Finite Group Databasebeta

← #11661679

Subgroups — #11661679

Order 768.

4726 conjugacy classes of subgroups.

The subgroup lattice has 1322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#1010C211yesmaximal, characteristic, complemented
2C2×D3×#137C211yesmaximal, characteristic, complemented
3C2×#5773C211yesmaximal, characteristic, complemented
4#86035C211yesmaximal, characteristic, complemented
5C3×#3005C211yesmaximal, characteristic, complemented
6#84081C211yesmaximal, characteristic, complemented
7#83979C211yesmaximal, characteristic, complemented
8#83945C211yesmaximal, characteristic, complemented
9#82933C211yesmaximal, characteristic, complemented
10#80232C214yesmaximal, complemented
11#80230C214yesmaximal, complemented
12#80088C214yesmaximal, complemented
13#80086C214yesmaximal, complemented
14#78958C211yesmaximal, characteristic, complemented
15D3×#419C211yesmaximal, characteristic, complemented
16#78927C211yesmaximal, characteristic, complemented
17#78924C211yesmaximal, characteristic, complemented
18#78645C211yesmaximal, characteristic, complemented
19#78630C211yesmaximal, characteristic, complemented
20#60368—31nomaximal, Sylow
21C22×C3×#41C2211yescharacteristic, complemented
22C2×#1010—28no—
23C2×#1010—28no—
24C2×#1010—22no—
25C2×#1010—22no—
26C2×#1010C2214yes—
27C2×#1010C2214yescomplemented
28C2×D3×#41C2211yescharacteristic
29C22×D3×Q8C2211yescharacteristic
30C22×D3×Q8C2211yescharacteristic, complemented
31C22×#237—21no—
32C22×#237—21no—
33C22×#237C2211yescharacteristic
34C22×#237C2211yescharacteristic, complemented
35C22×#235—21no—
36C22×#235C2211yescharacteristic
37C23×Dic6—21no—
38C23×Dic6C2211yescharacteristic, complemented
39C2×C3×#137C2211yescharacteristic
40C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
41C3×#525C2211yescharacteristic
42#5828C2211yescharacteristic
43C2×#951C2211yescharacteristic
44C2×#951C2211yescharacteristic
45C2×#942C2211yescharacteristic
46C2×#932C2211yescharacteristic
47#5791C2211yescharacteristic
48D3×#137—28no—
49#5773—28no—
50C2×#918C2212yescomplemented
51C2×D3×Q16C2212yescomplemented
52C2×#916C2212yescomplemented
53C2×#915C2212yescomplemented
54C2×#915C2212yescomplemented
55C2×D3×SD16C2212yescomplemented
56C2×#912C2212yescomplemented
57C2×#911C2212yescomplemented
58C2×#909C2211yescharacteristic
59C2×#909C2211yescharacteristic
60C2×D3×M16C2211yescharacteristic
61C2×D3×M16C2211yescharacteristic
62#5653—21no—
63#5648—21no—
64#5629C2212yescomplemented
65#5628C2212yescomplemented
66#5608C2212yescomplemented
67#5607C2212yescomplemented
68#5592—21no—
69#5589—21no—
70#5548—22no—
71#5547—22no—
72#5524C2211yescharacteristic
73D3×#117C2211yescharacteristic
74C3×#452C2214yescomplemented
75C3×#449C2214yescomplemented
76C3×#419C2211yescharacteristic, complemented
77C3×#418C2211yescharacteristic, complemented
78C3×#407C2211yescharacteristic, complemented
79#5239C2214yescomplemented
80#5238C2214yescomplemented
81#5225C2211yescharacteristic, complemented
82#5215C2211yescharacteristic, complemented
83#5207C2211yescharacteristic, complemented
84#5186C2214yescomplemented
85#5173C2214yescomplemented
86#5170C2214yescomplemented
87#5158C2214yescomplemented
88#5126C2211yescharacteristic, complemented
89#5126C2211yescharacteristic, complemented
90#5120C2211yescharacteristic, complemented
91#5120C2211yescharacteristic, complemented
92#5050C2214yescomplemented
93#5040C2214yescomplemented
94#5004C2211yescharacteristic, complemented
95#5004C2211yescharacteristic, complemented
96#4809C2214yescomplemented
97#4806C2214yescomplemented
98#4802C2214yescomplemented
99D3×#103C2214yescomplemented
100#4783C2214yescomplemented
101#4781C2214yescomplemented
102#4772C2214yescomplemented
103#4771C2214yescomplemented
104#4739C2214yescomplemented
105#4738C2214yescomplemented
106#4727C2214yescomplemented
107#4727C2214yescomplemented
108C22×2−1+4—31no—
109C2×#575—31no—
110C22×#137—31no—
111#3449—31no—
112#3013—34no—
113#3013—34no—
114#3011—34no—
115#3010—34no—
116#3005—31no—
117#3005—31no—
118#3005—31no—
119#3005D311yescharacteristic, complemented
120#3004—31no—
121#3004—31no—
122#3004—31no—
123#3004—31no—
124#2896—31no—
125C2×#419—31no—
126#2879—31no—
127C2×C3×#41—24no—
128C2×C3×#41—24no—
129C2×C3×#41—22no—
130C2×C3×#41C2311yescharacteristic
131C2×C3×#41C2314yes—
132C22×C3×Q8C2311yescharacteristic
133C22×C3×D4—21no—
134C22×C3×D4C2311yescharacteristic
135C23×C3×C4—21no—
136C23×C3×C4C2311yescharacteristic
137C22×#67—21no—
138C22×#67—21no—
139C22×#67D411yescharacteristic
140C22×#67D411yescharacteristic
141C23×Dic3—21no—
142C23×Dic3—21no—
143C23×Dic3—21no—
144#1010—232no—
145#1010—232no—
146#1010—216no—
147#1010—216no—
148#1010—216no—
149#1010—216no—
150D3×#41—24no—
151D3×#41—24no—
152C2×#239C2311yescharacteristic
153C2×D3×Q8—24no—
154C2×D3×Q8—24no—
155C2×D3×Q8—21no—
156C2×D3×Q8—21no—
157C2×D3×Q8—22no—
158C2×D3×Q8—24no—
159C2×D3×Q8D418yescomplemented
160C2×D3×Q8C2314yes—
161C2×D3×Q8C2311yescharacteristic
162C2×D3×Q8C2312yes—
163C2×D3×Q8C2312yes—
164C2×#237—216no—
165C2×#237—216no—
166C2×#237—24no—
167C2×#237—24no—
168C2×#237—24no—
169C2×#237—24no—
170C2×#237—24no—
171C2×#237—21no—
172C2×#237—21no—
173C2×#237—21no—
174C2×#237—24no—
175C2×#237—22no—
176C2×#237—24no—
177C2×#237D418yescomplemented
178C2×#237C2314yes—
179C2×#237C2311yescharacteristic
180C2×#237C2312yes—
181C2×#237C2312yes—
182C2×D3×D4—21no—
183C2×D3×D4C2311yescharacteristic
184C2×#235—216no—
185C2×#235—24no—
186C2×#235—24no—
187C2×#235—24no—
188C2×#235—24no—
189C2×#235—21no—
190C2×#235D412yes—
191C2×#235D412yes—
192C2×#235C2312yes—
193C2×#235C2312yes—
194C2×#235C2311yescharacteristic
195C22×D12D411yescharacteristic
196C22×C4×D3—21no—
197C22×C4×D3—21no—
198C22×C4×D3—21no—
199C22×C4×D3C2311yescharacteristic
200C22×C4×D3C2311yescharacteristic
201C22×Dic6—216no—
202C22×Dic6—21no—
203C22×Dic6—22no—
204C22×Dic6—21no—
205C22×Dic6—21no—
206C22×Dic6—24no—
207C22×Dic6—24no—
208C22×Dic6—24no—
209C22×Dic6—24no—
210C22×Dic6D411yescharacteristic
211C22×Dic6C2314yes—
212C22×Dic6C2311yescharacteristic
213C22×Dic6C2311yescharacteristic
214C3×#137—24no—
215C3×AGL(1,ℤ/8)—24no—
216C2×C3×Q16C2312yes—
217C2×C3×SD16C2312yes—
218C2×C3×SD16C2312yes—
219C2×C3×D8C2312yes—
220C2×C3×M16C2311yescharacteristic
221C2×C3×M16C2311yescharacteristic
222C3×#123—21no—
223C3×C22⋊Q8C2312yes—
224C3×#121C2312yes—
225C3×#120—21no—
226C3×C4×D4—22no—
227C3×#117C2311yescharacteristic
228#953—21no—
229#951—24no—
230#951—24no—
231#946C2312yes—
232C2×#216C2312yes—
233C2×#216C2312yes—
234C2×#216C2312yes—
235#942—24no—
236C2×#215C2312yes—
237#940—22no—
238#939—22no—
239#938—22no—
240#938C2312yes—
241#937—21no—
242#937—22no—
243#935—21no—
244C2×#214C2312yes—
245C2×#214C2312yes—
246C2×#214C2312yes—
247#932—24no—
248C2×#213C2312yes—
249#930C2312yes—
250#929—21no—
251C4×#67—22no—
252C4×#67—22no—
253#926C2311yescharacteristic
254#924C2312yes—
255C2×#208C2311yescharacteristic
256C2×#208C2311yescharacteristic
257#918—28no—
258D3×Q16—28no—
259#916—28no—
260#915—28no—
261#915—28no—
262D3×SD16—28no—
263#912—28no—
264#911—28no—
265#909—24no—
266#909—24no—
267D3×M16—24no—
268D3×M16—24no—
269C2×Dic12C2312yes—
270C2×Dic12C2312yes—
271C2×#204C2312yes—
272C2×#204C2312yes—
273C2×ΓL(1,𝔽25)C2312yes—
274C2×ΓL(1,𝔽25)C2312yes—
275C2×D3×C8C2312yes—
276C2×D3×C8C2312yes—
277#897C2312yes—
278#896—22no—
279#895—22no—
280#895C2312yes—
281#894—22no—
282#892C2312yes—
283D3×C4⋊C4C2312yes—
284#888—22no—
285#886—21no—
286#885—22no—
287#885—22no—
288#884—22no—
289#884—22no—
290#884—22no—
291#883—22no—
292#882—21no—
293#882—22no—
294D3×C22⋊C4—21no—
295#878—22no—
296#877—21no—
297C4×D12—22no—
298#872—21no—
299C42×D3—21no—
300C3×#103C2314yes—
301C3×#102C2314yes—
302C3×C22⋊C8C2314yes—
303#835C2314yes—
304#832C2314yes—
305#830C2314yes—
306(C2×D3)⋊C8C2314yes—
307(C2×D3)⋊C8C2314yes—
308#816C2314yes—
309#816C2314yes—
310#810C2314yes—
311#810C2314yes—
312C2×2−1+4—34no—
313C2×2−1+4—34no—
314C2×2−1+4—68no—
315C2×2−1+4—68no—
316C2×2−1+4—62no—
317C2×2−1+4—62no—
318C22×#41—31no—
319C22×#41—31no—
320C22×#41—31no—
321C22×#41—31no—
322C22×#41—61no—
323C22×#41—61no—
324C22×#41—61no—
325C22×#41C2×D311yescharacteristic, complemented
326C23×Q8—31no—
327C23×Q8—31no—
328C23×Q8—31no—
329C23×Q8—61no—
330#575—68no—
331C2×#137—31no—
332C2×#137—31no—
333C2×#137—31no—
334C2×#137—32no—
335C2×#137—32no—
336C2×#137—32no—
337C2×#137—31no—
338C2×#137—31no—
339C2×#137—68no—
340C2×#137C2×D311yescharacteristic
341C2×AGL(1,ℤ/8)—31no—
342C2×AGL(1,ℤ/8)—32no—
343C2×AGL(1,ℤ/8)C2×D311yescharacteristic
344C2×#135—32no—
345C2×#135—32no—
346C22×Q16—32no—
347C22×SD16—32no—
348C22×M16—31no—
349C22×M16—31no—
350#537—32no—
351#537—32no—
352#536—32no—
353#536—61no—
354#535—32no—
355#535—61no—
356#534—61no—
357#534—61no—
358#532—62no—
359#525—31no—
360#525—31no—
361#525—31no—
362#525—62no—
363#525C2×D311yescharacteristic
364C2×#117—31no—
365#452—34no—
366#452—34no—
367#452—34no—
368#452C2×D314yescomplemented
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#448—34no—
381#419—31no—
382#419—31no—
383#419—31no—
384#419—31no—
385#419—31no—
386#419—34no—
387#419C2×D311yescharacteristic, complemented
388#418—31no—
389#418C2×D311yescharacteristic, complemented
390#417—34no—
391#416—34no—
392C2×#103—34no—
393#408—34no—
394#408—34no—
395#407—31no—
396#407—31no—
397#407—31no—
398#407C2×D311yescharacteristic, complemented
399C24×C3—21no—
400C24×C3C2×D411yescharacteristic
401C23×D3—21no—
402C23×D3C2×D411yescharacteristic
403C23×D3C2×D411yescharacteristic
404C3×#41—216no—
405C3×#41—28no—
406C3×#41—28no—
407C3×#41—22no—
408C3×#41—22no—
409C2×C3×Q8—22no—
410C2×C3×Q8—21no—
411C2×C3×Q8C2×D414yes—
412C2×C3×Q8C2411yescharacteristic
413C2×C3×Q8C2412yes—
414C2×C3×D4—28no—
415C2×C3×D4—24no—
416C2×C3×D4—21no—
417C2×C3×D4—22no—
418C2×C3×D4—21no—
419C2×C3×D4—22no—
420C2×C3×D4C2×D414yes—
421C2×C3×D4C2411yescharacteristic
422C2×C3×D4C2412yes—
423C22×C3×C4—28no—
424C22×C3×C4—21no—
425C22×C3×C4—24no—
426C22×C3×C4—22no—
427C22×C3×C4—22no—
428C22×C3×C4—21no—
429C22×C3×C4C2×D412yes—
430C22×C3×C4C2×D411yescharacteristic
431C22×C3×C4C2412yes—
432C22×C3×C4C2411yescharacteristic
433C2×#67—28no—
434C2×#67—24no—
435C2×#67—28no—
436C2×#67—24no—
437C2×#67—22no—
438C2×#67—22no—
439C2×#67—21no—
440C2×#67—21no—
441C2×#67—22no—
442C2×#67—22no—
443C2×#67—24no—
444C2×#67—21no—
445C2×#67C2×D412yes—
446C2×#67C2×D412yes—
447C2×#67C2×D412yes—
448C2×#67C2×D412yes—
449C22×Dic3—28no—
450C22×Dic3—28no—
451C22×Dic3—21no—
452C22×Dic3—21no—
453C22×Dic3—24no—
454C22×Dic3—28no—
455C22×Dic3—24no—
456C22×Dic3—22no—
457C22×Dic3—22no—
458C22×Dic3—21no—
459C22×Dic3C2×D411yescharacteristic
460C22×Dic3C2×D411yescharacteristic
461#239—22no—
462#239—22no—
463D3×Q8—216no—
464D3×Q8—28no—
465D3×Q8—28no—
466D3×Q8—28no—
467D3×Q8—24no—
468D3×Q8—24no—
469D3×Q8—28no—
470D3×Q8—22no—
471D3×Q8—22no—
472D3×Q8C2×D418yes—
473D3×Q8C2×D418yes—
474#237—232no—
475#237—232no—
476#237—216no—
477#237—232no—
478#237—232no—
479#237—28no—
480#237—28no—
481#237—28no—
482#237—24no—
483#237—24no—
484#237—22no—
485#237—22no—
486#237—28no—
487#237—44no—
488#237C2×D418yes—
489#237C2×D418yes—
490D3×D4—22no—
491D3×D4—22no—
492D3×D4—44no—
493#235—232no—
494#235—232no—
495#235—28no—
496#235—28no—
497#235—24no—
498#235—24no—
499#235—24no—
500#235—24no—
501#235—22no—
502#235—22no—
503#235—44no—
504C2×D12—24no—
505C2×D12—21no—
506C2×D12—22no—
507C2×D12C2×D412yes—
508C2×D12C2×D412yes—
509C2×D12C2411yescharacteristic
510C2×C4×D3—28no—
511C2×C4×D3—28no—
512C2×C4×D3—24no—
513C2×C4×D3—22no—
514C2×C4×D3—22no—
515C2×C4×D3—22no—
516C2×C4×D3—22no—
517C2×C4×D3—21no—
518C2×C4×D3—21no—
519C2×C4×D3—21no—
520C2×C4×D3—22no—
521C2×C4×D3—44no—
522C2×C4×D3C2×D412yes—
523C2×C4×D3C2×D411yescharacteristic
524C2×C4×D3C2×D411yescharacteristic
525C2×C4×D3C2×D414yes—
526C2×C4×D3C2×D414yes—
527C2×C4×D3C2412yes—
528C2×C4×D3C2411yescharacteristic
529C2×C4×D3C2411yescharacteristic
530C2×Dic6—28no—
531C2×Dic6—28no—
532C2×Dic6—216no—
533C2×Dic6—232no—
534C2×Dic6—232no—
535C2×Dic6—24no—
536C2×Dic6—21no—
537C2×Dic6—21no—
538C2×Dic6—22no—
539C2×Dic6—22no—
540C2×Dic6—24no—
541C2×Dic6—28no—
542C2×Dic6—24no—
543C2×Dic6—22no—
544C2×Dic6—22no—
545C2×Dic6—28no—
546C2×Dic6—28no—
547C2×Dic6—21no—
548C2×Dic6C2×D412yes—
549C2×Dic6C2×D412yes—
550C2×Dic6C2×D414yes—
551C2×Dic6C2×D414yes—
552C2×Dic6C2411yescharacteristic
553C2×Dic6C2412yes—
554C2×Dic6C2412yes—
555C3×Q16—24no—
556C3×SD16—24no—
557C3×SD16—24no—
558C3×D8—24no—
559C3×M16—22no—
560C3×M16—22no—
561C2×C3×C8C2412yes—
562C2×C3×C8C2412yes—
563C3×C4⋊C4—22no—
564C3×C4⋊C4C2412yes—
565C3×C22⋊C4—21no—
566C3×C22⋊C4—22no—
567C3×C22⋊C4—22no—
568C3×C42—21no—
569#217—21no—
570#217—22no—
571#217—22no—
572#216—24no—
573#216—24no—
574#216—24no—
575#215—24no—
576#214—24no—
577#214—24no—
578#214—24no—
579#213—24no—
580(C2×D3)⋊C4—22no—
581(C2×D3)⋊C4—22no—
582(C2×D3)⋊C4—22no—
583(C2×D3)⋊C4—22no—
584(C2×D3)⋊C4—22no—
585C4⋊Dic3—22no—
586C4⋊Dic3C2412yes—
587Dic3⋊C4—22no—
588Dic3⋊C4—22no—
589Dic3⋊C4—22no—
590C4×Dic3—21no—
591C4×Dic3—22no—
592#208—22no—
593#208—22no—
594C2×C3⋊C8C2412yes—
595C2×C3⋊C8C2412yes—
596Dic12—24no—
597Dic12—24no—
598#204—24no—
599#204—24no—
600ΓL(1,𝔽25)—24no—
601ΓL(1,𝔽25)—24no—
602D3×C8—24no—
603D3×C8—24no—
6042−1+4—616no—
6052−1+4—616no—
6062−1+4—616no—
6072−1+4—616no—
6082−1+4—632no—
6092−1+4—632no—
610C2×#41—24no—
611C2×#41—24no—
612C2×#41—22no—
613C2×#41—32no—
614C2×#41—32no—
615C2×#41—32no—
616C2×#41—32no—
617C2×#41—31no—
618C2×#41—38no—
619C2×#41—32no—
620C2×#41—32no—
621C2×#41—31no—
622C2×#41—34no—
623C2×#41—31no—
624C2×#41—64no—
625C2×#41—64no—
626C2×#41—61no—
627C2×#41—64no—
628C2×#41—64no—
629C2×#41—616no—
630C2×#41—61no—
631C2×#41—61no—
632C2×#41—64no—
633C2×#41—62no—
634C2×#41—61no—
635C2×#41—64no—
636C2×#41—64no—
637C2×#41—64no—
638C2×#41—64no—
639C2×#41—64no—
640C2×#41—64no—
641C2×#41—64no—
642C2×#41—616no—
643C2×#41—616no—
644C2×#41—64no—
645C2×#41C22×D311yescharacteristic
646C2×#41C22×D314yes—
647C22×Q8—31no—
648C22×Q8—38no—
649C22×Q8—32no—
650C22×Q8—32no—
651C22×Q8—31no—
652C22×Q8—34no—
653C22×Q8—31no—
654C22×Q8—31no—
655C22×Q8—34no—
656C22×Q8—61no—
657C22×Q8—61no—
658C22×Q8—64no—
659C22×Q8—64no—
660C22×Q8—64no—
661C22×Q8—64no—
662C22×Q8—616no—
663C22×Q8—61no—
664C22×Q8—61no—
665C22×Q8—64no—
666C22×Q8—62no—
667C22×Q8—64no—
668C22×Q8—64no—
669C22×Q8—61no—
670C22×Q8—62no—
671C22×Q8C22×D311yescharacteristic
672C22×D4—21no—
673C22×D4—31no—
674C22×D4—31no—
675C22×D4—31no—
676C22×D4—31no—
677C22×D4—61no—
678C22×D4—61no—
679C22×D4—61no—
680C22×D4C22×D311yescharacteristic
681C23×C4—21no—
682C23×C4—31no—
683C23×C4—31no—
684C23×C4—61no—
685C23×C4—61no—
686C23×C4—61no—
687C23×C4—61no—
688C23×C4—61no—
689C23×C4—61no—
690C23×C4C22×D311yescharacteristic
691#137—24no—
692#137—64no—
693#137—64no—
694#137—68no—
695#137—68no—
696#137—68no—
697#137—64no—
698#137—64no—
699#137—64no—
700AGL(1,ℤ/8)—24no—
701AGL(1,ℤ/8)—68no—
702AGL(1,ℤ/8)—64no—
703#135—68no—
704#135—68no—
705C2×Q16—32no—
706C2×Q16—32no—
707C2×Q16—32no—
708C2×Q16—32no—
709C2×Q16—32no—
710C2×Q16—68no—
711C2×Q16C22×D312yes—
712C2×SD16—32no—
713C2×SD16—32no—
714C2×SD16—32no—
715C2×SD16—32no—
716C2×SD16—32no—
717C2×SD16—32no—
718C2×SD16—68no—
719C2×SD16C22×D312yes—
720C2×SD16C22×D312yes—
721C2×D8—32no—
722C2×D8C22×D312yes—
723C2×M16—31no—
724C2×M16—31no—
725C2×M16—32no—
726C2×M16—32no—
727C2×M16—64no—
728C2×M16—64no—
729C2×M16C22×D311yescharacteristic
730C2×M16C22×D311yescharacteristic
731C22×C8—32no—
732C22×C8—32no—
733C4⋊Q8—62no—
734#127—62no—
735#124—62no—
736#124—62no—
737#123—21no—
738#123—61no—
739#123—62no—
740#123—62no—
741#123—61no—
742#123—61no—
743C22⋊Q8—32no—
744C22⋊Q8—32no—
745C22⋊Q8—32no—
746C22⋊Q8—62no—
747C22⋊Q8—62no—
748C22⋊Q8C22×D312yes—
749#121—32no—
750#121—32no—
751#121—32no—
752#121—62no—
753#121—62no—
754#121—62no—
755#121—62no—
756#121—62no—
757#121—62no—
758#121C22×D312yes—
759#120—21no—
760#120—62no—
761#120—61no—
762#120—62no—
763#120—61no—
764#120—61no—
765C4×D4—22no—
766C4×D4—62no—
767C4×D4—62no—
768C4×D4—62no—
769#117—31no—
770#117—32no—
771#117—61no—
772#117—61no—
773#117C22×D311yescharacteristic
774C2×C4⋊C4—32no—
775C2×C22⋊C4—61no—
776C2×C42—61no—
777#103—34no—
778#103—34no—
779#103—34no—
780#103—34no—
781#103—34no—
782#103C22×D314yes—
783#102—34no—
784#102C22×D314yes—
785C22⋊C8—34no—
786C22⋊C8—34no—
787C22⋊C8—34no—
788C22⋊C8C22×D314yes—
789C23×C3—22no—
790C23×C3—24no—
791C23×C3—22no—
792C23×C3—21no—
793C23×C3—42no—
794C23×C3—44no—
795C23×C3C22×D412yes—
796C23×C3C22×D411yescharacteristic
797C22×D3—22no—
798C22×D3—21no—
799C22×D3—42no—
800C22×D3—42no—
801C22×D3—42no—
802C22×D3—82no—
803C22×D3#12014yes—
804C22×D3C22×D412yes—
805C22×D3C22×D411yescharacteristic
806C22×D3C22×D411yescharacteristic
807C3×Q8—24no—
808C3×Q8—22no—
809C3×Q8—21no—
810C3×Q8—21no—
811C3×Q8C22×D414yes—
812C3×D4—216no—
813C3×D4—24no—
814C3×D4—22no—
815C3×D4—21no—
816C3×D4—21no—
817C3×D4—42no—
818C3×D4—82no—
819C3×D4C22×D414yes—
820C2×C3×C4—216no—
821C2×C3×C4—22no—
822C2×C3×C4—24no—
823C2×C3×C4—22no—
824C2×C3×C4—24no—
825C2×C3×C4—22no—
826C2×C3×C4—22no—
827C2×C3×C4—22no—
828C2×C3×C4—21no—
829C2×C3×C4—42no—
830C2×C3×C4C22×D412yes—
831C2×C3×C4C22×D411yescharacteristic
832C2×C3×C4C22×D412yes—
833C2×C3×C4C22×D412yes—
834C2×C3×C4C2511yescharacteristic
835#67—216no—
836#67—24no—
837#67—24no—
838#67—28no—
839#67—28no—
840#67—24no—
841#67—24no—
842#67—42no—
843#67—42no—
844#67—42no—
845#67—82no—
846#67—82no—
847C2×Dic3—216no—
848C2×Dic3—216no—
849C2×Dic3—22no—
850C2×Dic3—24no—
851C2×Dic3—24no—
852C2×Dic3—22no—
853C2×Dic3—22no—
854C2×Dic3—28no—
855C2×Dic3—28no—
856C2×Dic3—22no—
857C2×Dic3—21no—
858C2×Dic3—42no—
859C2×Dic3#12014yes—
860C2×Dic3C22×D412yes—
861C2×Dic3C22×D411yescharacteristic
862C2×Dic3C22×D411yescharacteristic
863D12—24no—
864D12—24no—
865D12—21no—
866D12—21no—
867D12—42no—
868D12—82no—
869C4×D3—216no—
870C4×D3—28no—
871C4×D3—28no—
872C4×D3—24no—
873C4×D3—22no—
874C4×D3—22no—
875C4×D3—42no—
876C4×D3—42no—
877C4×D3—42no—
878C4×D3—82no—
879C4×D3#12014yes—
880C4×D3#12014yes—
881C4×D3C22×D412yes—
882C4×D3C22×D412yes—
883C4×D3C22×D412yes—
884C4×D3C22×D412yes—
885Dic6—216no—
886Dic6—216no—
887Dic6—24no—
888Dic6—24no—
889Dic6—22no—
890Dic6—22no—
891Dic6—24no—
892Dic6—24no—
893Dic6—28no—
894Dic6—28no—
895Dic6—21no—
896Dic6—21no—
897Dic6—42no—
898Dic6C22×D414yes—
899Dic6C22×D414yes—
900C3×C8—22no—
901C3×C8—22no—
902C3⋊C8—22no—
903C3⋊C8—22no—
904C24—21no—
905C24—31no—
906C24—31no—
907C24—61no—
908C24D3×D411yescharacteristic
909#41—216no—
910#41—28no—
911#41—28no—
912#41—22no—
913#41—22no—
914#41—38no—
915#41—38no—
916#41—64no—
917#41—64no—
918#41—64no—
919#41—64no—
920#41—68no—
921#41—68no—
922#41—632no—
923#41—632no—
924#41—64no—
925#41—64no—
926#41—68no—
927#41—68no—
928#41—62no—
929#41—62no—
930#41—62no—
931#41—62no—
932#41—68no—
933#41—632no—
934#41—632no—
935#41—632no—
936#41—632no—
937#41—616no—
938#41—68no—
939#41—62no—
940#41—62no—
941#41—124no—
942#41—124no—
943C2×Q8—21no—
944C2×Q8—22no—
945C2×Q8—32no—
946C2×Q8—32no—
947C2×Q8—38no—
948C2×Q8—38no—
949C2×Q8—34no—
950C2×Q8—34no—
951C2×Q8—32no—
952C2×Q8—32no—
953C2×Q8—31no—
954C2×Q8—62no—
955C2×Q8—62no—
956C2×Q8—64no—
957C2×Q8—64no—
958C2×Q8—68no—
959C2×Q8—61no—
960C2×Q8—68no—
961C2×Q8—68no—
962C2×Q8—68no—
963C2×Q8—68no—
964C2×Q8—632no—
965C2×Q8—632no—
966C2×Q8—616no—
967C2×Q8—64no—
968C2×Q8—64no—
969C2×Q8—68no—
970C2×Q8—68no—
971C2×Q8—62no—
972C2×Q8—62no—
973C2×Q8—68no—
974C2×Q8—616no—
975C2×Q8—68no—
976C2×Q8—64no—
977C2×Q8—61no—
978C2×Q8—61no—
979C2×Q8—62no—
980C2×Q8—62no—
981C2×Q8D3×D414yes—
982C2×Q8C23×D311yescharacteristic
983C2×Q8C23×D312yes—
984C2×D4—28no—
985C2×D4—24no—
986C2×D4—21no—
987C2×D4—22no—
988C2×D4—22no—
989C2×D4—21no—
990C2×D4—32no—
991C2×D4—32no—
992C2×D4—32no—
993C2×D4—32no—
994C2×D4—32no—
995C2×D4—32no—
996C2×D4—31no—
997C2×D4—64no—
998C2×D4—61no—
999C2×D4—62no—
1000C2×D4—62no—
1001C2×D4—62no—
1002C2×D4—64no—
1003C2×D4—61no—
1004C2×D4—64no—
1005C2×D4—62no—
1006C2×D4—62no—
1007C2×D4—64no—
1008C2×D4—68no—
1009C2×D4—68no—
1010C2×D4—61no—
1011C2×D4—61no—
1012C2×D4—62no—
1013C2×D4—62no—
1014C2×D4—124no—
1015C2×D4D3×D414yes—
1016C2×D4C23×D311yescharacteristic
1017C2×D4C23×D312yes—
1018C22×C4—28no—
1019C22×C4—21no—
1020C22×C4—24no—
1021C22×C4—22no—
1022C22×C4—22no—
1023C22×C4—21no—
1024C22×C4—31no—
1025C22×C4—31no—
1026C22×C4—31no—
1027C22×C4—34no—
1028C22×C4—34no—
1029C22×C4—31no—
1030C22×C4—31no—
1031C22×C4—31no—
1032C22×C4—32no—
1033C22×C4—32no—
1034C22×C4—61no—
1035C22×C4—62no—
1036C22×C4—62no—
1037C22×C4—64no—
1038C22×C4—68no—
1039C22×C4—68no—
1040C22×C4—61no—
1041C22×C4—62no—
1042C22×C4—62no—
1043C22×C4—62no—
1044C22×C4—68no—
1045C22×C4—64no—
1046C22×C4—61no—
1047C22×C4—68no—
1048C22×C4—68no—
1049C22×C4—61no—
1050C22×C4—61no—
1051C22×C4—64no—
1052C22×C4—62no—
1053C22×C4—62no—
1054C22×C4—61no—
1055C22×C4—124no—
1056C22×C4D3×D412yes—
1057C22×C4D3×D411yescharacteristic
1058C22×C4C23×D312yes—
1059C22×C4C23×D311yescharacteristic
1060Q16—24no—
1061Q16—64no—
1062Q16—64no—
1063Q16—64no—
1064Q16—64no—
1065Q16—64no—
1066SD16—24no—
1067SD16—24no—
1068SD16—64no—
1069SD16—64no—
1070SD16—64no—
1071SD16—64no—
1072SD16—64no—
1073SD16—64no—
1074D8—24no—
1075D8—64no—
1076M16—22no—
1077M16—22no—
1078M16—64no—
1079M16—64no—
1080M16—62no—
1081M16—62no—
1082C2×C8—32no—
1083C2×C8—32no—
1084C2×C8—64no—
1085C2×C8—64no—
1086C2×C8C23×D312yes—
1087C2×C8C23×D312yes—
1088C4⋊C4—22no—
1089C4⋊C4—32no—
1090C4⋊C4—62no—
1091C4⋊C4—62no—
1092C4⋊C4—62no—
1093C4⋊C4—62no—
1094C4⋊C4C23×D312yes—
1095C22⋊C4—21no—
1096C22⋊C4—22no—
1097C22⋊C4—22no—
1098C22⋊C4—62no—
1099C22⋊C4—62no—
1100C22⋊C4—62no—
1101C22⋊C4—62no—
1102C22⋊C4—62no—
1103C22⋊C4—61no—
1104C22⋊C4—62no—
1105C22⋊C4—62no—
1106C42—21no—
1107C42—62no—
1108C42—61no—
1109C22×C3—22no—
1110C22×C3—22no—
1111C22×C3—22no—
1112C22×C3—22no—
1113C22×C3—24no—
1114C22×C3—44no—
1115C22×C3—48no—
1116C22×C3—44no—
1117C22×C3—42no—
1118C22×C3—41no—
1119C22×C3C2×#12012yes—
1120C22×C3C23×D411yescharacteristic
1121C2×D3—22no—
1122C2×D3—22no—
1123C2×D3—22no—
1124C2×D3—22no—
1125C2×D3—22no—
1126C2×D3—44no—
1127C2×D3—44no—
1128C2×D3—42no—
1129C2×D3—41no—
1130C2×D3—84no—
1131C2×D3C2×#12012yes—
1132C2×D3C2×#12012yes—
1133C3×C4—22no—
1134C3×C4—24no—
1135C3×C4—42no—
1136C3×C4—41no—
1137C3×C4C2×#12012yes—
1138C3×C4C23×D411yescharacteristic
1139C3×C4C23×D411yescharacteristic
1140Dic3—22no—
1141Dic3—24no—
1142Dic3—24no—
1143Dic3—42no—
1144Dic3—41no—
1145Dic3C2×#12012yes—
1146Dic3C2×#12012yes—
1147C23—22no—
1148C23—22no—
1149C23—24no—
1150C23—21no—
1151C23—31no—
1152C23—31no—
1153C23—34no—
1154C23—32no—
1155C23—42no—
1156C23—44no—
1157C23—62no—
1158C23—61no—
1159C23—122no—
1160C23—122no—
1161C23—122no—
1162C23—242no—
1163C23C2×D3×D412yes—
1164C23C2×D3×D411yescharacteristic
1165Q8—22no—
1166Q8—24no—
1167Q8—21no—
1168Q8—21no—
1169Q8—34no—
1170Q8—34no—
1171Q8—64no—
1172Q8—64no—
1173Q8—68no—
1174Q8—68no—
1175Q8—616no—
1176Q8—616no—
1177Q8—62no—
1178Q8—62no—
1179Q8—64no—
1180Q8—64no—
1181Q8—61no—
1182Q8—61no—
1183Q8—122no—
1184Q8C2×D3×D414yes—
1185D4—216no—
1186D4—22no—
1187D4—21no—
1188D4—21no—
1189D4—24no—
1190D4—42no—
1191D4—64no—
1192D4—64no—
1193D4—64no—
1194D4—64no—
1195D4—64no—
1196D4—64no—
1197D4—68no—
1198D4—68no—
1199D4—616no—
1200D4—61no—
1201D4—61no—
1202D4—82no—
1203D4—122no—
1204D4—122no—
1205D4—122no—
1206D4—122no—
1207D4—242no—
1208D4—242no—
1209D4—242no—
1210D4C2×D3×D414yes—
1211C2×C4—216no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—24no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—24no—
1218C2×C4—22no—
1219C2×C4—21no—
1220C2×C4—31no—
1221C2×C4—31no—
1222C2×C4—34no—
1223C2×C4—32no—
1224C2×C4—32no—
1225C2×C4—32no—
1226C2×C4—32no—
1227C2×C4—34no—
1228C2×C4—34no—
1229C2×C4—32no—
1230C2×C4—42no—
1231C2×C4—68no—
1232C2×C4—68no—
1233C2×C4—616no—
1234C2×C4—68no—
1235C2×C4—68no—
1236C2×C4—616no—
1237C2×C4—616no—
1238C2×C4—62no—
1239C2×C4—62no—
1240C2×C4—62no—
1241C2×C4—64no—
1242C2×C4—64no—
1243C2×C4—62no—
1244C2×C4—62no—
1245C2×C4—64no—
1246C2×C4—62no—
1247C2×C4—61no—
1248C2×C4—122no—
1249C2×C4—122no—
1250C2×C4—122no—
1251C2×C4—122no—
1252C2×C4—242no—
1253C2×C4C2×D3×D412yes—
1254C2×C4C2×D3×D412yes—
1255C2×C4C2×D3×D412yes—
1256C2×C4C2×D3×D411yescharacteristic
1257C2×C4C24×D311yescharacteristic
1258C8—22no—
1259C8—22no—
1260C8—62no—
1261C8—62no—
1262C2×C3—22no—
1263C2×C3—42no—
1264C2×C3—44no—
1265C2×C3—81no—
1266C2×C3C22×#12011yescharacteristic
1267C2×C3#358612yes—
1268D3—22no—
1269D3—22no—
1270D3—42no—
1271D3—81no—
1272C22—22no—
1273C22—22no—
1274C22—24no—
1275C22—22no—
1276C22—22no—
1277C22—32no—
1278C22—32no—
1279C22—44no—
1280C22—48no—
1281C22—44no—
1282C22—41no—
1283C22—42no—
1284C22—62no—
1285C22—62no—
1286C22—62no—
1287C22—62no—
1288C22—62no—
1289C22—124no—
1290C22—124no—
1291C22—121no—
1292C22—122no—
1293C22—244no—
1294C22D3×#12012yes—
1295C22C22×D3×D411yescharacteristic
1296C4—22no—
1297C4—24no—
1298C4—32no—
1299C4—32no—
1300C4—41no—
1301C4—42no—
1302C4—62no—
1303C4—64no—
1304C4—64no—
1305C4—121no—
1306C4—122no—
1307C4D3×#12012yes—
1308C4C22×D3×D411yescharacteristic
1309C4C22×D3×D411yescharacteristic
1310C3#6036811yescharacteristic, complemented, Sylow
1311C2—22no—
1312C2—42no—
1313C2—44no—
1314C2—62no—
1315C2—62no—
1316C2—81no—
1317C2—122no—
1318C2—241no—
1319C2C2×D3×#12011yescharacteristic
1320C2#8720112yes—
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3005C2
socleC22×C3C23×D4
hypercenter#3005D3
hypocenterC3#60368
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3005

Complements

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

NH ≅ G/Ntype
1. C22×#1010C2semidirect
2. C2×D3×#137C2semidirect
3. C2×#5773C2semidirect
4. #86035C2semidirect
5. C3×#3005C2semidirect
6. #84081C2semidirect
7. #83979C2semidirect
8. #83945C2semidirect
9. #82933C2semidirect
10. #80232C2semidirect
11. #80230C2semidirect
12. #80088C2semidirect
13. #80086C2semidirect
14. #78958C2semidirect
15. D3×#419C2semidirect
16. #78927C2semidirect
17. #78924C2semidirect
18. #78645C2semidirect
19. #78630C2semidirect
21. C22×C3×#41C22semidirect
27. C2×#1010C22semidirect
30. C22×D3×Q8C22semidirect
34. C22×#237C22semidirect
38. C23×Dic6C22semidirect
50. C2×#918C22semidirect
51. C2×D3×Q16C22semidirect
52. C2×#916C22semidirect
53. C2×#915C22semidirect
54. C2×#915C22semidirect
55. C2×D3×SD16C22semidirect
56. C2×#912C22semidirect
57. C2×#911C22semidirect
64. #5629C22semidirect
65. #5628C22semidirect
66. #5608C22semidirect
67. #5607C22semidirect
74. C3×#452C22semidirect
75. C3×#449C22semidirect
76. C3×#419C22semidirect
77. C3×#418C22semidirect
78. C3×#407C22semidirect
79. #5239C22semidirect
80. #5238C22semidirect
81. #5225C22semidirect
82. #5215C22semidirect
83. #5207C22semidirect
84. #5186C22semidirect
85. #5173C22semidirect
86. #5170C22semidirect
87. #5158C22semidirect
88. #5126C22semidirect
89. #5126C22semidirect
90. #5120C22semidirect
91. #5120C22semidirect
92. #5050C22semidirect
93. #5040C22semidirect
94. #5004C22semidirect
95. #5004C22semidirect
96. #4809C22semidirect
97. #4806C22semidirect
98. #4802C22semidirect
99. D3×#103C22semidirect
100. #4783C22semidirect
101. #4781C22semidirect
102. #4772C22semidirect
103. #4771C22semidirect
104. #4739C22semidirect
105. #4738C22semidirect
106. #4727C22semidirect
107. #4727C22semidirect
119. #3005D3semidirect
159. C2×D3×Q8D4semidirect
177. C2×#237D4semidirect
325. C22×#41C2×D3semidirect
368. #452C2×D3semidirect
376. #449C2×D3semidirect
387. #419C2×D3semidirect
389. #418C2×D3semidirect
398. #407C2×D3semidirect
1310. C3#60368semidirect

Maximal subgroups

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

subgroupindex
C22×#10102
C2×D3×#1372
C2×#57732
#860352
C3×#30052
#840812
#839792
#839452
#829332
#802322
#802302
#800882
#800862
#789582
D3×#4192
#789272
#789242
#786452
#786302
#603683