Finite Group Databasebeta

← #11675784

Subgroups — #11675784

Order 768.

1826 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86277C211yesmaximal, characteristic, complemented
2C2×#5730C211yesmaximal, characteristic, complemented
3C3×#3165C211yesmaximal, characteristic, complemented
4#83350C211yesmaximal, characteristic, complemented
5#83212C211yesmaximal, characteristic, complemented
6#81970C214yesmaximal, complemented
7#81969C214yesmaximal, complemented
8#81954C212yesmaximal, complemented
9#81953C212yesmaximal, complemented
10#81905C212yesmaximal, complemented
11#81904C212yesmaximal, complemented
12#79241C212yesmaximal, complemented
13#79239C212yesmaximal, complemented
14#79204C212yesmaximal, complemented
15#79199C212yesmaximal
16C4×#908C211yesmaximal, characteristic
17M16×Dic6C211yesmaximal, characteristic, complemented
18#61367—31nomaximal, Sylow
19C3×#533C2211yescharacteristic
20C2×C3×C4⋊Q8C2211yescharacteristic
21C2×#946—22no—
22C2×#908C2211yescharacteristic
23#5730—21no—
24#5730—22no—
25#5730—21no—
26#5730C2212yes—
27#5730C2212yes—
28#5730C2214yes—
29#5730C2211yescharacteristic, complemented
30#5727C2211yescharacteristic, complemented
31#5722C2211yescharacteristic, complemented
32#5721C2211yescharacteristic, complemented
33#5690C2212yescomplemented
34#5685C2212yescomplemented
35#5636—22no—
36#5635—21no—
37#5632—21no—
38#5578—22no—
39#5578—21no—
40C4×D3×Q8—21no—
41#5522C2212yes—
42#5517C2212yes—
43C2×#897—21no—
44C2×#893C2212yes—
45C2×D3×C4⋊C4—21no—
46C2×#890C2212yes—
47C4×#235C2211yescharacteristic
48C2×C4×D12C2211yescharacteristic
49C2×C4×Dic6C2211yescharacteristic
50C3×#501C2214yescomplemented
51C3×#500C2212yescomplemented
52C3×#498C2212yescomplemented
53C3×#428C2212yes—
54C3×#428C2212yes—
55C3×C4×M16C2211yescharacteristic
56#5133C2211yescharacteristic
57#5131C2211yescharacteristic
58#5121C2211yescharacteristic
59#5118C2212yes—
60Dic3×M16C2212yes—
61#5094C2212yescomplemented
62#5091C2212yescomplemented
63#5087C2212yes—
64#5087C2212yescomplemented
65#5084C2212yes—
66#5084C2212yescomplemented
67#5066C2214yes—
68#5001C2212yes—
69#4995C2212yes—
70#4966C2212yes—
71#4964C2212yes—
72#4924C2211yescharacteristic
73#4891C2214yes—
74#4891C2214yescomplemented
75#4890C2214yes—
76#4889C2214yes—
77#4878C2214yescomplemented
78#4877C2214yescomplemented
79#4876C2214yescomplemented
80#4872C2214yes—
81#4871C2214yes—
82#4871C2214yescomplemented
83#4870C2214yes—
84#4869C2214yes—
85#4858C2214yescomplemented
86#4857C2214yescomplemented
87#4856C2214yescomplemented
88#4852C2214yes—
89#4711C2212yes—
90#4710C2212yes—
91#4701C2214yescomplemented
92C4×D24C2212yes—
93C4×#204C2212yes—
94#4679C2212yescomplemented
95C8×Dic6C2212yescomplemented
96Q8×#41—31no—
97C2×#554—31no—
98#3389—34no—
99#3388—34no—
100#3385—32no—
101#3384—32no—
102#3381—32no—
103#3380—32no—
104#3166—32no—
105#3165D311yescharacteristic, complemented
106#3080—32no—
107#3079—31no—
108#3077—32no—
109#3077—31no—
110Q8×M16—31no—
111C4×AGL(1,ℤ/8)—32no—
112C4×AGL(1,ℤ/8)—31no—
113C22×C3×Q8—21no—
114C2×D3×Q8—21no—
115C2×#235C2311yescharacteristic
116C22×D12C2311yescharacteristic
117C22×C4×D3—21no—
118C22×C4×D3—22no—
119C22×Dic6D411yescharacteristic
120C2×C3×M16C2311yescharacteristic
121C2×C3×M16C2311yescharacteristic
122C3×C4⋊Q8—21no—
123C3×C4⋊Q8—21no—
124C3×C4⋊Q8C2311yescharacteristic
125C3×C4⋊Q8C2311yescharacteristic
126C3×C4⋊Q8C2312yes—
127C3×C4⋊Q8C2312yes—
128C3×#125C2312yes—
129C3×C22⋊Q8—21no—
130C3×C22⋊Q8—21no—
131C3×C4×Q8—21no—
132C3×C4×Q8—21no—
133C3×#117C2312yes—
134C2×C3×C4⋊C4—21no—
135C2×C3×C4⋊C4C2312yes—
136C2×C3×C42C2311yescharacteristic
137#946—21no—
138#946—22no—
139#946—24no—
140#946—24no—
141#946—24no—
142#946—24no—
143Q8×Dic3—21no—
144#944—21no—
145#944—22no—
146C4×#67—21no—
147C4×#67—21no—
148C2×(C2×D3)⋊C4—21no—
149C2×(C2×D3)⋊C4—22no—
150#926C2311yescharacteristic
151C2×C4⋊Dic3—22no—
152C2×C4⋊Dic3D411yescharacteristic
153C2×C4⋊Dic3C2311yescharacteristic
154C2×Dic3⋊C4—22no—
155C2×Dic3⋊C4D412yes—
156C2×C4×Dic3C2312yes—
157C2×#208C2312yes—
158#908Q818yescomplemented
159C2×D24C2312yes—
160C2×#204C2312yes—
161#897—21no—
162#897—22no—
163#897—22no—
164#897—24no—
165#897—22no—
166#896—22no—
167#896—22no—
168#896—22no—
169#893—22no—
170#893—22no—
171#893C2312yes—
172#893C2314yes—
173#893C2314yes—
174#893C2312yes—
175D3×C4⋊C4—21no—
176D3×C4⋊C4—22no—
177D3×C4⋊C4—24no—
178D3×C4⋊C4—22no—
179D3×C4⋊C4—22no—
180#890—22no—
181#890—22no—
182#890C2312yes—
183#890C2314yes—
184#890C2312yes—
185#890C2314yes—
186#889—22no—
187#889—22no—
188#889—22no—
189#888—22no—
190#888—21no—
191#888C2312yes—
192#888C2312yes—
193#887—21no—
194#887—22no—
195#887C2312yes—
196#887C2312yes—
197#67⋊C4—22no—
198#67⋊C4—22no—
199#878—22no—
200#878—22no—
201C4×D12—21no—
202C4×D12—21no—
203C4×D12C2311yescharacteristic
204C4×D12C2312yes—
205C4×D12C2311yescharacteristic
206C4×D12C2312yes—
207#872—21no—
208#872—22no—
209C42×D3—21no—
210C42×D3—22no—
211C4×Dic6—22no—
212C4×Dic6—22no—
213C4×Dic6D411yescharacteristic
214C4×Dic6D412yes—
215C4×Dic6D411yescharacteristic
216C4×Dic6C2311yescharacteristic
217C4×Dic6C2311yescharacteristic
218C4×Dic6C2312yes—
219C4×Dic6C2311yescharacteristic
220C4×Dic6C2311yescharacteristic
221C3×#107C2314yes—
222C3×#107C2314yes—
223C3×#106C2314yes—
224C3×#106C2314yes—
225C3×#97C2312yes—
226C3×C4×C8C2312yes—
227#821C2312yes—
228#821C2312yes—
229#821C2312yes—
230#818C2312yes—
231#817C2312yes—
232#816C2312yes—
233#815C2314yes—
234Dic3⋊C8C2314yes—
235Dic3⋊C8C2314yes—
236C8×Dic3C2314yes—
237#810C2314yes—
238#809C2314yes—
239#809C2314yes—
240#809C2314yes—
241#808C2314yes—
242#808C2314yes—
243#807C2314yes—
244#807C2314yes—
245C4⋊(C3⋊C8)C2312yes—
246C4⋊(C3⋊C8)C2312yes—
247C2×AGL(1,ℤ/8)—31no—
248Q82—31no—
249#557—31no—
250#557—32no—
251#554—31no—
252#554—32no—
253#554—32no—
254#554—34no—
255#554—32no—
256#554—61no—
257#554—62no—
258#554—61no—
259#554—62no—
260#554—61no—
261D4×Q8—31no—
262D4×Q8—61no—
263#533—32no—
264#533—62no—
265#533—61no—
266#533C2×D311yescharacteristic
267C2×C4⋊Q8C2×D311yescharacteristic
268C2×#125—32no—
269C2×C22⋊Q8—61no—
270C2×C22⋊Q8—62no—
271C4×#41—32no—
272C4×#41—31no—
273C2×C4×Q8—31no—
274C2×C4×Q8—61no—
275C2×C4×D4—32no—
276C2×C4×D4—31no—
277C22×C4⋊C4—61no—
278#501—34no—
279#501—34no—
280#501C2×D314yescomplemented
281#500C2×D312yescomplemented
282#499—34no—
283#499—34no—
284#498C2×D312yescomplemented
285#479—34no—
286#479—34no—
287#478—34no—
288#478—34no—
289#478—34no—
290#478—34no—
291#478—34no—
292#477—32no—
293#476—32no—
294#476—32no—
295#476—34no—
296#475—32no—
297#474—32no—
298#474—32no—
299#474—34no—
300#446—34no—
301#446—32no—
302C8×Q8—32no—
303#442—34no—
304#442—32no—
305#440—34no—
306#440—32no—
307C4×SD16—34no—
308C4×SD16—32no—
309C4×D8—34no—
310C4×D8—32no—
311#428—31no—
312#428—32no—
313#428—32no—
314#428C2×D312yes—
315#428C2×D312yes—
316#423—32no—
317#423—31no—
318#418—31no—
319#418—32no—
320#417—31no—
321#417—32no—
322C4×M16—32no—
323C4×M16C2×D311yescharacteristic
324C23×D3—21no—
325C2×C3×Q8—21no—
326C2×C3×Q8—21no—
327C2×C3×Q8—22no—
328C2×C3×Q8—22no—
329C2×C3×Q8—82no—
330C22×C3×C4—22no—
331C22×C3×C4C2×D411yescharacteristic
332C22×C3×C4C2×D411yescharacteristic
333C22×C3×C4C2411yescharacteristic
334C2×#67—21no—
335C22×Dic3—21no—
336C22×Dic3C2×D412yes—
337C22×Dic3C2×D412yes—
338D3×Q8—44no—
339#235—22no—
340#235C2×Q814yes—
341C2×D12—21no—
342C2×D12—22no—
343C2×D12C2×Q814yescomplemented
344C2×D12C2412yes—
345C2×D12C2411yescharacteristic
346C2×C4×D3—21no—
347C2×C4×D3—21no—
348C2×C4×D3—22no—
349C2×C4×D3—22no—
350C2×C4×D3—22no—
351C2×C4×D3—21no—
352C2×C4×D3—22no—
353C2×C4×D3—24no—
354C2×C4×D3—24no—
355C2×C4×D3—44no—
356C2×C4×D3—84no—
357C2×Dic6—22no—
358C2×Dic6—22no—
359C2×Dic6—42no—
360C2×Dic6C2×D411yescharacteristic
361C2×Dic6C2×D411yescharacteristic
362C2×Dic6C2×D412yes—
363C2×Dic6C2411yescharacteristic
364C3×M16—22no—
365C3×M16C2×Q814yescomplemented
366C2×C3×C8C2412yes—
367C2×C3×C8C2412yes—
368C3×C4⋊C4—21no—
369C3×C4⋊C4—22no—
370C3×C4⋊C4—22no—
371C3×C4⋊C4—21no—
372C3×C4⋊C4—22no—
373C3×C4⋊C4—22no—
374C3×C4⋊C4—22no—
375C3×C4⋊C4C2412yes—
376C3×C4⋊C4C2414yes—
377C3×C4⋊C4C2412yes—
378C3×C22⋊C4—22no—
379C3×C42—22no—
380C3×C42C2×D411yescharacteristic
381C3×C42C2×D411yescharacteristic
382C3×C42C2411yescharacteristic
383C3×C42C2411yescharacteristic
384#217—21no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4—22no—
388(C2×D3)⋊C4—22no—
389(C2×D3)⋊C4—22no—
390(C2×D3)⋊C4—22no—
391(C2×D3)⋊C4—24no—
392(C2×D3)⋊C4—24no—
393C4⋊Dic3—21no—
394C4⋊Dic3—22no—
395C4⋊Dic3—22no—
396C4⋊Dic3—24no—
397C4⋊Dic3—24no—
398C4⋊Dic3C2×D411yescharacteristic
399C4⋊Dic3C2×D412yes—
400C4⋊Dic3C2×D411yescharacteristic
401C4⋊Dic3C2411yescharacteristic
402C4⋊Dic3C2412yes—
403C4⋊Dic3C2411yescharacteristic
404Dic3⋊C4—21no—
405Dic3⋊C4—21no—
406Dic3⋊C4—22no—
407Dic3⋊C4—22no—
408Dic3⋊C4—22no—
409Dic3⋊C4—22no—
410Dic3⋊C4—22no—
411Dic3⋊C4—22no—
412Dic3⋊C4—24no—
413Dic3⋊C4—24no—
414Dic3⋊C4C2×D412yes—
415Dic3⋊C4C2×D412yes—
416Dic3⋊C4C2×D412yes—
417Dic3⋊C4C2×D412yes—
418C4×Dic3—21no—
419C4×Dic3—21no—
420C4×Dic3—21no—
421C4×Dic3—22no—
422C4×Dic3—22no—
423C4×Dic3C2×D412yes—
424C4×Dic3C2×D412yes—
425C4×Dic3C2412yes—
426C4×Dic3C2412yes—
427#208—24no—
428C2×C3⋊C8C2414yes—
429D24C2×Q818yescomplemented
430#204C2×Q818yescomplemented
431C2×#41—31no—
432C22×Q8—21no—
433C22×Q8—31no—
434C22×Q8—61no—
435C22×D4—31no—
436C23×C4—62no—
437C23×C4—61no—
438AGL(1,ℤ/8)—38no—
439C2×SD16—32no—
440C2×D8—32no—
441C2×M16—32no—
442C2×M16C22×D311yescharacteristic
443C2×M16C22×D311yescharacteristic
444C4⋊Q8—21no—
445C4⋊Q8—21no—
446C4⋊Q8—32no—
447C4⋊Q8—32no—
448C4⋊Q8—61no—
449C4⋊Q8—62no—
450C4⋊Q8—62no—
451C4⋊Q8—61no—
452C4⋊Q8C22×D312yes—
453C4⋊Q8C22×D312yes—
454C4⋊Q8C22×D311yescharacteristic
455C4⋊Q8C22×D311yescharacteristic
456#125—34no—
457#125—34no—
458#125—32no—
459#125—32no—
460#125—62no—
461#125—62no—
462#125—62no—
463#125—62no—
464#125—62no—
465#125C22×D312yes—
466C22⋊Q8—21no—
467C22⋊Q8—21no—
468C22⋊Q8—62no—
469C22⋊Q8—62no—
470C22⋊Q8—62no—
471C22⋊Q8—62no—
472C22⋊Q8—62no—
473C22⋊Q8—62no—
474C22⋊Q8—62no—
475C22⋊Q8—64no—
476C22⋊Q8—62no—
477C22⋊Q8—61no—
478C22⋊Q8—64no—
479C22⋊Q8—64no—
480C22⋊Q8—64no—
481C22⋊Q8—64no—
482C22⋊Q8—61no—
483C22⋊Q8—62no—
484C4×Q8—21no—
485C4×Q8—21no—
486C4×Q8—31no—
487C4×Q8—32no—
488C4×Q8—31no—
489C4×Q8—31no—
490C4×Q8—31no—
491C4×Q8—32no—
492C4×Q8—32no—
493C4×Q8—32no—
494C4×Q8—31no—
495C4×Q8—31no—
496C4×Q8—62no—
497C4×Q8—62no—
498C4×Q8—62no—
499C4×Q8—61no—
500C4×Q8—61no—
501C4×D4—34no—
502C4×D4—34no—
503C4×D4—32no—
504C4×D4—32no—
505C4×D4—32no—
506C4×D4—32no—
507C4×D4—31no—
508C4×D4—31no—
509C4×D4—62no—
510C4×D4—62no—
511C4×D4—62no—
512C4×D4—62no—
513C4×D4—61no—
514C4×D4—61no—
515C4×D4—61no—
516C4×D4—61no—
517#117—31no—
518#117—62no—
519#117—61no—
520#117C22×D312yes—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—31no—
523C2×C4⋊C4—32no—
524C2×C4⋊C4—31no—
525C2×C4⋊C4—62no—
526C2×C4⋊C4—64no—
527C2×C4⋊C4—62no—
528C2×C4⋊C4—62no—
529C2×C4⋊C4—61no—
530C2×C4⋊C4—62no—
531C2×C4⋊C4—62no—
532C2×C4⋊C4C22×D312yes—
533C2×C22⋊C4—62no—
534C2×C22⋊C4—61no—
535C2×C42—32no—
536C2×C42—62no—
537C2×C42—61no—
538C2×C42C22×D311yescharacteristic
539#107—32no—
540#107—34no—
541#107—34no—
542#107C22×D314yes—
543#107C22×D314yes—
544#106—32no—
545#106—34no—
546#106—34no—
547#106C22×D314yes—
548#106C22×D314yes—
549C4⋊C8—34no—
550C4⋊C8—34no—
551C4⋊C8—32no—
552C4⋊C8—32no—
553#103—32no—
554#103—34no—
555#102—32no—
556#102—32no—
557#102—32no—
558#102—34no—
559#102—34no—
560#102—34no—
561#97—34no—
562#97C22×D312yes—
563C4×C8—34no—
564C4×C8C22×D312yes—
565C23×C3C22×D411yescharacteristic
566C22×D3—24no—
567C22×D3—21no—
568C22×D3—22no—
569C22×D3—42no—
570C22×D3—42no—
571C3×Q8—42no—
572C3×Q8—81no—
573C3×Q8—82no—
574C3×Q8—82no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—24no—
579C2×C3×C4—41no—
580C2×C3×C4—44no—
581C2×C3×C4C22×D411yescharacteristic
582C2×C3×C4C22×D411yescharacteristic
583C2×C3×C4C22×D411yescharacteristic
584C2×C3×C4C22×D411yescharacteristic
585C2×C3×C4C22×D411yescharacteristic
586C2×C3×C4C22×Q812yes—
587C2×C3×C42−1+412yes—
588C2×C3×C4C2511yescharacteristic
589#67—24no—
590C2×Dic3—21no—
591C2×Dic3—21no—
592C2×Dic3—21no—
593C2×Dic3—22no—
594C2×Dic3—42no—
595C2×Dic3—42no—
596C2×Dic3—42no—
597C2×Dic3C22×D412yes—
598C2×Dic3C22×D412yes—
599C2×Dic3C22×D412yes—
600C2×Dic3C22×D412yes—
601D12—24no—
602D12—22no—
603D12—21no—
604D12C22×Q814yes—
605D12C22×Q812yes—
606C4×D3—24no—
607C4×D3—44no—
608C4×D3—44no—
609C4×D3—44no—
610C4×D3—42no—
611C4×D3—82no—
612C4×D3—84no—
613C4×D3—84no—
614C4×D3—81no—
615Dic6—22no—
616Dic6—22no—
617Dic6—21no—
618Dic6—42no—
619Dic6—44no—
620Dic6—82no—
621Dic6C22×Q812yes—
622C3×C8—22no—
623C3×C8C22×Q814yes—
624C3⋊C8—24no—
625C24—61no—
626#41—34no—
627#41—62no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—22no—
631C2×Q8—22no—
632C2×Q8—31no—
633C2×Q8—31no—
634C2×Q8—32no—
635C2×Q8—31no—
636C2×Q8—62no—
637C2×Q8—62no—
638C2×Q8—82no—
639C2×Q8—122no—
640C2×Q8—124no—
641C2×D4—34no—
642C2×D4—31no—
643C2×D4—32no—
644C2×D4—61no—
645C2×D4—61no—
646C2×D4—62no—
647C22×C4—22no—
648C22×C4—32no—
649C22×C4—32no—
650C22×C4—62no—
651C22×C4—62no—
652C22×C4—64no—
653C22×C4—64no—
654C22×C4—61no—
655C22×C4—61no—
656C22×C4—61no—
657C22×C4—62no—
658C22×C4—62no—
659C22×C4—61no—
660C22×C4—124no—
661C22×C4—244no—
662C22×C4D3×D411yescharacteristic
663C22×C4D3×D411yescharacteristic
664C22×C4C23×D311yescharacteristic
665SD16—38no—
666D8—38no—
667M16—22no—
668M16—64no—
669M16D3×Q814yescomplemented
670C2×C8—34no—
671C2×C8C23×D312yes—
672C2×C8C23×D312yes—
673C4⋊C4—22no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—21no—
677C4⋊C4—22no—
678C4⋊C4—21no—
679C4⋊C4—22no—
680C4⋊C4—31no—
681C4⋊C4—32no—
682C4⋊C4—31no—
683C4⋊C4—32no—
684C4⋊C4—32no—
685C4⋊C4—32no—
686C4⋊C4—32no—
687C4⋊C4—31no—
688C4⋊C4—31no—
689C4⋊C4—32no—
690C4⋊C4—64no—
691C4⋊C4—64no—
692C4⋊C4—62no—
693C4⋊C4—62no—
694C4⋊C4—62no—
695C4⋊C4—64no—
696C4⋊C4—64no—
697C4⋊C4—62no—
698C4⋊C4—62no—
699C4⋊C4—62no—
700C4⋊C4—62no—
701C4⋊C4—62no—
702C4⋊C4—61no—
703C4⋊C4—61no—
704C4⋊C4—61no—
705C4⋊C4C23×D312yes—
706C4⋊C4C23×D312yes—
707C4⋊C4C23×D314yes—
708C22⋊C4—22no—
709C22⋊C4—64no—
710C22⋊C4—64no—
711C22⋊C4—62no—
712C22⋊C4—62no—
713C22⋊C4—61no—
714C22⋊C4—62no—
715C22⋊C4—62no—
716C22⋊C4—61no—
717C22⋊C4—61no—
718C42—22no—
719C42—32no—
720C42—32no—
721C42—32no—
722C42—32no—
723C42—62no—
724C42—62no—
725C42—61no—
726C42—61no—
727C42—61no—
728C42D3×D411yescharacteristic
729C42D3×D411yescharacteristic
730C42C23×D311yescharacteristic
731C42C23×D311yescharacteristic
732C22×C3—21no—
733C22×C3—21no—
734C22×C3D4×Q812yes—
735C22×C3C23×D411yescharacteristic
736C2×D3—22no—
737C2×D3—24no—
738C2×D3—48no—
739C2×D3—42no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—42no—
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—21no—
746C3×C4—42no—
747C3×C4—44no—
748C3×C4—42no—
749C3×C4D4×Q812yes—
750C3×C4#57512yes—
751C3×C4C23×Q811yescharacteristic
752C3×C4C2×2−1+411yescharacteristic
753Dic3—22no—
754Dic3—22no—
755Dic3—22no—
756Dic3—22no—
757Dic3—22no—
758Dic3—41no—
759Dic3—41no—
760Dic3—42no—
761C23—61no—
762C23—62no—
763C23—64no—
764C23—122no—
765C23—122no—
766C23C2×D3×D411yescharacteristic
767Q8—32no—
768Q8—42no—
769Q8—61no—
770Q8—62no—
771Q8—62no—
772Q8—82no—
773Q8—82no—
774Q8—81no—
775Q8—122no—
776Q8—124no—
777Q8—242no—
778D4—32no—
779D4—34no—
780D4—64no—
781D4—62no—
782D4—61no—
783D4—64no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—24no—
788C2×C4—32no—
789C2×C4—32no—
790C2×C4—32no—
791C2×C4—32no—
792C2×C4—41no—
793C2×C4—44no—
794C2×C4—61no—
795C2×C4—64no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—62no—
799C2×C4—124no—
800C2×C4—124no—
801C2×C4—122no—
802C2×C4—122no—
803C2×C4—122no—
804C2×C4—124no—
805C2×C4—122no—
806C2×C4—241no—
807C2×C4—244no—
808C2×C4—244no—
809C2×C4—242no—
810C2×C4C2×D3×D411yescharacteristic
811C2×C4C2×D3×D411yescharacteristic
812C2×C4C2×D3×D411yescharacteristic
813C2×C4C2×D3×D411yescharacteristic
814C2×C4C2×D3×D411yescharacteristic
815C2×C4C2×D3×Q812yes—
816C2×C4#100712yes—
817C2×C4C24×D311yescharacteristic
818C8—22no—
819C8—64no—
820C8C2×D3×Q814yes—
821C2×C3—22no—
822C2×C3C2×D4×Q811yescharacteristic
823C2×C3C2×#57511yescharacteristic
824C2×C3#358511yescharacteristic
825D3—42no—
826D3—44no—
827C22—21no—
828C22—21no—
829C22—62no—
830C22—64no—
831C22—128no—
832C22—122no—
833C22—121no—
834C22—121no—
835C22—122no—
836C22#572712yes—
837C22C22×D3×D411yescharacteristic
838C4—21no—
839C4—21no—
840C4—21no—
841C4—44no—
842C4—42no—
843C4—42no—
844C4—62no—
845C4—62no—
846C4—62no—
847C4—62no—
848C4—62no—
849C4—121no—
850C4—122no—
851C4—121no—
852C4#572712yes—
853C4#577712yes—
854C4C22×D3×Q811yescharacteristic
855C4C2×#100711yescharacteristic
856C3#6136711yescharacteristic, complemented, Sylow
857C2—22no—
858C2—124no—
859C2—122no—
860C2C2×#572711yescharacteristic
861C2#8719211yescharacteristic
862C2C2×#577711yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3165C2
socleC22×C3C23×D4
prime radicalC2×#908C22
hypercenter#3165D3
hypocenterC3#61367
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3165

Complements

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

NH ≅ G/Ntype
1. #86277C2semidirect
2. C2×#5730C2semidirect
3. C3×#3165C2semidirect
4. #83350C2semidirect
5. #83212C2semidirect
6. #81970C2semidirect
7. #81969C2semidirect
8. #81954C2semidirect
9. #81953C2semidirect
10. #81905C2semidirect
11. #81904C2semidirect
12. #79241C2semidirect
13. #79239C2semidirect
14. #79204C2semidirect
17. M16×Dic6C2semidirect
29. #5730C22semidirect
30. #5727C22semidirect
31. #5722C22semidirect
32. #5721C22semidirect
33. #5690C22semidirect
34. #5685C22semidirect
50. C3×#501C22semidirect
51. C3×#500C22semidirect
52. C3×#498C22semidirect
61. #5094C22semidirect
62. #5091C22semidirect
64. #5087C22semidirect
66. #5084C22semidirect
74. #4891C22semidirect
77. #4878C22semidirect
78. #4877C22semidirect
79. #4876C22semidirect
82. #4871C22semidirect
85. #4858C22semidirect
86. #4857C22semidirect
87. #4856C22semidirect
91. #4701C22semidirect
94. #4679C22semidirect
95. C8×Dic6C22semidirect
105. #3165D3semidirect
158. #908Q8semidirect
280. #501C2×D3semidirect
281. #500C2×D3semidirect
284. #498C2×D3semidirect
343. C2×D12C2×Q8semidirect
365. C3×M16C2×Q8semidirect
429. D24C2×Q8semidirect
430. #204C2×Q8semidirect
669. M16D3×Q8semidirect
856. C3#61367semidirect

Maximal subgroups

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

subgroupindex
#862772
C2×#57302
C3×#31652
#833502
#832122
#819702
#819692
#819542
#819532
#819052
#819042
#792412
#792392
#792042
#791992
C4×#9082
M16×Dic62
#613673