Finite Group Databasebeta

← #11670539

Subgroups — #11670539

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#87274C211yesmaximal, characteristic, complemented
2C22×#950C211yesmaximal, characteristic, complemented
3C2×#5778C211yesmaximal, characteristic, complemented
4#86040C211yesmaximal, characteristic, complemented
5C3×#3005C211yesmaximal, characteristic, complemented
6#83970C211yesmaximal, characteristic, complemented
7#83947C211yesmaximal, characteristic, complemented
8#83939C211yesmaximal, characteristic, complemented
9#82922C211yesmaximal, characteristic, complemented
10#80270C214yesmaximal, complemented
11#80267C214yesmaximal, complemented
12#80126C214yesmaximal, complemented
13#80123C214yesmaximal, complemented
14#78961C211yesmaximal, characteristic, complemented
15#78947C211yesmaximal, characteristic, complemented
16#78944C211yesmaximal, characteristic, complemented
17#78931C211yesmaximal, characteristic, complemented
18#78638C211yesmaximal, characteristic, complemented
19#78626C211yesmaximal, characteristic, complemented
20#61052—31nomaximal, Sylow
21C22×C3×#41C2211yescharacteristic, complemented
22C2×#1009C2211yescharacteristic
23C2×#1007C2211yescharacteristic
24C22×#235C2211yescharacteristic
25C2×C3×#137C2211yescharacteristic
26C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
27C3×#525C2211yescharacteristic
28#5834—22no—
29#5834C2214yescomplemented
30#5831—22no—
31#5831C2214yescomplemented
32#5825C2211yescharacteristic
33C2×#950—28no—
34C2×#950C2211yescharacteristic
35C2×#950C2214yescomplemented
36C2×#950C2214yescomplemented
37#5812C2211yescharacteristic, complemented
38C22×#216C2211yescharacteristic, complemented
39C22×#215C2211yescharacteristic
40#5805—22no—
41#5805C2211yescharacteristic
42#5805C2211yescharacteristic, complemented
43C22×#214C2211yescharacteristic, complemented
44C22×#213C2211yescharacteristic
45#5791—22no—
46#5791C2211yescharacteristic
47#5791C2211yescharacteristic, complemented
48C23×C3⋊C8C2211yescharacteristic, complemented
49#5778—28no—
50C2×#919C2212yescomplemented
51C2×#918C2212yescomplemented
52C2×#914C2212yescomplemented
53C2×D3×SD16C2212yescomplemented
54C2×#909C2211yescharacteristic, complemented
55C2×#908C2211yescharacteristic
56C2×#907C2211yescharacteristic
57D3×#123—22no—
58#5631C2214yescomplemented
59#5612C2214yescomplemented
60#5589—22no—
61#5551—22no—
62#5550—22no—
63#5526C2211yescharacteristic
64#5521C2211yescharacteristic
65C3×#452C2214yescomplemented
66C3×#449C2214yescomplemented
67C3×#419C2211yescharacteristic, complemented
68C3×#418C2211yescharacteristic, complemented
69C3×#407C2211yescharacteristic, complemented
70#5233C2211yescharacteristic
71#5182C2214yescomplemented
72#5175C2212yescomplemented
73#5172C2214yescomplemented
74#5167C2212yescomplemented
75#5166C2214yescomplemented
76#5156C2214yescomplemented
77#5155C2212yescomplemented
78#5154C2212yescomplemented
79#5131C2211yescharacteristic
80#5129C2211yescharacteristic
81#5122C2211yescharacteristic, complemented
82#5120C2211yescharacteristic, complemented
83#5119C2211yescharacteristic, complemented
84#5051C2212yescomplemented
85#5048C2212yescomplemented
86#5041C2212yescomplemented
87#5038C2212yescomplemented
88#5002C2211yescharacteristic, complemented
89#4998C2211yescharacteristic, complemented
90#4817C2214yescomplemented
91#4809C2214yescomplemented
92#4808C2214yescomplemented
93#4788C2214yescomplemented
94#4787C2214yescomplemented
95#4786C2214yescomplemented
96#4780C2214yescomplemented
97#4778C2214yescomplemented
98#4734C2214yescomplemented
99#4733C2214yescomplemented
100#4730C2214yescomplemented
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#3011—31no—
116#3008—31no—
117#3005—31no—
118#3005D311yescharacteristic, complemented
119#2949—31no—
120#2929—31no—
121C2×C3×#41—22no—
122C2×C3×#41—24no—
123C2×C3×#41—42no—
124C2×C3×#41C2311yescharacteristic
125C2×C3×#41C2314yes—
126C22×C3×Q8C2311yescharacteristic
127C22×C3×D4—21no—
128C22×C3×D4C2311yescharacteristic
129C23×C3×C4—21no—
130C23×C3×C4C2311yescharacteristic
131C22×#67—21no—
132#1009—24no—
133#1009—42no—
134#1007—24no—
135#1007—42no—
136C2×#239—21no—
137C2×#239C2312yes—
138C2×#239C2312yes—
139C2×D3×Q8—21no—
140C2×D3×Q8C2312yes—
141C2×D3×D4—22no—
142C2×D3×D4C2312yes—
143C2×#235—22no—
144C2×#235—22no—
145C2×#235—24no—
146C2×#235—21no—
147C2×#235—42no—
148C2×#235C2311yescharacteristic
149C2×#235C2311yescharacteristic
150C2×#235C2314yes—
151C22×D12—21no—
152C22×D12C2311yescharacteristic
153C22×C4×D3—21no—
154C22×Dic6C2311yescharacteristic
155C3×#137—24no—
156C3×AGL(1,ℤ/8)—42no—
157C2×C3×Q16C2312yes—
158C2×C3×SD16C2312yes—
159C2×C3×SD16C2312yes—
160C2×C3×D8C2312yes—
161C2×C3×M16C2311yescharacteristic
162C2×C3×M16C2311yescharacteristic
163C3×#123—21no—
164C3×C22⋊Q8C2312yes—
165C3×#121C2312yes—
166C3×#120—21no—
167C3×C4×D4—22no—
168C3×#117C2311yescharacteristic
169#953—21no—
170#953—22no—
171#953—22no—
172#953D412yes—
173#950—216no—
174#950—216no—
175#950—24no—
176Q8×Dic3—22no—
177Q8×Dic3C2314yes—
178#944C2312yes—
179C2×#216—24no—
180C2×#216C2314yes—
181C2×#216C2311yescharacteristic
182C2×#215D418yescomplemented
183C2×#215C2311yescharacteristic
184C2×#215C2312yes—
185C2×#215C2312yes—
186#940—24no—
187#940—21no—
188#940C2312yes—
189#938—24no—
190#938—24no—
191#938—24no—
192#938—22no—
193#938C2314yes—
194#937—24no—
195#936—21no—
196#936—24no—
197#936C2312yes—
198#936C2312yes—
199#935—22no—
200C2×#214—24no—
201C2×#214C2312yes—
202C2×#214C2311yescharacteristic
203C2×#214C2312yes—
204C2×#213—24no—
205C2×#213C2311yescharacteristic
206C2×#213C2314yes—
207#930—24no—
208#930D412yes—
209#930C2312yes—
210#929—21no—
211#929D412yes—
212C4×#67—22no—
213C4×#67—24no—
214C4×#67—24no—
215C4×#67C2314yes—
216#926—22no—
217#926C2311yescharacteristic
218#926C2311yescharacteristic
219#924—22no—
220#924—24no—
221#924D412yes—
222#924C2312yes—
223C22×C3⋊C8—24no—
224C22×C3⋊C8C2311yescharacteristic
225C22×C3⋊C8C2312yes—
226C22×C3⋊C8C2312yes—
227C22×C3⋊C8C2311yescharacteristic
228#919—28no—
229#918—28no—
230#914—28no—
231D3×SD16—28no—
232#909—42no—
233#908—24no—
234#907—24no—
235C2×Dic12C2312yes—
236C2×D24C2312yes—
237C2×#204C2312yes—
238C2×#204C2312yes—
239C2×ΓL(1,𝔽25)C2312yes—
240C2×D3×C8C2312yes—
241#897C2314yes—
242#894—24no—
243#893C2314yes—
244D3×C4⋊C4—24no—
245#886—22no—
246#884—24no—
247#883—24no—
248#883—24no—
249D3×C22⋊C4—22no—
250D3×C22⋊C4—24no—
251#875—21no—
252C4×D12—22no—
253#869—21no—
254C3×#103C2314yes—
255C3×#102C2314yes—
256C3×C22⋊C8C2314yes—
257#835C2312yes—
258#832C2312yes—
259#821C2314yes—
260(C2×D3)⋊C8C2314yes—
261#816C2314yes—
262#815C2312yes—
263Dic3⋊C8C2314yes—
264C8×Dic3C2312yes—
265#810C2312yes—
266#809C2312yes—
267#808C2312yes—
268#807C2312yes—
269C2×2−1+4—31no—
270C2×H(5,𝔽2)—31no—
271C22×#41—31no—
272C22×#41C2×D311yescharacteristic, complemented
273#577—68no—
274C2×#137—32no—
275C2×#137—31no—
276C2×#137C2×D311yescharacteristic
277C2×AGL(1,ℤ/8)—32no—
278C2×AGL(1,ℤ/8)—31no—
279C2×AGL(1,ℤ/8)C2×D311yescharacteristic
280C2×#135—31no—
281C2×#135—34no—
282C2×#135—34no—
283C2×#135—32no—
284C2×#135—68no—
285C22×Q16—31no—
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#536—31no—
302#535—31no—
303#535—31no—
304#535—62no—
305#534—62no—
306#525—31no—
307#525—31no—
308#525—62no—
309#525C2×D311yescharacteristic
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—32no—
321#465—32no—
322#465—34no—
323#464—34no—
324#463—34no—
325#462—34no—
326#459—34no—
327#452—34no—
328#452—34no—
329#452C2×D314yescomplemented
330#451—34no—
331#449—34no—
332#449—34no—
333#449C2×D314yescomplemented
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#418C2×D311yescharacteristic, complemented
345#416—31no—
346#416—31no—
347#408—31no—
348#407C2×D311yescharacteristic, complemented
349#405—31no—
350C24×C3—21no—
351C24×C3C2×D411yescharacteristic
352C23×D3—21no—
353C23×D3—22no—
354C3×#41—28no—
355C3×#41—22no—
356C3×#41—22no—
357C3×#41—44no—
358C3×#41—48no—
359C2×C3×Q8—21no—
360C2×C3×Q8—22no—
361C2×C3×Q8C2×D414yes—
362C2×C3×Q8C2411yescharacteristic
363C2×C3×Q8C2412yes—
364C2×C3×D4—21no—
365C2×C3×D4—24no—
366C2×C3×D4—22no—
367C2×C3×D4—22no—
368C2×C3×D4—21no—
369C2×C3×D4—22no—
370C2×C3×D4—44no—
371C2×C3×D4C2411yescharacteristic
372C2×C3×D4C2412yes—
373C22×C3×C4—21no—
374C22×C3×C4—22no—
375C22×C3×C4—22no—
376C22×C3×C4—21no—
377C22×C3×C4—24no—
378C22×C3×C4—44no—
379C22×C3×C4C2×D412yes—
380C22×C3×C4C2×D411yescharacteristic
381C22×C3×C4C2412yes—
382C22×C3×C4C2411yescharacteristic
383C2×#67—24no—
384C2×#67—21no—
385C2×#67—22no—
386C2×#67—24no—
387C2×#67—22no—
388C2×#67—24no—
389C2×#67—44no—
390C2×#67C2×D412yes—
391C2×#67C2×D414yes—
392C22×Dic3—21no—
393#239—24no—
394#239—24no—
395#239—42no—
396#239—42no—
397#239—44no—
398D3×Q8—24no—
399D3×Q8—42no—
400D3×Q8—44no—
401D3×D4—24no—
402D3×D4—42no—
403D3×D4—48no—
404#235—22no—
405#235—22no—
406#235—22no—
407#235—22no—
408#235—28no—
409#235—44no—
410#235—44no—
411#235—48no—
412#235—48no—
413C2×D12—21no—
414C2×D12—22no—
415C2×D12—22no—
416C2×D12—22no—
417C2×D12—44no—
418C2×D12C2×D411yescharacteristic
419C2×D12C2×D414yes—
420C2×D12C2411yescharacteristic
421C2×D12C2412yes—
422C2×C4×D3—22no—
423C2×C4×D3—24no—
424C2×C4×D3—21no—
425C2×C4×D3—22no—
426C2×C4×D3—22no—
427C2×C4×D3—24no—
428C2×C4×D3—44no—
429C2×C4×D3C2412yes—
430C2×Dic6—22no—
431C2×Dic6—22no—
432C2×Dic6—21no—
433C2×Dic6—22no—
434C2×Dic6C2×D411yescharacteristic
435C2×Dic6C2411yescharacteristic
436C2×Dic6C2412yes—
437C3×Q16—24no—
438C3×SD16—24no—
439C3×SD16—42no—
440C3×D8—42no—
441C3×M16—22no—
442C3×M16—22no—
443C2×C3×C8C2412yes—
444C2×C3×C8C2412yes—
445C3×C4⋊C4—22no—
446C3×C4⋊C4C2412yes—
447C3×C22⋊C4—21no—
448C3×C22⋊C4—22no—
449C3×C22⋊C4—22no—
450C3×C42—21no—
451#217—22no—
452#217—21no—
453#217—24no—
454#217—24no—
455#217—24no—
456#217C2×D412yes—
457#217C2×D414yes—
458#216—28no—
459#216—22no—
460#215—22no—
461#215C2×D418yes—
462#215C2×D418yes—
463#214—22no—
464#214—24no—
465#214—24no—
466#213—28no—
467#213—22no—
468(C2×D3)⋊C4—24no—
469(C2×D3)⋊C4—22no—
470(C2×D3)⋊C4—24no—
471(C2×D3)⋊C4C2×D414yes—
472C4⋊Dic3—24no—
473C4⋊Dic3—24no—
474C4⋊Dic3C2×D412yes—
475C4⋊Dic3C2412yes—
476Dic3⋊C4—22no—
477Dic3⋊C4—24no—
478Dic3⋊C4C2×D414yes—
479C4×Dic3—21no—
480C4×Dic3—24no—
481C4×Dic3C2412yes—
482C2×C3⋊C8—22no—
483C2×C3⋊C8—24no—
484C2×C3⋊C8—24no—
485C2×C3⋊C8C2×D414yes—
486C2×C3⋊C8C2412yes—
487C2×C3⋊C8C2411yescharacteristic
488C2×C3⋊C8C2411yescharacteristic
489Dic12—42no—
490D24—24no—
491#204—24no—
492#204—42no—
493ΓL(1,𝔽25)—24no—
494D3×C8—24no—
4952−1+4—64no—
4962−1+4—122no—
497H(5,𝔽2)—64no—
498H(5,𝔽2)—122no—
499C2×#41—22no—
500C2×#41—24no—
501C2×#41—31no—
502C2×#41—32no—
503C2×#41—32no—
504C2×#41—31no—
505C2×#41—34no—
506C2×#41—42no—
507C2×#41—62no—
508C2×#41—61no—
509C2×#41—64no—
510C2×#41—61no—
511C2×#41—62no—
512C2×#41—122no—
513C2×#41C22×D311yescharacteristic
514C2×#41C22×D314yes—
515C22×Q8—32no—
516C22×Q8—31no—
517C22×Q8—61no—
518C22×Q8C22×D311yescharacteristic
519C22×D4—21no—
520C22×D4—32no—
521C22×D4—31no—
522C22×D4—61no—
523C22×D4—62no—
524C22×D4—61no—
525C22×D4C22×D311yescharacteristic
526C23×C4—21no—
527C23×C4—61no—
528C23×C4C22×D311yescharacteristic
529#137—24no—
530#137—68no—
531#137—122no—
532AGL(1,ℤ/8)—42no—
533AGL(1,ℤ/8)—64no—
534AGL(1,ℤ/8)—68no—
535#135—64no—
536#135—68no—
537#135—616no—
538#135—616no—
539C2×Q16—34no—
540C2×Q16—31no—
541C2×Q16—32no—
542C2×Q16—64no—
543C2×Q16C22×D312yes—
544C2×SD16—38no—
545C2×SD16—32no—
546C2×SD16—32no—
547C2×SD16—31no—
548C2×SD16—31no—
549C2×SD16—32no—
550C2×SD16—32no—
551C2×SD16—32no—
552C2×SD16—32no—
553C2×SD16—64no—
554C2×SD16—68no—
555C2×SD16C22×D312yes—
556C2×SD16C22×D312yes—
557C2×D8—34no—
558C2×D8—31no—
559C2×D8—32no—
560C2×D8—64no—
561C2×D8C22×D312yes—
562#131—64no—
563C2×M16—32no—
564C2×M16C22×D311yescharacteristic
565C2×M16C22×D311yescharacteristic
566C22×C8—31no—
567C22×C8—31no—
568C22×C8—32no—
569C22×C8—32no—
570C22×C8—32no—
571C22×C8—64no—
572C4⋊Q8—32no—
573C4⋊Q8—61no—
574#127—32no—
575#127—61no—
576#127—64no—
577#124—32no—
578#124—32no—
579#124—61no—
580#124—64no—
581#124—61no—
582#123—21no—
583#123—32no—
584#123—64no—
585#123—64no—
586#123—62no—
587#123—64no—
588#123—62no—
589#123—61no—
590C22⋊Q8—32no—
591C22⋊Q8—32no—
592C22⋊Q8—34no—
593C22⋊Q8—64no—
594C22⋊Q8—62no—
595C22⋊Q8C22×D312yes—
596#121—32no—
597#121—34no—
598#121—32no—
599#121—64no—
600#121—64no—
601#121—64no—
602#121—64no—
603#121—62no—
604#121—64no—
605#121C22×D312yes—
606#120—21no—
607#120—32no—
608#120—62no—
609#120—64no—
610#120—62no—
611#120—61no—
612C4×Q8—34no—
613C4×Q8—62no—
614C4×D4—22no—
615C4×D4—34no—
616C4×D4—34no—
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—32no—
632#103—34no—
633#103—32no—
634#103C22×D314yes—
635#102—32no—
636#102—34no—
637#102—32no—
638#102C22×D314yes—
639C22⋊C8—34no—
640C22⋊C8C22×D314yes—
641#97—32no—
642C4×C8—32no—
643C23×C3—22no—
644C23×C3—21no—
645C23×C3—22no—
646C23×C3—42no—
647C23×C3—42no—
648C23×C3—82no—
649C23×C3C22×D412yes—
650C23×C3C22×D411yescharacteristic
651C22×D3—22no—
652C22×D3—24no—
653C22×D3—21no—
654C22×D3—44no—
655C22×D3—84no—
656C22×D3—82no—
657C22×D3C22×D412yes—
658C3×Q8—24no—
659C3×Q8—22no—
660C3×Q8—21no—
661C3×Q8—21no—
662C3×Q8C22×D414yes—
663C3×D4—22no—
664C3×D4—21no—
665C3×D4—21no—
666C3×D4—22no—
667C3×D4—48no—
668C3×D4—42no—
669C3×D4—42no—
670C3×D4—82no—
671C2×C3×C4—22no—
672C2×C3×C4—24no—
673C2×C3×C4—22no—
674C2×C3×C4—24no—
675C2×C3×C4—22no—
676C2×C3×C4—22no—
677C2×C3×C4—21no—
678C2×C3×C4—22no—
679C2×C3×C4—48no—
680C2×C3×C4—42no—
681C2×C3×C4C22×D412yes—
682C2×C3×C4C22×D411yescharacteristic
683C2×C3×C4C22×D412yes—
684C2×C3×C4H(5,𝔽2)12yes—
685C2×C3×C4C2511yescharacteristic
686#67—24no—
687#67—44no—
688#67—44no—
689#67—48no—
690#67—42no—
691#67—84no—
692#67—84no—
693#67—82no—
694C2×Dic3—22no—
695C2×Dic3—22no—
696C2×Dic3—21no—
697C2×Dic3—42no—
698C2×Dic3C22×D414yes—
699C2×Dic3C22×D412yes—
700D12—24no—
701D12—22no—
702D12—21no—
703D12—22no—
704D12—21no—
705D12—44no—
706D12—44no—
707D12C22×D414yes—
708C4×D3—22no—
709C4×D3—22no—
710C4×D3—44no—
711C4×D3—44no—
712C4×D3—48no—
713C4×D3—44no—
714C4×D3—42no—
715C4×D3—84no—
716Dic6—22no—
717Dic6—21no—
718Dic6—22no—
719Dic6—22no—
720Dic6—21no—
721Dic6—44no—
722Dic6—42no—
723C3×C8—22no—
724C3×C8—22no—
725C3⋊C8—22no—
726C3⋊C8C22×D412yes—
727C3⋊C8C22×D412yes—
728C24—21no—
729C24—62no—
730C24—61no—
731C24D3×D411yescharacteristic
732#41—28no—
733#41—22no—
734#41—22no—
735#41—44no—
736#41—48no—
737#41—68no—
738#41—62no—
739#41—62no—
740#41—64no—
741#41—64no—
742#41—62no—
743#41—62no—
744#41—124no—
745#41—128no—
746#41—128no—
747#41—124no—
748#41—122no—
749#41—122no—
750#41—124no—
751C2×Q8—21no—
752C2×Q8—22no—
753C2×Q8—31no—
754C2×Q8—31no—
755C2×Q8—32no—
756C2×Q8—62no—
757C2×Q8—61no—
758C2×Q8—64no—
759C2×Q8—62no—
760C2×Q8—62no—
761C2×Q8—122no—
762C2×Q8—124no—
763C2×Q8D3×D414yes—
764C2×Q8C23×D311yescharacteristic
765C2×Q8C23×D312yes—
766C2×D4—21no—
767C2×D4—24no—
768C2×D4—22no—
769C2×D4—22no—
770C2×D4—21no—
771C2×D4—22no—
772C2×D4—32no—
773C2×D4—34no—
774C2×D4—34no—
775C2×D4—31no—
776C2×D4—32no—
777C2×D4—31no—
778C2×D4—44no—
779C2×D4—62no—
780C2×D4—62no—
781C2×D4—62no—
782C2×D4—64no—
783C2×D4—64no—
784C2×D4—61no—
785C2×D4—64no—
786C2×D4—64no—
787C2×D4—62no—
788C2×D4—61no—
789C2×D4—62no—
790C2×D4—124no—
791C2×D4—122no—
792C2×D4—128no—
793C2×D4—124no—
794C2×D4C23×D311yescharacteristic
795C2×D4C23×D312yes—
796C22×C4—21no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—21no—
800C22×C4—24no—
801C22×C4—32no—
802C22×C4—44no—
803C22×C4—62no—
804C22×C4—62no—
805C22×C4—64no—
806C22×C4—62no—
807C22×C4—61no—
808C22×C4—64no—
809C22×C4—61no—
810C22×C4—124no—
811C22×C4D3×D412yes—
812C22×C4D3×D411yescharacteristic
813C22×C4C23×D312yes—
814C22×C4C23×D311yescharacteristic
815Q16—24no—
816Q16—62no—
817Q16—68no—
818Q16—122no—
819SD16—24no—
820SD16—38no—
821SD16—38no—
822SD16—42no—
823SD16—64no—
824SD16—62no—
825SD16—64no—
826SD16—64no—
827SD16—62no—
828SD16—122no—
829D8—42no—
830D8—64no—
831D8—62no—
832D8—68no—
833M16—22no—
834M16—22no—
835M16—64no—
836C2×C8—34no—
837C2×C8—31no—
838C2×C8—31no—
839C2×C8—32no—
840C2×C8—64no—
841C2×C8—64no—
842C2×C8—64no—
843C2×C8—62no—
844C2×C8C23×D312yes—
845C2×C8C23×D312yes—
846C4⋊C4—22no—
847C4⋊C4—34no—
848C4⋊C4—32no—
849C4⋊C4—32no—
850C4⋊C4—64no—
851C4⋊C4—64no—
852C4⋊C4—64no—
853C4⋊C4—62no—
854C4⋊C4C23×D312yes—
855C22⋊C4—21no—
856C22⋊C4—22no—
857C22⋊C4—22no—
858C22⋊C4—32no—
859C22⋊C4—34no—
860C22⋊C4—34no—
861C22⋊C4—64no—
862C22⋊C4—64no—
863C22⋊C4—64no—
864C22⋊C4—64no—
865C22⋊C4—64no—
866C22⋊C4—61no—
867C22⋊C4—62no—
868C22⋊C4—62no—
869C42—21no—
870C42—32no—
871C42—64no—
872C42—61no—
873C22×C3—22no—
874C22×C3—22no—
875C22×C3—22no—
876C22×C3—22no—
877C22×C3—44no—
878C22×C3—44no—
879C22×C3—42no—
880C22×C3—41no—
881C22×C3—42no—
882C22×C3—84no—
883C22×C3D4212yes—
884C22×C3C23×D411yescharacteristic
885C2×D3—24no—
886C2×D3—22no—
887C2×D3—24no—
888C2×D3—44no—
889C2×D3—42no—
890C2×D3—41no—
891C2×D3—84no—
892C2×D3—164no—
893C3×C4—24no—
894C3×C4—22no—
895C3×C4—42no—
896C3×C4—41no—
897C3×C4D4212yes—
898C3×C4C23×D411yescharacteristic
899C3×C4C2×H(5,𝔽2)11yescharacteristic
900Dic3—24no—
901Dic3—22no—
902Dic3—42no—
903Dic3—41no—
904Dic3—42no—
905C23—22no—
906C23—21no—
907C23—22no—
908C23—32no—
909C23—42no—
910C23—42no—
911C23—62no—
912C23—64no—
913C23—61no—
914C23—82no—
915C23—124no—
916C23—242no—
917C23—244no—
918C23C2×D3×D412yes—
919C23C2×D3×D411yescharacteristic
920Q8—22no—
921Q8—24no—
922Q8—21no—
923Q8—21no—
924Q8—62no—
925Q8—61no—
926Q8—62no—
927Q8—62no—
928Q8—61no—
929Q8—124no—
930Q8—122no—
931Q8C2×D3×D414yes—
932D4—22no—
933D4—21no—
934D4—21no—
935D4—22no—
936D4—34no—
937D4—48no—
938D4—42no—
939D4—42no—
940D4—64no—
941D4—61no—
942D4—62no—
943D4—61no—
944D4—64no—
945D4—62no—
946D4—82no—
947D4—124no—
948D4—124no—
949D4—124no—
950D4—124no—
951D4—128no—
952D4—122no—
953D4—244no—
954D4—242no—
955D4—244no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—24no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—24no—
962C2×C4—22no—
963C2×C4—21no—
964C2×C4—34no—
965C2×C4—32no—
966C2×C4—48no—
967C2×C4—42no—
968C2×C4—62no—
969C2×C4—62no—
970C2×C4—62no—
971C2×C4—61no—
972C2×C4—62no—
973C2×C4—124no—
974C2×C4—128no—
975C2×C4—124no—
976C2×C4—124no—
977C2×C4—122no—
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×C3—82no—
994C2×C3C2×D4211yescharacteristic
995C2×C3#358412yes—
996D3—42no—
997D3—44no—
998D3—81no—
999C22—22no—
1000C22—22no—
1001C22—22no—
1002C22—22no—
1003C22—44no—
1004C22—42no—
1005C22—41no—
1006C22—42no—
1007C22—44no—
1008C22—62no—
1009C22—64no—
1010C22—64no—
1011C22—84no—
1012C22—124no—
1013C22—121no—
1014C22—122no—
1015C22—244no—
1016C22—484no—
1017C22#559012yes—
1018C22C22×D3×D411yescharacteristic
1019C4—22no—
1020C4—24no—
1021C4—41no—
1022C4—42no—
1023C4—62no—
1024C4—64no—
1025C4—122no—
1026C4—121no—
1027C4—122no—
1028C4#559012yes—
1029C4C22×D3×D411yescharacteristic
1030C4C2×#100411yescharacteristic
1031C3#6105211yescharacteristic, complemented, Sylow
1032C2—22no—
1033C2—42no—
1034C2—82no—
1035C2—81no—
1036C2—122no—
1037C2—124no—
1038C2—241no—
1039C2C2×#559011yescharacteristic
1040C2#8719912yes—
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3005C2
socleC22×C3C23×D4
hypercenter#3005D3
hypocenterC3#61052
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. #87274C2semidirect
2. C22×#950C2semidirect
3. C2×#5778C2semidirect
4. #86040C2semidirect
5. C3×#3005C2semidirect
6. #83970C2semidirect
7. #83947C2semidirect
8. #83939C2semidirect
9. #82922C2semidirect
10. #80270C2semidirect
11. #80267C2semidirect
12. #80126C2semidirect
13. #80123C2semidirect
14. #78961C2semidirect
15. #78947C2semidirect
16. #78944C2semidirect
17. #78931C2semidirect
18. #78638C2semidirect
19. #78626C2semidirect
21. C22×C3×#41C22semidirect
29. #5834C22semidirect
31. #5831C22semidirect
35. C2×#950C22semidirect
36. C2×#950C22semidirect
37. #5812C22semidirect
38. C22×#216C22semidirect
42. #5805C22semidirect
43. C22×#214C22semidirect
47. #5791C22semidirect
48. C23×C3⋊C8C22semidirect
50. C2×#919C22semidirect
51. C2×#918C22semidirect
52. C2×#914C22semidirect
53. C2×D3×SD16C22semidirect
54. C2×#909C22semidirect
58. #5631C22semidirect
59. #5612C22semidirect
65. C3×#452C22semidirect
66. C3×#449C22semidirect
67. C3×#419C22semidirect
68. C3×#418C22semidirect
69. C3×#407C22semidirect
71. #5182C22semidirect
72. #5175C22semidirect
73. #5172C22semidirect
74. #5167C22semidirect
75. #5166C22semidirect
76. #5156C22semidirect
77. #5155C22semidirect
78. #5154C22semidirect
81. #5122C22semidirect
82. #5120C22semidirect
83. #5119C22semidirect
84. #5051C22semidirect
85. #5048C22semidirect
86. #5041C22semidirect
87. #5038C22semidirect
88. #5002C22semidirect
89. #4998C22semidirect
90. #4817C22semidirect
91. #4809C22semidirect
92. #4808C22semidirect
93. #4788C22semidirect
94. #4787C22semidirect
95. #4786C22semidirect
96. #4780C22semidirect
97. #4778C22semidirect
98. #4734C22semidirect
99. #4733C22semidirect
100. #4730C22semidirect
101. #67⋊C8C22semidirect
118. #3005D3semidirect
182. C2×#215D4semidirect
272. C22×#41C2×D3semidirect
329. #452C2×D3semidirect
333. #449C2×D3semidirect
342. #419C2×D3semidirect
344. #418C2×D3semidirect
348. #407C2×D3semidirect
1031. C3#61052semidirect

Maximal subgroups

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

subgroupindex
#872742
C22×#9502
C2×#57782
#860402
C3×#30052
#839702
#839472
#839392
#829222
#802702
#802672
#801262
#801232
#789612
#789472
#789442
#789312
#786382
#786262
#610523