Finite Group Databasebeta

← #29682598

Subgroups — #29682598

Order 15616.

1000 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#430×D61C211yesmaximal, characteristic, complemented
2C2×#16839777C211yesmaximal, characteristic
3#421×D61C211yesmaximal, characteristic
4#413×D61C211yesmaximal, characteristic
5#21454236C211yesmaximal, 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#21445527C211yesmaximal, characteristic, complemented
15C61×#1932C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C2×M16×D61C2211yescharacteristic
18C2×M16×D61C2211yescharacteristic
19C2×M16×D61C2211yescharacteristic
20C2×M16×D61C2211yescharacteristic
21C2×#14519734C2211yescharacteristic
22#117×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—
32#16839777—21no—
33#16839777—21no—
34#16839777—21no—
35#16839777—21no—
36C2×#14519705C2211yescharacteristic
37C2×#14519704C2211yescharacteristic
38C2×#14519703C2211yescharacteristic
39#104×D61—22no—
40#16839746C2211yescharacteristic
41#16839745C412yescomplemented
42#16839744C2211yescharacteristic
43#16839744C2211yescharacteristic
44#16839743C412yescomplemented
45#101×D61C412yescomplemented
46#100×D61C412yescomplemented
47#16839719—21no—
48#16839719—21no—
49#16839716—21no—
50#16839716—21no—
51C4×#11758194C2211yescharacteristic, complemented
52M16×Dic61C2211yescharacteristic, complemented
53M16×Dic61C2211yescharacteristic, complemented
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×D61C2311yescharacteristic
85C2×#11758194C2311yescharacteristic
86C2×#11758194C2311yescharacteristic
87C2×#11758194C2311yescharacteristic
88C2×#11758194C2311yescharacteristic
89C2×#11758189—21no—
90C2×#11758189—21no—
91C2×#11758189—21no—
92C2×#11758189—21no—
93M16×D61—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×D61C2×C412yes—
104M16×D61C2×C412yes—
105M16×D61C2×C412yes—
106M16×D61C2×C412yes—
107M16×D61D412yes—
108M16×D61D412yes—
109C2×C8×D61—21no—
110C2×C8×D61—21no—
111C2×C8×D61—21no—
112C2×C8×D61—21no—
113#14519736C2311yescharacteristic
114#14519735—21no—
115#14519734—21no—
116#14519734—21no—
117#14519734—21no—
118#14519734D411yescharacteristic
119#14519734D411yescharacteristic
120#14519734D411yescharacteristic
121#14519734D411yescharacteristic
122#14519733—21no—
123C2×#11758196—21no—
124C4⋊C4×D61—21no—
125C2×#11758198—21no—
126C22⋊C4×D61—21no—
127C2×C4×Dic61C2311yescharacteristic
128C42×D61—21no—
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—41no—
224C2×C4×D61—41no—
225C2×C4×D61—41no—
226C2×C4×D61—41no—
227C2×C4×D61—41no—
228C2×C4×D61C22×C411yescharacteristic
229C2×C4×D61C22×C411yescharacteristic
230C2×C4×D61C2×D411yescharacteristic
231C2×C4×D61C2×D411yescharacteristic
232C2×C4×D61C2×D411yescharacteristic
233C2×C4×D61C2×D411yescharacteristic
234C2×C4×D61#4111yescharacteristic
235C2×C4×D61#4111yescharacteristic
236C2×C4×D61#4111yescharacteristic
237C2×C4×D61#4111yescharacteristic
238C2×C4×D61#4111yescharacteristic
239C2×C4×D61#4111yescharacteristic
240C2×Dic122—21no—
241C2×Dic122C22×C411yescharacteristic
242M16×C61—21no—
243M16×C61—21no—
244M16×C61—21no—
245M16×C61—21no—
246M16×C61—21no—
247M16×C61C22×C412yes—
248M16×C61C22×C412yes—
249M16×C61C2×D412yes—
250C2×C8×C61—21no—
251C2×C8×C61—21no—
252C2×C8×C61—21no—
253C2×C8×C61—21no—
254C4⋊C4×C61—21no—
255C22⋊C4×C61—21no—
256C42×C61—21no—
257C42×C61—21no—
258C42×C61C2×D411yescharacteristic
259C42×C61C2×D411yescharacteristic
260C22⋊Dic61—21no—
261#11758198—21no—
262#11758198—21no—
263#11758198—21no—
264#11758198—21no—
265#11758198—41no—
266C4⋊Dic61—21no—
267#11758196—21no—
268#11758196—21no—
269#11758196—21no—
270#11758196—21no—
271#11758196—41no—
272C4×Dic61—21no—
273C4×Dic61—21no—
274C4×Dic61—41no—
275C4×Dic61C2×D411yescharacteristic
276C4×Dic61C2×D411yescharacteristic
277#11758194—21no—
278#11758194—21no—
279#11758194—21no—
280#11758194—21no—
281#11758194—21no—
282#11758194C22×C412yes—
283#11758194C22×C412yes—
284#11758194C2×D412yes—
285C2×#92418—21no—
286C2×#92418—21no—
287C2×#92418—21no—
288C2×#92418—21no—
289#11758189—22no—
290#11758189—22no—
291#11758189—22no—
292#11758189—22no—
293#11758189—22no—
294#11758189—22no—
295#11758189—41no—
296#11758189—41no—
297C8×D61—22no—
298C8×D61—22no—
299C8×D61—22no—
300C8×D61—22no—
301C8×D61—22no—
302C8×D61—22no—
303C8×D61—41no—
304C8×D61—41no—
305C23×C61—21no—
306C23×C61C2×#4111yescharacteristic
307C22×D61—21no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—81no—
311C22×D61—82no—
312C22×D61#11711yescharacteristic
313C22×D61#11711yescharacteristic
314C22×D61#12311yescharacteristic
315C22×D61#12311yescharacteristic
316C22×D61#12411yescharacteristic
317C22×D61#12411yescharacteristic
318Q8×C61—21no—
319Q8×C61—21no—
320D4×C61—21no—
321D4×C61—21no—
322D4×C61—41no—
323D4×C61—41no—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—81no—
331C2×C4×C61C23×C411yescharacteristic
332C2×C4×C61C22×D411yescharacteristic
333C2×C4×C61C22×D411yescharacteristic
334C2×C4×C61C2×#4111yescharacteristic
335C2×C4×C61C2×#4111yescharacteristic
336C2×C4×C61C2×#4111yescharacteristic
337C22⋊D61—41no—
338C22⋊D61—41no—
339C22⋊D61—41no—
340C22⋊D61—41no—
341C22⋊D61—41no—
342C22⋊D61—41no—
343C2×Dic61—21no—
344C2×Dic61—21no—
345C2×Dic61—21no—
346C2×Dic61—41no—
347C2×Dic61—41no—
348C2×Dic61—41no—
349C2×Dic61—81no—
350C2×Dic61#11711yescharacteristic
351C2×Dic61#11711yescharacteristic
352C2×Dic61#12311yescharacteristic
353C2×Dic61#12311yescharacteristic
354C2×Dic61#12411yescharacteristic
355C2×Dic61#12411yescharacteristic
356D244—21no—
357D244—21no—
358D244—41no—
359D244—41no—
360C4×D61—41no—
361C4×D61—41no—
362C4×D61—41no—
363C4×D61—41no—
364C4×D61—41no—
365C4×D61—41no—
366C4×D61—82no—
367C4×D61C4×D411yescharacteristic
368C4×D61C4×D411yescharacteristic
369C4×D61C4×D411yescharacteristic
370C4×D61C4×D411yescharacteristic
371C4×D61C4×D411yescharacteristic
372C4×D61C4×D411yescharacteristic
373C4×D61C4×D411yescharacteristic
374C4×D61C4×D411yescharacteristic
375C4×D61#12111yescharacteristic
376C4×D61#12111yescharacteristic
377C4×D61#12111yescharacteristic
378C4×D61#12111yescharacteristic
379C4×D61#12611yescharacteristic
380C4×D61#12611yescharacteristic
381C4×D61#12611yescharacteristic
382C4×D61#12611yescharacteristic
383Dic122—21no—
384Dic122—21no—
385Dic122—41no—
386Dic122—41no—
387C8×C61—22no—
388C8×C61—22no—
389C8×C61—22no—
390C8×C61—41no—
391#92418—22no—
392#92418—22no—
393#92418—22no—
394#92418—41no—
395#21080—611nomaximal, Sylow
396C22×C61—41no—
397C22×C61—41no—
398C22×C61—81no—
399C22×C61C2×#11711yescharacteristic
400C22×C61C2×#12311yescharacteristic
401C22×C61C2×#12411yescharacteristic
402C2×D61—41no—
403C2×D61—41no—
404C2×D61—41no—
405C2×D61—41no—
406C2×D61—41no—
407C2×D61—41no—
408C2×D61—41no—
409C2×D61—82no—
410C2×D61—82no—
411C2×D61—81no—
412C2×D61#38811yescharacteristic
413C2×D61#38811yescharacteristic
414C2×D61#38811yescharacteristic
415C2×D61#38811yescharacteristic
416C4×C61—41no—
417C4×C61—41no—
418C4×C61—41no—
419C4×C61—81no—
420C4×C61C2×C4×D411yescharacteristic
421C4×C61C2×C4×D411yescharacteristic
422C4×C61C2×#12111yescharacteristic
423C4×C61C2×#12611yescharacteristic
424Dic61—41no—
425Dic61—41no—
426Dic61—41no—
427Dic61—81no—
428Dic61#38811yescharacteristic
429Dic61#38811yescharacteristic
430Dic61#38811yescharacteristic
431Dic61#38811yescharacteristic
432C2×#430—611no—
433C2×#421—611no—
434C2×#421—611no—
435C2×#413—611no—
436#2873—611no—
437#1932—611no—
438#1932—611no—
439#1932—611no—
440#1932—611no—
441#1932—611no—
442#1932—611no—
443#1932—611no—
444#1932D6111yescharacteristic, complemented
445C2×#344—611no—
446#1733—611no—
447C2×C61—21no—
448C2×C61—21no—
449C2×C61—21no—
450C2×C61—81no—
451C2×C61C2×#38811yescharacteristic
452D61—21no—
453D61—21no—
454D61—21no—
455D61—21no—
456D61—81no—
457C22×#41—611no—
458C22×M16—611no—
459C22×M16—611no—
460C22×M16—611no—
461C22×M16—611no—
462C2×#117—611no—
463C2×#117—611no—
464#430—611no—
465#430—611no—
466#430—611no—
467#430—1222no—
468#430C2×D6111yescharacteristic, complemented
469C2×#108—1222no—
470#421—611no—
471#421—611no—
472#421—611no—
473#421—1221no—
474#421—1221no—
475#421—1221no—
476#421—1221no—
477#421—1222no—
478#421C2×D6111yescharacteristic
479C2×#104—611no—
480C2×#104—611no—
481C2×#104—611no—
482C2×#104—1222no—
483C2×#104C2×D6111yescharacteristic
484#413—611no—
485#413—611no—
486#413—611no—
487#413—612no—
488#413—612no—
489#413C2×D6111yescharacteristic
490C2×#101—612no—
491C2×#100—612no—
492#405—1221no—
493#405—1221no—
494#405—1221no—
495#405—1221no—
496C4×M16—611no—
497C4×M16—611no—
498C4×M16—611no—
499C4×M16C2×D6111yescharacteristic, complemented
500#344—611no—
501#344—611no—
502#344—611no—
503#344C2×D6111yescharacteristic, complemented
504#339—611no—
505#339—611no—
506#339—611no—
507#339C2×D6111yescharacteristic, complemented
508C61#2108011yescharacteristic, complemented, Sylow
509C2×#41—611no—
510C2×#41—611no—
511C2×#41—611no—
512C2×#41—1221no—
513C2×#41—1221no—
514C2×#41—1221no—
515C2×#41—1221no—
516C2×#41—1221no—
517C2×#41—1221no—
518C2×#41—1221no—
519C2×#41—1221no—
520C2×#41—1221no—
521C2×#41—1221no—
522C2×#41C22×D6111yescharacteristic
523C22×Q8—611no—
524C22×D4—611no—
525C22×D4—1221no—
526C23×C4—611no—
527C23×C4—1221no—
528C2×M16—611no—
529C2×M16—611no—
530C2×M16—611no—
531C2×M16—612no—
532C2×M16—612no—
533C2×M16—612no—
534C2×M16—612no—
535C2×M16—612no—
536C2×M16—612no—
537C2×M16—611no—
538C2×M16—1221no—
539C2×M16—1221no—
540C2×M16—1221no—
541C2×M16—1221no—
542C2×M16—1221no—
543C2×M16—1221no—
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×M16C22×D6111yescharacteristic
553C2×M16C22×D6111yescharacteristic
554C2×M16C22×D6111yescharacteristic
555C2×M16C22×D6111yescharacteristic
556C22×C8—1221no—
557C22×C8—1221no—
558C22×C8—1221no—
559C22×C8—1221no—
560#117—611no—
561#117—611no—
562#117—611no—
563#117—611no—
564#117—611no—
565#117—1221no—
566#117—1221no—
567#117—1221no—
568#117—1221no—
569#117—1221no—
570#117C22×D6111yescharacteristic
571C2×C4⋊C4—1221no—
572C2×C4⋊C4—1221no—
573C2×C22⋊C4—1221no—
574C2×C22⋊C4—1221no—
575C2×C42—611no—
576C2×C42—1221no—
577C2×C42C22×D6111yescharacteristic
578#108—22no—
579#108—1222no—
580#108—1222no—
581#108—1222no—
582#104—22no—
583#104—21no—
584#104—21no—
585#104—1222no—
586#104—1221no—
587#104—1221no—
588#104—1221no—
589#104—1221no—
590#104—1222no—
591#104—1222no—
592#104—1221no—
593#104—1221no—
594#101—612no—
595#101—612no—
596#101—612no—
597#101C4×D6112yescomplemented
598#100—612no—
599#100—612no—
600#100—612no—
601#100C4×D6112yescomplemented
602#97—21no—
603#97—1221no—
604#97—1221no—
605#97—1221no—
606C4×C8—21no—
607C4×C8—1221no—
608C4×C8—1221no—
609C4×C8—1221no—
610C24—611no—
611C24—1221no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—1221no—
617#41—1221no—
618#41—1221no—
619#41—1221no—
620#41—1221no—
621#41—1221no—
622#41—1221no—
623#41—1221no—
624#41—1221no—
625#41—1221no—
626#41—1221no—
627#41—1221no—
628#41—2441no—
629#41—2441no—
630#41—2441no—
631#41—2441no—
632#41—2441no—
633#41—2441no—
634#41—2441no—
635#41—2441no—
636C2×Q8—611no—
637C2×Q8—1221no—
638C2×Q8—1221no—
639C2×Q8—1221no—
640C2×Q8—1221no—
641C2×Q8—1221no—
642C2×Q8C2×C4×D6111yescharacteristic
643C2×D4—21no—
644C2×D4—611no—
645C2×D4—1221no—
646C2×D4—1221no—
647C2×D4—1221no—
648C2×D4—1221no—
649C2×D4—1221no—
650C2×D4—1221no—
651C2×D4—1221no—
652C2×D4—1221no—
653C2×D4—2441no—
654C2×D4—2441no—
655C2×D4—2441no—
656C2×D4—2441no—
657C2×D4C2×C4×D6111yescharacteristic
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—611no—
661C22×C4—611no—
662C22×C4—611no—
663C22×C4—611no—
664C22×C4—611no—
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—1221no—
674C22×C4—1221no—
675C22×C4—1221no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—2441no—
679C22×C4—2441no—
680C22×C4—2441no—
681C22×C4—2441no—
682C22×C4—2441no—
683C22×C4C23×D6111yescharacteristic
684M16—21no—
685M16—21no—
686M16—21no—
687M16—21no—
688M16—21no—
689M16—612no—
690M16—612no—
691M16—612no—
692M16—1222no—
693M16—1222no—
694M16—1222no—
695M16—1222no—
696M16—1222no—
697M16—1222no—
698M16—1221no—
699M16—1221no—
700M16—1221no—
701M16—1221no—
702M16—1221no—
703M16—2441no—
704M16—2441no—
705M16C2×C4×D6112yes—
706M16C2×C4×D6112yes—
707M16D4×D6112yes—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—1222no—
713C2×C8—1222no—
714C2×C8—1222no—
715C2×C8—1222no—
716C2×C8—1222no—
717C2×C8—1222no—
718C2×C8—1221no—
719C2×C8—1221no—
720C2×C8—1221no—
721C2×C8—1221no—
722C2×C8—2441no—
723C2×C8—2441no—
724C4⋊C4—21no—
725C4⋊C4—1221no—
726C4⋊C4—1221no—
727C4⋊C4—1221no—
728C4⋊C4—1221no—
729C4⋊C4—1221no—
730C4⋊C4—2441no—
731C22⋊C4—21no—
732C22⋊C4—1221no—
733C22⋊C4—1221no—
734C22⋊C4—1221no—
735C22⋊C4—1221no—
736C22⋊C4—1221no—
737C22⋊C4—2441no—
738C42—21no—
739C42—21no—
740C42—611no—
741C42—611no—
742C42—1221no—
743C42—1221no—
744C42—2441no—
745C42D4×D6111yescharacteristic
746C42D4×D6111yescharacteristic
747C23—21no—
748C23—611no—
749C23—611no—
750C23—611no—
751C23—611no—
752C23—611no—
753C23—611no—
754C23—1221no—
755C23—4881no—
756C23—4882no—
757C23—2441no—
758C23—2441no—
759C23#41×D6111yescharacteristic
760Q8—21no—
761Q8—21no—
762Q8—1221no—
763Q8—1221no—
764Q8—2441no—
765Q8—2441no—
766D4—21no—
767D4—21no—
768D4—41no—
769D4—41no—
770D4—1221no—
771D4—1221no—
772D4—2441no—
773D4—2441no—
774D4—2441no—
775D4—2441no—
776D4—2441no—
777D4—2441no—
778D4—2441no—
779D4—2441no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—81no—
787C2×C4—611no—
788C2×C4—611no—
789C2×C4—611no—
790C2×C4—611no—
791C2×C4—611no—
792C2×C4—611no—
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—1221no—
810C2×C4—1221no—
811C2×C4—1221no—
812C2×C4—4882no—
813C2×C4—4881no—
814C2×C4—2441no—
815C2×C4—2441no—
816C2×C4—2441no—
817C2×C4—2441no—
818C2×C4—2441no—
819C2×C4—2441no—
820C2×C4—2441no—
821C2×C4—2441no—
822C2×C4—2441no—
823C2×C4C22×C4×D6111yescharacteristic
824C2×C4C2×D4×D6111yescharacteristic
825C2×C4C2×D4×D6111yescharacteristic
826C2×C4#41×D6111yescharacteristic
827C2×C4#41×D6111yescharacteristic
828C2×C4#41×D6111yescharacteristic
829C8—22no—
830C8—22no—
831C8—22no—
832C8—41no—
833C8—1222no—
834C8—1222no—
835C8—1222no—
836C8—2441no—
837C22—41no—
838C22—41no—
839C22—81no—
840C22—611no—
841C22—611no—
842C22—611no—
843C22—611no—
844C22—4881no—
845C22—4882no—
846C22—4882no—
847C22—2441no—
848C22—2441no—
849C22—2441no—
850C22—2441no—
851C22—2441no—
852C22—2441no—
853C22—2441no—
854C22#117×D6111yescharacteristic
855C22#123×D6111yescharacteristic
856C22#124×D6111yescharacteristic
857C4—41no—
858C4—41no—
859C4—41no—
860C4—81no—
861C4—611no—
862C4—611no—
863C4—611no—
864C4—611no—
865C4—4881no—
866C4—2441no—
867C4—2441no—
868C4—2441no—
869C4C4×D4×D6111yescharacteristic
870C4C4×D4×D6111yescharacteristic
871C4#121×D6111yescharacteristic
872C4#126×D6111yescharacteristic
873C2—21no—
874C2—21no—
875C2—21no—
876C2—81no—
877C2—1221no—
878C2—1221no—
879C2—1221no—
880C2—1221no—
881C2—4881no—
882C2#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
hypocenterC61#21080
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. #21454236C2semidirect
6. #21446491C2semidirect
7. #21446490C2semidirect
8. #21446489C2semidirect
9. #21446488C2semidirect
10. #21446487C2semidirect
11. #21446486C2semidirect
12. #21446485C2semidirect
13. #344×D61C2semidirect
14. #21445527C2semidirect
15. C61×#1932C2semidirect
23. #16839811C22semidirect
24. #16839810C22semidirect
25. #16839810C22semidirect
41. #16839745C4semidirect
44. #16839743C4semidirect
45. #101×D61C4semidirect
46. #100×D61C4semidirect
51. C4×#11758194C22semidirect
52. M16×Dic61C22semidirect
53. 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
444. #1932D61semidirect
468. #430C2×D61semidirect
499. C4×M16C2×D61semidirect
503. #344C2×D61semidirect
507. #339C2×D61semidirect
508. C61#21080semidirect
597. #101C4×D61semidirect
601. #100C4×D61semidirect

Maximal subgroups

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

subgroupindex
#430×D612
C2×#168397772
#421×D612
#413×D612
#214542362
#214464912
#214464902
#214464892
#214464882
#214464872
#214464862
#214464852
#344×D612
#214455272
C61×#19322
#2108061