Finite Group Databasebeta

← #11662614

Subgroups — #11662614

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#87201C211yesmaximal, characteristic, complemented
2#87200C211yesmaximal, characteristic, complemented
3C2×#5770C211yesmaximal, characteristic, complemented
4#87160C211yesmaximal, characteristic, complemented
5C3×#3067C211yesmaximal, characteristic, complemented
6#84003C211yesmaximal, characteristic, complemented
7#84002C211yesmaximal, characteristic, complemented
8#83928C211yesmaximal, characteristic, complemented
9C2×#5141C211yesmaximal, characteristic, complemented
10#80944C214yesmaximal, complemented
11#80938C214yesmaximal, complemented
12#80929C214yesmaximal, complemented
13D3×#471C214yesmaximal, complemented
14C2×#4898C211yesmaximal, characteristic, complemented
15#79252C211yesmaximal, characteristic, complemented
16#78721C211yesmaximal, characteristic, complemented
17#78720C211yesmaximal, characteristic, complemented
18#78715C211yesmaximal, characteristic, complemented
19#78714C211yesmaximal, characteristic, complemented
20#60470—31nomaximal, Sylow
21#5964C2211yescharacteristic
22C2×#1010C2211yescharacteristic
23C2×#1009C2211yescharacteristic
24C3×#575C2211yescharacteristic
25C3×#575C2211yescharacteristic, complemented
26C2×C3×#135C2211yescharacteristic, complemented
27C2×C3×#131C2211yescharacteristic, complemented
28C2×#951C2211yescharacteristic, complemented
29C2×#951C2211yescharacteristic, complemented
30#5822C2211yescharacteristic
31#5822C2211yescharacteristic, complemented
32C2×#949C2211yescharacteristic
33C2×#949C2211yescharacteristic, complemented
34#5819C2211yescharacteristic, complemented
35#5779—22no—
36#5778—22no—
37#5777C2214yes—
38D3×#137C2214yescomplemented
39#5775—22no—
40#5774—22no—
41#5773C2214yescomplemented
42D3×AGL(1,ℤ/8)C2214yes—
43#5771—22no—
44#5770—22no—
45#5770—22no—
46#5770—22no—
47#5770—22no—
48#5770—22no—
49#5770—22no—
50#5769—22no—
51C2×#918C2212yescomplemented
52C2×#916C2212yescomplemented
53C2×D3×SD16C2212yescomplemented
54C2×#911C2212yescomplemented
55#5750—22no—
56#5750C2214yescomplemented
57D3×#131—22no—
58D3×#131C2214yescomplemented
59C2×#909C2211yescharacteristic, complemented
60C2×#908C2211yescharacteristic
61#5745—22no—
62#5745C2211yescharacteristic
63#5745C2211yescharacteristic
64#5745C2211yescharacteristic
65#5745C2211yescharacteristic, complemented
66C22×#204C2211yescharacteristic, complemented
67C2×#901—22no—
68C2×#901C2211yescharacteristic
69C2×#901C2211yescharacteristic, complemented
70C3×#473C2212yescomplemented
71C3×#472C2212yescomplemented
72C3×#471C2212yescomplemented
73C3×#471C2212yescomplemented
74C2×C3×#108C2211yescharacteristic, complemented
75C3×#413C2211yescharacteristic, complemented
76C3×#413C2211yescharacteristic, complemented
77#5237C2211yescharacteristic, complemented
78#5237C2211yescharacteristic, complemented
79#5204C2214yescomplemented
80#5203C2214yescomplemented
81#5200C2214yescomplemented
82#5199C2214yescomplemented
83#5192C2212yescomplemented
84#5177C2212yescomplemented
85#5177C2212yescomplemented
86#5160C2212yescomplemented
87#5141C2214yescomplemented
88#5141C2214yescomplemented
89C2×#824C2211yescharacteristic, complemented
90C2×#824C2211yescharacteristic, complemented
91C2×#823C2211yescharacteristic, complemented
92C2×#823C2211yescharacteristic, complemented
93#5124C2211yescharacteristic, complemented
94#5124C2211yescharacteristic, complemented
95C2×#819C2211yescharacteristic, complemented
96#4898C2214yescomplemented
97#4898C2214yescomplemented
98#4893C2214yescomplemented
99D3×#108C2214yescomplemented
100#4755C2214yescomplemented
101#4754C2214yescomplemented
102#4751C2214yescomplemented
103D3×#101C2214yescomplemented
104#4749C2214yescomplemented
105#4748C2214yescomplemented
106#4745C2214yescomplemented
107D3×#100C2214yescomplemented
108#3586—31no—
109#3585—31no—
110C2×#577—31no—
111#3573—31no—
112#3069—34no—
113#3069—31no—
114#3069—31no—
115#3068—34no—
116#3068—31no—
117#3068—31no—
118#3067—34no—
119#3067—31no—
120#3067D311yescharacteristic, complemented
121C2×#471—34no—
122C2×#471—31no—
123C2×#471—31no—
124#2916—31no—
125#2889—31no—
126#2888—31no—
127C2×C3×#41C2311yescharacteristic
128C2×C3×#41C2311yescharacteristic
129C2×C3×#41C2311yescharacteristic
130#1010—21no—
131#1010—22no—
132#1010—22no—
133#1010—22no—
134#1010—22no—
135#1010D412yes—
136#1009—21no—
137#1009—22no—
138#1009—22no—
139#1009—22no—
140#1009—22no—
141#1009D412yes—
142D3×#41—22no—
143D3×#41C2314yes—
144#1007D412yes—
145C2×#239C2312yes—
146C2×D3×Q8C2312yes—
147#1004—22no—
148#1004D412yes—
149C2×#237—22no—
150C2×#237C2312yes—
151C2×D3×D4—22no—
152C2×D3×D4C2312yes—
153C2×#235—22no—
154C2×#235—21no—
155C2×#235—21no—
156C2×#235C2311yescharacteristic
157C2×#235C2311yescharacteristic
158C22×D12—21no—
159C22×D12C2311yescharacteristic
160C22×Dic6—21no—
161C22×Dic6C2311yescharacteristic
162C3×#137—21no—
163C3×#137—21no—
164C3×#137C2312yes—
165C3×#137C2312yes—
166C3×AGL(1,ℤ/8)—21no—
167C3×AGL(1,ℤ/8)—21no—
168C3×AGL(1,ℤ/8)C2312yes—
169C3×AGL(1,ℤ/8)C2312yes—
170C3×#135—22no—
171C3×#135—22no—
172C3×#135—21no—
173C3×#135—21no—
174C3×#135—21no—
175C3×#135—21no—
176C2×C3×Q16C2311yescharacteristic
177C2×C3×SD16C2311yescharacteristic
178C2×C3×SD16C2311yescharacteristic
179C2×C3×D8C2311yescharacteristic
180C3×#131—21no—
181C3×#131—21no—
182C3×#131C2312yes—
183C3×#131C2312yes—
184C2×C3×M16—21no—
185C2×C3×M16C2311yescharacteristic
186C2×C3×M16C2311yescharacteristic
187C2×C3×M16C2311yescharacteristic
188C22×C3×C8—21no—
189C22×C3×C8C2311yescharacteristic
190#951—22no—
191#951—21no—
192#951—21no—
193#951—22no—
194#951—22no—
195#951C2314yes—
196#950—22no—
197#950—22no—
198#949—22no—
199#949—21no—
200#949—21no—
201#949—22no—
202#949—22no—
203#949C2314yes—
204#948—22no—
205#948C2314yes—
206C2×#216—21no—
207C2×#216C2312yes—
208#942C2312yes—
209#942C2312yes—
210C2×#215—21no—
211C2×#215C2312yes—
212C2×#214—21no—
213C2×#214C2312yes—
214#932C2312yes—
215#932C2312yes—
216C2×#213—21no—
217C2×#213C2312yes—
218C2×#208—22no—
219C2×#208C2311yescharacteristic
220C2×#208C2311yescharacteristic
221C2×#208C2311yescharacteristic
222C2×#208C2311yescharacteristic
223#919—24no—
224#918—24no—
225#918—24no—
226#918—24no—
227#918—24no—
228D3×Q16—24no—
229#916—24no—
230#916—24no—
231#916—24no—
232#916—24no—
233#915—24no—
234#915—24no—
235#914—24no—
236#914—24no—
237D3×SD16—24no—
238D3×SD16—24no—
239D3×SD16—24no—
240D3×SD16—24no—
241#912—24no—
242#911—24no—
243#911—24no—
244#911—24no—
245#911—24no—
246D3×D8—24no—
247#909—22no—
248#909C2314yes—
249#908—22no—
250#908C2314yes—
251#907—22no—
252#907—22no—
253#907—22no—
254#907—24no—
255#907—24no—
256#907C2314yes—
257D3×M16—22no—
258D3×M16—24no—
259D3×M16—24no—
260D3×M16C2314yes—
261D3×M16C2314yes—
262D3×M16C2314yes—
263C2×Dic12—21no—
264C2×D24—21no—
265C2×#204—21no—
266C2×#204—21no—
267C2×#204—21no—
268C2×#204—21no—
269C2×#204—21no—
270C2×#204—21no—
271C2×#204C2312yes—
272C2×#204C2312yes—
273#901—22no—
274#901—22no—
275#901—22no—
276#901—21no—
277#901—21no—
278#901—22no—
279#901—24no—
280#901—24no—
281#901D412yes—
282#901D412yes—
283#901D412yes—
284#901D412yes—
285#901C2312yes—
286#901C2312yes—
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×#108C2312yes—
294C3×#108C2312yes—
295C3×#101C2312yes—
296C3×#101C2312yes—
297C3×#100C2312yes—
298C3×#100C2312yes—
299#836C2312yes—
300#836C2312yes—
301#833C2312yes—
302#833C2312yes—
303#824C2314yes—
304#824C2314yes—
305#823C2314yes—
306#823C2314yes—
307#822C2314yes—
308#822C2314yes—
309#819C2312yes—
310#819C2312yes—
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#575C2×D311yescharacteristic
331#575C2×D311yescharacteristic, complemented
332C2×#137—31no—
333C2×#137—32no—
334C2×#137—31no—
335C2×#137—34no—
336C2×#137—31no—
337C2×AGL(1,ℤ/8)—31no—
338C2×AGL(1,ℤ/8)—32no—
339C2×AGL(1,ℤ/8)—31no—
340C2×AGL(1,ℤ/8)—34no—
341C2×AGL(1,ℤ/8)—31no—
342C2×#135—32no—
343C2×#135C2×D311yescharacteristic, complemented
344C22×SD16—32no—
345C22×SD16—31no—
346#568—31no—
347#568—31no—
348#568—31no—
349#568—31no—
350#568—34no—
351#568—31no—
352#568—62no—
353#568—62no—
354C2×#131—31no—
355C2×#131—34no—
356C2×#131—31no—
357C2×#131—62no—
358C2×#131—62no—
359C2×#131C2×D311yescharacteristic, complemented
360#473—34no—
361#473—32no—
362#473—34no—
363#473C2×D312yescomplemented
364#472—34no—
365#472—32no—
366#472—34no—
367#472C2×D312yescomplemented
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—34no—
378#471C2×D312yescomplemented
379#471C2×D312yescomplemented
380#430—31no—
381#430—31no—
382#430—34no—
383C2×#108—31no—
384C2×#108—34no—
385C2×#108C2×D311yescharacteristic, complemented
386#413—31no—
387#413—31no—
388#413—34no—
389#413—34no—
390#413C2×D311yescharacteristic, complemented
391#413C2×D311yescharacteristic, complemented
392C2×#101—31no—
393C2×#101—31no—
394C2×#101—34no—
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×#41—21no—
407C3×#41—21no—
408C3×#41—21no—
409C3×#41—21no—
410C3×#41C2×D412yes—
411C3×#41C2412yes—
412C2×C3×Q8C2×D411yescharacteristic
413C2×C3×Q8C2411yescharacteristic
414C2×C3×Q8C2411yescharacteristic
415C2×C3×D4—21no—
416C2×C3×D4—21no—
417C2×C3×D4—21no—
418C2×C3×D4C2×D411yescharacteristic
419C2×C3×D4C2411yescharacteristic
420C2×C3×D4C2411yescharacteristic
421C22×C3×C4—21no—
422C22×C3×C4—21no—
423C22×C3×C4—21no—
424C22×C3×C4C2411yescharacteristic
425C2×#67—21no—
426C2×#67—24no—
427C2×#67—22no—
428C2×#67—22no—
429C2×#67#4112yes—
430C22×Dic3—21no—
431C22×Dic3—22no—
432#239—22no—
433#239—24no—
434#239—24no—
435#239C2×D414yes—
436D3×Q8—22no—
437D3×Q8—24no—
438D3×Q8—24no—
439D3×Q8C2×D414yes—
440#237—24no—
441#237—24no—
442#237—24no—
443#237—24no—
444#237—22no—
445#237—44no—
446#237—44no—
447#237C2×D414yes—
448D3×D4—24no—
449D3×D4—24no—
450D3×D4—22no—
451D3×D4—24no—
452D3×D4—24no—
453D3×D4—44no—
454D3×D4—44no—
455D3×D4C2×D414yes—
456#235—21no—
457#235—21no—
458#235—24no—
459#235—22no—
460#235—24no—
461#235—22no—
462#235—42no—
463#235—42no—
464#235—42no—
465#235—42no—
466#235C2×D412yes—
467#235C2×D412yes—
468#235C2×D412yes—
469#235C2×D412yes—
470#235C2×D412yes—
471#235C2412yes—
472C2×D12—22no—
473C2×D12—21no—
474C2×D12—21no—
475C2×D12—21no—
476C2×D12—21no—
477C2×D12—22no—
478C2×D12—21no—
479C2×D12—42no—
480C2×D12—42no—
481C2×D12C2×D411yescharacteristic
482C2×D12#4111yescharacteristic
483C2×D12C2412yes—
484C2×C4×D3—21no—
485C2×C4×D3—24no—
486C2×C4×D3—22no—
487C2×C4×D3—22no—
488C2×C4×D3C2412yes—
489C2×Dic6—22no—
490C2×Dic6—21no—
491C2×Dic6—21no—
492C2×Dic6—21no—
493C2×Dic6—21no—
494C2×Dic6—21no—
495C2×Dic6—22no—
496C2×Dic6—42no—
497C2×Dic6—42no—
498C2×Dic6C2×D411yescharacteristic
499C2×Dic6#4111yescharacteristic
500C2×Dic6C2412yes—
501C3×Q16—22no—
502C3×Q16—22no—
503C3×Q16—21no—
504C3×Q16—21no—
505C3×SD16—22no—
506C3×SD16—22no—
507C3×SD16—22no—
508C3×SD16—22no—
509C3×SD16—21no—
510C3×SD16—21no—
511C3×SD16—21no—
512C3×SD16—21no—
513C3×D8—22no—
514C3×D8—22no—
515C3×D8—21no—
516C3×D8—21no—
517C3×M16—21no—
518C3×M16—21no—
519C3×M16—21no—
520C3×M16—22no—
521C3×M16—22no—
522C3×M16C2412yes—
523C3×M16C2412yes—
524C3×M16C2412yes—
525C2×C3×C8—21no—
526C2×C3×C8—21no—
527C2×C3×C8—21no—
528C2×C3×C8—22no—
529C2×C3×C8—22no—
530C2×C3×C8C2×D411yescharacteristic
531C2×C3×C8C2×D411yescharacteristic
532C2×C3×C8C2×D411yescharacteristic
533C2×C3×C8C2×D411yescharacteristic
534C2×C3×C8C2411yescharacteristic
535C2×C3×C8C2411yescharacteristic
536#216—24no—
537#216—22no—
538#216—22no—
539#216—24no—
540#215—24no—
541#215—22no—
542#215—22no—
543#215—24no—
544#214—24no—
545#214—22no—
546#214—22no—
547#214—24no—
548#213—24no—
549#213—22no—
550#213—22no—
551#213—24no—
552#208—21no—
553#208—21no—
554#208—21no—
555#208—24no—
556#208C2×D412yes—
557#208C2×D412yes—
558#208C2412yes—
559#208C2412yes—
560#208C2412yes—
561C2×C3⋊C8—21no—
562C2×C3⋊C8—21no—
563C2×C3⋊C8—21no—
564C2×C3⋊C8—24no—
565C2×C3⋊C8C2412yes—
566Dic12—24no—
567D24—24no—
568#204—24no—
569#204—24no—
570#204—22no—
571#204—22no—
572#204—22no—
573#204—22no—
574ΓL(1,𝔽25)—24no—
575ΓL(1,𝔽25)—24no—
576ΓL(1,𝔽25)—24no—
577ΓL(1,𝔽25)—22no—
578ΓL(1,𝔽25)—22no—
579ΓL(1,𝔽25)—24no—
580ΓL(1,𝔽25)C2×D414yes—
581ΓL(1,𝔽25)C2×D414yes—
582D3×C8—24no—
583D3×C8—24no—
584D3×C8—24no—
585D3×C8—22no—
586D3×C8—22no—
587D3×C8—24no—
588D3×C8C2×D414yes—
589D3×C8C2×D414yes—
5902−1+4—32no—
5912−1+4—32no—
5922−1+4—61no—
5932−1+4—62no—
5942−1+4—62no—
5952−1+4—62no—
5962−1+4—62no—
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—61no—
611C2×#41—61no—
612C2×#41—62no—
613C2×#41—62no—
614C2×#41—62no—
615C2×#41C22×D311yescharacteristic
616C2×#41C22×D311yescharacteristic
617C2×#41C22×D311yescharacteristic
618C22×Q8—32no—
619C22×Q8—31no—
620C22×Q8—61no—
621C22×D4—32no—
622C22×D4—31no—
623C22×D4—61no—
624C22×D4—62no—
625#137—21no—
626#137—21no—
627#137—34no—
628#137—32no—
629#137—32no—
630#137—34no—
631#137—62no—
632#137—64no—
633#137—64no—
634#137—62no—
635#137—62no—
636#137—64no—
637#137—64no—
638#137—64no—
639#137—64no—
640#137—61no—
641#137—61no—
642#137—62no—
643#137C22×D312yes—
644#137C22×D312yes—
645AGL(1,ℤ/8)—21no—
646AGL(1,ℤ/8)—21no—
647AGL(1,ℤ/8)—34no—
648AGL(1,ℤ/8)—32no—
649AGL(1,ℤ/8)—32no—
650AGL(1,ℤ/8)—34no—
651AGL(1,ℤ/8)—62no—
652AGL(1,ℤ/8)—64no—
653AGL(1,ℤ/8)—64no—
654AGL(1,ℤ/8)—62no—
655AGL(1,ℤ/8)—62no—
656AGL(1,ℤ/8)—64no—
657AGL(1,ℤ/8)—64no—
658AGL(1,ℤ/8)—64no—
659AGL(1,ℤ/8)—64no—
660AGL(1,ℤ/8)—61no—
661AGL(1,ℤ/8)—61no—
662AGL(1,ℤ/8)—62no—
663AGL(1,ℤ/8)C22×D312yes—
664AGL(1,ℤ/8)C22×D312yes—
665#135—22no—
666#135—22no—
667#135—21no—
668#135—21no—
669#135—21no—
670#135—21no—
671#135—64no—
672#135—64no—
673#135—64no—
674#135—64no—
675#135—64no—
676#135—64no—
677#135—62no—
678#135—62no—
679C2×Q16—32no—
680C2×Q16—61no—
681C2×Q16—64no—
682C2×Q16—61no—
683C2×Q16C22×D311yescharacteristic
684C2×SD16—32no—
685C2×SD16—32no—
686C2×SD16—32no—
687C2×SD16—32no—
688C2×SD16—61no—
689C2×SD16—61no—
690C2×SD16—64no—
691C2×SD16—64no—
692C2×SD16—64no—
693C2×SD16—64no—
694C2×SD16—61no—
695C2×SD16—61no—
696C2×SD16—61no—
697C2×SD16—61no—
698C2×SD16—61no—
699C2×SD16—61no—
700C2×SD16C22×D311yescharacteristic
701C2×SD16C22×D311yescharacteristic
702C2×D8—32no—
703C2×D8—61no—
704C2×D8—64no—
705C2×D8—61no—
706C2×D8C22×D311yescharacteristic
707#131—21no—
708#131—21no—
709#131—32no—
710#131—32no—
711#131—32no—
712#131—32no—
713#131—34no—
714#131—34no—
715#131—32no—
716#131—32no—
717#131—64no—
718#131—62no—
719#131—64no—
720#131—62no—
721#131—62no—
722#131—62no—
723#131—64no—
724#131—64no—
725#131—62no—
726#131—62no—
727#131—62no—
728#131—62no—
729#131—61no—
730#131—61no—
731#131C22×D312yes—
732#131C22×D312yes—
733C2×M16—21no—
734C2×M16—31no—
735C2×M16—32no—
736C2×M16—31no—
737C2×M16—31no—
738C2×M16—31no—
739C2×M16—34no—
740C2×M16—34no—
741C2×M16—34no—
742C2×M16—64no—
743C2×M16—64no—
744C2×M16—62no—
745C2×M16—64no—
746C2×M16—62no—
747C2×M16—61no—
748C2×M16C22×D311yescharacteristic
749C2×M16C22×D311yescharacteristic
750C2×M16C22×D311yescharacteristic
751C22×C8—21no—
752C22×C8—32no—
753C22×C8—64no—
754C22×C8—61no—
755C22×C8C22×D311yescharacteristic
756#108—34no—
757#108—34no—
758#108—32no—
759#108—32no—
760#108C22×D312yes—
761#108C22×D312yes—
762#101—32no—
763#101—32no—
764#101—34no—
765#101—34no—
766#101C22×D312yes—
767#101C22×D312yes—
768#100—32no—
769#100—32no—
770#100—34no—
771#100—34no—
772#100C22×D312yes—
773#100C22×D312yes—
774C23×C3—21no—
775C23×C3—21no—
776C23×C3—21no—
777C23×C3C2×#4111yescharacteristic
778C22×D3—21no—
779C22×D3—24no—
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—21no—
789C3×Q8—21no—
790C3×Q8—21no—
791C3×Q8—21no—
792C3×Q8C22×D412yes—
793C3×D4—22no—
794C3×D4—22no—
795C3×D4—21no—
796C3×D4—21no—
797C3×D4—21no—
798C3×D4—21no—
799C3×D4—21no—
800C3×D4—41no—
801C3×D4—41no—
802C3×D4—41no—
803C3×D4—41no—
804C3×D4C22×D412yes—
805C2×C3×C4—21no—
806C2×C3×C4—22no—
807C2×C3×C4—22no—
808C2×C3×C4—21no—
809C2×C3×C4—21no—
810C2×C3×C4—41no—
811C2×C3×C4—41no—
812C2×C3×C4—41no—
813C2×C3×C4—41no—
814C2×C3×C4C22×D411yescharacteristic
815C2×C3×C4C22×D411yescharacteristic
816C2×C3×C4C22×D411yescharacteristic
817C2×C3×C4C22×D411yescharacteristic
818C2×C3×C4C2×#4111yescharacteristic
819C2×C3×C4C2511yescharacteristic
820#67—22no—
821#67—22no—
822#67—24no—
823#67—24no—
824#67—44no—
825#67—44no—
826#67#12114yes—
827#67#12114yes—
828C2×Dic3—21no—
829C2×Dic3—24no—
830C2×Dic3—22no—
831C2×Dic3—41no—
832C2×Dic3—41no—
833C2×Dic3—44no—
834C2×Dic3C2×#4112yes—
835D12—24no—
836D12—21no—
837D12—22no—
838D12—22no—
839D12—44no—
840D12—41no—
841D12—41no—
842D12#12112yes—
843D12#12112yes—
844D12C22×D412yes—
845C4×D3—24no—
846C4×D3—22no—
847C4×D3—22no—
848C4×D3—24no—
849C4×D3—44no—
850C4×D3—44no—
851C4×D3C22×D414yes—
852C4×D3C22×D414yes—
853Dic6—21no—
854Dic6—24no—
855Dic6—22no—
856Dic6—22no—
857Dic6—41no—
858Dic6—41no—
859Dic6—44no—
860Dic6#12112yes—
861Dic6#12112yes—
862Dic6C22×D412yes—
863C3×C8—22no—
864C3×C8—22no—
865C3×C8—22no—
866C3×C8C22×D411yescharacteristic
867C3×C8C22×D411yescharacteristic
868C3×C8C22×D411yescharacteristic
869C3×C8C22×D411yescharacteristic
870C3⋊C8—22no—
871C3⋊C8—22no—
872C3⋊C8—22no—
873C3⋊C8C22×D414yes—
874C24—62no—
875C24—61no—
876#41—21no—
877#41—21no—
878#41—21no—
879#41—21no—
880#41—21no—
881#41—21no—
882#41—21no—
883#41—21no—
884#41—21no—
885#41—21no—
886#41—32no—
887#41—32no—
888#41—32no—
889#41—32no—
890#41—34no—
891#41—34no—
892#41—32no—
893#41—32no—
894#41—64no—
895#41—64no—
896#41—62no—
897#41—62no—
898#41—64no—
899#41—64no—
900#41—64no—
901#41—64no—
902#41—64no—
903#41—64no—
904#41—62no—
905#41—62no—
906#41—61no—
907#41—61no—
908#41—122no—
909#41—122no—
910#41—122no—
911#41—122no—
912#41—124no—
913#41—124no—
914#41D3×D412yes—
915#41C23×D312yes—
916C2×Q8—31no—
917C2×Q8—34no—
918C2×Q8—31no—
919C2×Q8—32no—
920C2×Q8—62no—
921C2×Q8—62no—
922C2×Q8—64no—
923C2×Q8—64no—
924C2×Q8—62no—
925C2×Q8—61no—
926C2×Q8—61no—
927C2×Q8—61no—
928C2×Q8—61no—
929C2×Q8—61no—
930C2×Q8—122no—
931C2×Q8—122no—
932C2×Q8D3×D411yescharacteristic
933C2×Q8C23×D311yescharacteristic
934C2×Q8C23×D311yescharacteristic
935C2×D4—21no—
936C2×D4—21no—
937C2×D4—21no—
938C2×D4—32no—
939C2×D4—34no—
940C2×D4—31no—
941C2×D4—31no—
942C2×D4—32no—
943C2×D4—62no—
944C2×D4—62no—
945C2×D4—64no—
946C2×D4—64no—
947C2×D4—62no—
948C2×D4—64no—
949C2×D4—62no—
950C2×D4—64no—
951C2×D4—64no—
952C2×D4—61no—
953C2×D4—62no—
954C2×D4—61no—
955C2×D4—61no—
956C2×D4—61no—
957C2×D4—61no—
958C2×D4—61no—
959C2×D4—122no—
960C2×D4—122no—
961C2×D4—124no—
962C2×D4—124no—
963C2×D4D3×D411yescharacteristic
964C2×D4C23×D311yescharacteristic
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—22no—
978Q16—22no—
979Q16—21no—
980Q16—21no—
981Q16—64no—
982Q16—64no—
983Q16—62no—
984Q16—62no—
985Q16—64no—
986SD16—22no—
987SD16—22no—
988SD16—22no—
989SD16—22no—
990SD16—21no—
991SD16—21no—
992SD16—21no—
993SD16—21no—
994SD16—64no—
995SD16—64no—
996SD16—64no—
997SD16—64no—
998SD16—62no—
999SD16—62no—
1000SD16—62no—
1001SD16—62no—
1002SD16—64no—
1003SD16—64no—
1004SD16—62no—
1005SD16—62no—
1006SD16—62no—
1007SD16—62no—
1008D8—22no—
1009D8—22no—
1010D8—21no—
1011D8—21no—
1012D8—64no—
1013D8—64no—
1014D8—62no—
1015D8—62no—
1016D8—64no—
1017M16—21no—
1018M16—21no—
1019M16—21no—
1020M16—22no—
1021M16—22no—
1022M16—32no—
1023M16—32no—
1024M16—34no—
1025M16—34no—
1026M16—32no—
1027M16—32no—
1028M16—32no—
1029M16—64no—
1030M16—64no—
1031M16—64no—
1032M16—64no—
1033M16—64no—
1034M16—61no—
1035M16—61no—
1036M16—61no—
1037M16—62no—
1038M16—62no—
1039M16C23×D312yes—
1040M16C23×D312yes—
1041M16C23×D312yes—
1042C2×C8—21no—
1043C2×C8—21no—
1044C2×C8—21no—
1045C2×C8—22no—
1046C2×C8—22no—
1047C2×C8—32no—
1048C2×C8—34no—
1049C2×C8—34no—
1050C2×C8—64no—
1051C2×C8—64no—
1052C2×C8—64no—
1053C2×C8—64no—
1054C2×C8—64no—
1055C2×C8—61no—
1056C2×C8—61no—
1057C2×C8—61no—
1058C2×C8—62no—
1059C2×C8—62no—
1060C2×C8D3×D411yescharacteristic
1061C2×C8D3×D411yescharacteristic
1062C2×C8D3×D411yescharacteristic
1063C2×C8D3×D411yescharacteristic
1064C2×C8C23×D311yescharacteristic
1065C2×C8C23×D311yescharacteristic
1066C22×C3—22no—
1067C22×C3—41no—
1068C22×C3—41no—
1069C22×C3—41no—
1070C22×C3—81no—
1071C22×C3—81no—
1072C22×C3—81no—
1073C22×C3C2×#12111yescharacteristic
1074C22×C3C2×#12111yescharacteristic
1075C22×C3C22×#4111yescharacteristic
1076C2×D3—22no—
1077C2×D3—42no—
1078C2×D3—42no—
1079C2×D3—84no—
1080C2×D3—81no—
1081C2×D3—82no—
1082C2×D3—164no—
1083C2×D3—161no—
1084C2×D3—161no—
1085C2×D3C2×#12114yes—
1086C3×C4—22no—
1087C3×C4—41no—
1088C3×C4—41no—
1089C3×C4C2×#12111yescharacteristic
1090C3×C4C2×#12111yescharacteristic
1091C3×C4C23×D411yescharacteristic
1092C3×C4C23×D411yescharacteristic
1093Dic3—22no—
1094Dic3—42no—
1095Dic3C2×#12114yes—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—32no—
1100C23—64no—
1101C23—61no—
1102C23—62no—
1103C23—124no—
1104C23—121no—
1105C23—121no—
1106C23—481no—
1107C23—482no—
1108C23D3×#4111yescharacteristic
1109Q8—21no—
1110Q8—21no—
1111Q8—21no—
1112Q8—21no—
1113Q8—21no—
1114Q8—32no—
1115Q8—32no—
1116Q8—32no—
1117Q8—64no—
1118Q8—61no—
1119Q8—62no—
1120Q8—62no—
1121Q8—124no—
1122Q8—121no—
1123Q8—121no—
1124Q8C2×D3×D412yes—
1125D4—22no—
1126D4—22no—
1127D4—21no—
1128D4—21no—
1129D4—21no—
1130D4—21no—
1131D4—21no—
1132D4—34no—
1133D4—34no—
1134D4—32no—
1135D4—32no—
1136D4—32no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—64no—
1142D4—64no—
1143D4—64no—
1144D4—62no—
1145D4—62no—
1146D4—62no—
1147D4—62no—
1148D4—61no—
1149D4—124no—
1150D4—124no—
1151D4—124no—
1152D4—121no—
1153D4—121no—
1154D4C2×D3×D412yes—
1155C2×C4—21no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—21no—
1159C2×C4—21no—
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—62no—
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—34no—
1189C8—62no—
1190C8—62no—
1191C8—62no—
1192C8C2×D3×D411yescharacteristic
1193C8C2×D3×D411yescharacteristic
1194C8C2×D3×D411yescharacteristic
1195C8C2×D3×D411yescharacteristic
1196C2×C3—21no—
1197C2×C3—21no—
1198C2×C3—21no—
1199C2×C3—42no—
1200C2×C3—81no—
1201C2×C3—81no—
1202C2×C3C22×#12111yescharacteristic
1203D3—24no—
1204D3—42no—
1205D3—82no—
1206C22—22no—
1207C22—34no—
1208C22—41no—
1209C22—41no—
1210C22—41no—
1211C22—62no—
1212C22—81no—
1213C22—81no—
1214C22—81no—
1215C22—122no—
1216C22—122no—
1217C22—241no—
1218C22—242no—
1219C22—244no—
1220C22—481no—
1221C22—481no—
1222C22—484no—
1223C22D3×#12111yescharacteristic
1224C22D3×#12111yescharacteristic
1225C22C2×D3×#4111yescharacteristic
1226C4—22no—
1227C4—34no—
1228C4—41no—
1229C4—41no—
1230C4—62no—
1231C4—122no—
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—81no—
1244C2—122no—
1245C2—242no—
1246C2C2×D3×#12111yescharacteristic
subgroupG/H
centerC2C2×D3×#121
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3067C2
socleC2×C3C22×#121
hypercenter#3067D3
hypocenterC3#60470
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C22×C4 ◁ #3067

Complements

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

NH ≅ G/Ntype
1. #87201C2semidirect
2. #87200C2semidirect
3. C2×#5770C2semidirect
4. #87160C2semidirect
5. C3×#3067C2semidirect
6. #84003C2semidirect
7. #84002C2semidirect
8. #83928C2semidirect
9. C2×#5141C2semidirect
10. #80944C2semidirect
11. #80938C2semidirect
12. #80929C2semidirect
13. D3×#471C2semidirect
14. C2×#4898C2semidirect
15. #79252C2semidirect
16. #78721C2semidirect
17. #78720C2semidirect
18. #78715C2semidirect
19. #78714C2semidirect
25. C3×#575C22semidirect
26. C2×C3×#135C22semidirect
27. C2×C3×#131C22semidirect
28. C2×#951C22semidirect
29. C2×#951C22semidirect
31. #5822C22semidirect
33. C2×#949C22semidirect
34. #5819C22semidirect
38. D3×#137C22semidirect
41. #5773C22semidirect
51. C2×#918C22semidirect
52. C2×#916C22semidirect
53. C2×D3×SD16C22semidirect
54. C2×#911C22semidirect
56. #5750C22semidirect
58. D3×#131C22semidirect
59. C2×#909C22semidirect
65. #5745C22semidirect
66. C22×#204C22semidirect
69. C2×#901C22semidirect
70. C3×#473C22semidirect
71. C3×#472C22semidirect
72. C3×#471C22semidirect
73. C3×#471C22semidirect
74. C2×C3×#108C22semidirect
75. C3×#413C22semidirect
76. C3×#413C22semidirect
77. #5237C22semidirect
78. #5237C22semidirect
79. #5204C22semidirect
80. #5203C22semidirect
81. #5200C22semidirect
82. #5199C22semidirect
83. #5192C22semidirect
84. #5177C22semidirect
85. #5177C22semidirect
86. #5160C22semidirect
87. #5141C22semidirect
88. #5141C22semidirect
89. C2×#824C22semidirect
90. C2×#824C22semidirect
91. C2×#823C22semidirect
92. C2×#823C22semidirect
93. #5124C22semidirect
94. #5124C22semidirect
95. C2×#819C22semidirect
96. #4898C22semidirect
97. #4898C22semidirect
98. #4893C22semidirect
99. D3×#108C22semidirect
100. #4755C22semidirect
101. #4754C22semidirect
102. #4751C22semidirect
103. D3×#101C22semidirect
104. #4749C22semidirect
105. #4748C22semidirect
106. #4745C22semidirect
107. D3×#100C22semidirect
120. #3067D3semidirect
331. #575C2×D3semidirect
343. C2×#135C2×D3semidirect
359. C2×#131C2×D3semidirect
363. #473C2×D3semidirect
367. #472C2×D3semidirect
378. #471C2×D3semidirect
379. #471C2×D3semidirect
385. C2×#108C2×D3semidirect
390. #413C2×D3semidirect
391. #413C2×D3semidirect
1236. C3#60470semidirect

Maximal subgroups

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

subgroupindex
#872012
#872002
C2×#57702
#871602
C3×#30672
#840032
#840022
#839282
C2×#51412
#809442
#809382
#809292
D3×#4712
C2×#48982
#792522
#787212
#787202
#787152
#787142
#604703