Finite Group Databasebeta

← #11664271

Subgroups — #11664271

Order 768.

2130 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86205C211yesmaximal, characteristic, complemented
2C4×#1004C211yesmaximal, characteristic, complemented
3C2×C3×#474C211yesmaximal, characteristic, complemented
4#83212C211yesmaximal, characteristic, complemented
5#82307C211yesmaximal, characteristic, complemented
6#80953C214yesmaximal, complemented
7#80952C214yesmaximal, complemented
8#80951C212yesmaximal, complemented
9#80950C212yesmaximal, complemented
10#80949C212yesmaximal, complemented
11#80948C212yesmaximal, complemented
12#79141C212yesmaximal, complemented
13#79136C212yesmaximal, complemented
14#79021C211yesmaximal, characteristic, complemented
15#79000C211yesmaximal, characteristic, complemented
16#78747C212yesmaximal, complemented
17#78726C212yesmaximal, complemented
18#60596—31nomaximal, Sylow
19C2×#1004C2211yescharacteristic
20C2×C3×C4⋊Q8C2211yescharacteristic, complemented
21C2×C3×C4×D4C2211yescharacteristic
22#5817—22no—
23#5798C2211yescharacteristic
24C2×#932C2212yes—
25C2×C4×#67—22no—
26C2×#904C2212yes—
27#5734—21no—
28#5733C2214yescomplemented
29#5732—21no—
30#5730—21no—
31#5728C2212yescomplemented
32#5726—21no—
33#5725C2212yescomplemented
34#5546—21no—
35#5546C2212yes—
36#5545—21no—
37#5545C2212yes—
38C4×D3×D4—21no—
39C4×D3×D4C2212yes—
40C4×#237—21no—
41C4×#237C2212yes—
42#5514—22no—
43#5510C2212yes—
44#5504C2211yescharacteristic
45#5504C2211yescharacteristic
46#5504C2212yescomplemented
47#5486—22no—
48#5477C2211yescharacteristic, complemented
49C4×#235C2211yescharacteristic
50C4×#235C2211yescharacteristic
51C3×#474C2212yescomplemented
52C3×#474C2212yescomplemented
53C3×#474C2214yescomplemented
54C2×C3×#107C2212yescomplemented
55C2×C3×C4⋊C8C2211yescharacteristic, complemented
56C2×C3×#102C2212yes—
57#5113C2212yescomplemented
58#5110C2212yes—
59#5101C2212yescomplemented
60#5094C2212yescomplemented
61#5091C2212yescomplemented
62#5087C2212yescomplemented
63#5084C2212yescomplemented
64#5019C2212yescomplemented
65#5016C2214yescomplemented
66#5015C2212yescomplemented
67#4966C2212yes—
68#4966C2212yescomplemented
69#4964C2212yescomplemented
70#4924C2211yescharacteristic, complemented
71#4889C2214yescomplemented
72#4889C2214yescomplemented
73#4888C2214yescomplemented
74#4885C2214yescomplemented
75#4884C2214yescomplemented
76#4882C2214yescomplemented
77#4873C2214yescomplemented
78#4872C2214yescomplemented
79#4849C2211yescharacteristic, complemented
80#4848C2211yescharacteristic, complemented
81#4845C2212yescomplemented
82#4844C2212yescomplemented
83#4843C2211yescharacteristic, complemented
84#4841C2211yescharacteristic, complemented
85#4840C2214yescomplemented
86#4835C2212yescomplemented
87#4833C2212yescomplemented
88#4785C2214yescomplemented
89#4783C2214yes—
90#4781C2214yes—
91#4776C2214yes—
92#4773C2214yes—
93#4758C2214yescomplemented
94#4757C2214yescomplemented
95#4756C2214yescomplemented
96#3511—31no—
97C4×H(5,𝔽2)—31no—
98#3124—34no—
99#3118—34no—
100#3115—32no—
101#3110—32no—
102#3107—32no—
103#3100—32no—
104#3098—32no—
105#3079—31no—
106C2×#474D311yescharacteristic, complemented
107#3036—31no—
108#3035—31no—
109#3012—32no—
110#2951—32no—
111#2946—32no—
112#2925—31no—
113C22×C3×Q8—21no—
114C22×C3×D4C2311yescharacteristic
115C23×C3×C4—21no—
116C22×#67—22no—
117C2×#239—22no—
118#1004—24no—
119#1004—24no—
120C2×#237—21no—
121C2×#237C2312yes—
122C2×D3×D4—21no—
123C2×D3×D4C2312yes—
124C2×#235C2311yescharacteristic
125C2×#235C2312yes—
126C2×#235C2311yescharacteristic
127C22×C4×D3—22no—
128C22×C3×C8C2312yes—
129C3×C4⋊Q8—21no—
130C3×C4⋊Q8—21no—
131C3×C4⋊Q8C2312yes—
132C3×C4⋊Q8C2312yes—
133C3×C4×D4—21no—
134C3×C4×D4—21no—
135C3×C4×D4C2312yes—
136C3×C4×D4C2312yes—
137C2×C3×C4⋊C4—21no—
138C2×C3×C4⋊C4C2312yes—
139C2×C3×C4⋊C4C2311yescharacteristic
140C2×C3×C22⋊C4—21no—
141C2×C3×C42C2311yescharacteristic
142C2×#217—22no—
143#947—24no—
144#947—22no—
145#946—22no—
146#946—24no—
147Q8×Dic3—22no—
148D4×Dic3—21no—
149D4×Dic3—21no—
150D4×Dic3C2312yes—
151D4×Dic3C2312yes—
152C2×#214C2314yes—
153#932—28no—
154C2×#213C2314yes—
155#930—21no—
156#930—21no—
157#930—24no—
158C4×#67—21no—
159C4×#67—21no—
160C4×#67—22no—
161C4×#67—22no—
162C4×#67—22no—
163C4×#67—24no—
164C4×#67—22no—
165C4×#67—22no—
166C4×#67—22no—
167C4×#67D412yes—
168C4×#67D412yes—
169C2×(C2×D3)⋊C4—22no—
170#926C2311yescharacteristic
171#926C2311yescharacteristic
172C2×Dic3⋊C4—22no—
173C2×C4×Dic3—22no—
174C2×#208C2312yes—
175C2×Dic12C2312yes—
176#904—28no—
177C2×D24C2312yes—
178C2×#204C2312yes—
179C2×#204C2312yes—
180#898—24no—
181#897—22no—
182#897C2314yes—
183#895—22no—
184#895—22no—
185#895C2314yes—
186#894—24no—
187#893—21no—
188#893—22no—
189#893C2312yes—
190#893C2314yes—
191#892—22no—
192#892—22no—
193#892—21no—
194#892C2312yes—
195D3×C4⋊C4—22no—
196D3×C4⋊C4—21no—
197D3×C4⋊C4C2312yes—
198#890—22no—
199#887—21no—
200#887C2312yes—
201#887C2314yes—
202#67⋊C4—22no—
203#67⋊C4—22no—
204#67⋊C4—22no—
205#67⋊C4—22no—
206D3×C22⋊C4—22no—
207D3×C22⋊C4—22no—
208#877—22no—
209#877—22no—
210#875C2312yes—
211#874C2311yescharacteristic
212C4×D12—21no—
213C4×D12—21no—
214C4×D12D411yescharacteristic
215C4×D12D411yescharacteristic
216C4×D12C2311yescharacteristic
217C4×D12C2311yescharacteristic
218#872—21no—
219#872C2312yes—
220C42×D3—21no—
221C42×D3C2312yes—
222#869C2311yescharacteristic
223C4×Dic6D411yescharacteristic
224C4×Dic6D411yescharacteristic
225C4×Dic6C2311yescharacteristic
226C4×Dic6C2311yescharacteristic
227C3×#107C2314yes—
228C3×#107C2314yes—
229C3×C4⋊C8C2311yescharacteristic
230C3×C4⋊C8C2311yescharacteristic
231C3×C4⋊C8C2312yes—
232C3×#102C2314yes—
233C3×#102C2314yes—
234#821C2312yes—
235#821C2312yes—
236(C2×D3)⋊C8C2314yes—
237(C2×D3)⋊C8C2314yes—
238#816C2312yes—
239#816C2312yes—
240#815C2314yes—
241C8×Dic3C2314yes—
242#810C2314yes—
243#810C2314yes—
244#809C2314yes—
245#809C2314yes—
246#808C2314yes—
247#807C2314yes—
248C4⋊(C3⋊C8)C2312yes—
249C4⋊(C3⋊C8)C2312yes—
250C2×H(5,𝔽2)—31no—
251C2×AGL(1,ℤ/8)—32no—
252C2×#135—32no—
253#556—61no—
254#555—61no—
255#554—61no—
256#553—62no—
257#548—62no—
258#547—61no—
259#542—34no—
260#537—32no—
261#533—32no—
262#532—32no—
263#532—31no—
264C2×C4⋊Q8C2×D311yescharacteristic, complemented
265#520—31no—
266#520—32no—
267#520—31no—
268#520—32no—
269#520—61no—
270#518—31no—
271#518—32no—
272#518—62no—
273#518—61no—
274C4×#41—31no—
275C4×#41—32no—
276C4×#41—31no—
277C4×#41—61no—
278C2×C4×D4—32no—
279C2×C4×D4—61no—
280C2×C4×D4—62no—
281C2×C4×D4C2×D311yescharacteristic
282#485—34no—
283#484—34no—
284#482—34no—
285#480—34no—
286#477—32no—
287#476—32no—
288#475—32no—
289#474—32no—
290#474C2×D312yescomplemented
291#474C2×D312yescomplemented
292#474C2×D314yescomplemented
293#464—32no—
294#463—34no—
295#463—32no—
296#462—31no—
297#461—32no—
298#461—31no—
299#460—31no—
300#459—32no—
301#459—31no—
302#452—34no—
303#450—34no—
304#449—34no—
305#447—34no—
306#442—34no—
307#440—34no—
308#440—34no—
309#440—34no—
310C4×Q16—34no—
311C4×SD16—34no—
312C4×D8—34no—
313C4×D8—34no—
314#433—34no—
315#432—32no—
316#431—32no—
317#428—32no—
318C2×#107C2×D312yescomplemented
319#423—31no—
320C2×C4⋊C8C2×D311yescharacteristic, complemented
321#417—32no—
322#417—32no—
323#416—32no—
324C2×#102C2×D312yes—
325#408—32no—
326#405—32no—
327C24×C3—21no—
328C23×D3—22no—
329C2×C3×Q8—22no—
330C2×C3×Q8—22no—
331C2×C3×Q8—82no—
332C2×C3×D4—21no—
333C2×C3×D4—22no—
334C2×C3×D4#4114yescomplemented
335C2×C3×D4C2412yes—
336C22×C3×C4—21no—
337C22×C3×C4—22no—
338C22×C3×C4—22no—
339C22×C3×C4—22no—
340C22×C3×C4—82no—
341C22×C3×C4C2×D411yescharacteristic
342C22×C3×C4C2×D411yescharacteristic
343C22×C3×C4C2411yescharacteristic
344C2×#67—216no—
345C2×#67—21no—
346C2×#67—22no—
347C2×#67—22no—
348C2×#67—22no—
349C2×#67C2×D412yes—
350C22×Dic3—22no—
351C22×Dic3—22no—
352C22×Dic3—22no—
353#239—84no—
354#237—28no—
355#237—24no—
356#237—24no—
357D3×D4—28no—
358D3×D4—24no—
359D3×D4—24no—
360#235—22no—
361#235—22no—
362#235—22no—
363#235—24no—
364#235—24no—
365#235#4114yescomplemented
366C2×D12—21no—
367C2×D12—21no—
368C2×D12—24no—
369C2×D12C2×D411yescharacteristic
370C2×D12C2412yes—
371C2×D12C2411yescharacteristic
372C2×C4×D3—21no—
373C2×C4×D3—21no—
374C2×C4×D3—22no—
375C2×C4×D3—22no—
376C2×C4×D3—21no—
377C2×C4×D3—22no—
378C2×C4×D3—24no—
379C2×C4×D3—84no—
380C2×C4×D3C2×D412yes—
381C2×C4×D3C2×D412yes—
382C2×C4×D3C2412yes—
383C2×Dic6C2×D411yescharacteristic
384C2×Dic6C2412yes—
385C2×Dic6C2411yescharacteristic
386C2×C3×C8—24no—
387C2×C3×C8C2412yes—
388C2×C3×C8C2412yes—
389C3×C4⋊C4—21no—
390C3×C4⋊C4—22no—
391C3×C4⋊C4—22no—
392C3×C4⋊C4—22no—
393C3×C4⋊C4C2414yes—
394C3×C4⋊C4C2412yes—
395C3×C22⋊C4—22no—
396C3×C22⋊C4—22no—
397C3×C42C2×D411yescharacteristic
398C3×C42C2×D411yescharacteristic
399C3×C42C2411yescharacteristic
400C3×C42C2411yescharacteristic
401#217—21no—
402#217—22no—
403#217—22no—
404#217C2×D412yes—
405#214—28no—
406#213—28no—
407(C2×D3)⋊C4—22no—
408(C2×D3)⋊C4—24no—
409(C2×D3)⋊C4—21no—
410(C2×D3)⋊C4—21no—
411(C2×D3)⋊C4—22no—
412(C2×D3)⋊C4—22no—
413(C2×D3)⋊C4—22no—
414(C2×D3)⋊C4—24no—
415(C2×D3)⋊C4—24no—
416(C2×D3)⋊C4C2×D412yes—
417(C2×D3)⋊C4C2×D412yes—
418C4⋊Dic3—21no—
419C4⋊Dic3—21no—
420C4⋊Dic3—24no—
421C4⋊Dic3C2×D411yescharacteristic
422C4⋊Dic3C2×D411yescharacteristic
423C4⋊Dic3C2411yescharacteristic
424C4⋊Dic3C2411yescharacteristic
425Dic3⋊C4—21no—
426Dic3⋊C4—21no—
427Dic3⋊C4—22no—
428Dic3⋊C4—22no—
429Dic3⋊C4—24no—
430Dic3⋊C4C2×D412yes—
431Dic3⋊C4C2×D412yes—
432C4×Dic3—21no—
433C4×Dic3—21no—
434C4×Dic3—21no—
435C4×Dic3—22no—
436C4×Dic3—22no—
437C4×Dic3—24no—
438C4×Dic3C2×D412yes—
439C4×Dic3C2×D412yes—
440C4×Dic3C2412yes—
441#208—24no—
442C2×C3⋊C8C2414yes—
443Dic12—24no—
444D24—24no—
445#204—24no—
446#204—24no—
447H(5,𝔽2)—64no—
448H(5,𝔽2)—64no—
449C2×#41—31no—
450C2×#41—32no—
451C2×#41—31no—
452C2×#41—32no—
453C2×#41—62no—
454C2×#41—61no—
455C22×Q8—21no—
456C22×D4—32no—
457C22×D4—61no—
458C22×D4—62no—
459C22×D4C22×D311yescharacteristic
460C23×C4—21no—
461C23×C4—62no—
462AGL(1,ℤ/8)—68no—
463#135—68no—
464C2×Q16—32no—
465C2×SD16—34no—
466C2×SD16—32no—
467C2×SD16—32no—
468C2×D8—34no—
469C2×D8—32no—
470C2×M16—32no—
471C22×C8C22×D312yes—
472C4⋊Q8—21no—
473C4⋊Q8—21no—
474C4⋊Q8—31no—
475C4⋊Q8C22×D312yes—
476C4⋊Q8C22×D312yes—
477#127—31no—
478#126—64no—
479#125—62no—
480#124—32no—
481#124—62no—
482#124—64no—
483#123—64no—
484C22⋊Q8—34no—
485C22⋊Q8—62no—
486C22⋊Q8—64no—
487C22⋊Q8—62no—
488#121—34no—
489#121—62no—
490#121—62no—
491#121—64no—
492#121—61no—
493#121—61no—
494C4×Q8—31no—
495C4×Q8—31no—
496C4×Q8—32no—
497C4×Q8—34no—
498C4×Q8—31no—
499C4×Q8—31no—
500C4×Q8—62no—
501C4×Q8—61no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—32no—
505C4×D4—32no—
506C4×D4—32no—
507C4×D4—32no—
508C4×D4—32no—
509C4×D4—34no—
510C4×D4—31no—
511C4×D4—31no—
512C4×D4—31no—
513C4×D4—31no—
514C4×D4—62no—
515C4×D4—62no—
516C4×D4—62no—
517C4×D4—62no—
518C4×D4—62no—
519C4×D4—62no—
520C4×D4—62no—
521C4×D4—62no—
522C4×D4—64no—
523C4×D4—61no—
524C4×D4—62no—
525C4×D4—61no—
526C4×D4—61no—
527C4×D4—62no—
528C4×D4—62no—
529C4×D4—61no—
530C4×D4—61no—
531C4×D4—61no—
532C4×D4—61no—
533C4×D4C22×D312yes—
534C4×D4C22×D312yes—
535#117—31no—
536#117—32no—
537#117—31no—
538#117—32no—
539#117—62no—
540#117—62no—
541#117—61no—
542#117—62no—
543#117—62no—
544#117—61no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—32no—
547C2×C4⋊C4—61no—
548C2×C4⋊C4—62no—
549C2×C4⋊C4—62no—
550C2×C4⋊C4C22×D311yescharacteristic
551C2×C4⋊C4C22×D312yes—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—62no—
554C2×C22⋊C4—62no—
555C2×C22⋊C4—62no—
556C2×C22⋊C4—62no—
557C2×C42—32no—
558C2×C42—62no—
559C2×C42—61no—
560C2×C42C22×D311yescharacteristic
561#107—34no—
562#107C22×D314yes—
563#107C22×D314yes—
564#106—34no—
565C4⋊C8—32no—
566C4⋊C8—32no—
567C4⋊C8C22×D311yescharacteristic
568C4⋊C8C22×D311yescharacteristic
569C4⋊C8C22×D312yes—
570#103—32no—
571#103—32no—
572#103—34no—
573#103—34no—
574#102—32no—
575#102—32no—
576#102—34no—
577#102—34no—
578#102C22×D314yes—
579#102C22×D314yes—
580C22⋊C8—34no—
581C22⋊C8—34no—
582#97—34no—
583C4×C8—34no—
584C23×C3—22no—
585C23×C3—24no—
586C23×C3—81no—
587C23×C3—81no—
588C23×C3C22×D411yescharacteristic
589C22×D3—21no—
590C22×D3—28no—
591C22×D3—22no—
592C22×D3—82no—
593C22×D3—82no—
594C22×D3C22×D412yes—
595C3×Q8—44no—
596C3×Q8—82no—
597C3×D4—24no—
598C3×D4—22no—
599C3×D4C2×#4114yes—
600C2×C3×C4—22no—
601C2×C3×C4—22no—
602C2×C3×C4—24no—
603C2×C3×C4—41no—
604C2×C3×C4—44no—
605C2×C3×C4—82no—
606C2×C3×C4—81no—
607C2×C3×C4—82no—
608C2×C3×C4C22×D411yescharacteristic
609C2×C3×C4C22×D411yescharacteristic
610C2×C3×C4C22×D411yescharacteristic
611C2×C3×C4C22×D411yescharacteristic
612C2×C3×C4C22×D411yescharacteristic
613C2×C3×C4C2×#4112yes—
614C2×C3×C4C2×#4112yes—
615C2×C3×C4C2511yescharacteristic
616#67—28no—
617#67—28no—
618#67—24no—
619#67—24no—
620#67—44no—
621C2×Dic3—28no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—21no—
625C2×Dic3—22no—
626C2×Dic3—82no—
627C2×Dic3—82no—
628C2×Dic3C22×D412yes—
629C2×Dic3C22×D412yes—
630C2×Dic3C22×D412yes—
631D12—22no—
632D12—21no—
633D12—22no—
634D12—22no—
635D12—42no—
636D12—42no—
637D12—84no—
638D12C2×#4112yes—
639C4×D3—24no—
640C4×D3—24no—
641C4×D3—22no—
642C4×D3—22no—
643C4×D3—42no—
644C4×D3—44no—
645C4×D3—42no—
646C4×D3—82no—
647C4×D3—84no—
648C4×D3—81no—
649C4×D3—82no—
650Dic6—22no—
651Dic6—21no—
652Dic6—22no—
653Dic6—22no—
654Dic6C2×#4112yes—
655C3×C8—22no—
656C3×C8—22no—
657C3⋊C8—24no—
658C24—21no—
659C24—62no—
660#41—34no—
661#41—64no—
662#41—68no—
663#41—64no—
664#41—62no—
665#41—62no—
666#41—62no—
667#41—64no—
668#41—64no—
669#41—244no—
670C2×Q8—22no—
671C2×Q8—22no—
672C2×Q8—31no—
673C2×Q8—31no—
674C2×Q8—32no—
675C2×Q8—82no—
676C2×D4—21no—
677C2×D4—22no—
678C2×D4—32no—
679C2×D4—31no—
680C2×D4—31no—
681C2×D4—32no—
682C2×D4—64no—
683C2×D4—62no—
684C2×D4—64no—
685C2×D4—68no—
686C2×D4—62no—
687C2×D4—616no—
688C2×D4—61no—
689C2×D4—64no—
690C2×D4—62no—
691C2×D4—61no—
692C2×D4—61no—
693C2×D4#23914yescomplemented
694C2×D4C23×D312yes—
695C22×C4—21no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—32no—
700C22×C4—32no—
701C22×C4—32no—
702C22×C4—62no—
703C22×C4—64no—
704C22×C4—62no—
705C22×C4—62no—
706C22×C4—62no—
707C22×C4—62no—
708C22×C4—61no—
709C22×C4—61no—
710C22×C4—62no—
711C22×C4—61no—
712C22×C4—82no—
713C22×C4—244no—
714C22×C4D3×D411yescharacteristic
715C22×C4D3×D411yescharacteristic
716C22×C4C23×D311yescharacteristic
717Q16—64no—
718SD16—64no—
719SD16—64no—
720SD16—68no—
721D8—64no—
722D8—68no—
723M16—64no—
724C2×C8—24no—
725C2×C8—34no—
726C2×C8C23×D312yes—
727C2×C8C23×D312yes—
728C4⋊C4—22no—
729C4⋊C4—22no—
730C4⋊C4—21no—
731C4⋊C4—22no—
732C4⋊C4—31no—
733C4⋊C4—32no—
734C4⋊C4—31no—
735C4⋊C4—32no—
736C4⋊C4—31no—
737C4⋊C4—31no—
738C4⋊C4—62no—
739C4⋊C4—62no—
740C4⋊C4—64no—
741C4⋊C4—64no—
742C4⋊C4—61no—
743C4⋊C4—61no—
744C4⋊C4—61no—
745C4⋊C4—61no—
746C4⋊C4C23×D312yes—
747C4⋊C4C23×D314yes—
748C22⋊C4—22no—
749C22⋊C4—22no—
750C22⋊C4—32no—
751C22⋊C4—32no—
752C22⋊C4—32no—
753C22⋊C4—62no—
754C22⋊C4—64no—
755C22⋊C4—64no—
756C22⋊C4—62no—
757C22⋊C4—64no—
758C22⋊C4—62no—
759C22⋊C4—62no—
760C22⋊C4—61no—
761C22⋊C4—61no—
762C22⋊C4—61no—
763C22⋊C4—62no—
764C22⋊C4—62no—
765C42—32no—
766C42—32no—
767C42—32no—
768C42—62no—
769C42—62no—
770C42—64no—
771C42—61no—
772C42—61no—
773C42—61no—
774C42D3×D411yescharacteristic
775C42D3×D411yescharacteristic
776C42C23×D311yescharacteristic
777C42C23×D311yescharacteristic
778C22×C3—21no—
779C22×C3—21no—
780C22×C3—24no—
781C22×C3—42no—
782C22×C3—42no—
783C22×C3—84no—
784C22×C3#52512yes—
785C22×C3C23×D411yescharacteristic
786C2×D3—22no—
787C2×D3—22no—
788C2×D3—22no—
789C2×D3—22no—
790C2×D3—41no—
791C2×D3—41no—
792C2×D3—42no—
793C2×D3—42no—
794C2×D3—42no—
795C2×D3—88no—
796C3×C4—21no—
797C3×C4—21no—
798C3×C4—21no—
799C3×C4—42no—
800C3×C4—44no—
801C3×C4#52512yes—
802C3×C4#57612yes—
803C3×C4C22×#4111yescharacteristic
804C3×C4C22×#4111yescharacteristic
805Dic3—22no—
806Dic3—22no—
807Dic3—22no—
808Dic3—22no—
809Dic3—41no—
810Dic3—42no—
811Dic3—41no—
812C23—22no—
813C23—24no—
814C23—32no—
815C23—68no—
816C23—61no—
817C23—62no—
818C23—81no—
819C23—81no—
820C23—242no—
821C23—242no—
822C23C2×D3×D411yescharacteristic
823Q8—32no—
824Q8—44no—
825Q8—61no—
826Q8—62no—
827Q8—62no—
828Q8—62no—
829Q8—82no—
830D4—22no—
831D4—24no—
832D4—32no—
833D4—68no—
834D4—68no—
835D4—64no—
836D4—64no—
837D4—61no—
838D4—62no—
839D4—62no—
840D4—62no—
841D4—122no—
842D4—124no—
843D4—122no—
844D4—244no—
845D4C2×#23914yes—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—24no—
849C2×C4—32no—
850C2×C4—32no—
851C2×C4—32no—
852C2×C4—41no—
853C2×C4—44no—
854C2×C4—68no—
855C2×C4—61no—
856C2×C4—62no—
857C2×C4—62no—
858C2×C4—64no—
859C2×C4—64no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—62no—
863C2×C4—82no—
864C2×C4—81no—
865C2×C4—82no—
866C2×C4—122no—
867C2×C4—122no—
868C2×C4—124no—
869C2×C4—241no—
870C2×C4—242no—
871C2×C4—244no—
872C2×C4—242no—
873C2×C4—242no—
874C2×C4—242no—
875C2×C4C2×D3×D411yescharacteristic
876C2×C4C2×D3×D411yescharacteristic
877C2×C4C2×D3×D411yescharacteristic
878C2×C4C2×D3×D411yescharacteristic
879C2×C4C2×D3×D411yescharacteristic
880C2×C4C2×#23912yes—
881C2×C4D3×#4112yes—
882C2×C4C24×D311yescharacteristic
883C8—22no—
884C8—22no—
885C8—64no—
886C2×C3—22no—
887C2×C3—44no—
888C2×C3C2×#52511yescharacteristic
889C2×C3C2×#57611yescharacteristic
890C2×C3#358611yescharacteristic
891D3—42no—
892D3—42no—
893D3—82no—
894C22—21no—
895C22—21no—
896C22—24no—
897C22—42no—
898C22—42no—
899C22—62no—
900C22—62no—
901C22—62no—
902C22—62no—
903C22—84no—
904C22—121no—
905C22—121no—
906C22—122no—
907C22—122no—
908C22—122no—
909C22—248no—
910C22#562712yes—
911C22C22×D3×D411yescharacteristic
912C4—21no—
913C4—21no—
914C4—21no—
915C4—42no—
916C4—44no—
917C4—62no—
918C4—62no—
919C4—62no—
920C4—62no—
921C4—121no—
922C4—121no—
923C4—122no—
924C4#562712yes—
925C4#575712yes—
926C4C22×#23911yescharacteristic
927C4C2×D3×#4111yescharacteristic
928C3#6059611yescharacteristic, complemented, Sylow
929C2—22no—
930C2—44no—
931C2—122no—
932C2—122no—
933C2—242no—
934C2C2×#562711yescharacteristic
935C2C2×#575711yescharacteristic
936C2#8719711yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#474C2
socleC22×C3C23×D4
hypercenterC2×#474D3
hypocenterC3#60596
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. #86205C2semidirect
2. C4×#1004C2semidirect
3. C2×C3×#474C2semidirect
4. #83212C2semidirect
5. #82307C2semidirect
6. #80953C2semidirect
7. #80952C2semidirect
8. #80951C2semidirect
9. #80950C2semidirect
10. #80949C2semidirect
11. #80948C2semidirect
12. #79141C2semidirect
13. #79136C2semidirect
14. #79021C2semidirect
15. #79000C2semidirect
16. #78747C2semidirect
17. #78726C2semidirect
20. C2×C3×C4⋊Q8C22semidirect
28. #5733C22semidirect
31. #5728C22semidirect
33. #5725C22semidirect
46. #5504C22semidirect
48. #5477C22semidirect
51. C3×#474C22semidirect
52. C3×#474C22semidirect
53. C3×#474C22semidirect
54. C2×C3×#107C22semidirect
55. C2×C3×C4⋊C8C22semidirect
57. #5113C22semidirect
59. #5101C22semidirect
60. #5094C22semidirect
61. #5091C22semidirect
62. #5087C22semidirect
63. #5084C22semidirect
64. #5019C22semidirect
65. #5016C22semidirect
66. #5015C22semidirect
68. #4966C22semidirect
69. #4964C22semidirect
70. #4924C22semidirect
71. #4889C22semidirect
72. #4889C22semidirect
73. #4888C22semidirect
74. #4885C22semidirect
75. #4884C22semidirect
76. #4882C22semidirect
77. #4873C22semidirect
78. #4872C22semidirect
79. #4849C22semidirect
80. #4848C22semidirect
81. #4845C22semidirect
82. #4844C22semidirect
83. #4843C22semidirect
84. #4841C22semidirect
85. #4840C22semidirect
86. #4835C22semidirect
87. #4833C22semidirect
88. #4785C22semidirect
93. #4758C22semidirect
94. #4757C22semidirect
95. #4756C22semidirect
106. C2×#474D3semidirect
264. C2×C4⋊Q8C2×D3semidirect
290. #474C2×D3semidirect
291. #474C2×D3semidirect
292. #474C2×D3semidirect
318. C2×#107C2×D3semidirect
320. C2×C4⋊C8C2×D3semidirect
334. C2×C3×D4#41semidirect
365. #235#41semidirect
693. C2×D4#239semidirect
928. C3#60596semidirect

Maximal subgroups

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

subgroupindex
#862052
C4×#10042
C2×C3×#4742
#832122
#823072
#809532
#809522
#809512
#809502
#809492
#809482
#791412
#791362
#790212
#790002
#787472
#787262
#605963