Finite Group Databasebeta

← #11670553

Subgroups — #11670553

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#87273C211yesmaximal, characteristic, complemented
2C22×#950C211yesmaximal, characteristic, complemented
3C2×#5775C211yesmaximal, characteristic, complemented
4#86023C211yesmaximal, characteristic, complemented
5C3×#3005C211yesmaximal, characteristic, complemented
6#83983C211yesmaximal, characteristic, complemented
7#83974C211yesmaximal, characteristic, complemented
8#83934C211yesmaximal, characteristic, complemented
9#82922C211yesmaximal, characteristic, complemented
10#80272C214yesmaximal, complemented
11#80244C214yesmaximal, complemented
12#80130C214yesmaximal, complemented
13#80128C214yesmaximal, complemented
14#78977C211yesmaximal, characteristic, complemented
15#78963C211yesmaximal, characteristic, complemented
16#78928C211yesmaximal, characteristic, complemented
17#78916C211yesmaximal, characteristic, complemented
18#78638C211yesmaximal, characteristic, complemented
19#78626C211yesmaximal, characteristic, complemented
20#61052—31nomaximal, Sylow
21C22×C3×#41C2211yescharacteristic
22C2×#1010C2211yescharacteristic
23C2×#1004C2211yescharacteristic
24C22×#235C2211yescharacteristic, complemented
25C2×C3×#137C2211yescharacteristic, complemented
26C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
27C3×#525C2211yescharacteristic, complemented
28#5830C2211yescharacteristic, complemented
29#5829—22no—
30#5829C2214yescomplemented
31#5824—22no—
32#5824C2214yescomplemented
33C2×#950—28no—
34C2×#950C2211yescharacteristic
35C2×#950C2214yescomplemented
36C2×#950C2214yescomplemented
37#5816C2211yescharacteristic
38#5816C2211yescharacteristic
39C22×#216C2211yescharacteristic, complemented
40C22×#215C2211yescharacteristic, complemented
41#5804—22no—
42#5798C2211yescharacteristic
43C22×#214C2211yescharacteristic
44C22×#213C2211yescharacteristic
45#5791C2211yescharacteristic
46#5791C2211yescharacteristic
47C2×#929—22no—
48C23×C3⋊C8C2211yescharacteristic, complemented
49#5775—28no—
50C2×#915C2212yescomplemented
51C2×D3×SD16C2212yescomplemented
52C2×#912C2212yescomplemented
53C2×#911C2212yescomplemented
54C2×#909C2211yescharacteristic
55C2×#908C2211yescharacteristic
56C2×#907C2211yescharacteristic
57#5656—22no—
58#5633C2214yescomplemented
59#5599C2214yescomplemented
60#5592—22no—
61#5553—22no—
62#5552—22no—
63#5525C2211yescharacteristic
64#5516C2211yescharacteristic, complemented
65C3×#452C2214yescomplemented
66C3×#449C2214yescomplemented
67C3×#419C2211yescharacteristic, complemented
68C3×#418C2211yescharacteristic
69C3×#407C2211yescharacteristic, complemented
70#5233C2211yescharacteristic, complemented
71#5191C2212yescomplemented
72#5190C2212yescomplemented
73#5186C2214yescomplemented
74#5176C2212yescomplemented
75#5175C2212yescomplemented
76#5173C2214yescomplemented
77#5165C2214yescomplemented
78#5150C2214yescomplemented
79#5131C2211yescharacteristic, complemented
80#5129C2211yescharacteristic
81#5122C2211yescharacteristic, complemented
82#5120C2211yescharacteristic, complemented
83#5119C2211yescharacteristic, complemented
84#5051C2212yescomplemented
85#5048C2212yescomplemented
86#5041C2212yescomplemented
87#5038C2212yescomplemented
88#5002C2211yescharacteristic
89#4998C2211yescharacteristic, complemented
90#4812C2214yescomplemented
91#4807C2214yescomplemented
92#4798C2214yescomplemented
93#4795C2214yescomplemented
94#4781C2214yescomplemented
95#4773C2214yescomplemented
96#4758C2214yescomplemented
97#4757C2214yescomplemented
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—
132C22×#67—22no—
133#1010—24no—
134#1010—42no—
135C2×D3×Q8C2312yes—
136#1004—24no—
137#1004—42no—
138C2×#237—22no—
139C2×#237—21no—
140C2×#237C2312yes—
141C2×#237C2312yes—
142C2×D3×D4—21no—
143C2×D3×D4C2312yes—
144C2×#235—22no—
145C2×#235—21no—
146C2×#235—24no—
147C2×#235—42no—
148C2×#235C2311yescharacteristic
149C2×#235C2311yescharacteristic
150C2×#235C2314yes—
151C22×D12C2311yescharacteristic
152C22×C4×D3—21no—
153C22×Dic6—21no—
154C22×Dic6C2311yescharacteristic
155C3×#137—42no—
156C3×AGL(1,ℤ/8)—24no—
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#953D412yes—
171C2×#217—22no—
172#950—216no—
173#950—216no—
174#950—24no—
175#947—21no—
176#947C2312yes—
177#947C2312yes—
178#946—22no—
179#946C2314yes—
180#944—21no—
181#944C2312yes—
182C2×#216—24no—
183C2×#216C2314yes—
184C2×#216C2311yescharacteristic
185C2×#215—24no—
186C2×#215C2312yes—
187C2×#215C2312yes—
188C2×#215C2311yescharacteristic
189#940—24no—
190#940C2312yes—
191#939—24no—
192#939—24no—
193#939—24no—
194#937—24no—
195#937—22no—
196#935—24no—
197D4×Dic3—22no—
198D4×Dic3C2314yes—
199C2×#214D418yescomplemented
200C2×#214C2311yescharacteristic
201C2×#214C2312yes—
202C2×#214C2312yes—
203C2×#213—24no—
204C2×#213C2314yes—
205C2×#213C2311yescharacteristic
206#930—22no—
207#930D412yes—
208#930C2312yes—
209#929—21no—
210#929—22no—
211#929—22no—
212#929—24no—
213#929—24no—
214#929D412yes—
215C4×#67—22no—
216C4×#67C2314yes—
217C2×(C2×D3)⋊C4—24no—
218#926C2311yescharacteristic
219#926C2311yescharacteristic
220#924D412yes—
221#924C2312yes—
222C2×Dic3⋊C4—24no—
223C22×C3⋊C8—24no—
224C22×C3⋊C8C2311yescharacteristic
225C22×C3⋊C8C2312yes—
226C22×C3⋊C8C2312yes—
227C22×C3⋊C8C2311yescharacteristic
228#915—28no—
229D3×SD16—28no—
230#912—28no—
231#911—28no—
232#909—24no—
233#908—42no—
234#907—24no—
235C2×Dic12C2312yes—
236C2×D24C2312yes—
237C2×#204C2312yes—
238C2×#204C2312yes—
239C2×ΓL(1,𝔽25)C2312yes—
240C2×D3×C8C2312yes—
241#896—24no—
242#895C2314yes—
243#893—24no—
244#887C2314yes—
245#885—24no—
246#884—24no—
247#884—24no—
248#882—22no—
249#67⋊C4—24no—
250#877—22no—
251#875—21no—
252#874—21no—
253C4×Dic6—22no—
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
273#577—68no—
274C2×#137—32no—
275C2×#137—31no—
276C2×#137C2×D311yescharacteristic, complemented
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, complemented
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
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×Q8—22no—
362C2×C3×Q8C2411yescharacteristic
363C2×C3×Q8C2412yes—
364C2×C3×D4—24no—
365C2×C3×D4—21no—
366C2×C3×D4—22no—
367C2×C3×D4—21no—
368C2×C3×D4—22no—
369C2×C3×D4—44no—
370C2×C3×D4C2×D414yes—
371C2×C3×D4C2411yescharacteristic
372C2×C3×D4C2412yes—
373C22×C3×C4—22no—
374C22×C3×C4—22no—
375C22×C3×C4—21no—
376C22×C3×C4—24no—
377C22×C3×C4—21no—
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—22no—
387C2×#67—22no—
388C2×#67—22no—
389C2×#67—24no—
390C2×#67—44no—
391C2×#67—48no—
392C2×#67C2×D412yes—
393C2×#67C2×D414yes—
394C22×Dic3—21no—
395C22×Dic3—22no—
396C22×Dic3—22no—
397C22×Dic3—24no—
398D3×Q8—24no—
399D3×Q8—42no—
400#237—24no—
401#237—24no—
402#237—42no—
403#237—42no—
404#237—44no—
405#237—48no—
406D3×D4—24no—
407D3×D4—42no—
408D3×D4—44no—
409#235—22no—
410#235—22no—
411#235—22no—
412#235—22no—
413#235—28no—
414#235—44no—
415#235—44no—
416#235—48no—
417C2×D12—22no—
418C2×D12—22no—
419C2×D12—21no—
420C2×D12—24no—
421C2×D12C2×D411yescharacteristic
422C2×D12C2411yescharacteristic
423C2×D12C2412yes—
424C2×C4×D3—22no—
425C2×C4×D3—24no—
426C2×C4×D3—21no—
427C2×C4×D3—44no—
428C2×C4×D3C2412yes—
429C2×Dic6—21no—
430C2×Dic6—22no—
431C2×Dic6—22no—
432C2×Dic6—44no—
433C2×Dic6C2×D411yescharacteristic
434C2×Dic6C2×D414yes—
435C2×Dic6C2411yescharacteristic
436C2×Dic6C2412yes—
437C3×Q16—42no—
438C3×SD16—24no—
439C3×SD16—42no—
440C3×D8—24no—
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#217C2×D412yes—
455#217C2×D414yes—
456#216—28no—
457#216—22no—
458#215—22no—
459#215—24no—
460#215—24no—
461#214—22no—
462#214C2×D418yes—
463#214C2×D418yes—
464#213—28no—
465#213—22no—
466(C2×D3)⋊C4—24no—
467(C2×D3)⋊C4—22no—
468(C2×D3)⋊C4—24no—
469(C2×D3)⋊C4—24no—
470(C2×D3)⋊C4—24no—
471(C2×D3)⋊C4C2×D414yes—
472C4⋊Dic3C2×D412yes—
473C4⋊Dic3C2412yes—
474Dic3⋊C4—22no—
475Dic3⋊C4—24no—
476Dic3⋊C4—24no—
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—24no—
490D24—42no—
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—61no—
508C2×#41—64no—
509C2×#41—62no—
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—42no—
530#137—64no—
531#137—68no—
532AGL(1,ℤ/8)—24no—
533AGL(1,ℤ/8)—68no—
534AGL(1,ℤ/8)—122no—
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—32no—
549C2×SD16—32no—
550C2×SD16—31no—
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—62no—
585#123—64no—
586#123—64no—
587#123—64no—
588#123—62no—
589#123—61no—
590C22⋊Q8—32no—
591C22⋊Q8—34no—
592C22⋊Q8—32no—
593C22⋊Q8—64no—
594C22⋊Q8—62no—
595C22⋊Q8C22×D312yes—
596#121—32no—
597#121—32no—
598#121—34no—
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—62no—
610#120—64no—
611#120—61no—
612C4×Q8—34no—
613C4×Q8—62no—
614C4×D4—22no—
615C4×D4—34no—
616C4×D4—34no—
617C4×D4—64no—
618C4×D4—64no—
619C4×D4—62no—
620C4×D4—62no—
621#117—31no—
622#117—31no—
623#117—62no—
624#117C22×D311yescharacteristic
625C2×C4⋊C4—64no—
626C2×C22⋊C4—64no—
627C2×C22⋊C4—62no—
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—22no—
645C23×C3—24no—
646C23×C3—21no—
647C23×C3—42no—
648C23×C3—82no—
649C23×C3C22×D412yes—
650C23×C3C22×D411yescharacteristic
651C22×D3—21no—
652C22×D3—22no—
653C22×D3—44no—
654C22×D3—42no—
655C22×D3—84no—
656C22×D3—82no—
657C22×D3C22×D412yes—
658C3×Q8—22no—
659C3×Q8—21no—
660C3×Q8—22no—
661C3×Q8—21no—
662C3×Q8—42no—
663C3×D4—24no—
664C3×D4—21no—
665C3×D4—22no—
666C3×D4—21no—
667C3×D4—48no—
668C3×D4—42no—
669C3×D4—82no—
670C3×D4C22×D414yes—
671C2×C3×C4—22no—
672C2×C3×C4—24no—
673C2×C3×C4—22no—
674C2×C3×C4—22no—
675C2×C3×C4—22no—
676C2×C3×C4—22no—
677C2×C3×C4—21no—
678C2×C3×C4—48no—
679C2×C3×C4—42no—
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—44no—
691#67—44no—
692#67—42no—
693#67—84no—
694#67—82no—
695C2×Dic3—24no—
696C2×Dic3—22no—
697C2×Dic3—22no—
698C2×Dic3—21no—
699C2×Dic3—44no—
700C2×Dic3—44no—
701C2×Dic3—84no—
702C2×Dic3C22×D414yes—
703C2×Dic3C22×D412yes—
704D12—22no—
705D12—21no—
706D12—22no—
707D12—22no—
708D12—21no—
709D12—42no—
710D12—84no—
711C4×D3—22no—
712C4×D3—22no—
713C4×D3—48no—
714C4×D3—44no—
715C4×D3—42no—
716Dic6—24no—
717Dic6—22no—
718Dic6—22no—
719Dic6—21no—
720Dic6—21no—
721Dic6—44no—
722Dic6C22×D414yes—
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—124no—
747#41—122no—
748#41—122no—
749#41—128no—
750#41—124no—
751C2×Q8—21no—
752C2×Q8—22no—
753C2×Q8—22no—
754C2×Q8—31no—
755C2×Q8—34no—
756C2×Q8—32no—
757C2×Q8—31no—
758C2×Q8—62no—
759C2×Q8—61no—
760C2×Q8—62no—
761C2×Q8—64no—
762C2×Q8—124no—
763C2×Q8—122no—
764C2×Q8C23×D311yescharacteristic
765C2×Q8C23×D312yes—
766C2×D4—21no—
767C2×D4—24no—
768C2×D4—22no—
769C2×D4—21no—
770C2×D4—22no—
771C2×D4—32no—
772C2×D4—34no—
773C2×D4—31no—
774C2×D4—31no—
775C2×D4—32no—
776C2×D4—44no—
777C2×D4—64no—
778C2×D4—62no—
779C2×D4—64no—
780C2×D4—64no—
781C2×D4—62no—
782C2×D4—62no—
783C2×D4—61no—
784C2×D4—64no—
785C2×D4—62no—
786C2×D4—62no—
787C2×D4—61no—
788C2×D4—62no—
789C2×D4—122no—
790C2×D4—124no—
791C2×D4—124no—
792C2×D4—128no—
793C2×D4D3×D414yes—
794C2×D4C23×D311yescharacteristic
795C2×D4C23×D312yes—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—21no—
799C22×C4—24no—
800C22×C4—21no—
801C22×C4—32no—
802C22×C4—44no—
803C22×C4—62no—
804C22×C4—62no—
805C22×C4—62no—
806C22×C4—64no—
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—42no—
816Q16—64no—
817Q16—62no—
818Q16—68no—
819SD16—24no—
820SD16—38no—
821SD16—38no—
822SD16—42no—
823SD16—64no—
824SD16—62no—
825SD16—62no—
826SD16—64no—
827SD16—64no—
828SD16—122no—
829D8—24no—
830D8—62no—
831D8—68no—
832D8—122no—
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—24no—
877C22×C3—22no—
878C22×C3—44no—
879C22×C3—44no—
880C22×C3—42no—
881C22×C3—41no—
882C22×C3—84no—
883C22×C3D4212yes—
884C22×C3C23×D411yescharacteristic
885C2×D3—24no—
886C2×D3—22no—
887C2×D3—44no—
888C2×D3—42no—
889C2×D3—42no—
890C2×D3—41no—
891C2×D3—84no—
892C2×D3—164no—
893C3×C4—22no—
894C3×C4—42no—
895C3×C4—41no—
896C3×C4—42no—
897C3×C4D4212yes—
898C3×C4C23×D411yescharacteristic
899C3×C4C2×H(5,𝔽2)11yescharacteristic
900Dic3—24no—
901Dic3—24no—
902Dic3—22no—
903Dic3—42no—
904Dic3—41no—
905C23—22no—
906C23—22no—
907C23—24no—
908C23—21no—
909C23—32no—
910C23—42no—
911C23—61no—
912C23—62no—
913C23—82no—
914C23—124no—
915C23—122no—
916C23—242no—
917C23—244no—
918C23C2×D3×D412yes—
919C23C2×D3×D411yescharacteristic
920Q8—21no—
921Q8—22no—
922Q8—22no—
923Q8—21no—
924Q8—34no—
925Q8—42no—
926Q8—62no—
927Q8—64no—
928Q8—62no—
929Q8—61no—
930Q8—61no—
931Q8—124no—
932D4—21no—
933D4—22no—
934D4—21no—
935D4—24no—
936D4—48no—
937D4—42no—
938D4—64no—
939D4—62no—
940D4—61no—
941D4—61no—
942D4—62no—
943D4—62no—
944D4—82no—
945D4—124no—
946D4—124no—
947D4—128no—
948D4—124no—
949D4—124no—
950D4—122no—
951D4—122no—
952D4—244no—
953D4—244no—
954D4—242no—
955D4C2×D3×D414yes—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—24no—
960C2×C4—22no—
961C2×C4—21no—
962C2×C4—22no—
963C2×C4—34no—
964C2×C4—32no—
965C2×C4—48no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—62no—
969C2×C4—64no—
970C2×C4—62no—
971C2×C4—62no—
972C2×C4—62no—
973C2×C4—61no—
974C2×C4—128no—
975C2×C4—124no—
976C2×C4—124no—
977C2×C4—124no—
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—44no—
992C2×C3—42no—
993C2×C3—81no—
994C2×C3C2×D4211yescharacteristic
995C2×C3#358412yes—
996D3—42no—
997D3—82no—
998D3—81no—
999C22—22no—
1000C22—22no—
1001C22—24no—
1002C22—22no—
1003C22—22no—
1004C22—44no—
1005C22—44no—
1006C22—41no—
1007C22—42no—
1008C22—62no—
1009C22—64no—
1010C22—84no—
1011C22—122no—
1012C22—121no—
1013C22—124no—
1014C22—122no—
1015C22—244no—
1016C22—484no—
1017C22#559012yes—
1018C22C22×D3×D411yescharacteristic
1019C4—22no—
1020C4—42no—
1021C4—41no—
1022C4—42no—
1023C4—62no—
1024C4—64no—
1025C4—64no—
1026C4—121no—
1027C4—122no—
1028C4#559012yes—
1029C4C22×D3×D411yescharacteristic
1030C4C2×#100411yescharacteristic
1031C3#6105211yescharacteristic, complemented, Sylow
1032C2—22no—
1033C2—42no—
1034C2—44no—
1035C2—81no—
1036C2—122no—
1037C2—242no—
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. #87273C2semidirect
2. C22×#950C2semidirect
3. C2×#5775C2semidirect
4. #86023C2semidirect
5. C3×#3005C2semidirect
6. #83983C2semidirect
7. #83974C2semidirect
8. #83934C2semidirect
9. #82922C2semidirect
10. #80272C2semidirect
11. #80244C2semidirect
12. #80130C2semidirect
13. #80128C2semidirect
14. #78977C2semidirect
15. #78963C2semidirect
16. #78928C2semidirect
17. #78916C2semidirect
18. #78638C2semidirect
19. #78626C2semidirect
24. C22×#235C22semidirect
25. C2×C3×#137C22semidirect
27. C3×#525C22semidirect
28. #5830C22semidirect
30. #5829C22semidirect
32. #5824C22semidirect
35. C2×#950C22semidirect
36. C2×#950C22semidirect
39. C22×#216C22semidirect
40. C22×#215C22semidirect
48. C23×C3⋊C8C22semidirect
50. C2×#915C22semidirect
51. C2×D3×SD16C22semidirect
52. C2×#912C22semidirect
53. C2×#911C22semidirect
58. #5633C22semidirect
59. #5599C22semidirect
64. #5516C22semidirect
65. C3×#452C22semidirect
66. C3×#449C22semidirect
67. C3×#419C22semidirect
69. C3×#407C22semidirect
70. #5233C22semidirect
71. #5191C22semidirect
72. #5190C22semidirect
73. #5186C22semidirect
74. #5176C22semidirect
75. #5175C22semidirect
76. #5173C22semidirect
77. #5165C22semidirect
78. #5150C22semidirect
79. #5131C22semidirect
81. #5122C22semidirect
82. #5120C22semidirect
83. #5119C22semidirect
84. #5051C22semidirect
85. #5048C22semidirect
86. #5041C22semidirect
87. #5038C22semidirect
89. #4998C22semidirect
90. #4812C22semidirect
91. #4807C22semidirect
92. #4798C22semidirect
93. #4795C22semidirect
94. #4781C22semidirect
95. #4773C22semidirect
96. #4758C22semidirect
97. #4757C22semidirect
98. #4734C22semidirect
99. #4733C22semidirect
100. #4730C22semidirect
101. #67⋊C8C22semidirect
118. #3005D3semidirect
199. C2×#214D4semidirect
276. C2×#137C2×D3semidirect
309. #525C2×D3semidirect
329. #452C2×D3semidirect
333. #449C2×D3semidirect
342. #419C2×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
#872732
C22×#9502
C2×#57752
#860232
C3×#30052
#839832
#839742
#839342
#829222
#802722
#802442
#801302
#801282
#789772
#789632
#789282
#789162
#786382
#786262
#610523