—
520#107—611no—
521#107—611no—
522#106—611no—
523#106C2×#692311yescharacteristic, complemented
524C4⋊C8—1221no—
525C4⋊C8—1221no—
526C4⋊C8—1221no—
527C4⋊C8—1221no—
528#104—1222no—
529#104—1222no—
530#104—1222no—
531#104—1222no—
532#103—611no—
533#103—611no—
534#103—611no—
535#103C2×#692311yescharacteristic, complemented
536#102—611no—
537#102—611no—
538#102—611no—
539#102C2×#692311yescharacteristic, complemented
540C22⋊C8—1221no—
541C22⋊C8—1221no—
542C22⋊C8—1221no—
543C22⋊C8—1221no—
544C22⋊C8—1221no—
545C22⋊C8—1221no—
546C22⋊C8—1221no—
547C22⋊C8—1221no—
548#97—1221no—
549#97—1221no—
550C4×C8—614no—
551C4×C8—1222no—
552C4×C8—1222no—
553C4×C8—1222no—
554C4×C8—1221no—
555C4×C8—1221no—
556C24—611no—
557#41—1221no—
558#41—1221no—
559#41—1221no—
560#41—1221no—
561#41—1221no—
562#41—1221no—
563#41—1221no—
564#41—1221no—
565C2×Q8—611no—
566C2×Q8C22×#692311yescharacteristic
567C2×D4—21no—
568C2×D4—611no—
569C2×D4—1221no—
570C2×D4—1221no—
571C2×D4—1221no—
572C2×D4—1221no—
573C2×D4—1221no—
574C2×D4C22×#692311yescharacteristic
575C22×C4—611no—
576C22×C4—611no—
577C22×C4—611no—
578C22×C4—611no—
579C22×C4—611no—
580C22×C4—1221no—
581C22×C4—1221no—
582C22×C4—1221no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1224no—
589C22×C4—1224no—
590C22×C4—1224no—
591C22×C4C22×#692311yescharacteristic
592Q16—1222no—
593SD16—22no—
594SD16—1222no—
595D8—1222no—
596M16—1221no—
597M16—1221no—
598M16—1221no—
599M16—1221no—
600M16—1221no—
601M16—1221no—
602M16—1221no—
603M16—1221no—
604M16—2442no—
605M16—2442no—
606C2×C8—22no—
607C2×C8—612no—
608C2×C8—611no—
609C2×C8—611no—
610C2×C8—612no—
611C2×C8—611no—
612C2×C8—612no—
613C2×C8—612no—
614C2×C8—611no—
615C2×C8—611no—
616C2×C8—611no—
617C2×C8—1222no—
618C2×C8—1221no—
619C2×C8—1221no—
620C2×C8—1222no—
621C2×C8—1222no—
622C2×C8—1222no—
623C2×C8—1222no—
624C2×C8—1222no—
625C2×C8—1221no—
626C2×C8—1221no—
627C2×C8—1222no—
628C2×C8—1221no—
629C2×C8—1221no—
630C2×C8—1221no—
631C2×C8—1221no—
632C2×C8—2442no—
633C2×C8—2442no—
634C2×C8C22×#692311yescharacteristic
635C2×C8C22×#692311yescharacteristic
636C4⋊C4—21no—
637C4⋊C4—611no—
638C4⋊C4—611no—
639C4⋊C4—1221no—
640C4⋊C4—1221no—
641C4⋊C4—1221no—
642C4⋊C4C22×#692311yescharacteristic
643C4⋊C4C22×#692311yescharacteristic
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—1221no—
647C22⋊C4—1221no—
648C22⋊C4—1221no—
649C22⋊C4—1221no—
650C22⋊C4—1221no—
651C22⋊C4—1221no—
652C22⋊C4—1221no—
653C22⋊C4—1221no—
654C42—612no—
655C42—612no—
656C42—1221no—
657C42—1221no—
658C42—1221no—
659C42—1221no—
660C42—1224no—
661C23—21no—
662C23—611no—
663C23—611no—
664C23—1221no—
665C23—1221no—
666C23—1222no—
667C23—1222no—
668C23—1221no—
669C23D4×#692311yescharacteristic
670Q8—21no—
671Q8—21no—
672Q8—1221no—
673Q8—1221no—
674D4—21no—
675D4—21no—
676D4—42no—
677D4—1221no—
678D4—1221no—
679D4—2442no—
680D4—2441no—
681D4—2441no—
682D4—2442no—
683D4—2441no—
684D4—2441no—
685D4—2442no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—611no—
692C2×C4—611no—
693C2×C4—611no—
694C2×C4—611no—
695C2×C4—611no—
696C2×C4—611no—
697C2×C4—1221no—
698C2×C4—1221no—
699C2×C4—1221no—
700C2×C4—1221no—
701C2×C4—1221no—
702C2×C4—1221no—
703C2×C4—1222no—
704C2×C4—1222no—
705C2×C4—12216no—
706C2×C4—1222no—
707C2×C4—1222no—
708C2×C4—1222no—
709C2×C4—1222no—
710C2×C4—1221no—
711C2×C4—1221no—
712C2×C4—1221no—
713C2×C4—1221no—
714C2×C4—1221no—
715C2×C4—2441no—
716C2×C4—2441no—
717C2×C4—2441no—
718C2×C4—2441no—
719C2×C4D4×#692311yescharacteristic
720C2×C4C23×#692311yescharacteristic
721C8—21no—
722C8—612no—
723C8—612no—
724C8—612no—
725C8—1221no—
726C8—1221no—
727C8—1221no—
728C8—2441no—
729C8—2441no—
730C8—2441no—
731C8—2441no—
732C8D4×#692312yes—
733C22—21no—
734C22—21no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—611no—
739C22—611no—
740C22—612no—
741C22—1224no—
742C22—1224no—
743C22—1221no—
744C22—1221no—
745C22—1221no—
746C22—1221no—
747C22—2441no—
748C22—2441no—
749C22—2441no—
750C22#1684080512yescomplemented
751C22C2×D4×#692311yescharacteristic
752C4—21no—
753C4—41no—
754C4—41no—
755C4—41no—
756C4—611no—
757C4—611no—
758C4—1224no—
759C4—1224no—
760C4—1221no—
761C4—2441no—
762C4—2441no—
763C4—2441no—
764C4C2×D4×#692311yescharacteristic
765C4#41×#692311yescharacteristic
766C2—22no—
767C2—81no—
768C2—1221no—
769C2—1221no—
770C2—1222no—
771C2—4881no—
772C2#121×#692311yescharacteristic
773C2C2×#1684080511yescharacteristic
774C2D61⋊#44311yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#465C4
socleC22×C61C2×C4×D4
prime radical#21455395C2
cosocleC2×C4×D61C24
hypercenter#465#6923
hypocenterC61#21544
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×#16840805C2semidirect
2. #21462535C2semidirect
3. #21462533C2semidirect
4. C22×C8×#6923C2semidirect
5. #21461971C2semidirect
6. #21461926C2semidirect
7. #21461913C2semidirect
8. #21461912C2semidirect
9. #21461837C2semidirect
10. #21461836C2semidirect
11. #21461698C2semidirect
12. #21461622C2semidirect
13. #21461596C2semidirect
14. #21461594C2semidirect
58. #16840002C4semidirect
59. #16840001C4semidirect
60. #16839997C4semidirect
61. #16839996C4semidirect
62. #16839992C4semidirect
63. #16839991C4semidirect
64. #16839988C4semidirect
68. C61×#465C4semidirect
120. C8×#6923D4semidirect
126. C2×#11758202C2×C4semidirect
127. C2×#11758190C2×C4semidirect
128. C2×#11758199C2×C4semidirect
152. #14519710C2×C4semidirect
153. #14519710C2×C4semidirect
154. #14519709C2×C4semidirect
155. #14519702C2×C4semidirect
156. #14519701C2×C4semidirect
157. #14519700C2×C4semidirect
158. #14519699C2×C4semidirect
159. #14519698C2×C4semidirect
160. #14519697C2×C4semidirect
161. C2×SD16×C61C2×C4semidirect
165. #106×C61C2×C4semidirect
166. #103×C61C2×C4semidirect
167. #102×C61C2×C4semidirect
351. C22×C61#443semidirect
362. C2×D61#443semidirect
418. #465#6923semidirect
456. C61#21544semidirect
465. C2×SD16C2×#6923semidirect
523. #106C2×#6923semidirect
535. #103C2×#6923semidirect
539. #102C2×#6923semidirect
750. C22#16840805semidirect

Maximal subgroups

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

subgroupindex
C2×#168408052
#214625352
#214625332
C22×C8×#69232
#214619712
#214619262
#214619132
#214619122
#214618372
#214618362
#214616982
#214616222
#214615962
#214615942
#214553952
#2154461