Finite Group Databasebeta

← #11670542

Subgroups — #11670542

Order 768.

2722 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5778C211yesmaximal, characteristic, complemented
2C22×#919C211yesmaximal, characteristic, complemented
3#86354C211yesmaximal, characteristic, complemented
4#85874C211yesmaximal, characteristic, complemented
5C3×#3044C211yesmaximal, characteristic, complemented
6#83980C211yesmaximal, characteristic, complemented
7#83884C211yesmaximal, characteristic, complemented
8#83402C211yesmaximal, characteristic, complemented
9#82548C211yesmaximal, characteristic, complemented
10#80630C214yesmaximal, complemented
11#80628C214yesmaximal, complemented
12#80502C214yesmaximal, complemented
13#80500C214yesmaximal, complemented
14#79086C211yesmaximal, characteristic, complemented
15#79073C211yesmaximal, characteristic, complemented
16#78963C211yesmaximal, characteristic, complemented
17#78959C211yesmaximal, characteristic, complemented
18#78838C211yesmaximal, characteristic, complemented
19#78834C211yesmaximal, characteristic, complemented
20#61052—31nomaximal, Sylow
21C2×#1009C2211yescharacteristic
22C2×#1007C2211yescharacteristic
23C22×#239C2211yescharacteristic
24C22×#239C2211yescharacteristic, complemented
25C2×C3×#137C2211yescharacteristic
26C22×C3×Q16C2211yescharacteristic, complemented
27C3×#536C2211yescharacteristic
28C3×#519C2211yescharacteristic, complemented
29#5828C2211yescharacteristic
30C2×#950C2211yescharacteristic
31C2×#949C2211yescharacteristic
32#5816C2211yescharacteristic
33C2×#942C2211yescharacteristic, complemented
34C22×#215C2211yescharacteristic
35C22×#215C2211yescharacteristic, complemented
36#5778—28no—
37C2×#919—28no—
38C2×#919C2214yescomplemented
39C2×#919C2212yescomplemented
40C2×#919C2214yescomplemented
41C2×#918C2212yescomplemented
42C2×#914C2212yescomplemented
43C2×D3×SD16C2212yescomplemented
44C2×#908C2211yescharacteristic
45C2×#907C2211yescharacteristic
46C22×D24C2211yescharacteristic
47C22×D3×C8C2211yescharacteristic, complemented
48#5726C2214yescomplemented
49#5676C2214yescomplemented
50#5653—22no—
51D3×#123—22no—
52#5631—22no—
53#5630—22no—
54#5577—22no—
55#5577C2214yescomplemented
56#5576—22no—
57#5576C2214yescomplemented
58#5525—22no—
59#5525C2211yescharacteristic
60#5525C2211yescharacteristic, complemented
61#5524—22no—
62#5524C2211yescharacteristic
63#5524C2211yescharacteristic, complemented
64#5521C2211yescharacteristic
65C3×#464C2214yescomplemented
66C3×#462C2214yescomplemented
67C3×#424C2211yescharacteristic, complemented
68C3×#419C2211yescharacteristic, complemented
69C3×#416C2211yescharacteristic
70#5225C2211yescharacteristic, complemented
71#5187C2214yescomplemented
72#5187C2214yescomplemented
73#5186C2214yescomplemented
74#5172C2214yescomplemented
75#5131C2211yescharacteristic, complemented
76#5126C2211yescharacteristic, complemented
77#5113C2211yescharacteristic, complemented
78#5110C2211yescharacteristic
79#5086C2212yescomplemented
80#5085C2212yescomplemented
81#5059C2212yescomplemented
82#5058C2212yescomplemented
83#5026C2214yescomplemented
84C4×#215C2214yescomplemented
85#5001C2211yescharacteristic
86#4998C2211yescharacteristic, complemented
87#4997C2211yescharacteristic, complemented
88#4844C2214yescomplemented
89#4843C2214yescomplemented
90#4836C2214yescomplemented
91#4834C2214yescomplemented
92#4813C2212yescomplemented
93#4812C2214yescomplemented
94#4810C2214yescomplemented
95#4810C2214yescomplemented
96#4808C2214yescomplemented
97#4807C2214yescomplemented
98#4807C2212yescomplemented
99#4778C2212yescomplemented
100#4775C2212yescomplemented
101#4773C2214yescomplemented
102C2×#577—31no—
103C22×#135—31no—
104#3487—31no—
105#3485—31no—
106#3284—34no—
107#3282—34no—
108#3269—34no—
109#3268—34no—
110#3154—31no—
111#3057—31no—
112#3050—31no—
113#3044D311yescharacteristic, complemented
114#3041—31no—
115#3011—31no—
116#3008—31no—
117#3005—31no—
118#3005—31no—
119#2949—31no—
120#2929—31no—
121C2×C3×#41C2311yescharacteristic
122C22×C3×Q8C2311yescharacteristic
123C22×C3×Q8C2311yescharacteristic
124#1009—24no—
125#1009—42no—
126#1007—24no—
127#1007—42no—
128C2×#239—21no—
129C2×#239—22no—
130C2×#239—22no—
131C2×#239—24no—
132C2×#239—24no—
133C2×#239—42no—
134C2×#239—42no—
135C2×#239C2314yes—
136C2×#239C2314yes—
137C2×#239C2312yes—
138C2×#239C2312yes—
139C2×D3×Q8—21no—
140C2×D3×Q8C2312yes—
141C2×D3×D4—22no—
142C2×D3×D4C2312yes—
143C2×#235—22no—
144C2×#235—21no—
145C2×#235C2311yescharacteristic
146C2×#235C2311yescharacteristic
147C22×D12—21no—
148C22×D12—21no—
149C22×D12—21no—
150C22×D12C2311yescharacteristic
151C22×D12C2311yescharacteristic
152C22×C4×D3—21no—
153C22×C4×D3—21no—
154C22×C4×D3C2311yescharacteristic
155C3×#137—24no—
156C2×C3×Q16—24no—
157C2×C3×Q16C2314yes—
158C2×C3×Q16C2312yes—
159C2×C3×SD16C2312yes—
160C2×C3×M16C2311yescharacteristic
161C22×C3×C8C2311yescharacteristic
162C3×C4⋊Q8C2312yes—
163C3×#124C2312yes—
164C3×#123—22no—
165C3×C22⋊Q8—22no—
166C3×C4×Q8—22no—
167C3×C4×Q8C2314yes—
168C3×#117—22no—
169C3×#117C2311yescharacteristic
170C3×#117C2311yescharacteristic
171#950—24no—
172#949—42no—
173#947—21no—
174#946C2314yes—
175#946C2312yes—
176#944—21no—
177C2×#216C2311yescharacteristic
178C2×#216C2312yes—
179#942—42no—
180C2×#215—24no—
181C2×#215D418yescomplemented
182C2×#215C2312yes—
183C2×#215C2312yes—
184C2×#215C2311yescharacteristic
185C2×#215C2312yes—
186C2×#215C2312yes—
187C2×#215C2312yes—
188C2×#215C2312yes—
189#938C2312yes—
190#937—21no—
191#935—21no—
192C2×#214C2311yescharacteristic
193C2×#213C2311yescharacteristic
194C2×#213C2312yes—
195#929—22no—
196C4×#67—22no—
197#926C2311yescharacteristic
198C2×#208C2311yescharacteristic
199C22×C3⋊C8C2311yescharacteristic
200#919—216no—
201#919—216no—
202#919—28no—
203#918—28no—
204#914—28no—
205D3×SD16—28no—
206#908—24no—
207#907—24no—
208C2×D24—24no—
209C2×D24C2314yes—
210C2×D24C2312yes—
211C2×#204C2312yes—
212C2×ΓL(1,𝔽25)C2312yes—
213C2×D3×C8—24no—
214C2×D3×C8C2312yes—
215C2×D3×C8C2312yes—
216C2×D3×C8C2312yes—
217#897—24no—
218#897D412yes—
219#897C2312yes—
220#895—24no—
221#895—24no—
222#895—22no—
223#895—24no—
224#895—24no—
225#895D412yes—
226#895C2312yes—
227#895C2314yes—
228#894—24no—
229#894—24no—
230#893—22no—
231D3×C4⋊C4—24no—
232#886—21no—
233#886D412yes—
234#884—24no—
235#883—24no—
236#882—21no—
237#882—22no—
238#882—24no—
239#882—22no—
240#882D412yes—
241D3×C22⋊C4—22no—
242D3×C22⋊C4—24no—
243#875—21no—
244#875—24no—
245#875C2312yes—
246#874—24no—
247#874—21no—
248#874C2312yes—
249C4×D12—22no—
250C4×D12—24no—
251C4×D12—24no—
252C4×D12C2314yes—
253C4×D12C2314yes—
254C3×C4⋊C8C2314yes—
255C3×#103C2312yes—
256C3×#103C2314yes—
257C3×#102C2312yes—
258#835C2314yes—
259#821C2314yes—
260#821C2312yes—
261(C2×D3)⋊C8C2314yes—
262(C2×D3)⋊C8C2314yes—
263#816C2312yes—
264#809C2314yes—
265#808C2312yes—
266#807C2312yes—
267#803C2312yes—
268C4×C3⋊C8C2312yes—
269C2×2−1+4—31no—
270C2×H(5,𝔽2)—31no—
271C22×#41—31no—
272C22×#41—31no—
273#577—68no—
274C2×#137—31no—
275C2×#137—32no—
276C2×#137C2×D311yescharacteristic
277C2×AGL(1,ℤ/8)—31no—
278C2×AGL(1,ℤ/8)—32no—
279C2×AGL(1,ℤ/8)—31no—
280C2×#135—31no—
281C2×#135—34no—
282C2×#135—34no—
283C2×#135—32no—
284C2×#135—68no—
285C22×Q16C2×D311yescharacteristic, complemented
286C22×SD16—31no—
287C22×SD16—31no—
288C22×SD16—32no—
289C22×D8—31no—
290C2×#131—31no—
291C23×C8—31no—
292#550—34no—
293#550—62no—
294#548—34no—
295#548—62no—
296#547—34no—
297#547—62no—
298#546—34no—
299#546—62no—
300#536—31no—
301#536C2×D311yescharacteristic
302#535—31no—
303#535—31no—
304#535—62no—
305#534—62no—
306#525—31no—
307#525—31no—
308#525—31no—
309#525—62no—
310C2×#123—62no—
311#519C2×D311yescharacteristic, complemented
312#518—31no—
313#497—32no—
314#496—32no—
315#495—32no—
316#492—32no—
317#468—34no—
318#467—32no—
319#466—32no—
320#465—34no—
321#465—32no—
322#465—32no—
323#464C2×D314yescomplemented
324#463—34no—
325#462C2×D314yescomplemented
326#459—34no—
327#452—34no—
328#452—34no—
329#452—34no—
330#451—34no—
331#449—34no—
332#449—34no—
333#449—34no—
334#447—34no—
335#440—34no—
336C4×SD16—34no—
337#435—34no—
338C8×D4—34no—
339#427—31no—
340#424C2×D311yescharacteristic, complemented
341#419—31no—
342#419C2×D311yescharacteristic, complemented
343#418—31no—
344#418—31no—
345#416—31no—
346#416C2×D311yescharacteristic
347#408—31no—
348#407—31no—
349#405—31no—
350C23×D3—21no—
351C23×D3—21no—
352C23×D3—22no—
353C23×D3C2×D411yescharacteristic
354C3×#41—22no—
355C3×#41—22no—
356C2×C3×Q8—21no—
357C2×C3×Q8—21no—
358C2×C3×Q8—22no—
359C2×C3×Q8—22no—
360C2×C3×Q8—22no—
361C2×C3×Q8C2×D414yes—
362C2×C3×Q8C2412yes—
363C2×C3×Q8C2411yescharacteristic
364C2×C3×Q8C2412yes—
365C2×C3×D4—21no—
366C2×C3×D4C2411yescharacteristic
367C22×C3×C4—21no—
368C22×C3×C4—21no—
369C22×C3×C4—21no—
370C22×C3×C4C2411yescharacteristic
371C2×#67—21no—
372C2×#67—22no—
373C2×#67—22no—
374C2×#67C2×D412yes—
375C22×Dic3C2×D411yescharacteristic
376#239—24no—
377#239—28no—
378#239—24no—
379#239—28no—
380#239—44no—
381#239—44no—
382#239—42no—
383#239—42no—
384#239—48no—
385#239—48no—
386#239—44no—
387D3×Q8—24no—
388D3×Q8—42no—
389D3×Q8—44no—
390D3×D4—24no—
391D3×D4—42no—
392D3×D4—48no—
393#235—22no—
394#235—22no—
395#235—22no—
396#235—22no—
397#235—44no—
398#235—48no—
399C2×D12—21no—
400C2×D12—22no—
401C2×D12—22no—
402C2×D12—22no—
403C2×D12—22no—
404C2×D12—24no—
405C2×D12—24no—
406C2×D12—22no—
407C2×D12—21no—
408C2×D12—24no—
409C2×D12—22no—
410C2×D12—24no—
411C2×D12—44no—
412C2×D12—44no—
413C2×D12—44no—
414C2×D12C2×D411yescharacteristic
415C2×D12C2×D414yes—
416C2×D12C2×D414yes—
417C2×D12C2411yescharacteristic
418C2×D12C2412yes—
419C2×D12C2412yes—
420C2×C4×D3—22no—
421C2×C4×D3—22no—
422C2×C4×D3—22no—
423C2×C4×D3—21no—
424C2×C4×D3—22no—
425C2×C4×D3—24no—
426C2×C4×D3—24no—
427C2×C4×D3—22no—
428C2×C4×D3—24no—
429C2×C4×D3—44no—
430C2×C4×D3—44no—
431C2×C4×D3C2×D412yes—
432C2×C4×D3C2412yes—
433C2×C4×D3C2412yes—
434C2×Dic6—22no—
435C2×Dic6C2×D411yescharacteristic
436C2×Dic6C2411yescharacteristic
437C3×Q16—24no—
438C3×Q16—28no—
439C3×SD16—24no—
440C3×M16—22no—
441C2×C3×C8—22no—
442C2×C3×C8C2412yes—
443C2×C3×C8C2412yes—
444C3×C4⋊C4—24no—
445C3×C4⋊C4—24no—
446C3×C4⋊C4C2×D412yes—
447C3×C4⋊C4C2412yes—
448C3×C22⋊C4—21no—
449C3×C22⋊C4—24no—
450C3×C22⋊C4C2×D412yes—
451C3×C42—24no—
452C3×C42—21no—
453C3×C42C2412yes—
454#217—21no—
455#217—22no—
456#216—22no—
457#216—42no—
458#215—24no—
459#215—24no—
460#215—22no—
461#215—42no—
462#215—42no—
463#215C2×D418yes—
464#215C2×D418yes—
465#214—22no—
466#213—22no—
467#213—42no—
468(C2×D3)⋊C4—22no—
469(C2×D3)⋊C4—24no—
470(C2×D3)⋊C4—22no—
471(C2×D3)⋊C4—24no—
472(C2×D3)⋊C4—24no—
473(C2×D3)⋊C4—22no—
474(C2×D3)⋊C4—24no—
475(C2×D3)⋊C4C2×D414yes—
476(C2×D3)⋊C4C2×D414yes—
477C4⋊Dic3—22no—
478C4⋊Dic3C2×D414yes—
479C4⋊Dic3C2412yes—
480Dic3⋊C4—24no—
481Dic3⋊C4—22no—
482C4×Dic3—21no—
483#208—22no—
484C2×C3⋊C8C2×D414yes—
485C2×C3⋊C8C2412yes—
486C2×C3⋊C8C2411yescharacteristic
487C2×C3⋊C8C2411yescharacteristic
488D24—28no—
489D24—24no—
490#204—24no—
491ΓL(1,𝔽25)—24no—
492D3×C8—24no—
493D3×C8—24no—
494D3×C8—24no—
4952−1+4—64no—
4962−1+4—122no—
497H(5,𝔽2)—64no—
498H(5,𝔽2)—122no—
499C2×#41—31no—
500C2×#41—34no—
501C2×#41—32no—
502C2×#41—34no—
503C2×#41—32no—
504C2×#41—31no—
505C2×#41—62no—
506C2×#41—61no—
507C2×#41—62no—
508C2×#41—62no—
509C2×#41—61no—
510C2×#41—64no—
511C2×#41—64no—
512C2×#41—122no—
513C2×#41—122no—
514C2×#41C22×D311yescharacteristic
515C22×Q8—32no—
516C22×Q8—61no—
517C22×Q8C22×D311yescharacteristic
518C22×Q8C22×D311yescharacteristic
519C22×D4—32no—
520C22×D4—31no—
521C22×D4—31no—
522C22×D4—61no—
523C22×D4—61no—
524C22×D4—61no—
525C22×D4—62no—
526C23×C4—31no—
527C23×C4—61no—
528C23×C4—61no—
529#137—24no—
530#137—68no—
531#137—122no—
532AGL(1,ℤ/8)—64no—
533AGL(1,ℤ/8)—68no—
534AGL(1,ℤ/8)—122no—
535#135—64no—
536#135—616no—
537#135—616no—
538#135—68no—
539C2×Q16—24no—
540C2×Q16—31no—
541C2×Q16—32no—
542C2×Q16C22×D314yes—
543C2×Q16C22×D312yes—
544C2×SD16—38no—
545C2×SD16—32no—
546C2×SD16—32no—
547C2×SD16—32no—
548C2×SD16—32no—
549C2×SD16—31no—
550C2×SD16—31no—
551C2×SD16—32no—
552C2×SD16—32no—
553C2×SD16—32no—
554C2×SD16—64no—
555C2×SD16—68no—
556C2×SD16C22×D312yes—
557C2×D8—31no—
558C2×D8—32no—
559C2×D8—34no—
560C2×D8—32no—
561C2×D8—64no—
562#131—64no—
563C2×M16—31no—
564C2×M16—32no—
565C2×M16C22×D311yescharacteristic
566C22×C8—31no—
567C22×C8—32no—
568C22×C8—32no—
569C22×C8—32no—
570C22×C8—64no—
571C22×C8C22×D311yescharacteristic
572C4⋊Q8—61no—
573C4⋊Q8C22×D312yes—
574#127—32no—
575#127—61no—
576#127—64no—
577#124—32no—
578#124—64no—
579#124—61no—
580#124—61no—
581#124C22×D312yes—
582#123—22no—
583#123—32no—
584#123—64no—
585#123—61no—
586#123—64no—
587#123—64no—
588#123—62no—
589#123—61no—
590C22⋊Q8—22no—
591C22⋊Q8—32no—
592C22⋊Q8—32no—
593C22⋊Q8—34no—
594C22⋊Q8—32no—
595C22⋊Q8—64no—
596#121—32no—
597#121—32no—
598#121—32no—
599#121—34no—
600#121—64no—
601#121—64no—
602#121—64no—
603#121—64no—
604#121—64no—
605#121—62no—
606#120—32no—
607#120—62no—
608#120—64no—
609#120—61no—
610#120—61no—
611#120—62no—
612C4×Q8—22no—
613C4×Q8C22×D314yes—
614C4×D4—34no—
615C4×D4—34no—
616C4×D4—64no—
617C4×D4—64no—
618C4×D4—62no—
619C4×D4—62no—
620C4×D4—62no—
621#117—22no—
622#117—31no—
623#117C22×D311yescharacteristic
624#117C22×D311yescharacteristic
625C2×C4⋊C4—64no—
626C2×C22⋊C4—64no—
627C2×C22⋊C4—62no—
628#107—32no—
629#106—32no—
630C4⋊C8C22×D314yes—
631#103—34no—
632#103—32no—
633#103C22×D312yes—
634#103C22×D314yes—
635#102—32no—
636#102—34no—
637#102—34no—
638#102C22×D312yes—
639C22⋊C8—34no—
640C22⋊C8—34no—
641#97—32no—
642C4×C8—32no—
643C23×C3—21no—
644C23×C3C22×D411yescharacteristic
645C22×D3—22no—
646C22×D3—22no—
647C22×D3—24no—
648C22×D3—22no—
649C22×D3—21no—
650C22×D3—42no—
651C22×D3—44no—
652C22×D3—42no—
653C22×D3—84no—
654C22×D3—82no—
655C22×D3—82no—
656C22×D3C22×D412yes—
657C22×D3C22×D412yes—
658C3×Q8—24no—
659C3×Q8—22no—
660C3×Q8—22no—
661C3×Q8—21no—
662C3×Q8—21no—
663C3×Q8—22no—
664C3×Q8—42no—
665C3×Q8C22×D414yes—
666C3×D4—21no—
667C3×D4—21no—
668C3×D4—42no—
669C2×C3×C4—24no—
670C2×C3×C4—22no—
671C2×C3×C4—22no—
672C2×C3×C4—21no—
673C2×C3×C4—22no—
674C2×C3×C4—42no—
675C2×C3×C4—42no—
676C2×C3×C4C22×D414yes—
677C2×C3×C4C22×D411yescharacteristic
678C2×C3×C4C22×D412yes—
679C2×C3×C4H(5,𝔽2)12yes—
680C2×C3×C4C2511yescharacteristic
681#67—24no—
682#67—44no—
683#67—42no—
684#67—82no—
685C2×Dic3—22no—
686C2×Dic3—22no—
687C2×Dic3—21no—
688C2×Dic3C22×D412yes—
689C2×Dic3C22×D412yes—
690D12—24no—
691D12—22no—
692D12—21no—
693D12—22no—
694D12—22no—
695D12—22no—
696D12—21no—
697D12—44no—
698D12—48no—
699D12—44no—
700D12—44no—
701D12—48no—
702D12—42no—
703D12—84no—
704D12—84no—
705D12—82no—
706D12C22×D414yes—
707C4×D3—24no—
708C4×D3—22no—
709C4×D3—22no—
710C4×D3—22no—
711C4×D3—22no—
712C4×D3—48no—
713C4×D3—44no—
714C4×D3—48no—
715C4×D3—44no—
716C4×D3—44no—
717C4×D3—42no—
718C4×D3—84no—
719Dic6—22no—
720Dic6—21no—
721Dic6—21no—
722Dic6—44no—
723C3×C8—22no—
724C3×C8—22no—
725C3⋊C8—22no—
726C3⋊C8C22×D412yes—
727C3⋊C8C22×D412yes—
728C24—31no—
729C24—62no—
730C24—61no—
731C24—61no—
732#41—22no—
733#41—22no—
734#41—62no—
735#41—62no—
736#41—68no—
737#41—64no—
738#41—68no—
739#41—64no—
740#41—62no—
741#41—62no—
742#41—128no—
743#41—124no—
744#41—124no—
745#41—124no—
746#41—122no—
747#41—122no—
748#41—128no—
749#41—128no—
750#41—124no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—22no—
754C2×Q8—22no—
755C2×Q8—22no—
756C2×Q8—31no—
757C2×Q8—31no—
758C2×Q8—62no—
759C2×Q8—64no—
760C2×Q8—122no—
761C2×Q8—124no—
762C2×Q8D3×D414yes—
763C2×Q8C23×D312yes—
764C2×Q8C23×D311yescharacteristic
765C2×Q8C23×D312yes—
766C2×D4—21no—
767C2×D4—32no—
768C2×D4—34no—
769C2×D4—31no—
770C2×D4—34no—
771C2×D4—32no—
772C2×D4—32no—
773C2×D4—31no—
774C2×D4—64no—
775C2×D4—62no—
776C2×D4—64no—
777C2×D4—62no—
778C2×D4—62no—
779C2×D4—64no—
780C2×D4—62no—
781C2×D4—64no—
782C2×D4—61no—
783C2×D4—62no—
784C2×D4—61no—
785C2×D4—62no—
786C2×D4—61no—
787C2×D4—64no—
788C2×D4—62no—
789C2×D4—62no—
790C2×D4—124no—
791C2×D4—124no—
792C2×D4—124no—
793C2×D4—122no—
794C2×D4—128no—
795C2×D4C23×D311yescharacteristic
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—31no—
800C22×C4—32no—
801C22×C4—32no—
802C22×C4—32no—
803C22×C4—64no—
804C22×C4—62no—
805C22×C4—62no—
806C22×C4—64no—
807C22×C4—62no—
808C22×C4—62no—
809C22×C4—62no—
810C22×C4—61no—
811C22×C4—64no—
812C22×C4—124no—
813C22×C4—124no—
814C22×C4C23×D311yescharacteristic
815Q16—28no—
816Q16—24no—
817Q16—62no—
818Q16—122no—
819SD16—24no—
820SD16—38no—
821SD16—38no—
822SD16—64no—
823SD16—62no—
824SD16—64no—
825SD16—64no—
826SD16—62no—
827SD16—122no—
828SD16—122no—
829D8—68no—
830D8—64no—
831D8—62no—
832D8—122no—
833M16—22no—
834M16—64no—
835M16—62no—
836C2×C8—22no—
837C2×C8—34no—
838C2×C8—31no—
839C2×C8—31no—
840C2×C8—32no—
841C2×C8—64no—
842C2×C8—64no—
843C2×C8—64no—
844C2×C8C23×D312yes—
845C2×C8C23×D312yes—
846C4⋊C4—24no—
847C4⋊C4—24no—
848C4⋊C4—34no—
849C4⋊C4—32no—
850C4⋊C4—62no—
851C4⋊C4—64no—
852C4⋊C4—62no—
853C4⋊C4D3×D412yes—
854C4⋊C4C23×D312yes—
855C22⋊C4—21no—
856C22⋊C4—24no—
857C22⋊C4—34no—
858C22⋊C4—34no—
859C22⋊C4—62no—
860C22⋊C4—64no—
861C22⋊C4—64no—
862C22⋊C4—62no—
863C22⋊C4—62no—
864C22⋊C4—62no—
865C22⋊C4—61no—
866C22⋊C4—64no—
867C22⋊C4—64no—
868C22⋊C4D3×D412yes—
869C42—24no—
870C42—21no—
871C42—61no—
872C42C23×D312yes—
873C22×C3—22no—
874C22×C3—42no—
875C22×C3—41no—
876C22×C3D4212yes—
877C22×C3C23×D411yescharacteristic
878C2×D3—22no—
879C2×D3—24no—
880C2×D3—22no—
881C2×D3—22no—
882C2×D3—22no—
883C2×D3—24no—
884C2×D3—44no—
885C2×D3—44no—
886C2×D3—42no—
887C2×D3—44no—
888C2×D3—41no—
889C2×D3—42no—
890C2×D3—84no—
891C2×D3—84no—
892C2×D3—164no—
893C3×C4—24no—
894C3×C4—24no—
895C3×C4—42no—
896C3×C4—41no—
897C3×C4—42no—
898C3×C4D4212yes—
899C3×C4C23×D411yescharacteristic
900C3×C4C2×H(5,𝔽2)11yescharacteristic
901Dic3—22no—
902Dic3—22no—
903Dic3—42no—
904Dic3—41no—
905C23—21no—
906C23—32no—
907C23—32no—
908C23—62no—
909C23—62no—
910C23—64no—
911C23—62no—
912C23—61no—
913C23—122no—
914C23—124no—
915C23—122no—
916C23—242no—
917C23—242no—
918C23—244no—
919C23C2×D3×D411yescharacteristic
920Q8—22no—
921Q8—24no—
922Q8—22no—
923Q8—21no—
924Q8—21no—
925Q8—22no—
926Q8—42no—
927Q8—62no—
928Q8—61no—
929Q8—61no—
930Q8—124no—
931Q8C2×D3×D414yes—
932D4—21no—
933D4—21no—
934D4—34no—
935D4—42no—
936D4—64no—
937D4—61no—
938D4—62no—
939D4—62no—
940D4—62no—
941D4—61no—
942D4—64no—
943D4—62no—
944D4—124no—
945D4—128no—
946D4—124no—
947D4—124no—
948D4—128no—
949D4—124no—
950D4—122no—
951D4—122no—
952D4—244no—
953D4—244no—
954D4—242no—
955D4—242no—
956C2×C4—22no—
957C2×C4—24no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—21no—
961C2×C4—32no—
962C2×C4—32no—
963C2×C4—42no—
964C2×C4—42no—
965C2×C4—62no—
966C2×C4—62no—
967C2×C4—62no—
968C2×C4—62no—
969C2×C4—62no—
970C2×C4—64no—
971C2×C4—62no—
972C2×C4—61no—
973C2×C4—128no—
974C2×C4—124no—
975C2×C4—124no—
976C2×C4—128no—
977C2×C4—124no—
978C2×C4—122no—
979C2×C4—244no—
980C2×C4C2×D3×D414yes—
981C2×C4C2×D3×D412yes—
982C2×C4C2×D3×D411yescharacteristic
983C2×C4#100912yes—
984C2×C4C24×D311yescharacteristic
985C8—22no—
986C8—22no—
987C8—32no—
988C8—32no—
989C8—62no—
990C2×C3—22no—
991C2×C3—81no—
992C2×C3C2×D4211yescharacteristic
993C2×C3#358412yes—
994D3—42no—
995D3—42no—
996D3—44no—
997D3—81no—
998D3—82no—
999C22—22no—
1000C22—42no—
1001C22—41no—
1002C22—62no—
1003C22—64no—
1004C22—62no—
1005C22—62no—
1006C22—62no—
1007C22—64no—
1008C22—124no—
1009C22—124no—
1010C22—122no—
1011C22—124no—
1012C22—121no—
1013C22—122no—
1014C22—244no—
1015C22—244no—
1016C22—484no—
1017C22#560912yes—
1018C22C22×D3×D411yescharacteristic
1019C4—24no—
1020C4—24no—
1021C4—42no—
1022C4—41no—
1023C4—42no—
1024C4—62no—
1025C4—62no—
1026C4—122no—
1027C4—121no—
1028C4#560912yes—
1029C4C22×D3×D411yescharacteristic
1030C4C2×#100911yescharacteristic
1031C3#6105211yescharacteristic, complemented, Sylow
1032C2—22no—
1033C2—81no—
1034C2—122no—
1035C2—122no—
1036C2—124no—
1037C2—242no—
1038C2—241no—
1039C2C2×#560911yescharacteristic
1040C2#8721012yes—
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3044C2
socleC22×C3C23×D4
hypercenter#3044D3
hypocenterC3#61052
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #117 ◁ #3044

Complements

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

NH ≅ G/Ntype
1. C2×#5778C2semidirect
2. C22×#919C2semidirect
3. #86354C2semidirect
4. #85874C2semidirect
5. C3×#3044C2semidirect
6. #83980C2semidirect
7. #83884C2semidirect
8. #83402C2semidirect
9. #82548C2semidirect
10. #80630C2semidirect
11. #80628C2semidirect
12. #80502C2semidirect
13. #80500C2semidirect
14. #79086C2semidirect
15. #79073C2semidirect
16. #78963C2semidirect
17. #78959C2semidirect
18. #78838C2semidirect
19. #78834C2semidirect
24. C22×#239C22semidirect
26. C22×C3×Q16C22semidirect
28. C3×#519C22semidirect
33. C2×#942C22semidirect
35. C22×#215C22semidirect
38. C2×#919C22semidirect
39. C2×#919C22semidirect
40. C2×#919C22semidirect
41. C2×#918C22semidirect
42. C2×#914C22semidirect
43. C2×D3×SD16C22semidirect
47. C22×D3×C8C22semidirect
48. #5726C22semidirect
49. #5676C22semidirect
55. #5577C22semidirect
57. #5576C22semidirect
60. #5525C22semidirect
63. #5524C22semidirect
65. C3×#464C22semidirect
66. C3×#462C22semidirect
67. C3×#424C22semidirect
68. C3×#419C22semidirect
70. #5225C22semidirect
71. #5187C22semidirect
72. #5187C22semidirect
73. #5186C22semidirect
74. #5172C22semidirect
75. #5131C22semidirect
76. #5126C22semidirect
77. #5113C22semidirect
79. #5086C22semidirect
80. #5085C22semidirect
81. #5059C22semidirect
82. #5058C22semidirect
83. #5026C22semidirect
84. C4×#215C22semidirect
86. #4998C22semidirect
87. #4997C22semidirect
88. #4844C22semidirect
89. #4843C22semidirect
90. #4836C22semidirect
91. #4834C22semidirect
92. #4813C22semidirect
93. #4812C22semidirect
94. #4810C22semidirect
95. #4810C22semidirect
96. #4808C22semidirect
97. #4807C22semidirect
98. #4807C22semidirect
99. #4778C22semidirect
100. #4775C22semidirect
101. #4773C22semidirect
113. #3044D3semidirect
181. C2×#215D4semidirect
285. C22×Q16C2×D3semidirect
311. #519C2×D3semidirect
323. #464C2×D3semidirect
325. #462C2×D3semidirect
340. #424C2×D3semidirect
342. #419C2×D3semidirect
1031. C3#61052semidirect

Maximal subgroups

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

subgroupindex
C2×#57782
C22×#9192
#863542
#858742
C3×#30442
#839802
#838842
#834022
#825482
#806302
#806282
#805022
#805002
#790862
#790732
#789632
#789592
#788382
#788342
#610523