Finite Group Databasebeta

← #11662618

Subgroups — #11662618

Order 768.

2604 conjugacy classes of subgroups.

The subgroup lattice has 1248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#87200C211yesmaximal, characteristic, complemented
2#87197C211yesmaximal, characteristic, complemented
3C2×#5778C211yesmaximal, characteristic, complemented
4#87166C211yesmaximal, characteristic, complemented
5C3×#3069C211yesmaximal, characteristic, complemented
6#84001C211yesmaximal, characteristic, complemented
7#83998C211yesmaximal, characteristic, complemented
8C2×#5203C211yesmaximal, characteristic, complemented
9#83814C211yesmaximal, characteristic, complemented
10#80944C214yesmaximal, complemented
11#80943C214yesmaximal, complemented
12#80930C214yesmaximal, complemented
13D3×#471C214yesmaximal, complemented
14#79261C211yesmaximal, characteristic, complemented
15#79260C211yesmaximal, characteristic, complemented
16#78719C211yesmaximal, characteristic, complemented
17#78714C211yesmaximal, characteristic, complemented
18C2×#4754C211yesmaximal, characteristic, complemented
19#78706C211yesmaximal, characteristic, complemented
20#60470—31nomaximal, Sylow
21#5964C2211yescharacteristic
22C2×#1009C2211yescharacteristic
23C2×#1007C2211yescharacteristic
24C3×#575C2211yescharacteristic
25C2×C3×#137C2211yescharacteristic, complemented
26C2×C3×#137C2211yescharacteristic, complemented
27C3×#568C2211yescharacteristic, complemented
28#5822C2211yescharacteristic
29#5822C2211yescharacteristic, complemented
30C2×#950C2211yescharacteristic, complemented
31C2×#949C2211yescharacteristic
32C2×#948C2211yescharacteristic, complemented
33C2×#942C2211yescharacteristic, complemented
34C22×#215C2211yescharacteristic, complemented
35#5779—22no—
36#5778—22no—
37#5778—22no—
38#5778—22no—
39#5778—22no—
40#5778—22no—
41#5778—22no—
42#5777C2214yes—
43#5777C2214yescomplemented
44D3×#137C2214yescomplemented
45#5774—22no—
46D3×AGL(1,ℤ/8)C2214yes—
47#5770—22no—
48#5769—22no—
49#5766—22no—
50C2×#919C2212yescomplemented
51C2×#918C2212yescomplemented
52#5762—22no—
53C2×#914C2212yescomplemented
54C2×D3×SD16C2212yescomplemented
55#5750—22no—
56#5750C2214yescomplemented
57D3×#131—22no—
58D3×#131C2214yescomplemented
59#5748C2211yescharacteristic, complemented
60C2×#908C2211yescharacteristic
61C2×#908C2211yescharacteristic, complemented
62#5745—22no—
63#5745C2211yescharacteristic
64#5745C2211yescharacteristic
65#5745C2211yescharacteristic
66#5745C2211yescharacteristic, complemented
67C2×#907—22no—
68C2×#907C2211yescharacteristic
69C2×#907C2211yescharacteristic, complemented
70C3×#473C2214yescomplemented
71C3×#471C2214yescomplemented
72C3×#430C2211yescharacteristic, complemented
73C3×#413C2211yescharacteristic, complemented
74C2×C3×#101C2211yescharacteristic, complemented
75#5237C2211yescharacteristic, complemented
76C2×#836C2211yescharacteristic, complemented
77#5204C2212yescomplemented
78#5203C2214yescomplemented
79#5203C2214yescomplemented
80#5203C2212yescomplemented
81#5200C2212yescomplemented
82#5199C2212yescomplemented
83#5192C2214yescomplemented
84#5177C2214yescomplemented
85#5142C2214yescomplemented
86#5141C2214yescomplemented
87#5132C2211yescharacteristic, complemented
88#5132C2211yescharacteristic, complemented
89C2×#823C2211yescharacteristic, complemented
90C2×#823C2211yescharacteristic, complemented
91#5125C2211yescharacteristic, complemented
92C2×#822C2211yescharacteristic, complemented
93C2×#822C2211yescharacteristic, complemented
94#4898C2214yescomplemented
95#4897C2214yescomplemented
96#4893C2214yescomplemented
97D3×#108C2214yescomplemented
98#4755C2212yescomplemented
99#4754C2214yescomplemented
100#4754C2214yescomplemented
101#4754C2212yescomplemented
102#4751C2214yescomplemented
103#4751C2214yescomplemented
104D3×#101C2214yescomplemented
105#4749C2212yescomplemented
106#4748C2212yescomplemented
107D3×#100C2214yescomplemented
108#3586—31no—
109#3585—31no—
110C2×#577—31no—
111#3573—31no—
112#3069—34no—
113#3069—31no—
114#3069D311yescharacteristic, complemented
115#3068—34no—
116#3068—31no—
117#3068—31no—
118#3067—34no—
119#3067—31no—
120#3067—31no—
121C2×#471—34no—
122C2×#471—31no—
123C2×#471—31no—
124#2916—31no—
125#2889—31no—
126#2888—31no—
127C2×C3×#41C2311yescharacteristic
128C2×C3×#41C2311yescharacteristic
129C22×C3×Q8C2311yescharacteristic
130#1010—21no—
131#1010D412yes—
132#1009—21no—
133#1009—22no—
134#1009—22no—
135#1009—22no—
136#1009—22no—
137#1009D412yes—
138D3×#41—22no—
139D3×#41C2314yes—
140#1007—22no—
141#1007—22no—
142#1007—22no—
143#1007—22no—
144#1007D412yes—
145C2×#239—21no—
146C2×#239C2312yes—
147C2×#239C2312yes—
148C2×D3×Q8—21no—
149C2×D3×Q8C2312yes—
150#1004—22no—
151#1004D412yes—
152C2×D3×D4—22no—
153C2×D3×D4C2312yes—
154C2×#235—22no—
155C2×#235—22no—
156C2×#235—21no—
157C2×#235C2311yescharacteristic
158C2×#235C2311yescharacteristic
159C2×#235C2311yescharacteristic
160C22×D12—21no—
161C22×D12C2311yescharacteristic
162C3×#137—22no—
163C3×#137—21no—
164C3×#137—22no—
165C3×#137—22no—
166C3×#137C2314yes—
167C3×#137C2312yes—
168C3×AGL(1,ℤ/8)—21no—
169C3×AGL(1,ℤ/8)C2312yes—
170C3×#135—22no—
171C2×C3×Q16—21no—
172C2×C3×Q16C2312yes—
173C2×C3×SD16—21no—
174C2×C3×SD16C2312yes—
175C3×#131—22no—
176C3×#131C2314yes—
177C2×C3×M16—22no—
178C2×C3×M16C2311yescharacteristic
179C2×C3×M16C2311yescharacteristic
180C2×C3×M16C2311yescharacteristic
181C2×C3×M16C2311yescharacteristic
182#951—21no—
183#951C2312yes—
184#950—22no—
185#950—22no—
186#950—21no—
187#950—21no—
188#950—21no—
189#950—21no—
190#949—22no—
191#949—21no—
192#949C2314yes—
193#949C2312yes—
194#948—21no—
195#948—21no—
196#948C2312yes—
197#948C2312yes—
198C2×#216—21no—
199C2×#216C2311yescharacteristic
200#942—21no—
201#942—22no—
202#942C2314yes—
203#942C2312yes—
204C2×#215—21no—
205C2×#215—21no—
206C2×#215—21no—
207C2×#215—21no—
208C2×#215—21no—
209C2×#215—21no—
210C2×#215C2312yes—
211C2×#215C2312yes—
212C2×#215C2311yescharacteristic
213C2×#214C2311yescharacteristic
214#932—21no—
215#932C2312yes—
216C2×#213—21no—
217C2×#213C2311yescharacteristic
218C2×#208—21no—
219C2×#208C2311yescharacteristic
220C2×#208C2311yescharacteristic
221C2×#208C2311yescharacteristic
222C22×C3⋊C8—21no—
223C22×C3⋊C8C2311yescharacteristic
224#919—24no—
225#919—24no—
226#919—24no—
227#919—24no—
228#918—24no—
229#918—24no—
230#918—24no—
231#918—24no—
232#918—24no—
233D3×Q16—24no—
234#916—24no—
235#916—24no—
236#915—24no—
237#914—24no—
238#914—24no—
239#914—24no—
240#914—24no—
241#914—24no—
242D3×SD16—24no—
243D3×SD16—24no—
244D3×SD16—24no—
245D3×SD16—24no—
246#911—24no—
247D3×D8—24no—
248#909—21no—
249#909C2312yes—
250#908—22no—
251#908—21no—
252#908—22no—
253#908—22no—
254#908C2312yes—
255#908C2314yes—
256#907—22no—
257#907—22no—
258#907—22no—
259#907—22no—
260#907—21no—
261#907—21no—
262#907—24no—
263#907—24no—
264#907D412yes—
265#907D412yes—
266#907D412yes—
267#907D412yes—
268#907C2312yes—
269#907C2312yes—
270D3×M16—22no—
271D3×M16—24no—
272D3×M16—24no—
273D3×M16C2314yes—
274D3×M16C2314yes—
275D3×M16C2314yes—
276#904—22no—
277C2×D24—21no—
278C2×D24C2312yes—
279C2×#204—21no—
280C2×#204C2312yes—
281#901—22no—
282#901—22no—
283#901—22no—
284#901—24no—
285#901—24no—
286#901C2314yes—
287C2×ΓL(1,𝔽25)—21no—
288C2×ΓL(1,𝔽25)—24no—
289C2×ΓL(1,𝔽25)C2312yes—
290C2×D3×C8—21no—
291C2×D3×C8—24no—
292C2×D3×C8C2312yes—
293C3×#108C2314yes—
294C3×#101C2314yes—
295C3×#101C2312yes—
296C3×#100C2312yes—
297#836C2314yes—
298#836C2312yes—
299#833C2312yes—
300#824C2312yes—
301#824C2312yes—
302#823C2314yes—
303#823C2314yes—
304#823C2312yes—
305#823C2312yes—
306#822C2312yes—
307#822C2312yes—
308#822C2312yes—
309#822C2312yes—
310#819C2314yes—
311#585—31no—
312C2×2−1+4—31no—
313C2×H(5,𝔽2)—31no—
314#578—62no—
315#578—62no—
316#577—62no—
317#577—62no—
318#577—62no—
319#577—62no—
320#577—62no—
321#577—62no—
322#577—62no—
323#577—62no—
324#576—62no—
325#576—62no—
326#575—31no—
327#575—31no—
328#575—34no—
329#575—34no—
330#575—31no—
331#575C2×D311yescharacteristic
332C2×#137—32no—
333C2×#137—31no—
334C2×#137—34no—
335C2×#137C2×D311yescharacteristic, complemented
336C2×#137C2×D311yescharacteristic, complemented
337C2×AGL(1,ℤ/8)—32no—
338C2×AGL(1,ℤ/8)—31no—
339C2×AGL(1,ℤ/8)—34no—
340C2×AGL(1,ℤ/8)—31no—
341C2×AGL(1,ℤ/8)—31no—
342C2×#135—31no—
343C2×#135—32no—
344C22×SD16—31no—
345C22×SD16—32no—
346#568—31no—
347#568—31no—
348#568—31no—
349#568—34no—
350#568—31no—
351#568—62no—
352#568—62no—
353#568C2×D311yescharacteristic, complemented
354C2×#131—31no—
355C2×#131—31no—
356C2×#131—34no—
357C2×#131—31no—
358C2×#131—62no—
359C2×#131—62no—
360#473—32no—
361#473—34no—
362#473—32no—
363#473C2×D314yescomplemented
364#472—32no—
365#472—34no—
366#472—34no—
367#472—32no—
368#471—34no—
369#471—34no—
370#471—32no—
371#471—32no—
372#471—34no—
373#471—34no—
374#471—34no—
375#471—34no—
376#471—34no—
377#471—32no—
378#471—32no—
379#471C2×D314yescomplemented
380#430—31no—
381#430—34no—
382#430C2×D311yescharacteristic, complemented
383C2×#108—31no—
384C2×#108—31no—
385C2×#108—34no—
386#413—31no—
387#413—31no—
388#413—31no—
389#413—34no—
390#413—34no—
391#413C2×D311yescharacteristic, complemented
392C2×#101—31no—
393C2×#101—34no—
394C2×#101C2×D311yescharacteristic, complemented
395C2×#100—31no—
396C2×#100—31no—
397C2×#100—34no—
398C23×D3—21no—
399C23×D3—22no—
400C3×#41—21no—
401C3×#41—21no—
402C3×#41—21no—
403C3×#41—21no—
404C3×#41—21no—
405C3×#41—21no—
406C3×#41C2×D412yes—
407C3×#41C2412yes—
408C2×C3×Q8—21no—
409C2×C3×Q8—21no—
410C2×C3×Q8—21no—
411C2×C3×Q8—21no—
412C2×C3×Q8—21no—
413C2×C3×Q8C2×D411yescharacteristic
414C2×C3×Q8C2412yes—
415C2×C3×Q8C2411yescharacteristic
416C2×C3×D4—21no—
417C2×C3×D4—21no—
418C2×C3×D4C2×D411yescharacteristic
419C2×C3×D4C2411yescharacteristic
420C22×C3×C4—21no—
421C22×C3×C4—21no—
422C22×C3×C4—21no—
423C22×C3×C4C2411yescharacteristic
424C2×#67—21no—
425C2×#67—24no—
426C2×#67—21no—
427C2×#67—22no—
428C2×#67#4112yes—
429#239—22no—
430#239—24no—
431#239—24no—
432#239—24no—
433#239—24no—
434#239—42no—
435#239—42no—
436#239C2×D414yes—
437D3×Q8—22no—
438D3×Q8—24no—
439D3×Q8—24no—
440D3×Q8—42no—
441D3×Q8—42no—
442D3×Q8C2×D414yes—
443#237—24no—
444#237—24no—
445#237—22no—
446#237C2×D414yes—
447D3×D4—24no—
448D3×D4—24no—
449D3×D4—22no—
450D3×D4—24no—
451D3×D4—24no—
452D3×D4—44no—
453D3×D4—44no—
454D3×D4C2×D414yes—
455#235—21no—
456#235—21no—
457#235—24no—
458#235—22no—
459#235—24no—
460#235—21no—
461#235—21no—
462#235—21no—
463#235—21no—
464#235—22no—
465#235—44no—
466#235—44no—
467#235—42no—
468#235—42no—
469#235C2×D412yes—
470#235C2×D412yes—
471#235C2×D412yes—
472#235C2×D412yes—
473#235C2×D412yes—
474#235C2412yes—
475C2×D12—22no—
476C2×D12—21no—
477C2×D12—21no—
478C2×D12—21no—
479C2×D12—21no—
480C2×D12—22no—
481C2×D12—22no—
482C2×D12—21no—
483C2×D12—42no—
484C2×D12—42no—
485C2×D12C2×D411yescharacteristic
486C2×D12#4111yescharacteristic
487C2×D12C2412yes—
488C2×D12C2411yescharacteristic
489C2×C4×D3—21no—
490C2×C4×D3—24no—
491C2×C4×D3—22no—
492C2×C4×D3—21no—
493C2×C4×D3—22no—
494C2×C4×D3—22no—
495C2×C4×D3C2412yes—
496C2×Dic6—22no—
497C2×Dic6—22no—
498C2×Dic6C2×D411yescharacteristic
499C2×Dic6#4111yescharacteristic
500C2×Dic6C2411yescharacteristic
501C3×Q16—24no—
502C3×Q16—22no—
503C3×Q16—24no—
504C3×SD16—22no—
505C3×SD16—24no—
506C3×SD16—22no—
507C3×SD16—24no—
508C3×D8—22no—
509C3×M16—21no—
510C3×M16—21no—
511C3×M16—21no—
512C3×M16—24no—
513C3×M16C2×D412yes—
514C3×M16C2×D412yes—
515C3×M16C2412yes—
516C3×M16C2412yes—
517C3×M16C2412yes—
518C2×C3×C8—21no—
519C2×C3×C8—21no—
520C2×C3×C8—21no—
521C2×C3×C8—24no—
522C2×C3×C8C2412yes—
523#216—22no—
524#216—24no—
525#216—22no—
526#216—21no—
527#216—21no—
528#215—24no—
529#215—22no—
530#215—24no—
531#215—22no—
532#215—22no—
533#215—22no—
534#215—22no—
535#215—22no—
536#215—21no—
537#215—21no—
538#214—22no—
539#214—22no—
540#214—21no—
541#214—21no—
542#213—24no—
543#213—22no—
544#213—22no—
545#213—21no—
546#213—21no—
547#208—21no—
548#208—21no—
549#208—21no—
550#208—22no—
551#208—22no—
552#208C2412yes—
553#208C2412yes—
554#208C2412yes—
555C2×C3⋊C8—21no—
556C2×C3⋊C8—21no—
557C2×C3⋊C8—21no—
558C2×C3⋊C8—22no—
559C2×C3⋊C8—22no—
560C2×C3⋊C8C2×D411yescharacteristic
561C2×C3⋊C8C2×D411yescharacteristic
562C2×C3⋊C8C2×D411yescharacteristic
563C2×C3⋊C8C2×D411yescharacteristic
564C2×C3⋊C8C2411yescharacteristic
565C2×C3⋊C8C2411yescharacteristic
566Dic12—22no—
567D24—24no—
568D24—22no—
569D24—24no—
570#204—22no—
571#204—24no—
572#204—22no—
573#204—24no—
574ΓL(1,𝔽25)—24no—
575ΓL(1,𝔽25)—24no—
576ΓL(1,𝔽25)—24no—
577ΓL(1,𝔽25)—24no—
578ΓL(1,𝔽25)—22no—
579ΓL(1,𝔽25)—22no—
580ΓL(1,𝔽25)C2×D414yes—
581ΓL(1,𝔽25)C2×D414yes—
582D3×C8—24no—
583D3×C8—24no—
584D3×C8—24no—
585D3×C8—24no—
586D3×C8—22no—
587D3×C8—22no—
588D3×C8C2×D414yes—
589D3×C8C2×D414yes—
5902−1+4—32no—
5912−1+4—32no—
5922−1+4—62no—
5932−1+4—62no—
5942−1+4—62no—
5952−1+4—62no—
5962−1+4—61no—
597H(5,𝔽2)—32no—
598H(5,𝔽2)—32no—
599H(5,𝔽2)—62no—
600H(5,𝔽2)—61no—
601H(5,𝔽2)—62no—
602H(5,𝔽2)—62no—
603H(5,𝔽2)—62no—
604H(5,𝔽2)—62no—
605C2×#41—31no—
606C2×#41—34no—
607C2×#41—32no—
608C2×#41—32no—
609C2×#41—31no—
610C2×#41—31no—
611C2×#41—62no—
612C2×#41—61no—
613C2×#41—62no—
614C2×#41—61no—
615C2×#41—62no—
616C2×#41C22×D311yescharacteristic
617C2×#41C22×D311yescharacteristic
618C22×Q8—32no—
619C22×Q8—61no—
620C22×Q8C22×D311yescharacteristic
621C22×D4—32no—
622C22×D4—31no—
623C22×D4—61no—
624C22×D4—62no—
625#137—22no—
626#137—21no—
627#137—22no—
628#137—22no—
629#137—32no—
630#137—34no—
631#137—32no—
632#137—32no—
633#137—61no—
634#137—64no—
635#137—64no—
636#137—64no—
637#137—64no—
638#137—64no—
639#137—64no—
640#137—62no—
641#137—61no—
642#137—61no—
643#137C22×D314yes—
644#137C22×D312yes—
645AGL(1,ℤ/8)—21no—
646AGL(1,ℤ/8)—34no—
647AGL(1,ℤ/8)—32no—
648AGL(1,ℤ/8)—32no—
649AGL(1,ℤ/8)—34no—
650AGL(1,ℤ/8)—32no—
651AGL(1,ℤ/8)—61no—
652AGL(1,ℤ/8)—62no—
653AGL(1,ℤ/8)—64no—
654AGL(1,ℤ/8)—64no—
655AGL(1,ℤ/8)—64no—
656AGL(1,ℤ/8)—64no—
657AGL(1,ℤ/8)—64no—
658AGL(1,ℤ/8)—64no—
659AGL(1,ℤ/8)—61no—
660AGL(1,ℤ/8)—62no—
661AGL(1,ℤ/8)—61no—
662AGL(1,ℤ/8)—62no—
663AGL(1,ℤ/8)—62no—
664AGL(1,ℤ/8)C22×D312yes—
665#135—22no—
666#135—62no—
667#135—64no—
668#135—64no—
669#135—61no—
670#135—61no—
671#135—61no—
672#135—61no—
673#135—64no—
674#135—64no—
675#135—64no—
676#135—64no—
677#135—62no—
678#135—62no—
679C2×Q16—21no—
680C2×Q16—31no—
681C2×Q16—64no—
682C2×Q16—61no—
683C2×Q16C22×D312yes—
684C2×SD16—21no—
685C2×SD16—32no—
686C2×SD16—32no—
687C2×SD16—31no—
688C2×SD16—31no—
689C2×SD16—32no—
690C2×SD16—61no—
691C2×SD16—64no—
692C2×SD16—64no—
693C2×SD16—61no—
694C2×SD16—61no—
695C2×SD16—61no—
696C2×SD16—61no—
697C2×SD16—64no—
698C2×SD16—64no—
699C2×SD16—61no—
700C2×SD16—61no—
701C2×SD16C22×D312yes—
702C2×D8—31no—
703C2×D8—32no—
704C2×D8—61no—
705C2×D8—64no—
706C2×D8—61no—
707#131—22no—
708#131—32no—
709#131—32no—
710#131—32no—
711#131—32no—
712#131—32no—
713#131—32no—
714#131—32no—
715#131—32no—
716#131—34no—
717#131—64no—
718#131—64no—
719#131—62no—
720#131—62no—
721#131—62no—
722#131—61no—
723#131—64no—
724#131—61no—
725#131—61no—
726#131—61no—
727#131—64no—
728#131—62no—
729#131—62no—
730#131—62no—
731#131—62no—
732#131C22×D314yes—
733C2×M16—22no—
734C2×M16—32no—
735C2×M16—31no—
736C2×M16—31no—
737C2×M16—31no—
738C2×M16—34no—
739C2×M16—34no—
740C2×M16—34no—
741C2×M16—61no—
742C2×M16—64no—
743C2×M16—64no—
744C2×M16—61no—
745C2×M16—64no—
746C2×M16—62no—
747C2×M16C22×D311yescharacteristic
748C2×M16C22×D311yescharacteristic
749C2×M16C22×D311yescharacteristic
750C2×M16C22×D311yescharacteristic
751C22×C8—31no—
752C22×C8—32no—
753C22×C8—61no—
754C22×C8—64no—
755C22×C8—61no—
756#108—32no—
757#108—32no—
758#108—32no—
759#108—32no—
760#108—34no—
761#108C22×D314yes—
762#101—34no—
763#101—32no—
764#101—32no—
765#101—32no—
766#101C22×D314yes—
767#101C22×D312yes—
768#100—32no—
769#100—34no—
770#100—34no—
771#100—32no—
772#100—32no—
773#100C22×D312yes—
774C23×C3—21no—
775C23×C3—21no—
776C23×C3C2×#4111yescharacteristic
777C22×D3—21no—
778C22×D3—24no—
779C22×D3—21no—
780C22×D3—22no—
781C22×D3—41no—
782C22×D3—41no—
783C22×D3—44no—
784C22×D3—162no—
785C22×D3—161no—
786C22×D3C2×#4112yes—
787C3×Q8—21no—
788C3×Q8—22no—
789C3×Q8—22no—
790C3×Q8—21no—
791C3×Q8—21no—
792C3×Q8—41no—
793C3×Q8—41no—
794C3×Q8C22×D412yes—
795C3×D4—22no—
796C3×D4—22no—
797C3×D4—21no—
798C3×D4—21no—
799C3×D4—21no—
800C3×D4—41no—
801C3×D4—41no—
802C3×D4C22×D412yes—
803C2×C3×C4—21no—
804C2×C3×C4—22no—
805C2×C3×C4—22no—
806C2×C3×C4—22no—
807C2×C3×C4—21no—
808C2×C3×C4—41no—
809C2×C3×C4—41no—
810C2×C3×C4—41no—
811C2×C3×C4—41no—
812C2×C3×C4C22×D411yescharacteristic
813C2×C3×C4C22×D411yescharacteristic
814C2×C3×C4C22×D411yescharacteristic
815C2×C3×C4C22×D411yescharacteristic
816C2×C3×C4C2×#4111yescharacteristic
817C2×C3×C4C2511yescharacteristic
818#67—22no—
819#67—22no—
820#67—24no—
821#67—24no—
822#67—41no—
823#67—41no—
824#67—44no—
825#67#12114yes—
826#67#12114yes—
827C2×Dic3—21no—
828C2×Dic3—24no—
829C2×Dic3—21no—
830C2×Dic3C2×#4112yes—
831D12—24no—
832D12—21no—
833D12—22no—
834D12—21no—
835D12—22no—
836D12—21no—
837D12—44no—
838D12—44no—
839D12—41no—
840D12—41no—
841D12#12112yes—
842D12#12112yes—
843D12C22×D412yes—
844C4×D3—24no—
845C4×D3—22no—
846C4×D3—22no—
847C4×D3—24no—
848C4×D3—44no—
849C4×D3—41no—
850C4×D3—41no—
851C4×D3—44no—
852C4×D3—44no—
853C4×D3C22×D414yes—
854C4×D3C22×D414yes—
855Dic6—21no—
856Dic6—24no—
857Dic6—21no—
858Dic6—21no—
859Dic6—44no—
860Dic6#12112yes—
861Dic6#12112yes—
862Dic6C22×D412yes—
863C3×C8—22no—
864C3×C8—22no—
865C3×C8—22no—
866C3×C8C22×D414yes—
867C3⋊C8—22no—
868C3⋊C8—22no—
869C3⋊C8—22no—
870C3⋊C8C22×D411yescharacteristic
871C3⋊C8C22×D411yescharacteristic
872C3⋊C8C22×D411yescharacteristic
873C3⋊C8C22×D411yescharacteristic
874C24—62no—
875C24—61no—
876#41—21no—
877#41—21no—
878#41—21no—
879#41—21no—
880#41—21no—
881#41—21no—
882#41—32no—
883#41—32no—
884#41—32no—
885#41—32no—
886#41—34no—
887#41—34no—
888#41—32no—
889#41—32no—
890#41—64no—
891#41—64no—
892#41—62no—
893#41—62no—
894#41—64no—
895#41—64no—
896#41—64no—
897#41—64no—
898#41—64no—
899#41—64no—
900#41—62no—
901#41—62no—
902#41—61no—
903#41—61no—
904#41—61no—
905#41—61no—
906#41—61no—
907#41—61no—
908#41—124no—
909#41—124no—
910#41—122no—
911#41—122no—
912#41—122no—
913#41—122no—
914#41D3×D412yes—
915#41C23×D312yes—
916C2×Q8—21no—
917C2×Q8—21no—
918C2×Q8—21no—
919C2×Q8—21no—
920C2×Q8—21no—
921C2×Q8—31no—
922C2×Q8—34no—
923C2×Q8—31no—
924C2×Q8—31no—
925C2×Q8—62no—
926C2×Q8—62no—
927C2×Q8—64no—
928C2×Q8—64no—
929C2×Q8—62no—
930C2×Q8—122no—
931C2×Q8—122no—
932C2×Q8D3×D411yescharacteristic
933C2×Q8C23×D312yes—
934C2×Q8C23×D311yescharacteristic
935C2×D4—21no—
936C2×D4—21no—
937C2×D4—32no—
938C2×D4—34no—
939C2×D4—31no—
940C2×D4—31no—
941C2×D4—31no—
942C2×D4—32no—
943C2×D4—62no—
944C2×D4—62no—
945C2×D4—62no—
946C2×D4—64no—
947C2×D4—64no—
948C2×D4—62no—
949C2×D4—64no—
950C2×D4—62no—
951C2×D4—64no—
952C2×D4—64no—
953C2×D4—61no—
954C2×D4—61no—
955C2×D4—61no—
956C2×D4—61no—
957C2×D4—61no—
958C2×D4—61no—
959C2×D4—61no—
960C2×D4—122no—
961C2×D4—122no—
962C2×D4—124no—
963C2×D4—124no—
964C2×D4D3×D411yescharacteristic
965C2×D4C23×D311yescharacteristic
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—32no—
970C22×C4—64no—
971C22×C4—62no—
972C22×C4—62no—
973C22×C4—62no—
974C22×C4—61no—
975C22×C4—61no—
976C22×C4C23×D311yescharacteristic
977Q16—24no—
978Q16—22no—
979Q16—24no—
980Q16—62no—
981Q16—61no—
982Q16—61no—
983Q16—64no—
984Q16—62no—
985Q16—62no—
986SD16—22no—
987SD16—24no—
988SD16—22no—
989SD16—24no—
990SD16—62no—
991SD16—64no—
992SD16—62no—
993SD16—61no—
994SD16—61no—
995SD16—62no—
996SD16—62no—
997SD16—62no—
998SD16—62no—
999SD16—61no—
1000SD16—61no—
1001SD16—62no—
1002SD16—64no—
1003SD16—62no—
1004SD16—64no—
1005SD16—62no—
1006SD16—62no—
1007SD16—64no—
1008D8—22no—
1009D8—64no—
1010D8—62no—
1011D8—61no—
1012D8—61no—
1013D8—62no—
1014D8—64no—
1015D8—62no—
1016D8—64no—
1017M16—21no—
1018M16—21no—
1019M16—21no—
1020M16—24no—
1021M16—34no—
1022M16—34no—
1023M16—32no—
1024M16—32no—
1025M16—32no—
1026M16—62no—
1027M16—62no—
1028M16—64no—
1029M16—64no—
1030M16—64no—
1031M16—62no—
1032M16—62no—
1033M16—61no—
1034M16—61no—
1035M16—61no—
1036M16—64no—
1037M16D3×D412yes—
1038M16D3×D412yes—
1039M16C23×D312yes—
1040M16C23×D312yes—
1041M16C23×D312yes—
1042C2×C8—21no—
1043C2×C8—21no—
1044C2×C8—21no—
1045C2×C8—24no—
1046C2×C8—31no—
1047C2×C8—31no—
1048C2×C8—31no—
1049C2×C8—31no—
1050C2×C8—31no—
1051C2×C8—31no—
1052C2×C8—34no—
1053C2×C8—34no—
1054C2×C8—62no—
1055C2×C8—62no—
1056C2×C8—64no—
1057C2×C8—64no—
1058C2×C8—64no—
1059C2×C8—62no—
1060C2×C8—62no—
1061C2×C8—61no—
1062C2×C8—61no—
1063C2×C8—61no—
1064C2×C8—64no—
1065C2×C8C23×D312yes—
1066C22×C3—22no—
1067C22×C3—41no—
1068C22×C3—41no—
1069C22×C3—81no—
1070C22×C3—81no—
1071C22×C3C2×#12111yescharacteristic
1072C22×C3C2×#12111yescharacteristic
1073C22×C3C22×#4111yescharacteristic
1074C2×D3—22no—
1075C2×D3—42no—
1076C2×D3—41no—
1077C2×D3—42no—
1078C2×D3—84no—
1079C2×D3—81no—
1080C2×D3—81no—
1081C2×D3—82no—
1082C2×D3—164no—
1083C2×D3—161no—
1084C2×D3—161no—
1085C2×D3C2×#12114yes—
1086C3×C4—22no—
1087C3×C4—42no—
1088C3×C4—41no—
1089C3×C4C2×#12111yescharacteristic
1090C3×C4C2×#12111yescharacteristic
1091C3×C4C23×D411yescharacteristic
1092C3×C4C23×D411yescharacteristic
1093Dic3—22no—
1094Dic3—41no—
1095Dic3C2×#12114yes—
1096C23—21no—
1097C23—21no—
1098C23—32no—
1099C23—64no—
1100C23—61no—
1101C23—61no—
1102C23—62no—
1103C23—124no—
1104C23—121no—
1105C23—121no—
1106C23—481no—
1107C23—482no—
1108C23D3×#4111yescharacteristic
1109Q8—21no—
1110Q8—22no—
1111Q8—22no—
1112Q8—21no—
1113Q8—21no—
1114Q8—32no—
1115Q8—32no—
1116Q8—32no—
1117Q8—41no—
1118Q8—41no—
1119Q8—64no—
1120Q8—61no—
1121Q8—61no—
1122Q8—61no—
1123Q8—124no—
1124Q8C2×D3×D412yes—
1125D4—22no—
1126D4—22no—
1127D4—21no—
1128D4—21no—
1129D4—21no—
1130D4—34no—
1131D4—34no—
1132D4—32no—
1133D4—32no—
1134D4—32no—
1135D4—41no—
1136D4—41no—
1137D4—64no—
1138D4—64no—
1139D4—64no—
1140D4—62no—
1141D4—62no—
1142D4—61no—
1143D4—62no—
1144D4—61no—
1145D4—62no—
1146D4—61no—
1147D4—124no—
1148D4—124no—
1149D4—124no—
1150D4—121no—
1151D4—121no—
1152D4—121no—
1153D4—121no—
1154D4C2×D3×D412yes—
1155C2×C4—21no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—21no—
1159C2×C4—22no—
1160C2×C4—32no—
1161C2×C4—34no—
1162C2×C4—34no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—64no—
1168C2×C4—64no—
1169C2×C4—64no—
1170C2×C4—61no—
1171C2×C4—62no—
1172C2×C4—62no—
1173C2×C4—61no—
1174C2×C4—124no—
1175C2×C4—124no—
1176C2×C4—124no—
1177C2×C4—121no—
1178C2×C4—121no—
1179C2×C4C2×D3×D411yescharacteristic
1180C2×C4C2×D3×D411yescharacteristic
1181C2×C4C2×D3×D411yescharacteristic
1182C2×C4C2×D3×D411yescharacteristic
1183C2×C4D3×#4111yescharacteristic
1184C2×C4C24×D311yescharacteristic
1185C8—22no—
1186C8—22no—
1187C8—22no—
1188C8—31no—
1189C8—31no—
1190C8—31no—
1191C8—31no—
1192C8—62no—
1193C8—62no—
1194C8—62no—
1195C8C2×D3×D414yes—
1196C2×C3—21no—
1197C2×C3—21no—
1198C2×C3—21no—
1199C2×C3—42no—
1200C2×C3—81no—
1201C2×C3C22×#12111yescharacteristic
1202D3—24no—
1203D3—42no—
1204D3—81no—
1205D3—82no—
1206C22—22no—
1207C22—34no—
1208C22—41no—
1209C22—41no—
1210C22—62no—
1211C22—81no—
1212C22—81no—
1213C22—122no—
1214C22—121no—
1215C22—122no—
1216C22—241no—
1217C22—242no—
1218C22—241no—
1219C22—244no—
1220C22—481no—
1221C22—481no—
1222C22—484no—
1223C22D3×#12111yescharacteristic
1224C22D3×#12111yescharacteristic
1225C22C2×D3×#4111yescharacteristic
1226C4—22no—
1227C4—34no—
1228C4—41no—
1229C4—42no—
1230C4—62no—
1231C4—121no—
1232C4D3×#12111yescharacteristic
1233C4D3×#12111yescharacteristic
1234C4C22×D3×D411yescharacteristic
1235C4C22×D3×D411yescharacteristic
1236C3#6047011yescharacteristic, complemented, Sylow
1237C2—21no—
1238C2—21no—
1239C2—21no—
1240C2—42no—
1241C2—64no—
1242C2—81no—
1243C2—122no—
1244C2—242no—
1245C2—241no—
1246C2C2×D3×#12111yescharacteristic
subgroupG/H
centerC2C2×D3×#121
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3069C2
socleC2×C3C22×#121
hypercenter#3069D3
hypocenterC3#60470
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C22×C4 ◁ #3069

Complements

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

NH ≅ G/Ntype
1. #87200C2semidirect
2. #87197C2semidirect
3. C2×#5778C2semidirect
4. #87166C2semidirect
5. C3×#3069C2semidirect
6. #84001C2semidirect
7. #83998C2semidirect
8. C2×#5203C2semidirect
9. #83814C2semidirect
10. #80944C2semidirect
11. #80943C2semidirect
12. #80930C2semidirect
13. D3×#471C2semidirect
14. #79261C2semidirect
15. #79260C2semidirect
16. #78719C2semidirect
17. #78714C2semidirect
18. C2×#4754C2semidirect
19. #78706C2semidirect
25. C2×C3×#137C22semidirect
26. C2×C3×#137C22semidirect
27. C3×#568C22semidirect
29. #5822C22semidirect
30. C2×#950C22semidirect
32. C2×#948C22semidirect
33. C2×#942C22semidirect
34. C22×#215C22semidirect
43. #5777C22semidirect
44. D3×#137C22semidirect
50. C2×#919C22semidirect
51. C2×#918C22semidirect
53. C2×#914C22semidirect
54. C2×D3×SD16C22semidirect
56. #5750C22semidirect
58. D3×#131C22semidirect
59. #5748C22semidirect
61. C2×#908C22semidirect
66. #5745C22semidirect
69. C2×#907C22semidirect
70. C3×#473C22semidirect
71. C3×#471C22semidirect
72. C3×#430C22semidirect
73. C3×#413C22semidirect
74. C2×C3×#101C22semidirect
75. #5237C22semidirect
76. C2×#836C22semidirect
77. #5204C22semidirect
78. #5203C22semidirect
79. #5203C22semidirect
80. #5203C22semidirect
81. #5200C22semidirect
82. #5199C22semidirect
83. #5192C22semidirect
84. #5177C22semidirect
85. #5142C22semidirect
86. #5141C22semidirect
87. #5132C22semidirect
88. #5132C22semidirect
89. C2×#823C22semidirect
90. C2×#823C22semidirect
91. #5125C22semidirect
92. C2×#822C22semidirect
93. C2×#822C22semidirect
94. #4898C22semidirect
95. #4897C22semidirect
96. #4893C22semidirect
97. D3×#108C22semidirect
98. #4755C22semidirect
99. #4754C22semidirect
100. #4754C22semidirect
101. #4754C22semidirect
102. #4751C22semidirect
103. #4751C22semidirect
104. D3×#101C22semidirect
105. #4749C22semidirect
106. #4748C22semidirect
107. D3×#100C22semidirect
114. #3069D3semidirect
335. C2×#137C2×D3semidirect
336. C2×#137C2×D3semidirect
353. #568C2×D3semidirect
363. #473C2×D3semidirect
379. #471C2×D3semidirect
382. #430C2×D3semidirect
391. #413C2×D3semidirect
394. C2×#101C2×D3semidirect
1236. C3#60470semidirect

Maximal subgroups

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

subgroupindex
#872002
#871972
C2×#57782
#871662
C3×#30692
#840012
#839982
C2×#52032
#838142
#809442
#809432
#809302
D3×#4712
#792612
#792602
#787192
#787142
C2×#47542
#787062
#604703