Finite Group Databasebeta

← #11675102

Subgroups — #11675102

Order 768.

1814 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86277C211yesmaximal, characteristic, complemented
2C2×#5542C211yesmaximal, characteristic, complemented
3C3×#3077C211yesmaximal, characteristic, complemented
4#83337C211yesmaximal, characteristic, complemented
5C4×#932C211yesmaximal, characteristic
6#81155C214yesmaximal, complemented
7#81154C214yesmaximal, complemented
8#81091C212yesmaximal, complemented
9#81087C212yesmaximal, complemented
10#80994C212yesmaximal, complemented
11#80993C212yesmaximal, complemented
12#79245C212yesmaximal, complemented
13#79200C212yesmaximal, complemented
14#79057C211yesmaximal, characteristic, complemented
15#79046C211yesmaximal, characteristic, complemented
16#78943C212yesmaximal
17#78922C212yesmaximal, complemented
18#61323—31nomaximal, Sylow
19C3×#533C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21C2×#936C2212yes—
22C2×#932C2211yescharacteristic
23C2×#926—21no—
24C2×#924—21no—
25C2×#909C2212yes—
26#5730C2211yescharacteristic, complemented
27#5727C2211yescharacteristic, complemented
28#5722C2211yescharacteristic, complemented
29#5721C2211yescharacteristic, complemented
30#5690C2212yescomplemented
31#5685C2212yescomplemented
32#5636—22no—
33#5635—21no—
34#5632—21no—
35#5578—22no—
36#5578—21no—
37C4×D3×Q8—21no—
38#5542—21no—
39#5542—22no—
40#5542—21no—
41#5542C2214yes—
42#5542C2212yes—
43#5542C2212yes—
44#5522C2212yes—
45#5517C2212yes—
46C2×#887C2212yes—
47C2×#879—22no—
48C4×#235C2211yescharacteristic
49C2×#869C2211yescharacteristic
50C2×C4×Dic6C2211yescharacteristic
51C3×#478C2214yes—
52C3×#476C2212yes—
53C3×#474C2212yes—
54C3×#428C2212yes—
55C3×#423C2211yescharacteristic
56C3×#418C2212yes—
57#5215C2211yescharacteristic
58#5120C2212yes—
59#5118C2212yes—
60Dic3×M16C2212yes—
61#5093C2212yescomplemented
62#5093C2212yescomplemented
63#5069C2214yescomplemented
64#5018C2212yes—
65C4×#214C2212yes—
66#5014C2212yes—
67C4×#213C2212yes—
68#5004C2212yes—
69#5004C2212yes—
70#4966C2211yescharacteristic
71#4964C2211yescharacteristic
72C4×#208C2211yescharacteristic
73#4889C2214yescomplemented
74#4877C2214yescomplemented
75#4875C2214yescomplemented
76#4873C2214yescomplemented
77#4857C2214yescomplemented
78#4854C2214yescomplemented
79#4853C2214yescomplemented
80#4852C2214yescomplemented
81#4849C2212yescomplemented
82#4849C2212yescomplemented
83#4841C2212yescomplemented
84#4841C2212yescomplemented
85#4831C2212yescomplemented
86#4830C2212yescomplemented
87#4828C2214yescomplemented
88#4787C2214yes—
89#4787C2214yes—
90#4768C2214yes—
91#4768C2214yes—
92#4767C2214yes—
93#4767C2214yes—
94#4765C2214yes—
95#4765C2214yes—
96Q8×#41—31no—
97C2×#556—31no—
98#3377—34no—
99#3376—34no—
100#3369—32no—
101#3367—32no—
102#3364—32no—
103#3360—32no—
104#3140—32no—
105#3139—31no—
106#3078—32no—
107#3077D311yescharacteristic, complemented
108#3040—32no—
109#3039—31no—
110Q8×M16—31no—
111C4×#137—32no—
112C4×AGL(1,ℤ/8)—31no—
113C22×C3×D4C2311yescharacteristic
114C23×C3×C4—21no—
115C2×D3×Q8—21no—
116C2×#235C2311yescharacteristic
117C22×Dic6D411yescharacteristic
118C22×Dic6C2312yes—
119C2×C3×M16C2312yes—
120C3×C4⋊Q8C2311yescharacteristic
121C3×C4⋊Q8C2311yescharacteristic
122C3×#125C2312yes—
123C3×C22⋊Q8—21no—
124C3×C22⋊Q8—21no—
125C3×C4×Q8—21no—
126C3×C4×Q8—21no—
127C3×C4×D4—21no—
128C3×C4×D4—21no—
129C3×C4×D4C2312yes—
130C3×C4×D4C2312yes—
131C3×#117C2312yes—
132C2×C3×C4⋊C4C2311yescharacteristic
133C2×C3×C22⋊C4—21no—
134C2×C3×C42C2311yescharacteristic
135C2×#217—22no—
136C2×#217—22no—
137#946—21no—
138#946—22no—
139Q8×Dic3—21no—
140#944—21no—
141#944—22no—
142#936—22no—
143#936—22no—
144#936C2314yes—
145#936C2314yes—
146C2×#214C2312yes—
147#932—24no—
148C2×#213C2312yes—
149C4×#67—21no—
150C4×#67—21no—
151#926—22no—
152#926—24no—
153#926—22no—
154#926C2311yescharacteristic
155C2×C4⋊Dic3—21no—
156C2×C4⋊Dic3—21no—
157C2×C4⋊Dic3D411yescharacteristic
158#924—22no—
159#924—22no—
160#924—24no—
161C2×Dic3⋊C4—22no—
162C2×Dic3⋊C4D412yes—
163C2×C4×Dic3—22no—
164C2×C4×Dic3C2312yes—
165C2×#208C2311yescharacteristic
166C2×#208C2311yescharacteristic
167#909—28no—
168C2×Dic12C2314yes—
169C2×#204C2314yes—
170#897—21no—
171#897—22no—
172#896—22no—
173#896—22no—
174#896—22no—
175#893C2312yes—
176#893C2312yes—
177D3×C4⋊C4—21no—
178D3×C4⋊C4—22no—
179#890C2312yes—
180#890C2312yes—
181#889—22no—
182#889—22no—
183#889—22no—
184#888—22no—
185#888—21no—
186#888C2312yes—
187#888C2312yes—
188#887—21no—
189#887—22no—
190#887—22no—
191#887—22no—
192#887C2312yes—
193#887C2314yes—
194#887C2314yes—
195#887C2312yes—
196#67⋊C4—22no—
197#67⋊C4—22no—
198#879—24no—
199#879—24no—
200#879—24no—
201#879—24no—
202#878—22no—
203#878—22no—
204C4×D12C2311yescharacteristic
205C4×D12C2311yescharacteristic
206#872—21no—
207#872—22no—
208C42×D3—21no—
209C42×D3—22no—
210#869—21no—
211#869—21no—
212#869C2312yes—
213#869C2312yes—
214C4×Dic6—22no—
215C4×Dic6—22no—
216C4×Dic6D411yescharacteristic
217C4×Dic6D412yes—
218C4×Dic6D411yescharacteristic
219C4×Dic6C2311yescharacteristic
220C4×Dic6C2311yescharacteristic
221C4×Dic6C2312yes—
222C4×Dic6C2311yescharacteristic
223C4×Dic6C2311yescharacteristic
224C3×#107C2314yes—
225C3×#106C2314yes—
226C3×C4⋊C8C2312yes—
227C3×C4⋊C8C2312yes—
228C3×#102C2314yes—
229C3×#102C2314yes—
230#832C2312yes—
231#832C2312yes—
232#816C2314yes—
233#816C2314yes—
234#815C2314yes—
235Dic3⋊C8C2314yes—
236Dic3⋊C8C2314yes—
237C8×Dic3C2314yes—
238#810C2312yes—
239#810C2314yes—
240#810C2314yes—
241#810C2314yes—
242#810C2314yes—
243#809C2312yes—
244#808C2312yes—
245#807C2312yes—
246#803C2312yes—
247C4×C3⋊C8C2312yes—
248C2×#137—32no—
249C2×AGL(1,ℤ/8)—31no—
250Q82—31no—
251#557—31no—
252#557—32no—
253#556—32no—
254#556—32no—
255#556—34no—
256#556—61no—
257#556—62no—
258#556—61no—
259#554—31no—
260#554—32no—
261#554—61no—
262#554—62no—
263D4×Q8—31no—
264D4×Q8—61no—
265#533—32no—
266#533—62no—
267#533—61no—
268#533C2×D311yescharacteristic
269C2×C4⋊Q8—31no—
270C2×#126—62no—
271C2×#124—32no—
272C2×C22⋊Q8—61no—
273C4×#41—32no—
274C4×#41—31no—
275C2×C4×Q8—31no—
276C2×C4×Q8—32no—
277C2×C4×Q8—61no—
278C2×C4×D4C2×D311yescharacteristic
279C2×#117—61no—
280#491—34no—
281#489—34no—
282#489—34no—
283#488—34no—
284#488—34no—
285#487—32no—
286#487—32no—
287#479—34no—
288#479—34no—
289#478C2×D314yes—
290#477—34no—
291#476C2×D312yes—
292#475—34no—
293#474C2×D312yes—
294#464—34no—
295#464—34no—
296#463—34no—
297#463—34no—
298#462—32no—
299#462—32no—
300#461—32no—
301#461—32no—
302#446—32no—
303#446—34no—
304C8×Q8—32no—
305#442—32no—
306#441—34no—
307#440—32no—
308#440—34no—
309C4×Q16—34no—
310C4×SD16—32no—
311C4×SD16—34no—
312C4×D8—32no—
313#428—31no—
314#428C2×D312yes—
315#423—32no—
316#423C2×D311yescharacteristic
317#419—32no—
318#419—32no—
319#419—32no—
320#418—31no—
321#418C2×D312yes—
322#417—31no—
323C4×M16—32no—
324C4×M16—31no—
325C24×C3—21no—
326C2×C3×Q8—21no—
327C2×C3×Q8—21no—
328C2×C3×D4—21no—
329C2×C3×D4—22no—
330C2×C3×D4—22no—
331C2×C3×D4C2412yes—
332C22×C3×C4—21no—
333C22×C3×C4—22no—
334C22×C3×C4—22no—
335C22×C3×C4—44no—
336C22×C3×C4C2×D411yescharacteristic
337C22×C3×C4C2×D411yescharacteristic
338C22×C3×C4C2411yescharacteristic
339C2×#67—21no—
340C22×Dic3—22no—
341C22×Dic3C2×D412yes—
342C22×Dic3C2×D412yes—
343D3×Q8—44no—
344#235—22no—
345#235#4114yes—
346C2×D12C2411yescharacteristic
347C2×C4×D3—21no—
348C2×C4×D3—21no—
349C2×C4×D3—22no—
350C2×C4×D3—21no—
351C2×C4×D3—22no—
352C2×Dic6—24no—
353C2×Dic6—24no—
354C2×Dic6—22no—
355C2×Dic6—22no—
356C2×Dic6—22no—
357C2×Dic6—42no—
358C2×Dic6C2×D411yescharacteristic
359C2×Dic6C2×D411yescharacteristic
360C2×Dic6C2×D412yes—
361C2×Dic6C2414yes—
362C2×Dic6C2411yescharacteristic
363C3×M16—24no—
364C2×C3×C8C2414yes—
365C3×C4⋊C4—21no—
366C3×C4⋊C4—21no—
367C3×C4⋊C4—22no—
368C3×C4⋊C4—22no—
369C3×C4⋊C4—21no—
370C3×C4⋊C4C2412yes—
371C3×C4⋊C4C2412yes—
372C3×C4⋊C4C2412yes—
373C3×C22⋊C4—22no—
374C3×C22⋊C4—22no—
375C3×C22⋊C4—22no—
376C3×C42—22no—
377C3×C42C2×D411yescharacteristic
378C3×C42C2×D411yescharacteristic
379C3×C42C2411yescharacteristic
380C3×C42C2411yescharacteristic
381#217—21no—
382#217—24no—
383#217—24no—
384#217—24no—
385#217—24no—
386#214—24no—
387#213—24no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—21no—
390(C2×D3)⋊C4—22no—
391(C2×D3)⋊C4—22no—
392C4⋊Dic3—22no—
393C4⋊Dic3—22no—
394C4⋊Dic3—22no—
395C4⋊Dic3—22no—
396C4⋊Dic3—22no—
397C4⋊Dic3—22no—
398C4⋊Dic3C2×D411yescharacteristic
399C4⋊Dic3C2×D412yes—
400C4⋊Dic3C2×D411yescharacteristic
401C4⋊Dic3C2411yescharacteristic
402C4⋊Dic3C2411yescharacteristic
403Dic3⋊C4—21no—
404Dic3⋊C4—21no—
405Dic3⋊C4—22no—
406Dic3⋊C4—22no—
407Dic3⋊C4—22no—
408Dic3⋊C4—22no—
409Dic3⋊C4—22no—
410Dic3⋊C4—22no—
411Dic3⋊C4—24no—
412Dic3⋊C4—24no—
413Dic3⋊C4C2×D412yes—
414Dic3⋊C4C2×D412yes—
415Dic3⋊C4C2×D412yes—
416Dic3⋊C4C2×D412yes—
417C4×Dic3—21no—
418C4×Dic3—21no—
419C4×Dic3—21no—
420C4×Dic3—22no—
421C4×Dic3—22no—
422C4×Dic3—24no—
423C4×Dic3—24no—
424C4×Dic3C2×D412yes—
425C4×Dic3C2×D412yes—
426C4×Dic3C2412yes—
427C4×Dic3C2412yes—
428#208—22no—
429#208—22no—
430C2×C3⋊C8C2412yes—
431C2×C3⋊C8C2412yes—
432Dic12—28no—
433#204—28no—
434C2×#41—31no—
435C22×Q8—31no—
436C22×Q8—32no—
437C22×Q8—61no—
438C22×D4C22×D311yescharacteristic
439C23×C4—21no—
440#137—68no—
441AGL(1,ℤ/8)—64no—
442C2×Q16—34no—
443C2×SD16—32no—
444C2×SD16—34no—
445C2×D8—32no—
446C2×M16—31no—
447C2×M16—31no—
448C2×M16C22×D312yes—
449C4⋊Q8—32no—
450C4⋊Q8—32no—
451C4⋊Q8—32no—
452C4⋊Q8—32no—
453C4⋊Q8—61no—
454C4⋊Q8—62no—
455C4⋊Q8—62no—
456C4⋊Q8—61no—
457C4⋊Q8—61no—
458C4⋊Q8—61no—
459C4⋊Q8C22×D311yescharacteristic
460C4⋊Q8C22×D311yescharacteristic
461#126—64no—
462#126—64no—
463#126—64no—
464#126—64no—
465#125—32no—
466#125—32no—
467#125—62no—
468#125—62no—
469#125—62no—
470#125C22×D312yes—
471#124—34no—
472#124—34no—
473#124—62no—
474#124—62no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477C22⋊Q8—62no—
478C22⋊Q8—62no—
479C22⋊Q8—62no—
480C22⋊Q8—62no—
481C22⋊Q8—62no—
482C22⋊Q8—62no—
483C22⋊Q8—61no—
484C22⋊Q8—61no—
485C22⋊Q8—62no—
486C22⋊Q8—62no—
487C22⋊Q8—62no—
488C22⋊Q8—64no—
489C4×Q8—21no—
490C4×Q8—21no—
491C4×Q8—31no—
492C4×Q8—32no—
493C4×Q8—31no—
494C4×Q8—31no—
495C4×Q8—31no—
496C4×Q8—32no—
497C4×Q8—34no—
498C4×Q8—34no—
499C4×Q8—32no—
500C4×Q8—32no—
501C4×Q8—31no—
502C4×Q8—31no—
503C4×Q8—62no—
504C4×Q8—62no—
505C4×Q8—62no—
506C4×Q8—62no—
507C4×Q8—62no—
508C4×Q8—61no—
509C4×Q8—61no—
510C4×D4—21no—
511C4×D4—21no—
512C4×D4—32no—
513C4×D4—32no—
514C4×D4—31no—
515C4×D4—31no—
516C4×D4—62no—
517C4×D4—62no—
518C4×D4—61no—
519C4×D4—61no—
520C4×D4C22×D312yes—
521C4×D4C22×D312yes—
522#117—31no—
523#117—62no—
524#117—62no—
525#117—64no—
526#117—62no—
527#117—61no—
528#117C22×D312yes—
529C2×C4⋊C4—31no—
530C2×C4⋊C4—32no—
531C2×C4⋊C4—62no—
532C2×C4⋊C4—61no—
533C2×C4⋊C4—62no—
534C2×C4⋊C4—61no—
535C2×C4⋊C4—61no—
536C2×C4⋊C4C22×D311yescharacteristic
537C2×C22⋊C4—21no—
538C2×C22⋊C4—62no—
539C2×C22⋊C4—62no—
540C2×C42—32no—
541C2×C42—62no—
542C2×C42—62no—
543C2×C42—61no—
544C2×C42C22×D311yescharacteristic
545#107—32no—
546#107C22×D314yes—
547#106—32no—
548#106C22×D314yes—
549C4⋊C8—34no—
550C4⋊C8—34no—
551C4⋊C8C22×D312yes—
552C4⋊C8C22×D312yes—
553#103—34no—
554#103—34no—
555#103—32no—
556#103—34no—
557#103—34no—
558#103—34no—
559#103—34no—
560#102—32no—
561#102—32no—
562#102—32no—
563#102C22×D314yes—
564#102C22×D314yes—
565#97—34no—
566#97—32no—
567C4×C8—34no—
568C4×C8—32no—
569C23×C3—22no—
570C23×C3—42no—
571C23×C3—42no—
572C23×C3—42no—
573C23×C3C22×D411yescharacteristic
574C22×D3—21no—
575C3×Q8—42no—
576C3×Q8—81no—
577C3×D4—22no—
578C3×D4—22no—
579C3×D4—42no—
580C2×C3×C4—22no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—41no—
585C2×C3×C4—44no—
586C2×C3×C4—42no—
587C2×C3×C4—44no—
588C2×C3×C4C22×D411yescharacteristic
589C2×C3×C4C22×D411yescharacteristic
590C2×C3×C4C22×D411yescharacteristic
591C2×C3×C4C22×D411yescharacteristic
592C2×C3×C4C22×D411yescharacteristic
593C2×C3×C4C2×#4112yes—
594C2×C3×C42−1+412yes—
595C2×C3×C4C2511yescharacteristic
596#67—24no—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—24no—
601C2×Dic3—42no—
602C2×Dic3—42no—
603C2×Dic3—44no—
604C2×Dic3C22×D412yes—
605C2×Dic3C22×D412yes—
606C2×Dic3C22×D412yes—
607C2×Dic3C22×D412yes—
608D12—21no—
609D12C2×#4112yes—
610C4×D3—24no—
611C4×D3—44no—
612C4×D3—42no—
613C4×D3—82no—
614C4×D3—81no—
615Dic6—22no—
616Dic6—22no—
617Dic6—21no—
618Dic6—24no—
619Dic6—24no—
620Dic6—42no—
621Dic6—44no—
622Dic6—44no—
623Dic6—82no—
624Dic6C2×#4112yes—
625C3×C8—24no—
626C3⋊C8—22no—
627C3⋊C8—22no—
628C24—21no—
629#41—34no—
630#41—62no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—31no—
634C2×Q8—31no—
635C2×Q8—32no—
636C2×Q8—31no—
637C2×Q8—34no—
638C2×Q8—62no—
639C2×Q8—62no—
640C2×Q8—62no—
641C2×Q8—64no—
642C2×Q8—64no—
643C2×Q8—122no—
644C2×Q8—124no—
645C2×D4—21no—
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—31no—
649C2×D4—61no—
650C2×D4C23×D312yes—
651C22×C4—21no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—32no—
655C22×C4—32no—
656C22×C4—44no—
657C22×C4—62no—
658C22×C4—62no—
659C22×C4—61no—
660C22×C4—62no—
661C22×C4—61no—
662C22×C4—61no—
663C22×C4D3×D411yescharacteristic
664C22×C4D3×D411yescharacteristic
665C22×C4C23×D311yescharacteristic
666Q16—68no—
667SD16—68no—
668SD16—64no—
669D8—64no—
670M16—24no—
671M16—62no—
672M16—62no—
673C2×C8—32no—
674C2×C8—32no—
675C2×C8C23×D314yes—
676C4⋊C4—22no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—22no—
681C4⋊C4—31no—
682C4⋊C4—32no—
683C4⋊C4—32no—
684C4⋊C4—31no—
685C4⋊C4—32no—
686C4⋊C4—32no—
687C4⋊C4—32no—
688C4⋊C4—31no—
689C4⋊C4—31no—
690C4⋊C4—64no—
691C4⋊C4—64no—
692C4⋊C4—62no—
693C4⋊C4—62no—
694C4⋊C4—62no—
695C4⋊C4—62no—
696C4⋊C4—62no—
697C4⋊C4—62no—
698C4⋊C4—62no—
699C4⋊C4—62no—
700C4⋊C4—62no—
701C4⋊C4—62no—
702C4⋊C4—62no—
703C4⋊C4—62no—
704C4⋊C4—61no—
705C4⋊C4—61no—
706C4⋊C4C23×D312yes—
707C4⋊C4C23×D312yes—
708C4⋊C4C23×D312yes—
709C22⋊C4—22no—
710C22⋊C4—22no—
711C22⋊C4—22no—
712C22⋊C4—62no—
713C22⋊C4—62no—
714C22⋊C4—64no—
715C22⋊C4—64no—
716C22⋊C4—64no—
717C22⋊C4—64no—
718C22⋊C4—61no—
719C22⋊C4—61no—
720C22⋊C4—61no—
721C42—22no—
722C42—32no—
723C42—32no—
724C42—32no—
725C42—32no—
726C42—64no—
727C42—64no—
728C42—62no—
729C42—62no—
730C42—61no—
731C42—61no—
732C42—61no—
733C42D3×D411yescharacteristic
734C42D3×D411yescharacteristic
735C42C23×D311yescharacteristic
736C42C23×D311yescharacteristic
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—42no—
740C22×C3—42no—
741C22×C3—42no—
742C22×C3—84no—
743C22×C3#54812yes—
744C22×C3C23×D411yescharacteristic
745C2×D3—22no—
746C2×D3—41no—
747C2×D3—41no—
748C3×C4—21no—
749C3×C4—21no—
750C3×C4—21no—
751C3×C4—42no—
752C3×C4—42no—
753C3×C4—42no—
754C3×C4#54812yes—
755C3×C4#57512yes—
756C3×C4C22×#4111yescharacteristic
757C3×C4C2×2−1+411yescharacteristic
758Dic3—22no—
759Dic3—22no—
760Dic3—22no—
761Dic3—22no—
762Dic3—22no—
763Dic3—41no—
764Dic3—44no—
765Dic3—41no—
766C23—22no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—61no—
771C23C2×D3×D411yescharacteristic
772Q8—32no—
773Q8—42no—
774Q8—61no—
775Q8—62no—
776Q8—62no—
777Q8—64no—
778Q8—64no—
779Q8—81no—
780Q8—122no—
781Q8—124no—
782Q8—124no—
783Q8—242no—
784D4—22no—
785D4—22no—
786D4—32no—
787D4—42no—
788D4—64no—
789D4—61no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—32no—
795C2×C4—32no—
796C2×C4—32no—
797C2×C4—32no—
798C2×C4—41no—
799C2×C4—44no—
800C2×C4—42no—
801C2×C4—44no—
802C2×C4—61no—
803C2×C4—64no—
804C2×C4—64no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—124no—
808C2×C4—122no—
809C2×C4—122no—
810C2×C4—124no—
811C2×C4—122no—
812C2×C4—241no—
813C2×C4—242no—
814C2×C4C2×D3×D411yescharacteristic
815C2×C4C2×D3×D411yescharacteristic
816C2×C4C2×D3×D411yescharacteristic
817C2×C4C2×D3×D411yescharacteristic
818C2×C4C2×D3×D411yescharacteristic
819C2×C4#100712yes—
820C2×C4D3×#4112yes—
821C2×C4C24×D311yescharacteristic
822C8—24no—
823C8—62no—
824C8—62no—
825C2×C3—22no—
826C2×C3—82no—
827C2×C3C2×#54811yescharacteristic
828C2×C3C2×#57511yescharacteristic
829C2×C3#358611yescharacteristic
830D3—42no—
831C22—21no—
832C22—21no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—62no—
837C22—84no—
838C22—121no—
839C22—121no—
840C22#563312yes—
841C22C22×D3×D411yescharacteristic
842C4—21no—
843C4—21no—
844C4—21no—
845C4—42no—
846C4—42no—
847C4—42no—
848C4—62no—
849C4—62no—
850C4—62no—
851C4—62no—
852C4—62no—
853C4—121no—
854C4—121no—
855C4—124no—
856C4#563312yes—
857C4#577312yes—
858C4C2×#100711yescharacteristic
859C4C2×D3×#4111yescharacteristic
860C3#6132311yescharacteristic, complemented, Sylow
861C2—22no—
862C2—82no—
863C2—122no—
864C2C2×#563311yescharacteristic
865C2C2×#577311yescharacteristic
866C2#8720111yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3077C2
socleC22×C3C23×D4
prime radicalC2×#932C22
hypercenter#3077D3
hypocenterC3#61323
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3077

Complements

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

NH ≅ G/Ntype
1. #86277C2semidirect
2. C2×#5542C2semidirect
3. C3×#3077C2semidirect
4. #83337C2semidirect
6. #81155C2semidirect
7. #81154C2semidirect
8. #81091C2semidirect
9. #81087C2semidirect
10. #80994C2semidirect
11. #80993C2semidirect
12. #79245C2semidirect
13. #79200C2semidirect
14. #79057C2semidirect
15. #79046C2semidirect
17. #78922C2semidirect
26. #5730C22semidirect
27. #5727C22semidirect
28. #5722C22semidirect
29. #5721C22semidirect
30. #5690C22semidirect
31. #5685C22semidirect
61. #5093C22semidirect
62. #5093C22semidirect
63. #5069C22semidirect
73. #4889C22semidirect
74. #4877C22semidirect
75. #4875C22semidirect
76. #4873C22semidirect
77. #4857C22semidirect
78. #4854C22semidirect
79. #4853C22semidirect
80. #4852C22semidirect
81. #4849C22semidirect
82. #4849C22semidirect
83. #4841C22semidirect
84. #4841C22semidirect
85. #4831C22semidirect
86. #4830C22semidirect
87. #4828C22semidirect
107. #3077D3semidirect
860. C3#61323semidirect

Maximal subgroups

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

subgroupindex
#862772
C2×#55422
C3×#30772
#833372
C4×#9322
#811552
#811542
#810912
#810872
#809942
#809932
#792452
#792002
#790572
#790462
#789432
#789222
#613233