Finite Group Databasebeta

← #11675782

Subgroups — #11675782

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×#5543C211yesmaximal, characteristic, complemented
3C3×#3077C211yesmaximal, characteristic, complemented
4#83341C211yesmaximal, characteristic, complemented
5C4×#932C211yesmaximal, characteristic
6#81163C214yesmaximal, complemented
7#81161C214yesmaximal, complemented
8#81056C212yesmaximal, complemented
9#81054C212yesmaximal, complemented
10#80959C212yesmaximal, complemented
11#80958C212yesmaximal, complemented
12#79241C212yesmaximal, complemented
13#79204C212yesmaximal, complemented
14#79060C211yesmaximal, characteristic, complemented
15#79046C211yesmaximal, characteristic, complemented
16#78917C212yesmaximal, complemented
17#78914C212yesmaximal
18#61367—31nomaximal, Sylow
19C3×#533C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21C2×D4×Dic3C2212yes—
22C2×#932C2211yescharacteristic
23C22×C4⋊Dic3—21no—
24C2×#924—21no—
25#5730C2211yescharacteristic, complemented
26#5727C2211yescharacteristic, complemented
27#5722C2211yescharacteristic, complemented
28#5721C2211yescharacteristic, complemented
29#5690C2212yescomplemented
30#5685C2212yescomplemented
31#5636—22no—
32#5635—21no—
33#5632—21no—
34#5578—22no—
35#5578—21no—
36C4×D3×Q8—21no—
37#5543—21no—
38#5543—22no—
39#5543—21no—
40#5543C2214yes—
41#5543C2212yes—
42#5543C2212yes—
43#5522C2212yes—
44#5517C2212yes—
45C2×#890C2212yes—
46C2×#878—22no—
47C4×#235C2211yescharacteristic
48C2×#869C2211yescharacteristic
49C2×C4×Dic6C2211yescharacteristic
50C3×#478C2214yes—
51C3×#476C2212yes—
52C3×#474C2212yes—
53C3×#428C2212yes—
54C3×#423C2211yescharacteristic
55C3×#418C2212yes—
56#5215C2211yescharacteristic
57#5133C2212yes—
58#5121C2212yes—
59#5118C2212yes—
60Dic3×M16C2212yes—
61#5080C2212yescomplemented
62#5078C2212yescomplemented
63#5064C2214yescomplemented
64#5018C2212yes—
65C4×#214C2212yes—
66#5014C2212yes—
67C4×#213C2212yes—
68#4995C2212yes—
69#4995C2212yes—
70#4966C2211yescharacteristic
71#4964C2211yescharacteristic
72C4×#208C2211yescharacteristic
73#4891C2214yescomplemented
74#4878C2214yescomplemented
75#4877C2214yescomplemented
76#4876C2214yescomplemented
77#4871C2214yescomplemented
78#4858C2214yescomplemented
79#4857C2214yescomplemented
80#4856C2214yescomplemented
81#4851C2212yescomplemented
82#4850C2212yescomplemented
83#4846C2212yescomplemented
84#4842C2212yescomplemented
85#4831C2212yescomplemented
86#4830C2212yescomplemented
87#4828C2214yescomplemented
88#4785C2214yes—
89#4766C2214yes—
90#4763C2214yes—
91#4761C2214yes—
92#4759C2214yes—
93#4758C2214yes—
94#4757C2214yes—
95#4756C2214yes—
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#3165—31no—
106#3080—32no—
107#3079—31no—
108#3077—32no—
109#3077D311yescharacteristic, complemented
110Q8×M16—31no—
111C4×AGL(1,ℤ/8)—32no—
112C4×AGL(1,ℤ/8)—31no—
113C22×C3×D4C2311yescharacteristic
114C23×C3×C4—21no—
115C23×Dic3—22no—
116C2×D3×Q8—21no—
117C2×#235C2311yescharacteristic
118C22×Dic6—21no—
119C22×Dic6D411yescharacteristic
120C2×C3×M16C2312yes—
121C3×C4⋊Q8C2311yescharacteristic
122C3×C4⋊Q8C2311yescharacteristic
123C3×#125C2312yes—
124C3×C22⋊Q8—21no—
125C3×C22⋊Q8—21no—
126C3×C4×Q8—21no—
127C3×C4×Q8—21no—
128C3×C4×D4—21no—
129C3×C4×D4—21no—
130C3×C4×D4C2312yes—
131C3×C4×D4C2312yes—
132C3×#117C2312yes—
133C2×C3×C4⋊C4C2311yescharacteristic
134C2×C3×C22⋊C4—21no—
135C2×C3×C42C2311yescharacteristic
136C2×#217—22no—
137#946—21no—
138#946—22no—
139Q8×Dic3—21no—
140#944—21no—
141#944—22no—
142D4×Dic3—22no—
143D4×Dic3—22no—
144D4×Dic3C2314yes—
145D4×Dic3C2314yes—
146C2×#214C2312yes—
147#932Q818yescomplemented
148C2×#213C2312yes—
149C4×#67—21no—
150C4×#67—21no—
151#926C2311yescharacteristic
152C2×C4⋊Dic3—21no—
153C2×C4⋊Dic3—22no—
154C2×C4⋊Dic3—22no—
155C2×C4⋊Dic3—24no—
156C2×C4⋊Dic3—22no—
157C2×C4⋊Dic3D411yescharacteristic
158C2×C4⋊Dic3C2312yes—
159#924—22no—
160#924—22no—
161#924—24no—
162C2×Dic3⋊C4—22no—
163C2×Dic3⋊C4D412yes—
164C2×C4×Dic3C2312yes—
165C2×#208C2311yescharacteristic
166C2×#208C2311yescharacteristic
167#897—21no—
168#897—22no—
169#896—22no—
170#896—22no—
171#896—22no—
172#893C2312yes—
173#893C2312yes—
174D3×C4⋊C4—21no—
175D3×C4⋊C4—22no—
176#890—22no—
177#890—22no—
178#890C2314yes—
179#890C2314yes—
180#890C2312yes—
181#890C2312yes—
182#889—22no—
183#889—22no—
184#889—22no—
185#888—22no—
186#888—21no—
187#888C2312yes—
188#888C2312yes—
189#887—21no—
190#887—22no—
191#887C2312yes—
192#887C2312yes—
193#67⋊C4—22no—
194#67⋊C4—22no—
195#878—22no—
196#878—22no—
197#878—24no—
198#878—24no—
199#878—24no—
200#878—24no—
201C4×D12C2311yescharacteristic
202C4×D12C2311yescharacteristic
203#872—21no—
204#872—22no—
205C42×D3—21no—
206C42×D3—22no—
207#869—21no—
208#869—21no—
209#869C2312yes—
210#869C2312yes—
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×#106C2314yes—
223C3×C4⋊C8C2312yes—
224C3×C4⋊C8C2312yes—
225C3×#102C2314yes—
226C3×#102C2314yes—
227#832C2312yes—
228#832C2312yes—
229#821C2314yes—
230#818C2314yes—
231#817C2314yes—
232#816C2314yes—
233#815C2314yes—
234Dic3⋊C8C2314yes—
235Dic3⋊C8C2314yes—
236C8×Dic3C2314yes—
237#810C2312yes—
238#809C2312yes—
239#808C2314yes—
240#808C2314yes—
241#808C2312yes—
242#807C2314yes—
243#807C2312yes—
244#807C2314yes—
245#803C2312yes—
246C4×C3⋊C8C2312yes—
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—32no—
255#554—34no—
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⋊Q8—31no—
268C2×#125—32no—
269C2×C22⋊Q8—62no—
270C2×C22⋊Q8—61no—
271C4×#41—32no—
272C4×#41—31no—
273C2×C4×Q8—31no—
274C2×C4×Q8—61no—
275C2×C4×D4—32no—
276C2×C4×D4C2×D311yescharacteristic
277C22×C4⋊C4—61no—
278#501—34no—
279#501—34no—
280#501—34no—
281#500—32no—
282#499—34no—
283#499—34no—
284#498—32no—
285#479—34no—
286#479—34no—
287#478—34no—
288#478—34no—
289#478—34no—
290#478—34no—
291#478C2×D314yes—
292#477—32no—
293#476—32no—
294#476—34no—
295#476C2×D312yes—
296#475—32no—
297#474—32no—
298#474—34no—
299#474C2×D312yes—
300#446—32no—
301#446—34no—
302C8×Q8—32no—
303#442—32no—
304#442—34no—
305#440—32no—
306#440—34no—
307C4×SD16—32no—
308C4×SD16—34no—
309C4×D8—32no—
310C4×D8—34no—
311#428—32no—
312#428—32no—
313#428—32no—
314#428—31no—
315#428C2×D312yes—
316#423—32no—
317#423C2×D311yescharacteristic
318#418—31no—
319#418C2×D312yes—
320#417—32no—
321#417—31no—
322C4×M16—32no—
323C4×M16—31no—
324C24×C3—21no—
325C2×C3×Q8—21no—
326C2×C3×Q8—21no—
327C2×C3×D4—21no—
328C2×C3×D4—22no—
329C2×C3×D4C2×Q814yescomplemented
330C2×C3×D4C2412yes—
331C22×C3×C4—21no—
332C22×C3×C4—22no—
333C22×C3×C4—22no—
334C22×C3×C4—44no—
335C22×C3×C4C2×D411yescharacteristic
336C22×C3×C4C2×D411yescharacteristic
337C22×C3×C4C2411yescharacteristic
338C2×#67—21no—
339C22×Dic3—22no—
340C22×Dic3—24no—
341C22×Dic3—24no—
342C22×Dic3—84no—
343C22×Dic3C2×D412yes—
344C22×Dic3C2×D412yes—
345D3×Q8—44no—
346#235—22no—
347#235C2×Q814yes—
348C2×D12C2411yescharacteristic
349C2×C4×D3—21no—
350C2×C4×D3—21no—
351C2×C4×D3—22no—
352C2×C4×D3—21no—
353C2×C4×D3—22no—
354C2×Dic6—22no—
355C2×Dic6—22no—
356C2×Dic6—22no—
357C2×Dic6—22no—
358C2×Dic6—42no—
359C2×Dic6—82no—
360C2×Dic6C2×D411yescharacteristic
361C2×Dic6C2×D411yescharacteristic
362C2×Dic6C2×D412yes—
363C2×Dic6C2411yescharacteristic
364C3×M16—24no—
365C2×C3×C8C2414yes—
366C3×C4⋊C4—21no—
367C3×C4⋊C4—22no—
368C3×C4⋊C4—22no—
369C3×C4⋊C4—21no—
370C3×C4⋊C4—21no—
371C3×C4⋊C4C2412yes—
372C3×C4⋊C4C2412yes—
373C3×C4⋊C4C2412yes—
374C3×C22⋊C4—22no—
375C3×C22⋊C4—22no—
376C3×C22⋊C4—22no—
377C3×C42—22no—
378C3×C42C2×D411yescharacteristic
379C3×C42C2×D411yescharacteristic
380C3×C42C2411yescharacteristic
381C3×C42C2411yescharacteristic
382#217—21no—
383#217—24no—
384#217—24no—
385#214C2×Q818yescomplemented
386#213C2×Q818yescomplemented
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—22no—
390(C2×D3)⋊C4—22no—
391C4⋊Dic3—22no—
392C4⋊Dic3—22no—
393C4⋊Dic3—22no—
394C4⋊Dic3—22no—
395C4⋊Dic3—22no—
396C4⋊Dic3—24no—
397C4⋊Dic3—24no—
398C4⋊Dic3C2×D411yescharacteristic
399C4⋊Dic3C2×D412yes—
400C4⋊Dic3C2×D411yescharacteristic
401C4⋊Dic3C2414yes—
402C4⋊Dic3C2411yescharacteristic
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—22no—
428#208C2×Q814yescomplemented
429C2×C3⋊C8C2412yes—
430C2×C3⋊C8C2412yes—
431C2×#41—31no—
432C22×Q8—31no—
433C22×Q8—61no—
434C22×Q8—61no—
435C22×D4C22×D311yescharacteristic
436C23×C4—21no—
437C23×C4—62no—
438AGL(1,ℤ/8)—38no—
439C2×SD16—32no—
440C2×D8—32no—
441C2×M16—31no—
442C2×M16—31no—
443C2×M16C22×D312yes—
444C4⋊Q8—32no—
445C4⋊Q8—32no—
446C4⋊Q8—32no—
447C4⋊Q8—32no—
448C4⋊Q8—61no—
449C4⋊Q8—62no—
450C4⋊Q8—62no—
451C4⋊Q8—61no—
452C4⋊Q8—61no—
453C4⋊Q8—61no—
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—64no—
469C22⋊Q8—64no—
470C22⋊Q8—64no—
471C22⋊Q8—64no—
472C22⋊Q8—62no—
473C22⋊Q8—62no—
474C22⋊Q8—62no—
475C22⋊Q8—62no—
476C22⋊Q8—62no—
477C22⋊Q8—62no—
478C22⋊Q8—61no—
479C22⋊Q8—61no—
480C22⋊Q8—62no—
481C22⋊Q8—62no—
482C22⋊Q8—62no—
483C22⋊Q8—64no—
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—21no—
502C4×D4—21no—
503C4×D4—34no—
504C4×D4—34no—
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×D4C22×D312yes—
516C4×D4C22×D312yes—
517#117—31no—
518#117—62no—
519#117—61no—
520#117C22×D312yes—
521C2×C4⋊C4—31no—
522C2×C4⋊C4—32no—
523C2×C4⋊C4—32no—
524C2×C4⋊C4—62no—
525C2×C4⋊C4—61no—
526C2×C4⋊C4—62no—
527C2×C4⋊C4—64no—
528C2×C4⋊C4—62no—
529C2×C4⋊C4—62no—
530C2×C4⋊C4—62no—
531C2×C4⋊C4—61no—
532C2×C4⋊C4C22×D311yescharacteristic
533C2×C22⋊C4—21no—
534C2×C22⋊C4—62no—
535C2×C42—32no—
536C2×C42—62no—
537C2×C42—61no—
538C2×C42C22×D311yescharacteristic
539#107—34no—
540#107—32no—
541#107—34no—
542#107—34no—
543#107C22×D314yes—
544#106—34no—
545#106—34no—
546#106—32no—
547#106—34no—
548#106C22×D314yes—
549C4⋊C8—34no—
550C4⋊C8—34no—
551C4⋊C8C22×D312yes—
552C4⋊C8C22×D312yes—
553#103—34no—
554#103—32no—
555#102—32no—
556#102—32no—
557#102—34no—
558#102—32no—
559#102C22×D314yes—
560#102C22×D314yes—
561#97—34no—
562#97—32no—
563C4×C8—34no—
564C4×C8—32no—
565C23×C3—24no—
566C23×C3—22no—
567C23×C3—42no—
568C23×C3—42no—
569C23×C3C22×D411yescharacteristic
570C22×D3—21no—
571C3×Q8—42no—
572C3×Q8—81no—
573C3×D4—24no—
574C3×D4—22no—
575C3×D4C22×Q814yes—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—22no—
579C2×C3×C4—22no—
580C2×C3×C4—41no—
581C2×C3×C4—44no—
582C2×C3×C4—42no—
583C2×C3×C4—44no—
584C2×C3×C4C22×D411yescharacteristic
585C2×C3×C4C22×D411yescharacteristic
586C2×C3×C4C22×D411yescharacteristic
587C2×C3×C4C22×D411yescharacteristic
588C2×C3×C4C22×D411yescharacteristic
589C2×C3×C4C22×Q812yes—
590C2×C3×C42−1+412yes—
591C2×C3×C4C2511yescharacteristic
592#67—24no—
593C2×Dic3—21no—
594C2×Dic3—21no—
595C2×Dic3—21no—
596C2×Dic3—24no—
597C2×Dic3—42no—
598C2×Dic3—42no—
599C2×Dic3—44no—
600C2×Dic3—84no—
601C2×Dic3—84no—
602C2×Dic3C22×D412yes—
603C2×Dic3C22×D412yes—
604C2×Dic3C22×D412yes—
605C2×Dic3C22×D412yes—
606D12—21no—
607D12C22×Q812yes—
608C4×D3—24no—
609C4×D3—44no—
610C4×D3—42no—
611C4×D3—82no—
612C4×D3—81no—
613Dic6—22no—
614Dic6—22no—
615Dic6—21no—
616Dic6—42no—
617Dic6—44no—
618Dic6—82no—
619Dic6—82no—
620Dic6—82no—
621Dic6C22×Q812yes—
622C3×C8—24no—
623C3⋊C8—22no—
624C3⋊C8C22×Q814yes—
625C24—21no—
626#41—34no—
627#41—62no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—31no—
631C2×Q8—31no—
632C2×Q8—32no—
633C2×Q8—31no—
634C2×Q8—62no—
635C2×Q8—62no—
636C2×Q8—62no—
637C2×Q8—62no—
638C2×Q8—122no—
639C2×Q8—124no—
640C2×Q8—242no—
641C2×D4—21no—
642C2×D4—22no—
643C2×D4—31no—
644C2×D4—61no—
645C2×D4D3×Q814yescomplemented
646C2×D4C23×D312yes—
647C22×C4—21no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—32no—
651C22×C4—32no—
652C22×C4—44no—
653C22×C4—62no—
654C22×C4—62no—
655C22×C4—64no—
656C22×C4—64no—
657C22×C4—61no—
658C22×C4—62no—
659C22×C4—61no—
660C22×C4—61no—
661C22×C4—244no—
662C22×C4D3×D411yescharacteristic
663C22×C4D3×D411yescharacteristic
664C22×C4C23×D311yescharacteristic
665SD16—38no—
666D8—38no—
667M16—24no—
668M16—34no—
669M16—62no—
670C2×C8—32no—
671C2×C8—32no—
672C2×C8C23×D314yes—
673C4⋊C4—22no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—22no—
678C4⋊C4—31no—
679C4⋊C4—32no—
680C4⋊C4—31no—
681C4⋊C4—32no—
682C4⋊C4—32no—
683C4⋊C4—32no—
684C4⋊C4—32no—
685C4⋊C4—31no—
686C4⋊C4—31no—
687C4⋊C4—34no—
688C4⋊C4—64no—
689C4⋊C4—64no—
690C4⋊C4—62no—
691C4⋊C4—62no—
692C4⋊C4—62no—
693C4⋊C4—64no—
694C4⋊C4—64no—
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—61no—
704C4⋊C4—61no—
705C4⋊C4C23×D312yes—
706C4⋊C4C23×D312yes—
707C4⋊C4C23×D312yes—
708C22⋊C4—22no—
709C22⋊C4—22no—
710C22⋊C4—22no—
711C22⋊C4—62no—
712C22⋊C4—62no—
713C22⋊C4—64no—
714C22⋊C4—64no—
715C22⋊C4—61no—
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×C3—24no—
735C22×C3—48no—
736C22×C3—42no—
737C22×C3—42no—
738C22×C3D4×Q812yes—
739C22×C3C23×D411yescharacteristic
740C2×D3—22no—
741C2×D3—41no—
742C2×D3—41no—
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—21no—
746C3×C4—42no—
747C3×C4—42no—
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—44no—
760Dic3—41no—
761C23—24no—
762C23—22no—
763C23—42no—
764C23—42no—
765C23—61no—
766C23C2×D3×D411yescharacteristic
767Q8—32no—
768Q8—42no—
769Q8—61no—
770Q8—62no—
771Q8—62no—
772Q8—81no—
773Q8—122no—
774Q8—124no—
775Q8—242no—
776Q8—242no—
777Q8—242no—
778D4—24no—
779D4—22no—
780D4—32no—
781D4—64no—
782D4—61no—
783D4C2×D3×Q814yes—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—32no—
789C2×C4—32no—
790C2×C4—32no—
791C2×C4—32no—
792C2×C4—41no—
793C2×C4—44no—
794C2×C4—42no—
795C2×C4—44no—
796C2×C4—61no—
797C2×C4—64no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—64no—
801C2×C4—124no—
802C2×C4—122no—
803C2×C4—122no—
804C2×C4—124no—
805C2×C4—122no—
806C2×C4—241no—
807C2×C4—242no—
808C2×C4—244no—
809C2×C4—244no—
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#101012yes—
817C2×C4C24×D311yescharacteristic
818C8—24no—
819C8—34no—
820C8—62no—
821C2×C3—22no—
822C2×C3—44no—
823C2×C3C2×D4×Q811yescharacteristic
824C2×C3C2×#57511yescharacteristic
825C2×C3#358511yescharacteristic
826D3—42no—
827C22—21no—
828C22—21no—
829C22—24no—
830C22—48no—
831C22—42no—
832C22—42no—
833C22—62no—
834C22—121no—
835C22—121no—
836C22#563212yes—
837C22C22×D3×D411yescharacteristic
838C4—21no—
839C4—21no—
840C4—21no—
841C4—42no—
842C4—42no—
843C4—42no—
844C4—62no—
845C4—62no—
846C4—62no—
847C4—62no—
848C4—62no—
849C4—121no—
850C4—124no—
851C4—121no—
852C4#563212yes—
853C4#577312yes—
854C4C22×D3×Q811yescharacteristic
855C4C2×#101011yescharacteristic
856C3#6136711yescharacteristic, complemented, Sylow
857C2—22no—
858C2—44no—
859C2—122no—
860C2C2×#563211yescharacteristic
861C2C2×#577311yescharacteristic
862C2#8720011yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3077C2
socleC22×C3C23×D4
prime radicalC2×#932C22
hypercenter#3077D3
hypocenterC3#61367
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×#5543C2semidirect
3. C3×#3077C2semidirect
4. #83341C2semidirect
6. #81163C2semidirect
7. #81161C2semidirect
8. #81056C2semidirect
9. #81054C2semidirect
10. #80959C2semidirect
11. #80958C2semidirect
12. #79241C2semidirect
13. #79204C2semidirect
14. #79060C2semidirect
15. #79046C2semidirect
16. #78917C2semidirect
25. #5730C22semidirect
26. #5727C22semidirect
27. #5722C22semidirect
28. #5721C22semidirect
29. #5690C22semidirect
30. #5685C22semidirect
61. #5080C22semidirect
62. #5078C22semidirect
63. #5064C22semidirect
73. #4891C22semidirect
74. #4878C22semidirect
75. #4877C22semidirect
76. #4876C22semidirect
77. #4871C22semidirect
78. #4858C22semidirect
79. #4857C22semidirect
80. #4856C22semidirect
81. #4851C22semidirect
82. #4850C22semidirect
83. #4846C22semidirect
84. #4842C22semidirect
85. #4831C22semidirect
86. #4830C22semidirect
87. #4828C22semidirect
109. #3077D3semidirect
147. #932Q8semidirect
329. C2×C3×D4C2×Q8semidirect
385. #214C2×Q8semidirect
386. #213C2×Q8semidirect
428. #208C2×Q8semidirect
645. C2×D4D3×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×#55432
C3×#30772
#833412
C4×#9322
#811632
#811612
#810562
#810542
#809592
#809582
#792412
#792042
#790602
#790462
#789172
#789142
#613673