Finite Group Databasebeta

← #11675109

Subgroups — #11675109

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×#5732C211yesmaximal, characteristic, complemented
3C3×#3139C211yesmaximal, characteristic, complemented
4#83350C211yesmaximal, characteristic, complemented
5#83209C211yesmaximal, characteristic, complemented
6#81735C214yesmaximal, complemented
7#81734C214yesmaximal, complemented
8#81626C212yesmaximal, complemented
9#81625C212yesmaximal, complemented
10#81622C212yesmaximal, complemented
11#81621C212yesmaximal, complemented
12#78975C212yesmaximal
13#78954C212yesmaximal, complemented
14#78949C212yesmaximal, complemented
15#78946C212yesmaximal, complemented
16C4×#908C211yesmaximal, characteristic
17M16×Dic6C211yesmaximal, characteristic, complemented
18#61323—31nomaximal, Sylow
19C3×#533C2211yescharacteristic
20C2×C3×C4⋊Q8C2211yescharacteristic
21C2×#947C2212yes—
22C2×Q8×Dic3C2212yes—
23C2×#942C2212yes—
24C2×#908C2211yescharacteristic
25#5732—21no—
26#5732—22no—
27#5732—21no—
28#5732C2214yes—
29#5732C2212yes—
30#5732C2212yes—
31#5730C2211yescharacteristic, complemented
32#5727C2211yescharacteristic, complemented
33#5722C2211yescharacteristic, complemented
34#5721C2211yescharacteristic, complemented
35#5690C2212yescomplemented
36#5685C2212yescomplemented
37#5636—22no—
38#5635—21no—
39#5632—21no—
40#5578—22no—
41#5578—21no—
42C4×D3×Q8—21no—
43#5522C2212yes—
44#5517C2212yes—
45C2×#898—22no—
46C2×#897—21no—
47C2×#892—21no—
48C4×#235C2211yescharacteristic
49C2×C4×D12C2211yescharacteristic
50C2×C4×Dic6C2211yescharacteristic
51C3×#491C2214yescomplemented
52C3×#487C2212yescomplemented
53C3×#487C2212yescomplemented
54C3×#419C2212yes—
55C3×#419C2212yes—
56C3×C4×M16C2211yescharacteristic
57#5225C2212yes—
58#5133C2211yescharacteristic
59#5131C2211yescharacteristic
60#5121C2211yescharacteristic
61#5118C2212yes—
62Dic3×M16C2212yes—
63#5090C2212yescomplemented
64#5090C2212yescomplemented
65#5087C2212yes—
66#5084C2212yes—
67#5083C2212yescomplemented
68#5083C2212yescomplemented
69#5066C2214yes—
70#5001C2212yes—
71#4995C2212yes—
72#4924C2211yescharacteristic
73#4819C2214yes—
74#4819C2214yes—
75#4817C2214yescomplemented
76#4800C2214yes—
77#4800C2214yes—
78#4799C2214yescomplemented
79#4798C2214yes—
80#4798C2214yes—
81#4796C2214yescomplemented
82#4794C2214yes—
83#4794C2214yes—
84#4793C2214yescomplemented
85#4791C2214yescomplemented
86#4790C2214yescomplemented
87#4789C2214yescomplemented
88#4788C2214yescomplemented
89#4711C2212yes—
90#4710C2212yes—
91#4701C2214yescomplemented
92C4×D24C2212yes—
93C4×#204C2212yes—
94#4679C2212yescomplemented
95C8×Dic6C2212yescomplemented
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#3139D311yescharacteristic, complemented
106#3078—32no—
107#3077—31no—
108#3040—32no—
109#3039—31no—
110Q8×M16—31no—
111C4×#137—32no—
112C4×AGL(1,ℤ/8)—31no—
113C22×C3×Q8C2312yes—
114C2×D3×Q8—21no—
115C2×#235C2311yescharacteristic
116C22×D12C2311yescharacteristic
117C22×C4×D3—21no—
118C22×Dic6D411yescharacteristic
119C2×C3×M16C2311yescharacteristic
120C2×C3×M16C2311yescharacteristic
121C3×C4⋊Q8—21no—
122C3×C4⋊Q8—21no—
123C3×C4⋊Q8C2312yes—
124C3×C4⋊Q8C2312yes—
125C3×C4⋊Q8C2311yescharacteristic
126C3×C4⋊Q8C2311yescharacteristic
127C3×#125C2312yes—
128C3×C22⋊Q8—21no—
129C3×C22⋊Q8—21no—
130C3×C4×Q8—21no—
131C3×C4×Q8—21no—
132C3×#117C2312yes—
133C2×C3×C4⋊C4—21no—
134C2×C3×C4⋊C4—21no—
135C2×C3×C42C2311yescharacteristic
136#947—22no—
137#947—22no—
138#947C2314yes—
139#947C2314yes—
140#946—21no—
141#946—22no—
142Q8×Dic3—21no—
143Q8×Dic3—22no—
144Q8×Dic3—22no—
145Q8×Dic3C2314yes—
146Q8×Dic3C2314yes—
147#944—21no—
148#944—22no—
149C2×#216C2314yes—
150#942—28no—
151C2×#215C2314yes—
152C4×#67—21no—
153C4×#67—21no—
154C2×(C2×D3)⋊C4—21no—
155C2×(C2×D3)⋊C4—22no—
156C2×(C2×D3)⋊C4—22no—
157#926C2311yescharacteristic
158C2×C4⋊Dic3—22no—
159C2×C4⋊Dic3D411yescharacteristic
160C2×C4⋊Dic3C2311yescharacteristic
161C2×Dic3⋊C4D412yes—
162C2×C4×Dic3—22no—
163C2×C4×Dic3C2312yes—
164C2×#208C2312yes—
165#908—24no—
166C2×D24C2312yes—
167C2×#204C2312yes—
168#898—24no—
169#898—24no—
170#898—24no—
171#898—24no—
172#897—21no—
173#897—22no—
174#897—22no—
175#897—24no—
176#897—22no—
177#896—22no—
178#896—22no—
179#896—22no—
180#893C2312yes—
181#893C2312yes—
182#892—22no—
183#892—24no—
184#892—22no—
185D3×C4⋊C4—21no—
186D3×C4⋊C4—22no—
187#890C2312yes—
188#890C2312yes—
189#889—22no—
190#889—22no—
191#889—22no—
192#888—22no—
193#888—21no—
194#888C2312yes—
195#888C2312yes—
196#887—21no—
197#887—22no—
198#887C2312yes—
199#887C2312yes—
200#67⋊C4—22no—
201#67⋊C4—22no—
202#878—22no—
203#878—22no—
204C4×D12—21no—
205C4×D12—21no—
206C4×D12C2311yescharacteristic
207C4×D12C2312yes—
208C4×D12C2311yescharacteristic
209C4×D12C2312yes—
210#872—21no—
211#872—22no—
212C42×D3—21no—
213C42×D3—22no—
214C4×Dic6—22no—
215C4×Dic6—22no—
216C4×Dic6D411yescharacteristic
217C4×Dic6D412yes—
218C4×Dic6D411yescharacteristic
219C4×Dic6C2311yescharacteristic
220C4×Dic6C2311yescharacteristic
221C4×Dic6C2312yes—
222C4×Dic6C2311yescharacteristic
223C4×Dic6C2311yescharacteristic
224C3×#103C2314yes—
225C3×#103C2314yes—
226C3×#103C2314yes—
227C3×#103C2314yes—
228C3×#97C2312yes—
229C3×C4×C8C2312yes—
230#835C2314yes—
231#835C2314yes—
232#821C2312yes—
233#821C2312yes—
234#821C2312yes—
235#818C2312yes—
236#817C2312yes—
237#816C2312yes—
238#815C2314yes—
239Dic3⋊C8C2314yes—
240Dic3⋊C8C2314yes—
241C8×Dic3C2314yes—
242#809C2314yes—
243#809C2314yes—
244#808C2314yes—
245#807C2314yes—
246C4⋊(C3⋊C8)C2312yes—
247C4⋊(C3⋊C8)C2312yes—
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⋊Q8C2×D311yescharacteristic
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×D4—31no—
279C2×#117—61no—
280#491C2×D314yescomplemented
281#489—34no—
282#489—34no—
283#488—34no—
284#488—34no—
285#487C2×D312yescomplemented
286#487C2×D312yescomplemented
287#479—34no—
288#479—34no—
289#478—34no—
290#477—34no—
291#476—32no—
292#475—34no—
293#474—32no—
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—34no—
303#446—32no—
304C8×Q8—32no—
305#442—32no—
306#441—34no—
307#440—34no—
308#440—32no—
309C4×Q16—34no—
310C4×SD16—34no—
311C4×SD16—32no—
312C4×D8—32no—
313#428—31no—
314#428—32no—
315#423—32no—
316#423—31no—
317#419—32no—
318#419C2×D312yes—
319#419C2×D312yes—
320#418—31no—
321#418—32no—
322#417—31no—
323C4×M16—32no—
324C4×M16C2×D311yescharacteristic
325C23×D3—21no—
326C2×C3×Q8—21no—
327C2×C3×Q8—22no—
328C2×C3×Q8—21no—
329C2×C3×Q8—24no—
330C2×C3×Q8—24no—
331C2×C3×Q8C2414yes—
332C22×C3×C4—22no—
333C22×C3×C4C2×D411yescharacteristic
334C22×C3×C4C2×D411yescharacteristic
335C22×C3×C4C2411yescharacteristic
336C2×#67—21no—
337C22×Dic3—21no—
338C22×Dic3C2×D412yes—
339C22×Dic3C2×D412yes—
340D3×Q8—44no—
341#235—22no—
342#235#4114yes—
343C2×D12—22no—
344C2×D12—22no—
345C2×D12—21no—
346C2×D12C2412yes—
347C2×D12C2411yescharacteristic
348C2×C4×D3—21no—
349C2×C4×D3—21no—
350C2×C4×D3—22no—
351C2×C4×D3—22no—
352C2×C4×D3—22no—
353C2×C4×D3—21no—
354C2×C4×D3—22no—
355C2×C4×D3—44no—
356C2×Dic6—22no—
357C2×Dic6—22no—
358C2×Dic6—42no—
359C2×Dic6C2×D411yescharacteristic
360C2×Dic6C2×D411yescharacteristic
361C2×Dic6C2×D412yes—
362C2×Dic6C2411yescharacteristic
363C3×M16—22no—
364C3×M16—22no—
365C2×C3×C8C2412yes—
366C2×C3×C8C2412yes—
367C3×C4⋊C4—21no—
368C3×C4⋊C4—22no—
369C3×C4⋊C4—22no—
370C3×C4⋊C4—21no—
371C3×C4⋊C4—22no—
372C3×C4⋊C4—22no—
373C3×C4⋊C4—22no—
374C3×C4⋊C4—22no—
375C3×C4⋊C4C2412yes—
376C3×C4⋊C4C2412yes—
377C3×C22⋊C4—22no—
378C3×C42—22no—
379C3×C42C2×D411yescharacteristic
380C3×C42C2×D411yescharacteristic
381C3×C42C2411yescharacteristic
382C3×C42C2411yescharacteristic
383#217—21no—
384#216—28no—
385#215—28no—
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4—22no—
389(C2×D3)⋊C4—22no—
390(C2×D3)⋊C4—22no—
391(C2×D3)⋊C4—22no—
392(C2×D3)⋊C4—24no—
393(C2×D3)⋊C4—24no—
394(C2×D3)⋊C4—24no—
395(C2×D3)⋊C4—24no—
396C4⋊Dic3—21no—
397C4⋊Dic3—22no—
398C4⋊Dic3—22no—
399C4⋊Dic3—24no—
400C4⋊Dic3—24no—
401C4⋊Dic3C2×D411yescharacteristic
402C4⋊Dic3C2×D412yes—
403C4⋊Dic3C2×D411yescharacteristic
404C4⋊Dic3C2412yes—
405C4⋊Dic3C2411yescharacteristic
406C4⋊Dic3C2411yescharacteristic
407Dic3⋊C4—21no—
408Dic3⋊C4—21no—
409Dic3⋊C4—22no—
410Dic3⋊C4—22no—
411Dic3⋊C4—22no—
412Dic3⋊C4—22no—
413Dic3⋊C4—22no—
414Dic3⋊C4—22no—
415Dic3⋊C4C2×D412yes—
416Dic3⋊C4C2×D412yes—
417Dic3⋊C4C2×D412yes—
418Dic3⋊C4C2×D412yes—
419C4×Dic3—21no—
420C4×Dic3—21no—
421C4×Dic3—21no—
422C4×Dic3—22no—
423C4×Dic3—22no—
424C4×Dic3—24no—
425C4×Dic3—24no—
426C4×Dic3C2×D412yes—
427C4×Dic3C2×D412yes—
428C4×Dic3C2412yes—
429C4×Dic3C2412yes—
430#208—24no—
431C2×C3⋊C8C2414yes—
432D24—24no—
433#204—24no—
434C2×#41—31no—
435C22×Q8—31no—
436C22×Q8—61no—
437C22×Q8C22×D312yes—
438C22×D4—31no—
439C23×C4—61no—
440#137—68no—
441AGL(1,ℤ/8)—64no—
442C2×Q16—34no—
443C2×SD16—34no—
444C2×SD16—32no—
445C2×D8—32no—
446C2×M16—32no—
447C2×M16C22×D311yescharacteristic
448C2×M16C22×D311yescharacteristic
449C4⋊Q8—21no—
450C4⋊Q8—21no—
451C4⋊Q8—32no—
452C4⋊Q8—32no—
453C4⋊Q8—61no—
454C4⋊Q8—62no—
455C4⋊Q8—62no—
456C4⋊Q8—61no—
457C4⋊Q8C22×D312yes—
458C4⋊Q8C22×D312yes—
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—62no—
484C22⋊Q8—64no—
485C22⋊Q8—62no—
486C22⋊Q8—61no—
487C22⋊Q8—61no—
488C22⋊Q8—62no—
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—32no—
511C4×D4—32no—
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×D4—61no—
521C4×D4—61no—
522#117—31no—
523#117—62no—
524#117—62no—
525#117—64no—
526#117—62no—
527#117—61no—
528#117C22×D312yes—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—31no—
532C2×C4⋊C4—32no—
533C2×C4⋊C4—31no—
534C2×C4⋊C4—62no—
535C2×C4⋊C4—61no—
536C2×C4⋊C4—62no—
537C2×C22⋊C4—62no—
538C2×C22⋊C4—62no—
539C2×C22⋊C4—61no—
540C2×C42—32no—
541C2×C42—62no—
542C2×C42—62no—
543C2×C42—61no—
544C2×C42C22×D311yescharacteristic
545#107—32no—
546#107—34no—
547#106—32no—
548#106—34no—
549C4⋊C8—34no—
550C4⋊C8—34no—
551C4⋊C8—32no—
552C4⋊C8—32no—
553#103—34no—
554#103—34no—
555#103—32no—
556#103C22×D314yes—
557#103C22×D314yes—
558#103C22×D314yes—
559#103C22×D314yes—
560#102—32no—
561#102—32no—
562#102—32no—
563#102—34no—
564#102—34no—
565#97—34no—
566#97C22×D312yes—
567C4×C8—34no—
568C4×C8C22×D312yes—
569C23×C3C22×D411yescharacteristic
570C22×D3—21no—
571C22×D3—22no—
572C22×D3—42no—
573C22×D3—42no—
574C22×D3—42no—
575C3×Q8—24no—
576C3×Q8—24no—
577C3×Q8—44no—
578C3×Q8—42no—
579C3×Q8—81no—
580C2×C3×C4—22no—
581C2×C3×C4—24no—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—41no—
585C2×C3×C4—44no—
586C2×C3×C4C22×D411yescharacteristic
587C2×C3×C4C22×D411yescharacteristic
588C2×C3×C4C22×D411yescharacteristic
589C2×C3×C4C22×D411yescharacteristic
590C2×C3×C4C22×D411yescharacteristic
591C2×C3×C4C2×#4112yes—
592C2×C3×C42−1+412yes—
593C2×C3×C4C2511yescharacteristic
594#67—24no—
595C2×Dic3—21no—
596C2×Dic3—22no—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—42no—
600C2×Dic3—42no—
601C2×Dic3—42no—
602C2×Dic3C22×D412yes—
603C2×Dic3C22×D412yes—
604C2×Dic3C22×D412yes—
605C2×Dic3C22×D412yes—
606D12—22no—
607D12—21no—
608D12—22no—
609D12—42no—
610D12C2×#4112yes—
611C4×D3—24no—
612C4×D3—44no—
613C4×D3—44no—
614C4×D3—44no—
615C4×D3—42no—
616C4×D3—82no—
617C4×D3—81no—
618Dic6—22no—
619Dic6—22no—
620Dic6—21no—
621Dic6—42no—
622Dic6—44no—
623Dic6—82no—
624Dic6C2×#4112yes—
625C3×C8—22no—
626C3×C8—22no—
627C3⋊C8—24no—
628C24—61no—
629#41—34no—
630#41—62no—
631C2×Q8—21no—
632C2×Q8—22no—
633C2×Q8—21no—
634C2×Q8—24no—
635C2×Q8—24no—
636C2×Q8—31no—
637C2×Q8—31no—
638C2×Q8—32no—
639C2×Q8—31no—
640C2×Q8—62no—
641C2×Q8—62no—
642C2×Q8—122no—
643C2×Q8—124no—
644C2×Q8C23×D314yes—
645C2×D4—31no—
646C2×D4—32no—
647C2×D4—61no—
648C2×D4—61no—
649C2×D4—62no—
650C2×D4—62no—
651C22×C4—22no—
652C22×C4—32no—
653C22×C4—32no—
654C22×C4—62no—
655C22×C4—62no—
656C22×C4—61no—
657C22×C4—61no—
658C22×C4—61no—
659C22×C4—62no—
660C22×C4—62no—
661C22×C4—61no—
662C22×C4—124no—
663C22×C4D3×D411yescharacteristic
664C22×C4D3×D411yescharacteristic
665C22×C4C23×D311yescharacteristic
666Q16—68no—
667SD16—64no—
668SD16—68no—
669D8—64no—
670M16—22no—
671M16—22no—
672M16—64no—
673C2×C8—34no—
674C2×C8C23×D312yes—
675C2×C8C23×D312yes—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—22no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—22no—
684C4⋊C4—31no—
685C4⋊C4—32no—
686C4⋊C4—32no—
687C4⋊C4—31no—
688C4⋊C4—32no—
689C4⋊C4—32no—
690C4⋊C4—32no—
691C4⋊C4—31no—
692C4⋊C4—31no—
693C4⋊C4—32no—
694C4⋊C4—64no—
695C4⋊C4—64no—
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⋊C4—61no—
707C4⋊C4C23×D312yes—
708C4⋊C4C23×D312yes—
709C22⋊C4—22no—
710C22⋊C4—64no—
711C22⋊C4—64no—
712C22⋊C4—64no—
713C22⋊C4—64no—
714C22⋊C4—62no—
715C22⋊C4—62no—
716C22⋊C4—61no—
717C22⋊C4—62no—
718C22⋊C4—62no—
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#54812yes—
740C22×C3C23×D411yescharacteristic
741C2×D3—22no—
742C2×D3—41no—
743C2×D3—41no—
744C2×D3—42no—
745C2×D3—42no—
746C2×D3—42no—
747C2×D3—84no—
748C3×C4—21no—
749C3×C4—21no—
750C3×C4—21no—
751C3×C4—42no—
752C3×C4—44no—
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—41no—
765Dic3—42no—
766C23—61no—
767C23—62no—
768C23—122no—
769C23—122no—
770C23—122no—
771C23C2×D3×D411yescharacteristic
772Q8—24no—
773Q8—24no—
774Q8—32no—
775Q8—44no—
776Q8—42no—
777Q8—61no—
778Q8—62no—
779Q8—62no—
780Q8—81no—
781Q8—122no—
782Q8—124no—
783Q8—242no—
784D4—32no—
785D4—64no—
786D4—62no—
787D4—61no—
788D4—62no—
789D4—122no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—24no—
794C2×C4—32no—
795C2×C4—32no—
796C2×C4—32no—
797C2×C4—32no—
798C2×C4—41no—
799C2×C4—44no—
800C2×C4—61no—
801C2×C4—64no—
802C2×C4—62no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—124no—
806C2×C4—124no—
807C2×C4—122no—
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×C4D3×#4112yes—
820C2×C4#101012yes—
821C2×C4C24×D311yescharacteristic
822C8—22no—
823C8—22no—
824C8—64no—
825C2×C3—22no—
826C2×C3C2×#54811yescharacteristic
827C2×C3C2×#57511yescharacteristic
828C2×C3#358611yescharacteristic
829D3—42no—
830D3—82no—
831C22—21no—
832C22—21no—
833C22—62no—
834C22—121no—
835C22—121no—
836C22—122no—
837C22—122no—
838C22—122no—
839C22—244no—
840C22#567712yes—
841C22C22×D3×D411yescharacteristic
842C4—21no—
843C4—21no—
844C4—21no—
845C4—44no—
846C4—42no—
847C4—42no—
848C4—62no—
849C4—62no—
850C4—62no—
851C4—62no—
852C4—62no—
853C4—122no—
854C4—121no—
855C4—121no—
856C4#567712yes—
857C4#577712yes—
858C4C2×D3×#4111yescharacteristic
859C4C2×#101011yescharacteristic
860C3#6132311yescharacteristic, complemented, Sylow
861C2—22no—
862C2—122no—
863C2—242no—
864C2C2×#567711yescharacteristic
865C2C2×#577711yescharacteristic
866C2#8719711yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3139C2
socleC22×C3C23×D4
prime radicalC2×#908C22
hypercenter#3139D3
hypocenterC3#61323
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3139

Complements

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

NH ≅ G/Ntype
1. #86277C2semidirect
2. C2×#5732C2semidirect
3. C3×#3139C2semidirect
4. #83350C2semidirect
5. #83209C2semidirect
6. #81735C2semidirect
7. #81734C2semidirect
8. #81626C2semidirect
9. #81625C2semidirect
10. #81622C2semidirect
11. #81621C2semidirect
13. #78954C2semidirect
14. #78949C2semidirect
15. #78946C2semidirect
17. M16×Dic6C2semidirect
31. #5730C22semidirect
32. #5727C22semidirect
33. #5722C22semidirect
34. #5721C22semidirect
35. #5690C22semidirect
36. #5685C22semidirect
51. C3×#491C22semidirect
52. C3×#487C22semidirect
53. C3×#487C22semidirect
63. #5090C22semidirect
64. #5090C22semidirect
67. #5083C22semidirect
68. #5083C22semidirect
75. #4817C22semidirect
78. #4799C22semidirect
81. #4796C22semidirect
84. #4793C22semidirect
85. #4791C22semidirect
86. #4790C22semidirect
87. #4789C22semidirect
88. #4788C22semidirect
91. #4701C22semidirect
94. #4679C22semidirect
95. C8×Dic6C22semidirect
105. #3139D3semidirect
280. #491C2×D3semidirect
285. #487C2×D3semidirect
286. #487C2×D3semidirect
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×#57322
C3×#31392
#833502
#832092
#817352
#817342
#816262
#816252
#816222
#816212
#789752
#789542
#789492
#789462
C4×#9082
M16×Dic62
#613233