Finite Group Databasebeta

← #11670552

Subgroups — #11670552

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
1#87290C211yesmaximal, characteristic, complemented
2C2×#5837C211yesmaximal, characteristic, complemented
3C22×#919C211yesmaximal, characteristic, complemented
4#86354C211yesmaximal, characteristic, complemented
5C3×#3011C211yesmaximal, characteristic, complemented
6#83980C211yesmaximal, characteristic, complemented
7#83974C211yesmaximal, characteristic, complemented
8#83877C211yesmaximal, characteristic, complemented
9#83398C211yesmaximal, characteristic, complemented
10#80270C214yesmaximal, complemented
11#80266C214yesmaximal, complemented
12#80207C214yesmaximal, complemented
13#80205C214yesmaximal, complemented
14#78959C211yesmaximal, characteristic, complemented
15#78947C211yesmaximal, characteristic, complemented
16#78862C211yesmaximal, characteristic, complemented
17#78838C211yesmaximal, characteristic, complemented
18#78670C211yesmaximal, characteristic, complemented
19#78655C211yesmaximal, characteristic, complemented
20#61052—31nomaximal, Sylow
21C2×C3×2−1+4C2211yescharacteristic
22C2×#1009C2211yescharacteristic
23C22×#239C2211yescharacteristic
24C22×#239C2211yescharacteristic, complemented
25C2×C3×#137C2211yescharacteristic, complemented
26C22×C3×Q16C2211yescharacteristic, complemented
27C3×#536C2211yescharacteristic
28#5837—28no—
29#5834—22no—
30#5834C2214yescomplemented
31#5830—22no—
32#5830C2211yescharacteristic
33#5830C2211yescharacteristic, complemented
34#5828—22no—
35#5828C2211yescharacteristic
36#5828C2211yescharacteristic, complemented
37C2×#950C2211yescharacteristic
38C2×#950C2212yescomplemented
39C2×#949C2211yescharacteristic
40C2×#949C2212yescomplemented
41C2×#948C2211yescharacteristic
42#5817—22no—
43#5817C2214yescomplemented
44#5816C2211yescharacteristic
45#5812C2211yescharacteristic, complemented
46C2×#942C2211yescharacteristic
47C2×#942C2212yescomplemented
48C22×#215C2211yescharacteristic
49C22×#215C2211yescharacteristic, complemented
50C22×#215C2212yescomplemented
51C2×#919—28no—
52C2×#919C2214yescomplemented
53C2×#919C2214yescomplemented
54C2×#908C2211yescharacteristic
55C22×D24C2211yescharacteristic
56C22×D3×C8C2211yescharacteristic, complemented
57#5726—22no—
58#5676—22no—
59#5653—22no—
60D3×#123—22no—
61#5631C2214yescomplemented
62#5630C2214yescomplemented
63#5524C2211yescharacteristic
64#5521C2211yescharacteristic
65C3×#452C2214yescomplemented
66C3×#451C2214yescomplemented
67C3×#419C2211yescharacteristic, complemented
68C3×#416C2211yescharacteristic, complemented
69C3×#408C2211yescharacteristic
70#5225C2211yescharacteristic, complemented
71#5191C2212yescomplemented
72#5190C2212yescomplemented
73#5187C2214yescomplemented
74#5185C2214yescomplemented
75#5182C2214yescomplemented
76#5176C2212yescomplemented
77#5175C2212yescomplemented
78#5172C2214yescomplemented
79#5131C2211yescharacteristic
80#5126C2211yescharacteristic, complemented
81#5122C2211yescharacteristic, complemented
82#5113C2211yescharacteristic
83#5102C2211yescharacteristic, complemented
84#5049C2214yescomplemented
85#5048C2214yescomplemented
86#5001C2211yescharacteristic, complemented
87#4998C2211yescharacteristic, complemented
88#4819C2214yescomplemented
89#4817C2214yescomplemented
90#4813C2212yescomplemented
91#4810C2214yescomplemented
92#4808C2214yescomplemented
93#4807C2212yescomplemented
94#4788C2214yescomplemented
95#4786C2214yescomplemented
96#4778C2212yescomplemented
97#4775C2212yescomplemented
98#4734C2214yescomplemented
99#4732C2214yescomplemented
100#4728C2214yescomplemented
101#67⋊C8C2214yescomplemented
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#3044—31no—
114#3041—31no—
115#3011D311yescharacteristic, complemented
116#3008—31no—
117#3005—31no—
118#3005—31no—
119#2949—31no—
120#2929—31no—
121C3×2−1+4—24no—
122C3×2−1+4—42no—
123C2×C3×#41—22no—
124C2×C3×#41—21no—
125C2×C3×#41C2311yescharacteristic
126C2×C3×#41C2312yes—
127C2×C3×#41C2311yescharacteristic
128C22×C3×Q8—21no—
129C22×C3×Q8C2311yescharacteristic
130C22×C3×Q8C2312yes—
131C22×C3×Q8C2311yescharacteristic
132#1009—24no—
133#1009—42no—
134C2×#239—21no—
135C2×#239—22no—
136C2×#239—22no—
137C2×#239—24no—
138C2×#239—24no—
139C2×#239—42no—
140C2×#239—42no—
141C2×#239C2314yes—
142C2×#239C2314yes—
143C2×D3×D4—22no—
144C2×D3×D4—21no—
145C2×#235C2311yescharacteristic
146C2×#235C2312yes—
147C22×D12—21no—
148C22×D12—21no—
149C22×D12C2311yescharacteristic
150C22×D12C2312yes—
151C22×D12C2311yescharacteristic
152C22×C4×D3—21no—
153C22×C4×D3—21no—
154C22×C4×D3C2311yescharacteristic
155C3×#137—42no—
156C2×C3×Q16—24no—
157C2×C3×Q16C2314yes—
158C2×C3×Q16C2312yes—
159C2×C3×SD16C2312yes—
160C2×C3×M16C2311yescharacteristic
161C22×C3×C8C2311yescharacteristic
162C3×C4⋊Q8—21no—
163C3×#124—21no—
164C3×#123—22no—
165C3×C22⋊Q8C2314yes—
166C3×#117C2311yescharacteristic
167#950—28no—
168#950—24no—
169#949—24no—
170#949—28no—
171#948—24no—
172#947—21no—
173#947—24no—
174#947C2312yes—
175#947C2312yes—
176#946—22no—
177#946—24no—
178#946D412yes—
179#946C2312yes—
180Q8×Dic3—22no—
181Q8×Dic3C2314yes—
182#944C2312yes—
183C2×#216C2312yes—
184C2×#216C2311yescharacteristic
185#942—24no—
186#942—28no—
187C2×#215—28no—
188C2×#215—24no—
189C2×#215D418yescomplemented
190C2×#215C2312yes—
191C2×#215C2312yes—
192C2×#215C2312yes—
193C2×#215C2312yes—
194C2×#215C2311yescharacteristic
195C2×#215C2312yes—
196C2×#215C2312yes—
197#940—21no—
198#940—24no—
199#940C2312yes—
200#938—24no—
201#938D412yes—
202#938C2312yes—
203#937—21no—
204#937—22no—
205#937—22no—
206#937D412yes—
207#935—21no—
208#935D412yes—
209C2×#214C2311yescharacteristic
210C2×#213C2312yes—
211C2×#213C2311yescharacteristic
212#930—24no—
213#930—24no—
214#930—22no—
215#930C2314yes—
216#929—22no—
217C4×#67—22no—
218C4×#67—24no—
219C4×#67—24no—
220C4×#67C2314yes—
221#926—22no—
222#926C2311yescharacteristic
223#926C2311yescharacteristic
224C2×#208C2311yescharacteristic
225C2×#208C2312yes—
226C22×C3⋊C8C2312yes—
227C22×C3⋊C8C2311yescharacteristic
228#919—216no—
229#919—216no—
230#908—42no—
231C2×D24—24no—
232C2×D24C2314yes—
233C2×D24C2312yes—
234C2×#204C2312yes—
235C2×D3×C8—24no—
236C2×D3×C8C2312yes—
237C2×D3×C8C2312yes—
238#897C2312yes—
239#895—24no—
240#895C2312yes—
241#894—24no—
242#894—24no—
243#893C2314yes—
244D3×C4⋊C4—24no—
245#886—21no—
246#884—24no—
247#883—24no—
248#882—21no—
249#882—24no—
250D3×C22⋊C4—22no—
251D3×C22⋊C4—24no—
252C4×D12—22no—
253C4×D12—22no—
254C3×#103C2312yes—
255C3×#103C2314yes—
256C3×#102C2312yes—
257C3×C22⋊C8C2314yes—
258#835C2314yes—
259#821C2314yes—
260#821C2312yes—
261(C2×D3)⋊C8C2314yes—
262#816C2312yes—
263#815C2312yes—
264Dic3⋊C8C2314yes—
265C8×Dic3C2312yes—
266#809C2314yes—
267#808C2312yes—
268#807C2312yes—
269C2×2−1+4C2×D311yescharacteristic
270C2×H(5,𝔽2)—31no—
271C22×#41—31no—
272C22×#41—31no—
273#577—68no—
274C2×#137—31no—
275C2×#137—32no—
276C2×#137C2×D311yescharacteristic, complemented
277C2×AGL(1,ℤ/8)—31no—
278C2×AGL(1,ℤ/8)—32no—
279C2×AGL(1,ℤ/8)—31no—
280C2×#135—31no—
281C2×#135—32no—
282C2×#135—34no—
283C2×#135—34no—
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#519—31no—
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#464—34no—
324#463—34no—
325#462—34no—
326#459—34no—
327#452—34no—
328#452—34no—
329#452C2×D314yescomplemented
330#451C2×D314yescomplemented
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#424—31no—
341#419—31no—
342#419C2×D311yescharacteristic, complemented
343#418—31no—
344#418—31no—
345#416—31no—
346#416C2×D311yescharacteristic, complemented
347#408C2×D311yescharacteristic
348#407—31no—
349#405—31no—
350C23×D3—21no—
351C23×D3—22no—
352C23×D3—21no—
353C23×D3C2×D411yescharacteristic
354C3×#41—22no—
355C3×#41—22no—
356C3×#41—24no—
357C3×#41—22no—
358C3×#41—22no—
359C3×#41—42no—
360C3×#41—48no—
361C3×#41—44no—
362C2×C3×Q8—21no—
363C2×C3×Q8—22no—
364C2×C3×Q8—21no—
365C2×C3×Q8—22no—
366C2×C3×Q8—24no—
367C2×C3×Q8—22no—
368C2×C3×Q8—22no—
369C2×C3×Q8—42no—
370C2×C3×Q8—44no—
371C2×C3×Q8C2×D414yes—
372C2×C3×Q8C2×D411yescharacteristic
373C2×C3×Q8C2412yes—
374C2×C3×Q8C2411yescharacteristic
375C2×C3×Q8C2412yes—
376C2×C3×D4—21no—
377C2×C3×D4—22no—
378C2×C3×D4C2×D412yes—
379C2×C3×D4C2×D411yescharacteristic
380C2×C3×D4C2411yescharacteristic
381C22×C3×C4—21no—
382C22×C3×C4—22no—
383C22×C3×C4—21no—
384C22×C3×C4—22no—
385C22×C3×C4—21no—
386C22×C3×C4C2412yes—
387C22×C3×C4C2411yescharacteristic
388C2×#67—21no—
389C2×#67—22no—
390C2×#67—24no—
391C2×#67—22no—
392C2×#67—24no—
393C2×#67C2×D414yes—
394C22×Dic3C2×D411yescharacteristic
395#239—28no—
396#239—28no—
397#239—44no—
398#239—44no—
399#239—48no—
400#239—48no—
401#239—44no—
402D3×D4—44no—
403D3×D4—48no—
404#235—22no—
405#235—22no—
406#235—24no—
407#235—42no—
408C2×D12—21no—
409C2×D12—22no—
410C2×D12—22no—
411C2×D12—22no—
412C2×D12—24no—
413C2×D12—24no—
414C2×D12—24no—
415C2×D12—22no—
416C2×D12—21no—
417C2×D12—22no—
418C2×D12—42no—
419C2×D12—44no—
420C2×D12—44no—
421C2×D12C2×D414yes—
422C2×D12C2412yes—
423C2×D12C2411yescharacteristic
424C2×D12C2412yes—
425C2×C4×D3—22no—
426C2×C4×D3—22no—
427C2×C4×D3—21no—
428C2×C4×D3—22no—
429C2×C4×D3—24no—
430C2×C4×D3—24no—
431C2×C4×D3—24no—
432C2×C4×D3—44no—
433C2×C4×D3—44no—
434C2×C4×D3C2×D412yes—
435C2×C4×D3C2412yes—
436C2×Dic6C2411yescharacteristic
437C3×Q16—28no—
438C3×Q16—42no—
439C3×SD16—42no—
440C3×M16—22no—
441C2×C3×C8—22no—
442C2×C3×C8C2412yes—
443C2×C3×C8C2412yes—
444C3×C4⋊C4—24no—
445C3×C4⋊C4C2412yes—
446C3×C22⋊C4—21no—
447C3×C22⋊C4—24no—
448C3×C42—21no—
449#217—21no—
450#217—22no—
451#217C2×D414yes—
452#217C2×D412yes—
453#216—24no—
454#216—22no—
455#215—24no—
456#215—24no—
457#215—24no—
458#215—24no—
459#215—22no—
460#215C2×D418yes—
461#215C2×D418yes—
462#214—22no—
463#213—24no—
464#213—22no—
465(C2×D3)⋊C4—22no—
466(C2×D3)⋊C4—22no—
467(C2×D3)⋊C4—24no—
468(C2×D3)⋊C4—22no—
469(C2×D3)⋊C4—24no—
470(C2×D3)⋊C4—24no—
471(C2×D3)⋊C4—24no—
472(C2×D3)⋊C4C2×D414yes—
473C4⋊Dic3—22no—
474C4⋊Dic3—24no—
475C4⋊Dic3C2×D412yes—
476C4⋊Dic3C2412yes—
477Dic3⋊C4—24no—
478Dic3⋊C4—22no—
479Dic3⋊C4C2×D414yes—
480C4×Dic3—21no—
481C4×Dic3—24no—
482C4×Dic3C2412yes—
483#208—22no—
484#208—24no—
485C2×C3⋊C8—24no—
486C2×C3⋊C8C2×D414yes—
487C2×C3⋊C8C2412yes—
488C2×C3⋊C8C2411yescharacteristic
489C2×C3⋊C8C2411yescharacteristic
490D24—28no—
491D24—42no—
492#204—42no—
493D3×C8—24no—
494D3×C8—24no—
4952−1+4—24no—
4962−1+4—42no—
497H(5,𝔽2)—64no—
498H(5,𝔽2)—122no—
499C2×#41—22no—
500C2×#41—21no—
501C2×#41—34no—
502C2×#41—34no—
503C2×#41—31no—
504C2×#41—32no—
505C2×#41—62no—
506C2×#41—62no—
507C2×#41—61no—
508C2×#41—64no—
509C2×#41—64no—
510C2×#41—122no—
511C2×#41—122no—
512C2×#41C22×D311yescharacteristic
513C2×#41C22×D312yes—
514C2×#41C22×D311yescharacteristic
515C22×Q8—21no—
516C22×Q8C22×D311yescharacteristic
517C22×Q8C22×D312yes—
518C22×Q8C22×D311yescharacteristic
519C22×D4—31no—
520C22×D4—31no—
521C22×D4—32no—
522C22×D4—61no—
523C22×D4—61no—
524C22×D4—62no—
525C22×D4—61no—
526C23×C4—31no—
527C23×C4—61no—
528C23×C4—61no—
529#137—42no—
530#137—68no—
531#137—64no—
532AGL(1,ℤ/8)—68no—
533AGL(1,ℤ/8)—64no—
534AGL(1,ℤ/8)—122no—
535#135—64no—
536#135—616no—
537#135—616no—
538#135—68no—
539C2×Q16—24no—
540C2×Q16—32no—
541C2×Q16—31no—
542C2×Q16C22×D314yes—
543C2×Q16C22×D312yes—
544C2×SD16—38no—
545C2×SD16—32no—
546C2×SD16—32no—
547C2×SD16—31no—
548C2×SD16—32no—
549C2×SD16—32no—
550C2×SD16—32no—
551C2×SD16—32no—
552C2×SD16—31no—
553C2×SD16—32no—
554C2×SD16—64no—
555C2×SD16—68no—
556C2×SD16C22×D312yes—
557C2×D8—32no—
558C2×D8—31no—
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—21no—
573C4⋊Q8—32no—
574#127—32no—
575#127—64no—
576#127—61no—
577#124—21no—
578#124—32no—
579#124—32no—
580#124—64no—
581#124—61no—
582#123—22no—
583#123—32no—
584#123—64no—
585#123—61no—
586#123—64no—
587#123—62no—
588#123—64no—
589#123—61no—
590C22⋊Q8—32no—
591C22⋊Q8—32no—
592C22⋊Q8—32no—
593C22⋊Q8—64no—
594C22⋊Q8—62no—
595C22⋊Q8C22×D314yes—
596#121—32no—
597#121—32no—
598#121—34no—
599#121—32no—
600#121—64no—
601#121—64no—
602#121—64no—
603#121—64no—
604#121—62no—
605#121—64no—
606#120—32no—
607#120—64no—
608#120—61no—
609#120—62no—
610#120—61no—
611#120—62no—
612C4×Q8—34no—
613C4×Q8—62no—
614C4×D4—34no—
615C4×D4—34no—
616C4×D4—62no—
617C4×D4—62no—
618C4×D4—64no—
619C4×D4—64no—
620C4×D4—62no—
621#117—31no—
622#117—31no—
623#117—62no—
624#117C22×D311yescharacteristic
625C2×C4⋊C4—64no—
626C2×C22⋊C4—62no—
627C2×C22⋊C4—64no—
628#107—32no—
629#106—32no—
630C4⋊C8—34no—
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⋊C8C22×D314yes—
641#97—32no—
642C4×C8—32no—
643C23×C3—21no—
644C23×C3C22×D412yes—
645C23×C3C22×D411yescharacteristic
646C22×D3—22no—
647C22×D3—22no—
648C22×D3—24no—
649C22×D3—21no—
650C22×D3—22no—
651C22×D3—42no—
652C22×D3—44no—
653C22×D3—42no—
654C22×D3—82no—
655C22×D3—82no—
656C22×D3—84no—
657C22×D3C22×D412yes—
658C3×Q8—24no—
659C3×Q8—22no—
660C3×Q8—22no—
661C3×Q8—21no—
662C3×Q8—22no—
663C3×Q8—22no—
664C3×Q8—21no—
665C3×Q8—44no—
666C3×Q8—42no—
667C3×Q8C22×D414yes—
668C3×D4—24no—
669C3×D4—22no—
670C3×D4—21no—
671C3×D4—21no—
672C3×D4—44no—
673C3×D4—42no—
674C2×C3×C4—24no—
675C2×C3×C4—22no—
676C2×C3×C4—22no—
677C2×C3×C4—22no—
678C2×C3×C4—21no—
679C2×C3×C4—22no—
680C2×C3×C4—22no—
681C2×C3×C4—44no—
682C2×C3×C4—44no—
683C2×C3×C4—42no—
684C2×C3×C4—42no—
685C2×C3×C4C22×D412yes—
686C2×C3×C4C22×D411yescharacteristic
687C2×C3×C4C22×D412yes—
688C2×C3×C4H(5,𝔽2)12yes—
689C2×C3×C4C2511yescharacteristic
690#67—44no—
691#67—44no—
692#67—42no—
693#67—84no—
694#67—82no—
695#67—84no—
696C2×Dic3—22no—
697C2×Dic3—22no—
698C2×Dic3—21no—
699C2×Dic3C22×D414yes—
700C2×Dic3C22×D412yes—
701D12—24no—
702D12—22no—
703D12—21no—
704D12—22no—
705D12—22no—
706D12—21no—
707D12—44no—
708D12—48no—
709D12—48no—
710D12—42no—
711D12—82no—
712D12C22×D414yes—
713C4×D3—24no—
714C4×D3—22no—
715C4×D3—22no—
716C4×D3—48no—
717C4×D3—48no—
718C4×D3—44no—
719C4×D3—42no—
720C4×D3—84no—
721Dic6—21no—
722Dic6—21no—
723C3×C8—22no—
724C3×C8—22no—
725C3⋊C8—22no—
726C3⋊C8C22×D412yes—
727C3⋊C8C22×D412yes—
728C24—31no—
729C24—61no—
730C24—62no—
731C24—61no—
732#41—22no—
733#41—22no—
734#41—24no—
735#41—22no—
736#41—22no—
737#41—42no—
738#41—48no—
739#41—44no—
740#41—64no—
741#41—68no—
742#41—68no—
743#41—62no—
744#41—62no—
745#41—122no—
746#41—124no—
747#41—124no—
748#41—128no—
749#41—128no—
750#41—124no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—22no—
754C2×Q8—22no—
755C2×Q8—24no—
756C2×Q8—22no—
757C2×Q8—22no—
758C2×Q8—31no—
759C2×Q8—42no—
760C2×Q8—44no—
761C2×Q8D3×D414yes—
762C2×Q8D3×D411yescharacteristic
763C2×Q8C23×D312yes—
764C2×Q8C23×D311yescharacteristic
765C2×Q8C23×D312yes—
766C2×D4—21no—
767C2×D4—22no—
768C2×D4—34no—
769C2×D4—34no—
770C2×D4—32no—
771C2×D4—31no—
772C2×D4—32no—
773C2×D4—64no—
774C2×D4—64no—
775C2×D4—64no—
776C2×D4—62no—
777C2×D4—64no—
778C2×D4—61no—
779C2×D4—62no—
780C2×D4—62no—
781C2×D4—64no—
782C2×D4—61no—
783C2×D4—62no—
784C2×D4—62no—
785C2×D4—61no—
786C2×D4—62no—
787C2×D4—62no—
788C2×D4—122no—
789C2×D4—124no—
790C2×D4—124no—
791C2×D4—124no—
792C2×D4—128no—
793C2×D4D3×D412yes—
794C2×D4D3×D411yescharacteristic
795C2×D4C23×D311yescharacteristic
796C22×C4—21no—
797C22×C4—22no—
798C22×C4—21no—
799C22×C4—22no—
800C22×C4—21no—
801C22×C4—31no—
802C22×C4—32no—
803C22×C4—32no—
804C22×C4—64no—
805C22×C4—64no—
806C22×C4—64no—
807C22×C4—62no—
808C22×C4—62no—
809C22×C4—62no—
810C22×C4—61no—
811C22×C4—124no—
812C22×C4—124no—
813C22×C4C23×D312yes—
814C22×C4C23×D311yescharacteristic
815Q16—28no—
816Q16—42no—
817Q16—62no—
818Q16—64no—
819SD16—38no—
820SD16—38no—
821SD16—42no—
822SD16—62no—
823SD16—62no—
824SD16—64no—
825SD16—64no—
826SD16—64no—
827SD16—64no—
828SD16—122no—
829D8—68no—
830D8—62no—
831D8—64no—
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—34no—
848C4⋊C4—32no—
849C4⋊C4—32no—
850C4⋊C4—62no—
851C4⋊C4—64no—
852C4⋊C4—64no—
853C4⋊C4—62no—
854C4⋊C4C23×D312yes—
855C22⋊C4—21no—
856C22⋊C4—24no—
857C22⋊C4—32no—
858C22⋊C4—34no—
859C22⋊C4—34no—
860C22⋊C4—62no—
861C22⋊C4—64no—
862C22⋊C4—64no—
863C22⋊C4—64no—
864C22⋊C4—62no—
865C22⋊C4—62no—
866C22⋊C4—62no—
867C22⋊C4—61no—
868C22⋊C4—64no—
869C42—21no—
870C42—32no—
871C42—64no—
872C42—61no—
873C22×C3—22no—
874C22×C3—24no—
875C22×C3—22no—
876C22×C3—42no—
877C22×C3—41no—
878C22×C3D4212yes—
879C22×C3C23×D411yescharacteristic
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—42no—
889C2×D3—41no—
890C2×D3—84no—
891C2×D3—84no—
892C2×D3—164no—
893C3×C4—24no—
894C3×C4—22no—
895C3×C4—42no—
896C3×C4—42no—
897C3×C4—41no—
898C3×C4D4212yes—
899C3×C4C23×D411yescharacteristic
900C3×C4C2×H(5,𝔽2)11yescharacteristic
901Dic3—24no—
902Dic3—22no—
903Dic3—42no—
904Dic3—41no—
905C23—21no—
906C23—32no—
907C23—62no—
908C23—62no—
909C23—64no—
910C23—61no—
911C23—62no—
912C23—122no—
913C23—124no—
914C23—122no—
915C23—242no—
916C23—242no—
917C23—244no—
918C23C2×D3×D412yes—
919C23C2×D3×D411yescharacteristic
920Q8—22no—
921Q8—24no—
922Q8—22no—
923Q8—21no—
924Q8—22no—
925Q8—22no—
926Q8—21no—
927Q8—44no—
928Q8—42no—
929Q8—61no—
930Q8—61no—
931Q8C2×D3×D414yes—
932D4—24no—
933D4—21no—
934D4—21no—
935D4—22no—
936D4—34no—
937D4—44no—
938D4—42no—
939D4—62no—
940D4—61no—
941D4—62no—
942D4—61no—
943D4—62no—
944D4—64no—
945D4—124no—
946D4—128no—
947D4—128no—
948D4—124no—
949D4—124no—
950D4—122no—
951D4—122no—
952D4—242no—
953D4—244no—
954D4—244no—
955D4—242no—
956C2×C4—22no—
957C2×C4—24no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—21no—
963C2×C4—34no—
964C2×C4—32no—
965C2×C4—44no—
966C2×C4—44no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—62no—
970C2×C4—62no—
971C2×C4—62no—
972C2×C4—64no—
973C2×C4—62no—
974C2×C4—61no—
975C2×C4—128no—
976C2×C4—124no—
977C2×C4—128no—
978C2×C4—122no—
979C2×C4—244no—
980C2×C4C2×D3×D412yes—
981C2×C4C2×D3×D412yes—
982C2×C4C2×D3×D411yescharacteristic
983C2×C4#100412yes—
984C2×C4C24×D311yescharacteristic
985C8—22no—
986C8—22no—
987C8—32no—
988C8—32no—
989C8—62no—
990C2×C3—22no—
991C2×C3—42no—
992C2×C3—81no—
993C2×C3C2×D4211yescharacteristic
994C2×C3#358412yes—
995D3—42no—
996D3—44no—
997D3—82no—
998D3—81no—
999C22—22no—
1000C22—22no—
1001C22—24no—
1002C22—41no—
1003C22—42no—
1004C22—62no—
1005C22—64no—
1006C22—62no—
1007C22—62no—
1008C22—124no—
1009C22—124no—
1010C22—122no—
1011C22—121no—
1012C22—124no—
1013C22—122no—
1014C22—244no—
1015C22—244no—
1016C22—484no—
1017C22#559012yes—
1018C22C22×D3×D411yescharacteristic
1019C4—24no—
1020C4—22no—
1021C4—41no—
1022C4—42no—
1023C4—42no—
1024C4—62no—
1025C4—64no—
1026C4—121no—
1027C4—122no—
1028C4#559012yes—
1029C4C22×D3×D411yescharacteristic
1030C4C2×#100411yescharacteristic
1031C3#6105211yescharacteristic, complemented, Sylow
1032C2—22no—
1033C2—42no—
1034C2—81no—
1035C2—122no—
1036C2—124no—
1037C2—242no—
1038C2—241no—
1039C2C2×#559011yescharacteristic
1040C2#8721012yes—
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3011C2
socleC22×C3C23×D4
hypercenter#3011D3
hypocenterC3#61052
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3011

Complements

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

NH ≅ G/Ntype
1. #87290C2semidirect
2. C2×#5837C2semidirect
3. C22×#919C2semidirect
4. #86354C2semidirect
5. C3×#3011C2semidirect
6. #83980C2semidirect
7. #83974C2semidirect
8. #83877C2semidirect
9. #83398C2semidirect
10. #80270C2semidirect
11. #80266C2semidirect
12. #80207C2semidirect
13. #80205C2semidirect
14. #78959C2semidirect
15. #78947C2semidirect
16. #78862C2semidirect
17. #78838C2semidirect
18. #78670C2semidirect
19. #78655C2semidirect
24. C22×#239C22semidirect
25. C2×C3×#137C22semidirect
26. C22×C3×Q16C22semidirect
30. #5834C22semidirect
33. #5830C22semidirect
36. #5828C22semidirect
38. C2×#950C22semidirect
40. C2×#949C22semidirect
43. #5817C22semidirect
45. #5812C22semidirect
47. C2×#942C22semidirect
49. C22×#215C22semidirect
50. C22×#215C22semidirect
52. C2×#919C22semidirect
53. C2×#919C22semidirect
56. C22×D3×C8C22semidirect
61. #5631C22semidirect
62. #5630C22semidirect
65. C3×#452C22semidirect
66. C3×#451C22semidirect
67. C3×#419C22semidirect
68. C3×#416C22semidirect
70. #5225C22semidirect
71. #5191C22semidirect
72. #5190C22semidirect
73. #5187C22semidirect
74. #5185C22semidirect
75. #5182C22semidirect
76. #5176C22semidirect
77. #5175C22semidirect
78. #5172C22semidirect
80. #5126C22semidirect
81. #5122C22semidirect
83. #5102C22semidirect
84. #5049C22semidirect
85. #5048C22semidirect
86. #5001C22semidirect
87. #4998C22semidirect
88. #4819C22semidirect
89. #4817C22semidirect
90. #4813C22semidirect
91. #4810C22semidirect
92. #4808C22semidirect
93. #4807C22semidirect
94. #4788C22semidirect
95. #4786C22semidirect
96. #4778C22semidirect
97. #4775C22semidirect
98. #4734C22semidirect
99. #4732C22semidirect
100. #4728C22semidirect
101. #67⋊C8C22semidirect
115. #3011D3semidirect
189. C2×#215D4semidirect
276. C2×#137C2×D3semidirect
285. C22×Q16C2×D3semidirect
329. #452C2×D3semidirect
330. #451C2×D3semidirect
342. #419C2×D3semidirect
346. #416C2×D3semidirect
1031. C3#61052semidirect

Maximal subgroups

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

subgroupindex
#872902
C2×#58372
C22×#9192
#863542
C3×#30112
#839802
#839742
#838772
#833982
#802702
#802662
#802072
#802052
#789592
#789472
#788622
#788382
#786702
#786552
#610523