Finite Group Databasebeta

← #30588407

Subgroups — #30588407

Order 15616.

7856 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459904C212yesmaximal, complemented
2#21459851C216yesmaximal, complemented
3#21459825C212yesmaximal, complemented
4#21459780C216yesmaximal, complemented
5#21459730C213yesmaximal, complemented
6#21459695C213yesmaximal, complemented
7#21459638C211yesmaximal, characteristic, complemented
8#21459597C211yesmaximal, characteristic, complemented
9#21459554C216yesmaximal, complemented
10#21459488C212yesmaximal, complemented
11#21459445C212yesmaximal, complemented
12#21459429C216yesmaximal, complemented
13#21459414C212yesmaximal, complemented
14D4×#11758222C216yesmaximal, complemented
15#21459235C216yesmaximal, complemented
16#21459115C213yesmaximal, complemented
17C2×#16840312C213yesmaximal, complemented
18C4×#14519823C212yesmaximal, complemented
19C2×C4×#41×C61C211yesmaximal, characteristic, complemented
20C2×#14519823C2212yes—
21C22×#11758222C2216yescomplemented
22#16840497C2216yescomplemented
23#16840497C2216yescomplemented
24Q8×Dic122C2212yescomplemented
25#16840491C2212yescomplemented
26#16840485C2216yescomplemented
27#16840477C2216yescomplemented
28#16840475C22112yescomplemented
29#16840472C2216yescomplemented
30#16840469C2216yescomplemented
31#16840460C22112yescomplemented
32#16840458C22112yescomplemented
33#16840456C22112yescomplemented
34#16840436C22124yescomplemented
35#16840434C2212yescomplemented
36#16840434C2212yescomplemented
37#16840433C2216yescomplemented
38#16840433C2216yescomplemented
39#16840431C2214yescomplemented
40D4×Dic122C2216yescomplemented
41#16840423C2214yescomplemented
42#16840421C22112yescomplemented
43#16840417C2216yescomplemented
44#16840413C22112yescomplemented
45#16840408C22112yescomplemented
46#16840408C22112yescomplemented
47#16840402C22124yescomplemented
48#16840400C22112yescomplemented
49D4×D244C2216yescomplemented
50D4×D244C2216yescomplemented
51D4×C22⋊D61C22112yescomplemented
52#16840390C2216yescomplemented
53#16840384C22112yescomplemented
54#16840383C22112yescomplemented
55#16840367C22112yescomplemented
56#16840363C22112yescomplemented
57#16840345C22124yescomplemented
58#16840340C2216yescomplemented
59#16840331C2216yescomplemented
60#16840326C2216yescomplemented
61#16840319C2213yescomplemented
62#16840319C2211yescharacteristic, complemented
63#16840319C2213yescomplemented
64#16840312C2213yescomplemented
65#16840312C2216yescomplemented
66#16840312C2216yescomplemented
67#16840312C2216yescomplemented
68#16840312C2216yescomplemented
69#16840312C2216yescomplemented
70#16840312C2216yescomplemented
71#16840312C2213yescomplemented
72#16840312C2216yescomplemented
73#16840312C2213yescomplemented
74#16840309C22112yescomplemented
75C2×#14519777C2213yescomplemented
76C2×#14519774C2213yescomplemented
77#16840299C22112yescomplemented
78#16840296C2216yescomplemented
79#16840296C2216yescomplemented
80#16840296C2216yescomplemented
81#16840296C2216yescomplemented
82#16840296C2216yescomplemented
83#16840296C2216yescomplemented
84C2×#14519765C2216yescomplemented
85#16840273C2216yescomplemented
86#16840273C2216yescomplemented
87#16840273C2216yescomplemented
88#16840271C22124yescomplemented
89C2×#14519751C2216yescomplemented
90C2×#14519751C2216yescomplemented
91#16840245C2212yes—
92#16840244C2214yescomplemented
93#16840242C2216yescomplemented
94#16840236C2216yescomplemented
95#16840234C22112yescomplemented
96C4×#11758226C2214yescomplemented
97C4×#11758222C2216yescomplemented
98C4×#11758222C2216yescomplemented
99C4×#11758222C2216yescomplemented
100C2×C4×D244C2216yescomplemented
101C2×C4×D244C2216yescomplemented
102C4×D4×D61C22112yescomplemented
103C22×#41×C61C2211yescharacteristic
104C4×#41×C61C2211yescharacteristic
105C4×#41×C61C2211yescharacteristic
106C4×#41×C61C2213yescomplemented
107C4×#41×C61C2213yescomplemented
108C4×#41×C61C2213yescomplemented
109C4×#41×C61C2211yescharacteristic, complemented
110C4×#41×C61C2213yescomplemented
111C4×#41×C61C2211yescharacteristic, complemented
112C2×C4×Q8×C61C2211yescharacteristic, complemented
113C2×C4×Q8×C61C2211yescharacteristic, complemented
114C2×C4×D4×C61C2213yescomplemented
115C2×C4×D4×C61C2213yescomplemented
116C2×#117×C61C2213yescomplemented
117C22×C42×C61C2213yescomplemented
118#14519823—216no—
119C2×#11758226C2314yes—
120C2×#11758222—424no—
121C2×#11758222C2316yes—
122C2×#11758222C2316yes—
123C2×#11758222C2316yes—
124C2×#11758222C23112yes—
125C2×#11758222C23112yes—
126C2×#11758222C23112yes—
127C22×Dic122C2316yes—
128C22×D244C2316yes—
129C22×D244C2316yes—
130C22×D244C2316yes—
131C22×C22⋊D61C23112yes—
132C2×D4×D61C23112yes—
133C22×C4×D61C23112yes—
134#14519777C2316yes—
135#14519777C2316yes—
136#14519777C2313yes—
137#14519777C2316yes—
138#14519777C2311yescharacteristic
139#14519777C2311yescharacteristic
140#14519776C23112yes—
141#14519774C2316yes—
142#14519774C2316yes—
143#14519774C2313yes—
144#14519774C2316yes—
145#14519773C23112yes—
146#14519772C23124yes—
147#14519771C23112yes—
148#14519771C23112yes—
149#14519769C2316yes—
150#14519769C2312yes—
151#14519769C2316yes—
152#14519768C23112yes—
153#14519766C23112yes—
154#14519765C23112yes—
155#14519765C23112yes—
156#14519765C2316yes—
157#14519765C2316yes—
158#14519765C23112yes—
159#14519765C2316yes—
160#14519763C23124yes—
161#14519762C23124yes—
162#14519762C23124yes—
163#14519760C23112yes—
164#14519760C23112yes—
165#14519760C23112yes—
166#14519759C23124yes—
167#14519756C2316yes—
168#14519756C2312yes—
169#14519756C2312yes—
170#14519756C2316yes—
171#14519756C2316yes—
172#14519756C2316yes—
173#14519755C23124yes—
174#14519754C23124yes—
175#14519753C23112yes—
176#14519752C23112yes—
177#14519752C23112yes—
178#14519751C23112yes—
179#14519751C2316yes—
180#14519751C23112yes—
181#14519751C23112yes—
182#14519751C23112yes—
183#14519751C2316yes—
184#14519751C2316yes—
185#14519751C23112yes—
186#14519751C23112yes—
187#14519751C2316yes—
188#14519751C2316yes—
189#14519751C2316yes—
190#14519750C23124yes—
191#14519750C23124yes—
192#14519749C23124yes—
193#14519748C23112yes—
194#14519747C23124yes—
195#14519746C23112yes—
196#14519745C23124yes—
197Q8×Dic61C2314yes—
198C4×Dic122C2316yes—
199C4×Dic122C2316yes—
200C4×Dic122C2312yes—
201C4×Dic122C2312yes—
202C4×Dic122C2316yes—
203C4×Dic122C2316yes—
204C4×D244C23112yes—
205C4×D244C23112yes—
206C4×D244C2316yes—
207C4×D244C23112yes—
208C4×D244C2316yes—
209C4×D244C2316yes—
210C4×D244C23112yes—
211C4×D244C23112yes—
212C4×D244C23112yes—
213C4×D244C2316yes—
214C4×D244C2316yes—
215C4×D244C2316yes—
216D4×Dic61C23112yes—
217#14519739C23112yes—
218#14519739C23112yes—
219C4×C22⋊D61C23112yes—
220C4×C22⋊D61C23112yes—
221C4×C22⋊D61C23112yes—
222C4×C22⋊D61C23112yes—
223C4×C22⋊D61C23112yes—
224C4×C22⋊D61C23112yes—
225#14519737C23124yes—
226#14519736C2316yes—
227#14519736C2312yes—
228#14519736C2316yes—
229#14519735C23112yes—
230#14519734C23112yes—
231#14519734C23112yes—
232#14519734C23112yes—
233C2×C4⋊Dic61C2316yes—
234C2×C4⋊Dic61C2316yes—
235C4⋊C4×D61C23112yes—
236C2×#11758198C23112yes—
237C2×#11758198C23112yes—
238C22⋊C4×D61C23124yes—
239C42×D61C23112yes—
240C2×#41×C61—28no—
241C2×#41×C61C2313yes—
242C2×#41×C61C2313yes—
243C2×#41×C61C2311yescharacteristic
244C2×#41×C61C2311yescharacteristic
245C22×Q8×C61C2311yescharacteristic
246C22×D4×C61C2313yes—
247C23×C4×C61C2313yes—
248C23×C4×C61C2313yes—
249C23×C4×C61C2313yes—
250C4×Q8×C61C2313yes—
251C4×Q8×C61C2313yes—
252C4×Q8×C61C2311yescharacteristic
253C4×Q8×C61C2311yescharacteristic
254C4×Q8×C61C2311yescharacteristic
255C4×Q8×C61C2311yescharacteristic
256C4×Q8×C61C2313yes—
257C4×Q8×C61C2313yes—
258C4×D4×C61C2316yes—
259C4×D4×C61C2313yes—
260C4×D4×C61C2313yes—
261C4×D4×C61C2313yes—
262C4×D4×C61C2313yes—
263C4×D4×C61C2316yes—
264C4×D4×C61C2313yes—
265C4×D4×C61C2316yes—
266C4×D4×C61C2313yes—
267C4×D4×C61C2313yes—
268C4×D4×C61C2316yes—
269C4×D4×C61C2313yes—
270#117×C61C2313yes—
271#117×C61C2313yes—
272#117×C61C2313yes—
273#117×C61C2313yes—
274#117×C61C2316yes—
275#117×C61C2316yes—
276C2×C4⋊C4×C61C2313yes—
277C2×C4⋊C4×C61C2313yes—
278C2×C22⋊C4×C61C2316yes—
279C2×C42×C61C2313yes—
280C2×C42×C61C2313yes—
281C2×C42×C61C2313yes—
282C2×C42×C61C2313yes—
283C2×C42×C61C2313yes—
284C2×C42×C61C2313yes—
285C2×C42×C61C2313yes—
286C2×C42×C61C2313yes—
287C2×C42×C61C2313yes—
288C2×C42×C61C2313yes—
289C2×C42×C61C2311yescharacteristic
290C2×C42×C61C2313yes—
291C24×C61C2413yes—
292C23×D61C24112yes—
293#41×C61—24no—
294#41×C61—212no—
295#41×C61—212no—
296#41×C61#4118yescomplemented
297C2×Q8×C61—24no—
298C2×Q8×C61C2413yes—
299C2×Q8×C61C2411yescharacteristic
300C2×D4×C61—212no—
301C2×D4×C61C2416yes—
302C2×D4×C61C2413yes—
303C2×D4×C61C2413yes—
304C22×C4×C61—212no—
305C22×C4×C61—212no—
306C22×C4×C61—46no—
307C22×C4×C61C2413yes—
308C22×C4×C61C2413yes—
309C22×C4×C61C2413yes—
310C22×C4×C61C2413yes—
311C22×C4×C61C2413yes—
312C22×C4×C61C2413yes—
313C22×C4×C61C2413yes—
314C22×C4×C61C2411yescharacteristic
315C22×C4×C61C2411yescharacteristic
316C22×C4×C61C2413yes—
317C22×C4×C61C2413yes—
318C22×C4×C61C2413yes—
319C22×C4×C61C2413yes—
320C22×C4×C61C2413yes—
321C22×C4×C61C2413yes—
322C22×C4×C61C2413yes—
323C22×C4×C61C2413yes—
324C22×C4×C61C2411yescharacteristic
325C2×C22⋊D61—424no—
326C2×C22⋊D61C24112yes—
327C2×C22⋊D61C24112yes—
328C2×C22⋊D61C24124yes—
329C2×C22⋊D61C24112yes—
330C22×Dic61C24112yes—
331#11758226—216no—
332D4×D61—248no—
333#11758222—224no—
334#11758222—224no—
335#11758222—424no—
336#11758222—412no—
337#11758222—424no—
338#11758222—424no—
339C2×D244—224no—
340C2×D244—412no—
341C2×D244—412no—
342C2×D244C24112yes—
343C2×D244C2416yes—
344C2×D244C2416yes—
345C2×D244C2416yes—
346C2×D244C24112yes—
347C2×D244C24112yes—
348C2×C4×D61—424no—
349C2×C4×D61C24112yes—
350C2×C4×D61C24112yes—
351C2×C4×D61C24124yes—
352C2×C4×D61C24112yes—
353C2×Dic122—412no—
354C2×Dic122C2416yes—
355C2×Dic122C2412yes—
356C2×Dic122C2412yes—
357C2×Dic122C24112yes—
358C4⋊C4×C61C2413yes—
359C4⋊C4×C61C2413yes—
360C4⋊C4×C61C2413yes—
361C4⋊C4×C61C2413yes—
362C4⋊C4×C61C2416yes—
363C4⋊C4×C61C2416yes—
364C22⋊C4×C61C2416yes—
365C22⋊C4×C61C2416yes—
366C22⋊C4×C61C2416yes—
367C22⋊C4×C61C2416yes—
368C42×C61C2411yescharacteristic
369C42×C61C2411yescharacteristic
370C42×C61C2411yescharacteristic
371C42×C61C2411yescharacteristic
372C42×C61C2413yes—
373C42×C61C2413yes—
374C42×C61C2413yes—
375C42×C61C2413yes—
376C42×C61C2413yes—
377C42×C61C2413yes—
378C42×C61C2413yes—
379C42×C61C2413yes—
380C42×C61C2413yes—
381C42×C61C2413yes—
382C42×C61C2413yes—
383C42×C61C2413yes—
384C22⋊Dic61C24112yes—
385C22⋊Dic61C2414yes—
386C22⋊Dic61C24112yes—
387#11758198C24112yes—
388#11758198C24124yes—
389#11758198C24112yes—
390#11758198C24112yes—
391#11758198C24124yes—
392#11758198C24112yes—
393#11758198C24112yes—
394#11758198C24112yes—
395C4⋊Dic61C24112yes—
396C4⋊Dic61C2416yes—
397C4⋊Dic61C2416yes—
398C4⋊Dic61C24112yes—
399C4⋊Dic61C2412yes—
400C4⋊Dic61C2412yes—
401C4⋊Dic61C2412yes—
402C4⋊Dic61C2412yes—
403#11758196C24112yes—
404#11758196C2414yes—
405#11758196C2414yes—
406#11758196C24112yes—
407#11758196C24112yes—
408#11758196C24112yes—
409C4×Dic61C2414yes—
410C4×Dic61C24112yes—
411C4×Dic61C24112yes—
412C23×C61—26no—
413C23×C61—26no—
414C23×C61—43no—
415C23×C61C2513yes—
416C23×C61C2513yes—
417C23×C61C2511yescharacteristic
418C22×D61—224no—
419C22×D61—412no—
420C22×D61—412no—
421C22×D61C25112yes—
422Q8×C61—26no—
423Q8×C61C2×#4114yescomplemented
424D4×C61—212no—
425D4×C61—26no—
426D4×C61C2×#41112yescomplemented
427C2×C4×C61—26no—
428C2×C4×C61—26no—
429C2×C4×C61—22no—
430C2×C4×C61—26no—
431C2×C4×C61—26no—
432C2×C4×C61—26no—
433C2×C4×C61—26no—
434C2×C4×C61—26no—
435C2×C4×C61—26no—
436C2×C4×C61—26no—
437C2×C4×C61—26no—
438C2×C4×C61—26no—
439C2×C4×C61—22no—
440C2×C4×C61—43no—
441C2×C4×C61—43no—
442C2×C4×C61—43no—
443C2×C4×C61C2×#41112yescomplemented
444C2×C4×C61H(5,𝔽2)14yescomplemented
445C2×C4×C61C2513yes—
446C2×C4×C61C2513yes—
447C2×C4×C61C2511yescharacteristic
448C2×C4×C61C2511yescharacteristic
449C2×C4×C61C2513yes—
450C2×C4×C61C2513yes—
451C2×C4×C61C2513yes—
452C2×C4×C61C2513yes—
453C2×C4×C61C2511yescharacteristic
454C2×C4×C61C2511yescharacteristic
455C2×C4×C61C2511yescharacteristic
456C2×C4×C61C2511yescharacteristic
457C22⋊D61—224no—
458C22⋊D61—224no—
459C22⋊D61—424no—
460C22⋊D61—412no—
461C2×Dic61—412no—
462C2×Dic61C2514yes—
463C2×Dic61C2514yes—
464C2×Dic61C25112yes—
465D244—212no—
466D244—224no—
467D244—212no—
468D244—212no—
469D244—412no—
470D244—412no—
471C4×D61—224no—
472C4×D61—224no—
473C4×D61—424no—
474C4×D61—412no—
475Dic122—24no—
476Dic122—212no—
477Dic122—24no—
478Dic122—412no—
479#62800—611nomaximal, Sylow
480C22×C61—21no—
481C22×C61—23no—
482C22×C61—21no—
483C22×C61—23no—
484C22×C61—23no—
485C22×C61—23no—
486C22×C61—23no—
487C22×C61—412no—
488C22×C61C22×#4116yes—
489C22×C61C2×H(5,𝔽2)12yes—
490C22×C61C2611yescharacteristic
491C2×D61—212no—
492C2×D61—212no—
493C2×D61—212no—
494C2×D61—824no—
495C4×C61—21no—
496C4×C61—23no—
497C4×C61—23no—
498C4×C61—23no—
499C4×C61—23no—
500C4×C61—23no—
501C4×C61—21no—
502C4×C61C22×#4112yes—
503C4×C61C22×#4116yes—
504C4×C61C2×H(5,𝔽2)12yes—
505C4×C61C2×H(5,𝔽2)12yes—
506C4×C61#58512yes—
507Dic61—24no—
508Dic61—212no—
509Dic61—24no—
510#3522—612no—
511#3519—616no—
512#3517—612no—
513#3514—616no—
514#3511—613no—
515#3508—613no—
516#3503—611no—
517#3498—611no—
518#3494—616no—
519#3488—612no—
520#3483—612no—
521#3481—616no—
522#3480—612no—
523D4×#41—616no—
524#3460—616no—
525#3444—613no—
526C2×#532—613no—
527C4×H(5,𝔽2)—612no—
528C2×C4×#41D6111yescharacteristic, complemented
529C2×C61—26no—
530C2×C61—22no—
531C2×C61—43no—
532C2×C61C23×#4111yescharacteristic
533C2×C61C22×H(5,𝔽2)11yescharacteristic
534C2×C61C2×#58511yescharacteristic
535D61—412no—
536C2×H(5,𝔽2)—612no—
537C22×#41—616no—
538C22×#41C2×D6111yescharacteristic
539#559—616no—
540#559—616no—
541Q82—612no—
542#557—612no—
543#556—616no—
544#555—616no—
545#555—6112no—
546#554—616no—
547#554—616no—
548#553—6112no—
549#553—6112no—
550#553—6112no—
551#551—6124no—
552#550—614no—
553#550—612no—
554#550—612no—
555#550—616no—
556#550—616no—
557D4×Q8—616no—
558#548—614no—
559#548—6112no—
560#547—616no—
561#547—6112no—
562#546—6112no—
563#546—6112no—
564#546—6112no—
565#546—6124no—
566D42—6112no—
567D42—616no—
568D42—616no—
569#544—616no—
570#542—6112no—
571#542—6112no—
572#540—6112no—
573#540—6112no—
574#538—6124no—
575#537—616no—
576#535—616no—
577#535—616no—
578#533—611no—
579#533—613no—
580#533—613no—
581#532—6112no—
582#532—613no—
583#532—616no—
584#532—616no—
585#532—616no—
586#532—616no—
587#532—616no—
588#532—616no—
589#532—616no—
590#532—613no—
591#532—613no—
592C2×C4⋊Q8—613no—
593C2×#127—613no—
594#529—6112no—
595#529—616no—
596#529—616no—
597#529—616no—
598#529—616no—
599#529—616no—
600#529—616no—
601C2×#124—616no—
602#525—616no—
603#525—616no—
604#525—616no—
605#525—6124no—
606C2×#121—616no—
607C2×#121—616no—
608#520—612no—
609#520—614no—
610#520—616no—
611#518—6112no—
612#518—616no—
613C4×#41—614no—
614C4×#41—616no—
615C4×#41—616no—
616C4×#41—616no—
617C4×#41C2×D6111yescharacteristic
618C4×#41C2×D6111yescharacteristic
619C4×#41C2×D6113yescomplemented
620C4×#41C2×D6113yescomplemented
621C4×#41C2×D6111yescharacteristic, complemented
622C4×#41C2×D6113yescomplemented
623C4×#41C2×D6113yescomplemented
624C4×#41C2×D6111yescharacteristic, complemented
625C2×C4×Q8C2×D6111yescharacteristic, complemented
626C2×C4×Q8C2×D6111yescharacteristic, complemented
627C2×C4×D4—6112no—
628C2×C4×D4—616no—
629C2×C4×D4—616no—
630C2×C4×D4C2×D6113yescomplemented
631C2×C4×D4C2×D6113yescomplemented
632C2×#117C2×D6113yescomplemented
633C22×C42C2×D6113yescomplemented
634C61#6280011yescharacteristic, complemented, Sylow
635H(5,𝔽2)—12216no—
636C2×#41—28no—
637C2×#41—614no—
638C2×#41—616no—
639C2×#41—616no—
640C2×#41—616no—
641C2×#41—6112no—
642C2×#41—6112no—
643C2×#41—6112no—
644C2×#41—24424no—
645C2×#41C22×D6113yes—
646C2×#41C22×D6113yes—
647C2×#41C22×D6111yescharacteristic
648C2×#41C22×D6111yescharacteristic
649C22×Q8—616no—
650C22×Q8C22×D6111yescharacteristic
651C22×D4—6112no—
652C22×D4—6112no—
653C22×D4—616no—
654C22×D4—616no—
655C22×D4—616no—
656C22×D4C22×D6113yes—
657C23×C4—6112no—
658C23×C4C22×D6113yes—
659C23×C4C22×D6113yes—
660C23×C4C22×D6113yes—
661C4⋊Q8—6112no—
662C4⋊Q8—613no—
663C4⋊Q8—616no—
664C4⋊Q8—616no—
665C4⋊Q8—616no—
666C4⋊Q8—611no—
667C4⋊Q8—611no—
668#127—6112no—
669#127—613no—
670#127—616no—
671#127—616no—
672#127—616no—
673#126—6124no—
674#126—6112no—
675#126—6112no—
676#125—6112no—
677#125—612no—
678#125—616no—
679#125—616no—
680#124—6112no—
681#124—6124no—
682#124—616no—
683#124—6112no—
684#124—6112no—
685#124—6112no—
686#124—616no—
687#124—616no—
688#123—6112no—
689#123—6112no—
690#123—6112no—
691#123—6124no—
692#123—6124no—
693#123—6124no—
694C22⋊Q8—6112no—
695C22⋊Q8—612no—
696C22⋊Q8—612no—
697C22⋊Q8—616no—
698C22⋊Q8—616no—
699C22⋊Q8—616no—
700C22⋊Q8—616no—
701C22⋊Q8—6124no—
702C22⋊Q8—6124no—
703#121—6124no—
704#121—6112no—
705#121—616no—
706#121—616no—
707#121—6112no—
708#121—6112no—
709#121—6112no—
710#121—6112no—
711#121—6112no—
712#121—6112no—
713#121—616no—
714#121—616no—
715#121—616no—
716#121—616no—
717#121—6112no—
718#121—6112no—
719#121—6124no—
720#121—6124no—
721#120—6112no—
722#120—6124no—
723#120—6124no—
724C4×Q8—614no—
725C4×Q8—612no—
726C4×Q8—612no—
727C4×Q8—616no—
728C4×Q8—616no—
729C4×Q8—616no—
730C4×Q8—616no—
731C4×Q8C22×D6111yescharacteristic
732C4×Q8C22×D6111yescharacteristic
733C4×Q8C22×D6111yescharacteristic
734C4×Q8C22×D6111yescharacteristic
735C4×Q8C22×D6113yes—
736C4×Q8C22×D6113yes—
737C4×Q8C22×D6113yes—
738C4×Q8C22×D6113yes—
739C4×D4—6112no—
740C4×D4—6112no—
741C4×D4—6112no—
742C4×D4—6112no—
743C4×D4—6112no—
744C4×D4—6112no—
745C4×D4—6112no—
746C4×D4—6112no—
747C4×D4—6112no—
748C4×D4—6124no—
749C4×D4—6112no—
750C4×D4—616no—
751C4×D4—616no—
752C4×D4—6112no—
753C4×D4—6112no—
754C4×D4—6112no—
755C4×D4—6112no—
756C4×D4—6112no—
757C4×D4—616no—
758C4×D4—616no—
759C4×D4—616no—
760C4×D4—616no—
761C4×D4C22×D6113yes—
762C4×D4C22×D6113yes—
763C4×D4C22×D6113yes—
764C4×D4C22×D6113yes—
765C4×D4C22×D6116yes—
766C4×D4C22×D6113yes—
767C4×D4C22×D6116yes—
768C4×D4C22×D6113yes—
769C4×D4C22×D6116yes—
770C4×D4C22×D6116yes—
771C4×D4C22×D6113yes—
772C4×D4C22×D6113yes—
773#117—612no—
774#117—616no—
775#117—616no—
776#117—6112no—
777#117—6112no—
778#117—6112no—
779#117—6112no—
780#117C22×D6113yes—
781#117C22×D6113yes—
782#117C22×D6116yes—
783#117C22×D6116yes—
784#117C22×D6113yes—
785#117C22×D6113yes—
786C2×C4⋊C4—616no—
787C2×C4⋊C4—616no—
788C2×C4⋊C4—6112no—
789C2×C4⋊C4C22×D6113yes—
790C2×C4⋊C4C22×D6113yes—
791C2×C22⋊C4—6112no—
792C2×C22⋊C4—6112no—
793C2×C22⋊C4—6124no—
794C2×C22⋊C4C22×D6116yes—
795C2×C42—6112no—
796C2×C42C22×D6113yes—
797C2×C42C22×D6113yes—
798C2×C42C22×D6113yes—
799C2×C42C22×D6113yes—
800C2×C42C22×D6113yes—
801C2×C42C22×D6113yes—
802C2×C42C22×D6113yes—
803C2×C42C22×D6113yes—
804C2×C42C22×D6113yes—
805C2×C42C22×D6113yes—
806C2×C42C22×D6113yes—
807C2×C42C22×D6111yescharacteristic
808C24—6112no—
809C24C23×D6113yes—
810#41—24no—
811#41—212no—
812#41—212no—
813#41—12216no—
814#41—12224no—
815#41—12224no—
816#41—24424no—
817#41—24424no—
818#41—24424no—
819#41—24412no—
820#41#1175822218yescomplemented
821C2×Q8—24no—
822C2×Q8—612no—
823C2×Q8—612no—
824C2×Q8—616no—
825C2×Q8—6112no—
826C2×Q8—24412no—
827C2×Q8C23×D6113yes—
828C2×Q8C23×D6111yescharacteristic
829C2×D4—212no—
830C2×D4—6112no—
831C2×D4—6112no—
832C2×D4—6112no—
833C2×D4—6124no—
834C2×D4—6112no—
835C2×D4—616no—
836C2×D4—616no—
837C2×D4—616no—
838C2×D4—6112no—
839C2×D4—6112no—
840C2×D4—12248no—
841C2×D4—12224no—
842C2×D4—24412no—
843C2×D4—24412no—
844C2×D4—24424no—
845C2×D4C23×D6116yes—
846C2×D4C23×D6113yes—
847C2×D4C23×D6113yes—
848C22×C4—212no—
849C22×C4—212no—
850C22×C4—46no—
851C22×C4—6112no—
852C22×C4—6112no—
853C22×C4—6112no—
854C22×C4—6112no—
855C22×C4—6124no—
856C22×C4—24424no—
857C22×C4C23×D6111yescharacteristic
858C22×C4C23×D6111yescharacteristic
859C22×C4C23×D6113yes—
860C22×C4C23×D6113yes—
861C22×C4C23×D6113yes—
862C22×C4C23×D6113yes—
863C22×C4C23×D6113yes—
864C22×C4C23×D6113yes—
865C22×C4C23×D6113yes—
866C22×C4C23×D6113yes—
867C22×C4C23×D6113yes—
868C22×C4C23×D6113yes—
869C22×C4C23×D6113yes—
870C22×C4C23×D6113yes—
871C22×C4C23×D6113yes—
872C22×C4C23×D6113yes—
873C22×C4C23×D6113yes—
874C22×C4C23×D6111yescharacteristic
875C4⋊C4—6112no—
876C4⋊C4—6112no—
877C4⋊C4—616no—
878C4⋊C4—616no—
879C4⋊C4—6112no—
880C4⋊C4—614no—
881C4⋊C4—614no—
882C4⋊C4—6112no—
883C4⋊C4—6112no—
884C4⋊C4—6112no—
885C4⋊C4—612no—
886C4⋊C4—612no—
887C4⋊C4—612no—
888C4⋊C4—612no—
889C4⋊C4C23×D6113yes—
890C4⋊C4C23×D6113yes—
891C4⋊C4C23×D6113yes—
892C4⋊C4C23×D6113yes—
893C4⋊C4C23×D6116yes—
894C4⋊C4C23×D6116yes—
895C22⋊C4—6112no—
896C22⋊C4—614no—
897C22⋊C4—6112no—
898C22⋊C4—6112no—
899C22⋊C4—6124no—
900C22⋊C4—6112no—
901C22⋊C4—6112no—
902C22⋊C4—6124no—
903C22⋊C4—6112no—
904C22⋊C4—6112no—
905C22⋊C4—6112no—
906C22⋊C4C23×D6116yes—
907C22⋊C4C23×D6116yes—
908C22⋊C4C23×D6116yes—
909C22⋊C4C23×D6116yes—
910C42—6112no—
911C42—6112no—
912C42—614no—
913C42C23×D6111yescharacteristic
914C42C23×D6111yescharacteristic
915C42C23×D6113yes—
916C42C23×D6113yes—
917C42C23×D6113yes—
918C42C23×D6113yes—
919C42C23×D6113yes—
920C42C23×D6113yes—
921C42C23×D6113yes—
922C42C23×D6113yes—
923C42C23×D6113yes—
924C42C23×D6113yes—
925C42C23×D6113yes—
926C42C23×D6111yescharacteristic
927C42C23×D6111yescharacteristic
928C42C23×D6113yes—
929C23—26no—
930C23—26no—
931C23—43no—
932C23—6112no—
933C23—12224no—
934C23—24412no—
935C23—24412no—
936C23C24×D6113yes—
937C23C24×D6113yes—
938C23C24×D6111yescharacteristic
939Q8—26no—
940Q8—1224no—
941Q8—12212no—
942Q8—1224no—
943Q8—24412no—
944Q8C2×#1175822214yescomplemented
945D4—212no—
946D4—26no—
947D4—12224no—
948D4—12224no—
949D4—12212no—
950D4—12224no—
951D4—12212no—
952D4—12212no—
953D4—24412no—
954D4—24412no—
955D4—24424no—
956D4—24412no—
957D4C2×#11758222112yescomplemented
958C2×C4—26no—
959C2×C4—26no—
960C2×C4—22no—
961C2×C4—26no—
962C2×C4—26no—
963C2×C4—26no—
964C2×C4—26no—
965C2×C4—26no—
966C2×C4—26no—
967C2×C4—26no—
968C2×C4—22no—
969C2×C4—26no—
970C2×C4—26no—
971C2×C4—43no—
972C2×C4—43no—
973C2×C4—43no—
974C2×C4—614no—
975C2×C4—614no—
976C2×C4—6112no—
977C2×C4—12224no—
978C2×C4—12224no—
979C2×C4—24424no—
980C2×C4—24412no—
981C2×C4—24412no—
982C2×C4C2×#11758222112yescomplemented
983C2×C4#1451982314yescomplemented
984C2×C4C24×D6113yes—
985C2×C4C24×D6111yescharacteristic
986C2×C4C24×D6111yescharacteristic
987C2×C4C24×D6113yes—
988C2×C4C24×D6113yes—
989C2×C4C24×D6113yes—
990C2×C4C24×D6113yes—
991C2×C4C24×D6113yes—
992C2×C4C24×D6111yescharacteristic
993C2×C4C24×D6111yescharacteristic
994C2×C4C24×D6111yescharacteristic
995C2×C4C24×D6111yescharacteristic
996C22—21no—
997C22—23no—
998C22—21no—
999C22—23no—
1000C22—23no—
1001C22—23no—
1002C22—23no—
1003C22—412no—
1004C22—12212no—
1005C22—12212no—
1006C22—12212no—
1007C22—48824no—
1008C22C22×#1175822216yes—
1009C22C2×#1451982312yes—
1010C22C25×D6111yescharacteristic
1011C4—21no—
1012C4—23no—
1013C4—23no—
1014C4—23no—
1015C4—21no—
1016C4—23no—
1017C4—23no—
1018C4—1224no—
1019C4—12212no—
1020C4—1224no—
1021C4C22×#1175822212yes—
1022C4C22×#1175822216yes—
1023C4C2×#1451982312yes—
1024C4C2×#1451982312yes—
1025C4#1684059812yes—
1026C2—22no—
1027C2—26no—
1028C2—43no—
1029C2—24412no—
1030C2C23×#1175822211yescharacteristic
1031C2C22×#1451982311yescharacteristic
1032C2C2×#1684059811yescharacteristic
subgroupG/H
centerC2×C4C24×D61
commutator, socle, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C4×#41×C61C2
hypercenterC2×C4×#41D61
hypocenterC61#62800
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #21459904C2semidirect
2. #21459851C2semidirect
3. #21459825C2semidirect
4. #21459780C2semidirect
5. #21459730C2semidirect
6. #21459695C2semidirect
7. #21459638C2semidirect
8. #21459597C2semidirect
9. #21459554C2semidirect
10. #21459488C2semidirect
11. #21459445C2semidirect
12. #21459429C2semidirect
13. #21459414C2semidirect
14. D4×#11758222C2semidirect
15. #21459235C2semidirect
16. #21459115C2semidirect
17. C2×#16840312C2semidirect
18. C4×#14519823C2semidirect
19. C2×C4×#41×C61C2semidirect
21. C22×#11758222C22semidirect
22. #16840497C22semidirect
23. #16840497C22semidirect
24. Q8×Dic122C22semidirect
25. #16840491C22semidirect
26. #16840485C22semidirect
27. #16840477C22semidirect
28. #16840475C22semidirect
29. #16840472C22semidirect
30. #16840469C22semidirect
31. #16840460C22semidirect
32. #16840458C22semidirect
33. #16840456C22semidirect
34. #16840436C22semidirect
35. #16840434C22semidirect
36. #16840434C22semidirect
37. #16840433C22semidirect
38. #16840433C22semidirect
39. #16840431C22semidirect
40. D4×Dic122C22semidirect
41. #16840423C22semidirect
42. #16840421C22semidirect
43. #16840417C22semidirect
44. #16840413C22semidirect
45. #16840408C22semidirect
46. #16840408C22semidirect
47. #16840402C22semidirect
48. #16840400C22semidirect
49. D4×D244C22semidirect
50. D4×D244C22semidirect
51. D4×C22⋊D61C22semidirect
52. #16840390C22semidirect
53. #16840384C22semidirect
54. #16840383C22semidirect
55. #16840367C22semidirect
56. #16840363C22semidirect
57. #16840345C22semidirect
58. #16840340C22semidirect
59. #16840331C22semidirect
60. #16840326C22semidirect
61. #16840319C22semidirect
62. #16840319C22semidirect
63. #16840319C22semidirect
64. #16840312C22semidirect
65. #16840312C22semidirect
66. #16840312C22semidirect
67. #16840312C22semidirect
68. #16840312C22semidirect
69. #16840312C22semidirect
70. #16840312C22semidirect
71. #16840312C22semidirect
72. #16840312C22semidirect
73. #16840312C22semidirect
74. #16840309C22semidirect
75. C2×#14519777C22semidirect
76. C2×#14519774C22semidirect
77. #16840299C22semidirect
78. #16840296C22semidirect
79. #16840296C22semidirect
80. #16840296C22semidirect
81. #16840296C22semidirect
82. #16840296C22semidirect
83. #16840296C22semidirect
84. C2×#14519765C22semidirect
85. #16840273C22semidirect
86. #16840273C22semidirect
87. #16840273C22semidirect
88. #16840271C22semidirect
89. C2×#14519751C22semidirect
90. C2×#14519751C22semidirect
92. #16840244C22semidirect
93. #16840242C22semidirect
94. #16840236C22semidirect
95. #16840234C22semidirect
96. C4×#11758226C22semidirect
97. C4×#11758222C22semidirect
98. C4×#11758222C22semidirect
99. C4×#11758222C22semidirect
100. C2×C4×D244C22semidirect
101. C2×C4×D244C22semidirect
102. C4×D4×D61C22semidirect
106. C4×#41×C61C22semidirect
107. C4×#41×C61C22semidirect
108. C4×#41×C61C22semidirect
109. C4×#41×C61C22semidirect
110. C4×#41×C61C22semidirect
111. C4×#41×C61C22semidirect
112. C2×C4×Q8×C61C22semidirect
113. C2×C4×Q8×C61C22semidirect
114. C2×C4×D4×C61C22semidirect
115. C2×C4×D4×C61C22semidirect
116. C2×#117×C61C22semidirect
117. C22×C42×C61C22semidirect
296. #41×C61#41semidirect
423. Q8×C61C2×#41semidirect
426. D4×C61C2×#41semidirect
443. C2×C4×C61C2×#41semidirect
444. C2×C4×C61H(5,𝔽2)semidirect
528. C2×C4×#41D61semidirect
619. C4×#41C2×D61semidirect
620. C4×#41C2×D61semidirect
621. C4×#41C2×D61semidirect
622. C4×#41C2×D61semidirect
623. C4×#41C2×D61semidirect
624. C4×#41C2×D61semidirect
625. C2×C4×Q8C2×D61semidirect
626. C2×C4×Q8C2×D61semidirect
630. C2×C4×D4C2×D61semidirect
631. C2×C4×D4C2×D61semidirect
632. C2×#117C2×D61semidirect
633. C22×C42C2×D61semidirect
634. C61#62800semidirect
820. #41#11758222semidirect
944. Q8C2×#11758222semidirect
957. D4C2×#11758222semidirect
982. C2×C4C2×#11758222semidirect
983. C2×C4#14519823semidirect

Maximal subgroups

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

subgroupindex
#214599042
#214598512
#214598252
#214597802
#214597302
#214596952
#214596382
#214595972
#214595542
#214594882
#214594452
#214594292
#214594142
D4×#117582222
#214592352
#214591152
C2×#168403122
C4×#145198232
C2×C4×#41×C612
#6280061