Finite Group Databasebeta

← D61×#2042 #29707683

Subgroups — D61×#2042 #29707683

Order 15616.

1670 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#124×D61C211yesmaximal, characteristic
2C2×#103×D61C211yesmaximal, characteristic, complemented
3C2×#103×D61C211yesmaximal, characteristic, complemented
4C2×#102×D61C211yesmaximal, characteristic
5C2×#102×D61C211yesmaximal, characteristic
6#389×D61C211yesmaximal, characteristic, complemented
7#21447061C211yesmaximal, characteristic, complemented
8#21447060C211yesmaximal, characteristic, complemented
9#21447059C211yesmaximal, characteristic, complemented
10#21447058C211yesmaximal, characteristic, complemented
11#21447057C211yesmaximal, characteristic, complemented
12#21447056C211yesmaximal, characteristic, complemented
13#21447055C211yesmaximal, characteristic, complemented
14#336×D61C211yesmaximal, characteristic, complemented
15C61×#2042C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C22×D4×D61C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20C2×#14519766C2211yescharacteristic
21C2×#14519765C2211yescharacteristic
22C2×#14519764C2211yescharacteristic
23C2×#14519763—21no—
24C2×#14519763—21no—
25#124×D61—24no—
26#124×D61—24no—
27C2×C4⋊C4×D61—21no—
28C2×C4⋊C4×D61C2211yescharacteristic
29C2×C4⋊C4×D61C2211yescharacteristic
30C2×C22⋊C4×D61—21no—
31C2×C22⋊C4×D61—21no—
32C2×C42×D61C2211yescharacteristic
33C2×#14519702C2211yescharacteristic, complemented
34C2×#14519702C2211yescharacteristic, complemented
35C2×#14519701C2211yescharacteristic, complemented
36C2×#14519701C2211yescharacteristic, complemented
37C2×#14519700C2211yescharacteristic, complemented
38C2×#14519700C2211yescharacteristic, complemented
39#103×D61—24no—
40#103×D61—24no—
41C2×#14519699C2211yescharacteristic
42C2×#14519699C2211yescharacteristic
43C2×#14519698C2211yescharacteristic
44C2×#14519698C2211yescharacteristic
45C2×#14519697C2211yescharacteristic
46C2×#14519697C2211yescharacteristic
47#102×D61—24no—
48#102×D61—24no—
49#16839661C2211yescharacteristic, complemented
50#16839660C2211yescharacteristic, complemented
51#16839659—21no—
52#16839658C2211yescharacteristic, complemented
53#16839657—21no—
54#95×D61—21no—
55#16839517C2211yescharacteristic, complemented
56#16839516C2211yescharacteristic, complemented
57#16839516C2211yescharacteristic, complemented
58C2×#124×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic, complemented
60C2×#103×C61C2211yescharacteristic, complemented
61C2×#102×C61C2211yescharacteristic
62C2×#102×C61C2211yescharacteristic
63C61×#389C2211yescharacteristic, complemented
64C61×#336C2211yescharacteristic, complemented
65C24×D61—21no—
66C22×Dic122—21no—
67C22×Dic122C2311yescharacteristic
68C2×Q8×D61—22no—
69C2×Q8×D61—22no—
70C2×Q8×D61—22no—
71C2×Q8×D61—22no—
72C2×Q8×D61—22no—
73C2×Q8×D61D414yes—
74C22×D244C2311yescharacteristic
75C22×C22⋊D61—21no—
76C2×D4×D61—22no—
77C2×D4×D61—22no—
78C2×D4×D61—22no—
79C2×D4×D61—22no—
80C2×D4×D61—22no—
81C2×D4×D61D414yes—
82C22×C4×D61—21no—
83C22×C4×D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61D411yescharacteristic
86C22×C4×D61D411yescharacteristic
87C22×C4×D61C2311yescharacteristic
88C22×#92418C2311yescharacteristic
89C22×#92418C2311yescharacteristic
90C2×C8×D61—22no—
91C2×C8×D61—22no—
92C2×C8×D61—22no—
93C2×C8×D61—22no—
94C2×C8×D61—22no—
95C2×C8×D61—22no—
96#14519766—22no—
97#14519766—22no—
98#14519765—22no—
99#14519765—22no—
100#14519764—22no—
101#14519764—22no—
102#14519763—28no—
103#14519763—28no—
104C2×C4⋊Dic61—21no—
105C2×C4⋊Dic61C2311yescharacteristic
106C2×C4⋊Dic61C2311yescharacteristic
107C2×#11758196—21no—
108C2×#11758196—21no—
109C2×#11758196—21no—
110C2×#11758196—21no—
111C4⋊C4×D61—22no—
112C4⋊C4×D61—22no—
113C4⋊C4×D61—22no—
114C4⋊C4×D61—44no—
115C4⋊C4×D61D414yes—
116C2×C22⋊Dic61—21no—
117C2×C22⋊Dic61—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C2×#11758198—21no—
121C2×#11758198—21no—
122C22⋊C4×D61—28no—
123C22⋊C4×D61—28no—
124C2×C4×Dic61D411yescharacteristic
125C2×C4×Dic61D411yescharacteristic
126C2×C4×Dic61C2311yescharacteristic
127C42×D61—22no—
128C42×D61—22no—
129#14519702—22no—
130#14519702—22no—
131#14519701—22no—
132#14519701—22no—
133#14519700—22no—
134#14519700—22no—
135#14519699—22no—
136#14519699—22no—
137#14519698—22no—
138#14519698—22no—
139#14519697—22no—
140#14519697—22no—
141#14519684—21no—
142#14519684—21no—
143#14519684—21no—
144C22×Q8×C61C2311yescharacteristic
145C22×D4×C61C2311yescharacteristic
146C22×C8×C61C2311yescharacteristic
147C22×C8×C61C2311yescharacteristic
148#124×C61—22no—
149#124×C61—22no—
150C2×C4⋊C4×C61—21no—
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C22⋊C4×C61—21no—
154C2×C22⋊C4×C61—21no—
155C2×C42×C61C2311yescharacteristic
156#103×C61—22no—
157#103×C61—22no—
158#102×C61—22no—
159#102×C61—22no—
160#95×C61—21no—
161C24×C61—21no—
162C23×D61—21no—
163C23×D61—24no—
164C23×D61—42no—
165C23×D61—42no—
166C23×D61—42no—
167C23×D61—42no—
168C23×D61—42no—
169C23×D61—42no—
170C23×D61C2×D411yescharacteristic
171C2×Q8×C61—21no—
172C2×Q8×C61—21no—
173C2×Q8×C61—21no—
174C2×Q8×C61—21no—
175C2×Q8×C61—21no—
176C2×Q8×C61C2×D412yes—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—21no—
181C2×D4×C61—21no—
182C2×D4×C61C2×D412yes—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2411yescharacteristic
189C2×C22⋊D61—24no—
190C2×C22⋊D61—42no—
191C2×C22⋊D61—42no—
192C22×Dic61—21no—
193C22×Dic61—21no—
194C22×Dic61—21no—
195C22×Dic61C2×D411yescharacteristic
196C22×Dic61C2×D411yescharacteristic
197C22×Dic61C2×D411yescharacteristic
198Q8×D61—28no—
199Q8×D61—28no—
200Q8×D61—44no—
201Q8×D61—44no—
202D4×D61—28no—
203D4×D61—28no—
204D4×D61—44no—
205D4×D61—44no—
206C2×D244—21no—
207C2×D244—21no—
208C2×D244—21no—
209C2×D244—21no—
210C2×D244—21no—
211C2×D244C2×D412yes—
212C2×C4×D61—24no—
213C2×C4×D61—22no—
214C2×C4×D61—22no—
215C2×C4×D61—24no—
216C2×C4×D61—22no—
217C2×C4×D61—22no—
218C2×C4×D61—22no—
219C2×C4×D61—22no—
220C2×C4×D61—42no—
221C2×C4×D61—42no—
222C2×C4×D61—42no—
223C2×C4×D61—42no—
224C2×C4×D61—42no—
225C2×C4×D61—42no—
226C2×C4×D61—42no—
227C2×C4×D61C2×D412yes—
228C2×C4×D61C2×D412yes—
229C2×C4×D61C2×D412yes—
230C2×C4×D61#4112yes—
231C2×C4×D61#4112yes—
232C2×C4×D61#4112yes—
233C2×Dic122—21no—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122—24no—
239C2×Dic122—42no—
240C2×Dic122—42no—
241C2×Dic122C2×D412yes—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—42no—
252C4⋊C4×C61C2×D412yes—
253C22⋊C4×C61—24no—
254C22⋊C4×C61—24no—
255C42×C61—21no—
256C42×C61—21no—
257C22⋊Dic61—24no—
258C22⋊Dic61—24no—
259#11758198—24no—
260#11758198—24no—
261#11758198—24no—
262#11758198—24no—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265C4⋊Dic61—21no—
266C4⋊Dic61—42no—
267C4⋊Dic61C2×D412yes—
268#11758196—24no—
269#11758196—42no—
270#11758196—42no—
271#11758196—42no—
272C4×Dic61—21no—
273C4×Dic61—21no—
274C4×Dic61—22no—
275C4×Dic61—22no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C8×D61—44no—
283C8×D61—44no—
284C23×C61—22no—
285C23×C61—41no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61C22×D411yescharacteristic
292C22×D61—22no—
293C22×D61—41no—
294C22×D61—41no—
295C22×D61—41no—
296C22×D61—41no—
297C22×D61—41no—
298C22×D61—41no—
299C22×D61—48no—
300C22×D61—48no—
301C22×D61—48no—
302C22×D61—84no—
303C22×D61—84no—
304C22×D61—84no—
305C22×D61—84no—
306C22×D61#12012yes—
307C22×D61#12112yes—
308C22×D61#12412yes—
309C22×D61#13512yes—
310C22×D61#13512yes—
311C22×D61AGL(1,ℤ/8)12yes—
312C22×D61#13712yes—
313Q8×C61—22no—
314Q8×C61—22no—
315Q8×C61—41no—
316Q8×C61—41no—
317D4×C61—22no—
318D4×C61—22no—
319D4×C61—41no—
320D4×C61—41no—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61C22×D411yescharacteristic
337C2×C4×C61C22×D411yescharacteristic
338C2×C4×C61C22×D411yescharacteristic
339C2×C4×C61C2×#4111yescharacteristic
340C2×C4×C61C2×#4111yescharacteristic
341C2×C4×C61C2×#4111yescharacteristic
342C22⋊D61—48no—
343C2×Dic61—21no—
344C2×Dic61—21no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—41no—
352C2×Dic61—41no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61#12012yes—
359C2×Dic61#12112yes—
360C2×Dic61#12412yes—
361D244—22no—
362D244—22no—
363D244—41no—
364D244—41no—
365C4×D61—48no—
366C4×D61—44no—
367C4×D61—44no—
368C4×D61—48no—
369C4×D61—84no—
370C4×D61#12114yes—
371C4×D61#12114yes—
372C4×D61#12314yes—
373C4×D61#12314yes—
374Dic122—22no—
375Dic122—22no—
376Dic122—41no—
377Dic122—41no—
378Dic122—48no—
379C8×C61—41no—
380C8×C61—41no—
381#92418—41no—
382#92418—41no—
383C2×#2042—611nomaximal, Sylow
384C22×C61—42no—
385C22×C61—42no—
386C22×C61—42no—
387C22×C61—81no—
388C22×C61—81no—
389C22×C61—81no—
390C22×C61—81no—
391C22×C61C2×#12011yescharacteristic
392C22×C61C2×#12111yescharacteristic
393C22×C61C2×#12411yescharacteristic
394C22×C61C2×#13511yescharacteristic
395C22×C61C2×#13511yescharacteristic
396C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
397C22×C61C2×#13711yescharacteristic
398C2×D61—42no—
399C2×D61—42no—
400C2×D61—42no—
401C2×D61—81no—
402C2×D61—81no—
403C2×D61—81no—
404C2×D61—81no—
405C2×D61—816no—
406C2×D61#39414yes—
407C2×D61#44914yes—
408C2×D61#45214yes—
409C2×D61#46314yes—
410C2×D61#46414yes—
411C2×D61#48814yes—
412C2×D61#48914yes—
413C4×C61—42no—
414C4×C61—41no—
415C4×C61—41no—
416C4×C61—42no—
417C4×C61—81no—
418C4×C61C2×#12111yescharacteristic
419C4×C61C2×#12111yescharacteristic
420C4×C61C2×#12311yescharacteristic
421C4×C61C2×#12311yescharacteristic
422Dic61—42no—
423Dic61—41no—
424Dic61—41no—
425Dic61—42no—
426Dic61—81no—
427Dic61#39414yes—
428C22×#124—611no—
429C22×#103—611no—
430C22×#103—611no—
431C22×#102—611no—
432C22×#102—611no—
433C2×#389—611no—
434#2042—611no—
435#2042—611no—
436#2042—611no—
437#2042—611no—
438#2042—611no—
439#2042—611no—
440#2042—611no—
441#2042D6111yescharacteristic, direct product factor
442C2×#336—611no—
443C2×C61—82no—
444C2×C61C2×#39411yescharacteristic
445C2×C61C2×#44911yescharacteristic
446C2×C61C2×#45211yescharacteristic
447C2×C61C2×#46311yescharacteristic
448C2×C61C2×#46411yescharacteristic
449C2×C61C2×#48811yescharacteristic
450C2×C61C2×#48911yescharacteristic
451D61—82no—
452D61#204218yesdirect product factor
453C23×Q8—611no—
454C23×D4—611no—
455C23×C8—611no—
456C23×C8—611no—
457C2×#124—611no—
458C2×#124—611no—
459C2×#124—611no—
460C2×#124—1221no—
461C2×#124—1221no—
462C2×#124—1224no—
463C2×#124—1224no—
464C2×#124C2×D6111yescharacteristic
465C22×C4⋊C4—611no—
466C22×C4⋊C4—611no—
467C22×C4⋊C4—1221no—
468C22×C22⋊C4—1221no—
469C22×C22⋊C4—1221no—
470C22×C42—611no—
471C2×#103—611no—
472C2×#103—611no—
473C2×#103—611no—
474C2×#103—611no—
475C2×#103—611no—
476C2×#103—611no—
477C2×#103—1224no—
478C2×#103—1224no—
479C2×#103C2×D6111yescharacteristic, complemented
480C2×#103C2×D6111yescharacteristic, complemented
481C2×#102—611no—
482C2×#102—611no—
483C2×#102—611no—
484C2×#102—611no—
485C2×#102—611no—
486C2×#102—611no—
487C2×#102—1224no—
488C2×#102—1224no—
489C2×#102C2×D6111yescharacteristic
490C2×#102C2×D6111yescharacteristic
491#389—611no—
492#389—611no—
493#389—611no—
494#389—1221no—
495#389—1221no—
496#389C2×D6111yescharacteristic, complemented
497C2×#95—1221no—
498#336—611no—
499#336—611no—
500#336—611no—
501#336C2×D6111yescharacteristic, complemented
502C61C2×#204211yescharacteristic, complemented, Sylow
503C25—1221no—
504C22×Q8—614no—
505C22×Q8—611no—
506C22×Q8—1221no—
507C22×Q8—1222no—
508C22×Q8—1222no—
509C22×Q8—1222no—
510C22×Q8—1222no—
511C22×Q8—1222no—
512C22×Q8C22×D6111yescharacteristic
513C22×D4—614no—
514C22×D4—611no—
515C22×D4—1222no—
516C22×D4—1222no—
517C22×D4—1222no—
518C22×D4—1222no—
519C22×D4—1222no—
520C22×D4—1221no—
521C22×D4C22×D6111yescharacteristic
522C23×C4—611no—
523C23×C4—611no—
524C23×C4—611no—
525C23×C4—1221no—
526C23×C4—1221no—
527C23×C4—1221no—
528C22×C8—611no—
529C22×C8—611no—
530C22×C8—1222no—
531C22×C8—1222no—
532C22×C8—1222no—
533C22×C8—1222no—
534C22×C8—1222no—
535C22×C8—1222no—
536C22×C8C22×D6111yescharacteristic
537C22×C8C22×D6111yescharacteristic
538#124—22no—
539#124—22no—
540#124—1222no—
541#124—1222no—
542#124—1228no—
543#124—1228no—
544#124—1222no—
545#124—1222no—
546#124—1222no—
547#124—1222no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—611no—
550C2×C4⋊C4—614no—
551C2×C4⋊C4—611no—
552C2×C4⋊C4—1222no—
553C2×C4⋊C4—1222no—
554C2×C4⋊C4—1222no—
555C2×C4⋊C4—1221no—
556C2×C4⋊C4—1221no—
557C2×C4⋊C4—1221no—
558C2×C4⋊C4—1221no—
559C2×C4⋊C4—1221no—
560C2×C4⋊C4—2444no—
561C2×C4⋊C4C22×D6111yescharacteristic
562C2×C4⋊C4C22×D6111yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—1228no—
566C2×C22⋊C4—1228no—
567C2×C22⋊C4—1221no—
568C2×C22⋊C4—1221no—
569C2×C22⋊C4—1221no—
570C2×C22⋊C4—1221no—
571C2×C22⋊C4—1221no—
572C2×C22⋊C4—1221no—
573C2×C42—611no—
574C2×C42—611no—
575C2×C42—611no—
576C2×C42—1222no—
577C2×C42—1222no—
578C2×C42C22×D6111yescharacteristic
579#103—22no—
580#103—22no—
581#103—1222no—
582#103—1222no—
583#103—1222no—
584#103—1222no—
585#103—1222no—
586#103—1222no—
587#102—22no—
588#102—22no—
589#102—1222no—
590#102—1222no—
591#102—1222no—
592#102—1222no—
593#102—1222no—
594#102—1222no—
595#95—21no—
596#95—1221no—
597#95—1221no—
598#95—1221no—
599C24—21no—
600C24—611no—
601C24—1224no—
602C24—1221no—
603C24—2442no—
604C24—2442no—
605C24—2442no—
606C24—2442no—
607C24—2442no—
608C24—2442no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—612no—
615C2×Q8—1224no—
616C2×Q8—1228no—
617C2×Q8—1228no—
618C2×Q8—1221no—
619C2×Q8—1221no—
620C2×Q8—1221no—
621C2×Q8—1221no—
622C2×Q8—1221no—
623C2×Q8—2442no—
624C2×Q8—2442no—
625C2×Q8—2444no—
626C2×Q8—2444no—
627C2×Q8D4×D6112yes—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—612no—
634C2×D4—1228no—
635C2×D4—1228no—
636C2×D4—1224no—
637C2×D4—1221no—
638C2×D4—1221no—
639C2×D4—1221no—
640C2×D4—1221no—
641C2×D4—1221no—
642C2×D4—2444no—
643C2×D4—2444no—
644C2×D4—2442no—
645C2×D4—2442no—
646C2×D4D4×D6112yes—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—611no—
651C22×C4—612no—
652C22×C4—612no—
653C22×C4—612no—
654C22×C4—612no—
655C22×C4—612no—
656C22×C4—612no—
657C22×C4—611no—
658C22×C4—611no—
659C22×C4—1222no—
660C22×C4—1222no—
661C22×C4—1224no—
662C22×C4—1224no—
663C22×C4—1222no—
664C22×C4—1222no—
665C22×C4—1222no—
666C22×C4—1222no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—2442no—
671C22×C4—2442no—
672C22×C4—2442no—
673C22×C4—2442no—
674C22×C4—2442no—
675C22×C4—2442no—
676C22×C4—2442no—
677C22×C4D4×D6111yescharacteristic
678C22×C4D4×D6111yescharacteristic
679C22×C4C23×D6111yescharacteristic
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—1221no—
687C2×C8—1221no—
688C2×C8—1221no—
689C2×C8—1221no—
690C2×C8—1221no—
691C2×C8—1221no—
692C2×C8—2444no—
693C2×C8—2444no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—42no—
698C4⋊C4—612no—
699C4⋊C4—1224no—
700C4⋊C4—1221no—
701C4⋊C4—1221no—
702C4⋊C4—1221no—
703C4⋊C4—2442no—
704C4⋊C4—2442no—
705C4⋊C4—2442no—
706C4⋊C4—2442no—
707C4⋊C4D4×D6112yes—
708C22⋊C4—24no—
709C22⋊C4—24no—
710C22⋊C4—1224no—
711C22⋊C4—1224no—
712C22⋊C4—1224no—
713C22⋊C4—1224no—
714C22⋊C4—1224no—
715C22⋊C4—1224no—
716C42—21no—
717C42—21no—
718C42—1222no—
719C42—1222no—
720C42—1221no—
721C42—1221no—
722C23—22no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—612no—
730C23—612no—
731C23—612no—
732C23—612no—
733C23—612no—
734C23—612no—
735C23—612no—
736C23—1222no—
737C23—4884no—
738C23—4884no—
739C23—4884no—
740C23—4884no—
741C23—2448no—
742C23—2448no—
743C23—2448no—
744C23—2441no—
745C23—2441no—
746C23—2441no—
747C23—2441no—
748C23—2441no—
749C23—2441no—
750C23C2×D4×D6111yescharacteristic
751Q8—22no—
752Q8—22no—
753Q8—41no—
754Q8—41no—
755Q8—1222no—
756Q8—1222no—
757Q8—2448no—
758Q8—2441no—
759Q8—2441no—
760D4—22no—
761D4—22no—
762D4—41no—
763D4—41no—
764D4—1222no—
765D4—1222no—
766D4—2448no—
767D4—2441no—
768D4—2441no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—612no—
785C2×C4—612no—
786C2×C4—612no—
787C2×C4—614no—
788C2×C4—614no—
789C2×C4—614no—
790C2×C4—614no—
791C2×C4—1221no—
792C2×C4—1221no—
793C2×C4—1222no—
794C2×C4—1222no—
795C2×C4—1221no—
796C2×C4—1221no—
797C2×C4—1221no—
798C2×C4—1221no—
799C2×C4—4884no—
800C2×C4—2444no—
801C2×C4—2444no—
802C2×C4—2448no—
803C2×C4—2448no—
804C2×C4—2441no—
805C2×C4—2441no—
806C2×C4—2441no—
807C2×C4—2441no—
808C2×C4—2441no—
809C2×C4—2441no—
810C2×C4—2441no—
811C2×C4C2×D4×D6111yescharacteristic
812C2×C4C2×D4×D6111yescharacteristic
813C2×C4C2×D4×D6111yescharacteristic
814C2×C4#41×D6111yescharacteristic
815C2×C4#41×D6111yescharacteristic
816C2×C4#41×D6111yescharacteristic
817C8—41no—
818C8—41no—
819C8—2441no—
820C8—2441no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—614no—
829C22—614no—
830C22—614no—
831C22—614no—
832C22—614no—
833C22—614no—
834C22—614no—
835C22—48816no—
836C22—4881no—
837C22—4881no—
838C22—4881no—
839C22—4881no—
840C22—2442no—
841C22—2442no—
842C22—2442no—
843C22#120×D6111yescharacteristic
844C22#121×D6111yescharacteristic
845C22#124×D6111yescharacteristic
846C22#135×D6111yescharacteristic
847C22#135×D6111yescharacteristic
848C22AGL(1,ℤ/8)×D6111yescharacteristic
849C22#137×D6111yescharacteristic
850C4—42no—
851C4—42no—
852C4—41no—
853C4—41no—
854C4—81no—
855C4—614no—
856C4—4881no—
857C4—2442no—
858C4—2442no—
859C4—2441no—
860C4—2441no—
861C4#121×D6111yescharacteristic
862C4#121×D6111yescharacteristic
863C4#123×D6111yescharacteristic
864C4#123×D6111yescharacteristic
865C2—82no—
866C2—618no—
867C2—4882no—
868C2#394×D6111yescharacteristic
869C2#449×D6111yescharacteristic
870C2#452×D6111yescharacteristic
871C2#463×D6111yescharacteristic
872C2#464×D6111yescharacteristic
873C2#488×D6111yescharacteristic
874C2#489×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2042C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
hypercenter#2042D61
hypocenterC61C2×#2042
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2042

Complements

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

NH ≅ G/Ntype
2. C2×#103×D61C2semidirect
3. C2×#103×D61C2semidirect
6. #389×D61C2semidirect
7. #21447061C2semidirect
8. #21447060C2semidirect
9. #21447059C2semidirect
10. #21447058C2semidirect
11. #21447057C2semidirect
12. #21447056C2semidirect
13. #21447055C2semidirect
14. #336×D61C2semidirect
15. C61×#2042C2semidirect
33. C2×#14519702C22semidirect
34. C2×#14519702C22semidirect
35. C2×#14519701C22semidirect
36. C2×#14519701C22semidirect
37. C2×#14519700C22semidirect
38. C2×#14519700C22semidirect
49. #16839661C22semidirect
50. #16839660C22semidirect
52. #16839658C22semidirect
55. #16839517C22semidirect
56. #16839516C22semidirect
57. #16839516C22semidirect
59. C2×#103×C61C22semidirect
60. C2×#103×C61C22semidirect
63. C61×#389C22semidirect
64. C61×#336C22semidirect
441. #2042D61direct (N × H)
452. D61#2042direct (N × H)
479. C2×#103C2×D61semidirect
480. C2×#103C2×D61semidirect
496. #389C2×D61semidirect
501. #336C2×D61semidirect
502. C61C2×#2042semidirect

Maximal subgroups

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

subgroupindex
C2×#124×D612
C2×#103×D612
C2×#102×D612
#389×D612
#214470612
#214470602
#214470592
#214470582
#214470572
#214470562
#214470552
#336×D612
C61×#20422
C2×#204261