Finite Group Databasebeta

← #11661675

Subgroups — #11661675

Order 768.

4726 conjugacy classes of subgroups.

The subgroup lattice has 1354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×2−1+4C211yesmaximal, characteristic, complemented
2C2×#5773C211yesmaximal, characteristic, complemented
3C22×#915C211yesmaximal, characteristic, complemented
4#86313C211yesmaximal, characteristic, complemented
5C3×#3010C211yesmaximal, characteristic, complemented
6#84117C211yesmaximal, characteristic, complemented
7#83948C211yesmaximal, characteristic, complemented
8#83860C211yesmaximal, characteristic, complemented
9#83390C211yesmaximal, characteristic, complemented
10#80088C214yesmaximal, complemented
11#80083C214yesmaximal, complemented
12#80042C214yesmaximal, complemented
13#80039C214yesmaximal, complemented
14#78961C211yesmaximal, characteristic, complemented
15D3×#419C211yesmaximal, characteristic, complemented
16#78837C211yesmaximal, characteristic, complemented
17#78830C211yesmaximal, characteristic, complemented
18#78679C211yesmaximal, characteristic, complemented
19#78662C211yesmaximal, characteristic, complemented
20#60368—31nomaximal, Sylow
21C2×C3×2−1+4C2211yescharacteristic
22D3×2−1+4—28no—
23D3×2−1+4—28no—
24C2×#1010—22no—
25C2×#1010—21no—
26C2×#1010C2211yescharacteristic
27C2×#1010C2211yescharacteristic
28C2×#1010C2212yescomplemented
29C2×D3×#41—22no—
30C2×D3×#41—21no—
31C2×D3×#41C2211yescharacteristic
32C2×D3×#41C2211yescharacteristic
33C2×D3×#41C2212yescomplemented
34C2×#1007—21no—
35C2×#1007C2211yescharacteristic
36C2×#1007C2212yescomplemented
37C22×D3×Q8—21no—
38C22×D3×Q8C2211yescharacteristic
39C22×D3×Q8C2212yescomplemented
40C22×#237C2211yescharacteristic
41C2×C3×AGL(1,ℤ/8)C2211yescharacteristic, complemented
42C22×C3×SD16C2211yescharacteristic, complemented
43C3×#535C2211yescharacteristic, complemented
44#5825C2211yescharacteristic, complemented
45C2×#951C2211yescharacteristic, complemented
46C22×#216C2211yescharacteristic, complemented
47#5805C2211yescharacteristic, complemented
48C22×#214C2211yescharacteristic, complemented
49C2×#932C2211yescharacteristic, complemented
50#5773—28no—
51C2×#916C2212yescomplemented
52C2×#915—28no—
53C2×#915C2214yes—
54C2×#915C2212yes—
55C2×#915C2214yescomplemented
56C2×#912C2212yescomplemented
57C2×#911C2212yes—
58C2×#909C2211yescharacteristic, complemented
59C2×D3×M16C2211yescharacteristic
60C22×Dic12C2211yescharacteristic, complemented
61C22×ΓL(1,𝔽25)C2211yescharacteristic
62#5716—21no—
63#5715—21no—
64#5675—21no—
65#5668—21no—
66#5608C2214yescomplemented
67#5606C2214yes—
68#5589—22no—
69#5586—22no—
70#5526C2211yescharacteristic, complemented
71D3×#117C2211yescharacteristic
72C3×#449C2214yescomplemented
73C3×#448C2214yescomplemented
74C3×#419C2211yescharacteristic, complemented
75C3×#416C2211yescharacteristic, complemented
76C3×#408C2211yescharacteristic, complemented
77#5239C2214yescomplemented
78#5234C2211yescharacteristic, complemented
79#5233C2211yescharacteristic, complemented
80#5228C2214yescomplemented
81#5225C2211yescharacteristic, complemented
82#5172C2214yescomplemented
83#5170C2214yescomplemented
84#5170C2214yescomplemented
85#5158C2214yescomplemented
86#5129C2211yescharacteristic, complemented
87#5120C2211yescharacteristic, complemented
88#5113C2211yescharacteristic, complemented
89#5110C2211yescharacteristic, complemented
90#5040C2214yescomplemented
91#5037C2214yescomplemented
92#5004C2211yescharacteristic, complemented
93#5002C2211yescharacteristic, complemented
94#4809C2214yescomplemented
95#4809C2214yescomplemented
96#4808C2214yescomplemented
97#4803C2212yescomplemented
98#4802C2214yescomplemented
99#4802C2212yescomplemented
100D3×#103C2214yescomplemented
101#4783C2214yescomplemented
102#4771C2212yescomplemented
103#4770C2212yescomplemented
104#4739C2214yescomplemented
105#4733C2214yescomplemented
106#4727C2214yescomplemented
107#4726C2214yescomplemented
108C22×2−1+4—31no—
109C2×#575—31no—
110C22×#137—31no—
111#3449—31no—
112#3013—34no—
113#3013—34no—
114#3011—31no—
115#3011—31no—
116#3011—31no—
117#3011—31no—
118#3010—31no—
119#3010—31no—
120#3010—31no—
121#3010D311yescharacteristic, complemented
122#3005—34no—
123#3004—34no—
124#2896—31no—
125C2×#419—31no—
126#2879—31no—
127C3×2−1+4—24no—
128C3×2−1+4—24no—
129C2×C3×#41—22no—
130C2×C3×#41—21no—
131C2×C3×#41C2312yes—
132C2×C3×#41C2311yescharacteristic
133C2×C3×#41C2311yescharacteristic
134C22×C3×Q8—21no—
135C22×C3×Q8C2312yes—
136C22×C3×Q8C2311yescharacteristic
137C22×C3×D4C2311yescharacteristic
138C22×#67—21no—
139C23×Dic3—21no—
140#1010—216no—
141#1010—232no—
142#1010—24no—
143#1010—28no—
144#1010—28no—
145#1010—24no—
146#1010—24no—
147#1010—24no—
148D3×#41—232no—
149D3×#41—216no—
150D3×#41—28no—
151D3×#41—28no—
152D3×#41—24no—
153D3×#41—24no—
154D3×#41—24no—
155D3×#41D418yescomplemented
156#1007—216no—
157#1007—24no—
158#1007—28no—
159#1007—28no—
160#1007—24no—
161C2×#239—21no—
162C2×#239—22no—
163C2×#239D411yescharacteristic
164C2×#239C2312yes—
165C2×#239C2311yescharacteristic
166C2×D3×Q8—216no—
167C2×D3×Q8—21no—
168C2×D3×Q8—28no—
169C2×D3×Q8—28no—
170C2×D3×Q8—21no—
171C2×D3×Q8—22no—
172C2×D3×Q8—21no—
173C2×D3×Q8—24no—
174C2×D3×Q8—22no—
175C2×D3×Q8—21no—
176C2×D3×Q8—22no—
177C2×D3×Q8D411yescharacteristic
178C2×D3×Q8D418yescomplemented
179C2×D3×Q8C2312yes—
180C2×D3×Q8C2312yes—
181C2×D3×Q8C2312yes—
182C2×D3×Q8C2312yes—
183C2×D3×Q8C2311yescharacteristic
184C2×#237—22no—
185C2×#237—21no—
186C2×#237—22no—
187C2×#237—22no—
188C2×#237—22no—
189C2×#237—21no—
190C2×#237—22no—
191C2×#237—24no—
192C2×#237—24no—
193C2×#237—21no—
194C2×#237—21no—
195C2×#237D411yescharacteristic
196C2×#237D412yes—
197C2×#237C2312yes—
198C2×#237C2312yes—
199C2×#237C2312yes—
200C2×#237C2311yescharacteristic
201C2×D3×D4—21no—
202C2×D3×D4—22no—
203C2×D3×D4D411yescharacteristic
204C2×D3×D4D412yes—
205C2×D3×D4C2311yescharacteristic
206C2×#235—22no—
207C2×#235—22no—
208C2×#235—22no—
209C2×#235—21no—
210C2×#235—22no—
211C2×#235—21no—
212C2×#235—22no—
213C2×#235C2311yescharacteristic
214C2×#235C2312yes—
215C2×#235C2312yes—
216C2×#235C2311yescharacteristic
217C22×C4×D3—21no—
218C22×C4×D3—22no—
219C22×C4×D3—21no—
220C22×C4×D3—22no—
221C22×C4×D3C2312yes—
222C22×C4×D3C2311yescharacteristic
223C22×Dic6—21no—
224C22×Dic6—22no—
225C22×Dic6—21no—
226C22×Dic6—22no—
227C22×Dic6C2311yescharacteristic
228C22×Dic6C2312yes—
229C22×Dic6C2311yescharacteristic
230C3×AGL(1,ℤ/8)—24no—
231C2×C3×SD16—24no—
232C2×C3×SD16C2314yes—
233C2×C3×SD16C2312yes—
234C2×C3×D8C2312yes—
235C2×C3×M16C2311yescharacteristic
236C22×C3×C8C2311yescharacteristic
237C3×#127—21no—
238C3×#124—21no—
239C3×#121C2314yes—
240C3×#120—22no—
241C3×#117C2311yescharacteristic
242#953—22no—
243#951—24no—
244#944—21no—
245C2×#216—24no—
246C2×#216C2312yes—
247C2×#216C2314yes—
248#940—21no—
249#939—24no—
250#938—24no—
251#938C2314yes—
252#937—24no—
253#936—21no—
254#936—21no—
255#935—22no—
256D4×Dic3—24no—
257C2×#214—24no—
258C2×#214C2314yes—
259C2×#214C2312yes—
260C2×#214C2312yes—
261#932—24no—
262C2×#213C2312yes—
263#926C2311yescharacteristic
264#924C2314yes—
265C2×#208C2311yescharacteristic
266C22×C3⋊C8C2311yescharacteristic
267#916—28no—
268#915—216no—
269#915—216no—
270#915—28no—
271#912—28no—
272#911—28no—
273#909—24no—
274D3×M16—24no—
275C2×Dic12—24no—
276C2×Dic12C2314yes—
277C2×Dic12C2312yes—
278C2×#204C2312yes—
279C2×ΓL(1,𝔽25)—24no—
280C2×ΓL(1,𝔽25)C2312yes—
281C2×ΓL(1,𝔽25)C2312yes—
282C2×ΓL(1,𝔽25)C2312yes—
283C2×D3×C8C2312yes—
284#897C2314yes—
285#892C2312yes—
286D3×C4⋊C4C2312yes—
287#886—22no—
288#884—24no—
289#883—24no—
290#67⋊C4—24no—
291D3×C22⋊C4—21no—
292#878—24no—
293#877—21no—
294#875—21no—
295#872—21no—
296C42×D3—21no—
297#869—21no—
298C3×#103C2312yes—
299C3×#103C2314yes—
300C3×#102C2312yes—
301C3×C22⋊C8C2314yes—
302#835C2312yes—
303#835C2314yes—
304#832C2312yes—
305#830C2314yes—
306#821C2312yes—
307(C2×D3)⋊C8C2314yes—
308(C2×D3)⋊C8C2314yes—
309#816C2314yes—
310#816C2312yes—
311#810C2312yes—
312#810C2314yes—
313#809C2312yes—
314C2×2−1+4—31no—
315C2×2−1+4—32no—
316C2×2−1+4—31no—
317C2×2−1+4—31no—
318C2×2−1+4—32no—
319C2×2−1+4—61no—
320C2×2−1+4—68no—
321C2×2−1+4—62no—
322C2×2−1+4—61no—
323C2×2−1+4—68no—
324C2×2−1+4C2×D311yescharacteristic
325C22×#41—31no—
326C22×#41—31no—
327C22×#41—32no—
328C22×#41—31no—
329C22×#41—62no—
330C22×#41—61no—
331C23×Q8—31no—
332C23×Q8—32no—
333C23×Q8—61no—
334#575—68no—
335C2×#137—31no—
336C2×#137—32no—
337C2×#137—34no—
338C2×#137—34no—
339C2×#137—31no—
340C2×#137—68no—
341C2×AGL(1,ℤ/8)—31no—
342C2×AGL(1,ℤ/8)—32no—
343C2×AGL(1,ℤ/8)C2×D311yescharacteristic, complemented
344C2×#135—32no—
345C2×#135—32no—
346C22×Q16—31no—
347C22×Q16—31no—
348C22×SD16—31no—
349C22×SD16C2×D311yescharacteristic, complemented
350C22×M16—31no—
351C22×M16—31no—
352#537—34no—
353#536—31no—
354#536—31no—
355#536—61no—
356#535—31no—
357#535—61no—
358#535C2×D311yescharacteristic, complemented
359#534—62no—
360#532—61no—
361#532—61no—
362#525—34no—
363#525—62no—
364C2×#117—31no—
365#452—34no—
366#452—34no—
367#452—34no—
368#452—34no—
369#451—34no—
370#451—34no—
371#451—34no—
372#451—34no—
373#449—34no—
374#449—34no—
375#449—34no—
376#449C2×D314yescomplemented
377#448—34no—
378#448—34no—
379#448—34no—
380#448C2×D314yescomplemented
381#419—31no—
382#419—31no—
383#419—31no—
384#419—34no—
385#419—32no—
386#419C2×D311yescharacteristic, complemented
387#418—32no—
388#417—32no—
389#417—32no—
390#416—31no—
391#416—31no—
392#416—31no—
393#416C2×D311yescharacteristic, complemented
394C2×#103—34no—
395#408—31no—
396#408—31no—
397#408—31no—
398#408—34no—
399#408C2×D311yescharacteristic, complemented
400#407—34no—
401C24×C3—21no—
402C23×D3—21no—
403C23×D3C2×D412yes—
404C23×D3C2×D411yescharacteristic
405C3×#41—216no—
406C3×#41—28no—
407C3×#41—24no—
408C3×#41—24no—
409C3×#41—22no—
410C3×#41—22no—
411C3×#41—22no—
412C3×#41C2×D414yes—
413C2×C3×Q8—28no—
414C2×C3×Q8—24no—
415C2×C3×Q8—24no—
416C2×C3×Q8—22no—
417C2×C3×Q8—21no—
418C2×C3×Q8—22no—
419C2×C3×Q8C2×D414yes—
420C2×C3×Q8C2×D411yescharacteristic
421C2×C3×Q8C2411yescharacteristic
422C2×C3×Q8C2412yes—
423C2×C3×D4—22no—
424C2×C3×D4—21no—
425C2×C3×D4—24no—
426C2×C3×D4—22no—
427C2×C3×D4—22no—
428C2×C3×D4—21no—
429C2×C3×D4C2×D412yes—
430C2×C3×D4C2×D411yescharacteristic
431C2×C3×D4C2412yes—
432C2×C3×D4C2411yescharacteristic
433C22×C3×C4—22no—
434C22×C3×C4—21no—
435C22×C3×C4—22no—
436C22×C3×C4—21no—
437C22×C3×C4C2412yes—
438C22×C3×C4C2411yescharacteristic
439C2×#67—22no—
440C2×#67—21no—
441C2×#67—22no—
442C2×#67—21no—
443C2×#67—22no—
444C2×#67—22no—
445C2×#67—24no—
446C2×#67—21no—
447C2×#67—44no—
448C2×#67C2×D412yes—
449C2×#67C2×D412yes—
450C2×#67C2×D412yes—
451C22×Dic3—22no—
452C22×Dic3—21no—
453C22×Dic3—22no—
454C22×Dic3—21no—
455C22×Dic3—21no—
456C22×Dic3—22no—
457C22×Dic3—22no—
458C22×Dic3—44no—
459C22×Dic3C2×D412yes—
460C22×Dic3C2×D411yescharacteristic
461#239—216no—
462#239—28no—
463#239—24no—
464#239—24no—
465#239—24no—
466#239—22no—
467#239C2×D414yes—
468D3×Q8—216no—
469D3×Q8—28no—
470D3×Q8—28no—
471D3×Q8—216no—
472D3×Q8—216no—
473D3×Q8—24no—
474D3×Q8—24no—
475D3×Q8—24no—
476D3×Q8—28no—
477D3×Q8—28no—
478D3×Q8—22no—
479D3×Q8—24no—
480D3×Q8—24no—
481D3×Q8—24no—
482D3×Q8—24no—
483D3×Q8C2×D414yes—
484D3×Q8C2×D418yes—
485D3×Q8C2×D418yes—
486#237—216no—
487#237—216no—
488#237—216no—
489#237—28no—
490#237—216no—
491#237—216no—
492#237—24no—
493#237—28no—
494#237—28no—
495#237—24no—
496#237—22no—
497#237—24no—
498#237—24no—
499#237—24no—
500#237—24no—
501#237—24no—
502#237—44no—
503#237—44no—
504#237C2×D414yes—
505D3×D4—216no—
506D3×D4—28no—
507D3×D4—28no—
508D3×D4—24no—
509D3×D4—22no—
510D3×D4C2×D414yes—
511#235—216no—
512#235—216no—
513#235—216no—
514#235—28no—
515#235—216no—
516#235—216no—
517#235—22no—
518#235—22no—
519#235—22no—
520#235—24no—
521#235—28no—
522#235—24no—
523#235—24no—
524#235—24no—
525#235C2×D414yes—
526C2×D12—22no—
527C2×D12—21no—
528C2×D12C2×D411yescharacteristic
529C2×D12C2×D412yes—
530C2×D12C2411yescharacteristic
531C2×C4×D3—216no—
532C2×C4×D3—216no—
533C2×C4×D3—28no—
534C2×C4×D3—22no—
535C2×C4×D3—21no—
536C2×C4×D3—22no—
537C2×C4×D3—22no—
538C2×C4×D3—22no—
539C2×C4×D3—22no—
540C2×C4×D3—21no—
541C2×C4×D3—22no—
542C2×C4×D3—21no—
543C2×C4×D3—28no—
544C2×C4×D3—24no—
545C2×C4×D3—24no—
546C2×C4×D3—22no—
547C2×C4×D3C2×D412yes—
548C2×C4×D3C2×D412yes—
549C2×C4×D3C2×D411yescharacteristic
550C2×C4×D3C2×D411yescharacteristic
551C2×C4×D3C2×D414yes—
552C2×C4×D3C2×D414yes—
553C2×C4×D3C2412yes—
554C2×C4×D3C2411yescharacteristic
555C2×C4×D3C2411yescharacteristic
556C2×Dic6—28no—
557C2×Dic6—216no—
558C2×Dic6—216no—
559C2×Dic6—22no—
560C2×Dic6—21no—
561C2×Dic6—22no—
562C2×Dic6—28no—
563C2×Dic6—22no—
564C2×Dic6—22no—
565C2×Dic6—22no—
566C2×Dic6—21no—
567C2×Dic6—22no—
568C2×Dic6—24no—
569C2×Dic6—24no—
570C2×Dic6—22no—
571C2×Dic6—22no—
572C2×Dic6—21no—
573C2×Dic6C2×D411yescharacteristic
574C2×Dic6C2×D412yes—
575C2×Dic6C2×D414yes—
576C2×Dic6C2412yes—
577C2×Dic6C2411yescharacteristic
578C2×Dic6C2412yes—
579C3×SD16—28no—
580C3×SD16—24no—
581C3×D8—24no—
582C3×M16—22no—
583C2×C3×C8—22no—
584C2×C3×C8C2412yes—
585C2×C3×C8C2412yes—
586C3×C4⋊C4C2412yes—
587C3×C22⋊C4—21no—
588C3×C22⋊C4—24no—
589C3×C42—21no—
590#217—21no—
591#217—24no—
592#217—24no—
593#216—28no—
594#216—24no—
595#214—24no—
596#214—24no—
597#214—28no—
598#213—24no—
599(C2×D3)⋊C4—22no—
600(C2×D3)⋊C4—24no—
601C4⋊Dic3—24no—
602C4⋊Dic3C2412yes—
603Dic3⋊C4—24no—
604Dic3⋊C4—22no—
605C4×Dic3—21no—
606C4×Dic3—22no—
607#208—22no—
608C2×C3⋊C8—22no—
609C2×C3⋊C8C2412yes—
610C2×C3⋊C8C2412yes—
611Dic12—28no—
612Dic12—24no—
613#204—24no—
614ΓL(1,𝔽25)—24no—
615ΓL(1,𝔽25)—24no—
616ΓL(1,𝔽25)—24no—
617D3×C8—24no—
6182−1+4—24no—
6192−1+4—24no—
6202−1+4—68no—
6212−1+4—68no—
6222−1+4—64no—
6232−1+4—616no—
6242−1+4—68no—
6252−1+4—64no—
6262−1+4—64no—
6272−1+4—64no—
6282−1+4—68no—
6292−1+4—632no—
6302−1+4—616no—
6312−1+4—64no—
6322−1+4—64no—
633C2×#41—22no—
634C2×#41—21no—
635C2×#41—31no—
636C2×#41—32no—
637C2×#41—31no—
638C2×#41—31no—
639C2×#41—32no—
640C2×#41—38no—
641C2×#41—31no—
642C2×#41—32no—
643C2×#41—31no—
644C2×#41—32no—
645C2×#41—32no—
646C2×#41—32no—
647C2×#41—31no—
648C2×#41—32no—
649C2×#41—61no—
650C2×#41—62no—
651C2×#41—62no—
652C2×#41—62no—
653C2×#41—62no—
654C2×#41—62no—
655C2×#41—61no—
656C2×#41—61no—
657C2×#41—62no—
658C2×#41—61no—
659C2×#41—61no—
660C2×#41—64no—
661C2×#41—64no—
662C2×#41—64no—
663C2×#41—64no—
664C2×#41—64no—
665C2×#41—62no—
666C2×#41—62no—
667C2×#41—62no—
668C2×#41—62no—
669C2×#41—61no—
670C2×#41—68no—
671C2×#41—68no—
672C2×#41—616no—
673C2×#41—632no—
674C2×#41—62no—
675C2×#41—61no—
676C2×#41C22×D312yes—
677C2×#41C22×D311yescharacteristic
678C2×#41C22×D311yescharacteristic
679C22×Q8—21no—
680C22×Q8—31no—
681C22×Q8—38no—
682C22×Q8—32no—
683C22×Q8—31no—
684C22×Q8—32no—
685C22×Q8—32no—
686C22×Q8—32no—
687C22×Q8—31no—
688C22×Q8—31no—
689C22×Q8—32no—
690C22×Q8—61no—
691C22×Q8—62no—
692C22×Q8—62no—
693C22×Q8—61no—
694C22×Q8—61no—
695C22×Q8—62no—
696C22×Q8—61no—
697C22×Q8—64no—
698C22×Q8—62no—
699C22×Q8—68no—
700C22×Q8—68no—
701C22×Q8—62no—
702C22×Q8—61no—
703C22×Q8—616no—
704C22×Q8—61no—
705C22×Q8C22×D312yes—
706C22×Q8C22×D311yescharacteristic
707C22×D4—31no—
708C22×D4—32no—
709C22×D4—31no—
710C22×D4—61no—
711C22×D4—62no—
712C22×D4—61no—
713C22×D4C22×D311yescharacteristic
714C23×C4—31no—
715C23×C4—32no—
716C23×C4—61no—
717C23×C4—62no—
718C23×C4—61no—
719C23×C4—62no—
720C23×C4—61no—
721#137—64no—
722#137—616no—
723#137—616no—
724#137—68no—
725#137—64no—
726AGL(1,ℤ/8)—24no—
727AGL(1,ℤ/8)—68no—
728AGL(1,ℤ/8)—64no—
729#135—68no—
730#135—68no—
731C2×Q16—34no—
732C2×Q16—32no—
733C2×Q16—34no—
734C2×Q16—32no—
735C2×Q16—64no—
736C2×Q16—64no—
737C2×SD16—24no—
738C2×SD16—34no—
739C2×SD16—32no—
740C2×SD16—32no—
741C2×SD16—32no—
742C2×SD16—64no—
743C2×SD16C22×D314yes—
744C2×SD16C22×D312yes—
745C2×D8—32no—
746C2×D8C22×D312yes—
747C2×M16—31no—
748C2×M16—32no—
749C2×M16—32no—
750C2×M16—32no—
751C2×M16—64no—
752C2×M16—64no—
753C2×M16C22×D311yescharacteristic
754C22×C8—31no—
755C22×C8—32no—
756C22×C8C22×D311yescharacteristic
757C4⋊Q8—61no—
758C4⋊Q8—61no—
759#127—21no—
760#127—61no—
761#124—21no—
762#124—61no—
763#124—61no—
764#124—61no—
765#123—64no—
766#123—62no—
767#123—62no—
768C22⋊Q8—34no—
769C22⋊Q8—34no—
770C22⋊Q8—64no—
771#121—34no—
772#121—64no—
773#121—64no—
774#121—64no—
775#121C22×D314yes—
776#120—22no—
777#120—64no—
778#120—62no—
779C4×D4—64no—
780C4×D4—64no—
781#117—31no—
782#117—32no—
783#117—61no—
784#117—61no—
785#117C22×D311yescharacteristic
786C2×C4⋊C4—32no—
787C2×C22⋊C4—61no—
788C2×C42—61no—
789#103—34no—
790#103—32no—
791#103—34no—
792#103—32no—
793#103—34no—
794#103—32no—
795#103C22×D314yes—
796#103C22×D312yes—
797#102—32no—
798#102—32no—
799#102—32no—
800#102C22×D312yes—
801C22⋊C8—34no—
802C22⋊C8—34no—
803C22⋊C8—34no—
804C22⋊C8C22×D314yes—
805C23×C3—21no—
806C23×C3—22no—
807C23×C3—42no—
808C23×C3—82no—
809C23×C3C22×D412yes—
810C23×C3C22×D411yescharacteristic
811C22×D3—21no—
812C22×D3—24no—
813C22×D3—24no—
814C22×D3—42no—
815C22×D3—44no—
816C22×D3—44no—
817C22×D3#12014yes—
818C22×D3C22×D412yes—
819C22×D3C22×D411yescharacteristic
820C22×D3C22×D411yescharacteristic
821C3×Q8—28no—
822C3×Q8—24no—
823C3×Q8—22no—
824C3×Q8—22no—
825C3×Q8—21no—
826C3×Q8C22×D412yes—
827C3×Q8C22×D414yes—
828C3×D4—28no—
829C3×D4—24no—
830C3×D4—24no—
831C3×D4—22no—
832C3×D4—21no—
833C3×D4—22no—
834C3×D4—22no—
835C3×D4—42no—
836C3×D4—84no—
837C3×D4C22×D412yes—
838C2×C3×C4—28no—
839C2×C3×C4—28no—
840C2×C3×C4—24no—
841C2×C3×C4—21no—
842C2×C3×C4—22no—
843C2×C3×C4—24no—
844C2×C3×C4—22no—
845C2×C3×C4—22no—
846C2×C3×C4—22no—
847C2×C3×C4C22×D412yes—
848C2×C3×C4C22×D411yescharacteristic
849C2×C3×C4C22×D412yes—
850C2×C3×C4C22×D412yes—
851C2×C3×C4C2511yescharacteristic
852#67—28no—
853#67—28no—
854#67—24no—
855#67—24no—
856#67—24no—
857#67—24no—
858#67—24no—
859#67—24no—
860#67—44no—
861#67—44no—
862#67—84no—
863C2×Dic3—28no—
864C2×Dic3—28no—
865C2×Dic3—24no—
866C2×Dic3—21no—
867C2×Dic3—22no—
868C2×Dic3—24no—
869C2×Dic3—24no—
870C2×Dic3—22no—
871C2×Dic3—22no—
872C2×Dic3—42no—
873C2×Dic3—44no—
874C2×Dic3—44no—
875C2×Dic3#12014yes—
876C2×Dic3C22×D412yes—
877C2×Dic3C22×D411yescharacteristic
878C2×Dic3C22×D411yescharacteristic
879D12—28no—
880D12—24no—
881D12—24no—
882D12—22no—
883D12—21no—
884D12C22×D412yes—
885C4×D3—28no—
886C4×D3—28no—
887C4×D3—28no—
888C4×D3—28no—
889C4×D3—28no—
890C4×D3—24no—
891C4×D3—24no—
892C4×D3—28no—
893C4×D3—24no—
894C4×D3—22no—
895C4×D3—22no—
896C4×D3—24no—
897C4×D3—24no—
898C4×D3—82no—
899C4×D3#12014yes—
900C4×D3#12014yes—
901C4×D3C22×D412yes—
902C4×D3C22×D412yes—
903C4×D3C22×D412yes—
904C4×D3C22×D412yes—
905Dic6—28no—
906Dic6—28no—
907Dic6—28no—
908Dic6—22no—
909Dic6—24no—
910Dic6—22no—
911Dic6—21no—
912Dic6—24no—
913Dic6—28no—
914Dic6—28no—
915Dic6—24no—
916Dic6—22no—
917Dic6—22no—
918Dic6—42no—
919Dic6C22×D412yes—
920Dic6C22×D414yes—
921C3×C8—22no—
922C3×C8—22no—
923C3⋊C8—22no—
924C3⋊C8—22no—
925C24—21no—
926C24—31no—
927C24—32no—
928C24—61no—
929#41—216no—
930#41—28no—
931#41—24no—
932#41—24no—
933#41—22no—
934#41—22no—
935#41—22no—
936#41—34no—
937#41—34no—
938#41—34no—
939#41—64no—
940#41—64no—
941#41—68no—
942#41—64no—
943#41—64no—
944#41—616no—
945#41—616no—
946#41—616no—
947#41—616no—
948#41—616no—
949#41—68no—
950#41—68no—
951#41—68no—
952#41—62no—
953#41—64no—
954#41—62no—
955#41—64no—
956#41—64no—
957#41—64no—
958#41—64no—
959#41—64no—
960#41—64no—
961#41—616no—
962#41—616no—
963#41—616no—
964#41—616no—
965#41—616no—
966#41—68no—
967#41—64no—
968#41—616no—
969#41—68no—
970#41—64no—
971#41—64no—
972#41—62no—
973#41—62no—
974#41—62no—
975#41—124no—
976#41—124no—
977#41D3×D414yes—
978C2×Q8—28no—
979C2×Q8—24no—
980C2×Q8—24no—
981C2×Q8—22no—
982C2×Q8—21no—
983C2×Q8—22no—
984C2×Q8—32no—
985C2×Q8—31no—
986C2×Q8—38no—
987C2×Q8—38no—
988C2×Q8—34no—
989C2×Q8—34no—
990C2×Q8—32no—
991C2×Q8—31no—
992C2×Q8—32no—
993C2×Q8—62no—
994C2×Q8—61no—
995C2×Q8—62no—
996C2×Q8—62no—
997C2×Q8—62no—
998C2×Q8—68no—
999C2×Q8—64no—
1000C2×Q8—64no—
1001C2×Q8—616no—
1002C2×Q8—616no—
1003C2×Q8—68no—
1004C2×Q8—64no—
1005C2×Q8—62no—
1006C2×Q8—64no—
1007C2×Q8—68no—
1008C2×Q8—64no—
1009C2×Q8—68no—
1010C2×Q8—64no—
1011C2×Q8—64no—
1012C2×Q8—616no—
1013C2×Q8—616no—
1014C2×Q8—616no—
1015C2×Q8—68no—
1016C2×Q8—68no—
1017C2×Q8—64no—
1018C2×Q8—64no—
1019C2×Q8—62no—
1020C2×Q8—61no—
1021C2×Q8—62no—
1022C2×Q8—61no—
1023C2×Q8—62no—
1024C2×Q8—62no—
1025C2×Q8D3×D414yes—
1026C2×Q8D3×D411yescharacteristic
1027C2×Q8C23×D311yescharacteristic
1028C2×Q8C23×D312yes—
1029C2×D4—22no—
1030C2×D4—21no—
1031C2×D4—24no—
1032C2×D4—22no—
1033C2×D4—22no—
1034C2×D4—21no—
1035C2×D4—34no—
1036C2×D4—32no—
1037C2×D4—32no—
1038C2×D4—32no—
1039C2×D4—32no—
1040C2×D4—31no—
1041C2×D4—31no—
1042C2×D4—61no—
1043C2×D4—62no—
1044C2×D4—62no—
1045C2×D4—64no—
1046C2×D4—61no—
1047C2×D4—68no—
1048C2×D4—68no—
1049C2×D4—616no—
1050C2×D4—61no—
1051C2×D4—62no—
1052C2×D4—62no—
1053C2×D4—61no—
1054C2×D4—62no—
1055C2×D4—62no—
1056C2×D4—64no—
1057C2×D4—124no—
1058C2×D4D3×D412yes—
1059C2×D4D3×D411yescharacteristic
1060C2×D4C23×D312yes—
1061C2×D4C23×D311yescharacteristic
1062C22×C4—22no—
1063C22×C4—21no—
1064C22×C4—22no—
1065C22×C4—21no—
1066C22×C4—31no—
1067C22×C4—31no—
1068C22×C4—31no—
1069C22×C4—34no—
1070C22×C4—34no—
1071C22×C4—31no—
1072C22×C4—31no—
1073C22×C4—32no—
1074C22×C4—32no—
1075C22×C4—32no—
1076C22×C4—32no—
1077C22×C4—64no—
1078C22×C4—64no—
1079C22×C4—61no—
1080C22×C4—62no—
1081C22×C4—68no—
1082C22×C4—61no—
1083C22×C4—62no—
1084C22×C4—62no—
1085C22×C4—62no—
1086C22×C4—62no—
1087C22×C4—68no—
1088C22×C4—616no—
1089C22×C4—616no—
1090C22×C4—62no—
1091C22×C4—61no—
1092C22×C4—62no—
1093C22×C4—62no—
1094C22×C4—62no—
1095C22×C4—62no—
1096C22×C4—61no—
1097C22×C4—62no—
1098C22×C4—61no—
1099C22×C4—61no—
1100C22×C4—124no—
1101C22×C4C23×D312yes—
1102C22×C4C23×D311yescharacteristic
1103Q16—68no—
1104Q16—64no—
1105Q16—68no—
1106Q16—64no—
1107SD16—28no—
1108SD16—24no—
1109SD16—64no—
1110SD16—68no—
1111SD16—64no—
1112SD16—64no—
1113D8—24no—
1114D8—64no—
1115M16—22no—
1116M16—64no—
1117M16—64no—
1118M16—64no—
1119M16—62no—
1120C2×C8—22no—
1121C2×C8—32no—
1122C2×C8—32no—
1123C2×C8—64no—
1124C2×C8—62no—
1125C2×C8C23×D312yes—
1126C2×C8C23×D312yes—
1127C4⋊C4—32no—
1128C4⋊C4—62no—
1129C4⋊C4—64no—
1130C4⋊C4—64no—
1131C4⋊C4C23×D312yes—
1132C22⋊C4—21no—
1133C22⋊C4—24no—
1134C22⋊C4—62no—
1135C22⋊C4—64no—
1136C22⋊C4—64no—
1137C22⋊C4—61no—
1138C22⋊C4—64no—
1139C42—21no—
1140C42—62no—
1141C42—61no—
1142C22×C3—22no—
1143C22×C3—24no—
1144C22×C3—22no—
1145C22×C3—22no—
1146C22×C3—42no—
1147C22×C3—44no—
1148C22×C3—42no—
1149C22×C3—84no—
1150C22×C3C2×#12012yes—
1151C22×C3C23×D411yescharacteristic
1152C2×D3—22no—
1153C2×D3—22no—
1154C2×D3—24no—
1155C2×D3—22no—
1156C2×D3—22no—
1157C2×D3—44no—
1158C2×D3—48no—
1159C2×D3—48no—
1160C2×D3—42no—
1161C2×D3C2×#12012yes—
1162C2×D3C2×#12012yes—
1163C3×C4—22no—
1164C3×C4—24no—
1165C3×C4—22no—
1166C3×C4—42no—
1167C3×C4C2×#12012yes—
1168C3×C4C23×D411yescharacteristic
1169C3×C4C23×D411yescharacteristic
1170Dic3—22no—
1171Dic3—22no—
1172Dic3—24no—
1173Dic3—42no—
1174Dic3—42no—
1175Dic3C2×#12012yes—
1176Dic3C2×#12012yes—
1177C23—21no—
1178C23—22no—
1179C23—31no—
1180C23—31no—
1181C23—34no—
1182C23—32no—
1183C23—42no—
1184C23—64no—
1185C23—64no—
1186C23—61no—
1187C23—82no—
1188C23—122no—
1189C23—124no—
1190C23—124no—
1191C23C2×D3×D412yes—
1192C23C2×D3×D411yescharacteristic
1193Q8—28no—
1194Q8—21no—
1195Q8—22no—
1196Q8—24no—
1197Q8—22no—
1198Q8—34no—
1199Q8—32no—
1200Q8—68no—
1201Q8—68no—
1202Q8—64no—
1203Q8—64no—
1204Q8—68no—
1205Q8—68no—
1206Q8—68no—
1207Q8—61no—
1208Q8—62no—
1209Q8—62no—
1210Q8—64no—
1211Q8—62no—
1212Q8—62no—
1213Q8—122no—
1214Q8C2×D3×D412yes—
1215Q8C2×D3×D414yes—
1216D4—28no—
1217D4—24no—
1218D4—24no—
1219D4—21no—
1220D4—22no—
1221D4—22no—
1222D4—22no—
1223D4—32no—
1224D4—42no—
1225D4—64no—
1226D4—64no—
1227D4—68no—
1228D4—64no—
1229D4—64no—
1230D4—64no—
1231D4—64no—
1232D4—68no—
1233D4—68no—
1234D4—64no—
1235D4—64no—
1236D4—61no—
1237D4—62no—
1238D4—84no—
1239D4—124no—
1240D4—124no—
1241D4—244no—
1242D4C2×D3×D412yes—
1243C2×C4—28no—
1244C2×C4—28no—
1245C2×C4—22no—
1246C2×C4—21no—
1247C2×C4—24no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—24no—
1251C2×C4—22no—
1252C2×C4—31no—
1253C2×C4—31no—
1254C2×C4—34no—
1255C2×C4—32no—
1256C2×C4—32no—
1257C2×C4—32no—
1258C2×C4—32no—
1259C2×C4—34no—
1260C2×C4—34no—
1261C2×C4—32no—
1262C2×C4—64no—
1263C2×C4—64no—
1264C2×C4—64no—
1265C2×C4—64no—
1266C2×C4—68no—
1267C2×C4—68no—
1268C2×C4—68no—
1269C2×C4—68no—
1270C2×C4—68no—
1271C2×C4—68no—
1272C2×C4—64no—
1273C2×C4—64no—
1274C2×C4—68no—
1275C2×C4—68no—
1276C2×C4—62no—
1277C2×C4—61no—
1278C2×C4—64no—
1279C2×C4—62no—
1280C2×C4—62no—
1281C2×C4—64no—
1282C2×C4—62no—
1283C2×C4—62no—
1284C2×C4—124no—
1285C2×C4—124no—
1286C2×C4—122no—
1287C2×C4—242no—
1288C2×C4C2×D3×D412yes—
1289C2×C4C2×D3×D412yes—
1290C2×C4C2×D3×D412yes—
1291C2×C4C2×D3×D411yescharacteristic
1292C2×C4C24×D311yescharacteristic
1293C8—22no—
1294C8—22no—
1295C8—62no—
1296C8—62no—
1297C2×C3—22no—
1298C2×C3—42no—
1299C2×C3—42no—
1300C2×C3—82no—
1301C2×C3C22×#12011yescharacteristic
1302C2×C3#358612yes—
1303D3—22no—
1304D3—22no—
1305D3—42no—
1306D3—42no—
1307C22—22no—
1308C22—22no—
1309C22—22no—
1310C22—24no—
1311C22—32no—
1312C22—32no—
1313C22—42no—
1314C22—42no—
1315C22—44no—
1316C22—62no—
1317C22—62no—
1318C22—62no—
1319C22—62no—
1320C22—64no—
1321C22—84no—
1322C22—124no—
1323C22—128no—
1324C22—128no—
1325C22—122no—
1326C22D3×#12012yes—
1327C22C22×D3×D411yescharacteristic
1328C4—24no—
1329C4—22no—
1330C4—22no—
1331C4—32no—
1332C4—32no—
1333C4—42no—
1334C4—62no—
1335C4—64no—
1336C4—62no—
1337C4—122no—
1338C4—122no—
1339C4D3×#12012yes—
1340C4C22×D3×D411yescharacteristic
1341C4C22×D3×D411yescharacteristic
1342C3#6036811yescharacteristic, complemented, Sylow
1343C2—22no—
1344C2—42no—
1345C2—42no—
1346C2—62no—
1347C2—62no—
1348C2—82no—
1349C2—122no—
1350C2—122no—
1351C2C2×D3×#12011yescharacteristic
1352C2#8720812yes—
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3010C2
socleC22×C3C23×D4
hypercenter#3010D3
hypocenterC3#60368
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3010

Complements

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

NH ≅ G/Ntype
1. C2×D3×2−1+4C2semidirect
2. C2×#5773C2semidirect
3. C22×#915C2semidirect
4. #86313C2semidirect
5. C3×#3010C2semidirect
6. #84117C2semidirect
7. #83948C2semidirect
8. #83860C2semidirect
9. #83390C2semidirect
10. #80088C2semidirect
11. #80083C2semidirect
12. #80042C2semidirect
13. #80039C2semidirect
14. #78961C2semidirect
15. D3×#419C2semidirect
16. #78837C2semidirect
17. #78830C2semidirect
18. #78679C2semidirect
19. #78662C2semidirect
28. C2×#1010C22semidirect
33. C2×D3×#41C22semidirect
36. C2×#1007C22semidirect
39. C22×D3×Q8C22semidirect
41. C2×C3×AGL(1,ℤ/8)C22semidirect
42. C22×C3×SD16C22semidirect
43. C3×#535C22semidirect
44. #5825C22semidirect
45. C2×#951C22semidirect
46. C22×#216C22semidirect
47. #5805C22semidirect
48. C22×#214C22semidirect
49. C2×#932C22semidirect
51. C2×#916C22semidirect
55. C2×#915C22semidirect
56. C2×#912C22semidirect
58. C2×#909C22semidirect
60. C22×Dic12C22semidirect
66. #5608C22semidirect
70. #5526C22semidirect
72. C3×#449C22semidirect
73. C3×#448C22semidirect
74. C3×#419C22semidirect
75. C3×#416C22semidirect
76. C3×#408C22semidirect
77. #5239C22semidirect
78. #5234C22semidirect
79. #5233C22semidirect
80. #5228C22semidirect
81. #5225C22semidirect
82. #5172C22semidirect
83. #5170C22semidirect
84. #5170C22semidirect
85. #5158C22semidirect
86. #5129C22semidirect
87. #5120C22semidirect
88. #5113C22semidirect
89. #5110C22semidirect
90. #5040C22semidirect
91. #5037C22semidirect
92. #5004C22semidirect
93. #5002C22semidirect
94. #4809C22semidirect
95. #4809C22semidirect
96. #4808C22semidirect
97. #4803C22semidirect
98. #4802C22semidirect
99. #4802C22semidirect
100. D3×#103C22semidirect
101. #4783C22semidirect
102. #4771C22semidirect
103. #4770C22semidirect
104. #4739C22semidirect
105. #4733C22semidirect
106. #4727C22semidirect
107. #4726C22semidirect
121. #3010D3semidirect
155. D3×#41D4semidirect
178. C2×D3×Q8D4semidirect
343. C2×AGL(1,ℤ/8)C2×D3semidirect
349. C22×SD16C2×D3semidirect
358. #535C2×D3semidirect
376. #449C2×D3semidirect
380. #448C2×D3semidirect
386. #419C2×D3semidirect
393. #416C2×D3semidirect
399. #408C2×D3semidirect
1342. C3#60368semidirect

Maximal subgroups

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

subgroupindex
C2×D3×2−1+42
C2×#57732
C22×#9152
#863132
C3×#30102
#841172
#839482
#838602
#833902
#800882
#800832
#800422
#800392
#789612
D3×#4192
#788372
#788302
#786792
#786622
#603683