Finite Group Databasebeta

← #29691305

Subgroups — #29691305

Order 15616.

1024 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839907C211yesmaximal, characteristic
2#21448508C211yesmaximal, characteristic, complemented
3#21448411C211yesmaximal, characteristic, complemented
4#21446692C211yesmaximal, characteristic, complemented
5#21446670C211yesmaximal, characteristic, complemented
6#21446506C211yesmaximal, characteristic, complemented
7#21446499C211yesmaximal, characteristic, complemented
8#21446456C211yesmaximal, characteristic, complemented
9#21446449C211yesmaximal, characteristic, complemented
10#21446164C211yesmaximal, characteristic, complemented
11#21446150C211yesmaximal, characteristic, complemented
12#21446134C211yesmaximal, characteristic, complemented
13#21446011C211yesmaximal, characteristic, complemented
14#21445587C211yesmaximal, characteristic, complemented
15C61×#1788C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C2×#14519751C2211yescharacteristic
19C2×#14519739C2211yescharacteristic
20C2×#14519736C2211yescharacteristic
21C22×C4⋊Dic61C2211yescharacteristic
22#16839907C418yescomplemented
23C2×#14519708C2211yescharacteristic
24C2×#14519708C2211yescharacteristic
25C2×#14519701C2211yescharacteristic
26C2×#14519699C2211yescharacteristic
27C2×#14519699C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×C22⋊#92418C2211yescharacteristic
30C2×#14519687C2211yescharacteristic
31C2×C8×Dic61C2211yescharacteristic
32#16839669C2211yescharacteristic
33#16839669C2211yescharacteristic
34#16839665C2211yescharacteristic
35#16839665C2211yescharacteristic
36#16839663C2211yescharacteristic
37#16839662—21no—
38#16839658C2211yescharacteristic
39#16839654—21no—
40#16839642—21no—
41#16839642—21no—
42#16839638—21no—
43#16839636—21no—
44#16839622—21no—
45#16839622—21no—
46C4⋊C4×Dic61C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53C22×#41×C61C2211yescharacteristic
54C2×#103×C61C2211yescharacteristic
55C2×#103×C61C2211yescharacteristic
56C2×#102×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C2×C22⋊C8×C61C2211yescharacteristic
59C61×#380C2211yescharacteristic
60C22×D244C2311yescharacteristic
61C22×C22⋊D61—21no—
62C23×Dic61—21no—
63C22×C4×D61—21no—
64C2×#11758201—41no—
65C2×#11758201—41no—
66C2×#11758201C2×C414yescomplemented
67C2×#11758199—41no—
68C2×#11758199—41no—
69C2×#11758199C2×C414yescomplemented
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72#14519751—22no—
73#14519751C2×C414yes—
74#14519739—41no—
75#14519739—41no—
76#14519736—41no—
77#14519736—41no—
78C2×C4⋊Dic61—21no—
79C2×C4⋊Dic61—41no—
80C2×C4⋊Dic61—41no—
81C2×C4⋊Dic61D411yescharacteristic
82C2×C4⋊Dic61D411yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×#11758196—21no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×C22⋊Dic61D411yescharacteristic
92C2×C22⋊Dic61D411yescharacteristic
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×C4×Dic61—21no—
98C2×C4×Dic61C2311yescharacteristic
99C2×C4×Dic61C2311yescharacteristic
100#14519708—41no—
101#14519708—41no—
102#14519701C2×C414yescomplemented
103#14519699—41no—
104#14519699—41no—
105#14519698C2×C414yescomplemented
106C22⋊#92418C2×C414yescomplemented
107#14519687—41no—
108C8×Dic61—41no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115C2×#41×C61—22no—
116C2×#41×C61—41no—
117C2×#41×C61—41no—
118C2×#41×C61—41no—
119C2×#41×C61—41no—
120C2×#41×C61C2×C414yescomplemented
121C22×Q8×C61C2311yescharacteristic
122C22×D4×C61—21no—
123C22×D4×C61C2311yescharacteristic
124C23×C4×C61—21no—
125C23×C4×C61C2311yescharacteristic
126C22×C8×C61C2311yescharacteristic
127C22×C8×C61C2311yescharacteristic
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C22⋊C4×C61—21no—
131#103×C61—41no—
132#103×C61—41no—
133#102×C61—41no—
134#102×C61—41no—
135C22⋊C8×C61—22no—
136#95×C61—21no—
137C24×C61—21no—
138C24×C61C2×D411yescharacteristic
139C23×D61—21no—
140#41×C61—44no—
141#41×C61—44no—
142#41×C61—44no—
143#41×C61—44no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61C22×C412yes—
150C2×D4×C61—24no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—42no—
157C2×D4×C61—42no—
158C2×D4×C61C22×C412yes—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—24no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—42no—
168C22×C4×C61—42no—
169C22×C4×C61C22×C412yes—
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61#4112yes—
172C22×C4×C61C2411yescharacteristic
173C2×C22⋊D61—24no—
174C2×C22⋊D61—81no—
175C2×C22⋊D61—81no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—42no—
180C22×Dic61—81no—
181C22×Dic61—81no—
182C22×Dic61C2×D411yescharacteristic
183C22×Dic61C2×D411yescharacteristic
184C22×Dic61C2×D411yescharacteristic
185C22×Dic61C2×D411yescharacteristic
186C2×D244—21no—
187C2×D244—21no—
188C2×D244—21no—
189C2×D244—21no—
190C2×D244—21no—
191C2×D244C22×C412yes—
192C2×C4×D61—42no—
193C2×C4×D61—81no—
194C2×C4×D61—81no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C22⋊C4×C61—81no—
206C22⋊Dic61—41no—
207C22⋊Dic61—41no—
208C22⋊Dic61—81no—
209C22⋊Dic61—81no—
210C22⋊Dic61—81no—
211C22⋊Dic61—81no—
212#11758201—44no—
213#11758199—44no—
214#11758198—24no—
215#11758198—42no—
216#11758198—81no—
217#11758198—81no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—41no—
224C4⋊Dic61—41no—
225C4⋊Dic61—42no—
226C4⋊Dic61C22×C412yes—
227#11758196—81no—
228C4×Dic61—21no—
229C4×Dic61—21no—
230C4×Dic61—21no—
231C4×Dic61—21no—
232C4×Dic61—81no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418C22×C412yes—
238C2×#92418C22×C412yes—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—22no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61C4×D412yes—
253C23×C61C22×D411yescharacteristic
254C22×D61—22no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—41no—
261Q8×C61—22no—
262Q8×C61—22no—
263Q8×C61—41no—
264Q8×C61—41no—
265D4×C61—22no—
266D4×C61—22no—
267D4×C61—48no—
268D4×C61—41no—
269D4×C61—41no—
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—22no—
277C2×C4×C61—48no—
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×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61C4×D412yes—
287C2×C4×C61C23×C411yescharacteristic
288C2×C4×C61C2×#4111yescharacteristic
289C2×C4×C61H(5,𝔽2)11yescharacteristic
290C2×C4×C61H(5,𝔽2)11yescharacteristic
291C2×C4×C61H(5,𝔽2)11yescharacteristic
292C2×C4×C61H(5,𝔽2)11yescharacteristic
293C22⋊D61—84no—
294C2×Dic61—22no—
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—21no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—84no—
316D244—22no—
317D244—22no—
318D244—41no—
319D244—41no—
320C4×D61—84no—
321C8×C61—41no—
322C8×C61—41no—
323#92418—22no—
324#92418—22no—
325#22053—611nomaximal, Sylow
326C22×C61—22no—
327C22×C61—22no—
328C22×C61—22no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—41no—
332C22×C61—41no—
333C22×C61—42no—
334C22×C61—42no—
335C22×C61—42no—
336C22×C61—81no—
337C22×C61—81no—
338C22×C61—81no—
339C22×C61—81no—
340C22×C61C2×C4×D411yescharacteristic
341C22×C61#53411yescharacteristic
342C22×C61#53511yescharacteristic
343C22×C61#57611yescharacteristic
344C22×C61#57711yescharacteristic
345C22×C61#57711yescharacteristic
346C22×C61#57711yescharacteristic
347C2×D61—42no—
348C2×D61—42no—
349C2×D61—42no—
350C2×D61—81no—
351C2×D61—81no—
352C2×D61—81no—
353C2×D61—81no—
354C4×C61—22no—
355C4×C61—42no—
356C4×C61—81no—
357C4×C61—81no—
358C4×C61#51811yescharacteristic
359C4×C61#51811yescharacteristic
360C4×C61#53811yescharacteristic
361C4×C61#53811yescharacteristic
362Dic61—41no—
363Dic61—41no—
364Dic61—42no—
365Dic61—41no—
366Dic61—41no—
367Dic61—81no—
368Dic61—81no—
369C2×#449—611no—
370#2324—611no—
371#2311—611no—
372#1972—611no—
373#1968—611no—
374#1935—611no—
375#1934—611no—
376#1927—611no—
377#1926—611no—
378#1879—611no—
379#1877—611no—
380#1874—611no—
381#1853—611no—
382#1788D6111yescharacteristic, complemented
383#1750—611no—
384C2×C61—42no—
385C2×C61—82no—
386C2×C61#232111yescharacteristic
387C2×C61#294611yescharacteristic
388C2×C61#295211yescharacteristic
389C2×C61#319811yescharacteristic
390C2×C61#320411yescharacteristic
391C2×C61#322111yescharacteristic
392C2×C61#322411yescharacteristic
393D61—82no—
394C22×#41C2×D6111yescharacteristic
395C22×SD16—611no—
396C22×D8—611no—
397C2×#121—611no—
398C2×C4×D4—611no—
399C2×#117—611no—
400C22×C4⋊C4—611no—
401#449—618no—
402C2×#106—611no—
403C2×#106—611no—
404C2×#103—611no—
405C2×#103C2×D6111yescharacteristic
406C2×#103C2×D6111yescharacteristic
407C2×#102—611no—
408C2×#102—611no—
409C2×#102—611no—
410C2×#102C2×D6111yescharacteristic
411C2×#102C2×D6111yescharacteristic
412C2×C22⋊C8—611no—
413C2×C22⋊C8C2×D6111yescharacteristic
414C2×#97—611no—
415C2×C4×C8—611no—
416#391—611no—
417#391—611no—
418#390—611no—
419#390—611no—
420#390—611no—
421#390—1221no—
422#389—611no—
423#388—1221no—
424#386—1221no—
425#386—1221no—
426#386—1221no—
427#385—1221no—
428#380—1221no—
429#380—1221no—
430#380C2×D6111yescharacteristic
431C4×C4⋊C4—611no—
432#340—611no—
433#340—611no—
434#340—611no—
435#340—611no—
436#336—611no—
437#336—611no—
438C61#2205311yescharacteristic, complemented, Sylow
439C2×#41—22no—
440C2×#41—41no—
441C2×#41—41no—
442C2×#41—41no—
443C2×#41—41no—
444C2×#41C4×D6114yescomplemented
445C22×Q8C22×D6111yescharacteristic
446C22×D4—21no—
447C22×D4—611no—
448C22×D4—1221no—
449C22×D4C22×D6111yescharacteristic
450C23×C4—21no—
451C23×C4—1221no—
452C23×C4—1221no—
453C23×C4C22×D6111yescharacteristic
454C2×SD16—614no—
455C2×SD16—2441no—
456C2×SD16—2441no—
457C2×D8—614no—
458C2×D8—2441no—
459C2×D8—2441no—
460C22×C8—611no—
461C22×C8—611no—
462C22×C8C22×D6111yescharacteristic
463C22×C8C22×D6111yescharacteristic
464#121—614no—
465#121—1222no—
466C4×D4—2441no—
467C4×D4—2441no—
468#117—2441no—
469#117—2441no—
470C2×C4⋊C4—611no—
471C2×C4⋊C4—611no—
472C2×C4⋊C4—611no—
473C2×C4⋊C4—611no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4—1221no—
476C2×C4⋊C4—1221no—
477C2×C4⋊C4—2441no—
478C2×C4⋊C4—2441no—
479C2×C4⋊C4C22×D6111yescharacteristic
480C2×C4⋊C4C22×D6111yescharacteristic
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×C22⋊C4—1221no—
491C2×C22⋊C4—1221no—
492C2×C42—611no—
493C2×C42—611no—
494C2×C42—1221no—
495#106—2441no—
496#106—2441no—
497#103—41no—
498#103—41no—
499#103—614no—
500#102—41no—
501#102—41no—
502#102—614no—
503#102—2441no—
504#102—2441no—
505C22⋊C8—22no—
506C22⋊C8—614no—
507#97—2441no—
508C4×C8—2441no—
509#95—21no—
510#95—1221no—
511#95—1221no—
512#95—1221no—
513#95—1221no—
514#95—1221no—
515#95—1221no—
516C24—21no—
517C24—1221no—
518C24D4×D6111yescharacteristic
519#41—44no—
520#41—44no—
521#41—44no—
522#41—44no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8C2×C4×D6112yes—
529C2×D4—24no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—612no—
538C2×D4—1224no—
539C2×D4—1221no—
540C2×D4—1221no—
541C2×D4—1221no—
542C2×D4—1221no—
543C2×D4—1221no—
544C2×D4—4881no—
545C2×D4—4881no—
546C2×D4C2×C4×D6112yes—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—24no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—611no—
558C22×C4—611no—
559C22×C4—611no—
560C22×C4—611no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—4881no—
565C22×C4—4881no—
566C22×C4—4881no—
567C22×C4—4881no—
568C22×C4—2442no—
569C22×C4—2442no—
570C22×C4C2×C4×D6112yes—
571C22×C4D4×D6111yescharacteristic
572C22×C4#1175822412yes—
573C22×C4C23×D6111yescharacteristic
574SD16—2444no—
575D8—2444no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—612no—
583C2×C8—612no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—612no—
593C4⋊C4—1221no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—1221no—
598C4⋊C4—4881no—
599C4⋊C4—2441no—
600C4⋊C4—2441no—
601C4⋊C4—2442no—
602C22⋊C4—81no—
603C22⋊C4—1224no—
604C22⋊C4—4881no—
605C22⋊C4—4881no—
606C22⋊C4—4881no—
607C22⋊C4—4881no—
608C22⋊C4—4881no—
609C22⋊C4—4881no—
610C22⋊C4—2442no—
611C22⋊C4—2441no—
612C22⋊C4—2441no—
613C42—1221no—
614C42—1221no—
615C42—1221no—
616C42—1221no—
617C42—4881no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—22no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—1222no—
632C23—2441no—
633C23—2441no—
634C23—2441no—
635C23—2441no—
636C23—2441no—
637C23—2441no—
638C23#1451973712yes—
639C23C2×D4×D6111yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—41no—
643Q8—41no—
644D4—22no—
645D4—22no—
646D4—48no—
647D4—41no—
648D4—41no—
649D4—1222no—
650D4—1222no—
651D4—4884no—
652D4—2441no—
653D4—2441no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—48no—
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—1222no—
671C2×C4—1221no—
672C2×C4—1221no—
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—4884no—
684C2×C4—4884no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4#1451973712yes—
694C2×C4C22×C4×D6111yescharacteristic
695C2×C4C2×#1175822411yescharacteristic
696C2×C4#1451982211yescharacteristic
697C2×C4#1451982211yescharacteristic
698C2×C4#1451982211yescharacteristic
699C2×C4#1451982211yescharacteristic
700C8—41no—
701C8—41no—
702C8—1222no—
703C8—1222no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—4881no—
719C22—4881no—
720C22—4881no—
721C22—4881no—
722C22—2442no—
723C22—2442no—
724C22—2442no—
725C22C2×#1451973711yescharacteristic
726C22#1684032211yescharacteristic
727C22#1684032711yescharacteristic
728C22#1684056411yescharacteristic
729C22#1684056911yescharacteristic
730C22#1684057111yescharacteristic
731C22#1684057211yescharacteristic
732C4—22no—
733C4—42no—
734C4—81no—
735C4—81no—
736C4—4881no—
737C4—4881no—
738C4—2441no—
739C4—2441no—
740C4—2442no—
741C4—2441no—
742C4—2441no—
743C4#1684023511yescharacteristic
744C4#1684023511yescharacteristic
745C4#1684034711yescharacteristic
746C4#1684034711yescharacteristic
747C2—42no—
748C2—82no—
749C2—4882no—
750C2#2144847411yescharacteristic
751C2#2145465411yescharacteristic
752C2#2145469811yescharacteristic
753C2#2145666811yescharacteristic
754C2#2145672711yescharacteristic
755C2#2145687811yescharacteristic
756C2#2145691911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1788C2
socleC23×C61C22×D4
prime radicalC2×#16839907C2
cosocleC22×C4×C61C24
hypercenter#1788D61
hypocenterC61#22053
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. #21448508C2semidirect
3. #21448411C2semidirect
4. #21446692C2semidirect
5. #21446670C2semidirect
6. #21446506C2semidirect
7. #21446499C2semidirect
8. #21446456C2semidirect
9. #21446449C2semidirect
10. #21446164C2semidirect
11. #21446150C2semidirect
12. #21446134C2semidirect
13. #21446011C2semidirect
14. #21445587C2semidirect
15. C61×#1788C2semidirect
22. #16839907C4semidirect
66. C2×#11758201C2×C4semidirect
69. C2×#11758199C2×C4semidirect
102. #14519701C2×C4semidirect
105. #14519698C2×C4semidirect
106. C22⋊#92418C2×C4semidirect
120. C2×#41×C61C2×C4semidirect
382. #1788D61semidirect
438. C61#22053semidirect
444. C2×#41C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399072
#214485082
#214484112
#214466922
#214466702
#214465062
#214464992
#214464562
#214464492
#214461642
#214461502
#214461342
#214460112
#214455872
C61×#17882
#2205361