Finite Group Databasebeta

← #11662628

Subgroups — #11662628

Order 768.

2630 conjugacy classes of subgroups.

The subgroup lattice has 1262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#87200C211yesmaximal, characteristic, complemented
2#87192C211yesmaximal, characteristic, complemented
3C2×#5774C211yesmaximal, characteristic, complemented
4#87166C211yesmaximal, characteristic, complemented
5C3×#3068C211yesmaximal, characteristic, complemented
6#84001C211yesmaximal, characteristic, complemented
7#83963C211yesmaximal, characteristic, complemented
8C2×#5199C211yesmaximal, characteristic, complemented
9#83814C211yesmaximal, characteristic, complemented
10#80938C214yesmaximal, complemented
11D3×#472C214yesmaximal, complemented
12#80930C214yesmaximal, complemented
13#80929C214yesmaximal, complemented
14#79261C211yesmaximal, characteristic, complemented
15#79260C211yesmaximal, characteristic, complemented
16#78719C211yesmaximal, characteristic, complemented
17#78714C211yesmaximal, characteristic, complemented
18C2×#4749C211yesmaximal, characteristic, complemented
19#78697C211yesmaximal, characteristic, complemented
20#60471—31nomaximal, Sylow
21#5964C2211yescharacteristic
22C2×#1009C2211yescharacteristic
23C2×#1004C2211yescharacteristic
24C3×#575C2211yescharacteristic, complemented
25C2×C3×AGL(1,ℤ/8)C2211yescharacteristic, complemented
26C2×C3×AGL(1,ℤ/8)C2211yescharacteristic, complemented
27C3×#568C2211yescharacteristic, complemented
28#5822C2211yescharacteristic, complemented
29#5822C2211yescharacteristic, complemented
30C2×#950C2211yescharacteristic, complemented
31C2×#949C2211yescharacteristic, complemented
32C2×#948C2211yescharacteristic, complemented
33C2×#932C2211yescharacteristic, complemented
34C22×#213C2211yescharacteristic, complemented
35#5778—22no—
36#5777C2214yescomplemented
37#5775—22no—
38#5774—22no—
39#5774—22no—
40#5774—22no—
41#5774—22no—
42#5774—22no—
43#5774—22no—
44#5773C2214yescomplemented
45D3×AGL(1,ℤ/8)C2214yescomplemented
46D3×AGL(1,ℤ/8)C2214yescomplemented
47#5770—22no—
48#5769—22no—
49#5762—22no—
50C2×#916C2212yescomplemented
51C2×#914C2212yescomplemented
52#5757—22no—
53C2×#911C2212yescomplemented
54C2×D3×D8C2212yescomplemented
55#5750—22no—
56#5750C2214yescomplemented
57D3×#131—22no—
58D3×#131C2214yescomplemented
59#5748C2211yescharacteristic, complemented
60C2×#908C2211yescharacteristic, complemented
61C2×#908C2211yescharacteristic, complemented
62#5745—22no—
63#5745C2211yescharacteristic
64#5745C2211yescharacteristic
65#5745C2211yescharacteristic
66#5745C2211yescharacteristic, complemented
67C2×#907—22no—
68C2×#907C2211yescharacteristic
69C2×#907C2211yescharacteristic, complemented
70C3×#472C2214yescomplemented
71C3×#471C2214yescomplemented
72C3×#430C2211yescharacteristic, complemented
73C3×#413C2211yescharacteristic, complemented
74C2×C3×#100C2211yescharacteristic, complemented
75#5237C2211yescharacteristic, complemented
76C2×#833C2211yescharacteristic, complemented
77#5204C2212yescomplemented
78#5203C2212yescomplemented
79#5200C2212yescomplemented
80#5199C2214yescomplemented
81#5199C2212yescomplemented
82#5199C2214yescomplemented
83#5177C2214yescomplemented
84#5160C2214yescomplemented
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#4754C2212yescomplemented
100#4751C2214yescomplemented
101#4749C2214yescomplemented
102#4749C2214yescomplemented
103#4749C2212yescomplemented
104#4748C2212yescomplemented
105#4745C2214yescomplemented
106D3×#100C2214yescomplemented
107D3×#100C2214yescomplemented
108#3585—31no—
109#3585—31no—
110C2×#576—31no—
111#3573—31no—
112#3068—34no—
113#3068—34no—
114#3068—31no—
115#3068—31no—
116#3068—31no—
117#3068D311yescharacteristic, complemented
118#3067—34no—
119#3067—31no—
120#3067—31no—
121C2×#472—34no—
122C2×#472—31no—
123C2×#472—31no—
124#2916—31no—
125#2888—31no—
126#2888—31no—
127C2×C3×#41C2311yescharacteristic
128C2×C3×#41C2311yescharacteristic
129C22×C3×D4C2311yescharacteristic
130C22×#67—22no—
131#1010—21no—
132#1010D412yes—
133#1009—21no—
134#1009—22no—
135#1009—22no—
136#1009—22no—
137#1009—22no—
138#1009D412yes—
139D3×#41—22no—
140D3×#41C2314yes—
141#1007D412yes—
142C2×#239C2312yes—
143#1004—22no—
144#1004—22no—
145#1004—22no—
146#1004—22no—
147#1004—22no—
148#1004D412yes—
149C2×#237—21no—
150C2×#237C2312yes—
151C2×D3×D4—22no—
152C2×D3×D4—21no—
153C2×D3×D4C2312yes—
154C2×D3×D4C2312yes—
155C2×#235—22no—
156C2×#235—21no—
157C2×#235C2311yescharacteristic
158C2×#235C2311yescharacteristic
159C2×#235C2311yescharacteristic
160C22×D12—21no—
161C22×D12C2311yescharacteristic
162C3×#137—21no—
163C3×#137C2312yes—
164C3×AGL(1,ℤ/8)—22no—
165C3×AGL(1,ℤ/8)—21no—
166C3×AGL(1,ℤ/8)—22no—
167C3×AGL(1,ℤ/8)—22no—
168C3×AGL(1,ℤ/8)C2314yes—
169C3×AGL(1,ℤ/8)C2312yes—
170C3×#135—22no—
171C2×C3×SD16—21no—
172C2×C3×SD16C2312yes—
173C2×C3×D8—21no—
174C2×C3×D8C2312yes—
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×#216C2311yescharacteristic
199#942—21no—
200#942C2312yes—
201C2×#215—21no—
202C2×#215C2311yescharacteristic
203C2×#214—21no—
204C2×#214C2311yescharacteristic
205#932—21no—
206#932—22no—
207#932C2312yes—
208#932C2314yes—
209C2×#213—21no—
210C2×#213—21no—
211C2×#213—21no—
212C2×#213—21no—
213C2×#213—21no—
214C2×#213—21no—
215C2×#213C2311yescharacteristic
216C2×#213C2312yes—
217C2×#213C2312yes—
218C2×#208—21no—
219C2×#208C2311yescharacteristic
220C2×#208C2311yescharacteristic
221C2×#208C2311yescharacteristic
222C22×C3⋊C8—21no—
223C22×C3⋊C8C2311yescharacteristic
224#919—24no—
225#918—24no—
226#916—24no—
227#916—24no—
228#916—24no—
229#916—24no—
230#915—24no—
231#914—24no—
232#914—24no—
233#914—24no—
234#914—24no—
235#914—24no—
236D3×SD16—24no—
237D3×SD16—24no—
238#912—24no—
239#911—24no—
240#911—24no—
241#911—24no—
242#911—24no—
243#911—24no—
244D3×D8—24no—
245D3×D8—24no—
246D3×D8—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×#101C2312yes—
295C3×#100C2312yes—
296C3×#100C2314yes—
297#836C2312yes—
298#833C2312yes—
299#833C2314yes—
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×H(5,𝔽2)—31no—
313C2×H(5,𝔽2)—31no—
314#577—62no—
315#577—62no—
316#577—62no—
317#577—62no—
318#576—62no—
319#576—62no—
320#576—62no—
321#576—62no—
322#576—62no—
323#576—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, complemented
332C2×AGL(1,ℤ/8)—32no—
333C2×AGL(1,ℤ/8)—32no—
334C2×AGL(1,ℤ/8)—31no—
335C2×AGL(1,ℤ/8)—31no—
336C2×AGL(1,ℤ/8)—34no—
337C2×AGL(1,ℤ/8)—34no—
338C2×AGL(1,ℤ/8)—31no—
339C2×AGL(1,ℤ/8)—31no—
340C2×AGL(1,ℤ/8)C2×D311yescharacteristic, complemented
341C2×AGL(1,ℤ/8)C2×D311yescharacteristic, complemented
342C2×#135—31no—
343C2×#135—32no—
344C22×D8—31no—
345C22×D8—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—32no—
362#472—32no—
363#472—34no—
364#472—34no—
365#472—34no—
366#472—34no—
367#472—34no—
368#472—32no—
369#472—34no—
370#472—34no—
371#472C2×D314yescomplemented
372#471—32no—
373#471—32no—
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×#100—31no—
393C2×#100—31no—
394C2×#100—31no—
395C2×#100—34no—
396C2×#100—34no—
397C2×#100C2×D311yescharacteristic, complemented
398C24×C3—21no—
399C23×D3—21no—
400C23×D3—22no—
401C23×D3—22no—
402C3×#41—21no—
403C3×#41—21no—
404C3×#41—21no—
405C3×#41—21no—
406C3×#41—21no—
407C3×#41—21no—
408C3×#41C2×D412yes—
409C3×#41C2412yes—
410C2×C3×Q8C2×D411yescharacteristic
411C2×C3×Q8C2411yescharacteristic
412C2×C3×D4—21no—
413C2×C3×D4—21no—
414C2×C3×D4—21no—
415C2×C3×D4—21no—
416C2×C3×D4—21no—
417C2×C3×D4—21no—
418C2×C3×D4—21no—
419C2×C3×D4C2×D411yescharacteristic
420C2×C3×D4C2412yes—
421C2×C3×D4C2411yescharacteristic
422C22×C3×C4—21no—
423C22×C3×C4—21no—
424C22×C3×C4C2411yescharacteristic
425C2×#67—21no—
426C2×#67—24no—
427C2×#67—21no—
428C2×#67—22no—
429C2×#67—22no—
430C2×#67—22no—
431C2×#67—44no—
432C2×#67—44no—
433C2×#67#4112yes—
434C22×Dic3—22no—
435#239—22no—
436#239—24no—
437#239—24no—
438#239C2×D414yes—
439D3×Q8—22no—
440D3×Q8C2×D414yes—
441#237—24no—
442#237—24no—
443#237—24no—
444#237—24no—
445#237—22no—
446#237—42no—
447#237—42no—
448#237C2×D414yes—
449D3×D4—24no—
450D3×D4—24no—
451D3×D4—22no—
452D3×D4—24no—
453D3×D4—24no—
454D3×D4—24no—
455D3×D4—24no—
456D3×D4—44no—
457D3×D4—44no—
458D3×D4—42no—
459D3×D4—42no—
460D3×D4C2×D414yes—
461#235—21no—
462#235—21no—
463#235—24no—
464#235—22no—
465#235—24no—
466#235—21no—
467#235—21no—
468#235—21no—
469#235—21no—
470#235—22no—
471#235—42no—
472#235—42no—
473#235C2×D412yes—
474#235C2×D412yes—
475#235C2×D412yes—
476#235C2×D412yes—
477#235C2×D412yes—
478#235C2412yes—
479C2×D12—22no—
480C2×D12—21no—
481C2×D12—21no—
482C2×D12—21no—
483C2×D12—21no—
484C2×D12—22no—
485C2×D12—21no—
486C2×D12—42no—
487C2×D12—42no—
488C2×D12C2×D411yescharacteristic
489C2×D12#4111yescharacteristic
490C2×D12C2412yes—
491C2×D12C2411yescharacteristic
492C2×C4×D3—21no—
493C2×C4×D3—24no—
494C2×C4×D3—21no—
495C2×C4×D3—22no—
496C2×C4×D3C2412yes—
497C2×Dic6—22no—
498C2×Dic6C2×D411yescharacteristic
499C2×Dic6#4111yescharacteristic
500C2×Dic6C2411yescharacteristic
501C3×Q16—22no—
502C3×SD16—22no—
503C3×SD16—24no—
504C3×SD16—22no—
505C3×SD16—24no—
506C3×D8—22no—
507C3×D8—24no—
508C3×D8—24no—
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—22no—
525#216—21no—
526#216—21no—
527#215—22no—
528#215—24no—
529#215—22no—
530#215—21no—
531#215—21no—
532#214—22no—
533#214—22no—
534#214—24no—
535#214—21no—
536#214—21no—
537#213—22no—
538#213—24no—
539#213—22no—
540#213—24no—
541#213—21no—
542#213—21no—
543#213—22no—
544#213—22no—
545#213—22no—
546#213—22no—
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—61no—
593H(5,𝔽2)—32no—
594H(5,𝔽2)—32no—
595H(5,𝔽2)—62no—
596H(5,𝔽2)—62no—
597H(5,𝔽2)—62no—
598H(5,𝔽2)—62no—
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—61no—
612C2×#41—62no—
613C2×#41—61no—
614C2×#41—62no—
615C2×#41C22×D311yescharacteristic
616C2×#41C22×D311yescharacteristic
617C22×D4—32no—
618C22×D4—32no—
619C22×D4—31no—
620C22×D4—61no—
621C22×D4—62no—
622C22×D4—61no—
623C22×D4—62no—
624C22×D4C22×D311yescharacteristic
625#137—21no—
626#137—32no—
627#137—32no—
628#137—32no—
629#137—61no—
630#137—64no—
631#137—64no—
632#137—61no—
633#137—61no—
634#137C22×D312yes—
635AGL(1,ℤ/8)—22no—
636AGL(1,ℤ/8)—21no—
637AGL(1,ℤ/8)—22no—
638AGL(1,ℤ/8)—22no—
639AGL(1,ℤ/8)—34no—
640AGL(1,ℤ/8)—32no—
641AGL(1,ℤ/8)—34no—
642AGL(1,ℤ/8)—32no—
643AGL(1,ℤ/8)—32no—
644AGL(1,ℤ/8)—34no—
645AGL(1,ℤ/8)—61no—
646AGL(1,ℤ/8)—62no—
647AGL(1,ℤ/8)—64no—
648AGL(1,ℤ/8)—64no—
649AGL(1,ℤ/8)—64no—
650AGL(1,ℤ/8)—64no—
651AGL(1,ℤ/8)—64no—
652AGL(1,ℤ/8)—64no—
653AGL(1,ℤ/8)—64no—
654AGL(1,ℤ/8)—64no—
655AGL(1,ℤ/8)—64no—
656AGL(1,ℤ/8)—64no—
657AGL(1,ℤ/8)—62no—
658AGL(1,ℤ/8)—61no—
659AGL(1,ℤ/8)—62no—
660AGL(1,ℤ/8)—61no—
661AGL(1,ℤ/8)—62no—
662AGL(1,ℤ/8)—62no—
663AGL(1,ℤ/8)C22×D312yes—
664AGL(1,ℤ/8)C22×D314yes—
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—31no—
680C2×SD16—21no—
681C2×SD16—31no—
682C2×SD16—31no—
683C2×SD16—32no—
684C2×SD16—61no—
685C2×SD16—64no—
686C2×SD16—64no—
687C2×SD16—61no—
688C2×SD16—61no—
689C2×SD16C22×D312yes—
690C2×D8—21no—
691C2×D8—32no—
692C2×D8—31no—
693C2×D8—32no—
694C2×D8—32no—
695C2×D8—61no—
696C2×D8—64no—
697C2×D8—64no—
698C2×D8—61no—
699C2×D8—61no—
700C2×D8—61no—
701C2×D8—61no—
702C2×D8—64no—
703C2×D8—64no—
704C2×D8—61no—
705C2×D8—61no—
706C2×D8C22×D312yes—
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—32no—
763#101—32no—
764#101—32no—
765#101C22×D312yes—
766#100—34no—
767#100—32no—
768#100—34no—
769#100—32no—
770#100—34no—
771#100—32no—
772#100C22×D312yes—
773#100C22×D314yes—
774C23×C3—21no—
775C23×C3—22no—
776C23×C3—21no—
777C23×C3—41no—
778C23×C3—41no—
779C23×C3—161no—
780C23×C3C2×#4111yescharacteristic
781C22×D3—21no—
782C22×D3—24no—
783C22×D3—22no—
784C22×D3—21no—
785C22×D3—41no—
786C22×D3—41no—
787C22×D3—44no—
788C22×D3—44no—
789C22×D3—162no—
790C22×D3—162no—
791C22×D3—161no—
792C22×D3C2×#4112yes—
793C3×Q8—21no—
794C3×Q8—21no—
795C3×Q8—21no—
796C3×Q8C22×D412yes—
797C3×D4—22no—
798C3×D4—22no—
799C3×D4—21no—
800C3×D4—22no—
801C3×D4—21no—
802C3×D4—21no—
803C3×D4—22no—
804C3×D4—41no—
805C3×D4—41no—
806C3×D4—41no—
807C3×D4—41no—
808C3×D4C22×D412yes—
809C2×C3×C4—21no—
810C2×C3×C4—22no—
811C2×C3×C4—22no—
812C2×C3×C4—21no—
813C2×C3×C4—41no—
814C2×C3×C4—41no—
815C2×C3×C4C22×D411yescharacteristic
816C2×C3×C4C22×D411yescharacteristic
817C2×C3×C4C22×D411yescharacteristic
818C2×C3×C4C22×D411yescharacteristic
819C2×C3×C4C2×#4111yescharacteristic
820C2×C3×C4C2511yescharacteristic
821#67—22no—
822#67—22no—
823#67—24no—
824#67—24no—
825#67—41no—
826#67—41no—
827#67—44no—
828#67—44no—
829#67—44no—
830#67#12114yes—
831#67#12114yes—
832C2×Dic3—21no—
833C2×Dic3—24no—
834C2×Dic3—21no—
835C2×Dic3—44no—
836C2×Dic3C2×#4112yes—
837D12—24no—
838D12—21no—
839D12—22no—
840D12—22no—
841D12—21no—
842D12—21no—
843D12—44no—
844D12—41no—
845D12—41no—
846D12#12112yes—
847D12#12112yes—
848D12C22×D412yes—
849C4×D3—24no—
850C4×D3—22no—
851C4×D3—22no—
852C4×D3—24no—
853C4×D3—41no—
854C4×D3—41no—
855C4×D3—44no—
856C4×D3C22×D414yes—
857C4×D3C22×D414yes—
858Dic6—21no—
859Dic6—24no—
860Dic6—21no—
861Dic6—21no—
862Dic6#12112yes—
863Dic6#12112yes—
864Dic6C22×D412yes—
865C3×C8—22no—
866C3×C8—22no—
867C3×C8—22no—
868C3×C8C22×D414yes—
869C3⋊C8—22no—
870C3⋊C8—22no—
871C3⋊C8—22no—
872C3⋊C8C22×D411yescharacteristic
873C3⋊C8C22×D411yescharacteristic
874C3⋊C8C22×D411yescharacteristic
875C3⋊C8C22×D411yescharacteristic
876C24—21no—
877C24—62no—
878C24—62no—
879C24—61no—
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—61no—
909#41—61no—
910#41—61no—
911#41—61no—
912#41—122no—
913#41—122no—
914#41—122no—
915#41—122no—
916#41D3×D412yes—
917#41C23×D312yes—
918C2×Q8—31no—
919C2×Q8—34no—
920C2×Q8—31no—
921C2×Q8—31no—
922C2×Q8—62no—
923C2×Q8—62no—
924C2×Q8D3×D411yescharacteristic
925C2×Q8C23×D311yescharacteristic
926C2×D4—21no—
927C2×D4—21no—
928C2×D4—21no—
929C2×D4—21no—
930C2×D4—21no—
931C2×D4—21no—
932C2×D4—21no—
933C2×D4—32no—
934C2×D4—34no—
935C2×D4—31no—
936C2×D4—31no—
937C2×D4—32no—
938C2×D4—31no—
939C2×D4—62no—
940C2×D4—62no—
941C2×D4—64no—
942C2×D4—64no—
943C2×D4—64no—
944C2×D4—64no—
945C2×D4—62no—
946C2×D4—62no—
947C2×D4—64no—
948C2×D4—62no—
949C2×D4—64no—
950C2×D4—64no—
951C2×D4—61no—
952C2×D4—62no—
953C2×D4—61no—
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×D4—122no—
964C2×D4—122no—
965C2×D4—124no—
966C2×D4—124no—
967C2×D4D3×D411yescharacteristic
968C2×D4C23×D312yes—
969C2×D4C23×D311yescharacteristic
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—32no—
973C22×C4—64no—
974C22×C4—62no—
975C22×C4—62no—
976C22×C4—61no—
977C22×C4—61no—
978C22×C4C23×D311yescharacteristic
979Q16—22no—
980Q16—62no—
981Q16—61no—
982Q16—61no—
983Q16—62no—
984Q16—62no—
985SD16—24no—
986SD16—22no—
987SD16—22no—
988SD16—24no—
989SD16—62no—
990SD16—62no—
991SD16—64no—
992SD16—61no—
993SD16—61no—
994SD16—61no—
995SD16—61no—
996SD16—64no—
997SD16—62no—
998SD16—62no—
999SD16—62no—
1000SD16—64no—
1001SD16—62no—
1002SD16—64no—
1003D8—24no—
1004D8—22no—
1005D8—24no—
1006D8—62no—
1007D8—64no—
1008D8—61no—
1009D8—62no—
1010D8—61no—
1011D8—62no—
1012D8—62no—
1013D8—62no—
1014D8—64no—
1015D8—62no—
1016D8—62no—
1017D8—64no—
1018D8—64no—
1019M16—21no—
1020M16—21no—
1021M16—21no—
1022M16—24no—
1023M16—34no—
1024M16—34no—
1025M16—32no—
1026M16—32no—
1027M16—32no—
1028M16—62no—
1029M16—62no—
1030M16—64no—
1031M16—64no—
1032M16—64no—
1033M16—62no—
1034M16—62no—
1035M16—61no—
1036M16—61no—
1037M16—61no—
1038M16—64no—
1039M16D3×D412yes—
1040M16D3×D412yes—
1041M16C23×D312yes—
1042M16C23×D312yes—
1043M16C23×D312yes—
1044C2×C8—21no—
1045C2×C8—21no—
1046C2×C8—21no—
1047C2×C8—24no—
1048C2×C8—31no—
1049C2×C8—31no—
1050C2×C8—31no—
1051C2×C8—31no—
1052C2×C8—31no—
1053C2×C8—31no—
1054C2×C8—34no—
1055C2×C8—34no—
1056C2×C8—62no—
1057C2×C8—62no—
1058C2×C8—64no—
1059C2×C8—64no—
1060C2×C8—64no—
1061C2×C8—62no—
1062C2×C8—62no—
1063C2×C8—61no—
1064C2×C8—61no—
1065C2×C8—61no—
1066C2×C8—64no—
1067C2×C8C23×D312yes—
1068C22×C3—22no—
1069C22×C3—41no—
1070C22×C3—42no—
1071C22×C3—41no—
1072C22×C3—81no—
1073C22×C3—81no—
1074C22×C3—82no—
1075C22×C3—161no—
1076C22×C3—161no—
1077C22×C3C2×#12111yescharacteristic
1078C22×C3C2×#12111yescharacteristic
1079C22×C3C22×#4111yescharacteristic
1080C2×D3—22no—
1081C2×D3—42no—
1082C2×D3—42no—
1083C2×D3—41no—
1084C2×D3—84no—
1085C2×D3—81no—
1086C2×D3—82no—
1087C2×D3—81no—
1088C2×D3—164no—
1089C2×D3—164no—
1090C2×D3—161no—
1091C2×D3—161no—
1092C2×D3C2×#12114yes—
1093C3×C4—22no—
1094C3×C4—41no—
1095C3×C4C2×#12111yescharacteristic
1096C3×C4C2×#12111yescharacteristic
1097C3×C4C23×D411yescharacteristic
1098C3×C4C23×D411yescharacteristic
1099Dic3—22no—
1100Dic3—41no—
1101Dic3C2×#12114yes—
1102C23—21no—
1103C23—21no—
1104C23—22no—
1105C23—32no—
1106C23—41no—
1107C23—41no—
1108C23—64no—
1109C23—61no—
1110C23—62no—
1111C23—61no—
1112C23—124no—
1113C23—124no—
1114C23—121no—
1115C23—121no—
1116C23—161no—
1117C23—481no—
1118C23—482no—
1119C23—482no—
1120C23D3×#4111yescharacteristic
1121Q8—21no—
1122Q8—21no—
1123Q8—21no—
1124Q8—32no—
1125Q8—32no—
1126Q8—32no—
1127Q8—64no—
1128Q8—61no—
1129Q8—61no—
1130Q8—61no—
1131Q8C2×D3×D412yes—
1132D4—22no—
1133D4—22no—
1134D4—21no—
1135D4—22no—
1136D4—22no—
1137D4—21no—
1138D4—21no—
1139D4—34no—
1140D4—34no—
1141D4—32no—
1142D4—32no—
1143D4—32no—
1144D4—41no—
1145D4—41no—
1146D4—41no—
1147D4—41no—
1148D4—64no—
1149D4—64no—
1150D4—64no—
1151D4—62no—
1152D4—62no—
1153D4—62no—
1154D4—61no—
1155D4—61no—
1156D4—62no—
1157D4—61no—
1158D4—124no—
1159D4—124no—
1160D4—124no—
1161D4—124no—
1162D4—121no—
1163D4—121no—
1164D4—121no—
1165D4—121no—
1166D4C2×D3×D412yes—
1167C2×C4—21no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—21no—
1171C2×C4—32no—
1172C2×C4—34no—
1173C2×C4—34no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—64no—
1177C2×C4—64no—
1178C2×C4—64no—
1179C2×C4—61no—
1180C2×C4—62no—
1181C2×C4—62no—
1182C2×C4—61no—
1183C2×C4—124no—
1184C2×C4—124no—
1185C2×C4—121no—
1186C2×C4—121no—
1187C2×C4C2×D3×D411yescharacteristic
1188C2×C4C2×D3×D411yescharacteristic
1189C2×C4C2×D3×D411yescharacteristic
1190C2×C4C2×D3×D411yescharacteristic
1191C2×C4D3×#4111yescharacteristic
1192C2×C4C24×D311yescharacteristic
1193C8—22no—
1194C8—22no—
1195C8—22no—
1196C8—31no—
1197C8—31no—
1198C8—31no—
1199C8—31no—
1200C8—62no—
1201C8—62no—
1202C8—62no—
1203C8C2×D3×D414yes—
1204C2×C3—21no—
1205C2×C3—21no—
1206C2×C3—21no—
1207C2×C3—42no—
1208C2×C3—81no—
1209C2×C3—82no—
1210C2×C3C22×#12111yescharacteristic
1211D3—24no—
1212D3—42no—
1213D3—82no—
1214D3—81no—
1215C22—22no—
1216C22—34no—
1217C22—41no—
1218C22—41no—
1219C22—42no—
1220C22—62no—
1221C22—81no—
1222C22—82no—
1223C22—81no—
1224C22—122no—
1225C22—122no—
1226C22—121no—
1227C22—161no—
1228C22—161no—
1229C22—241no—
1230C22—242no—
1231C22—241no—
1232C22—244no—
1233C22—481no—
1234C22—481no—
1235C22—484no—
1236C22—484no—
1237C22D3×#12111yescharacteristic
1238C22D3×#12111yescharacteristic
1239C22C2×D3×#4111yescharacteristic
1240C4—22no—
1241C4—34no—
1242C4—41no—
1243C4—62no—
1244C4—121no—
1245C4D3×#12111yescharacteristic
1246C4D3×#12111yescharacteristic
1247C4C22×D3×D411yescharacteristic
1248C4C22×D3×D411yescharacteristic
1249C3#6047111yescharacteristic, complemented, Sylow
1250C2—21no—
1251C2—21no—
1252C2—21no—
1253C2—42no—
1254C2—64no—
1255C2—82no—
1256C2—81no—
1257C2—122no—
1258C2—242no—
1259C2—241no—
1260C2C2×D3×#12111yescharacteristic
subgroupG/H
centerC2C2×D3×#121
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3068C2
socleC2×C3C22×#121
hypercenter#3068D3
hypocenterC3#60471
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C22×C4 ◁ #3068

Complements

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

NH ≅ G/Ntype
1. #87200C2semidirect
2. #87192C2semidirect
3. C2×#5774C2semidirect
4. #87166C2semidirect
5. C3×#3068C2semidirect
6. #84001C2semidirect
7. #83963C2semidirect
8. C2×#5199C2semidirect
9. #83814C2semidirect
10. #80938C2semidirect
11. D3×#472C2semidirect
12. #80930C2semidirect
13. #80929C2semidirect
14. #79261C2semidirect
15. #79260C2semidirect
16. #78719C2semidirect
17. #78714C2semidirect
18. C2×#4749C2semidirect
19. #78697C2semidirect
24. C3×#575C22semidirect
25. C2×C3×AGL(1,ℤ/8)C22semidirect
26. C2×C3×AGL(1,ℤ/8)C22semidirect
27. C3×#568C22semidirect
28. #5822C22semidirect
29. #5822C22semidirect
30. C2×#950C22semidirect
31. C2×#949C22semidirect
32. C2×#948C22semidirect
33. C2×#932C22semidirect
34. C22×#213C22semidirect
36. #5777C22semidirect
44. #5773C22semidirect
45. D3×AGL(1,ℤ/8)C22semidirect
46. D3×AGL(1,ℤ/8)C22semidirect
50. C2×#916C22semidirect
51. C2×#914C22semidirect
53. C2×#911C22semidirect
54. C2×D3×D8C22semidirect
56. #5750C22semidirect
58. D3×#131C22semidirect
59. #5748C22semidirect
60. C2×#908C22semidirect
61. C2×#908C22semidirect
66. #5745C22semidirect
69. C2×#907C22semidirect
70. C3×#472C22semidirect
71. C3×#471C22semidirect
72. C3×#430C22semidirect
73. C3×#413C22semidirect
74. C2×C3×#100C22semidirect
75. #5237C22semidirect
76. C2×#833C22semidirect
77. #5204C22semidirect
78. #5203C22semidirect
79. #5200C22semidirect
80. #5199C22semidirect
81. #5199C22semidirect
82. #5199C22semidirect
83. #5177C22semidirect
84. #5160C22semidirect
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. #4751C22semidirect
101. #4749C22semidirect
102. #4749C22semidirect
103. #4749C22semidirect
104. #4748C22semidirect
105. #4745C22semidirect
106. D3×#100C22semidirect
107. D3×#100C22semidirect
117. #3068D3semidirect
331. #575C2×D3semidirect
340. C2×AGL(1,ℤ/8)C2×D3semidirect
341. C2×AGL(1,ℤ/8)C2×D3semidirect
353. #568C2×D3semidirect
371. #472C2×D3semidirect
379. #471C2×D3semidirect
382. #430C2×D3semidirect
391. #413C2×D3semidirect
397. C2×#100C2×D3semidirect
1249. C3#60471semidirect

Maximal subgroups

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

subgroupindex
#872002
#871922
C2×#57742
#871662
C3×#30682
#840012
#839632
C2×#51992
#838142
#809382
D3×#4722
#809302
#809292
#792612
#792602
#787192
#787142
C2×#47492
#786972
#604713