Finite Group Databasebeta

← D61×#1644 #29655681

Subgroups — D61×#1644 #29655681

Order 15616.

1022 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#554×D61C211yesmaximal, characteristic
2#487×D61C211yesmaximal, characteristic, complemented
3#474×D61C211yesmaximal, characteristic
4#462×D61C211yesmaximal, characteristic, complemented
5#21445036C211yesmaximal, characteristic, complemented
6#21445035C211yesmaximal, characteristic, complemented
7#21445034C211yesmaximal, characteristic, complemented
8#21445033C211yesmaximal, characteristic, complemented
9#21445032C211yesmaximal, characteristic, complemented
10#21445031C211yesmaximal, characteristic, complemented
11#21445030C211yesmaximal, characteristic, complemented
12#333×D61C211yesmaximal, characteristic, complemented
13Q8⋊C8×D61C211yesmaximal, characteristic, complemented
14D4⋊C8×D61C211yesmaximal, characteristic
15C61×#1644C211yesmaximal, characteristic, complemented
16C2×Q16×D61—21no—
17#16840473C2211yescharacteristic
18#16840472C2211yescharacteristic
19#16840471—21no—
20#16840470—21no—
21#16840469C2211yescharacteristic
22#16840468—21no—
23#16840467—21no—
24#16840466—22no—
25C4⋊Q8×D61C2211yescharacteristic
26C4⋊Q8×D61C2211yescharacteristic
27#125×D61—21no—
28C22⋊Q8×D61—22no—
29C22⋊Q8×D61—21no—
30C4×Q8×D61C2211yescharacteristic
31C4×D4×D61—21no—
32C4×D4×D61C2211yescharacteristic
33C2×C4⋊C4×D61—21no—
34#16840114C2211yescharacteristic, complemented
35#16840113C2211yescharacteristic, complemented
36#16840112C2211yescharacteristic, complemented
37#16840111—22no—
38#16840043C2211yescharacteristic
39#16840042C2211yescharacteristic
40#16840041—21no—
41#16840040—21no—
42#16840039C2211yescharacteristic
43#16839973C2211yescharacteristic, complemented
44#16839972C2211yescharacteristic, complemented
45#16839971—21no—
46#16839970—21no—
47#16839969C2211yescharacteristic, complemented
48#107×D61—21no—
49C4⋊C8×D61C2211yescharacteristic
50C4⋊C8×D61C2211yescharacteristic
51#103×D61—21no—
52#103×D61—22no—
53#102×D61—21no—
54C4×C8×D61C2211yescharacteristic
55#16839511C2211yescharacteristic, complemented
56#16839510C2211yescharacteristic, complemented
57#16839510C2211yescharacteristic, complemented
58#16839494C2211yescharacteristic, complemented
59Q8⋊#92418C2211yescharacteristic, complemented
60#16839492C2211yescharacteristic, complemented
61#16839491C2211yescharacteristic
62D4⋊#92418C2211yescharacteristic
63#16839489C2211yescharacteristic
64C61×#554C2211yescharacteristic
65C61×#487C2211yescharacteristic, complemented
66C61×#474C2211yescharacteristic
67C61×#462C2211yescharacteristic, complemented
68C61×#333C2211yescharacteristic, complemented
69C61×Q8⋊C8C2211yescharacteristic, complemented
70C61×D4⋊C8C2211yescharacteristic
71C2×Q8×D61—21no—
72C2×Q8×D61D411yescharacteristic
73C2×Q8×D61D412yes—
74C2×D4×D61D411yescharacteristic
75C22×C4×D61—22no—
76C22×C4×D61—21no—
77C2×Dic244—21no—
78C2×#11758202—21no—
79C2×#11758202—21no—
80Q16×D61—44no—
81C2×C8×D61—21no—
82C2×C8×D61—21no—
83C2×C8×D61—21no—
84#14519777C2311yescharacteristic
85#14519777C2311yescharacteristic
86#14519776—21no—
87#14519776—21no—
88#14519776—21no—
89#14519776—21no—
90#14519775—21no—
91#14519775D412yes—
92#14519769—21no—
93#14519768—21no—
94#14519768—21no—
95#14519767—22no—
96#14519767—22no—
97#14519757—22no—
98#14519757—21no—
99#14519756—22no—
100#14519756—21no—
101#14519755—22no—
102#14519755—22no—
103#14519755—22no—
104#14519754—22no—
105#14519754—22no—
106#14519754—22no—
107#14519753—22no—
108#14519753—21no—
109Q8×Dic61D411yescharacteristic
110C4×Dic122—21no—
111C4×Dic122C2311yescharacteristic
112#14519742—21no—
113#14519742D411yescharacteristic
114C4×D244—21no—
115C4×D244C2311yescharacteristic
116D4×Dic61—21no—
117D4×Dic61D411yescharacteristic
118#14519739—21no—
119#14519739D411yescharacteristic
120C4×C22⋊D61—22no—
121C4×C22⋊D61—21no—
122#14519737—22no—
123#14519737—21no—
124C2×C4⋊Dic61—21no—
125C2×#11758196—22no—
126C4⋊C4×D61—22no—
127C4⋊C4×D61—22no—
128C4⋊C4×D61—22no—
129C4⋊C4×D61—21no—
130C4⋊C4×D61—21no—
131C4⋊C4×D61—21no—
132C4⋊C4×D61—21no—
133C4⋊C4×D61—21no—
134C4⋊C4×D61—21no—
135C4⋊C4×D61—21no—
136C4⋊C4×D61D411yescharacteristic
137C4⋊C4×D61D411yescharacteristic
138C22⋊C4×D61—22no—
139C22⋊C4×D61—21no—
140C42×D61—21no—
141C42×D61C2311yescharacteristic
142#14519711—21no—
143#14519710—21no—
144#14519710—21no—
145C4⋊#92418C2311yescharacteristic
146C4⋊#92418C2311yescharacteristic
147#14519706—21no—
148#14519706—21no—
149#14519702—22no—
150#14519702—21no—
151#14519701—22no—
152#14519701—21no—
153#14519700—22no—
154#14519700—21no—
155#14519699—21no—
156#14519698—21no—
157#14519697—21no—
158C4×#92418C2311yescharacteristic
159C8×Dic61—21no—
160C2×Q16×C61—21no—
161C4⋊Q8×C61C2311yescharacteristic
162C4⋊Q8×C61C2311yescharacteristic
163#125×C61—21no—
164C22⋊Q8×C61—22no—
165C22⋊Q8×C61—21no—
166C4×Q8×C61C2311yescharacteristic
167C4×D4×C61—21no—
168C4×D4×C61C2311yescharacteristic
169C2×C4⋊C4×C61—21no—
170#107×C61—21no—
171C4⋊C8×C61C2311yescharacteristic
172C4⋊C8×C61C2311yescharacteristic
173#103×C61—22no—
174#103×C61—21no—
175#102×C61—21no—
176C4×C8×C61C2311yescharacteristic
177C23×D61—21no—
178C2×Q8×C61—21no—
179C2×Q8×C61C2×D411yescharacteristic
180C2×Q8×C61C2×D412yes—
181C2×D4×C61C2×D411yescharacteristic
182C22×C4×C61—22no—
183C22×C4×C61—21no—
184C2×C22⋊D61—21no—
185C22×Dic61—22no—
186C22×Dic61—21no—
187Q8×D61—22no—
188Q8×D61—22no—
189Q8×D61—44no—
190Q8×D61—42no—
191Q8×D61—42no—
192D4×D61—22no—
193D4×D61Q1614yescomplemented
194C2×D244C2×D411yescharacteristic
195C2×C4×D61—21no—
196C2×C4×D61—22no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—22no—
202C2×C4×D61—22no—
203C2×C4×D61—42no—
204C2×C4×D61—42no—
205C2×C4×D61—41no—
206C2×C4×D61—84no—
207C2×C4×D61C2×D411yescharacteristic
208C2×C4×D61C2×D411yescharacteristic
209C2×C4×D61C2×D411yescharacteristic
210C2×Dic122—21no—
211C2×Dic122—21no—
212C2×Dic122—22no—
213C2×Dic122—41no—
214C2×Dic122C2×D411yescharacteristic
215C2×Dic122C2×D412yes—
216Q16×C61—42no—
217C2×C8×C61—21no—
218C2×C8×C61—21no—
219C2×C8×C61—21no—
220C4⋊C4×C61—22no—
221C4⋊C4×C61—22no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61—21no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61C2×D411yescharacteristic
228C4⋊C4×C61C2×D411yescharacteristic
229C22⋊C4×C61—22no—
230C22⋊C4×C61—21no—
231C42×C61—21no—
232C42×C61C2411yescharacteristic
233C22⋊Dic61—22no—
234C22⋊Dic61—21no—
235#11758202—42no—
236#11758202—42no—
237#11758198—22no—
238#11758198—22no—
239#11758198—21no—
240#11758198—21no—
241C4⋊Dic61—22no—
242C4⋊Dic61—22no—
243C4⋊Dic61—21no—
244C4⋊Dic61—21no—
245C4⋊Dic61—21no—
246C4⋊Dic61—21no—
247C4⋊Dic61—21no—
248C4⋊Dic61C2×D411yescharacteristic
249C4⋊Dic61C2×D411yescharacteristic
250#11758196—22no—
251#11758196—22no—
252#11758196—22no—
253#11758196—22no—
254#11758196—21no—
255#11758196—21no—
256#11758196—22no—
257#11758196—22no—
258#11758196—21no—
259#11758196—21no—
260#11758196—41no—
261#11758196—41no—
262C4×Dic61—21no—
263C4×Dic61—21no—
264C4×Dic61—21no—
265C4×Dic61C2×D411yescharacteristic
266C4×Dic61C2×D411yescharacteristic
267C4×Dic61C2×D411yescharacteristic
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—21no—
271Dic244—42no—
272C8×D61—42no—
273C8×D61—42no—
274C8×D61—42no—
275C23×C61—21no—
276C22×D61—21no—
277C22×D61—24no—
278C22×D61—42no—
279C22×D61—42no—
280C22×D61#12011yescharacteristic
281Q8×C61—21no—
282Q8×C61—21no—
283Q8×C61—42no—
284Q8×C61—41no—
285Q8×C61—41no—
286D4×C61—21no—
287D4×C61C2×Q1612yescomplemented
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—22no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—82no—
296C2×C4×C61C22×D411yescharacteristic
297C2×C4×C61C22×D411yescharacteristic
298C2×C4×C61C22×D411yescharacteristic
299C22⋊D61—24no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—22no—
304C2×Dic61—42no—
305C2×Dic61—41no—
306C2×Dic61—82no—
307C2×Dic61#12011yescharacteristic
308C2×Dic61#12011yescharacteristic
309C2×Dic61#12011yescharacteristic
310D244—21no—
311D244C2×Q1612yescomplemented
312C4×D61—22no—
313C4×D61—42no—
314C4×D61—42no—
315C4×D61—42no—
316C4×D61—44no—
317C4×D61—41no—
318C4×D61—41no—
319C4×D61—42no—
320C4×D61—82no—
321C4×D61—82no—
322C4×D61—82no—
323C4×D61C2×Q1612yes—
324C4×D61#13512yes—
325C4×D61AGL(1,ℤ/8)12yes—
326C4×D61#13712yes—
327Dic122—21no—
328Dic122—21no—
329Dic122—42no—
330Dic122—42no—
331Dic122—41no—
332Dic122—41no—
333Dic122—82no—
334Dic122—82no—
335C8×C61—41no—
336C8×C61—41no—
337C8×C61—41no—
338#92418—41no—
339#92418—41no—
340#92418—41no—
341C2×#1644—611nomaximal, Sylow
342C22×C61—22no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61C2×#12011yescharacteristic
346C2×D61—22no—
347C2×D61—41no—
348C2×D61—41no—
349C2×D61—48no—
350C2×D61#44912yes—
351C2×D61#45112yes—
352C2×D61#45512yes—
353C4×C61—21no—
354C4×C61—41no—
355C4×C61—41no—
356C4×C61—42no—
357C4×C61—41no—
358C4×C61—81no—
359C4×C61C22×Q1611yescharacteristic
360C4×C61C2×#13511yescharacteristic
361C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
362C4×C61C2×#13711yescharacteristic
363Dic61—21no—
364Dic61—41no—
365Dic61—41no—
366Dic61—42no—
367Dic61—41no—
368Dic61—81no—
369Dic61#44912yes—
370Dic61#45112yes—
371C2×#554—611no—
372C2×#487—611no—
373C2×#474—611no—
374C2×#462—611no—
375#1644—611no—
376#1644—611no—
377#1644—611no—
378#1644—611no—
379#1644—611no—
380#1644—611no—
381#1644—611no—
382#1644D6111yescharacteristic, direct product factor
383C2×#333—611no—
384C2×Q8⋊C8—611no—
385C2×D4⋊C8—611no—
386C2×C61—42no—
387C2×C61C2×#45111yescharacteristic
388C2×C61C2×#44911yescharacteristic
389C2×C61C2×#45511yescharacteristic
390D61—42no—
391D61#164414yesdirect product factor
392C22×Q16—1221no—
393#554—611no—
394#554—611no—
395#554—611no—
396#554—1221no—
397#554—1221no—
398#554—1221no—
399#554—1221no—
400#554—1222no—
401#554C2×D6111yescharacteristic
402C2×C4⋊Q8—611no—
403C2×C4⋊Q8—611no—
404C2×#125—1221no—
405C2×C22⋊Q8—1222no—
406C2×C22⋊Q8—1221no—
407C2×C4×Q8—611no—
408C2×C4×D4—611no—
409C2×C4×D4—1221no—
410C22×C4⋊C4—1221no—
411#487—611no—
412#487—611no—
413#487—611no—
414#487—1222no—
415#487C2×D6111yescharacteristic, complemented
416#474—611no—
417#474—611no—
418#474—611no—
419#474—1221no—
420#474—1221no—
421#474C2×D6111yescharacteristic
422#462—611no—
423#462—611no—
424#462—611no—
425#462—1221no—
426#462—1221no—
427#462C2×D6111yescharacteristic, complemented
428C2×#107—1221no—
429C2×C4⋊C8—611no—
430C2×C4⋊C8—611no—
431C2×#103—1221no—
432C2×#103—1222no—
433C2×#102—1221no—
434C2×C4×C8—611no—
435#333—611no—
436#333—611no—
437#333—611no—
438#333C2×D6111yescharacteristic, complemented
439Q8⋊C8—611no—
440Q8⋊C8—611no—
441Q8⋊C8—611no—
442Q8⋊C8C2×D6111yescharacteristic, complemented
443D4⋊C8—611no—
444D4⋊C8—611no—
445D4⋊C8—611no—
446D4⋊C8C2×D6111yescharacteristic
447C61C2×#164411yescharacteristic, complemented, Sylow
448C22×Q8—611no—
449C22×Q8—612no—
450C22×Q8—1221no—
451C22×D4—611no—
452C23×C4—1221no—
453C23×C4—1222no—
454C2×Q16—21no—
455C2×Q16—1221no—
456C2×Q16—1221no—
457C2×Q16—1221no—
458C2×Q16—2444no—
459C22×C8—1221no—
460C22×C8—1221no—
461C22×C8—1221no—
462C4⋊Q8—612no—
463C4⋊Q8—611no—
464C4⋊Q8—611no—
465C4⋊Q8—1221no—
466C4⋊Q8—1221no—
467C4⋊Q8—1221no—
468C4⋊Q8—1221no—
469C4⋊Q8—1221no—
470C4⋊Q8C22×D6111yescharacteristic
471C4⋊Q8C22×D6111yescharacteristic
472#125—21no—
473#125—1221no—
474#125—1221no—
475#125—1222no—
476#125—1222no—
477#125—1221no—
478C22⋊Q8—21no—
479C22⋊Q8—22no—
480C22⋊Q8—1222no—
481C22⋊Q8—1222no—
482C22⋊Q8—1222no—
483C22⋊Q8—1222no—
484C22⋊Q8—1221no—
485C22⋊Q8—1222no—
486C22⋊Q8—1222no—
487C22⋊Q8—1222no—
488C22⋊Q8—1221no—
489C22⋊Q8—1222no—
490C22⋊Q8—1221no—
491C22⋊Q8—1222no—
492C4×Q8—611no—
493C4×Q8—611no—
494C4×Q8—611no—
495C4×Q8—1221no—
496C4×Q8—1221no—
497C4×Q8C22×D6111yescharacteristic
498C4×D4—21no—
499C4×D4—611no—
500C4×D4—611no—
501C4×D4—611no—
502C4×D4—1221no—
503C4×D4—1221no—
504C4×D4—1221no—
505C4×D4—1222no—
506C4×D4—1221no—
507C4×D4—1222no—
508C4×D4—1221no—
509C4×D4C22×D6111yescharacteristic
510C2×C4⋊C4—21no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4—1222no—
518C2×C4⋊C4—1222no—
519C2×C4⋊C4—1222no—
520C2×C4⋊C4—1221no—
521C2×C4⋊C4—1221no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4—1222no—
524C2×C4⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1222no—
527C2×C42—611no—
528C2×C42—1221no—
529#107—21no—
530#107—1221no—
531#107—1221no—
532#107—1221no—
533C4⋊C8—611no—
534C4⋊C8—611no—
535C4⋊C8—1221no—
536C4⋊C8—1221no—
537C4⋊C8C22×D6111yescharacteristic
538C4⋊C8C22×D6111yescharacteristic
539#103—22no—
540#103—21no—
541#103—1222no—
542#103—1221no—
543#103—1221no—
544#103—1222no—
545#103—1222no—
546#103—1221no—
547#102—21no—
548#102—1221no—
549#102—1221no—
550#102—1221no—
551C4×C8—611no—
552C4×C8—1221no—
553C4×C8C22×D6111yescharacteristic
554C24—1221no—
555C2×Q8—21no—
556C2×Q8—611no—
557C2×Q8—612no—
558C2×Q8—1222no—
559C2×Q8—1221no—
560C2×Q8—1222no—
561C2×Q8—1222no—
562C2×Q8—1221no—
563C2×Q8—2441no—
564C2×Q8—2442no—
565C2×Q8—2442no—
566C2×Q8—2444no—
567C2×Q8D4×D6111yescharacteristic
568C2×Q8D4×D6112yes—
569C2×D4—614no—
570C2×D4—611no—
571C2×D4—1222no—
572C2×D4—1221no—
573C2×D4D4×D6111yescharacteristic
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—611no—
577C22×C4—611no—
578C22×C4—611no—
579C22×C4—1221no—
580C22×C4—1222no—
581C22×C4—1222no—
582C22×C4—1221no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—1222no—
586C22×C4—1221no—
587C22×C4—1222no—
588C22×C4—1221no—
589C22×C4—4884no—
590C22×C4—2442no—
591C22×C4—2442no—
592C22×C4—2441no—
593Q16—42no—
594Q16—2442no—
595Q16—2442no—
596Q16—2442no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—1221no—
601C2×C8—1221no—
602C2×C8—1221no—
603C2×C8—2442no—
604C2×C8—2442no—
605C2×C8—2442no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—611no—
614C4⋊C4—611no—
615C4⋊C4—1221no—
616C4⋊C4—1221no—
617C4⋊C4—1222no—
618C4⋊C4—1222no—
619C4⋊C4—1221no—
620C4⋊C4—1221no—
621C4⋊C4—1222no—
622C4⋊C4—1222no—
623C4⋊C4—1222no—
624C4⋊C4—1222no—
625C4⋊C4—1222no—
626C4⋊C4—1222no—
627C4⋊C4—1221no—
628C4⋊C4—1221no—
629C4⋊C4—1221no—
630C4⋊C4—1221no—
631C4⋊C4—1221no—
632C4⋊C4—2441no—
633C4⋊C4—2441no—
634C4⋊C4D4×D6111yescharacteristic
635C4⋊C4D4×D6111yescharacteristic
636C22⋊C4—22no—
637C22⋊C4—21no—
638C22⋊C4—1221no—
639C22⋊C4—1222no—
640C22⋊C4—1222no—
641C22⋊C4—1221no—
642C22⋊C4—1222no—
643C22⋊C4—1221no—
644C42—21no—
645C42—611no—
646C42—611no—
647C42—611no—
648C42—1221no—
649C42—1221no—
650C42—1221no—
651C42C23×D6111yescharacteristic
652C23—21no—
653C23—611no—
654C23—1224no—
655C23—1221no—
656C23—2442no—
657C23—2442no—
658Q8—21no—
659Q8—21no—
660Q8—42no—
661Q8—41no—
662Q8—41no—
663Q8—1221no—
664Q8—1221no—
665Q8—4882no—
666Q8—4882no—
667Q8—2442no—
668Q8—2442no—
669Q8—2441no—
670Q8—2441no—
671D4—21no—
672D4—612no—
673D4—1224no—
674D4—1221no—
675D4Q16×D6112yescomplemented
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—82no—
684C2×C4—611no—
685C2×C4—611no—
686C2×C4—612no—
687C2×C4—612no—
688C2×C4—612no—
689C2×C4—612no—
690C2×C4—611no—
691C2×C4—1222no—
692C2×C4—1221no—
693C2×C4—1221no—
694C2×C4—1221no—
695C2×C4—1222no—
696C2×C4—4882no—
697C2×C4—4882no—
698C2×C4—4882no—
699C2×C4—4882no—
700C2×C4—2442no—
701C2×C4—2442no—
702C2×C4—2444no—
703C2×C4—2442no—
704C2×C4—2442no—
705C2×C4—2442no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4C2×D4×D6111yescharacteristic
710C2×C4C2×D4×D6111yescharacteristic
711C2×C4C2×D4×D6111yescharacteristic
712C8—41no—
713C8—41no—
714C8—41no—
715C8—2441no—
716C8—2441no—
717C8—2441no—
718C22—22no—
719C22—41no—
720C22—41no—
721C22—612no—
722C22—612no—
723C22—612no—
724C22—1222no—
725C22—2448no—
726C22—2441no—
727C22—2441no—
728C22#120×D6111yescharacteristic
729C4—21no—
730C4—41no—
731C4—42no—
732C4—41no—
733C4—41no—
734C4—81no—
735C4—612no—
736C4—612no—
737C4—1221no—
738C4—4881no—
739C4—2441no—
740C4—2442no—
741C4—2441no—
742C4—2441no—
743C4C2×Q16×D6111yescharacteristic
744C4#135×D6111yescharacteristic
745C4AGL(1,ℤ/8)×D6111yescharacteristic
746C4#137×D6111yescharacteristic
747C2—42no—
748C2—614no—
749C2—2442no—
750C2#451×D6111yescharacteristic
751C2#449×D6111yescharacteristic
752C2#455×D6111yescharacteristic
subgroupG/H
centerC22#120×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1644C2
socleC22×C61C2×#120
prime radicalC2×D4×D61D4
hypercenter#1644D61
hypocenterC61C2×#1644
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1644

Complements

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

NH ≅ G/Ntype
2. #487×D61C2semidirect
4. #462×D61C2semidirect
5. #21445036C2semidirect
6. #21445035C2semidirect
7. #21445034C2semidirect
8. #21445033C2semidirect
9. #21445032C2semidirect
10. #21445031C2semidirect
11. #21445030C2semidirect
12. #333×D61C2semidirect
13. Q8⋊C8×D61C2semidirect
15. C61×#1644C2semidirect
34. #16840114C22semidirect
35. #16840113C22semidirect
36. #16840112C22semidirect
43. #16839973C22semidirect
44. #16839972C22semidirect
47. #16839969C22semidirect
55. #16839511C22semidirect
56. #16839510C22semidirect
57. #16839510C22semidirect
58. #16839494C22semidirect
59. Q8⋊#92418C22semidirect
60. #16839492C22semidirect
65. C61×#487C22semidirect
67. C61×#462C22semidirect
68. C61×#333C22semidirect
69. C61×Q8⋊C8C22semidirect
193. D4×D61Q16semidirect
287. D4×C61C2×Q16semidirect
311. D244C2×Q16semidirect
382. #1644D61direct (N × H)
391. D61#1644direct (N × H)
415. #487C2×D61semidirect
427. #462C2×D61semidirect
438. #333C2×D61semidirect
442. Q8⋊C8C2×D61semidirect
447. C61C2×#1644semidirect
675. D4Q16×D61semidirect

Maximal subgroups

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

subgroupindex
#554×D612
#487×D612
#474×D612
#462×D612
#214450362
#214450352
#214450342
#214450332
#214450322
#214450312
#214450302
#333×D612
Q8⋊C8×D612
D4⋊C8×D612
C61×#16442
C2×#164461