Finite Group Databasebeta

← D61×#1932 #29682590

Subgroups — D61×#1932 #29682590

Order 15616.

1046 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#430×D61C211yesmaximal, characteristic, complemented
2#421×D61C211yesmaximal, characteristic
3C2×#104×D61C211yesmaximal, characteristic
4#413×D61C211yesmaximal, characteristic
5C4×M16×D61C211yesmaximal, characteristic, complemented
6#21446491C211yesmaximal, characteristic, complemented
7#21446490C211yesmaximal, characteristic, complemented
8#21446489C211yesmaximal, characteristic, complemented
9#21446488C211yesmaximal, characteristic, complemented
10#21446487C211yesmaximal, characteristic, complemented
11#21446486C211yesmaximal, characteristic, complemented
12#21446485C211yesmaximal, characteristic, complemented
13#344×D61C211yesmaximal, characteristic, complemented
14#339×D61C211yesmaximal, characteristic, complemented
15C61×#1932C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C2×M16×D61C2211yescharacteristic
18C2×M16×D61C2211yescharacteristic
19C2×M16×D61C2211yescharacteristic
20C2×M16×D61C2211yescharacteristic
21#117×D61C2211yescharacteristic
22C2×C42×D61C2211yescharacteristic
23#16839811C2211yescharacteristic, complemented
24#16839810C2211yescharacteristic, complemented
25#16839810C2211yescharacteristic, complemented
26#16839809—22no—
27#108×D61—22no—
28#16839780C2211yescharacteristic
29#16839779C2211yescharacteristic
30#16839778C2211yescharacteristic
31#16839777—22no—
32C2×#14519705C2211yescharacteristic
33C2×#14519704C2211yescharacteristic
34C2×#14519703C2211yescharacteristic
35#104×D61—22no—
36#104×D61—21no—
37#104×D61—21no—
38#104×D61—21no—
39#104×D61—21no—
40#16839746C2211yescharacteristic
41#16839745C412yescomplemented
42#16839744C2211yescharacteristic
43#16839744C2211yescharacteristic
44#16839743C412yescomplemented
45#101×D61C412yescomplemented
46#100×D61C412yescomplemented
47C4×#11758194C2211yescharacteristic, complemented
48#16839714—21no—
49M16×Dic61C2211yescharacteristic, complemented
50M16×Dic61C2211yescharacteristic, complemented
51C4×#11758189—21no—
52#97×D61—21no—
53C4×C8×D61—21no—
54#16839534C2211yescharacteristic, complemented
55#16839533C2211yescharacteristic, complemented
56#16839532C2211yescharacteristic, complemented
57#16839523C2211yescharacteristic, complemented
58#16839522C2211yescharacteristic, complemented
59#16839521C2211yescharacteristic, complemented
60C61×#430C2211yescharacteristic, complemented
61C61×#421C2211yescharacteristic
62C2×#104×C61C2211yescharacteristic
63C61×#413C2211yescharacteristic
64C4×M16×C61C2211yescharacteristic, complemented
65C61×#344C2211yescharacteristic, complemented
66C61×#339C2211yescharacteristic, complemented
67C2×#11758226C2×C411yescharacteristic
68C2×#11758222—21no—
69C2×#11758222C2311yescharacteristic
70C2×#11758224—21no—
71C2×#11758224C2×C411yescharacteristic
72#41×D61—21no—
73#41×D61—21no—
74#41×D61—21no—
75#41×D61—21no—
76#41×D61—21no—
77#41×D61—21no—
78#41×D61—21no—
79#41×D61—21no—
80C2×Q8×D61C2×C411yescharacteristic
81C2×D4×D61—21no—
82C2×D4×D61C2×C411yescharacteristic
83C22×C4×D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61C2311yescharacteristic
86C2×#11758194C2311yescharacteristic
87C2×#11758194C2311yescharacteristic
88C2×#11758194C2311yescharacteristic
89C2×#11758194C2311yescharacteristic
90C2×#11758189—21no—
91C2×#11758189—21no—
92C2×#11758189—21no—
93C2×#11758189—21no—
94M16×D61—21no—
95M16×D61—21no—
96M16×D61—21no—
97M16×D61—21no—
98M16×D61—21no—
99M16×D61—21no—
100M16×D61—21no—
101M16×D61—21no—
102M16×D61—21no—
103M16×D61—21no—
104M16×D61C2×C412yes—
105M16×D61C2×C412yes—
106M16×D61C2×C412yes—
107M16×D61C2×C412yes—
108M16×D61D412yes—
109M16×D61D412yes—
110C2×C8×D61—21no—
111C2×C8×D61—21no—
112C2×C8×D61—21no—
113C2×C8×D61—21no—
114#14519736C2311yescharacteristic
115#14519735—21no—
116#14519734—21no—
117#14519733—21no—
118C4⋊C4×D61—21no—
119C22⋊C4×D61—21no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61C2311yescharacteristic
122C42×D61—21no—
123C42×D61—21no—
124C42×D61—21no—
125C42×D61D411yescharacteristic
126C42×D61D411yescharacteristic
127C42×D61D411yescharacteristic
128C42×D61D411yescharacteristic
129#14519713—22no—
130#14519712—22no—
131#14519712—22no—
132#14519705—21no—
133#14519705—21no—
134#14519705—22no—
135#14519704—21no—
136#14519704—21no—
137#14519704—22no—
138#14519703—22no—
139#14519703—21no—
140#14519703—21no—
141#14519696C2×C412yescomplemented
142#14519695C2×C412yescomplemented
143#14519695C2×C412yescomplemented
144#14519694C2×C412yescomplemented
145#14519693C2×C412yescomplemented
146#14519693C2×C412yescomplemented
147#14519688—21no—
148#14519687—21no—
149#14519687—21no—
150C4×#92418—21no—
151C8×Dic61—21no—
152C8×Dic61—21no—
153C2×#41×C61C2311yescharacteristic
154C2×M16×C61C2311yescharacteristic
155C2×M16×C61C2311yescharacteristic
156C2×M16×C61C2311yescharacteristic
157C2×M16×C61C2311yescharacteristic
158#117×C61C2311yescharacteristic
159C2×C42×C61C2311yescharacteristic
160#108×C61—22no—
161#104×C61—22no—
162#104×C61—21no—
163#104×C61—21no—
164#101×C61C2×C412yescomplemented
165#100×C61C2×C412yescomplemented
166#97×C61—21no—
167C4×C8×C61—21no—
168C23×D61—21no—
169C23×D61#4111yescharacteristic
170#41×C61—21no—
171#41×C61—21no—
172#41×C61—21no—
173#41×C61—21no—
174C2×Q8×C61C22×C411yescharacteristic
175C2×D4×C61—21no—
176C2×D4×C61C22×C411yescharacteristic
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61C2411yescharacteristic
180C2×C22⋊D61—21no—
181C2×C22⋊D61—21no—
182C2×C22⋊D61—21no—
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61#4111yescharacteristic
186#11758226—21no—
187#11758226—21no—
188#11758226—21no—
189#11758226—21no—
190Q8×D61—21no—
191Q8×D61—21no—
192Q8×D61—21no—
193Q8×D61—21no—
194#11758224—21no—
195#11758224—21no—
196#11758224—21no—
197#11758224—21no—
198#11758224—41no—
199#11758224—41no—
200#11758224—41no—
201#11758224—41no—
202D4×D61—21no—
203D4×D61—21no—
204D4×D61—21no—
205D4×D61—21no—
206D4×D61—41no—
207D4×D61—41no—
208D4×D61—41no—
209D4×D61—41no—
210#11758222—21no—
211#11758222—21no—
212#11758222—21no—
213#11758222—21no—
214#11758222—41no—
215#11758222—41no—
216#11758222—41no—
217#11758222—41no—
218C2×D244—21no—
219C2×D244C22×C411yescharacteristic
220C2×C4×D61—21no—
221C2×C4×D61—21no—
222C2×C4×D61—21no—
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—44no—
228C2×C4×D61—41no—
229C2×C4×D61—41no—
230C2×C4×D61—41no—
231C2×C4×D61—41no—
232C2×C4×D61—41no—
233C2×C4×D61C22×C411yescharacteristic
234C2×C4×D61C22×C411yescharacteristic
235C2×C4×D61C2×D411yescharacteristic
236C2×C4×D61C2×D411yescharacteristic
237C2×C4×D61C2×D411yescharacteristic
238C2×C4×D61C2×D411yescharacteristic
239C2×C4×D61#4111yescharacteristic
240C2×C4×D61#4111yescharacteristic
241C2×C4×D61#4111yescharacteristic
242C2×C4×D61#4111yescharacteristic
243C2×C4×D61#4111yescharacteristic
244C2×C4×D61#4111yescharacteristic
245C2×Dic122—21no—
246C2×Dic122C22×C411yescharacteristic
247M16×C61—21no—
248M16×C61—21no—
249M16×C61—21no—
250M16×C61—21no—
251M16×C61—21no—
252M16×C61C22×C412yes—
253M16×C61C22×C412yes—
254M16×C61C2×D412yes—
255C2×C8×C61—21no—
256C2×C8×C61—21no—
257C2×C8×C61—21no—
258C2×C8×C61—21no—
259C4⋊C4×C61—21no—
260C22⋊C4×C61—21no—
261C42×C61—21no—
262C42×C61—21no—
263C42×C61C2×D411yescharacteristic
264C42×C61C2×D411yescharacteristic
265C22⋊Dic61—21no—
266#11758198—41no—
267C4⋊Dic61—21no—
268#11758196—41no—
269C4×Dic61—21no—
270C4×Dic61—21no—
271C4×Dic61—21no—
272C4×Dic61—21no—
273C4×Dic61—21no—
274C4×Dic61—21no—
275C4×Dic61—41no—
276C4×Dic61C2×D411yescharacteristic
277C4×Dic61C2×D411yescharacteristic
278#11758194—21no—
279#11758194—21no—
280#11758194—21no—
281#11758194—21no—
282#11758194—21no—
283#11758194C22×C412yes—
284#11758194C22×C412yes—
285#11758194C2×D412yes—
286C2×#92418—21no—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418—21no—
290#11758189—22no—
291#11758189—22no—
292#11758189—22no—
293#11758189—22no—
294#11758189—22no—
295#11758189—22no—
296#11758189—41no—
297#11758189—41no—
298C8×D61—22no—
299C8×D61—22no—
300C8×D61—22no—
301C8×D61—22no—
302C8×D61—22no—
303C8×D61—22no—
304C8×D61—41no—
305C8×D61—41no—
306C23×C61—21no—
307C23×C61C2×#4111yescharacteristic
308C22×D61—21no—
309C22×D61—42no—
310C22×D61—41no—
311C22×D61—41no—
312C22×D61—82no—
313C22×D61#11711yescharacteristic
314C22×D61#11711yescharacteristic
315C22×D61#12311yescharacteristic
316C22×D61#12311yescharacteristic
317C22×D61#12411yescharacteristic
318C22×D61#12411yescharacteristic
319Q8×C61—21no—
320Q8×C61—21no—
321D4×C61—21no—
322D4×C61—21no—
323D4×C61—41no—
324D4×C61—41no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—42no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61C23×C411yescharacteristic
333C2×C4×C61C22×D411yescharacteristic
334C2×C4×C61C22×D411yescharacteristic
335C2×C4×C61C2×#4111yescharacteristic
336C2×C4×C61C2×#4111yescharacteristic
337C2×C4×C61C2×#4111yescharacteristic
338C22⋊D61—41no—
339C22⋊D61—41no—
340C22⋊D61—41no—
341C22⋊D61—41no—
342C22⋊D61—41no—
343C22⋊D61—41no—
344C2×Dic61—21no—
345C2×Dic61—21no—
346C2×Dic61—21no—
347C2×Dic61—42no—
348C2×Dic61—41no—
349C2×Dic61—41no—
350C2×Dic61—41no—
351C2×Dic61#11711yescharacteristic
352C2×Dic61#11711yescharacteristic
353C2×Dic61#12311yescharacteristic
354C2×Dic61#12311yescharacteristic
355C2×Dic61#12411yescharacteristic
356C2×Dic61#12411yescharacteristic
357D244—21no—
358D244—21no—
359D244—41no—
360D244—41no—
361C4×D61—24no—
362C4×D61—42no—
363C4×D61—42no—
364C4×D61—42no—
365C4×D61—41no—
366C4×D61—41no—
367C4×D61—41no—
368C4×D61—41no—
369C4×D61—41no—
370C4×D61—41no—
371C4×D61—82no—
372C4×D61C4×D411yescharacteristic
373C4×D61C4×D411yescharacteristic
374C4×D61C4×D411yescharacteristic
375C4×D61C4×D411yescharacteristic
376C4×D61C4×D411yescharacteristic
377C4×D61C4×D411yescharacteristic
378C4×D61C4×D411yescharacteristic
379C4×D61C4×D411yescharacteristic
380C4×D61#12111yescharacteristic
381C4×D61#12111yescharacteristic
382C4×D61#12111yescharacteristic
383C4×D61#12111yescharacteristic
384C4×D61#12611yescharacteristic
385C4×D61#12611yescharacteristic
386C4×D61#12611yescharacteristic
387C4×D61#12611yescharacteristic
388Dic122—21no—
389Dic122—21no—
390Dic122—41no—
391Dic122—41no—
392C8×C61—22no—
393C8×C61—22no—
394C8×C61—22no—
395C8×C61—41no—
396#92418—22no—
397#92418—22no—
398#92418—22no—
399#92418—41no—
400C2×#1932—611nomaximal, Sylow
401C22×C61—41no—
402C22×C61—41no—
403C22×C61—81no—
404C22×C61C2×#11711yescharacteristic
405C22×C61C2×#12311yescharacteristic
406C22×C61C2×#12411yescharacteristic
407C2×D61—22no—
408C2×D61—22no—
409C2×D61—22no—
410C2×D61—41no—
411C2×D61—41no—
412C2×D61—41no—
413C2×D61—41no—
414C2×D61—82no—
415C2×D61—82no—
416C2×D61—81no—
417C2×D61#38811yescharacteristic
418C2×D61#38811yescharacteristic
419C2×D61#38811yescharacteristic
420C2×D61#38811yescharacteristic
421C4×C61—22no—
422C4×C61—41no—
423C4×C61—41no—
424C4×C61—81no—
425C4×C61C2×C4×D411yescharacteristic
426C4×C61C2×C4×D411yescharacteristic
427C4×C61C2×#12111yescharacteristic
428C4×C61C2×#12611yescharacteristic
429Dic61—22no—
430Dic61—41no—
431Dic61—41no—
432Dic61—81no—
433Dic61#38811yescharacteristic
434Dic61#38811yescharacteristic
435Dic61#38811yescharacteristic
436Dic61#38811yescharacteristic
437C2×#430—611no—
438C2×#421—611no—
439C22×#104—611no—
440C2×#413—611no—
441C2×C4×M16—611no—
442#1932—611no—
443#1932—611no—
444#1932—611no—
445#1932—611no—
446#1932—611no—
447#1932—611no—
448#1932—611no—
449#1932D6111yescharacteristic, direct product factor
450C2×#344—611no—
451C2×#339—611no—
452C2×C61—21no—
453C2×C61—21no—
454C2×C61—21no—
455C2×C61—81no—
456C2×C61C2×#38811yescharacteristic
457D61—21no—
458D61—21no—
459D61—21no—
460D61—81no—
461D61#193212yesdirect product factor
462C22×#41—611no—
463C22×M16—611no—
464C22×M16—611no—
465C22×M16—611no—
466C22×M16—611no—
467C2×#117—611no—
468C22×C42—611no—
469#430—611no—
470#430—611no—
471#430—611no—
472#430—1222no—
473#430C2×D6111yescharacteristic, complemented
474C2×#108—1222no—
475#421—611no—
476#421—611no—
477#421—611no—
478#421—1222no—
479#421C2×D6111yescharacteristic
480C2×#104—611no—
481C2×#104—611no—
482C2×#104—611no—
483C2×#104—1221no—
484C2×#104—1221no—
485C2×#104—1221no—
486C2×#104—1221no—
487C2×#104—1222no—
488C2×#104C2×D6111yescharacteristic
489#413—611no—
490#413—611no—
491#413—611no—
492#413—612no—
493#413—612no—
494#413C2×D6111yescharacteristic
495C2×#101—612no—
496C2×#100—612no—
497C4×M16—611no—
498C4×M16—611no—
499C4×M16—611no—
500C4×M16—1221no—
501C4×M16—1221no—
502C4×M16C2×D6111yescharacteristic, complemented
503C2×#97—1221no—
504C2×C4×C8—1221no—
505#344—611no—
506#344—611no—
507#344—611no—
508#344C2×D6111yescharacteristic, complemented
509#339—611no—
510#339—611no—
511#339—611no—
512#339C2×D6111yescharacteristic, complemented
513C61C2×#193211yescharacteristic, complemented, Sylow
514C2×#41—611no—
515C2×#41—611no—
516C2×#41—611no—
517C2×#41—1221no—
518C2×#41—1221no—
519C2×#41—1221no—
520C2×#41—1221no—
521C2×#41—1221no—
522C2×#41—1221no—
523C2×#41—1221no—
524C2×#41—1221no—
525C2×#41—1221no—
526C2×#41—1221no—
527C2×#41C22×D6111yescharacteristic
528C22×Q8—611no—
529C22×D4—611no—
530C22×D4—1221no—
531C23×C4—611no—
532C23×C4—1221no—
533C23×C4—1221no—
534C2×M16—611no—
535C2×M16—611no—
536C2×M16—611no—
537C2×M16—612no—
538C2×M16—612no—
539C2×M16—612no—
540C2×M16—612no—
541C2×M16—612no—
542C2×M16—612no—
543C2×M16—611no—
544C2×M16—1221no—
545C2×M16—1221no—
546C2×M16—1221no—
547C2×M16—1221no—
548C2×M16—1221no—
549C2×M16—1221no—
550C2×M16—1221no—
551C2×M16—1221no—
552C2×M16—1221no—
553C2×M16—1221no—
554C2×M16—1221no—
555C2×M16—1221no—
556C2×M16—1221no—
557C2×M16—1221no—
558C2×M16C22×D6111yescharacteristic
559C2×M16C22×D6111yescharacteristic
560C2×M16C22×D6111yescharacteristic
561C2×M16C22×D6111yescharacteristic
562C22×C8—1221no—
563C22×C8—1221no—
564C22×C8—1221no—
565C22×C8—1221no—
566#117—611no—
567#117—1221no—
568#117—1221no—
569#117—1221no—
570#117C22×D6111yescharacteristic
571C2×C4⋊C4—1221no—
572C2×C22⋊C4—1221no—
573C2×C42—611no—
574C2×C42—611no—
575C2×C42—611no—
576C2×C42—611no—
577C2×C42—611no—
578C2×C42—1221no—
579C2×C42—1221no—
580C2×C42—1221no—
581C2×C42—1221no—
582C2×C42C22×D6111yescharacteristic
583#108—22no—
584#108—1222no—
585#108—1222no—
586#108—1222no—
587#104—22no—
588#104—21no—
589#104—21no—
590#104—1222no—
591#104—1221no—
592#104—1221no—
593#104—1221no—
594#104—1221no—
595#104—1222no—
596#104—1222no—
597#104—1221no—
598#104—1221no—
599#101—612no—
600#101—612no—
601#101—612no—
602#101C4×D6112yescomplemented
603#100—612no—
604#100—612no—
605#100—612no—
606#100C4×D6112yescomplemented
607#97—21no—
608#97—1221no—
609#97—1221no—
610#97—1221no—
611C4×C8—21no—
612C4×C8—1221no—
613C4×C8—1221no—
614C4×C8—1221no—
615C24—611no—
616C24—1221no—
617#41—21no—
618#41—21no—
619#41—21no—
620#41—21no—
621#41—1221no—
622#41—1221no—
623#41—1221no—
624#41—1221no—
625#41—1221no—
626#41—1221no—
627#41—1221no—
628#41—1221no—
629#41—1221no—
630#41—1221no—
631#41—1221no—
632#41—1221no—
633#41—2441no—
634#41—2441no—
635#41—2441no—
636#41—2441no—
637#41—2441no—
638#41—2441no—
639#41—2441no—
640#41—2441no—
641C2×Q8—611no—
642C2×Q8—1221no—
643C2×Q8—1221no—
644C2×Q8—1221no—
645C2×Q8—1221no—
646C2×Q8—1221no—
647C2×Q8C2×C4×D6111yescharacteristic
648C2×D4—21no—
649C2×D4—611no—
650C2×D4—1221no—
651C2×D4—1221no—
652C2×D4—1221no—
653C2×D4—1221no—
654C2×D4—1221no—
655C2×D4—1221no—
656C2×D4—1221no—
657C2×D4—1221no—
658C2×D4—2441no—
659C2×D4—2441no—
660C2×D4—2441no—
661C2×D4—2441no—
662C2×D4C2×C4×D6111yescharacteristic
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—611no—
666C22×C4—611no—
667C22×C4—611no—
668C22×C4—611no—
669C22×C4—611no—
670C22×C4—611no—
671C22×C4—611no—
672C22×C4—611no—
673C22×C4—611no—
674C22×C4—611no—
675C22×C4—611no—
676C22×C4—611no—
677C22×C4—611no—
678C22×C4—1221no—
679C22×C4—1221no—
680C22×C4—1221no—
681C22×C4—1221no—
682C22×C4—1221no—
683C22×C4—1221no—
684C22×C4—1221no—
685C22×C4—1221no—
686C22×C4—1221no—
687C22×C4—2441no—
688C22×C4—2441no—
689C22×C4—2441no—
690C22×C4—2441no—
691C22×C4—2444no—
692C22×C4—2441no—
693C22×C4C23×D6111yescharacteristic
694M16—21no—
695M16—21no—
696M16—21no—
697M16—21no—
698M16—21no—
699M16—612no—
700M16—612no—
701M16—612no—
702M16—1222no—
703M16—1222no—
704M16—1222no—
705M16—1222no—
706M16—1222no—
707M16—1222no—
708M16—1221no—
709M16—1221no—
710M16—1221no—
711M16—1221no—
712M16—1221no—
713M16—2441no—
714M16—2441no—
715M16C2×C4×D6112yes—
716M16C2×C4×D6112yes—
717M16D4×D6112yes—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—1222no—
723C2×C8—1222no—
724C2×C8—1222no—
725C2×C8—1222no—
726C2×C8—1222no—
727C2×C8—1222no—
728C2×C8—1221no—
729C2×C8—1221no—
730C2×C8—1221no—
731C2×C8—1221no—
732C2×C8—2441no—
733C2×C8—2441no—
734C4⋊C4—21no—
735C4⋊C4—1221no—
736C4⋊C4—2441no—
737C22⋊C4—21no—
738C22⋊C4—1221no—
739C22⋊C4—2441no—
740C42—21no—
741C42—21no—
742C42—611no—
743C42—611no—
744C42—1221no—
745C42—1221no—
746C42—1221no—
747C42—1221no—
748C42—1221no—
749C42—1221no—
750C42—2441no—
751C42D4×D6111yescharacteristic
752C42D4×D6111yescharacteristic
753C23—21no—
754C23—611no—
755C23—611no—
756C23—611no—
757C23—611no—
758C23—611no—
759C23—611no—
760C23—1221no—
761C23—4882no—
762C23—2441no—
763C23—2441no—
764C23—2442no—
765C23#41×D6111yescharacteristic
766Q8—21no—
767Q8—21no—
768Q8—1221no—
769Q8—1221no—
770Q8—2441no—
771Q8—2441no—
772D4—21no—
773D4—21no—
774D4—41no—
775D4—41no—
776D4—1221no—
777D4—1221no—
778D4—2441no—
779D4—2441no—
780D4—2441no—
781D4—2441no—
782D4—2441no—
783D4—2441no—
784D4—2441no—
785D4—2441no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—611no—
794C2×C4—611no—
795C2×C4—611no—
796C2×C4—611no—
797C2×C4—611no—
798C2×C4—611no—
799C2×C4—611no—
800C2×C4—611no—
801C2×C4—611no—
802C2×C4—611no—
803C2×C4—611no—
804C2×C4—611no—
805C2×C4—611no—
806C2×C4—611no—
807C2×C4—611no—
808C2×C4—611no—
809C2×C4—611no—
810C2×C4—611no—
811C2×C4—611no—
812C2×C4—611no—
813C2×C4—611no—
814C2×C4—611no—
815C2×C4—1224no—
816C2×C4—1221no—
817C2×C4—1221no—
818C2×C4—1221no—
819C2×C4—4882no—
820C2×C4—2442no—
821C2×C4—2441no—
822C2×C4—2441no—
823C2×C4—2442no—
824C2×C4—2441no—
825C2×C4—2441no—
826C2×C4—2442no—
827C2×C4—2441no—
828C2×C4—2441no—
829C2×C4—2442no—
830C2×C4—2441no—
831C2×C4—2441no—
832C2×C4—2441no—
833C2×C4C22×C4×D6111yescharacteristic
834C2×C4C2×D4×D6111yescharacteristic
835C2×C4C2×D4×D6111yescharacteristic
836C2×C4#41×D6111yescharacteristic
837C2×C4#41×D6111yescharacteristic
838C2×C4#41×D6111yescharacteristic
839C8—22no—
840C8—22no—
841C8—22no—
842C8—41no—
843C8—1222no—
844C8—1222no—
845C8—1222no—
846C8—2441no—
847C22—41no—
848C22—41no—
849C22—81no—
850C22—611no—
851C22—611no—
852C22—611no—
853C22—611no—
854C22—1222no—
855C22—1222no—
856C22—1222no—
857C22—4881no—
858C22—4882no—
859C22—4882no—
860C22—2441no—
861C22—2441no—
862C22—2441no—
863C22—2441no—
864C22#117×D6111yescharacteristic
865C22#123×D6111yescharacteristic
866C22#124×D6111yescharacteristic
867C4—22no—
868C4—41no—
869C4—41no—
870C4—81no—
871C4—611no—
872C4—611no—
873C4—611no—
874C4—611no—
875C4—1222no—
876C4—4881no—
877C4—2441no—
878C4—2441no—
879C4C4×D4×D6111yescharacteristic
880C4C4×D4×D6111yescharacteristic
881C4#121×D6111yescharacteristic
882C4#126×D6111yescharacteristic
883C2—21no—
884C2—21no—
885C2—21no—
886C2—81no—
887C2—612no—
888C2—1221no—
889C2—1221no—
890C2—1221no—
891C2—4881no—
892C2#388×D6111yescharacteristic
subgroupG/H
centerC4#121×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1932C2
socleC2×C61C2×#388
prime radicalC2×#41×D61C22
cosocleC22×C4×C61C24
hypercenter#1932D61
hypocenterC61C2×#1932
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #1932

Complements

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

NH ≅ G/Ntype
1. #430×D61C2semidirect
5. C4×M16×D61C2semidirect
6. #21446491C2semidirect
7. #21446490C2semidirect
8. #21446489C2semidirect
9. #21446488C2semidirect
10. #21446487C2semidirect
11. #21446486C2semidirect
12. #21446485C2semidirect
13. #344×D61C2semidirect
14. #339×D61C2semidirect
15. C61×#1932C2semidirect
23. #16839811C22semidirect
24. #16839810C22semidirect
25. #16839810C22semidirect
41. #16839745C4semidirect
44. #16839743C4semidirect
45. #101×D61C4semidirect
46. #100×D61C4semidirect
47. C4×#11758194C22semidirect
49. M16×Dic61C22semidirect
50. M16×Dic61C22semidirect
54. #16839534C22semidirect
55. #16839533C22semidirect
56. #16839532C22semidirect
57. #16839523C22semidirect
58. #16839522C22semidirect
59. #16839521C22semidirect
60. C61×#430C22semidirect
64. C4×M16×C61C22semidirect
65. C61×#344C22semidirect
66. C61×#339C22semidirect
141. #14519696C2×C4semidirect
142. #14519695C2×C4semidirect
143. #14519695C2×C4semidirect
144. #14519694C2×C4semidirect
145. #14519693C2×C4semidirect
146. #14519693C2×C4semidirect
164. #101×C61C2×C4semidirect
165. #100×C61C2×C4semidirect
449. #1932D61direct (N × H)
461. D61#1932direct (N × H)
473. #430C2×D61semidirect
502. C4×M16C2×D61semidirect
508. #344C2×D61semidirect
512. #339C2×D61semidirect
513. C61C2×#1932semidirect
602. #101C4×D61semidirect
606. #100C4×D61semidirect

Maximal subgroups

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

subgroupindex
#430×D612
#421×D612
C2×#104×D612
#413×D612
C4×M16×D612
#214464912
#214464902
#214464892
#214464882
#214464872
#214464862
#214464852
#344×D612
#339×D612
C61×#19322
C2×#193261