Finite Group Databasebeta

← #11670555

Subgroups — #11670555

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×#5775C211yesmaximal, characteristic, complemented
2C22×#912C211yesmaximal, characteristic, complemented
3#86315C211yesmaximal, characteristic, complemented
4#85858C211yesmaximal, characteristic, complemented
5C3×#3041C211yesmaximal, characteristic, complemented
6#83945C211yesmaximal, characteristic, complemented
7#83833C211yesmaximal, characteristic, complemented
8#83381C211yesmaximal, characteristic, complemented
9#82543C211yesmaximal, characteristic, complemented
10#80558C214yesmaximal, complemented
11#80554C214yesmaximal, complemented
12#80351C214yesmaximal, complemented
13#80348C214yesmaximal, complemented
14#79100C211yesmaximal, characteristic, complemented
15#79073C211yesmaximal, characteristic, complemented
16#78931C211yesmaximal, characteristic, complemented
17#78927C211yesmaximal, characteristic, complemented
18#78838C211yesmaximal, characteristic, complemented
19#78837C211yesmaximal, characteristic, complemented
20#61052—31nomaximal, Sylow
21C2×#1010C2211yescharacteristic
22C2×#1004C2211yescharacteristic
23C22×#237C2211yescharacteristic
24C22×#237C2211yescharacteristic, complemented
25C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
26C22×C3×D8C2211yescharacteristic
27C3×#535C2211yescharacteristic, complemented
28C3×#518C2211yescharacteristic
29#5828C2211yescharacteristic, complemented
30C2×#951C2211yescharacteristic, complemented
31C2×#950C2211yescharacteristic
32#5805C2211yescharacteristic
33C22×#214C2211yescharacteristic
34C22×#214C2211yescharacteristic, complemented
35C2×#932C2211yescharacteristic
36#5775—28no—
37C2×#915C2212yescomplemented
38C2×D3×SD16C2212yescomplemented
39C2×#912—28no—
40C2×#912C2214yescomplemented
41C2×#912C2214yescomplemented
42C2×#912C2212yescomplemented
43C2×#911C2212yescomplemented
44C2×#909C2211yescharacteristic
45C2×#907C2211yescharacteristic
46C22×Dic12C2211yescharacteristic, complemented
47C22×D3×C8C2211yescharacteristic, complemented
48#5718C2214yescomplemented
49#5677C2214yescomplemented
50#5599—22no—
51#5598—22no—
52#5592—22no—
53#5586—22no—
54#5555—22no—
55#5555C2214yescomplemented
56#5554—22no—
57#5554C2214yescomplemented
58#5526C2211yescharacteristic
59#5526C2211yescharacteristic
60#5524C2211yescharacteristic
61#5524C2211yescharacteristic
62#5516C2211yescharacteristic, complemented
63#5493—22no—
64C2×#886—22no—
65C3×#463C2214yescomplemented
66C3×#459C2214yescomplemented
67C3×#424C2211yescharacteristic, complemented
68C3×#418C2211yescharacteristic, complemented
69C3×#416C2211yescharacteristic, complemented
70#5215C2211yescharacteristic
71#5173C2214yescomplemented
72#5158C2214yescomplemented
73#5158C2214yescomplemented
74#5156C2214yescomplemented
75#5126C2211yescharacteristic, complemented
76#5120C2211yescharacteristic, complemented
77#5113C2211yescharacteristic
78#5110C2211yescharacteristic
79#5076C2212yescomplemented
80#5074C2212yescomplemented
81#5060C2212yescomplemented
82#5059C2212yescomplemented
83#5018C2214yescomplemented
84C4×#214C2214yescomplemented
85#5004C2211yescharacteristic, complemented
86#4998C2211yescharacteristic, complemented
87#4997C2211yescharacteristic, complemented
88#4849C2214yescomplemented
89#4845C2214yescomplemented
90#4836C2214yescomplemented
91#4834C2214yescomplemented
92#4813C2212yescomplemented
93#4809C2214yescomplemented
94#4807C2212yescomplemented
95#4783C2214yescomplemented
96#4783C2214yescomplemented
97#4781C2214yescomplemented
98#4780C2214yescomplemented
99#4778C2214yescomplemented
100#4778C2212yescomplemented
101#4775C2212yescomplemented
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#3041D311yescharacteristic, complemented
115#3011—31no—
116#3008—31no—
117#3005—31no—
118#3005—31no—
119#2949—31no—
120#2929—31no—
121C2×C3×#41C2311yescharacteristic
122C22×C3×D4C2311yescharacteristic
123C22×C3×D4C2311yescharacteristic
124C22×#67—21no—
125C22×#67—21no—
126C22×#67—22no—
127C23×Dic3—21no—
128C23×Dic3—21no—
129#1010—24no—
130#1010—42no—
131C2×D3×Q8C2312yes—
132#1004—24no—
133#1004—42no—
134C2×#237—24no—
135C2×#237—22no—
136C2×#237—22no—
137C2×#237—22no—
138C2×#237—24no—
139C2×#237—21no—
140C2×#237—42no—
141C2×#237—42no—
142C2×#237C2312yes—
143C2×#237C2314yes—
144C2×#237C2314yes—
145C2×#237C2312yes—
146C2×D3×D4—21no—
147C2×D3×D4C2312yes—
148C2×#235—21no—
149C2×#235C2311yescharacteristic
150C2×#235C2311yescharacteristic
151C22×C4×D3C2311yescharacteristic
152C22×Dic6—21no—
153C22×Dic6C2311yescharacteristic
154C22×Dic6C2311yescharacteristic
155C3×AGL(1,ℤ/8)—24no—
156C2×C3×SD16C2312yes—
157C2×C3×D8—24no—
158C2×C3×D8C2314yes—
159C2×C3×D8C2312yes—
160C2×C3×M16C2311yescharacteristic
161C22×C3×C8C2311yescharacteristic
162C3×#127C2312yes—
163C3×#124C2312yes—
164C3×#121—22no—
165C3×#120—22no—
166C3×C4×D4—22no—
167C3×C4×D4C2314yes—
168C3×#117C2311yescharacteristic
169C3×#117C2311yescharacteristic
170C2×C3×C22⋊C4—22no—
171#953—22no—
172#951—42no—
173#950—24no—
174#946C2312yes—
175C2×#216C2311yescharacteristic
176C2×#216C2312yes—
177C2×#215C2311yescharacteristic
178#940—24no—
179#940—21no—
180#939—24no—
181#939—24no—
182#938C2314yes—
183#938C2312yes—
184#937—21no—
185#936—21no—
186#935—21no—
187D4×Dic3—24no—
188C2×#214—24no—
189C2×#214D418yescomplemented
190C2×#214C2312yes—
191C2×#214C2312yes—
192C2×#214C2311yescharacteristic
193C2×#214C2312yes—
194C2×#214C2312yes—
195C2×#214C2312yes—
196C2×#214C2312yes—
197#932—42no—
198C2×#213C2311yescharacteristic
199C2×#213C2312yes—
200#930—24no—
201#930—24no—
202C4×#67—22no—
203C2×(C2×D3)⋊C4—24no—
204#926C2311yescharacteristic
205C2×C4⋊Dic3—24no—
206C2×#208C2311yescharacteristic
207C22×C3⋊C8C2311yescharacteristic
208#915—28no—
209D3×SD16—28no—
210#912—216no—
211#912—216no—
212#912—28no—
213#911—28no—
214#909—24no—
215#907—24no—
216C2×Dic12—24no—
217C2×Dic12C2314yes—
218C2×Dic12C2312yes—
219C2×#204C2312yes—
220C2×ΓL(1,𝔽25)C2312yes—
221C2×D3×C8—24no—
222C2×D3×C8C2312yes—
223C2×D3×C8C2312yes—
224C2×D3×C8C2312yes—
225#897—22no—
226#897D412yes—
227#897C2312yes—
228#897C2314yes—
229#895D412yes—
230#895C2312yes—
231#887—22no—
232#886—22no—
233#886—21no—
234#886—22no—
235#886—24no—
236#886—24no—
237#886—24no—
238#886D412yes—
239#885—24no—
240#884—24no—
241#882—21no—
242#882—24no—
243#882D412yes—
244#67⋊C4—24no—
245#878—24no—
246#877—22no—
247#875—21no—
248#875C2312yes—
249C4×D12—22no—
250C4×D12C2314yes—
251#869—21no—
252#869C2312yes—
253C4×Dic6C2314yes—
254C3×C4⋊C8C2314yes—
255C3×#103C2312yes—
256C3×#102C2312yes—
257C3×#102C2314yes—
258#832C2314yes—
259#821C2312yes—
260(C2×D3)⋊C8C2314yes—
261(C2×D3)⋊C8C2314yes—
262#816C2314yes—
263#816C2312yes—
264#810C2314yes—
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×#137—31no—
277C2×AGL(1,ℤ/8)—31no—
278C2×AGL(1,ℤ/8)—32no—
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×D8C2×D311yescharacteristic
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—62no—
304#535C2×D311yescharacteristic, complemented
305#534—62no—
306#525—31no—
307#525—31no—
308#525—31no—
309#525—62no—
310C2×#123—62no—
311#519—31no—
312#518C2×D311yescharacteristic
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—34no—
322#465—32no—
323#464—34no—
324#463C2×D314yescomplemented
325#462—34no—
326#459C2×D314yescomplemented
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#419—31no—
343#418—31no—
344#418C2×D311yescharacteristic, complemented
345#416—31no—
346#416C2×D311yescharacteristic, complemented
347#408—31no—
348#407—31no—
349#405—31no—
350C24×C3—21no—
351C24×C3—21no—
352C23×D3—22no—
353C23×D3C2×D411yescharacteristic
354C3×#41—22no—
355C3×#41—22no—
356C2×C3×Q8C2411yescharacteristic
357C2×C3×D4—21no—
358C2×C3×D4—21no—
359C2×C3×D4—22no—
360C2×C3×D4—21no—
361C2×C3×D4—24no—
362C2×C3×D4—22no—
363C2×C3×D4—22no—
364C2×C3×D4C2×D414yes—
365C2×C3×D4C2412yes—
366C2×C3×D4C2411yescharacteristic
367C2×C3×D4C2412yes—
368C22×C3×C4—21no—
369C22×C3×C4—24no—
370C22×C3×C4C2411yescharacteristic
371C2×#67—21no—
372C2×#67—24no—
373C2×#67—24no—
374C2×#67—22no—
375C2×#67—22no—
376C2×#67—24no—
377C2×#67—22no—
378C2×#67—22no—
379C2×#67—44no—
380C2×#67—48no—
381C2×#67—44no—
382C2×#67C2×D412yes—
383C22×Dic3—21no—
384C22×Dic3—21no—
385C22×Dic3—24no—
386C22×Dic3—22no—
387C22×Dic3—24no—
388C22×Dic3—22no—
389C22×Dic3—44no—
390C22×Dic3—44no—
391C22×Dic3C2×D411yescharacteristic
392D3×Q8—24no—
393D3×Q8—42no—
394#237—28no—
395#237—24no—
396#237—24no—
397#237—28no—
398#237—44no—
399#237—44no—
400#237—42no—
401#237—42no—
402#237—48no—
403#237—44no—
404#237—48no—
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—44no—
414C2×D12—22no—
415C2×D12C2×D411yescharacteristic
416C2×D12C2×D414yes—
417C2×D12C2411yescharacteristic
418C2×C4×D3—22no—
419C2×C4×D3—22no—
420C2×C4×D3—22no—
421C2×C4×D3—21no—
422C2×C4×D3C2×D412yes—
423C2×C4×D3C2412yes—
424C2×C4×D3C2412yes—
425C2×Dic6—21no—
426C2×Dic6—22no—
427C2×Dic6—22no—
428C2×Dic6—22no—
429C2×Dic6—21no—
430C2×Dic6—22no—
431C2×Dic6—44no—
432C2×Dic6C2×D411yescharacteristic
433C2×Dic6C2×D414yes—
434C2×Dic6C2411yescharacteristic
435C2×Dic6C2412yes—
436C2×Dic6C2412yes—
437C3×SD16—24no—
438C3×D8—24no—
439C3×D8—28no—
440C3×M16—22no—
441C2×C3×C8—22no—
442C2×C3×C8C2412yes—
443C2×C3×C8C2412yes—
444C3×C4⋊C4C2×D412yes—
445C3×C4⋊C4C2412yes—
446C3×C22⋊C4—21no—
447C3×C22⋊C4—24no—
448C3×C22⋊C4—24no—
449C3×C22⋊C4C2×D412yes—
450C3×C42—21no—
451C3×C42C2412yes—
452#217—21no—
453#217—24no—
454#217—22no—
455#216—22no—
456#216—42no—
457#215—22no—
458#214—24no—
459#214—24no—
460#214—22no—
461#214—42no—
462#214—42no—
463#214C2×D418yes—
464#214C2×D418yes—
465#213—22no—
466#213—42no—
467(C2×D3)⋊C4—22no—
468(C2×D3)⋊C4—24no—
469(C2×D3)⋊C4—22no—
470(C2×D3)⋊C4—24no—
471(C2×D3)⋊C4—22no—
472(C2×D3)⋊C4C2×D414yes—
473(C2×D3)⋊C4C2×D414yes—
474C4⋊Dic3—24no—
475C4⋊Dic3—24no—
476C4⋊Dic3—22no—
477C4⋊Dic3C2×D414yes—
478C4⋊Dic3C2412yes—
479Dic3⋊C4—24no—
480Dic3⋊C4—22no—
481C4×Dic3—24no—
482C4×Dic3—21no—
483#208—22no—
484C2×C3⋊C8C2×D414yes—
485C2×C3⋊C8C2412yes—
486C2×C3⋊C8C2411yescharacteristic
487C2×C3⋊C8C2411yescharacteristic
488Dic12—28no—
489Dic12—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—61no—
506C2×#41—62no—
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—31no—
517C22×Q8—31no—
518C22×Q8—61no—
519C22×D4—32no—
520C22×D4—61no—
521C22×D4—62no—
522C22×D4—61no—
523C22×D4—61no—
524C22×D4C22×D311yescharacteristic
525C22×D4C22×D311yescharacteristic
526C23×C4—31no—
527C23×C4—61no—
528C23×C4—61no—
529#137—64no—
530#137—68no—
531#137—122no—
532AGL(1,ℤ/8)—24no—
533AGL(1,ℤ/8)—68no—
534AGL(1,ℤ/8)—122no—
535#135—64no—
536#135—616no—
537#135—616no—
538#135—68no—
539C2×Q16—31no—
540C2×Q16—32no—
541C2×Q16—34no—
542C2×Q16—32no—
543C2×Q16—64no—
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—32no—
554C2×SD16—64no—
555C2×SD16—68no—
556C2×SD16C22×D312yes—
557C2×D8—24no—
558C2×D8—31no—
559C2×D8—32no—
560C2×D8C22×D314yes—
561C2×D8C22×D312yes—
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—32no—
573C4⋊Q8—61no—
574#127—61no—
575#127—64no—
576#127C22×D312yes—
577#124—32no—
578#124—61no—
579#124—64no—
580#124—61no—
581#124C22×D312yes—
582#123—32no—
583#123—64no—
584#123—64no—
585#123—64no—
586#123—61no—
587#123—62no—
588#123—61no—
589#123—62no—
590C22⋊Q8—32no—
591C22⋊Q8—32no—
592C22⋊Q8—32no—
593C22⋊Q8—34no—
594C22⋊Q8—64no—
595C22⋊Q8—62no—
596#121—22no—
597#121—32no—
598#121—32no—
599#121—34no—
600#121—32no—
601#121—64no—
602#121—64no—
603#121—64no—
604#121—64no—
605#121—64no—
606#120—22no—
607#120—32no—
608#120—64no—
609#120—61no—
610#120—61no—
611#120—62no—
612C4×Q8—34no—
613C4×Q8—62no—
614C4×D4—22no—
615C4×D4—34no—
616C4×D4—62no—
617C4×D4—64no—
618C4×D4—64no—
619C4×D4—62no—
620C4×D4C22×D314yes—
621#117—31no—
622#117—62no—
623#117C22×D311yescharacteristic
624#117C22×D311yescharacteristic
625C2×C4⋊C4—64no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—64no—
628#107—32no—
629#106—32no—
630C4⋊C8C22×D314yes—
631#103—32no—
632#103—34no—
633#103—34no—
634#103C22×D312yes—
635#102—34no—
636#102—32no—
637#102C22×D312yes—
638#102C22×D314yes—
639C22⋊C8—34no—
640C22⋊C8—34no—
641#97—32no—
642C4×C8—32no—
643C23×C3—22no—
644C23×C3—24no—
645C23×C3—22no—
646C23×C3—21no—
647C23×C3—42no—
648C23×C3—82no—
649C23×C3—82no—
650C23×C3C22×D411yescharacteristic
651C22×D3—22no—
652C22×D3—21no—
653C22×D3—42no—
654C22×D3—44no—
655C22×D3—84no—
656C22×D3C22×D412yes—
657C22×D3C22×D412yes—
658C3×Q8—21no—
659C3×Q8—21no—
660C3×D4—24no—
661C3×D4—21no—
662C3×D4—22no—
663C3×D4—22no—
664C3×D4—22no—
665C3×D4—21no—
666C3×D4—42no—
667C3×D4—42no—
668C3×D4—84no—
669C3×D4C22×D414yes—
670C2×C3×C4—21no—
671C2×C3×C4—22no—
672C2×C3×C4—42no—
673C2×C3×C4—84no—
674C2×C3×C4C22×D414yes—
675C2×C3×C4C22×D411yescharacteristic
676C2×C3×C4C22×D412yes—
677C2×C3×C4H(5,𝔽2)12yes—
678C2×C3×C4C2511yescharacteristic
679#67—24no—
680#67—44no—
681#67—48no—
682#67—44no—
683#67—44no—
684#67—48no—
685#67—42no—
686#67—84no—
687#67—82no—
688C2×Dic3—24no—
689C2×Dic3—22no—
690C2×Dic3—22no—
691C2×Dic3—22no—
692C2×Dic3—21no—
693C2×Dic3—22no—
694C2×Dic3—44no—
695C2×Dic3—48no—
696C2×Dic3—48no—
697C2×Dic3—44no—
698C2×Dic3—42no—
699C2×Dic3C22×D412yes—
700C2×Dic3C22×D412yes—
701D12—22no—
702D12—21no—
703D12—21no—
704D12—44no—
705D12—82no—
706C4×D3—24no—
707C4×D3—22no—
708C4×D3—22no—
709C4×D3—22no—
710C4×D3—22no—
711C4×D3—44no—
712C4×D3—42no—
713Dic6—24no—
714Dic6—22no—
715Dic6—22no—
716Dic6—22no—
717Dic6—21no—
718Dic6—21no—
719Dic6—22no—
720Dic6—44no—
721Dic6—42no—
722Dic6C22×D414yes—
723C3×C8—22no—
724C3×C8—22no—
725C3⋊C8—22no—
726C3⋊C8C22×D412yes—
727C3⋊C8C22×D412yes—
728C24—21no—
729C24—21no—
730C24—31no—
731C24—62no—
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—124no—
743#41—124no—
744#41—124no—
745#41—122no—
746#41—122no—
747#41—128no—
748#41—128no—
749#41—128no—
750#41—124no—
751C2×Q8—31no—
752C2×Q8—34no—
753C2×Q8—32no—
754C2×Q8—32no—
755C2×Q8—31no—
756C2×Q8—62no—
757C2×Q8—61no—
758C2×Q8—61no—
759C2×Q8—62no—
760C2×Q8—64no—
761C2×Q8—62no—
762C2×Q8—62no—
763C2×Q8—124no—
764C2×Q8—122no—
765C2×Q8C23×D311yescharacteristic
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—22no—
769C2×D4—21no—
770C2×D4—24no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—32no—
774C2×D4—31no—
775C2×D4—34no—
776C2×D4—31no—
777C2×D4—62no—
778C2×D4—62no—
779C2×D4—64no—
780C2×D4—64no—
781C2×D4—62no—
782C2×D4—64no—
783C2×D4—62no—
784C2×D4—61no—
785C2×D4—64no—
786C2×D4—62no—
787C2×D4—122no—
788C2×D4—124no—
789C2×D4—124no—
790C2×D4—128no—
791C2×D4—124no—
792C2×D4D3×D414yes—
793C2×D4C23×D312yes—
794C2×D4C23×D311yescharacteristic
795C2×D4C23×D312yes—
796C22×C4—21no—
797C22×C4—24no—
798C22×C4—31no—
799C22×C4—32no—
800C22×C4—32no—
801C22×C4—32no—
802C22×C4—62no—
803C22×C4—64no—
804C22×C4—62no—
805C22×C4—62no—
806C22×C4—64no—
807C22×C4—61no—
808C22×C4—62no—
809C22×C4—62no—
810C22×C4—61no—
811C22×C4—61no—
812C22×C4—124no—
813C22×C4—124no—
814C22×C4C23×D311yescharacteristic
815Q16—68no—
816Q16—64no—
817Q16—62no—
818Q16—122no—
819SD16—24no—
820SD16—38no—
821SD16—38no—
822SD16—64no—
823SD16—64no—
824SD16—64no—
825SD16—62no—
826SD16—62no—
827SD16—122no—
828SD16—122no—
829D8—28no—
830D8—24no—
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—34no—
847C4⋊C4—32no—
848C4⋊C4—62no—
849C4⋊C4—64no—
850C4⋊C4—62no—
851C4⋊C4—64no—
852C4⋊C4—64no—
853C4⋊C4D3×D412yes—
854C4⋊C4C23×D312yes—
855C22⋊C4—21no—
856C22⋊C4—24no—
857C22⋊C4—24no—
858C22⋊C4—34no—
859C22⋊C4—34no—
860C22⋊C4—62no—
861C22⋊C4—64no—
862C22⋊C4—62no—
863C22⋊C4—62no—
864C22⋊C4—62no—
865C22⋊C4—64no—
866C22⋊C4—61no—
867C22⋊C4—64no—
868C22⋊C4D3×D412yes—
869C42—21no—
870C42—61no—
871C42—64no—
872C42C23×D312yes—
873C22×C3—22no—
874C22×C3—24no—
875C22×C3—44no—
876C22×C3—42no—
877C22×C3—44no—
878C22×C3—41no—
879C22×C3—42no—
880C22×C3—84no—
881C22×C3—84no—
882C22×C3D4212yes—
883C22×C3C23×D411yescharacteristic
884C2×D3—22no—
885C2×D3—24no—
886C2×D3—22no—
887C2×D3—22no—
888C2×D3—22no—
889C2×D3—44no—
890C2×D3—42no—
891C2×D3—41no—
892C2×D3—164no—
893C3×C4—24no—
894C3×C4—42no—
895C3×C4—41no—
896C3×C4D4212yes—
897C3×C4C23×D411yescharacteristic
898C3×C4C2×H(5,𝔽2)11yescharacteristic
899Dic3—24no—
900Dic3—22no—
901Dic3—22no—
902Dic3—42no—
903Dic3—42no—
904Dic3—41no—
905C23—22no—
906C23—24no—
907C23—22no—
908C23—21no—
909C23—32no—
910C23—32no—
911C23—42no—
912C23—62no—
913C23—61no—
914C23—82no—
915C23—82no—
916C23—122no—
917C23—124no—
918C23—244no—
919C23C2×D3×D411yescharacteristic
920Q8—21no—
921Q8—21no—
922Q8—34no—
923Q8—62no—
924Q8—64no—
925Q8—62no—
926Q8—62no—
927Q8—61no—
928Q8—61no—
929Q8—62no—
930Q8—124no—
931Q8—122no—
932D4—21no—
933D4—22no—
934D4—22no—
935D4—22no—
936D4—21no—
937D4—24no—
938D4—42no—
939D4—42no—
940D4—64no—
941D4—61no—
942D4—61no—
943D4—62no—
944D4—84no—
945D4—124no—
946D4—124no—
947D4—128no—
948D4—124no—
949D4—124no—
950D4—128no—
951D4—122no—
952D4—242no—
953D4—242no—
954D4—244no—
955D4C2×D3×D414yes—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—32no—
959C2×C4—32no—
960C2×C4—42no—
961C2×C4—62no—
962C2×C4—62no—
963C2×C4—64no—
964C2×C4—62no—
965C2×C4—62no—
966C2×C4—62no—
967C2×C4—62no—
968C2×C4—64no—
969C2×C4—62no—
970C2×C4—62no—
971C2×C4—61no—
972C2×C4—84no—
973C2×C4—124no—
974C2×C4—128no—
975C2×C4—124no—
976C2×C4—128no—
977C2×C4—124no—
978C2×C4—122no—
979C2×C4—122no—
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—44no—
992C2×C3—81no—
993C2×C3—82no—
994C2×C3C2×D4211yescharacteristic
995C2×C3#358412yes—
996D3—42no—
997D3—42no—
998D3—81no—
999C22—22no—
1000C22—24no—
1001C22—44no—
1002C22—42no—
1003C22—44no—
1004C22—41no—
1005C22—42no—
1006C22—62no—
1007C22—64no—
1008C22—62no—
1009C22—62no—
1010C22—62no—
1011C22—84no—
1012C22—84no—
1013C22—124no—
1014C22—122no—
1015C22—121no—
1016C22—484no—
1017C22#560912yes—
1018C22C22×D3×D411yescharacteristic
1019C4—24no—
1020C4—42no—
1021C4—41no—
1022C4—62no—
1023C4—62no—
1024C4—64no—
1025C4—122no—
1026C4—121no—
1027C4—122no—
1028C4#560912yes—
1029C4C22×D3×D411yescharacteristic
1030C4C2×#100911yescharacteristic
1031C3#6105211yescharacteristic, complemented, Sylow
1032C2—22no—
1033C2—44no—
1034C2—82no—
1035C2—81no—
1036C2—122no—
1037C2—122no—
1038C2—241no—
1039C2C2×#560911yescharacteristic
1040C2#8720312yes—
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3041C2
socleC22×C3C23×D4
hypercenter#3041D3
hypocenterC3#61052
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #117 ◁ #3041

Complements

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

NH ≅ G/Ntype
1. C2×#5775C2semidirect
2. C22×#912C2semidirect
3. #86315C2semidirect
4. #85858C2semidirect
5. C3×#3041C2semidirect
6. #83945C2semidirect
7. #83833C2semidirect
8. #83381C2semidirect
9. #82543C2semidirect
10. #80558C2semidirect
11. #80554C2semidirect
12. #80351C2semidirect
13. #80348C2semidirect
14. #79100C2semidirect
15. #79073C2semidirect
16. #78931C2semidirect
17. #78927C2semidirect
18. #78838C2semidirect
19. #78837C2semidirect
24. C22×#237C22semidirect
27. C3×#535C22semidirect
29. #5828C22semidirect
30. C2×#951C22semidirect
34. C22×#214C22semidirect
37. C2×#915C22semidirect
38. C2×D3×SD16C22semidirect
40. C2×#912C22semidirect
41. C2×#912C22semidirect
42. C2×#912C22semidirect
43. C2×#911C22semidirect
46. C22×Dic12C22semidirect
47. C22×D3×C8C22semidirect
48. #5718C22semidirect
49. #5677C22semidirect
55. #5555C22semidirect
57. #5554C22semidirect
62. #5516C22semidirect
65. C3×#463C22semidirect
66. C3×#459C22semidirect
67. C3×#424C22semidirect
68. C3×#418C22semidirect
69. C3×#416C22semidirect
71. #5173C22semidirect
72. #5158C22semidirect
73. #5158C22semidirect
74. #5156C22semidirect
75. #5126C22semidirect
76. #5120C22semidirect
79. #5076C22semidirect
80. #5074C22semidirect
81. #5060C22semidirect
82. #5059C22semidirect
83. #5018C22semidirect
84. C4×#214C22semidirect
85. #5004C22semidirect
86. #4998C22semidirect
87. #4997C22semidirect
88. #4849C22semidirect
89. #4845C22semidirect
90. #4836C22semidirect
91. #4834C22semidirect
92. #4813C22semidirect
93. #4809C22semidirect
94. #4807C22semidirect
95. #4783C22semidirect
96. #4783C22semidirect
97. #4781C22semidirect
98. #4780C22semidirect
99. #4778C22semidirect
100. #4778C22semidirect
101. #4775C22semidirect
114. #3041D3semidirect
189. C2×#214D4semidirect
304. #535C2×D3semidirect
324. #463C2×D3semidirect
326. #459C2×D3semidirect
340. #424C2×D3semidirect
344. #418C2×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
C2×#57752
C22×#9122
#863152
#858582
C3×#30412
#839452
#838332
#833812
#825432
#805582
#805542
#803512
#803482
#791002
#790732
#789312
#789272
#788382
#788372
#610523