Finite Group Databasebeta

← D61×#3529 #30586900

Subgroups — D61×#3529 #30586900

Order 15616.

7418 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459960C213yesmaximal, complemented
2#21459959C211yesmaximal, characteristic, complemented
3#21459958C216yesmaximal, complemented
4#21459957C216yesmaximal, complemented
5#21459956C216yesmaximal, complemented
6#21459955C213yesmaximal, complemented
7#21459954C216yesmaximal, complemented
8#563×D61C213yesmaximal, complemented
9#562×D61C216yesmaximal, complemented
10H(3,𝔽4)×D61C211yesmaximal, characteristic, complemented
11#560×D61C216yesmaximal, complemented
12#532×D61C213yesmaximal, complemented
13#529×D61C216yesmaximal, complemented
14#525×D61C216yesmaximal, complemented
15C61×#3529C211yesmaximal, characteristic, complemented
16C2×#41×D61C2213yes—
17C2×#41×D61C2211yescharacteristic, complemented
18C23×C4×D61C2212yescomplemented
19#16840516C2216yescomplemented
20#16840515C2216yescomplemented
21#16840514C22112yescomplemented
22#16840513C22112yescomplemented
23#16840512C2213yescomplemented
24#16840511C2216yescomplemented
25#16840510C2216yescomplemented
26#16840509C22112yescomplemented
27#16840509C22112yescomplemented
28#16840508C22112yescomplemented
29#16840508C22112yescomplemented
30#16840507C22112yescomplemented
31#16840507C22112yescomplemented
32#16840506C2216yescomplemented
33#16840506C2216yescomplemented
34#16840505C2216yescomplemented
35#16840504C2213yescomplemented
36#16840504C2216yescomplemented
37#16840503C22112yescomplemented
38#16840502C2216yescomplemented
39#16840502C22112yescomplemented
40#16840501C2216yescomplemented
41#16840501C22112yescomplemented
42#16840500C22112yescomplemented
43#16840500C22112yescomplemented
44#16840500C22112yescomplemented
45#16840499C2216yescomplemented
46#16840313C2213yescomplemented
47#16840312C2213yescomplemented
48#16840311C2213yescomplemented
49#16840311C2213yescomplemented
50#16840310C2213yescomplemented
51#16840309C22112yescomplemented
52#16840308C2213yescomplemented
53#16840308C2213yescomplemented
54#16840307C22112yescomplemented
55C4⋊Q8×D61C2213yescomplemented
56#127×D61C2213yes—
57#16840299C2216yescomplemented
58#16840298C2216yescomplemented
59#16840297C2216yescomplemented
60#16840296C2216yescomplemented
61#16840295C22112yescomplemented
62#16840294C2216yescomplemented
63#16840293C2216yescomplemented
64#16840292C22112yescomplemented
65#16840291C2216yescomplemented
66#16840290C22112yescomplemented
67#16840289C22112yescomplemented
68#126×D61C22112yescomplemented
69#125×D61C2216yescomplemented
70#124×D61C2216yes—
71#124×D61C2213yes—
72#124×D61C2213yescomplemented
73#16840275C22112yescomplemented
74#16840274C2216yescomplemented
75#16840273C2216yescomplemented
76#16840272C22112yescomplemented
77#16840271C22112yescomplemented
78#16840271C22112yescomplemented
79#16840270C2216yescomplemented
80#16840270C2216yescomplemented
81#16840269C2216yescomplemented
82#16840268C2216yescomplemented
83#16840268C2216yescomplemented
84#123×D61C2216yes—
85#123×D61C2216yescomplemented
86#123×D61C22112yescomplemented
87C22⋊Q8×D61C22112yescomplemented
88C22⋊Q8×D61C2216yescomplemented
89#121×D61C22112yes—
90#121×D61C2216yes—
91#121×D61C22112yescomplemented
92#120×D61C2216yes—
93#120×D61C2216yescomplemented
94C4×Q8×D61C2212yescomplemented
95C4×D4×D61C2216yes—
96C4×D4×D61C22112yescomplemented
97#117×D61C2216yescomplemented
98C2×C42×D61C2213yescomplemented
99C61×#563C2213yescomplemented
100C61×#562C2216yescomplemented
101C61×H(3,𝔽4)C2211yescharacteristic, complemented
102C61×#560C2216yescomplemented
103C61×#532C2213yescomplemented
104C61×#529C2216yescomplemented
105C61×#525C2216yescomplemented
106C24×D61C2312yes—
107C2×#11758226C2313yes—
108C2×#11758226C2311yescharacteristic, complemented
109C2×#11758222C2313yes—
110C2×#11758222C2316yes—
111C2×#11758222C2313yescomplemented
112C2×#11758224C2313yes—
113C2×#11758224C2316yes—
114C2×#11758224C2313yescomplemented
115#41×D61—412no—
116#41×D61—44no—
117C2×Q8×D61C2312yes—
118C2×Q8×D61C2313yes—
119C2×Q8×D61C2311yescharacteristic
120C2×D4×D61C2316yes—
121C2×D4×D61C23112yes—
122C2×D4×D61C2313yes—
123C2×D4×D61C2316yes—
124C2×D4×D61C2313yes—
125C23×Dic61C2312yescomplemented
126C22×C4×D61—48no—
127C22×C4×D61C2313yes—
128C22×C4×D61C2316yes—
129C22×C4×D61C2316yes—
130C22×C4×D61C2316yes—
131C22×C4×D61C2316yescomplemented
132C22×C4×D61C2316yescomplemented
133#14519777C2313yescomplemented
134#14519776C23112yescomplemented
135#14519775C2313yescomplemented
136#14519775C2313yescomplemented
137#14519774C2313yes—
138#14519773C2313yes—
139#14519773C23112yes—
140#14519773C2313yes—
141#14519772C23112yescomplemented
142#14519772C23112yescomplemented
143#14519772C23112yescomplemented
144#14519771C23112yescomplemented
145#14519770C23112yescomplemented
146#14519770C23112yescomplemented
147#14519770C23112yescomplemented
148#14519769C2316yescomplemented
149#14519768C2316yescomplemented
150#14519768C2316yescomplemented
151#14519767C23112yescomplemented
152#14519767C23112yescomplemented
153#14519766C2316yes—
154#14519766C2313yes—
155#14519766C2313yescomplemented
156#14519765C2316yes—
157#14519765C2313yes—
158#14519765C2313yescomplemented
159#14519764C2316yes—
160#14519764C2313yes—
161#14519764C2313yescomplemented
162#14519763C23112yes—
163#14519763C23112yes—
164#14519763C23112yes—
165#14519763C23112yescomplemented
166#14519762C23112yes—
167#14519762C23112yescomplemented
168#14519762C23112yescomplemented
169#14519762C23112yescomplemented
170#14519761C2316yes—
171#14519761C23112yescomplemented
172#14519761C2316yescomplemented
173#14519760C2316yes—
174#14519760C23112yescomplemented
175#14519760C2316yescomplemented
176#14519759C23112yes—
177#14519759C23112yescomplemented
178#14519759C23112yescomplemented
179#14519759C23112yescomplemented
180#14519758C2316yes—
181#14519758C23112yescomplemented
182#14519758C2316yescomplemented
183#14519757C2316yescomplemented
184#14519757C23112yescomplemented
185#14519756C2316yescomplemented
186#14519756C23112yescomplemented
187#14519755C23112yescomplemented
188#14519755C23112yescomplemented
189#14519755C23112yescomplemented
190#14519754C23112yescomplemented
191#14519754C23112yescomplemented
192#14519754C23112yescomplemented
193#14519753C2316yescomplemented
194#14519753C23112yescomplemented
195#14519752C2316yes—
196#14519752C23112yes—
197#14519752C23112yescomplemented
198#14519751C2316yes—
199#14519751C23112yes—
200#14519751C23112yescomplemented
201#14519750C23112yes—
202#14519750C23112yes—
203#14519750C23112yes—
204#14519750C23112yescomplemented
205#14519750C23112yescomplemented
206#14519749C23112yes—
207#14519749C23112yes—
208#14519749C23112yes—
209#14519749C23112yescomplemented
210#14519749C23112yescomplemented
211#14519748C2316yes—
212#14519748C23112yes—
213#14519748C23112yescomplemented
214#14519747C23112yes—
215#14519747C2316yes—
216#14519747C2316yescomplemented
217#14519747C23112yescomplemented
218#14519746C2316yes—
219#14519746C2316yescomplemented
220#14519745C2316yes—
221#14519745C23112yes—
222#14519745C23112yescomplemented
223#14519745C2316yescomplemented
224Q8×Dic61C2312yescomplemented
225C4×Dic122C2316yescomplemented
226#14519742C2316yescomplemented
227C4×D244C2316yes—
228C4×D244C23112yescomplemented
229D4×Dic61C2316yes—
230D4×Dic61C23112yescomplemented
231#14519739C2316yes—
232#14519739C23112yescomplemented
233C4×C22⋊D61C23112yes—
234C4×C22⋊D61C23112yescomplemented
235C4×C22⋊D61C23112yescomplemented
236#14519737C23112yes—
237#14519737C23112yescomplemented
238#14519737C23112yescomplemented
239#14519736C2316yescomplemented
240#14519735C23112yescomplemented
241#14519734C23112yescomplemented
242#14519733C2316yescomplemented
243#14519733C2316yescomplemented
244C4⋊C4×D61C23112yes—
245C4⋊C4×D61C2316yes—
246C4⋊C4×D61C23112yes—
247C4⋊C4×D61C2316yes—
248C22⋊C4×D61C2316yes—
249C22⋊C4×D61C2316yes—
250C22⋊C4×D61C23112yes—
251C22⋊C4×D61C23112yes—
252C22⋊C4×D61C23112yes—
253C2×C4×Dic61C2316yescomplemented
254C2×C4×Dic61C2313yescomplemented
255C42×D61C2316yes—
256C42×D61C2313yes—
257C42×D61C2313yes—
258C42×D61C2316yescomplemented
259C42×D61C2313yescomplemented
260C42×D61C2313yescomplemented
261C2×#41×C61C2313yes—
262C2×#41×C61C2311yescharacteristic, complemented
263C23×C4×C61C2312yescomplemented
264C4⋊Q8×C61C2313yescomplemented
265#127×C61C2313yes—
266#126×C61C23112yescomplemented
267#125×C61C2316yescomplemented
268#124×C61C2313yes—
269#124×C61C2316yes—
270#124×C61C2313yescomplemented
271#123×C61C2316yes—
272#123×C61C23112yescomplemented
273#123×C61C2316yescomplemented
274C22⋊Q8×C61C2316yescomplemented
275C22⋊Q8×C61C23112yescomplemented
276#121×C61C2316yes—
277#121×C61C23112yes—
278#121×C61C23112yescomplemented
279#120×C61C2316yes—
280#120×C61C2316yescomplemented
281C4×Q8×C61C2312yescomplemented
282C4×D4×C61C2316yes—
283C4×D4×C61C23112yescomplemented
284#117×C61C2316yescomplemented
285C2×C42×C61C2313yescomplemented
286C24×C61C2412yes—
287C23×D61—44no—
288C23×D61—48no—
289C23×D61C2413yes—
290C23×D61C2416yes—
291C23×D61C2416yes—
292#41×C61—46no—
293#41×C61—42no—
294C2×Q8×C61C2413yes—
295C2×Q8×C61C2411yescharacteristic
296C2×Q8×C61C2412yes—
297C2×D4×C61C2413yes—
298C2×D4×C61C2416yes—
299C2×D4×C61C2413yes—
300C2×D4×C61C2416yes—
301C2×D4×C61C24112yes—
302C22×C4×C61—44no—
303C22×C4×C61C2416yes—
304C22×C4×C61C2413yes—
305C22×C4×C61C2416yes—
306C22×C4×C61C2416yes—
307C2×C22⋊D61C2416yes—
308C2×C22⋊D61C2416yes—
309C2×C22⋊D61C2416yes—
310C2×C22⋊D61C2416yes—
311C2×C22⋊D61C24112yes—
312C2×C22⋊D61C24112yes—
313C2×C22⋊D61C24112yes—
314C22×Dic61—44no—
315C22×Dic61C2416yes—
316C22×Dic61C2413yes—
317C22×Dic61C2416yes—
318C22×Dic61C2416yes—
319#11758226—46no—
320#11758226—42no—
321Q8×D61—44no—
322Q8×D61—46no—
323Q8×D61—42no—
324#11758224—412no—
325#11758224—46no—
326#11758224—46no—
327D4×D61—424no—
328D4×D61—412no—
329D4×D61—412no—
330D4×D61—46no—
331D4×D61—46no—
332#11758222—46no—
333#11758222—412no—
334#11758222—46no—
335C2×D244C2413yes—
336C2×D244C2416yes—
337C2×D244C2413yes—
338C2×D244C2416yes—
339C2×D244C24112yes—
340C2×C4×D61—224no—
341C2×C4×D61—212no—
342C2×C4×D61—412no—
343C2×C4×D61—412no—
344C2×C4×D61—412no—
345C2×C4×D61—412no—
346C2×C4×D61C2416yes—
347C2×C4×D61C2416yes—
348C2×C4×D61C2416yes—
349C2×C4×D61C2413yes—
350C2×C4×D61C2416yes—
351C2×C4×D61C2416yes—
352C2×C4×D61C2413yes—
353C2×C4×D61C2413yes—
354C2×C4×D61C24112yes—
355C2×C4×D61C2416yes—
356C2×C4×D61C2416yes—
357C2×C4×D61C2411yescharacteristic
358C2×Dic122C2413yes—
359C2×Dic122C2416yes—
360C2×Dic122C2413yes—
361C2×Dic122C2416yes—
362C4⋊C4×C61C24112yes—
363C4⋊C4×C61C2416yes—
364C4⋊C4×C61C24112yes—
365C4⋊C4×C61C2416yes—
366C22⋊C4×C61C2416yes—
367C22⋊C4×C61C2416yes—
368C22⋊C4×C61C24112yes—
369C22⋊C4×C61C24112yes—
370C22⋊C4×C61C24112yes—
371C42×C61C2416yes—
372C42×C61C2413yes—
373C42×C61C2413yes—
374C22⋊Dic61C2416yes—
375C22⋊Dic61C2416yes—
376C22⋊Dic61C24112yes—
377C22⋊Dic61C24112yes—
378C22⋊Dic61C24112yes—
379#11758198C24112yes—
380#11758198C24112yes—
381#11758198C24112yes—
382#11758198C24112yes—
383#11758198C24112yes—
384#11758198C24112yes—
385#11758198C24112yes—
386#11758198C24112yes—
387C4⋊Dic61C24112yes—
388C4⋊Dic61C2416yes—
389C4⋊Dic61C24112yes—
390C4⋊Dic61C2416yes—
391#11758196C24112yes—
392#11758196C24112yes—
393#11758196C24112yes—
394#11758196C24112yes—
395#11758196C24112yes—
396#11758196C24112yes—
397C4×Dic61C2416yes—
398C4×Dic61C2416yes—
399C4×Dic61C2416yes—
400C4×Dic61C2416yes—
401C4×Dic61C2413yes—
402C4×Dic61C2413yes—
403C4×Dic61C2416yes—
404C23×C61—42no—
405C23×C61—44no—
406C23×C61C2516yes—
407C23×C61C2513yes—
408C22×D61—212no—
409C22×D61—26no—
410C22×D61—212no—
411C22×D61—224no—
412C22×D61—46no—
413C22×D61—412no—
414C22×D61—432no—
415C22×D61C2516yes—
416C22×D61C2513yes—
417C22×D61C2511yescharacteristic
418Q8×C61—41no—
419Q8×C61—43no—
420Q8×C61—42no—
421D4×C61—43no—
422D4×C61—43no—
423D4×C61—46no—
424D4×C61—46no—
425D4×C61—412no—
426C2×C4×C61—212no—
427C2×C4×C61—26no—
428C2×C4×C61—46no—
429C2×C4×C61—46no—
430C2×C4×C61C2516yes—
431C2×C4×C61C2513yes—
432C2×C4×C61C2516yes—
433C2×C4×C61C2516yes—
434C2×C4×C61C2511yescharacteristic
435C22⋊D61—46no—
436C22⋊D61—46no—
437C22⋊D61—46no—
438C22⋊D61—46no—
439C22⋊D61—412no—
440C22⋊D61—412no—
441C22⋊D61—412no—
442C2×Dic61—212no—
443C2×Dic61—26no—
444C2×Dic61—46no—
445C2×Dic61—46no—
446C2×Dic61C2516yes—
447C2×Dic61C2516yes—
448C2×Dic61C2513yes—
449C2×Dic61C2516yes—
450C2×Dic61C2511yescharacteristic
451D244—43no—
452D244—43no—
453D244—46no—
454D244—46no—
455D244—412no—
456C4×D61—212no—
457C4×D61—26no—
458C4×D61—212no—
459C4×D61—212no—
460C4×D61—212no—
461C4×D61—26no—
462C4×D61—212no—
463C4×D61—26no—
464C4×D61—412no—
465C4×D61—46no—
466C4×D61—46no—
467C4×D61H(5,𝔽2)14yes—
468Dic122—43no—
469Dic122—46no—
470Dic122—43no—
471Dic122—46no—
472C2×#3529—611nomaximal, Sylow
473C22×C61—26no—
474C22×C61—23no—
475C22×C61—26no—
476C22×C61—212no—
477C22×C61—48no—
478C22×C61C2611yescharacteristic
479C2×D61—26no—
480C2×D61—23no—
481C2×D61—26no—
482C2×D61—212no—
483C2×D61—424no—
484C2×D61—412no—
485C2×D61—424no—
486C2×D61C2×H(5,𝔽2)12yes—
487C2×D61#58514yes—
488C4×C61—23no—
489C4×C61—26no—
490C4×C61—26no—
491C4×C61—26no—
492C4×C61C2×H(5,𝔽2)12yes—
493Dic61—23no—
494Dic61—26no—
495Dic61—26no—
496Dic61—26no—
497Dic61C2×H(5,𝔽2)12yes—
498#3529—613no—
499#3529—616no—
500#3529—611no—
501#3529—616no—
502#3529—613no—
503#3529—616no—
504#3529—616no—
505#3529D6111yescharacteristic, direct product factor
506C2×#563—613no—
507C2×#562—616no—
508C2×H(3,𝔽4)—611no—
509C2×#560—616no—
510C2×#532—613no—
511C2×#529—616no—
512C2×#525—616no—
513C2×C61—46no—
514C2×C61—43no—
515C2×C61C22×H(5,𝔽2)11yescharacteristic
516C2×C61C2×#58512yes—
517D61—43no—
518D61—46no—
519D61#352914yesdirect product factor
520C22×#41—613no—
521C22×#41—611no—
522C24×C4—612no—
523#563—616no—
524#563—6112no—
525#563—616no—
526#563—613no—
527#563—616no—
528#563—6112no—
529#563C2×D6113yescomplemented
530#562—616no—
531#562—616no—
532#562—616no—
533#562—6112no—
534#562—6112no—
535#562—6112no—
536#562—6112no—
537#562—6112no—
538#562—6112no—
539#562C2×D6116yescomplemented
540H(3,𝔽4)—616no—
541H(3,𝔽4)—613no—
542H(3,𝔽4)—616no—
543H(3,𝔽4)C2×D6111yescharacteristic, complemented
544#560—616no—
545#560—6112no—
546#560—616no—
547#560—6112no—
548#560—6112no—
549#560—6112no—
550#560—6112no—
551#560—616no—
552#560—6112no—
553#560C2×D6116yescomplemented
554#532—613no—
555#532—613no—
556#532—613no—
557#532—613no—
558#532—613no—
559#532—613no—
560#532—6112no—
561#532—6112no—
562#532—613no—
563#532C2×D6113yescomplemented
564C2×C4⋊Q8—613no—
565C2×#127—613no—
566#529—6112no—
567#529—616no—
568#529—616no—
569#529—6112no—
570#529—616no—
571#529—616no—
572#529—616no—
573#529—616no—
574#529—6112no—
575#529—6112no—
576#529—616no—
577#529C2×D6116yescomplemented
578C2×#126—6112no—
579C2×#125—616no—
580C2×#124—616no—
581C2×#124—613no—
582C2×#124—613no—
583#525—616no—
584#525—616no—
585#525—616no—
586#525—616no—
587#525—6112no—
588#525—6112no—
589#525—616no—
590#525—616no—
591#525—6112no—
592#525—6112no—
593#525—616no—
594#525C2×D6116yescomplemented
595C2×#123—616no—
596C2×#123—616no—
597C2×#123—6112no—
598C2×C22⋊Q8—6112no—
599C2×C22⋊Q8—616no—
600C2×#121—6112no—
601C2×#121—616no—
602C2×#121—6112no—
603C2×#120—616no—
604C2×#120—616no—
605C2×C4×Q8—612no—
606C2×C4×D4—616no—
607C2×C4×D4—6112no—
608C2×#117—616no—
609C22×C42—613no—
610C61C2×#352911yescharacteristic, complemented, Sylow
611C25—612no—
612C2×#41—613no—
613C2×#41—611no—
614C2×#41—616no—
615C2×#41—613no—
616C2×#41—613no—
617C2×#41—616no—
618C2×#41—613no—
619C2×#41—613no—
620C2×#41—24412no—
621C2×#41—2444no—
622C2×#41C22×D6113yes—
623C2×#41C22×D6111yescharacteristic, complemented
624C22×Q8—612no—
625C22×Q8—613no—
626C22×Q8—611no—
627C22×D4—616no—
628C22×D4—6112no—
629C22×D4—613no—
630C22×D4—616no—
631C22×D4—613no—
632C23×C4—612no—
633C23×C4—616no—
634C23×C4—613no—
635C23×C4—616no—
636C23×C4—616no—
637C23×C4—616no—
638C23×C4—616no—
639C23×C4—2448no—
640C23×C4C22×D6112yescomplemented
641C4⋊Q8—613no—
642C4⋊Q8—613no—
643C4⋊Q8—6112no—
644C4⋊Q8—613no—
645C4⋊Q8C22×D6113yescomplemented
646#127—613no—
647#127—613no—
648#127—6112no—
649#127—613no—
650#127C22×D6113yes—
651#126—6112no—
652#126—6112no—
653#126—6112no—
654#126—6112no—
655#126—6112no—
656#126—6112no—
657#126—6112no—
658#126C22×D61112yescomplemented
659#125—6112no—
660#125—6112no—
661#125—616no—
662#125—616no—
663#125—616no—
664#125C22×D6116yescomplemented
665#124—616no—
666#124—613no—
667#124—613no—
668#124—616no—
669#124—613no—
670#124—613no—
671#124—6112no—
672#124—6112no—
673#124—6112no—
674#124—6112no—
675#124—616no—
676#124—613no—
677#124—613no—
678#124C22×D6116yes—
679#124C22×D6113yes—
680#124C22×D6113yescomplemented
681#123—616no—
682#123—616no—
683#123—6112no—
684#123—616no—
685#123—616no—
686#123—6112no—
687#123—6112no—
688#123—6112no—
689#123—6112no—
690#123—6112no—
691#123—6112no—
692#123—616no—
693#123—6112no—
694#123—616no—
695#123—6112no—
696#123—6112no—
697#123—6112no—
698#123C22×D6116yes—
699#123C22×D6116yescomplemented
700#123C22×D61112yescomplemented
701C22⋊Q8—6112no—
702C22⋊Q8—616no—
703C22⋊Q8—6112no—
704C22⋊Q8—616no—
705C22⋊Q8—6112no—
706C22⋊Q8—6112no—
707C22⋊Q8—6112no—
708C22⋊Q8—6112no—
709C22⋊Q8—616no—
710C22⋊Q8—6112no—
711C22⋊Q8—6112no—
712C22⋊Q8—6112no—
713C22⋊Q8C22×D61112yescomplemented
714C22⋊Q8C22×D6116yescomplemented
715#121—6112no—
716#121—6112no—
717#121—6112no—
718#121—616no—
719#121—6112no—
720#121—6112no—
721#121—6112no—
722#121—6112no—
723#121—6112no—
724#121—616no—
725#121—6112no—
726#121—6112no—
727#121—616no—
728#121—6112no—
729#121—6112no—
730#121—6112no—
731#121—6112no—
732#121—6112no—
733#121—6112no—
734#121C22×D61112yes—
735#121C22×D6116yes—
736#121C22×D61112yescomplemented
737#120—616no—
738#120—616no—
739#120—616no—
740#120—6112no—
741#120—616no—
742#120—6112no—
743#120—6112no—
744#120—616no—
745#120—6112no—
746#120—616no—
747#120C22×D6116yes—
748#120C22×D6116yescomplemented
749C4×Q8—612no—
750C4×Q8—616no—
751C4×Q8—616no—
752C4×Q8C22×D6112yescomplemented
753C4×D4—616no—
754C4×D4—6112no—
755C4×D4—6112no—
756C4×D4—6112no—
757C4×D4—6112no—
758C4×D4—616no—
759C4×D4—6112no—
760C4×D4—6112no—
761C4×D4—6112no—
762C4×D4—6112no—
763C4×D4—616no—
764C4×D4—6112no—
765C4×D4C22×D6116yes—
766C4×D4C22×D61112yescomplemented
767#117—616no—
768#117—6112no—
769#117—616no—
770#117—616no—
771#117—6112no—
772#117C22×D6116yescomplemented
773C2×C4⋊C4—6112no—
774C2×C4⋊C4—6112no—
775C2×C4⋊C4—616no—
776C2×C4⋊C4—616no—
777C2×C22⋊C4—616no—
778C2×C22⋊C4—616no—
779C2×C22⋊C4—6112no—
780C2×C22⋊C4—6112no—
781C2×C22⋊C4—6112no—
782C2×C42—616no—
783C2×C42—613no—
784C2×C42—616no—
785C2×C42—613no—
786C2×C42—613no—
787C2×C42—613no—
788C2×C42—613no—
789C2×C42—616no—
790C2×C42C22×D6113yescomplemented
791C24—616no—
792C24—613no—
793C24—616no—
794C24—2444no—
795C24—2448no—
796C24C23×D6112yes—
797#41—46no—
798#41—42no—
799#41—24412no—
800#41—2446no—
801#41—2446no—
802#41—24412no—
803#41—2446no—
804#41—2446no—
805#41—2446no—
806#41—2442no—
807C2×Q8—616no—
808C2×Q8—616no—
809C2×Q8—613no—
810C2×Q8—613no—
811C2×Q8—2446no—
812C2×Q8—2442no—
813C2×Q8—2444no—
814C2×Q8C23×D6112yes—
815C2×Q8C23×D6113yes—
816C2×Q8C23×D6111yescharacteristic
817C2×D4—6112no—
818C2×D4—6112no—
819C2×D4—6112no—
820C2×D4—616no—
821C2×D4—616no—
822C2×D4—616no—
823C2×D4—616no—
824C2×D4—616no—
825C2×D4—6112no—
826C2×D4—613no—
827C2×D4—616no—
828C2×D4—613no—
829C2×D4—24412no—
830C2×D4—2446no—
831C2×D4—2446no—
832C2×D4—24424no—
833C2×D4—24412no—
834C2×D4C23×D6116yes—
835C2×D4C23×D61112yes—
836C2×D4C23×D6113yes—
837C2×D4C23×D6116yes—
838C2×D4C23×D6113yes—
839C22×C4—44no—
840C22×C4—611no—
841C22×C4—613no—
842C22×C4—616no—
843C22×C4—616no—
844C22×C4—616no—
845C22×C4—616no—
846C22×C4—616no—
847C22×C4—613no—
848C22×C4—613no—
849C22×C4—616no—
850C22×C4—616no—
851C22×C4—613no—
852C22×C4—616no—
853C22×C4—616no—
854C22×C4—616no—
855C22×C4—6112no—
856C22×C4—12224no—
857C22×C4—12212no—
858C22×C4—24412no—
859C22×C4—24412no—
860C22×C4—24412no—
861C22×C4—24412no—
862C22×C4—2444no—
863C22×C4C23×D6113yes—
864C22×C4C23×D6116yes—
865C22×C4C23×D6116yes—
866C22×C4C23×D6116yes—
867C4⋊C4—6112no—
868C4⋊C4—6112no—
869C4⋊C4—6112no—
870C4⋊C4—6112no—
871C4⋊C4—6112no—
872C4⋊C4—6112no—
873C4⋊C4—6112no—
874C4⋊C4—6112no—
875C4⋊C4—616no—
876C4⋊C4—616no—
877C4⋊C4C23×D61112yes—
878C4⋊C4C23×D6116yes—
879C4⋊C4C23×D61112yes—
880C4⋊C4C23×D6116yes—
881C22⋊C4—616no—
882C22⋊C4—616no—
883C22⋊C4—6112no—
884C22⋊C4—6112no—
885C22⋊C4—6112no—
886C22⋊C4—6112no—
887C22⋊C4—6112no—
888C22⋊C4—6112no—
889C22⋊C4—6112no—
890C22⋊C4—6112no—
891C22⋊C4—6112no—
892C22⋊C4—6112no—
893C22⋊C4—6112no—
894C22⋊C4C23×D6116yes—
895C22⋊C4C23×D6116yes—
896C22⋊C4C23×D61112yes—
897C22⋊C4C23×D61112yes—
898C22⋊C4C23×D61112yes—
899C42—616no—
900C42—616no—
901C42—613no—
902C42—616no—
903C42—613no—
904C42—616no—
905C42—616no—
906C42C23×D6113yes—
907C42C23×D6113yes—
908C42C23×D6116yes—
909C23—42no—
910C23—44no—
911C23—611no—
912C23—616no—
913C23—613no—
914C23—12212no—
915C23—1226no—
916C23—12212no—
917C23—12224no—
918C23—2446no—
919C23—24412no—
920C23—24432no—
921C23C24×D6116yes—
922C23C24×D6113yes—
923Q8—42no—
924Q8—43no—
925Q8—41no—
926Q8—2446no—
927Q8—2446no—
928Q8—2443no—
929Q8—2443no—
930D4—412no—
931D4—46no—
932D4—46no—
933D4—43no—
934D4—43no—
935D4—24412no—
936D4—2446no—
937D4—2446no—
938D4—2443no—
939D4—2443no—
940D4—24412no—
941D4—24412no—
942D4—24412no—
943D4—2446no—
944D4—2446no—
945D4—2446no—
946D4—2446no—
947C2×C4—212no—
948C2×C4—26no—
949C2×C4—46no—
950C2×C4—46no—
951C2×C4—611no—
952C2×C4—614no—
953C2×C4—616no—
954C2×C4—616no—
955C2×C4—613no—
956C2×C4—616no—
957C2×C4—12212no—
958C2×C4—1226no—
959C2×C4—12212no—
960C2×C4—1226no—
961C2×C4—12212no—
962C2×C4—12212no—
963C2×C4—12212no—
964C2×C4—1226no—
965C2×C4—12212no—
966C2×C4—1226no—
967C2×C4—2446no—
968C2×C4—2446no—
969C2×C4—24412no—
970C2×C4—2446no—
971C2×C4—2446no—
972C2×C4C24×D6116yes—
973C2×C4C24×D6116yes—
974C2×C4C24×D6113yes—
975C2×C4C24×D6116yes—
976C2×C4C24×D6111yescharacteristic
977C22—26no—
978C22—23no—
979C22—26no—
980C22—212no—
981C22—48no—
982C22—612no—
983C22—614no—
984C22—1226no—
985C22—1223no—
986C22—1226no—
987C22—12212no—
988C22—24412no—
989C22—24424no—
990C22—24424no—
991C22C25×D6111yescharacteristic
992C4—26no—
993C4—23no—
994C4—26no—
995C4—26no—
996C4—612no—
997C4—1226no—
998C4—1223no—
999C4—1226no—
1000C4—1226no—
1001C4H(5,𝔽2)×D6112yes—
1002C2—46no—
1003C2—43no—
1004C2—614no—
1005C2—2446no—
1006C2—2443no—
1007C2C2×H(5,𝔽2)×D6111yescharacteristic
1008C2#585×D6112yes—
subgroupG/H
centerC2×C4C24×D61
commutator, socle, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC61×#3529C2
hypercenter#3529D61
hypocenterC61C2×#3529
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ #3529

Complements

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

NH ≅ G/Ntype
1. #21459960C2semidirect
2. #21459959C2semidirect
3. #21459958C2semidirect
4. #21459957C2semidirect
5. #21459956C2semidirect
6. #21459955C2semidirect
7. #21459954C2semidirect
8. #563×D61C2semidirect
9. #562×D61C2semidirect
10. H(3,𝔽4)×D61C2semidirect
11. #560×D61C2semidirect
12. #532×D61C2semidirect
13. #529×D61C2semidirect
14. #525×D61C2semidirect
15. C61×#3529C2semidirect
17. C2×#41×D61C22semidirect
18. C23×C4×D61C22semidirect
19. #16840516C22semidirect
20. #16840515C22semidirect
21. #16840514C22semidirect
22. #16840513C22semidirect
23. #16840512C22semidirect
24. #16840511C22semidirect
25. #16840510C22semidirect
26. #16840509C22semidirect
27. #16840509C22semidirect
28. #16840508C22semidirect
29. #16840508C22semidirect
30. #16840507C22semidirect
31. #16840507C22semidirect
32. #16840506C22semidirect
33. #16840506C22semidirect
34. #16840505C22semidirect
35. #16840504C22semidirect
36. #16840504C22semidirect
37. #16840503C22semidirect
38. #16840502C22semidirect
39. #16840502C22semidirect
40. #16840501C22semidirect
41. #16840501C22semidirect
42. #16840500C22semidirect
43. #16840500C22semidirect
44. #16840500C22semidirect
45. #16840499C22semidirect
46. #16840313C22semidirect
47. #16840312C22semidirect
48. #16840311C22semidirect
49. #16840311C22semidirect
50. #16840310C22semidirect
51. #16840309C22semidirect
52. #16840308C22semidirect
53. #16840308C22semidirect
54. #16840307C22semidirect
55. C4⋊Q8×D61C22semidirect
57. #16840299C22semidirect
58. #16840298C22semidirect
59. #16840297C22semidirect
60. #16840296C22semidirect
61. #16840295C22semidirect
62. #16840294C22semidirect
63. #16840293C22semidirect
64. #16840292C22semidirect
65. #16840291C22semidirect
66. #16840290C22semidirect
67. #16840289C22semidirect
68. #126×D61C22semidirect
69. #125×D61C22semidirect
72. #124×D61C22semidirect
73. #16840275C22semidirect
74. #16840274C22semidirect
75. #16840273C22semidirect
76. #16840272C22semidirect
77. #16840271C22semidirect
78. #16840271C22semidirect
79. #16840270C22semidirect
80. #16840270C22semidirect
81. #16840269C22semidirect
82. #16840268C22semidirect
83. #16840268C22semidirect
85. #123×D61C22semidirect
86. #123×D61C22semidirect
87. C22⋊Q8×D61C22semidirect
88. C22⋊Q8×D61C22semidirect
91. #121×D61C22semidirect
93. #120×D61C22semidirect
94. C4×Q8×D61C22semidirect
96. C4×D4×D61C22semidirect
97. #117×D61C22semidirect
98. C2×C42×D61C22semidirect
99. C61×#563C22semidirect
100. C61×#562C22semidirect
101. C61×H(3,𝔽4)C22semidirect
102. C61×#560C22semidirect
103. C61×#532C22semidirect
104. C61×#529C22semidirect
105. C61×#525C22semidirect
108. C2×#11758226C23semidirect
111. C2×#11758222C23semidirect
114. C2×#11758224C23semidirect
125. C23×Dic61C23semidirect
131. C22×C4×D61C23semidirect
132. C22×C4×D61C23semidirect
133. #14519777C23semidirect
134. #14519776C23semidirect
135. #14519775C23semidirect
136. #14519775C23semidirect
141. #14519772C23semidirect
142. #14519772C23semidirect
143. #14519772C23semidirect
144. #14519771C23semidirect
145. #14519770C23semidirect
146. #14519770C23semidirect
147. #14519770C23semidirect
148. #14519769C23semidirect
149. #14519768C23semidirect
150. #14519768C23semidirect
151. #14519767C23semidirect
152. #14519767C23semidirect
155. #14519766C23semidirect
158. #14519765C23semidirect
161. #14519764C23semidirect
165. #14519763C23semidirect
167. #14519762C23semidirect
168. #14519762C23semidirect
169. #14519762C23semidirect
171. #14519761C23semidirect
172. #14519761C23semidirect
174. #14519760C23semidirect
175. #14519760C23semidirect
177. #14519759C23semidirect
178. #14519759C23semidirect
179. #14519759C23semidirect
181. #14519758C23semidirect
182. #14519758C23semidirect
183. #14519757C23semidirect
184. #14519757C23semidirect
185. #14519756C23semidirect
186. #14519756C23semidirect
187. #14519755C23semidirect
188. #14519755C23semidirect
189. #14519755C23semidirect
190. #14519754C23semidirect
191. #14519754C23semidirect
192. #14519754C23semidirect
193. #14519753C23semidirect
194. #14519753C23semidirect
197. #14519752C23semidirect
200. #14519751C23semidirect
204. #14519750C23semidirect
205. #14519750C23semidirect
209. #14519749C23semidirect
210. #14519749C23semidirect
213. #14519748C23semidirect
216. #14519747C23semidirect
217. #14519747C23semidirect
219. #14519746C23semidirect
222. #14519745C23semidirect
223. #14519745C23semidirect
224. Q8×Dic61C23semidirect
225. C4×Dic122C23semidirect
226. #14519742C23semidirect
228. C4×D244C23semidirect
230. D4×Dic61C23semidirect
232. #14519739C23semidirect
234. C4×C22⋊D61C23semidirect
235. C4×C22⋊D61C23semidirect
237. #14519737C23semidirect
238. #14519737C23semidirect
239. #14519736C23semidirect
240. #14519735C23semidirect
241. #14519734C23semidirect
242. #14519733C23semidirect
243. #14519733C23semidirect
253. C2×C4×Dic61C23semidirect
254. C2×C4×Dic61C23semidirect
258. C42×D61C23semidirect
259. C42×D61C23semidirect
260. C42×D61C23semidirect
262. C2×#41×C61C23semidirect
263. C23×C4×C61C23semidirect
264. C4⋊Q8×C61C23semidirect
266. #126×C61C23semidirect
267. #125×C61C23semidirect
270. #124×C61C23semidirect
272. #123×C61C23semidirect
273. #123×C61C23semidirect
274. C22⋊Q8×C61C23semidirect
275. C22⋊Q8×C61C23semidirect
278. #121×C61C23semidirect
280. #120×C61C23semidirect
281. C4×Q8×C61C23semidirect
283. C4×D4×C61C23semidirect
284. #117×C61C23semidirect
285. C2×C42×C61C23semidirect
505. #3529D61direct (N × H)
519. D61#3529direct (N × H)
529. #563C2×D61semidirect
539. #562C2×D61semidirect
543. H(3,𝔽4)C2×D61semidirect
553. #560C2×D61semidirect
563. #532C2×D61semidirect
577. #529C2×D61semidirect
594. #525C2×D61semidirect
610. C61C2×#3529semidirect
623. C2×#41C22×D61semidirect
640. C23×C4C22×D61semidirect
645. C4⋊Q8C22×D61semidirect
658. #126C22×D61semidirect
664. #125C22×D61semidirect
680. #124C22×D61semidirect
699. #123C22×D61semidirect
700. #123C22×D61semidirect
713. C22⋊Q8C22×D61semidirect
714. C22⋊Q8C22×D61semidirect
736. #121C22×D61semidirect
748. #120C22×D61semidirect
752. C4×Q8C22×D61semidirect
766. C4×D4C22×D61semidirect
772. #117C22×D61semidirect
790. C2×C42C22×D61semidirect

Maximal subgroups

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

subgroupindex
#214599602
#214599592
#214599582
#214599572
#214599562
#214599552
#214599542
#563×D612
#562×D612
H(3,𝔽4)×D612
#560×D612
#532×D612
#529×D612
#525×D612
C61×#35292
C2×#352961