Finite Group Databasebeta

← #29691341

Subgroups — #29691341

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×#16839909C211yesmaximal, characteristic
2#21448512C211yesmaximal, characteristic, complemented
3#21448407C211yesmaximal, characteristic, complemented
4#21446700C211yesmaximal, characteristic, complemented
5#21446685C211yesmaximal, characteristic, complemented
6#21446516C211yesmaximal, characteristic, complemented
7#21446495C211yesmaximal, characteristic, complemented
8#21446461C211yesmaximal, characteristic, complemented
9#21446440C211yesmaximal, characteristic, complemented
10#21446166C211yesmaximal, characteristic, complemented
11#21446152C211yesmaximal, characteristic, complemented
12#21446134C211yesmaximal, characteristic, complemented
13#21446009C211yesmaximal, characteristic, complemented
14#21445760C211yesmaximal, characteristic, complemented
15C61×#1750C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758190C2211yescharacteristic
18C22×D488C2211yescharacteristic
19C2×#14519751C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21C22×C4⋊Dic61C2211yescharacteristic
22#16839909C418yescomplemented
23C2×#14519711C2211yescharacteristic
24C2×#14519711C2211yescharacteristic
25C2×#14519702C2211yescharacteristic
26C2×#14519702C2211yescharacteristic
27C2×#14519702C2211yescharacteristic
28C2×#14519699C2211yescharacteristic
29C2×#14519699C2211yescharacteristic
30C2×#14519699C2211yescharacteristic
31C2×#14519699C2211yescharacteristic
32C2×#14519699C2211yescharacteristic
33#16839668C2211yescharacteristic
34#16839668C2211yescharacteristic
35#16839664C2211yescharacteristic
36#16839664C2211yescharacteristic
37#16839664C2211yescharacteristic
38#16839662—21no—
39#16839660C2211yescharacteristic
40#16839652—21no—
41#16839639—21no—
42#16839639—21no—
43#16839638—21no—
44#16839633—21no—
45#16839622C2211yescharacteristic
46#16839619—21no—
47#16839619—21no—
48C4×C4⋊Dic61C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53C2×#117×C61C2211yescharacteristic
54C2×C22⋊C8×C61C2211yescharacteristic
55C2×C22⋊C8×C61C2211yescharacteristic
56C2×#97×C61C2211yescharacteristic
57C2×C4×C8×C61C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C2×#11758222—22no—
61C2×#11758222—41no—
62C2×#11758222—41no—
63C2×#11758222—41no—
64C2×#11758222—41no—
65C2×#11758222C2×C414yescomplemented
66C22×Dic122C2311yescharacteristic
67C22×D244C2311yescharacteristic
68C22×D244C2311yescharacteristic
69C22×C22⋊D61—21no—
70C22×C22⋊D61—21no—
71C23×Dic61—21no—
72C22×C4×D61—21no—
73C22×C4×D61—21no—
74C2×#11758190—41no—
75C2×#11758190—41no—
76C2×#11758190C2×C414yescomplemented
77C2×D488—41no—
78C2×D488—41no—
79C2×D488C2×C414yescomplemented
80#14519751—22no—
81#14519751C2×C414yes—
82C4×D244—41no—
83C4×D244—41no—
84C2×C4⋊Dic61—21no—
85C2×C4⋊Dic61—41no—
86C2×C4⋊Dic61—41no—
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×C4⋊Dic61C2311yescharacteristic
91C2×C4⋊Dic61C2311yescharacteristic
92C2×#11758196—21no—
93C2×C22⋊Dic61—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×C4×Dic61—21no—
103#14519711—41no—
104#14519711—41no—
105#14519702—41no—
106#14519702—41no—
107#14519702C2×C414yescomplemented
108#14519699—41no—
109#14519699—41no—
110#14519699—41no—
111#14519699—41no—
112#14519699C2×C414yescomplemented
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119#14519684—21no—
120C23×C4×C61C2311yescharacteristic
121C22×C8×C61C2311yescharacteristic
122C22×C8×C61C2311yescharacteristic
123C22×C8×C61C2311yescharacteristic
124C22×C8×C61C2311yescharacteristic
125#117×C61—41no—
126#117×C61—41no—
127C2×C4⋊C4×C61D411yescharacteristic
128C2×C4⋊C4×C61D411yescharacteristic
129C2×C22⋊C4×C61D411yescharacteristic
130C2×C22⋊C4×C61D411yescharacteristic
131C2×C42×C61C2311yescharacteristic
132C2×C42×C61C2311yescharacteristic
133C22⋊C8×C61—22no—
134C22⋊C8×C61C2×C414yescomplemented
135#97×C61—41no—
136C4×C8×C61—41no—
137C24×C61C2×D411yescharacteristic
138C23×D61—21no—
139C23×D61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61C22×C412yes—
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61#4112yes—
151C22×C4×C61C2411yescharacteristic
152C2×C22⋊D61—24no—
153C2×C22⋊D61—24no—
154C2×C22⋊D61—42no—
155C2×C22⋊D61—42no—
156C2×C22⋊D61—81no—
157C2×C22⋊D61—81no—
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—42no—
165C22×Dic61—81no—
166C22×Dic61—81no—
167#11758222—44no—
168#11758222—44no—
169#11758222—44no—
170#11758222—44no—
171C2×D244—21no—
172C2×D244—21no—
173C2×D244—21no—
174C2×D244—21no—
175C2×D244—21no—
176C2×D244—21no—
177C2×D244—21no—
178C2×D244—21no—
179C2×D244—21no—
180C2×D244—21no—
181C2×D244C22×C412yes—
182C2×D244C22×C412yes—
183C2×C4×D61—24no—
184C2×C4×D61—42no—
185C2×C4×D61—42no—
186C2×C4×D61—42no—
187C2×C4×D61—81no—
188C2×C4×D61—81no—
189C2×Dic122—21no—
190C2×Dic122—21no—
191C2×Dic122—21no—
192C2×Dic122—21no—
193C2×Dic122—21no—
194C2×Dic122C22×C412yes—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61C22×C412yes—
206C2×C8×C61C22×C412yes—
207C4⋊C4×C61—41no—
208C4⋊C4×C61—41no—
209C22⋊C4×C61—41no—
210C22⋊C4×C61—41no—
211C42×C61—21no—
212C42×C61—21no—
213C42×C61—21no—
214C42×C61—21no—
215C22⋊Dic61—81no—
216#11758198—24no—
217#11758198—42no—
218#11758198—81no—
219#11758198—81no—
220#11758198—81no—
221#11758198—81no—
222#11758198—81no—
223#11758198—81no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61—42no—
234C4⋊Dic61C22×C412yes—
235#11758196—81no—
236C4×Dic61—81no—
237D488—44no—
238#11758190—44no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61C4×D412yes—
246C23×C61C22×D411yescharacteristic
247C22×D61—22no—
248C22×D61—22no—
249C22×D61—41no—
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—41no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61C4×D412yes—
280C2×C4×C61C23×C411yescharacteristic
281C2×C4×C61C2×#4111yescharacteristic
282C2×C4×C61H(5,𝔽2)11yescharacteristic
283C2×C4×C61H(5,𝔽2)11yescharacteristic
284C2×C4×C61H(5,𝔽2)11yescharacteristic
285C2×C4×C61H(5,𝔽2)11yescharacteristic
286C22⋊D61—48no—
287C22⋊D61—84no—
288C2×Dic61—22no—
289C2×Dic61—22no—
290C2×Dic61—41no—
291C2×Dic61—41no—
292C2×Dic61—41no—
293C2×Dic61—41no—
294C2×Dic61—41no—
295C2×Dic61—41no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—84no—
307D244—22no—
308D244—22no—
309D244—22no—
310D244—22no—
311D244—41no—
312D244—41no—
313D244—41no—
314D244—41no—
315C4×D61—48no—
316C4×D61—84no—
317Dic122—22no—
318Dic122—22no—
319Dic122—41no—
320Dic122—41no—
321C8×C61—22no—
322C8×C61—22no—
323C8×C61—41no—
324C8×C61—41no—
325#22055—611nomaximal, Sylow
326C22×C61—22no—
327C22×C61—22no—
328C22×C61—22no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—41no—
332C22×C61—41no—
333C22×C61C2×C4×D411yescharacteristic
334C22×C61#53411yescharacteristic
335C22×C61#53511yescharacteristic
336C22×C61#57611yescharacteristic
337C22×C61#57611yescharacteristic
338C22×C61#57711yescharacteristic
339C22×C61#57811yescharacteristic
340C2×D61—42no—
341C2×D61—42no—
342C2×D61—42no—
343C2×D61—42no—
344C2×D61—42no—
345C2×D61—42no—
346C2×D61—81no—
347C2×D61—81no—
348C2×D61—81no—
349C2×D61—81no—
350C2×D61—81no—
351C2×D61—81no—
352C2×D61—81no—
353C2×D61—81no—
354C4×C61—22no—
355C4×C61—41no—
356C4×C61—41no—
357C4×C61—41no—
358C4×C61—41no—
359C4×C61#51811yescharacteristic
360C4×C61#51811yescharacteristic
361C4×C61#53811yescharacteristic
362C4×C61#53811yescharacteristic
363Dic61—42no—
364Dic61—42no—
365Dic61—81no—
366Dic61—81no—
367Dic61—81no—
368Dic61—81no—
369C2×#449—611no—
370#2324—611no—
371#2311—611no—
372#1973—611no—
373#1970—611no—
374#1936—611no—
375#1933—611no—
376#1928—611no—
377#1925—611no—
378#1879—611no—
379#1877—611no—
380#1874—611no—
381#1852—611no—
382#1788—611no—
383#1750D6111yescharacteristic, complemented
384C2×C61—42no—
385C2×C61#232111yescharacteristic
386C2×C61#294611yescharacteristic
387C2×C61#295111yescharacteristic
388C2×C61#319811yescharacteristic
389C2×C61#320311yescharacteristic
390C2×C61#322011yescharacteristic
391C2×C61#322511yescharacteristic
392D61—82no—
393D61—82no—
394C22×#41—611no—
395C22×SD16—611no—
396C22×D8—611no—
397C2×#121—611no—
398C2×C4×D4—611no—
399C2×#117C2×D6111yescharacteristic
400C22×C4⋊C4—611no—
401#449—618no—
402C2×#107—611no—
403C2×#107—611no—
404C2×#103—611no—
405C2×#103—611no—
406C2×#103—611no—
407C2×#102—611no—
408C2×#102—611no—
409C2×#102—611no—
410C2×#102—611no—
411C2×#102—611no—
412C2×C22⋊C8C2×D6111yescharacteristic
413C2×C22⋊C8C2×D6111yescharacteristic
414C2×#97C2×D6111yescharacteristic
415C2×C4×C8C2×D6111yescharacteristic
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—611no—
429#380—1221no—
430#380—1221no—
431C4×C4⋊C4—611no—
432#340—611no—
433#340—611no—
434#340—611no—
435#340—611no—
436#336C2×D6111yescharacteristic
437#336C2×D6111yescharacteristic
438C61#2205511yescharacteristic, complemented, Sylow
439C2×#41—614no—
440C2×#41—1222no—
441C2×#41—2441no—
442C2×#41—2441no—
443C2×#41—2441no—
444C2×#41—2441no—
445C22×Q8—611no—
446C22×D4—611no—
447C22×D4—611no—
448C22×D4—1221no—
449C22×D4—1221no—
450C23×C4—1221no—
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×C8C22×D6111yescharacteristic
461C22×C8C22×D6111yescharacteristic
462C22×C8C22×D6111yescharacteristic
463C22×C8C22×D6111yescharacteristic
464#121—614no—
465#121—1222no—
466C4×D4—2441no—
467C4×D4—2441no—
468#117—41no—
469#117—41no—
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⋊C4D24411yescharacteristic
480C2×C4⋊C4D24411yescharacteristic
481C2×C22⋊C4—1221no—
482C2×C22⋊C4—1221no—
483C2×C22⋊C4—1221no—
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⋊C4D24411yescharacteristic
491C2×C22⋊C4D24411yescharacteristic
492C2×C42—1221no—
493C2×C42C22×D6111yescharacteristic
494C2×C42C22×D6111yescharacteristic
495#107—2441no—
496#107—2441no—
497#103—614no—
498#103—2441no—
499#103—2441no—
500#102—614no—
501#102—2441no—
502#102—2441no—
503#102—2441no—
504#102—2441no—
505C22⋊C8—22no—
506C22⋊C8C4×D6114yescomplemented
507#97—41no—
508C4×C8—41no—
509#95—1221no—
510#95—1221no—
511#95—1221no—
512#95—1221no—
513#95—1221no—
514#95—1221no—
515#95—1221no—
516C24—1221no—
517C24—1221no—
518C24C2×D24411yescharacteristic
519#41—2444no—
520#41—2444no—
521#41—2444no—
522#41—2444no—
523C2×Q8—612no—
524C2×Q8—1221no—
525C2×Q8—1221no—
526C2×Q8—1221no—
527C2×Q8—1221no—
528C2×Q8—1221no—
529C2×D4—612no—
530C2×D4—612no—
531C2×D4—1224no—
532C2×D4—1224no—
533C2×D4—1221no—
534C2×D4—1221no—
535C2×D4—1221no—
536C2×D4—1221no—
537C2×D4—1221no—
538C2×D4—1221no—
539C2×D4—1221no—
540C2×D4—1221no—
541C2×D4—1221no—
542C2×D4—1221no—
543C2×D4—4881no—
544C2×D4—4881no—
545C2×D4—2442no—
546C2×D4—2442no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—1221no—
552C22×C4—1221no—
553C22×C4—1224no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—4881no—
559C22×C4—4881no—
560C22×C4—4881no—
561C22×C4—4881no—
562C22×C4—2442no—
563C22×C4—2442no—
564C22×C4—2442no—
565C22×C4—2442no—
566C22×C4C2×C4×D6112yes—
567C22×C4C2×D24411yescharacteristic
568C22×C4C2×D24411yescharacteristic
569C22×C4C2×D24411yescharacteristic
570C22×C4C2×D24411yescharacteristic
571C22×C4C2×D24411yescharacteristic
572C22×C4#1175822212yes—
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—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8C2×C4×D6112yes—
587C2×C8C2×C4×D6112yes—
588C4⋊C4—41no—
589C4⋊C4—41no—
590C4⋊C4—612no—
591C4⋊C4—1221no—
592C4⋊C4—1221no—
593C4⋊C4—1221no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—1221no—
598C4⋊C4—1221no—
599C4⋊C4—1221no—
600C4⋊C4—4881no—
601C4⋊C4—2442no—
602C22⋊C4—41no—
603C22⋊C4—41no—
604C22⋊C4—1224no—
605C22⋊C4—4881no—
606C22⋊C4—4881no—
607C22⋊C4—4881no—
608C22⋊C4—4881no—
609C22⋊C4—4881no—
610C22⋊C4—4881no—
611C22⋊C4—4881no—
612C22⋊C4—2442no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—4881no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—1222no—
625C23—1222no—
626C23—2441no—
627C23—2441no—
628C23—2441no—
629C23—2441no—
630C23—2441no—
631C23—2441no—
632C23—2441no—
633C23—2441no—
634C23—2441no—
635C23—2441no—
636C23—2441no—
637C23—2441no—
638C23C4×D24412yes—
639C23C22×D24411yescharacteristic
640Q8—1222no—
641Q8—1222no—
642Q8—2441no—
643Q8—2441no—
644D4—1222no—
645D4—1222no—
646D4—1222no—
647D4—1222no—
648D4—4884no—
649D4—2448no—
650D4—2441no—
651D4—2441no—
652D4—2441no—
653D4—2441no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—4884no—
675C2×C4—4884no—
676C2×C4—2448no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2441no—
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×C4—2441no—
693C2×C4C4×D24412yes—
694C2×C4C22×C4×D6111yescharacteristic
695C2×C4C2×#1175822211yescharacteristic
696C2×C4#1451982211yescharacteristic
697C2×C4#1451982211yescharacteristic
698C2×C4#1451982311yescharacteristic
699C2×C4#1451982311yescharacteristic
700C8—22no—
701C8—22no—
702C8—41no—
703C8—41no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—4881no—
712C22—4881no—
713C22—4881no—
714C22—4881no—
715C22—4881no—
716C22—4881no—
717C22—4881no—
718C22—4881no—
719C22—2442no—
720C22—2442no—
721C22—2442no—
722C22—2442no—
723C22—2442no—
724C22—2442no—
725C22C2×C4×D24411yescharacteristic
726C22#1684032411yescharacteristic
727C22#1684033111yescharacteristic
728C22#1684056711yescharacteristic
729C22#1684056711yescharacteristic
730C22#1684057411yescharacteristic
731C22#1684057911yescharacteristic
732C4—22no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—41no—
737C4—4881no—
738C4—4881no—
739C4—4881no—
740C4—4881no—
741C4—2442no—
742C4—2442no—
743C4#1684023411yescharacteristic
744C4#1684023411yescharacteristic
745C4#1684034511yescharacteristic
746C4#1684034511yescharacteristic
747C2—42no—
748C2—4882no—
749C2—4882no—
750C2#2144847911yescharacteristic
751C2#2145465311yescharacteristic
752C2#2145469611yescharacteristic
753C2#2145667311yescharacteristic
754C2#2145672111yescharacteristic
755C2#2145687111yescharacteristic
756C2#2145693011yescharacteristic
subgroupG/H
centerC23C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1750C2
socleC23×C61C22×D4
prime radicalC2×#16839909C2
cosocleC22×C4×C61C24
hypercenter#1750D61
hypocenterC61#22055
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ #1750

Complements

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

NH ≅ G/Ntype
2. #21448512C2semidirect
3. #21448407C2semidirect
4. #21446700C2semidirect
5. #21446685C2semidirect
6. #21446516C2semidirect
7. #21446495C2semidirect
8. #21446461C2semidirect
9. #21446440C2semidirect
10. #21446166C2semidirect
11. #21446152C2semidirect
12. #21446134C2semidirect
13. #21446009C2semidirect
14. #21445760C2semidirect
15. C61×#1750C2semidirect
22. #16839909C4semidirect
65. C2×#11758222C2×C4semidirect
76. C2×#11758190C2×C4semidirect
79. C2×D488C2×C4semidirect
107. #14519702C2×C4semidirect
112. #14519699C2×C4semidirect
134. C22⋊C8×C61C2×C4semidirect
383. #1750D61semidirect
438. C61#22055semidirect
506. C22⋊C8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399092
#214485122
#214484072
#214467002
#214466852
#214465162
#214464952
#214464612
#214464402
#214461662
#214461522
#214461342
#214460092
#214457602
C61×#17502
#2205561