Finite Group Databasebeta

← #30544003

Subgroups — #30544003

Order 15616.

2742 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840527C211yesmaximal, characteristic, complemented
2#41×C22⋊D61C211yesmaximal, characteristic
3#21454561C213yesmaximal, complemented
4M16×C22⋊D61C213yesmaximal, complemented
5#21454544C213yesmaximal, complemented
6#21454541C213yesmaximal, complemented
7#21454529C213yesmaximal, complemented
8#21454522C213yesmaximal, complemented
9#21454520C213yesmaximal, complemented
10C2×#16839838C213yesmaximal, complemented
11#21454385C211yesmaximal, characteristic, complemented
12#21454268C211yesmaximal, characteristic, complemented
13#21454266C211yesmaximal, characteristic, complemented
14#131×Dic61C211yesmaximal, characteristic, complemented
15C2×C61×#568C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17#16840527—28no—
18C2×#14519785C2213yescomplemented
19C2×#14519784C2211yescharacteristic
20C2×#14519784C2211yescharacteristic
21C2×#14519783C2213yescomplemented
22C22×#11758189C2213yescomplemented
23C2×M16×D61C2213yescomplemented
24#16840431C411yescharacteristic
25Q8×C22⋊D61C411yescharacteristic
26#16840423C411yescharacteristic
27#16840419C411yescharacteristic
28#16840411C413yes—
29#16840406C413yes—
30#16840400C413yes—
31D4×C22⋊D61C413yes—
32#16840308C2213yes—
33#16840273C2213yes—
34#16840269C2213yes—
35#41×Dic61C2211yescharacteristic
36C2×C4×C22⋊D61C2213yes—
37#16839838C2211yescharacteristic
38#16839838C2213yes—
39#16839838C2213yescomplemented
40#16839838C2213yescomplemented
41#16839838C2213yescomplemented
42#16839838C2213yescomplemented
43#16839838C2213yescomplemented
44#16839838C2213yescomplemented
45#16839838C2216yescomplemented
46#16839833C2216yescomplemented
47#16839833C2216yescomplemented
48#16839831C2216yescomplemented
49#16839831C2216yescomplemented
50C8×C22⋊D61C2216yescomplemented
51C8×C22⋊D61C2216yescomplemented
52#16839790C2213yescomplemented
53#16839788C2213yescomplemented
54#16839785C2213yescomplemented
55C2×#14519706C2213yescomplemented
56#16839730C2213yescomplemented
57#16839729C2213yescomplemented
58#16839729C2213yescomplemented
59#16839728C2213yescomplemented
60#16839726C2213yescomplemented
61#16839725C2213yescomplemented
62C2×C22⋊#92418C2213yescomplemented
63C2×#14519689C2213yescomplemented
64#16839720C2213yescomplemented
65#16839717C2213yescomplemented
66M16×Dic61C2213yescomplemented
67C2×C8×Dic61C2213yescomplemented
68C22×#41×C61C2211yescharacteristic
69C61×#568—28no—
70C2×#131×C61C2211yescharacteristic
71C2×#131×C61C2211yescharacteristic
72C2×#131×C61C2213yescomplemented
73C2×#131×C61C2213yescomplemented
74C22×M16×C61C2213yescomplemented
75C22×M16×C61C2213yescomplemented
76C2×#11758226C2×C411yescharacteristic
77C2×#11758222C2313yes—
78C2×#11758224C2×C413yes—
79#41×D61—24no—
80#41×D61—24no—
81C2×Q8×D61C2×C411yescharacteristic
82C22×C22⋊D61C2×C413yes—
83C2×D4×D61C2×C413yes—
84C22×C4×D61C2313yes—
85#14519785—212no—
86#14519784—24no—
87#14519784—24no—
88#14519783—212no—
89C2×#11758194C2313yes—
90C2×#11758194C2313yes—
91C2×#11758189—212no—
92C2×#11758189C2313yes—
93C2×#11758189C2311yescharacteristic
94C2×#11758189C2313yes—
95C2×#11758189C2313yes—
96M16×D61—212no—
97C22×#92418C2313yes—
98C22×#92418C2313yes—
99C2×C8×D61C2316yes—
100#14519775C2×C413yes—
101#14519773C2×C413yes—
102#14519766C2×C413yes—
103#14519764C2×C413yes—
104#14519760C2×C416yes—
105#14519758C2×C416yes—
106#14519756C2×C413yes—
107#14519756C2×C413yes—
108#14519753C2×C413yes—
109#14519753C2×C413yes—
110#14519751C2×C413yes—
111#14519751C2×C413yes—
112#14519749C2×C416yes—
113#14519749C2×C416yes—
114#14519748C2×C413yes—
115#14519748C2×C413yes—
116#14519746C2×C416yes—
117#14519745C2×C416yes—
118Q8×Dic61C2×C411yescharacteristic
119Q8×Dic61C2×C411yescharacteristic
120D4×Dic61C2×C413yes—
121D4×Dic61C2×C413yes—
122C4×C22⋊D61C2×C413yes—
123C4×C22⋊D61C2×C413yes—
124C4×C22⋊D61C2×C413yes—
125C4×C22⋊D61C2×C413yes—
126C4×C22⋊D61C2311yescharacteristic
127C4×C22⋊D61C2313yes—
128C4×C22⋊D61C2313yes—
129C4×C22⋊D61C2313yes—
130C4×C22⋊D61C2316yes—
131#14519736C2313yes—
132C2×#11758196C2×C413yes—
133C2×C22⋊Dic61C2×C413yes—
134C2×#11758198C2×C413yes—
135C2×C4×Dic61C2313yes—
136#14519706C2311yescharacteristic
137#14519706C2313yes—
138#14519706C2313yes—
139#14519706C2313yes—
140#14519706C2316yes—
141C22⋊#92418C2311yescharacteristic
142C22⋊#92418C2313yes—
143C22⋊#92418C2313yes—
144C22⋊#92418C2313yes—
145C22⋊#92418C2316yes—
146#14519689C2311yescharacteristic
147#14519689C2313yes—
148#14519689C2313yes—
149#14519689C2313yes—
150#14519689C2316yes—
151#14519687C2316yes—
152C8×Dic61C2311yescharacteristic
153C8×Dic61C2313yes—
154C8×Dic61C2313yes—
155C8×Dic61C2313yes—
156C2×#41×C61—24no—
157C2×#41×C61—24no—
158C2×#41×C61C2×C413yes—
159C2×#41×C61C2×C411yescharacteristic
160C2×#41×C61C2313yes—
161C2×#41×C61C2311yescharacteristic
162C22×Q8×C61C2×C411yescharacteristic
163C22×D4×C61C2×C413yes—
164C23×C4×C61C2313yes—
165#131×C61—24no—
166#131×C61—212no—
167#131×C61—212no—
168#131×C61D418yescomplemented
169C2×M16×C61—212no—
170C2×M16×C61—212no—
171C2×M16×C61C2313yes—
172C2×M16×C61C2311yescharacteristic
173C2×M16×C61C2313yes—
174C2×M16×C61C2313yes—
175C2×M16×C61C2313yes—
176C2×M16×C61C2313yes—
177C22×C8×C61C2313yes—
178C22×C8×C61C2316yes—
179C22×C8×C61C2313yes—
180C24×C61C22×C413yes—
181C23×D61C22×C413yes—
182#41×C61—24no—
183#41×C61—212no—
184#41×C61—26no—
185#41×C61—26no—
186#41×C61C2×D414yes—
187#41×C61#4114yes—
188C2×Q8×C61—24no—
189C2×Q8×C61C22×C413yes—
190C2×Q8×C61C22×C411yescharacteristic
191C2×D4×C61—212no—
192C2×D4×C61C22×C416yes—
193C2×D4×C61C22×C413yes—
194C2×D4×C61C22×C413yes—
195C22×C4×C61—26no—
196C22×C4×C61—26no—
197C22×C4×C61C22×C413yes—
198C22×C4×C61C22×C413yes—
199C22×C4×C61C22×C413yes—
200C22×C4×C61C2413yes—
201C22×C4×C61C2411yescharacteristic
202C22×C4×C61C2413yes—
203C2×C22⋊D61—46no—
204C2×C22⋊D61C22×C416yes—
205C2×C22⋊D61C22×C411yescharacteristic
206C2×C22⋊D61C22×C413yes—
207C2×C22⋊D61C22×C413yes—
208C2×C22⋊D61C22×C413yes—
209C2×C22⋊D61C22×C416yes—
210C22×Dic61C22×C413yes—
211C22×Dic61C22×C413yes—
212C22×Dic61C22×C413yes—
213#11758226—24no—
214Q8×D61—24no—
215#11758224—212no—
216D4×D61—212no—
217#11758222—26no—
218#11758222—26no—
219C2×D244C22×C413yes—
220C2×C4×D61—26no—
221C2×C4×D61—26no—
222C2×C4×D61C22×C413yes—
223C2×C4×D61C22×C413yes—
224C2×C4×D61C2411yescharacteristic
225C2×C4×D61C2413yes—
226C2×Dic122C22×C413yes—
227M16×C61—26no—
228M16×C61—26no—
229M16×C61—22no—
230M16×C61—26no—
231M16×C61—26no—
232M16×C61C2×D4112yescomplemented
233C2×C8×C61—26no—
234C2×C8×C61—212no—
235C2×C8×C61C2×D4112yescomplemented
236C2×C8×C61C2411yescharacteristic
237C2×C8×C61C2413yes—
238C2×C8×C61C2411yescharacteristic
239C2×C8×C61C2413yes—
240C22⋊Dic61C22×C411yescharacteristic
241C22⋊Dic61C22×C413yes—
242C22⋊Dic61C22×C413yes—
243C22⋊Dic61C22×C413yes—
244C22⋊Dic61C22×C416yes—
245C22⋊Dic61C22×C416yes—
246#11758198C22×C411yescharacteristic
247#11758198C22×C413yes—
248#11758198C22×C413yes—
249#11758198C22×C413yes—
250#11758198C22×C416yes—
251C4⋊Dic61C22×C413yes—
252C4⋊Dic61C22×C413yes—
253#11758196C22×C411yescharacteristic
254#11758196C22×C413yes—
255#11758196C22×C413yes—
256#11758196C22×C413yes—
257#11758196C22×C416yes—
258C4×Dic61C22×C413yes—
259C4×Dic61C22×C413yes—
260C4×Dic61C2411yescharacteristic
261C4×Dic61C2413yes—
262#11758194—26no—
263#11758194—26no—
264C2×#92418—26no—
265C2×#92418—26no—
266C2×#92418C2411yescharacteristic
267C2×#92418C2413yes—
268C2×#92418C2413yes—
269C2×#92418C2411yescharacteristic
270#11758189—26no—
271#11758189—22no—
272#11758189—26no—
273#11758189—26no—
274C8×D61—212no—
275C23×C61—26no—
276C23×C61—43no—
277C23×C61—43no—
278C23×C61C23×C411yescharacteristic
279C23×C61C23×C413yes—
280C23×C61C23×C413yes—
281C22×D61—26no—
282C22×D61—43no—
283C22×D61—43no—
284C22×D61C23×C411yescharacteristic
285C22×D61C23×C413yes—
286Q8×C61—26no—
287Q8×C61C4×D414yes—
288D4×C61—212no—
289D4×C61—26no—
290D4×C61C4×D4112yes—
291C2×C4×C61—26no—
292C2×C4×C61—26no—
293C2×C4×C61—26no—
294C2×C4×C61—23no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—23no—
298C2×C4×C61C23×C411yescharacteristic
299C2×C4×C61C23×C413yes—
300C2×C4×C61C23×C413yes—
301C2×C4×C61C22×D416yes—
302C2×C4×C61C2×#4116yes—
303C2×C4×C61C2511yescharacteristic
304C22⋊D61—212no—
305C22⋊D61—22no—
306C22⋊D61—26no—
307C22⋊D61—43no—
308C22⋊D61—43no—
309C22⋊D61—46no—
310C2×Dic61—26no—
311C2×Dic61—26no—
312C2×Dic61—43no—
313C2×Dic61C23×C411yescharacteristic
314C2×Dic61C23×C413yes—
315C2×Dic61C23×C413yes—
316C2×Dic61C23×C413yes—
317C2×Dic61C23×C411yescharacteristic
318C2×Dic61C23×C411yescharacteristic
319D244—26no—
320C4×D61—26no—
321C4×D61—26no—
322C4×D61—23no—
323C4×D61—21no—
324C4×D61—21no—
325C4×D61—23no—
326Dic122—26no—
327C8×C61—21no—
328C8×C61—23no—
329C8×C61C22×D416yes—
330C8×C61C22×D412yes—
331#92418—23no—
332#92418—21no—
333#92418—21no—
334#92418—23no—
335#60147—611nomaximal, Sylow
336C22×C61—23no—
337C22×C61—23no—
338C22×C61—21no—
339C22×C61—23no—
340C22×C61—21no—
341C22×C61—23no—
342C22×C61—23no—
343C22×C61—21no—
344C22×C61—86no—
345C22×C61C2×C4×D416yes—
346C22×C61C24×C411yescharacteristic
347C2×D61—21no—
348C2×D61—23no—
349C2×D61—21no—
350C2×D61—23no—
351C2×D61—23no—
352C2×D61—21no—
353C2×D61—86no—
354C4×C61—21no—
355C4×C61—23no—
356C4×C61C2×C4×D416yes—
357C4×C61C23×D411yescharacteristic
358C4×C61C22×#4111yescharacteristic
359Dic61—23no—
360Dic61—21no—
361Dic61—23no—
362Dic61—21no—
363Dic61—23no—
364Dic61#56812yescomplemented
365C2×#568—611no—
366C2×#568D6111yescharacteristic, complemented
367D4×#41—611no—
368#2935—613no—
369D4×M16—613no—
370#2933—613no—
371#2933—613no—
372#2931—613no—
373#2930—613no—
374#2930—613no—
375C2×#436—613no—
376#2906—611no—
377#2880—611no—
378#2880—611no—
379C4×#131—611no—
380C2×C61—26no—
381C2×C61—43no—
382C2×C61—41no—
383C2×C61C22×C4×D411yescharacteristic
384C2×C61C2×#56811yescharacteristic
385C2×C61#357311yescharacteristic
386D61—43no—
387D61—41no—
388C22×#41—611no—
389C22×#41C2×D6111yescharacteristic
390#568—28no—
391#568—1228no—
392C2×#131—611no—
393C2×#131—611no—
394C2×#131—613no—
395C2×#131—613no—
396C2×#131C2×D6111yescharacteristic
397C2×#131C2×D6111yescharacteristic
398C2×#131C2×D6113yescomplemented
399C2×#131C2×D6113yescomplemented
400C22×M16—613no—
401C22×M16—613no—
402C22×M16C2×D6113yescomplemented
403C22×M16C2×D6113yescomplemented
404#550—611no—
405D4×Q8—611no—
406#548—611no—
407#548—611no—
408#547—613no—
409#546—613no—
410#546—613no—
411D42—613no—
412#532—613no—
413#525—613no—
414#525—613no—
415C4×#41—611no—
416C2×C4×D4—613no—
417#436—611no—
418#436—613no—
419#436—613no—
420#436—613no—
421#436—613no—
422#436—613no—
423#436—613no—
424#436—613no—
425#436—616no—
426#435—616no—
427#435—616no—
428#435—616no—
429#435—616no—
430C8×D4—616no—
431C8×D4—616no—
432#424—613no—
433#424—613no—
434#423—613no—
435C2×C4⋊C8—613no—
436#408—613no—
437#408—613no—
438#408—613no—
439#408—613no—
440#407—613no—
441#407—613no—
442C2×C22⋊C8—613no—
443C2×C22⋊C8—613no—
444#405—613no—
445#405—613no—
446C4×M16—613no—
447C2×C4×C8—613no—
448C61#6014711yescharacteristic, complemented, Sylow
449C2×#41—24no—
450C2×#41—24no—
451C2×#41—611no—
452C2×#41—613no—
453C2×#41—613no—
454C2×#41—1224no—
455C2×#41—1224no—
456C2×#41C4×D6113yes—
457C2×#41C4×D6111yescharacteristic
458C2×#41C22×D6113yes—
459C2×#41C22×D6111yescharacteristic
460C22×Q8—611no—
461C22×Q8C4×D6111yescharacteristic
462C22×D4—613no—
463C22×D4—613no—
464C22×D4C4×D6113yes—
465C23×C4—613no—
466C23×C4C22×D6113yes—
467#131—24no—
468#131—212no—
469#131—212no—
470#131—1224no—
471#131—1224no—
472#131—12212no—
473#131—12212no—
474#131C22⋊D6118yescomplemented
475C2×M16—212no—
476C2×M16—212no—
477C2×M16—613no—
478C2×M16—613no—
479C2×M16—613no—
480C2×M16—611no—
481C2×M16—613no—
482C2×M16—613no—
483C2×M16—12212no—
484C2×M16—12212no—
485C2×M16C22×D6113yes—
486C2×M16C22×D6111yescharacteristic
487C2×M16C22×D6113yes—
488C2×M16C22×D6113yes—
489C2×M16C22×D6113yes—
490C2×M16C22×D6113yes—
491C22×C8—613no—
492C22×C8—613no—
493C22×C8—616no—
494C22×C8C22×D6113yes—
495C22×C8C22×D6116yes—
496C22×C8C22×D6113yes—
497C4⋊Q8—613no—
498#127—613no—
499#124—613no—
500#124—613no—
501#123—616no—
502#123—616no—
503C22⋊Q8—613no—
504C22⋊Q8—613no—
505C22⋊Q8—613no—
506C22⋊Q8—613no—
507#121—613no—
508#121—613no—
509#121—616no—
510#121—616no—
511#121—613no—
512#121—613no—
513#120—616no—
514#120—616no—
515C4×Q8—611no—
516C4×Q8—611no—
517C4×D4—613no—
518C4×D4—613no—
519C4×D4—613no—
520C4×D4—613no—
521C4×D4—613no—
522C4×D4—613no—
523C4×D4—611no—
524C4×D4—613no—
525C4×D4—613no—
526C4×D4—613no—
527C4×D4—616no—
528#117—613no—
529C2×C4⋊C4—613no—
530C2×C22⋊C4—613no—
531C2×C22⋊C4—613no—
532C2×C42—613no—
533C4⋊C8—611no—
534C4⋊C8—613no—
535C4⋊C8—613no—
536C4⋊C8—613no—
537C4⋊C8—616no—
538C22⋊C8—611no—
539C22⋊C8—613no—
540C22⋊C8—613no—
541C22⋊C8—613no—
542C22⋊C8—616no—
543C22⋊C8—611no—
544C22⋊C8—613no—
545C22⋊C8—613no—
546C22⋊C8—613no—
547C22⋊C8—616no—
548#97—616no—
549C4×C8—611no—
550C4×C8—613no—
551C4×C8—613no—
552C4×C8—613no—
553C24—613no—
554C24C2×C4×D6113yes—
555#41—24no—
556#41—212no—
557#41—26no—
558#41—26no—
559#41—1224no—
560#41—12212no—
561#41—1226no—
562#41—1226no—
563#41#1175822214yes—
564#41C2×C22⋊D6114yes—
565C2×Q8—24no—
566C2×Q8—613no—
567C2×Q8—1224no—
568C2×Q8C2×C4×D6113yes—
569C2×Q8C2×C4×D6111yescharacteristic
570C2×D4—212no—
571C2×D4—611no—
572C2×D4—613no—
573C2×D4—616no—
574C2×D4—613no—
575C2×D4—613no—
576C2×D4—616no—
577C2×D4—613no—
578C2×D4—12212no—
579C2×D4—2446no—
580C2×D4C2×C4×D6116yes—
581C2×D4C2×C4×D6113yes—
582C2×D4C2×C4×D6113yes—
583C22×C4—26no—
584C22×C4—26no—
585C22×C4—613no—
586C22×C4—613no—
587C22×C4—613no—
588C22×C4—613no—
589C22×C4—613no—
590C22×C4—613no—
591C22×C4—611no—
592C22×C4—1226no—
593C22×C4—1226no—
594C22×C4C2×C4×D6113yes—
595C22×C4C2×C4×D6113yes—
596C22×C4C2×C4×D6113yes—
597C22×C4C23×D6113yes—
598C22×C4C23×D6111yescharacteristic
599C22×C4C23×D6113yes—
600M16—26no—
601M16—26no—
602M16—22no—
603M16—26no—
604M16—26no—
605M16—1226no—
606M16—1226no—
607M16—1226no—
608M16—1222no—
609M16—1226no—
610M16—1226no—
611M16C2×C22⋊D61112yescomplemented
612C2×C8—26no—
613C2×C8—212no—
614C2×C8—611no—
615C2×C8—613no—
616C2×C8—611no—
617C2×C8—613no—
618C2×C8—1226no—
619C2×C8—1226no—
620C2×C8—12212no—
621C2×C8C2×C22⋊D61112yescomplemented
622C2×C8C23×D6111yescharacteristic
623C2×C8C23×D6113yes—
624C2×C8C23×D6111yescharacteristic
625C2×C8C23×D6113yes—
626C4⋊C4—611no—
627C4⋊C4—613no—
628C4⋊C4—613no—
629C4⋊C4—613no—
630C4⋊C4—616no—
631C4⋊C4—613no—
632C4⋊C4—613no—
633C22⋊C4—611no—
634C22⋊C4—613no—
635C22⋊C4—613no—
636C22⋊C4—613no—
637C22⋊C4—616no—
638C22⋊C4—616no—
639C22⋊C4—611no—
640C22⋊C4—613no—
641C22⋊C4—613no—
642C22⋊C4—613no—
643C22⋊C4—616no—
644C42—613no—
645C42—613no—
646C42—611no—
647C42—613no—
648C23—26no—
649C23—43no—
650C23—43no—
651C23—611no—
652C23—613no—
653C23—1226no—
654C23—2443no—
655C23—2443no—
656C23C22×C4×D6111yescharacteristic
657C23C22×C4×D6113yes—
658C23C22×C4×D6113yes—
659Q8—26no—
660Q8—1226no—
661Q8C4×C22⋊D6114yes—
662D4—212no—
663D4—26no—
664D4—1226no—
665D4—1222no—
666D4—12212no—
667D4—1226no—
668D4—2446no—
669D4—2443no—
670D4—2443no—
671D4C4×C22⋊D61112yes—
672C2×C4—26no—
673C2×C4—26no—
674C2×C4—26no—
675C2×C4—23no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—23no—
679C2×C4—611no—
680C2×C4—611no—
681C2×C4—613no—
682C2×C4—613no—
683C2×C4—611no—
684C2×C4—613no—
685C2×C4—1226no—
686C2×C4—1226no—
687C2×C4—1226no—
688C2×C4—1226no—
689C2×C4—1223no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—1223no—
693C2×C4—2443no—
694C2×C4C22×C4×D6111yescharacteristic
695C2×C4C22×C4×D6113yes—
696C2×C4C22×C4×D6113yes—
697C2×C4C22×C22⋊D6116yes—
698C2×C4C2×#1175822216yes—
699C2×C4C24×D6111yescharacteristic
700C8—21no—
701C8—23no—
702C8—1223no—
703C8—1221no—
704C8—1221no—
705C8—1223no—
706C8C22×C22⋊D6116yes—
707C8C22×C22⋊D6112yes—
708C22—23no—
709C22—23no—
710C22—21no—
711C22—23no—
712C22—21no—
713C22—23no—
714C22—23no—
715C22—21no—
716C22—86no—
717C22—1221no—
718C22—1223no—
719C22—1221no—
720C22—1223no—
721C22—1223no—
722C22—1221no—
723C22—4886no—
724C22C2×C4×C22⋊D6116yes—
725C22C23×C4×D6111yescharacteristic
726C4—21no—
727C4—23no—
728C4—612no—
729C4—1221no—
730C4—1223no—
731C4—1223no—
732C4—1221no—
733C4—1223no—
734C4C2×C4×C22⋊D6116yes—
735C4C23×C22⋊D6111yescharacteristic
736C4C22×#1175822211yescharacteristic
737C2—26no—
738C2—41no—
739C2—43no—
740C2—2441no—
741C2—2443no—
742C2C22×C4×C22⋊D6111yescharacteristic
743C2#568×D6111yescharacteristic
744C2#2146053211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D61
commutator, socleC22×C61C24×C4
FittingC2×C61×#568C2
prime radical#41×C22⋊D61C2
cosocleC2×C4×C61C25
hypercenterC2×#568D61
hypocenterC61#60147
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×#568

Complements

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

NH ≅ G/Ntype
1. C2×#16840527C2semidirect
3. #21454561C2semidirect
4. M16×C22⋊D61C2semidirect
5. #21454544C2semidirect
6. #21454541C2semidirect
7. #21454529C2semidirect
8. #21454522C2semidirect
9. #21454520C2semidirect
10. C2×#16839838C2semidirect
11. #21454385C2semidirect
12. #21454268C2semidirect
13. #21454266C2semidirect
14. #131×Dic61C2semidirect
15. C2×C61×#568C2semidirect
18. C2×#14519785C22semidirect
21. C2×#14519783C22semidirect
22. C22×#11758189C22semidirect
23. C2×M16×D61C22semidirect
39. #16839838C22semidirect
40. #16839838C22semidirect
41. #16839838C22semidirect
42. #16839838C22semidirect
43. #16839838C22semidirect
44. #16839838C22semidirect
45. #16839838C22semidirect
46. #16839833C22semidirect
47. #16839833C22semidirect
48. #16839831C22semidirect
49. #16839831C22semidirect
50. C8×C22⋊D61C22semidirect
51. C8×C22⋊D61C22semidirect
52. #16839790C22semidirect
53. #16839788C22semidirect
54. #16839785C22semidirect
55. C2×#14519706C22semidirect
56. #16839730C22semidirect
57. #16839729C22semidirect
58. #16839729C22semidirect
59. #16839728C22semidirect
60. #16839726C22semidirect
61. #16839725C22semidirect
62. C2×C22⋊#92418C22semidirect
63. C2×#14519689C22semidirect
64. #16839720C22semidirect
65. #16839717C22semidirect
66. M16×Dic61C22semidirect
67. C2×C8×Dic61C22semidirect
72. C2×#131×C61C22semidirect
73. C2×#131×C61C22semidirect
74. C22×M16×C61C22semidirect
75. C22×M16×C61C22semidirect
168. #131×C61D4semidirect
232. M16×C61C2×D4semidirect
235. C2×C8×C61C2×D4semidirect
364. Dic61#568semidirect
366. C2×#568D61semidirect
398. C2×#131C2×D61semidirect
399. C2×#131C2×D61semidirect
402. C22×M16C2×D61semidirect
403. C22×M16C2×D61semidirect
448. C61#60147semidirect
474. #131C22⋊D61semidirect
611. M16C2×C22⋊D61semidirect
621. C2×C8C2×C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168405272
#41×C22⋊D612
#214545612
M16×C22⋊D612
#214545442
#214545412
#214545292
#214545222
#214545202
C2×#168398382
#214543852
#214542682
#214542662
#131×Dic612
C2×C61×#5682
#6014761