Finite Group Databasebeta

← D61×#2031 #29707433

Subgroups — D61×#2031 #29707433

Order 15616.

1234 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D61C211yesmaximal, characteristic, complemented
2#421×D61C211yesmaximal, characteristic
3C2×#104×D61C211yesmaximal, characteristic
4#410×D61C211yesmaximal, characteristic
5#21446994C211yesmaximal, characteristic, complemented
6#21446993C211yesmaximal, characteristic, complemented
7#21446992C211yesmaximal, characteristic, complemented
8#21446991C211yesmaximal, characteristic, complemented
9#21446990C211yesmaximal, characteristic, complemented
10#21446989C211yesmaximal, characteristic, complemented
11#21446988C211yesmaximal, characteristic, complemented
12#344×D61C211yesmaximal, characteristic, complemented
13#339×D61C211yesmaximal, characteristic, complemented
14H(3,ℤ/4)×D61C211yesmaximal, characteristic, complemented
15C61×#2031C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C2×M16×D61C2211yescharacteristic
18C2×M16×D61C2211yescharacteristic
19#16840319C2211yescharacteristic, complemented
20#16840318—21no—
21#16840317—21no—
22#16840316—22no—
23#16840315C2211yescharacteristic, complemented
24#16840315C2211yescharacteristic, complemented
25#16840314—22no—
26C4⋊Q8×D61—21no—
27#125×D61—21no—
28C22⋊Q8×D61—22no—
29C4×Q8×D61—22no—
30#117×D61C2211yescharacteristic
31#117×D61C2211yescharacteristic
32#117×D61C2211yescharacteristic
33C2×C42×D61C2211yescharacteristic
34#16839780C2211yescharacteristic
35#16839779C2211yescharacteristic
36#16839778C2211yescharacteristic
37#16839777—22no—
38C2×#14519705C2211yescharacteristic
39C2×#14519704C2211yescharacteristic
40C2×#14519703C2211yescharacteristic
41#104×D61—21no—
42#104×D61—21no—
43#104×D61—21no—
44#104×D61—21no—
45#104×D61—22no—
46#16839736C2211yescharacteristic
47#16839735C2211yescharacteristic
48#16839735C2211yescharacteristic
49#16839734—22no—
50#99×D61—22no—
51#16839534C2211yescharacteristic, complemented
52#16839533C2211yescharacteristic, complemented
53#16839532C2211yescharacteristic, complemented
54#16839523C2211yescharacteristic, complemented
55#16839522C2211yescharacteristic, complemented
56#16839521C2211yescharacteristic, complemented
57#16839519C2211yescharacteristic, complemented
58#16839518C2211yescharacteristic, complemented
59#16839518C2211yescharacteristic, complemented
60C61×#533C2211yescharacteristic, complemented
61C61×#421C2211yescharacteristic
62C2×#104×C61C2211yescharacteristic
63C61×#410C2211yescharacteristic
64C61×#344C2211yescharacteristic, complemented
65C61×#339C2211yescharacteristic, complemented
66C61×H(3,ℤ/4)C2211yescharacteristic, complemented
67C2×#11758226Q811yescharacteristic, complemented
68C2×#11758222—21no—
69C2×#11758222C2311yescharacteristic
70C2×#11758224—21no—
71C2×#11758224Q811yescharacteristic, complemented
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×D61—22no—
81C2×Q8×D61Q811yescharacteristic, complemented
82C2×D4×D61—21no—
83C2×D4×D61Q811yescharacteristic, complemented
84C22×C4×D61—21no—
85C22×C4×D61—21no—
86C22×C4×D61C2311yescharacteristic
87C2×#11758194C2311yescharacteristic
88C2×#11758194C2311yescharacteristic
89C2×#11758189—21no—
90C2×#11758189—21no—
91M16×D61—21no—
92M16×D61—21no—
93M16×D61—21no—
94M16×D61—21no—
95M16×D61—21no—
96M16×D61—21no—
97M16×D61—21no—
98M16×D61—21no—
99C2×C8×D61—21no—
100C2×C8×D61—21no—
101#14519777—21no—
102#14519776—22no—
103#14519776—21no—
104#14519776—21no—
105#14519775—22no—
106#14519769—21no—
107#14519768—21no—
108#14519768—21no—
109#14519767—22no—
110#14519767—22no—
111#14519757—22no—
112#14519756—22no—
113#14519755—22no—
114#14519755—22no—
115#14519754—22no—
116#14519754—22no—
117#14519753—22no—
118Q8×Dic61—22no—
119C4×Dic122—22no—
120C4×Dic122—22no—
121C4×Dic122—22no—
122#14519742—22no—
123#14519742—22no—
124#14519742—22no—
125#14519736C2311yescharacteristic
126#14519736C2311yescharacteristic
127#14519736C2311yescharacteristic
128#14519735—21no—
129#14519735—21no—
130#14519735—21no—
131#14519734—21no—
132#14519734—21no—
133#14519734D412yes—
134#14519733—21no—
135#14519733—21no—
136#14519733D412yes—
137C4⋊C4×D61—22no—
138C4⋊C4×D61—22no—
139C4⋊C4×D61—22no—
140C4⋊C4×D61—21no—
141C4⋊C4×D61—21no—
142C4⋊C4×D61—21no—
143C22⋊C4×D61—21no—
144C22⋊C4×D61—21no—
145C22⋊C4×D61D412yes—
146C2×C4×Dic61—21no—
147C2×C4×Dic61C2311yescharacteristic
148C42×D61—21no—
149C42×D61—21no—
150C42×D61—21no—
151C42×D61—21no—
152C42×D61D411yescharacteristic
153C42×D61D411yescharacteristic
154C42×D61D411yescharacteristic
155C42×D61D411yescharacteristic
156C42×D61D412yes—
157#14519705—21no—
158#14519705—21no—
159#14519705—22no—
160#14519704—21no—
161#14519704—21no—
162#14519704—22no—
163#14519703—21no—
164#14519703—21no—
165#14519703—22no—
166#14519692—22no—
167#14519691—22no—
168#14519691—22no—
169C2×#41×C61C2311yescharacteristic
170C2×M16×C61C2311yescharacteristic
171C2×M16×C61C2311yescharacteristic
172C4⋊Q8×C61—21no—
173#125×C61—21no—
174C22⋊Q8×C61—22no—
175C4×Q8×C61—22no—
176#117×C61C2311yescharacteristic
177#117×C61C2311yescharacteristic
178#117×C61C2311yescharacteristic
179C2×C42×C61C2311yescharacteristic
180#104×C61—21no—
181#104×C61—21no—
182#104×C61—22no—
183#99×C61—22no—
184C23×D61—21no—
185C23×D61C2×D411yescharacteristic
186#41×C61—21no—
187#41×C61—21no—
188#41×C61—21no—
189#41×C61—21no—
190C2×Q8×C61—22no—
191C2×Q8×C61C2×Q811yescharacteristic, complemented
192C2×D4×C61—21no—
193C2×D4×C61C2×Q811yescharacteristic, complemented
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61C2411yescharacteristic
197C2×C22⋊D61—21no—
198C2×C22⋊D61—21no—
199C2×C22⋊D61—21no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61C2×D411yescharacteristic
203#11758226—21no—
204#11758226—21no—
205#11758226—21no—
206#11758226—21no—
207Q8×D61—21no—
208Q8×D61—21no—
209Q8×D61—21no—
210Q8×D61—21no—
211Q8×D61—48no—
212#11758224—21no—
213#11758224—21no—
214#11758224—21no—
215#11758224—21no—
216#11758224—41no—
217#11758224—41no—
218#11758224—41no—
219#11758224—41no—
220D4×D61—21no—
221D4×D61—21no—
222D4×D61—21no—
223D4×D61—21no—
224D4×D61—41no—
225D4×D61—41no—
226D4×D61—41no—
227D4×D61—41no—
228#11758222—21no—
229#11758222—21no—
230#11758222—21no—
231#11758222—21no—
232#11758222—41no—
233#11758222—41no—
234#11758222—41no—
235#11758222—41no—
236C2×D244—21no—
237C2×D244C2×Q811yescharacteristic, complemented
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61—22no—
243C2×C4×D61—22no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—44no—
248C2×C4×D61—41no—
249C2×C4×D61—41no—
250C2×C4×D61—41no—
251C2×C4×D61—41no—
252C2×C4×D61—41no—
253C2×C4×D61C2×D411yescharacteristic
254C2×C4×D61C2×D411yescharacteristic
255C2×C4×D61C2×D411yescharacteristic
256C2×C4×D61C2×D411yescharacteristic
257C2×C4×D61C2×Q811yescharacteristic
258C2×C4×D61C2×Q811yescharacteristic
259C2×C4×D61#4111yescharacteristic
260C2×C4×D61#4111yescharacteristic
261C2×C4×D61#4111yescharacteristic
262C2×C4×D61#4111yescharacteristic
263C2×C4×D61#4111yescharacteristic
264C2×C4×D61#4111yescharacteristic
265C2×Dic122—22no—
266C2×Dic122—22no—
267C2×Dic122—22no—
268C2×Dic122—21no—
269C2×Dic122C2×Q811yescharacteristic, complemented
270M16×C61—21no—
271M16×C61—21no—
272M16×C61—21no—
273M16×C61—21no—
274C2×C8×C61—21no—
275C2×C8×C61—21no—
276C4⋊C4×C61—22no—
277C4⋊C4×C61—22no—
278C4⋊C4×C61—22no—
279C4⋊C4×C61—21no—
280C4⋊C4×C61—21no—
281C4⋊C4×C61—21no—
282C22⋊C4×C61—21no—
283C22⋊C4×C61—21no—
284C22⋊C4×C61C2×D412yes—
285C42×C61—21no—
286C42×C61—21no—
287C42×C61—21no—
288C42×C61C2×D411yescharacteristic
289C42×C61C2×D411yescharacteristic
290C42×C61C2×D412yes—
291C22⋊Dic61—21no—
292C22⋊Dic61—21no—
293C22⋊Dic61C2×D412yes—
294#11758198—22no—
295#11758198—22no—
296#11758198—41no—
297C4⋊Dic61—22no—
298C4⋊Dic61—22no—
299C4⋊Dic61—22no—
300C4⋊Dic61—21no—
301C4⋊Dic61—21no—
302C4⋊Dic61—21no—
303#11758196—22no—
304#11758196—22no—
305#11758196—22no—
306#11758196—22no—
307#11758196—22no—
308#11758196—22no—
309#11758196—22no—
310#11758196—22no—
311#11758196—41no—
312C4×Dic61—21no—
313C4×Dic61—21no—
314C4×Dic61—21no—
315C4×Dic61—21no—
316C4×Dic61—21no—
317C4×Dic61—21no—
318C4×Dic61—22no—
319C4×Dic61—22no—
320C4×Dic61—21no—
321C4×Dic61—41no—
322C4×Dic61C2×D411yescharacteristic
323C4×Dic61C2×D411yescharacteristic
324C4×Dic61C2×D412yes—
325#11758194—21no—
326#11758194—21no—
327#11758194—21no—
328#11758194—21no—
329C2×#92418—21no—
330C2×#92418—21no—
331#11758189—41no—
332#11758189—41no—
333#11758189—41no—
334#11758189—41no—
335C8×D61—41no—
336C8×D61—41no—
337C8×D61—41no—
338C8×D61—41no—
339C23×C61—21no—
340C23×C61C22×D411yescharacteristic
341C22×D61—21no—
342C22×D61—42no—
343C22×D61—41no—
344C22×D61—41no—
345C22×D61—82no—
346C22×D61#12011yescharacteristic
347C22×D61#12011yescharacteristic
348C22×D61C22⋊Q811yescharacteristic
349C22×D61C22⋊Q811yescharacteristic
350C22×D61#12411yescharacteristic
351C22×D61#12411yescharacteristic
352Q8×C61—21no—
353Q8×C61—21no—
354Q8×C61—44no—
355D4×C61—21no—
356D4×C61—21no—
357D4×C61—41no—
358D4×C61—41no—
359C2×C4×C61—21no—
360C2×C4×C61—21no—
361C2×C4×C61—22no—
362C2×C4×C61—22no—
363C2×C4×C61—21no—
364C2×C4×C61—42no—
365C2×C4×C61—41no—
366C2×C4×C61—41no—
367C2×C4×C61—41no—
368C2×C4×C61C22×D411yescharacteristic
369C2×C4×C61C22×D411yescharacteristic
370C2×C4×C61C22×Q811yescharacteristic
371C2×C4×C61C2×#4111yescharacteristic
372C2×C4×C61C2×#4111yescharacteristic
373C2×C4×C61C2×#4111yescharacteristic
374C22⋊D61—41no—
375C22⋊D61—41no—
376C22⋊D61—41no—
377C22⋊D61—41no—
378C22⋊D61—41no—
379C22⋊D61—41no—
380C2×Dic61—21no—
381C2×Dic61—21no—
382C2×Dic61—22no—
383C2×Dic61—22no—
384C2×Dic61—21no—
385C2×Dic61—42no—
386C2×Dic61—41no—
387C2×Dic61—41no—
388C2×Dic61—41no—
389C2×Dic61#12011yescharacteristic
390C2×Dic61#12011yescharacteristic
391C2×Dic61C22⋊Q811yescharacteristic
392C2×Dic61C22⋊Q811yescharacteristic
393C2×Dic61#12411yescharacteristic
394C2×Dic61#12411yescharacteristic
395D244—21no—
396D244—21no—
397D244—41no—
398D244—41no—
399C4×D61—24no—
400C4×D61—42no—
401C4×D61—42no—
402C4×D61—42no—
403C4×D61—44no—
404C4×D61—44no—
405C4×D61—41no—
406C4×D61—41no—
407C4×D61—41no—
408C4×D61—41no—
409C4×D61—41no—
410C4×D61—41no—
411C4×D61—82no—
412C4×D61C22⋊Q811yescharacteristic
413C4×D61C22⋊Q811yescharacteristic
414C4×D61C22⋊Q811yescharacteristic
415C4×D61C22⋊Q811yescharacteristic
416C4×D61C22⋊Q811yescharacteristic
417C4×D61C22⋊Q811yescharacteristic
418C4×D61C22⋊Q811yescharacteristic
419C4×D61C22⋊Q811yescharacteristic
420C4×D61#12411yescharacteristic
421C4×D61#12411yescharacteristic
422C4×D61#12411yescharacteristic
423C4×D61#12411yescharacteristic
424C4×D61#12411yescharacteristic
425C4×D61#12411yescharacteristic
426C4×D61#12411yescharacteristic
427C4×D61#12411yescharacteristic
428Dic122—21no—
429Dic122—21no—
430Dic122—44no—
431Dic122—44no—
432Dic122—44no—
433Dic122—41no—
434Dic122—41no—
435C8×C61—41no—
436C8×C61—41no—
437#92418—41no—
438#92418—41no—
439C2×#2031—611nomaximal, Sylow
440C22×C61—41no—
441C22×C61—41no—
442C22×C61—81no—
443C22×C61C2×#12011yescharacteristic
444C22×C61C2×C22⋊Q811yescharacteristic
445C22×C61C2×#12411yescharacteristic
446C2×D61—22no—
447C2×D61—22no—
448C2×D61—22no—
449C2×D61—41no—
450C2×D61—41no—
451C2×D61—41no—
452C2×D61—41no—
453C2×D61—82no—
454C2×D61—82no—
455C2×D61—81no—
456C2×D61#39311yescharacteristic
457C2×D61#39311yescharacteristic
458C2×D61#39311yescharacteristic
459C2×D61#39311yescharacteristic
460C4×C61—22no—
461C4×C61—42no—
462C4×C61—42no—
463C4×C61—41no—
464C4×C61—41no—
465C4×C61—81no—
466C4×C61C2×C22⋊Q811yescharacteristic
467C4×C61C2×C22⋊Q811yescharacteristic
468C4×C61C2×#12411yescharacteristic
469C4×C61C2×#12411yescharacteristic
470Dic61—22no—
471Dic61—42no—
472Dic61—42no—
473Dic61—41no—
474Dic61—41no—
475Dic61—81no—
476Dic61#39311yescharacteristic
477Dic61#39311yescharacteristic
478Dic61#39311yescharacteristic
479Dic61#39311yescharacteristic
480C2×#533—611no—
481C2×#421—611no—
482C22×#104—611no—
483C2×#410—611no—
484#2031—611no—
485#2031—611no—
486#2031—611no—
487#2031—611no—
488#2031—611no—
489#2031—611no—
490#2031—611no—
491#2031D6111yescharacteristic, direct product factor
492C2×#344—611no—
493C2×#339—611no—
494C2×H(3,ℤ/4)—611no—
495C2×C61—21no—
496C2×C61—21no—
497C2×C61—21no—
498C2×C61—81no—
499C2×C61C2×#39311yescharacteristic
500D61—21no—
501D61—21no—
502D61—21no—
503D61—81no—
504D61#203112yesdirect product factor
505C22×#41—611no—
506C22×M16—611no—
507C22×M16—611no—
508#533—611no—
509#533—611no—
510#533—611no—
511#533—1221no—
512#533—1221no—
513#533—1222no—
514#533—1222no—
515#533C2×D6111yescharacteristic, complemented
516C2×C4⋊Q8—1221no—
517C2×#125—1221no—
518C2×C22⋊Q8—1222no—
519C2×C4×Q8—1222no—
520C2×#117—611no—
521C2×#117—611no—
522C2×#117—611no—
523C22×C42—611no—
524#421—611no—
525#421—611no—
526#421—611no—
527#421—1222no—
528#421C2×D6111yescharacteristic
529C2×#104—611no—
530C2×#104—611no—
531C2×#104—611no—
532C2×#104—1221no—
533C2×#104—1221no—
534C2×#104—1221no—
535C2×#104—1221no—
536C2×#104—1222no—
537C2×#104C2×D6111yescharacteristic
538#410—611no—
539#410—611no—
540#410—611no—
541#410—1222no—
542#410C2×D6111yescharacteristic
543C2×#99—1222no—
544#344—611no—
545#344—611no—
546#344—611no—
547#344C2×D6111yescharacteristic, complemented
548#339—611no—
549#339—611no—
550#339—611no—
551#339C2×D6111yescharacteristic, complemented
552H(3,ℤ/4)—611no—
553H(3,ℤ/4)—611no—
554H(3,ℤ/4)—611no—
555H(3,ℤ/4)C2×D6111yescharacteristic, complemented
556C61C2×#203111yescharacteristic, complemented, Sylow
557C2×#41—611no—
558C2×#41—611no—
559C2×#41—611no—
560C2×#41—1221no—
561C2×#41—1221no—
562C2×#41—1221no—
563C2×#41—1221no—
564C2×#41—1221no—
565C2×#41—1221no—
566C2×#41—1221no—
567C2×#41—1221no—
568C2×#41—1221no—
569C2×#41—1221no—
570C2×#41C22×D6111yescharacteristic
571C22×Q8—611no—
572C22×Q8—1222no—
573C22×D4—611no—
574C22×D4—1221no—
575C23×C4—611no—
576C23×C4—1221no—
577C23×C4—1221no—
578C2×M16—611no—
579C2×M16—611no—
580C2×M16—1221no—
581C2×M16—1221no—
582C2×M16—1221no—
583C2×M16—1221no—
584C2×M16—1221no—
585C2×M16—1221no—
586C2×M16—1221no—
587C2×M16—1221no—
588C2×M16—1221no—
589C2×M16—1221no—
590C2×M16C22×D6111yescharacteristic
591C2×M16C22×D6111yescharacteristic
592C22×C8—1221no—
593C22×C8—1221no—
594C4⋊Q8—21no—
595C4⋊Q8—1221no—
596C4⋊Q8—1221no—
597C4⋊Q8—1222no—
598C4⋊Q8—1222no—
599C4⋊Q8—1221no—
600#125—21no—
601#125—1221no—
602#125—1221no—
603#125—1222no—
604#125—1222no—
605#125—1221no—
606C22⋊Q8—22no—
607C22⋊Q8—1222no—
608C22⋊Q8—1222no—
609C22⋊Q8—1222no—
610C22⋊Q8—1222no—
611C22⋊Q8—1222no—
612C22⋊Q8—1222no—
613C22⋊Q8—1222no—
614C4×Q8—22no—
615C4×Q8—1222no—
616C4×Q8—1222no—
617C4×Q8—1222no—
618C4×Q8—1222no—
619C4×Q8—1222no—
620C4×Q8—1222no—
621C4×Q8—1222no—
622#117—611no—
623#117—612no—
624#117—611no—
625#117—612no—
626#117—611no—
627#117—1221no—
628#117—1221no—
629#117—1221no—
630#117—1221no—
631#117—1221no—
632#117—1221no—
633#117—1221no—
634#117C22×D6111yescharacteristic
635#117C22×D6111yescharacteristic
636#117C22×D6111yescharacteristic
637C2×C4⋊C4—1221no—
638C2×C4⋊C4—1221no—
639C2×C4⋊C4—1222no—
640C2×C4⋊C4—1222no—
641C2×C4⋊C4—1222no—
642C2×C4⋊C4—1221no—
643C2×C22⋊C4—612no—
644C2×C22⋊C4—1221no—
645C2×C22⋊C4—1221no—
646C2×C42—611no—
647C2×C42—612no—
648C2×C42—611no—
649C2×C42—611no—
650C2×C42—611no—
651C2×C42—611no—
652C2×C42—1221no—
653C2×C42—1221no—
654C2×C42—1221no—
655C2×C42—1221no—
656C2×C42—1221no—
657C2×C42C22×D6111yescharacteristic
658#104—21no—
659#104—21no—
660#104—22no—
661#104—1221no—
662#104—1221no—
663#104—1222no—
664#104—1221no—
665#104—1221no—
666#104—1222no—
667#104—1221no—
668#104—1221no—
669#104—1222no—
670#99—22no—
671#99—1222no—
672#99—1222no—
673#99—1222no—
674C24—611no—
675C24—1221no—
676#41—21no—
677#41—21no—
678#41—21no—
679#41—21no—
680#41—1221no—
681#41—1221no—
682#41—1221no—
683#41—1221no—
684#41—1221no—
685#41—1221no—
686#41—1221no—
687#41—1221no—
688#41—1221no—
689#41—1221no—
690#41—1221no—
691#41—1221no—
692#41—2441no—
693#41—2441no—
694#41—2441no—
695#41—2441no—
696#41—2441no—
697#41—2441no—
698#41—2441no—
699#41—2441no—
700C2×Q8—22no—
701C2×Q8—611no—
702C2×Q8—1221no—
703C2×Q8—1222no—
704C2×Q8—1222no—
705C2×Q8—1222no—
706C2×Q8—1221no—
707C2×Q8—1221no—
708C2×Q8—1221no—
709C2×Q8—1221no—
710C2×Q8—2448no—
711C2×Q8Q8×D6111yescharacteristic, complemented
712C2×D4—21no—
713C2×D4—611no—
714C2×D4—1221no—
715C2×D4—1221no—
716C2×D4—1221no—
717C2×D4—1221no—
718C2×D4—1221no—
719C2×D4—1221no—
720C2×D4—1221no—
721C2×D4—1221no—
722C2×D4—2441no—
723C2×D4—2441no—
724C2×D4—2441no—
725C2×D4—2441no—
726C2×D4Q8×D6111yescharacteristic, complemented
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—611no—
730C22×C4—611no—
731C22×C4—611no—
732C22×C4—611no—
733C22×C4—611no—
734C22×C4—611no—
735C22×C4—611no—
736C22×C4—611no—
737C22×C4—611no—
738C22×C4—611no—
739C22×C4—611no—
740C22×C4—611no—
741C22×C4—611no—
742C22×C4—1221no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4—1221no—
746C22×C4—1221no—
747C22×C4—1222no—
748C22×C4—1222no—
749C22×C4—1221no—
750C22×C4—1221no—
751C22×C4—1221no—
752C22×C4—1221no—
753C22×C4—2441no—
754C22×C4—2441no—
755C22×C4—2441no—
756C22×C4—2441no—
757C22×C4—2444no—
758C22×C4—2441no—
759C22×C4C23×D6111yescharacteristic
760M16—21no—
761M16—21no—
762M16—21no—
763M16—21no—
764M16—1221no—
765M16—1221no—
766M16—1221no—
767M16—1221no—
768M16—2441no—
769M16—2441no—
770M16—2441no—
771M16—2441no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—1221no—
775C2×C8—1221no—
776C2×C8—2441no—
777C2×C8—2441no—
778C2×C8—2441no—
779C2×C8—2441no—
780C4⋊C4—22no—
781C4⋊C4—22no—
782C4⋊C4—22no—
783C4⋊C4—21no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—1222no—
787C4⋊C4—1222no—
788C4⋊C4—1222no—
789C4⋊C4—1222no—
790C4⋊C4—1222no—
791C4⋊C4—1222no—
792C4⋊C4—1222no—
793C4⋊C4—1222no—
794C4⋊C4—1222no—
795C4⋊C4—1222no—
796C4⋊C4—1222no—
797C4⋊C4—1221no—
798C4⋊C4—1221no—
799C4⋊C4—1221no—
800C4⋊C4—2441no—
801C22⋊C4—21no—
802C22⋊C4—21no—
803C22⋊C4—612no—
804C22⋊C4—1222no—
805C22⋊C4—1222no—
806C22⋊C4—1221no—
807C22⋊C4—1221no—
808C22⋊C4—2441no—
809C22⋊C4D4×D6112yes—
810C42—21no—
811C42—21no—
812C42—21no—
813C42—611no—
814C42—611no—
815C42—612no—
816C42—1221no—
817C42—1221no—
818C42—1221no—
819C42—1221no—
820C42—1222no—
821C42—1222no—
822C42—1221no—
823C42—1221no—
824C42—1221no—
825C42—2441no—
826C42D4×D6111yescharacteristic
827C42D4×D6111yescharacteristic
828C42D4×D6112yes—
829C23—21no—
830C23—611no—
831C23—611no—
832C23—611no—
833C23—611no—
834C23—611no—
835C23—611no—
836C23—1221no—
837C23—4882no—
838C23—2441no—
839C23—2441no—
840C23—2442no—
841C23C2×D4×D6111yescharacteristic
842Q8—21no—
843Q8—21no—
844Q8—44no—
845Q8—1221no—
846Q8—1221no—
847Q8—2444no—
848Q8—2441no—
849Q8—2441no—
850Q8—2444no—
851Q8—2444no—
852D4—21no—
853D4—21no—
854D4—41no—
855D4—41no—
856D4—1221no—
857D4—1221no—
858D4—2441no—
859D4—2441no—
860D4—2441no—
861D4—2441no—
862D4—2441no—
863D4—2441no—
864D4—2441no—
865D4—2441no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—21no—
871C2×C4—42no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—611no—
876C2×C4—611no—
877C2×C4—611no—
878C2×C4—611no—
879C2×C4—611no—
880C2×C4—611no—
881C2×C4—611no—
882C2×C4—611no—
883C2×C4—611no—
884C2×C4—611no—
885C2×C4—611no—
886C2×C4—611no—
887C2×C4—611no—
888C2×C4—611no—
889C2×C4—611no—
890C2×C4—611no—
891C2×C4—611no—
892C2×C4—611no—
893C2×C4—611no—
894C2×C4—611no—
895C2×C4—611no—
896C2×C4—611no—
897C2×C4—1224no—
898C2×C4—1221no—
899C2×C4—1221no—
900C2×C4—1222no—
901C2×C4—1222no—
902C2×C4—1221no—
903C2×C4—4882no—
904C2×C4—2442no—
905C2×C4—2441no—
906C2×C4—2441no—
907C2×C4—2442no—
908C2×C4—2441no—
909C2×C4—2441no—
910C2×C4—2442no—
911C2×C4—2444no—
912C2×C4—2444no—
913C2×C4—2441no—
914C2×C4—2441no—
915C2×C4—2442no—
916C2×C4—2441no—
917C2×C4—2441no—
918C2×C4—2441no—
919C2×C4C2×D4×D6111yescharacteristic
920C2×C4C2×D4×D6111yescharacteristic
921C2×C4C2×Q8×D6111yescharacteristic
922C2×C4#41×D6111yescharacteristic
923C2×C4#41×D6111yescharacteristic
924C2×C4#41×D6111yescharacteristic
925C8—41no—
926C8—41no—
927C8—2441no—
928C8—2441no—
929C22—41no—
930C22—41no—
931C22—81no—
932C22—611no—
933C22—611no—
934C22—611no—
935C22—611no—
936C22—1222no—
937C22—1222no—
938C22—1222no—
939C22—4881no—
940C22—4882no—
941C22—4882no—
942C22—2441no—
943C22—2441no—
944C22—2441no—
945C22—2441no—
946C22#120×D6111yescharacteristic
947C22C22⋊Q8×D6111yescharacteristic
948C22#124×D6111yescharacteristic
949C4—22no—
950C4—41no—
951C4—42no—
952C4—42no—
953C4—41no—
954C4—81no—
955C4—611no—
956C4—611no—
957C4—611no—
958C4—611no—
959C4—1222no—
960C4—4881no—
961C4—2441no—
962C4—2442no—
963C4—2442no—
964C4—2441no—
965C4C22⋊Q8×D6111yescharacteristic
966C4C22⋊Q8×D6111yescharacteristic
967C4#124×D6111yescharacteristic
968C4#124×D6111yescharacteristic
969C2—21no—
970C2—21no—
971C2—21no—
972C2—81no—
973C2—612no—
974C2—1221no—
975C2—1221no—
976C2—1221no—
977C2—4881no—
978C2#393×D6111yescharacteristic
subgroupG/H
centerC4#124×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2031C2
socleC2×C61C2×#393
prime radicalC2×#41×D61C22
hypercenter#2031D61
hypocenterC61C2×#2031
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #2031

Complements

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

NH ≅ G/Ntype
1. #533×D61C2semidirect
5. #21446994C2semidirect
6. #21446993C2semidirect
7. #21446992C2semidirect
8. #21446991C2semidirect
9. #21446990C2semidirect
10. #21446989C2semidirect
11. #21446988C2semidirect
12. #344×D61C2semidirect
13. #339×D61C2semidirect
14. H(3,ℤ/4)×D61C2semidirect
15. C61×#2031C2semidirect
19. #16840319C22semidirect
23. #16840315C22semidirect
24. #16840315C22semidirect
51. #16839534C22semidirect
52. #16839533C22semidirect
53. #16839532C22semidirect
54. #16839523C22semidirect
55. #16839522C22semidirect
56. #16839521C22semidirect
57. #16839519C22semidirect
58. #16839518C22semidirect
59. #16839518C22semidirect
60. C61×#533C22semidirect
64. C61×#344C22semidirect
65. C61×#339C22semidirect
66. C61×H(3,ℤ/4)C22semidirect
67. C2×#11758226Q8semidirect
71. C2×#11758224Q8semidirect
81. C2×Q8×D61Q8semidirect
83. C2×D4×D61Q8semidirect
191. C2×Q8×C61C2×Q8semidirect
193. C2×D4×C61C2×Q8semidirect
237. C2×D244C2×Q8semidirect
269. C2×Dic122C2×Q8semidirect
491. #2031D61direct (N × H)
504. D61#2031direct (N × H)
515. #533C2×D61semidirect
547. #344C2×D61semidirect
551. #339C2×D61semidirect
555. H(3,ℤ/4)C2×D61semidirect
556. C61C2×#2031semidirect
711. C2×Q8Q8×D61semidirect
726. C2×D4Q8×D61semidirect

Maximal subgroups

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

subgroupindex
#533×D612
#421×D612
C2×#104×D612
#410×D612
#214469942
#214469932
#214469922
#214469912
#214469902
#214469892
#214469882
#344×D612
#339×D612
H(3,ℤ/4)×D612
C61×#20312
C2×#203161