Finite Group Databasebeta

← D61×#3486 #30588174

Subgroups — D61×#3486 #30588174

Order 15616.

11254 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×2−1+4×D61C211yesmaximal, characteristic, complemented
2C23×Q8×D61C211yesmaximal, characteristic, complemented
3#21459471C211yesmaximal, characteristic, complemented
4#21459470C211yesmaximal, characteristic, complemented
5#21459469C218yesmaximal, complemented
6#21459468C216yesmaximal, complemented
7#21459467C211yesmaximal, characteristic, complemented
8#21459466C216yesmaximal, complemented
9#21459465C218yesmaximal, complemented
10D4×Q8×D61C218yesmaximal, complemented
11#548×D61C218yesmaximal, complemented
12#536×D61C216yesmaximal, complemented
13#525×D61C216yesmaximal, complemented
14#519×D61C211yesmaximal, characteristic, complemented
15C61×#3486C211yesmaximal, characteristic, complemented
16C2×#14519825C2214yescomplemented
17C2×#14519825C2211yescharacteristic, complemented
18C2×#14519824C2214yescomplemented
19C2×#14519824C2216yescomplemented
202−1+4×D61—216no—
21C2×#41×D61C2216yes—
22C2×#41×D61C2214yescomplemented
23C23×Dic122C2213yescomplemented
24C22×Q8×D61—216no—
25C22×Q8×D61C2218yes—
26C22×Q8×D61C2213yes—
27C22×Q8×D61C2211yescharacteristic
28C22×Q8×D61C2218yescomplemented
29C22×Q8×D61C2211yescharacteristic, complemented
30C22×Q8×D61C2213yescomplemented
31C22×Q8×D61C2214yescomplemented
32C23×C4×D61C2213yes—
33Q8×D244C2218yescomplemented
34D4×Dic122C22124yescomplemented
35#16840427C22124yescomplemented
36Q8×C22⋊D61C2218yescomplemented
37Q8×C22⋊D61C2218yescomplemented
38#16840425C22124yescomplemented
39#16840425C22124yescomplemented
40#16840424C2218yescomplemented
41#16840423C2218yescomplemented
42#16840422C22124yescomplemented
43#16840421C22124yescomplemented
44#16840420C22124yescomplemented
45#16840419C2218yescomplemented
46#16840418C22124yescomplemented
47#16840338C2216yescomplemented
48#16840337C22112yescomplemented
49#16840336C2216yescomplemented
50#16840335C22124yescomplemented
51#16840334C22124yescomplemented
52#16840333C2216yescomplemented
53#16840332C22112yescomplemented
54C4⋊Q8×D61C22112yescomplemented
55#124×D61C22112yescomplemented
56#16840275C22112yescomplemented
57#16840274C2216yescomplemented
58#16840273C2216yescomplemented
59#16840272C22112yescomplemented
60#16840271C22124yescomplemented
61#16840270C22112yescomplemented
62#16840269C2216yescomplemented
63#16840268C22112yescomplemented
64#123×D61C22112yes—
65C22⋊Q8×D61C22112yes—
66C22⋊Q8×D61C22124yescomplemented
67#121×D61C22112yes—
68#120×D61C2214yes—
69#16840240C2211yescharacteristic, complemented
70#16840239C2216yescomplemented
71#16840238C2218yescomplemented
72C4×Q8×D61C2218yescomplemented
73C4×D4×D61C22124yes—
74#117×D61C2216yes—
75C2×2−1+4×C61C2211yescharacteristic, complemented
76C23×Q8×C61C2211yescharacteristic, complemented
77D4×Q8×C61C2218yescomplemented
78C61×#548C2218yescomplemented
79C61×#536C2216yescomplemented
80C61×#525C2216yescomplemented
81C61×#519C2211yescharacteristic, complemented
82C24×D61C2311yescharacteristic
83#14519825—28no—
84#14519825—232no—
85#14519824—232no—
86#14519824—248no—
87C2×#11758226C2316yes—
88C2×#11758226C2314yescomplemented
89C2×#11758222C23112yes—
90C2×#11758222C2316yes—
91C2×#11758222C23112yescomplemented
92C2×#11758224C23112yes—
93C2×#11758224C2316yes—
94C2×#11758224C23112yescomplemented
95#41×D61—232no—
96#41×D61—248no—
97C22×Dic122—224no—
98C22×Dic122C2313yes—
99C22×Dic122C2316yes—
100C22×Dic122C23124yes—
101C22×Dic122C2313yes—
102C22×Dic122C23112yescomplemented
103C2×Q8×D61—28no—
104C2×Q8×D61—264no—
105C2×Q8×D61—232no—
106C2×Q8×D61—264no—
107C2×Q8×D61—224no—
108C2×Q8×D61—224no—
109C2×Q8×D61D4116yescomplemented
110C2×Q8×D61C2316yes—
111C2×Q8×D61C23112yes—
112C2×Q8×D61C23112yes—
113C2×Q8×D61C2318yes—
114C2×Q8×D61C23124yes—
115C2×Q8×D61C2314yes—
116C2×Q8×D61C2314yes—
117C2×Q8×D61C23112yescomplemented
118C2×Q8×D61C2314yescomplemented
119C2×D4×D61C2318yes—
120C2×D4×D61C2314yes—
121C2×D4×D61C2316yes—
122C23×Dic61C2313yes—
123C22×C4×D61—224no—
124C22×C4×D61C23112yes—
125C22×C4×D61C23112yes—
126C22×C4×D61C2313yes—
127C22×C4×D61C2313yes—
128C22×C4×D61C2313yes—
129C22×C4×D61C23112yes—
130C22×C4×D61C2313yes—
131#14519777C23112yescomplemented
132#14519776C23148yescomplemented
133#14519775C23112yescomplemented
134#14519775C23112yescomplemented
135#14519766C23112yescomplemented
136#14519765C23112yescomplemented
137#14519764C23112yescomplemented
138#14519763C23148yescomplemented
139#14519762C23124yes—
140#14519761C23112yes—
141#14519760C23112yes—
142#14519759C23124yes—
143#14519758C23112yes—
144#14519757C23112yes—
145#14519757C23124yescomplemented
146#14519756C23112yes—
147#14519756C23124yescomplemented
148#14519755C23124yes—
149#14519755C23148yescomplemented
150#14519754C23124yes—
151#14519754C23148yescomplemented
152#14519753C23112yes—
153#14519753C23124yescomplemented
154#14519752C23112yes—
155#14519751C23112yes—
156#14519750C23124yes—
157#14519749C23124yes—
158#14519748C23112yes—
159#14519747C2314yes—
160#14519747C2318yes—
161#14519746C2314yes—
162#14519745C2314yes—
163#14519745C2318yes—
164Q8×Dic61C2318yescomplemented
165C4×Dic122C23124yescomplemented
166#14519742C23124yescomplemented
167C4×D244C23124yes—
168D4×Dic61C23124yes—
169#14519739C23124yes—
170C4×C22⋊D61C23124yes—
171C4×C22⋊D61C23124yes—
172#14519737C23124yes—
173#14519737C23124yes—
174#14519736C2316yes—
175#14519735C23112yes—
176#14519734C23112yes—
177#14519733C23112yes—
178C4⋊C4×D61C23112yes—
179C4⋊C4×D61C23124yes—
180C22⋊C4×D61C2314yes—
181C22⋊C4×D61C2318yes—
182C22⋊C4×D61C23124yes—
183C42×D61C23112yes—
1842−1+4×C61—28no—
185C2×#41×C61C2316yes—
186C2×#41×C61C2314yescomplemented
187C22×Q8×C61—28no—
188C22×Q8×C61C2313yes—
189C22×Q8×C61C2318yes—
190C22×Q8×C61C2311yescharacteristic
191C22×Q8×C61C2314yescomplemented
192C23×C4×C61C2313yes—
193C4⋊Q8×C61C23112yescomplemented
194#124×C61C23112yescomplemented
195#123×C61C23112yes—
196C22⋊Q8×C61C23112yes—
197C22⋊Q8×C61C23124yescomplemented
198#121×C61C23112yes—
199#120×C61C2314yes—
200C4×Q8×C61C2318yescomplemented
201C4×D4×C61C23124yes—
202#117×C61C2316yes—
203C24×C61C2411yescharacteristic
204C23×D61—24no—
205C23×D61—28no—
206C23×D61C2411yescharacteristic
207C23×D61C2412yes—
208C23×D61C2414yes—
209C23×D61C2411yescharacteristic
210C23×D61C2412yes—
211#41×C61—216no—
212#41×C61—224no—
213C2×Q8×C61—232no—
214C2×Q8×C61—216no—
215C2×Q8×C61—212no—
216C2×Q8×C61C2×D418yescomplemented
217C2×Q8×C61C24112yes—
218C2×Q8×C61C2416yes—
219C2×Q8×C61C2414yes—
220C2×D4×C61C2414yes—
221C2×D4×C61C2416yes—
222C2×D4×C61C2418yes—
223C22×C4×C61—212no—
224C22×C4×C61C24112yes—
225C22×C4×C61C2413yes—
226C22×C4×C61C24112yes—
227C22×C4×C61C2413yes—
228C2×C22⋊D61C2414yes—
229C2×C22⋊D61C2414yes—
230C2×C22⋊D61C24112yes—
231C2×C22⋊D61C2418yes—
232C2×C22⋊D61C2418yes—
233C22×Dic61—212no—
234C22×Dic61C24112yes—
235C22×Dic61C2413yes—
236C22×Dic61C24112yes—
237C22×Dic61C2413yes—
238#11758226—216no—
239#11758226—224no—
240Q8×D61—232no—
241Q8×D61—216no—
242Q8×D61—248no—
243Q8×D61—248no—
244Q8×D61—224no—
245Q8×D61—296no—
246Q8×D61—248no—
247Q8×D61C2×D4132yes—
248Q8×D61C2×D4132yescomplemented
249#11758224—248no—
250#11758224—224no—
251#11758224—248no—
252D4×D61—216no—
253D4×D61—232no—
254D4×D61—224no—
255#11758222—224no—
256#11758222—248no—
257#11758222—248no—
258C2×D244C2414yes—
259C2×D244C2416yes—
260C2×D244C2418yes—
261C2×C4×D61—212no—
262C2×C4×D61—212no—
263C2×C4×D61—212no—
264C2×C4×D61—248no—
265C2×C4×D61—248no—
266C2×C4×D61—248no—
267C2×C4×D61C2×D4124yes—
268C2×C4×D61C2414yes—
269C2×C4×D61C2416yes—
270C2×C4×D61C24112yes—
271C2×C4×D61C24112yes—
272C2×C4×D61C2416yes—
273C2×C4×D61C24112yes—
274C2×C4×D61C24112yes—
275C2×C4×D61C2418yes—
276C2×C4×D61C2416yes—
277C2×C4×D61C2416yes—
278C2×Dic122—212no—
279C2×Dic122—224no—
280C2×Dic122—296no—
281C2×Dic122—248no—
282C2×Dic122C2×D4124yescomplemented
283C2×Dic122C24124yes—
284C2×Dic122C24112yes—
285C2×Dic122C24112yes—
286C2×Dic122C2416yes—
287C2×Dic122C24112yes—
288C4⋊C4×C61C24112yes—
289C4⋊C4×C61C24124yes—
290C22⋊C4×C61C2414yes—
291C22⋊C4×C61C2418yes—
292C22⋊C4×C61C24124yes—
293C42×C61C24112yes—
294C22⋊Dic61C2414yes—
295C22⋊Dic61C2418yes—
296C22⋊Dic61C24124yes—
297#11758198C2418yes—
298#11758198C2418yes—
299#11758198C24124yes—
300#11758198C2418yes—
301#11758198C24124yes—
302C4⋊Dic61C24112yes—
303C4⋊Dic61C24124yes—
304#11758196C24124yes—
305#11758196C24124yes—
306#11758196C24124yes—
307C4×Dic61C24124yes—
308C4×Dic61C24112yes—
309C23×C61—22no—
310C23×C61—24no—
311C23×C61C2514yes—
312C23×C61C2511yescharacteristic
313C23×C61C2512yes—
314C22×D61—232no—
315C22×D61—22no—
316C22×D61—24no—
317C22×D61—24no—
318C22×D61—24no—
319C22×D61—24no—
320C22×D61—24no—
321C22×D61—24no—
322C22×D61—24no—
323C22×D61—28no—
324C22×D61—216no—
325C22×D61C22×D414yes—
326C22×D612−1+418yescomplemented
327C22×D61C2514yes—
328C22×D61C2511yescharacteristic
329C22×D61C2512yes—
330C22×D61C2511yescharacteristic
331Q8×C61—224no—
332Q8×C61—212no—
333Q8×C61C22×D4116yes—
334D4×C61—28no—
335D4×C61—216no—
336D4×C61—212no—
337C2×C4×C61—26no—
338C2×C4×C61—224no—
339C2×C4×C61—224no—
340C2×C4×C61C22×D4112yes—
341C2×C4×C61C2518yes—
342C2×C4×C61C2514yes—
343C2×C4×C61C2516yes—
344C2×C4×C61C2516yes—
345C22⋊D61—28no—
346C22⋊D61—216no—
347C22⋊D61—28no—
348C22⋊D61—216no—
349C22⋊D61—224no—
350C2×Dic61—26no—
351C2×Dic61—224no—
352C2×Dic61—224no—
353C2×Dic61C22×D4112yes—
354C2×Dic61C2518yes—
355C2×Dic61C2514yes—
356C2×Dic61C2516yes—
357C2×Dic61C2516yes—
358D244—28no—
359D244—216no—
360D244—212no—
361C4×D61—28no—
362C4×D61—212no—
363C4×D61—212no—
364C4×D61—216no—
365C4×D61—224no—
366C4×D61—224no—
367C4×D61—224no—
368C4×D61—224no—
369C4×D61C22×D4124yes—
370C4×D61C22×D4124yes—
371Dic122—224no—
372Dic122—212no—
373Dic122—248no—
374Dic122—224no—
375Dic122C22×D4148yes—
376C2×#3486—611nomaximal, Sylow
377C22×C61—28no—
378C22×C61—22no—
379C22×C61—22no—
380C22×C61—22no—
381C22×C61—24no—
382C22×C61—28no—
383C22×C61C23×D412yes—
384C22×C61C2×2−1+414yescomplemented
385C22×C61C2611yescharacteristic
386C2×D61—216no—
387C2×D61—28no—
388C2×D61—22no—
389C2×D61—22no—
390C2×D61—22no—
391C2×D61—28no—
392C2×D61—216no—
393C2×D61—24no—
394C2×D61—28no—
395C2×D61—416no—
396C2×D61C23×D412yes—
397C2×D61C23×D412yes—
398C2×D61C2×2−1+414yes—
399C2×D61C2×2−1+414yescomplemented
400C4×C61—26no—
401C4×C61—24no—
402C4×C61—28no—
403C4×C61C23×D4112yes—
404Dic61—26no—
405Dic61—24no—
406Dic61—28no—
407Dic61C23×D4112yes—
408C22×2−1+4—611no—
409C24×Q8—611no—
410#3486—611no—
411#3486—611no—
412#3486—618no—
413#3486—618no—
414#3486—616no—
415#3486—616no—
416#3486—611no—
417#3486D6111yescharacteristic, direct product factor
418C2×D4×Q8—618no—
419C2×#548—618no—
420C2×#536—616no—
421C2×#525—616no—
422C2×#519—611no—
423C2×C61—22no—
424C2×C61—24no—
425C2×C61—44no—
426C2×C61C24×D411yescharacteristic
427C2×C61C22×2−1+412yes—
428D61—22no—
429D61—24no—
430D61—44no—
431D61#348614yesdirect product factor
432C2×2−1+4—616no—
433C2×2−1+4—614no—
434C2×2−1+4—611no—
435C2×2−1+4—614no—
436C2×2−1+4—12216no—
437C2×2−1+4C2×D6111yescharacteristic, complemented
438C22×#41—616no—
439C22×#41—614no—
440C23×Q8—611no—
441C23×Q8—613no—
442C23×Q8—618no—
443C23×Q8—618no—
444C23×Q8—613no—
445C23×Q8—611no—
446C23×Q8—614no—
447C23×Q8—613no—
448C23×Q8—12216no—
449C23×Q8C2×D6111yescharacteristic, complemented
450C24×C4—613no—
451D4×Q8—618no—
452D4×Q8—618no—
453D4×Q8—6124no—
454D4×Q8—6124no—
455D4×Q8—6124no—
456D4×Q8—618no—
457D4×Q8—6124no—
458D4×Q8C2×D6118yescomplemented
459#548—618no—
460#548—618no—
461#548—6124no—
462#548—6124no—
463#548—6124no—
464#548—618no—
465#548—6124no—
466#548C2×D6118yescomplemented
467#536—616no—
468#536—616no—
469#536—6112no—
470#536—6112no—
471#536—6124no—
472#536—6124no—
473#536—616no—
474#536C2×D6116yescomplemented
475C2×C4⋊Q8—6112no—
476C2×#124—6112no—
477#525—616no—
478#525—616no—
479#525—6112no—
480#525—6112no—
481#525—6112no—
482#525—6112no—
483#525—6124no—
484#525—616no—
485#525C2×D6116yescomplemented
486C2×#123—6112no—
487C2×C22⋊Q8—6112no—
488C2×C22⋊Q8—6124no—
489C2×#121—6112no—
490C2×#120—614no—
491#519—611no—
492#519—618no—
493#519—616no—
494#519C2×D6111yescharacteristic, complemented
495C2×C4×Q8—618no—
496C2×C4×D4—6124no—
497C2×#117—616no—
498C61C2×#348611yescharacteristic, complemented, Sylow
499C25—611no—
5002−1+4—28no—
5012−1+4—12232no—
5022−1+4—12232no—
5032−1+4—12248no—
5042−1+4—1228no—
505C2×#41—616no—
506C2×#41—614no—
507C2×#41—6112no—
508C2×#41—616no—
509C2×#41—6112no—
510C2×#41—6112no—
511C2×#41—616no—
512C2×#41—6112no—
513C2×#41—12248no—
514C2×#41—12232no—
515C2×#41C22×D6116yes—
516C2×#41C22×D6114yescomplemented
517C22×Q8—28no—
518C22×Q8—6116no—
519C22×Q8—614no—
520C22×Q8—614no—
521C22×Q8—6112no—
522C22×Q8—616no—
523C22×Q8—6112no—
524C22×Q8—6124no—
525C22×Q8—618no—
526C22×Q8—6112no—
527C22×Q8—614no—
528C22×Q8—613no—
529C22×Q8—616no—
530C22×Q8—613no—
531C22×Q8—6124no—
532C22×Q8—6112no—
533C22×Q8—12224no—
534C22×Q8—12224no—
535C22×Q8—12264no—
536C22×Q8—12264no—
537C22×Q8—12224no—
538C22×Q8—12232no—
539C22×Q8—1228no—
540C22×Q8C22×D6113yes—
541C22×Q8C22×D6118yes—
542C22×Q8C22×D6111yescharacteristic
543C22×Q8C22×D6114yescomplemented
544C22×D4—618no—
545C22×D4—614no—
546C22×D4—616no—
547C23×C4—613no—
548C23×C4—613no—
549C23×C4—6112no—
550C23×C4—6112no—
551C23×C4—613no—
552C23×C4—613no—
553C23×C4—6112no—
554C23×C4—613no—
555C23×C4—12224no—
556C23×C4C22×D6113yes—
557C4⋊Q8—6112no—
558C4⋊Q8—6112no—
559C4⋊Q8—6148no—
560C4⋊Q8—6112no—
561C4⋊Q8C22×D61112yescomplemented
562#124—6112no—
563#124—6112no—
564#124—6148no—
565#124—6112no—
566#124C22×D61112yescomplemented
567#123—6112no—
568#123—6112no—
569#123—6124no—
570#123—6124no—
571#123—6112no—
572#123C22×D61112yes—
573C22⋊Q8—6112no—
574C22⋊Q8—6124no—
575C22⋊Q8—6112no—
576C22⋊Q8—6124no—
577C22⋊Q8—6124no—
578C22⋊Q8—6112no—
579C22⋊Q8—6148no—
580C22⋊Q8—6124no—
581C22⋊Q8—6124no—
582C22⋊Q8—6148no—
583C22⋊Q8C22×D61112yes—
584C22⋊Q8C22×D61124yescomplemented
585#121—6112no—
586#121—6124no—
587#121—6112no—
588#121—6112no—
589#121—6124no—
590#121C22×D61112yes—
591#120—614no—
592#120—614no—
593#120—618no—
594#120—618no—
595#120—614no—
596#120C22×D6114yes—
597C4×Q8—618no—
598C4×Q8—6124no—
599C4×Q8—6124no—
600C4×Q8C22×D6118yescomplemented
601C4×D4—6124no—
602C4×D4—6124no—
603C4×D4—6124no—
604C4×D4—6124no—
605C4×D4—6124no—
606C4×D4—6124no—
607C4×D4—6124no—
608C4×D4C22×D61124yes—
609#117—616no—
610#117—6112no—
611#117—6112no—
612#117—6112no—
613#117C22×D6116yes—
614C2×C4⋊C4—6112no—
615C2×C4⋊C4—6124no—
616C2×C22⋊C4—614no—
617C2×C22⋊C4—618no—
618C2×C22⋊C4—6124no—
619C2×C42—6112no—
620C24—611no—
621C24—612no—
622C24—614no—
623C24—612no—
624C24—611no—
625C24—1224no—
626C24—1228no—
627C24C23×D6111yescharacteristic
628#41—216no—
629#41—224no—
630#41—12248no—
631#41—12248no—
632#41—12248no—
633#41—12224no—
634#41—12224no—
635#41—12248no—
636#41—12216no—
637#41—12224no—
638C2×Q8—232no—
639C2×Q8—216no—
640C2×Q8—212no—
641C2×Q8—6132no—
642C2×Q8—6132no—
643C2×Q8—6124no—
644C2×Q8—6112no—
645C2×Q8—6124no—
646C2×Q8—6112no—
647C2×Q8—6112no—
648C2×Q8—616no—
649C2×Q8—12224no—
650C2×Q8—12296no—
651C2×Q8—12248no—
652C2×Q8—12248no—
653C2×Q8—12248no—
654C2×Q8—12224no—
655C2×Q8—12296no—
656C2×Q8—12248no—
657C2×Q8—12232no—
658C2×Q8—12216no—
659C2×Q8—12212no—
660C2×Q8D4×D6118yescomplemented
661C2×Q8C23×D6116yes—
662C2×Q8C23×D61112yes—
663C2×Q8C23×D6114yes—
664C2×D4—618no—
665C2×D4—618no—
666C2×D4—614no—
667C2×D4—614no—
668C2×D4—6112no—
669C2×D4—618no—
670C2×D4—614no—
671C2×D4—616no—
672C2×D4—12224no—
673C2×D4—12216no—
674C2×D4—12232no—
675C2×D4C23×D6118yes—
676C2×D4C23×D6114yes—
677C2×D4C23×D6116yes—
678C22×C4—212no—
679C22×C4—613no—
680C22×C4—6124no—
681C22×C4—616no—
682C22×C4—616no—
683C22×C4—6112no—
684C22×C4—6112no—
685C22×C4—613no—
686C22×C4—618no—
687C22×C4—616no—
688C22×C4—614no—
689C22×C4—6112no—
690C22×C4—6112no—
691C22×C4—6112no—
692C22×C4—6112no—
693C22×C4—616no—
694C22×C4—12212no—
695C22×C4—12248no—
696C22×C4—12248no—
697C22×C4—12248no—
698C22×C4—12212no—
699C22×C4—12212no—
700C22×C4—12212no—
701C22×C4C23×D61112yes—
702C22×C4C23×D61112yes—
703C22×C4C23×D6113yes—
704C22×C4C23×D6113yes—
705C4⋊C4—6124no—
706C4⋊C4—6124no—
707C4⋊C4—6124no—
708C4⋊C4—6112no—
709C4⋊C4—6124no—
710C4⋊C4C23×D61112yes—
711C4⋊C4C23×D61124yes—
712C22⋊C4—614no—
713C22⋊C4—618no—
714C22⋊C4—6124no—
715C22⋊C4—618no—
716C22⋊C4—618no—
717C22⋊C4—618no—
718C22⋊C4—6124no—
719C22⋊C4—6124no—
720C22⋊C4C23×D6114yes—
721C22⋊C4C23×D6118yes—
722C22⋊C4C23×D61124yes—
723C42—6124no—
724C42—6112no—
725C42C23×D61112yes—
726C23—22no—
727C23—24no—
728C23—611no—
729C23—614no—
730C23—618no—
731C23—611no—
732C23—612no—
733C23—614no—
734C23—1224no—
735C23—1224no—
736C23—1224no—
737C23—1224no—
738C23—1224no—
739C23—1224no—
740C23—1228no—
741C23—12216no—
742C23—12232no—
743C23—1222no—
744C23—1224no—
745C23C24×D6114yes—
746C23C24×D6111yescharacteristic
747C23C24×D6112yes—
748Q8—224no—
749Q8—212no—
750Q8—6148no—
751Q8—12248no—
752Q8—12224no—
753Q8—12224no—
754Q8—12212no—
755Q8C2×D4×D61116yes—
756D4—28no—
757D4—216no—
758D4—212no—
759D4—12216no—
760D4—1228no—
761D4—12224no—
762D4—12216no—
763D4—1228no—
764D4—1228no—
765D4—12216no—
766D4—12212no—
767C2×C4—26no—
768C2×C4—224no—
769C2×C4—224no—
770C2×C4—6112no—
771C2×C4—616no—
772C2×C4—6124no—
773C2×C4—6124no—
774C2×C4—618no—
775C2×C4—616no—
776C2×C4—614no—
777C2×C4—12224no—
778C2×C4—12224no—
779C2×C4—1228no—
780C2×C4—12212no—
781C2×C4—12212no—
782C2×C4—12216no—
783C2×C4—12224no—
784C2×C4—12224no—
785C2×C4—1226no—
786C2×C4—12224no—
787C2×C4—12224no—
788C2×C4C2×D4×D61112yes—
789C2×C4C24×D6118yes—
790C2×C4C24×D6116yes—
791C2×C4C24×D6114yes—
792C2×C4C24×D6116yes—
793C22—28no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—24no—
798C22—28no—
799C22—612no—
800C22—614no—
801C22—612no—
802C22—614no—
803C22—1228no—
804C22—12216no—
805C22—1228no—
806C22—12216no—
807C22—1222no—
808C22—1222no—
809C22—1222no—
810C22—1224no—
811C22—1228no—
812C22—24416no—
813C22C22×D4×D6112yes—
814C222−1+4×D6114yescomplemented
815C22C25×D6111yescharacteristic
816C4—24no—
817C4—26no—
818C4—28no—
819C4—6112no—
820C4—1224no—
821C4—1226no—
822C4—1228no—
823C4C22×D4×D61112yes—
824C2—22no—
825C2—24no—
826C2—44no—
827C2—614no—
828C2—1222no—
829C2—1224no—
830C2—2444no—
831C2C23×D4×D6111yescharacteristic
832C2C2×2−1+4×D6112yes—
subgroupG/H
center, FrattiniC22C25×D61
commutator, socle, cosocleC22×C61C26
FittingC61×#3486C2
hypercenter#3486D61
hypocenterC61C2×#3486
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #3486

Complements

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

NH ≅ G/Ntype
1. C2×2−1+4×D61C2semidirect
2. C23×Q8×D61C2semidirect
3. #21459471C2semidirect
4. #21459470C2semidirect
5. #21459469C2semidirect
6. #21459468C2semidirect
7. #21459467C2semidirect
8. #21459466C2semidirect
9. #21459465C2semidirect
10. D4×Q8×D61C2semidirect
11. #548×D61C2semidirect
12. #536×D61C2semidirect
13. #525×D61C2semidirect
14. #519×D61C2semidirect
15. C61×#3486C2semidirect
16. C2×#14519825C22semidirect
17. C2×#14519825C22semidirect
18. C2×#14519824C22semidirect
19. C2×#14519824C22semidirect
22. C2×#41×D61C22semidirect
23. C23×Dic122C22semidirect
28. C22×Q8×D61C22semidirect
29. C22×Q8×D61C22semidirect
30. C22×Q8×D61C22semidirect
31. C22×Q8×D61C22semidirect
33. Q8×D244C22semidirect
34. D4×Dic122C22semidirect
35. #16840427C22semidirect
36. Q8×C22⋊D61C22semidirect
37. Q8×C22⋊D61C22semidirect
38. #16840425C22semidirect
39. #16840425C22semidirect
40. #16840424C22semidirect
41. #16840423C22semidirect
42. #16840422C22semidirect
43. #16840421C22semidirect
44. #16840420C22semidirect
45. #16840419C22semidirect
46. #16840418C22semidirect
47. #16840338C22semidirect
48. #16840337C22semidirect
49. #16840336C22semidirect
50. #16840335C22semidirect
51. #16840334C22semidirect
52. #16840333C22semidirect
53. #16840332C22semidirect
54. C4⋊Q8×D61C22semidirect
55. #124×D61C22semidirect
56. #16840275C22semidirect
57. #16840274C22semidirect
58. #16840273C22semidirect
59. #16840272C22semidirect
60. #16840271C22semidirect
61. #16840270C22semidirect
62. #16840269C22semidirect
63. #16840268C22semidirect
66. C22⋊Q8×D61C22semidirect
69. #16840240C22semidirect
70. #16840239C22semidirect
71. #16840238C22semidirect
72. C4×Q8×D61C22semidirect
75. C2×2−1+4×C61C22semidirect
76. C23×Q8×C61C22semidirect
77. D4×Q8×C61C22semidirect
78. C61×#548C22semidirect
79. C61×#536C22semidirect
80. C61×#525C22semidirect
81. C61×#519C22semidirect
88. C2×#11758226C23semidirect
91. C2×#11758222C23semidirect
94. C2×#11758224C23semidirect
102. C22×Dic122C23semidirect
109. C2×Q8×D61D4semidirect
117. C2×Q8×D61C23semidirect
118. C2×Q8×D61C23semidirect
131. #14519777C23semidirect
132. #14519776C23semidirect
133. #14519775C23semidirect
134. #14519775C23semidirect
135. #14519766C23semidirect
136. #14519765C23semidirect
137. #14519764C23semidirect
138. #14519763C23semidirect
145. #14519757C23semidirect
147. #14519756C23semidirect
149. #14519755C23semidirect
151. #14519754C23semidirect
153. #14519753C23semidirect
164. Q8×Dic61C23semidirect
165. C4×Dic122C23semidirect
166. #14519742C23semidirect
186. C2×#41×C61C23semidirect
191. C22×Q8×C61C23semidirect
193. C4⋊Q8×C61C23semidirect
194. #124×C61C23semidirect
197. C22⋊Q8×C61C23semidirect
200. C4×Q8×C61C23semidirect
216. C2×Q8×C61C2×D4semidirect
248. Q8×D61C2×D4semidirect
282. C2×Dic122C2×D4semidirect
326. C22×D612−1+4semidirect
384. C22×C61C2×2−1+4semidirect
399. C2×D61C2×2−1+4semidirect
417. #3486D61direct (N × H)
431. D61#3486direct (N × H)
437. C2×2−1+4C2×D61semidirect
449. C23×Q8C2×D61semidirect
458. D4×Q8C2×D61semidirect
466. #548C2×D61semidirect
474. #536C2×D61semidirect
485. #525C2×D61semidirect
494. #519C2×D61semidirect
498. C61C2×#3486semidirect
516. C2×#41C22×D61semidirect
543. C22×Q8C22×D61semidirect
561. C4⋊Q8C22×D61semidirect
566. #124C22×D61semidirect
584. C22⋊Q8C22×D61semidirect
600. C4×Q8C22×D61semidirect
660. C2×Q8D4×D61semidirect
814. C222−1+4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×2−1+4×D612
C23×Q8×D612
#214594712
#214594702
#214594692
#214594682
#214594672
#214594662
#214594652
D4×Q8×D612
#548×D612
#536×D612
#525×D612
#519×D612
C61×#34862
C2×#348661