Finite Group Databasebeta

← D61×#2052 #29707884

Subgroups — D61×#2052 #29707884

Order 15616.

1362 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#137×D61C211yesmaximal, characteristic
2C2×#108×D61C211yesmaximal, characteristic, complemented
3#417×D61C211yesmaximal, characteristic
4C2×#103×D61C211yesmaximal, characteristic, complemented
5C2×#101×D61C211yesmaximal, characteristic, complemented
6#408×D61C211yesmaximal, characteristic
7#21447121C211yesmaximal, characteristic, complemented
8#21447120C211yesmaximal, characteristic, complemented
9#21447119C211yesmaximal, characteristic, complemented
10#21447118C211yesmaximal, characteristic, complemented
11#21447117C211yesmaximal, characteristic, complemented
12#21447116C211yesmaximal, characteristic, complemented
13#21447115C211yesmaximal, characteristic, complemented
14#343×D61C211yesmaximal, characteristic, complemented
15C61×#2052C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C22×Q8×D61C2211yescharacteristic
18C2×#14519810C2211yescharacteristic
19C2×#14519809—21no—
20C2×#14519808C2211yescharacteristic
21C2×#14519807C2211yescharacteristic
22C2×#14519806—21no—
23#137×D61—24no—
24#137×D61—24no—
25C2×Q16×D61—21no—
26C2×SD16×D61—21no—
27C2×M16×D61C2211yescharacteristic
28C2×M16×D61C2211yescharacteristic
29C2×M16×D61C2211yescharacteristic
30C22×C8×D61C2211yescharacteristic
31C2×C4⋊C4×D61C2211yescharacteristic
32C2×#14519713C2211yescharacteristic, complemented
33C2×#14519712C2211yescharacteristic, complemented
34C2×#14519712C2211yescharacteristic, complemented
35#108×D61—24no—
36#16839764C2211yescharacteristic
37#16839763C2211yescharacteristic
38#16839762—21no—
39#16839761C2211yescharacteristic
40#16839760—21no—
41C2×#14519702C2211yescharacteristic, complemented
42C2×#14519701C2211yescharacteristic, complemented
43C2×#14519700C2211yescharacteristic, complemented
44#103×D61—22no—
45#103×D61—22no—
46#103×D61—21no—
47#102×D61—21no—
48C2×#14519696C2211yescharacteristic, complemented
49C2×#14519695C2211yescharacteristic, complemented
50C2×#14519695C2211yescharacteristic, complemented
51#101×D61—24no—
52#16839730C2211yescharacteristic
53#16839729C2211yescharacteristic
54#16839728C2211yescharacteristic
55#16839727—22no—
56C22⋊C8×D61—22no—
57#16839531C2211yescharacteristic, complemented
58#16839530C2211yescharacteristic, complemented
59#16839530C2211yescharacteristic, complemented
60C2×#137×C61C2211yescharacteristic
61C2×#108×C61C2211yescharacteristic, complemented
62C61×#417C2211yescharacteristic
63C2×#103×C61C2211yescharacteristic, complemented
64C2×#101×C61C2211yescharacteristic, complemented
65C61×#408C2211yescharacteristic
66C61×#343C2211yescharacteristic, complemented
67C2×#11758226D411yescharacteristic
68C2×#11758222—21no—
69C2×#11758222C2311yescharacteristic
70C2×#11758224—21no—
71C2×#11758224D411yescharacteristic
72#41×D61—22no—
73#41×D61—22no—
74#41×D61—22no—
75#41×D61—22no—
76C22×Dic122—21no—
77C22×Dic122C2311yescharacteristic
78C2×Q8×D61—22no—
79C2×Q8×D61—21no—
80C2×Q8×D61—21no—
81C2×Q8×D61—21no—
82C2×Q8×D61—22no—
83C2×Q8×D61—21no—
84C2×Q8×D61—22no—
85C2×Q8×D61D414yes—
86C2×Q8×D61D411yescharacteristic
87C2×D4×D61—21no—
88C2×D4×D61D411yescharacteristic
89C22×C4×D61—21no—
90C22×C4×D61—21no—
91C22×C4×D61—21no—
92C22×C4×D61C2311yescharacteristic
93#14519810—22no—
94#14519810—22no—
95#14519809—28no—
96#14519808—22no—
97#14519808—22no—
98#14519807—22no—
99#14519807—22no—
100#14519806—28no—
101C2×Dic244—21no—
102C2×#11758202—21no—
103C2×#11758202—21no—
104Q16×D61—28no—
105C2×#11758190—21no—
106C2×#11758200—21no—
107C2×#11758201—21no—
108SD16×D61—28no—
109C2×#11758194C2311yescharacteristic
110C2×#11758194C2311yescharacteristic
111C2×#11758194C2311yescharacteristic
112C2×#11758189—21no—
113C2×#11758189—21no—
114C2×#11758189—21no—
115M16×D61—22no—
116M16×D61—22no—
117M16×D61—22no—
118M16×D61—22no—
119M16×D61—22no—
120M16×D61D414yes—
121C22×#92418C2311yescharacteristic
122C2×C8×D61—22no—
123C2×C8×D61—21no—
124C2×C8×D61—22no—
125C2×C8×D61—21no—
126C2×C8×D61—21no—
127C2×C8×D61D412yes—
128C2×C8×D61D412yes—
129C2×C4⋊Dic61C2311yescharacteristic
130C2×#11758196—21no—
131C4⋊C4×D61—21no—
132C4⋊C4×D61—21no—
133C4⋊C4×D61—21no—
134C4⋊C4×D61—21no—
135#14519713—22no—
136#14519712—22no—
137#14519712—22no—
138#14519702—21no—
139#14519702—22no—
140#14519701—21no—
141#14519701—22no—
142#14519700—21no—
143#14519700—22no—
144#14519699—21no—
145#14519698—21no—
146#14519697—21no—
147#14519696—22no—
148#14519695—22no—
149#14519695—22no—
150C22⋊#92418—22no—
151#14519689—22no—
152#14519689—22no—
153C2×#41×C61C2311yescharacteristic
154C22×Q8×C61C2311yescharacteristic
155#137×C61—22no—
156#137×C61—22no—
157C2×Q16×C61—21no—
158C2×SD16×C61—21no—
159C2×M16×C61C2311yescharacteristic
160C2×M16×C61C2311yescharacteristic
161C2×M16×C61C2311yescharacteristic
162C22×C8×C61C2311yescharacteristic
163C2×C4⋊C4×C61C2311yescharacteristic
164#108×C61—22no—
165#103×C61—21no—
166#103×C61—22no—
167#102×C61—21no—
168#101×C61—22no—
169C22⋊C8×C61—22no—
170C23×D61—21no—
171C23×D61#4111yescharacteristic
172#41×C61—21no—
173#41×C61—21no—
174#41×C61—21no—
175#41×C61—21no—
176C2×Q8×C61—21no—
177C2×Q8×C61—21no—
178C2×Q8×C61—21no—
179C2×Q8×C61—21no—
180C2×Q8×C61—21no—
181C2×Q8×C61C2×D412yes—
182C2×Q8×C61C2×D411yescharacteristic
183C2×D4×C61—21no—
184C2×D4×C61C2×D411yescharacteristic
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61C2411yescharacteristic
189C2×C22⋊D61—21no—
190C2×C22⋊D61—21no—
191C2×C22⋊D61—21no—
192C22×Dic61—21no—
193C22×Dic61—21no—
194C22×Dic61—21no—
195C22×Dic61#4111yescharacteristic
196#11758226—22no—
197#11758226—22no—
198Q8×D61—24no—
199Q8×D61—24no—
200Q8×D61—22no—
201Q8×D61—24no—
202Q8×D61—24no—
203Q8×D61—22no—
204Q8×D61—42no—
205Q8×D61—42no—
206Q8×D61—42no—
207Q8×D61—42no—
208#11758224—22no—
209#11758224—22no—
210#11758224—42no—
211#11758224—42no—
212D4×D61—22no—
213D4×D61—22no—
214D4×D61—42no—
215D4×D61—42no—
216#11758222—21no—
217#11758222—21no—
218#11758222—21no—
219#11758222—21no—
220#11758222—42no—
221#11758222—42no—
222C2×D244—21no—
223C2×D244C2×D411yescharacteristic
224C2×C4×D61—21no—
225C2×C4×D61—24no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—41no—
229C2×C4×D61—41no—
230C2×C4×D61—42no—
231C2×C4×D61—42no—
232C2×C4×D61—42no—
233C2×C4×D61—41no—
234C2×C4×D61—41no—
235C2×C4×D61—82no—
236C2×C4×D61C2×D412yes—
237C2×C4×D61C2×D412yes—
238C2×C4×D61C2×D411yescharacteristic
239C2×C4×D61C2×D411yescharacteristic
240C2×C4×D61C2×D411yescharacteristic
241C2×C4×D61C2×D411yescharacteristic
242C2×C4×D61#4112yes—
243C2×C4×D61#4112yes—
244C2×Dic122—21no—
245C2×Dic122—21no—
246C2×Dic122—21no—
247C2×Dic122—21no—
248C2×Dic122—21no—
249C2×Dic122—21no—
250C2×Dic122—24no—
251C2×Dic122—41no—
252C2×Dic122—41no—
253C2×Dic122—42no—
254C2×Dic122C2×D412yes—
255C2×Dic122C2×D411yescharacteristic
256Q16×C61—24no—
257SD16×C61—24no—
258M16×C61—21no—
259M16×C61—21no—
260M16×C61—21no—
261M16×C61—21no—
262M16×C61—21no—
263M16×C61C2×D412yes—
264C2×C8×C61—21no—
265C2×C8×C61—21no—
266C2×C8×C61—21no—
267C2×C8×C61—21no—
268C2×C8×C61—21no—
269C2×C8×C61C2×D412yes—
270C4⋊C4×C61—21no—
271C4⋊C4×C61—21no—
272#11758202—24no—
273#11758202—24no—
274#11758201—24no—
275#11758200—24no—
276C4⋊Dic61—21no—
277C4⋊Dic61—21no—
278#11758196—41no—
279#11758196—41no—
280#11758194—21no—
281#11758194—21no—
282#11758194—21no—
283#11758194—21no—
284#11758194—21no—
285#11758194C2×D412yes—
286C2×#92418—21no—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418—21no—
291C2×#92418C2×D412yes—
292Dic244—24no—
293#11758190—24no—
294#11758189—24no—
295#11758189—42no—
296#11758189—42no—
297C8×D61—24no—
298C8×D61—24no—
299C8×D61—24no—
300C8×D61—42no—
301C8×D61—42no—
302C23×C61—21no—
303C23×C61C2×#4111yescharacteristic
304C22×D61—22no—
305C22×D61—22no—
306C22×D61—21no—
307C22×D61—42no—
308C22×D61—42no—
309C22×D61—42no—
310C22×D61#12111yescharacteristic
311C22×D61#12111yescharacteristic
312C22×D61#12312yes—
313C22×D61#12412yes—
314Q8×C61—22no—
315Q8×C61—21no—
316Q8×C61—22no—
317Q8×C61—21no—
318Q8×C61—41no—
319Q8×C61—41no—
320D4×C61—21no—
321D4×C61—21no—
322D4×C61—41no—
323D4×C61—41no—
324C2×C4×C61—21no—
325C2×C4×C61—22no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—81no—
332C2×C4×C61C22×D411yescharacteristic
333C2×C4×C61C22×D411yescharacteristic
334C2×C4×C61C22×D411yescharacteristic
335C2×C4×C61C22×D411yescharacteristic
336C2×C4×C61C2×#4111yescharacteristic
337C2×C4×C61C2×#4111yescharacteristic
338C22⋊D61—41no—
339C22⋊D61—41no—
340C22⋊D61—42no—
341C22⋊D61—42no—
342C2×Dic61—21no—
343C2×Dic61—22no—
344C2×Dic61—41no—
345C2×Dic61—41no—
346C2×Dic61—42no—
347C2×Dic61—41no—
348C2×Dic61—81no—
349C2×Dic61#12111yescharacteristic
350C2×Dic61#12111yescharacteristic
351C2×Dic61#12312yes—
352C2×Dic61#12412yes—
353D244—21no—
354D244—21no—
355D244—42no—
356C4×D61—42no—
357C4×D61—44no—
358C4×D61—44no—
359C4×D61—41no—
360C4×D61—41no—
361C4×D61—42no—
362C4×D61—82no—
363C4×D61—82no—
364C4×D61#12012yes—
365C4×D61#12012yes—
366C4×D61#12112yes—
367C4×D61#12112yes—
368C4×D61#12112yes—
369C4×D61#12112yes—
370C4×D61#12312yes—
371C4×D61#12312yes—
372Dic122—22no—
373Dic122—21no—
374Dic122—22no—
375Dic122—21no—
376Dic122—41no—
377Dic122—41no—
378Dic122—44no—
379Dic122—44no—
380Dic122—42no—
381C8×C61—22no—
382C8×C61—22no—
383C8×C61—41no—
384C8×C61—41no—
385#92418—22no—
386#92418—22no—
387#92418—41no—
388#92418—41no—
389C2×#2052—611nomaximal, Sylow
390C22×C61—21no—
391C22×C61—21no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61C2×#12111yescharacteristic
396C22×C61C2×#12311yescharacteristic
397C22×C61C2×#12411yescharacteristic
398C2×D61—21no—
399C2×D61—21no—
400C2×D61—24no—
401C2×D61—24no—
402C2×D61—41no—
403C2×D61—41no—
404C2×D61—41no—
405C2×D61—84no—
406C2×D61#39412yes—
407C2×D61#39412yes—
408C2×D61#47112yes—
409C2×D61#47312yes—
410C4×C61—42no—
411C4×C61—41no—
412C4×C61—81no—
413C4×C61C2×#12011yescharacteristic
414C4×C61C2×#12111yescharacteristic
415C4×C61C2×#12111yescharacteristic
416C4×C61C2×#12311yescharacteristic
417Dic61—42no—
418Dic61—41no—
419Dic61—81no—
420Dic61#39412yes—
421Dic61#39412yes—
422C22×#137—611no—
423C22×#108—611no—
424C2×#417—611no—
425C22×#103—611no—
426C22×#101—611no—
427C2×#408—611no—
428#2052—611no—
429#2052—611no—
430#2052—611no—
431#2052—611no—
432#2052—611no—
433#2052—611no—
434#2052—611no—
435#2052D6111yescharacteristic, direct product factor
436C2×#343—611no—
437C2×C61—21no—
438C2×C61—21no—
439C2×C61—81no—
440C2×C61C2×#39411yescharacteristic
441C2×C61C2×#47111yescharacteristic
442C2×C61C2×#47311yescharacteristic
443D61—22no—
444D61—81no—
445D61#205214yesdirect product factor
446C22×#41—611no—
447C23×Q8—611no—
448C2×#137—611no—
449C2×#137—611no—
450C2×#137—611no—
451C2×#137—1224no—
452C2×#137—1221no—
453C2×#137—1221no—
454C2×#137—1224no—
455C2×#137C2×D6111yescharacteristic
456C22×Q16—1221no—
457C22×SD16—1221no—
458C22×M16—611no—
459C22×M16—611no—
460C22×M16—611no—
461C23×C8—611no—
462C22×C4⋊C4—611no—
463C2×#108—611no—
464C2×#108—611no—
465C2×#108—611no—
466C2×#108—1224no—
467C2×#108C2×D6111yescharacteristic, complemented
468#417—611no—
469#417—611no—
470#417—611no—
471#417—1221no—
472#417—1221no—
473#417C2×D6111yescharacteristic
474C2×#103—611no—
475C2×#103—611no—
476C2×#103—611no—
477C2×#103—1222no—
478C2×#103—1222no—
479C2×#103—1221no—
480C2×#103C2×D6111yescharacteristic, complemented
481C2×#102—1221no—
482C2×#101—611no—
483C2×#101—611no—
484C2×#101—611no—
485C2×#101—1224no—
486C2×#101C2×D6111yescharacteristic, complemented
487#408—611no—
488#408—611no—
489#408—611no—
490#408—1222no—
491#408C2×D6111yescharacteristic
492C2×C22⋊C8—1222no—
493#343—611no—
494#343—611no—
495#343—611no—
496#343C2×D6111yescharacteristic, complemented
497C61C2×#205211yescharacteristic, complemented, Sylow
498C2×#41—611no—
499C2×#41—611no—
500C2×#41—611no—
501C2×#41—1221no—
502C2×#41—1221no—
503C2×#41—1222no—
504C2×#41—1222no—
505C2×#41—1222no—
506C2×#41—1222no—
507C2×#41C22×D6111yescharacteristic
508C22×Q8—611no—
509C22×Q8—614no—
510C22×Q8—611no—
511C22×Q8—1221no—
512C22×Q8—1222no—
513C22×Q8—1221no—
514C22×Q8—1221no—
515C22×Q8—1222no—
516C22×Q8—1222no—
517C22×Q8—1221no—
518C22×Q8—1221no—
519C22×Q8C22×D6111yescharacteristic
520C22×D4—611no—
521C22×D4—1221no—
522C23×C4—611no—
523C23×C4—1221no—
524C23×C4—1221no—
525C23×C4—1221no—
526#137—22no—
527#137—22no—
528#137—1222no—
529#137—1222no—
530#137—1222no—
531#137—1228no—
532#137—1228no—
533#137—1222no—
534#137—1222no—
535#137—1222no—
536C2×Q16—21no—
537C2×Q16—1221no—
538C2×Q16—1228no—
539C2×Q16—1221no—
540C2×Q16—1221no—
541C2×SD16—21no—
542C2×SD16—1221no—
543C2×SD16—1228no—
544C2×SD16—1221no—
545C2×SD16—1221no—
546C2×M16—611no—
547C2×M16—614no—
548C2×M16—611no—
549C2×M16—611no—
550C2×M16—1221no—
551C2×M16—1221no—
552C2×M16—1221no—
553C2×M16—1222no—
554C2×M16—1222no—
555C2×M16—1222no—
556C2×M16—1222no—
557C2×M16—1222no—
558C2×M16C22×D6111yescharacteristic
559C2×M16C22×D6111yescharacteristic
560C2×M16C22×D6111yescharacteristic
561C22×C8—611no—
562C22×C8—612no—
563C22×C8—612no—
564C22×C8—1222no—
565C22×C8—1222no—
566C22×C8—1221no—
567C22×C8—1221no—
568C22×C8—1221no—
569C22×C8C22×D6111yescharacteristic
570C2×C4⋊C4—611no—
571C2×C4⋊C4—1221no—
572C2×C4⋊C4—1221no—
573C2×C4⋊C4—1221no—
574C2×C4⋊C4—1221no—
575C2×C4⋊C4—1221no—
576C2×C4⋊C4C22×D6111yescharacteristic
577#108—22no—
578#108—1222no—
579#108—1222no—
580#108—1222no—
581#103—21no—
582#103—22no—
583#103—1222no—
584#103—1221no—
585#103—1221no—
586#103—1222no—
587#103—1221no—
588#103—1222no—
589#102—21no—
590#102—1221no—
591#102—1221no—
592#102—1221no—
593#101—22no—
594#101—1222no—
595#101—1222no—
596#101—1222no—
597C22⋊C8—22no—
598C22⋊C8—1222no—
599C22⋊C8—1222no—
600C22⋊C8—1222no—
601C24—611no—
602C24—1221no—
603#41—21no—
604#41—21no—
605#41—21no—
606#41—21no—
607#41—1222no—
608#41—1222no—
609#41—1222no—
610#41—1222no—
611#41—1221no—
612#41—1221no—
613#41—1221no—
614#41—1221no—
615#41—2442no—
616#41—2442no—
617#41—2442no—
618#41—2442no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—612no—
625C2×Q8—611no—
626C2×Q8—1224no—
627C2×Q8—1221no—
628C2×Q8—1224no—
629C2×Q8—1222no—
630C2×Q8—1224no—
631C2×Q8—1224no—
632C2×Q8—1224no—
633C2×Q8—1222no—
634C2×Q8—1221no—
635C2×Q8—1221no—
636C2×Q8—1221no—
637C2×Q8—1221no—
638C2×Q8—1221no—
639C2×Q8—2441no—
640C2×Q8—2441no—
641C2×Q8—2442no—
642C2×Q8—2442no—
643C2×Q8—2442no—
644C2×Q8—2442no—
645C2×Q8—2442no—
646C2×Q8D4×D6112yes—
647C2×Q8D4×D6111yescharacteristic
648C2×D4—21no—
649C2×D4—611no—
650C2×D4—1221no—
651C2×D4—1222no—
652C2×D4—1222no—
653C2×D4—1221no—
654C2×D4—1221no—
655C2×D4—1221no—
656C2×D4—2442no—
657C2×D4—2442no—
658C2×D4D4×D6111yescharacteristic
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—611no—
663C22×C4—611no—
664C22×C4—611no—
665C22×C4—611no—
666C22×C4—611no—
667C22×C4—612no—
668C22×C4—612no—
669C22×C4—612no—
670C22×C4—612no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1224no—
674C22×C4—1221no—
675C22×C4—1221no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—4882no—
679C22×C4—2442no—
680C22×C4—2442no—
681C22×C4—2441no—
682C22×C4—2441no—
683C22×C4—2441no—
684C22×C4—2441no—
685C22×C4—2442no—
686C22×C4C23×D6111yescharacteristic
687Q16—24no—
688Q16—1224no—
689Q16—1224no—
690Q16—1224no—
691SD16—24no—
692SD16—1224no—
693SD16—1224no—
694SD16—1224no—
695M16—21no—
696M16—21no—
697M16—21no—
698M16—21no—
699M16—21no—
700M16—612no—
701M16—1224no—
702M16—1221no—
703M16—1221no—
704M16—1221no—
705M16—1221no—
706M16—1221no—
707M16—2442no—
708M16—2442no—
709M16D4×D6112yes—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—612no—
716C2×C8—1224no—
717C2×C8—1224no—
718C2×C8—1224no—
719C2×C8—1221no—
720C2×C8—1221no—
721C2×C8—1221no—
722C2×C8—1221no—
723C2×C8—1221no—
724C2×C8—2442no—
725C2×C8—2442no—
726C2×C8D4×D6112yes—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—1221no—
730C4⋊C4—1221no—
731C4⋊C4—2441no—
732C4⋊C4—2441no—
733C23—21no—
734C23—611no—
735C23—611no—
736C23—612no—
737C23—612no—
738C23—1222no—
739C23—1222no—
740C23—1221no—
741C23—2442no—
742C23—2442no—
743C23—2442no—
744C23#41×D6111yescharacteristic
745Q8—22no—
746Q8—21no—
747Q8—22no—
748Q8—21no—
749Q8—41no—
750Q8—41no—
751Q8—1222no—
752Q8—1221no—
753Q8—1222no—
754Q8—1221no—
755Q8—2444no—
756Q8—2444no—
757Q8—2442no—
758Q8—2441no—
759Q8—2441no—
760D4—21no—
761D4—21no—
762D4—41no—
763D4—41no—
764D4—1221no—
765D4—1221no—
766D4—2442no—
767D4—2442no—
768D4—2442no—
769D4—2441no—
770D4—2441no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—81no—
779C2×C4—611no—
780C2×C4—611no—
781C2×C4—612no—
782C2×C4—612no—
783C2×C4—612no—
784C2×C4—612no—
785C2×C4—612no—
786C2×C4—612no—
787C2×C4—612no—
788C2×C4—612no—
789C2×C4—612no—
790C2×C4—612no—
791C2×C4—1221no—
792C2×C4—1222no—
793C2×C4—4882no—
794C2×C4—4882no—
795C2×C4—4881no—
796C2×C4—2442no—
797C2×C4—2442no—
798C2×C4—2444no—
799C2×C4—2444no—
800C2×C4—2442no—
801C2×C4—2441no—
802C2×C4—2441no—
803C2×C4—2441no—
804C2×C4—2441no—
805C2×C4—2441no—
806C2×C4C2×D4×D6111yescharacteristic
807C2×C4C2×D4×D6111yescharacteristic
808C2×C4C2×D4×D6111yescharacteristic
809C2×C4C2×D4×D6111yescharacteristic
810C2×C4#41×D6111yescharacteristic
811C2×C4#41×D6111yescharacteristic
812C8—22no—
813C8—22no—
814C8—41no—
815C8—41no—
816C8—1222no—
817C8—1222no—
818C8—2441no—
819C8—2441no—
820C22—21no—
821C22—21no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—612no—
826C22—612no—
827C22—612no—
828C22—612no—
829C22—1224no—
830C22—1224no—
831C22—1221no—
832C22—1221no—
833C22—4884no—
834C22—2441no—
835C22—2441no—
836C22—2441no—
837C22#121×D6111yescharacteristic
838C22#123×D6111yescharacteristic
839C22#124×D6111yescharacteristic
840C4—41no—
841C4—42no—
842C4—81no—
843C4—612no—
844C4—612no—
845C4—4881no—
846C4—2441no—
847C4—2442no—
848C4#120×D6111yescharacteristic
849C4#121×D6111yescharacteristic
850C4#121×D6111yescharacteristic
851C4#123×D6111yescharacteristic
852C2—21no—
853C2—21no—
854C2—81no—
855C2—614no—
856C2—1222no—
857C2—4881no—
858C2#394×D6111yescharacteristic
859C2#471×D6111yescharacteristic
860C2#473×D6111yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2052C2
socleC22×C61C2×#121
prime radicalC2×#41×D61C22
hypercenter#2052D61
hypocenterC61C2×#2052
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2052

Complements

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

NH ≅ G/Ntype
2. C2×#108×D61C2semidirect
4. C2×#103×D61C2semidirect
5. C2×#101×D61C2semidirect
7. #21447121C2semidirect
8. #21447120C2semidirect
9. #21447119C2semidirect
10. #21447118C2semidirect
11. #21447117C2semidirect
12. #21447116C2semidirect
13. #21447115C2semidirect
14. #343×D61C2semidirect
15. C61×#2052C2semidirect
32. C2×#14519713C22semidirect
33. C2×#14519712C22semidirect
34. C2×#14519712C22semidirect
41. C2×#14519702C22semidirect
42. C2×#14519701C22semidirect
43. C2×#14519700C22semidirect
48. C2×#14519696C22semidirect
49. C2×#14519695C22semidirect
50. C2×#14519695C22semidirect
57. #16839531C22semidirect
58. #16839530C22semidirect
59. #16839530C22semidirect
61. C2×#108×C61C22semidirect
63. C2×#103×C61C22semidirect
64. C2×#101×C61C22semidirect
66. C61×#343C22semidirect
435. #2052D61direct (N × H)
445. D61#2052direct (N × H)
467. C2×#108C2×D61semidirect
480. C2×#103C2×D61semidirect
486. C2×#101C2×D61semidirect
496. #343C2×D61semidirect
497. C61C2×#2052semidirect

Maximal subgroups

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

subgroupindex
C2×#137×D612
C2×#108×D612
#417×D612
C2×#103×D612
C2×#101×D612
#408×D612
#214471212
#214471202
#214471192
#214471182
#214471172
#214471162
#214471152
#343×D612
C61×#20522
C2×#205261