Finite Group Databasebeta

← #11675151

Subgroups — #11675151

Order 768.

1806 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#85819C211yesmaximal, characteristic, complemented
2#85766C211yesmaximal, characteristic, complemented
3C2×C3×C4×SD16C211yesmaximal, characteristic, complemented
4#83848C212yesmaximal, complemented
5#82431C211yesmaximal, characteristic, complemented
6#82307C211yesmaximal, characteristic
7#79630C214yesmaximal, complemented
8#79629C212yesmaximal, complemented
9#79628C212yesmaximal, complemented
10#79621C212yesmaximal, complemented
11#79620C214yesmaximal, complemented
12#79619C212yesmaximal, complemented
13#79130C212yesmaximal, complemented
14#78785C212yesmaximal, complemented
15#78726C212yesmaximal, complemented
16#78463C211yesmaximal, characteristic, complemented
17#78445C211yesmaximal, characteristic, complemented
18#61326—31nomaximal, Sylow
19C22×C3×SD16C2211yescharacteristic
20C2×C3×C4×Q8C2211yescharacteristic
21C2×C3×C4×D4C2211yescharacteristic
22#5816C2212yes—
23#5798C2212yes—
24C2×#932C2212yes—
25C2×#924—22no—
26#5585C2212yescomplemented
27#5584—21no—
28#5581—22no—
29#5579—21no—
30#5568C2214yescomplemented
31#5567C2212yescomplemented
32#5543—21no—
33#5543C2212yes—
34#5539—22no—
35#5539C2214yes—
36D4×Dic6—21no—
37D4×Dic6C2212yes—
38#5515—22no—
39#5504C2212yes—
40#5500C2212yes—
41#5483—22no—
42#5479—22no—
43#5477C2211yescharacteristic
44#5470C2211yescharacteristic
45#5470C2211yescharacteristic
46C3×C4×SD16C2212yes—
47C3×C4×SD16C2212yes—
48C3×C4×SD16C2212yes—
49C3×C4×SD16C2212yes—
50C2×C3×#106C2211yescharacteristic
51C2×C3×#103C2211yescharacteristic
52C2×C3×#102C2211yescharacteristic
53C2×C3×C4×C8C2211yescharacteristic
54#5225C2212yes—
55#5165C2214yes—
56#5165C2214yes—
57#5162C2214yes—
58#5162C2214yes—
59#5113C2212yes—
60#5113C2212yes—
61#5102C2212yes—
62#5101C2212yes—
63#5022C2214yescomplemented
64#5021C2212yescomplemented
65#5020C2212yescomplemented
66#5019C2212yes—
67#5016C2214yes—
68#5015C2212yes—
69#4966C2212yes—
70#4964C2212yes—
71#4924C2211yescharacteristic
72#4871C2214yescomplemented
73#4870C2214yescomplemented
74#4857C2214yescomplemented
75#4854C2214yescomplemented
76#4800C2214yescomplemented
77#4797C2214yescomplemented
78#4794C2214yescomplemented
79#4792C2214yescomplemented
80#4785C2214yes—
81#4758C2214yes—
82#4757C2214yes—
83#4756C2214yes—
84#4697C2212yescomplemented
85#4697C2212yescomplemented
86#4694C2211yescharacteristic, complemented
87#4694C2211yescharacteristic, complemented
88#4681C2211yescharacteristic, complemented
89#4681C2211yescharacteristic, complemented
90#4679C2212yescomplemented
91#4679C2212yescomplemented
92C8×Dic6C2212yescomplemented
93C8×Dic6C2212yescomplemented
94#3507—31no—
95#3501—31no—
96#3376—34no—
97#3373—32no—
98#3372—32no—
99#3361—32no—
100#3360—34no—
101#3359—32no—
102#3137—32no—
103#3131—31no—
104#3084—32no—
105#3078—31no—
106#3042—32no—
107#3036—31no—
108#2960—31no—
109#2946—32no—
110C2×C4×SD16D311yescharacteristic, complemented
111C22×C3×Q8C2311yescharacteristic
112C22×C3×D4C2311yescharacteristic
113C23×C3×C4—21no—
114C2×#235C2312yes—
115C22×Dic6—22no—
116C2×C3×SD16—24no—
117C2×C3×SD16C2312yes—
118C2×C3×SD16C2312yes—
119C22×C3×C8C2311yescharacteristic
120C22×C3×C8C2311yescharacteristic
121C3×C4×Q8—21no—
122C3×C4×Q8—21no—
123C3×C4×Q8C2312yes—
124C3×C4×Q8C2312yes—
125C3×C4×D4—21no—
126C3×C4×D4—21no—
127C3×C4×D4C2312yes—
128C3×C4×D4C2312yes—
129C2×C3×C4⋊C4—21no—
130C2×C3×C4⋊C4C2311yescharacteristic
131C2×C3×C4⋊C4C2311yescharacteristic
132C2×C3×C22⋊C4—21no—
133C2×C3×C42—21no—
134C2×C3×C42C2311yescharacteristic
135C2×#217—24no—
136#947C2314yes—
137#946—22no—
138#946—22no—
139#944C2314yes—
140D4×Dic3—22no—
141D4×Dic3—22no—
142D4×Dic3C2314yes—
143D4×Dic3C2314yes—
144C2×#214C2314yes—
145#932—28no—
146C2×#213C2314yes—
147#930—21no—
148#930—21no—
149#929—24no—
150C4×#67—24no—
151#926C2312yes—
152#926C2312yes—
153C2×C4⋊Dic3—22no—
154#924—21no—
155#924—21no—
156#924—22no—
157#924—24no—
158#924—22no—
159#924—24no—
160#924D412yes—
161#924D412yes—
162C2×Dic3⋊C4—24no—
163C2×#208C2312yes—
164#898—24no—
165#896—24no—
166#894—24no—
167#893C2314yes—
168#892—22no—
169D3×C4⋊C4—22no—
170#890—22no—
171#890C2314yes—
172#889—24no—
173#888—22no—
174#888C2314yes—
175#887C2314yes—
176#878—24no—
177#878—24no—
178#878—24no—
179#878—24no—
180#876—24no—
181#875—22no—
182#875C2312yes—
183#874C2311yescharacteristic
184C4×D12—21no—
185C4×D12—21no—
186C4×D12—22no—
187#872—24no—
188#870—22no—
189#870D412yes—
190#870C2312yes—
191#869D411yescharacteristic
192#869D411yescharacteristic
193#869C2311yescharacteristic
194#869C2311yescharacteristic
195#869C2311yescharacteristic
196C4×Dic6—22no—
197C4×Dic6—21no—
198C4×Dic6—21no—
199C4×Dic6C2312yes—
200C4×Dic6C2312yes—
201C3×#106C2312yes—
202C3×#106C2312yes—
203C3×#103C2312yes—
204C3×#103C2312yes—
205C3×#102C2312yes—
206C3×#102C2312yes—
207C3×C4×C8C2311yescharacteristic
208C3×C4×C8C2311yescharacteristic
209C3×C4×C8C2311yescharacteristic
210C3×C4×C8C2311yescharacteristic
211#835C2314yes—
212#835C2314yes—
213#821C2312yes—
214#821C2312yes—
215#821C2312yes—
216#821C2312yes—
217#816C2312yes—
218#816C2312yes—
219#816C2312yes—
220#816C2312yes—
221#815C2314yes—
222Dic3⋊C8C2314yes—
223Dic3⋊C8C2314yes—
224C8×Dic3C2314yes—
225#810C2314yes—
226#809C2314yes—
227#808C2314yes—
228#807C2314yes—
229C4⋊(C3⋊C8)C2312yes—
230C4⋊(C3⋊C8)C2312yes—
231C2×AGL(1,ℤ/8)—32no—
232C22×SD16C2×D311yescharacteristic
233#559—32no—
234#557—32no—
235#556—34no—
236#556—61no—
237#554—34no—
238#554—32no—
239#554—62no—
240#554—61no—
241#554—61no—
242#552—62no—
243D4×Q8—32no—
244D4×Q8—61no—
245#544—32no—
246#543—62no—
247#539—62no—
248#536—32no—
249#533—31no—
250#533—31no—
251#532—31no—
252#529—62no—
253C2×C22⋊Q8—62no—
254#520—32no—
255#518—32no—
256C2×C4×Q8C2×D311yescharacteristic
257C2×C4×D4C2×D311yescharacteristic
258#491—34no—
259#489—34no—
260#488—34no—
261#488—32no—
262#488—32no—
263#487—34no—
264#487—31no—
265#487—31no—
266#486—31no—
267#486—31no—
268#479—34no—
269#479—34no—
270#478—34no—
271#477—32no—
272#476—34no—
273#475—32no—
274#475—34no—
275#463—34no—
276#463—34no—
277#463—34no—
278#461—34no—
279#461—34no—
280#461—32no—
281#459—32no—
282#446—32no—
283#446—32no—
284C8×Q8—32no—
285C8×Q8—32no—
286#442—34no—
287#440—34no—
288C4×SD16—34no—
289C4×SD16C2×D312yes—
290C4×SD16C2×D312yes—
291C4×SD16C2×D312yes—
292C4×SD16C2×D312yes—
293C4×D8—34no—
294#428—32no—
295C2×#106C2×D311yescharacteristic
296#424—32no—
297#423—31no—
298#419—32no—
299#417—32no—
300#416—32no—
301#416—32no—
302C2×#103C2×D311yescharacteristic
303C2×#102C2×D311yescharacteristic
304#405—32no—
305C2×C4×C8C2×D311yescharacteristic
306C24×C3—21no—
307C2×C3×Q8—21no—
308C2×C3×Q8—22no—
309C2×C3×Q8—22no—
310C2×C3×Q8C2412yes—
311C2×C3×D4—21no—
312C2×C3×D4—22no—
313C2×C3×D4#4114yes—
314C2×C3×D4C2412yes—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—22no—
319C22×C3×C4—22no—
320C22×C3×C4—82no—
321C22×C3×C4C2×D411yescharacteristic
322C22×C3×C4C2×D411yescharacteristic
323C22×C3×C4C2411yescharacteristic
324C2×#67—22no—
325C22×Dic3—24no—
326C22×Dic3—24no—
327#235—24no—
328#235—24no—
329C2×D12—21no—
330C2×D12—21no—
331C2×D12C2412yes—
332C2×C4×D3—22no—
333C2×C4×D3—24no—
334C2×Dic6—21no—
335C2×Dic6—21no—
336C2×Dic6—24no—
337C2×Dic6—84no—
338C2×Dic6C2×D412yes—
339C2×Dic6C2×D412yes—
340C2×Dic6C2412yes—
341C3×SD16—24no—
342C3×SD16—24no—
343C2×C3×C8—22no—
344C2×C3×C8—22no—
345C2×C3×C8C2411yescharacteristic
346C2×C3×C8C2411yescharacteristic
347C2×C3×C8C2411yescharacteristic
348C2×C3×C8C2411yescharacteristic
349C3×C4⋊C4—21no—
350C3×C4⋊C4—22no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—22no—
353C3×C4⋊C4C2412yes—
354C3×C4⋊C4C2412yes—
355C3×C22⋊C4—22no—
356C3×C22⋊C4—22no—
357C3×C42—22no—
358C3×C42—22no—
359C3×C42C2×D411yescharacteristic
360C3×C42C2×D411yescharacteristic
361C3×C42C2411yescharacteristic
362C3×C42C2411yescharacteristic
363#217—22no—
364#217—24no—
365#217—24no—
366#217C2×D414yes—
367#214—28no—
368#213—28no—
369(C2×D3)⋊C4—22no—
370(C2×D3)⋊C4—22no—
371(C2×D3)⋊C4—24no—
372(C2×D3)⋊C4—24no—
373(C2×D3)⋊C4—24no—
374C4⋊Dic3—21no—
375C4⋊Dic3—21no—
376C4⋊Dic3—21no—
377C4⋊Dic3—21no—
378C4⋊Dic3—24no—
379C4⋊Dic3C2×D412yes—
380C4⋊Dic3C2×D412yes—
381C4⋊Dic3C2×D412yes—
382C4⋊Dic3C2×D412yes—
383C4⋊Dic3C2412yes—
384C4⋊Dic3C2412yes—
385Dic3⋊C4—22no—
386Dic3⋊C4—22no—
387Dic3⋊C4—24no—
388Dic3⋊C4—24no—
389Dic3⋊C4—24no—
390Dic3⋊C4—24no—
391Dic3⋊C4—24no—
392Dic3⋊C4C2×D414yes—
393Dic3⋊C4C2×D414yes—
394C4×Dic3—22no—
395C4×Dic3—24no—
396C4×Dic3C2414yes—
397#208—24no—
398C2×C3⋊C8C2414yes—
399C2×#41—32no—
400C22×Q8—62no—
401C22×Q8C22×D311yescharacteristic
402C22×D4C22×D311yescharacteristic
403C23×C4—21no—
404AGL(1,ℤ/8)—68no—
405C2×SD16—24no—
406C2×SD16—34no—
407C2×SD16C22×D312yes—
408C2×SD16C22×D312yes—
409C2×D8—34no—
410C2×M16—32no—
411C22×C8C22×D311yescharacteristic
412C22×C8C22×D311yescharacteristic
413C4⋊Q8—34no—
414C4⋊Q8—34no—
415C4⋊Q8—31no—
416C4⋊Q8—31no—
417C4⋊Q8—31no—
418C4⋊Q8—31no—
419C4⋊Q8—31no—
420C4⋊Q8—62no—
421#127—31no—
422#126—64no—
423#126—64no—
424#125—34no—
425#125—32no—
426#125—32no—
427#125—62no—
428#125—64no—
429#125—62no—
430#124—34no—
431#124—32no—
432#124—62no—
433#123—64no—
434#123—64no—
435C22⋊Q8—32no—
436C22⋊Q8—32no—
437C22⋊Q8—64no—
438C22⋊Q8—64no—
439C22⋊Q8—64no—
440C22⋊Q8—64no—
441C22⋊Q8—64no—
442C22⋊Q8—64no—
443C22⋊Q8—62no—
444C22⋊Q8—64no—
445C22⋊Q8—62no—
446C22⋊Q8—62no—
447C22⋊Q8—62no—
448C22⋊Q8—61no—
449C22⋊Q8—61no—
450#121—61no—
451#121—61no—
452C4×Q8—21no—
453C4×Q8—21no—
454C4×Q8—32no—
455C4×Q8—32no—
456C4×Q8—34no—
457C4×Q8—62no—
458C4×Q8—61no—
459C4×Q8—61no—
460C4×Q8C22×D312yes—
461C4×Q8C22×D312yes—
462C4×D4—21no—
463C4×D4—21no—
464C4×D4—34no—
465C4×D4—34no—
466C4×D4—34no—
467C4×D4—62no—
468C4×D4—64no—
469C4×D4—62no—
470C4×D4—62no—
471C4×D4—61no—
472C4×D4—61no—
473C4×D4C22×D312yes—
474C4×D4C22×D312yes—
475#117—32no—
476#117—32no—
477#117—64no—
478#117—62no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—62no—
481C2×C4⋊C4—64no—
482C2×C4⋊C4—62no—
483C2×C4⋊C4C22×D311yescharacteristic
484C2×C4⋊C4C22×D311yescharacteristic
485C2×C22⋊C4—21no—
486C2×C22⋊C4—64no—
487C2×C42—21no—
488C2×C42C22×D311yescharacteristic
489#107—34no—
490#106—34no—
491#106C22×D312yes—
492#106C22×D312yes—
493C4⋊C8—34no—
494C4⋊C8—34no—
495C4⋊C8—32no—
496C4⋊C8—32no—
497#103—34no—
498#103—34no—
499#103—32no—
500#103—32no—
501#103—32no—
502#103—32no—
503#103—34no—
504#103C22×D312yes—
505#103C22×D312yes—
506#102—32no—
507#102—32no—
508#102—32no—
509#102—32no—
510#102—34no—
511#102C22×D312yes—
512#102C22×D312yes—
513#97—34no—
514C4×C8—34no—
515C4×C8C22×D311yescharacteristic
516C4×C8C22×D311yescharacteristic
517C4×C8C22×D311yescharacteristic
518C4×C8C22×D311yescharacteristic
519C23×C3—22no—
520C23×C3—24no—
521C23×C3—81no—
522C23×C3—81no—
523C23×C3C22×D411yescharacteristic
524C22×D3—22no—
525C3×Q8—22no—
526C3×Q8—22no—
527C3×Q8—42no—
528C3×D4—24no—
529C3×D4—22no—
530C3×D4C2×#4114yes—
531C2×C3×C4—22no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—41no—
536C2×C3×C4—42no—
537C2×C3×C4—44no—
538C2×C3×C4—82no—
539C2×C3×C4—81no—
540C2×C3×C4—81no—
541C2×C3×C4C22×D411yescharacteristic
542C2×C3×C4C22×D411yescharacteristic
543C2×C3×C4C22×D411yescharacteristic
544C2×C3×C4C22×D411yescharacteristic
545C2×C3×C4C22×D411yescharacteristic
546C2×C3×C4C2×#4112yes—
547C2×C3×C42−1+412yes—
548C2×C3×C4C2511yescharacteristic
549#67—44no—
550C2×Dic3—22no—
551C2×Dic3—22no—
552C2×Dic3—22no—
553C2×Dic3—84no—
554C2×Dic3—84no—
555C2×Dic3C22×D414yes—
556C2×Dic3C22×D414yes—
557D12—22no—
558D12—22no—
559D12—42no—
560D12—81no—
561C4×D3—44no—
562C4×D3—84no—
563Dic6—24no—
564Dic6—22no—
565Dic6—22no—
566Dic6—42no—
567Dic6—42no—
568Dic6—84no—
569Dic6—81no—
570C3×C8—21no—
571C3×C8—21no—
572C3×C8—21no—
573C3×C8—21no—
574C3⋊C8—24no—
575C24—21no—
576#41—64no—
577#41—64no—
578C2×Q8—21no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8—32no—
582C2×Q8—32no—
583C2×Q8—32no—
584C2×Q8—64no—
585C2×Q8—61no—
586C2×Q8—61no—
587C2×Q8—244no—
588C2×Q8C23×D312yes—
589C2×D4—21no—
590C2×D4—22no—
591C2×D4—32no—
592C2×D4—62no—
593C2×D4—61no—
594C2×D4—61no—
595C2×D4#23514yes—
596C2×D4C23×D312yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—64no—
603C22×C4—64no—
604C22×C4—64no—
605C22×C4—62no—
606C22×C4—82no—
607C22×C4D3×D411yescharacteristic
608C22×C4D3×D411yescharacteristic
609C22×C4C23×D311yescharacteristic
610SD16—24no—
611SD16—24no—
612SD16—68no—
613D8—68no—
614M16—64no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—34no—
618C2×C8C23×D311yescharacteristic
619C2×C8C23×D311yescharacteristic
620C2×C8C23×D311yescharacteristic
621C2×C8C23×D311yescharacteristic
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—32no—
627C4⋊C4—34no—
628C4⋊C4—32no—
629C4⋊C4—32no—
630C4⋊C4—34no—
631C4⋊C4—32no—
632C4⋊C4—32no—
633C4⋊C4—32no—
634C4⋊C4—64no—
635C4⋊C4—64no—
636C4⋊C4—64no—
637C4⋊C4—64no—
638C4⋊C4—64no—
639C4⋊C4—64no—
640C4⋊C4—62no—
641C4⋊C4—61no—
642C4⋊C4—61no—
643C4⋊C4—61no—
644C4⋊C4—62no—
645C4⋊C4—61no—
646C4⋊C4C23×D312yes—
647C4⋊C4C23×D312yes—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—34no—
651C22⋊C4—64no—
652C22⋊C4—64no—
653C22⋊C4—64no—
654C22⋊C4—64no—
655C22⋊C4—64no—
656C22⋊C4—62no—
657C22⋊C4—62no—
658C22⋊C4—62no—
659C42—22no—
660C42—22no—
661C42—34no—
662C42—64no—
663C42—62no—
664C42D3×D411yescharacteristic
665C42D3×D411yescharacteristic
666C42C23×D311yescharacteristic
667C42C23×D311yescharacteristic
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—24no—
671C22×C3—42no—
672C22×C3—42no—
673C22×C3—84no—
674C22×C3#54812yes—
675C22×C3C23×D411yescharacteristic
676C2×D3—42no—
677C2×D3—42no—
678C2×D3—42no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—21no—
682C3×C4—42no—
683C3×C4—42no—
684C3×C4—42no—
685C3×C4#54812yes—
686C3×C4#57712yes—
687C3×C4C22×#4111yescharacteristic
688C3×C4C2×2−1+411yescharacteristic
689Dic3—24no—
690Dic3—24no—
691Dic3—42no—
692Dic3—42no—
693Dic3—42no—
694C23—22no—
695C23—24no—
696C23—62no—
697C23—81no—
698C23—81no—
699C23C2×D3×D411yescharacteristic
700Q8—22no—
701Q8—22no—
702Q8—42no—
703Q8—64no—
704Q8—62no—
705Q8—62no—
706Q8—122no—
707Q8—122no—
708Q8—241no—
709Q8—244no—
710D4—22no—
711D4—24no—
712D4—62no—
713D4—62no—
714D4—124no—
715D4—122no—
716D4—241no—
717D4C2×#23514yes—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—34no—
723C2×C4—34no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—44no—
727C2×C4—62no—
728C2×C4—62no—
729C2×C4—62no—
730C2×C4—82no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—124no—
734C2×C4—244no—
735C2×C4—244no—
736C2×C4—244no—
737C2×C4C2×#23512yes—
738C2×C4C2×D3×D411yescharacteristic
739C2×C4C2×D3×D411yescharacteristic
740C2×C4C2×D3×D411yescharacteristic
741C2×C4C2×D3×D411yescharacteristic
742C2×C4C2×D3×D411yescharacteristic
743C2×C4#101012yes—
744C2×C4C24×D311yescharacteristic
745C8—21no—
746C8—21no—
747C8—21no—
748C8—21no—
749C8—64no—
750C2×C3—22no—
751C2×C3—44no—
752C2×C3C2×#54811yescharacteristic
753C2×C3C2×#57711yescharacteristic
754C2×C3#358411yescharacteristic
755D3—82no—
756C22—21no—
757C22—21no—
758C22—24no—
759C22—42no—
760C22—42no—
761C22—84no—
762C22—122no—
763C22—122no—
764C22—122no—
765C22#555212yes—
766C22C22×D3×D411yescharacteristic
767C4—21no—
768C4—21no—
769C4—21no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—64no—
774C4—64no—
775C4—122no—
776C4—122no—
777C4—122no—
778C4#555212yes—
779C4#576212yes—
780C4C22×#23511yescharacteristic
781C4C2×#101011yescharacteristic
782C3#6132611yescharacteristic, complemented, Sylow
783C2—22no—
784C2—44no—
785C2—242no—
786C2C2×#555211yescharacteristic
787C2C2×#576211yescharacteristic
788C2#8718711yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×C4×SD16C2
socleC22×C3C23×D4
prime radical#82307C2
hypercenterC2×C4×SD16D3
hypocenterC3#61326
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. #85819C2semidirect
2. #85766C2semidirect
3. C2×C3×C4×SD16C2semidirect
4. #83848C2semidirect
5. #82431C2semidirect
7. #79630C2semidirect
8. #79629C2semidirect
9. #79628C2semidirect
10. #79621C2semidirect
11. #79620C2semidirect
12. #79619C2semidirect
13. #79130C2semidirect
14. #78785C2semidirect
15. #78726C2semidirect
16. #78463C2semidirect
17. #78445C2semidirect
26. #5585C22semidirect
30. #5568C22semidirect
31. #5567C22semidirect
63. #5022C22semidirect
64. #5021C22semidirect
65. #5020C22semidirect
72. #4871C22semidirect
73. #4870C22semidirect
74. #4857C22semidirect
75. #4854C22semidirect
76. #4800C22semidirect
77. #4797C22semidirect
78. #4794C22semidirect
79. #4792C22semidirect
84. #4697C22semidirect
85. #4697C22semidirect
86. #4694C22semidirect
87. #4694C22semidirect
88. #4681C22semidirect
89. #4681C22semidirect
90. #4679C22semidirect
91. #4679C22semidirect
92. C8×Dic6C22semidirect
93. C8×Dic6C22semidirect
110. C2×C4×SD16D3semidirect
782. C3#61326semidirect

Maximal subgroups

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

subgroupindex
#858192
#857662
C2×C3×C4×SD162
#838482
#824312
#823072
#796302
#796292
#796282
#796212
#796202
#796192
#791302
#787852
#787262
#784632
#784452
#613263