Finite Group Databasebeta

← #11662135

Subgroups — #11662135

Order 768.

2714 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#135C211yesmaximal, characteristic, complemented
2#87268C211yesmaximal, characteristic, complemented
3#87260C211yesmaximal, characteristic, complemented
4C2×#5822C211yesmaximal, characteristic, complemented
5#84072C211yesmaximal, characteristic, complemented
6#83902C214yesmaximal, complemented
7#83901C214yesmaximal, complemented
8#83900C218yesmaximal, complemented
9#83877C212yesmaximal, complemented
10#83849C212yesmaximal, complemented
11#83848C212yesmaximal, complemented
12#83826C212yesmaximal, complemented
13C2×#5113C211yesmaximal, characteristic, complemented
14C2×#5102C211yesmaximal, characteristic, complemented
15#60422—31nomaximal, Sylow
16C22×C3×#41C2211yescharacteristic
17C22×C3×#41C2211yescharacteristic
18C22×#235C2211yescharacteristic
19C2×C3×#135—28no—
20C2×C3×#135C2214yes—
21C2×C3×#135C2214yescomplemented
22C22×C3×Q16C2211yescharacteristic, complemented
23C22×C3×SD16C2211yescharacteristic, complemented
24C22×C3×SD16C2211yescharacteristic, complemented
25C22×C3×D8C2211yescharacteristic, complemented
26C23×C3×C8C2211yescharacteristic
27#5833—22no—
28#5832C2214yescomplemented
29#5830C2212yescomplemented
30#5828—22no—
31#5827—22no—
32#5827C2214yescomplemented
33Dic3×#41—22no—
34Dic3×#41C2214yescomplemented
35#5825C2212yescomplemented
36C2×#951C2212yescomplemented
37#5822—28no—
38C2×#950C2214yescomplemented
39C2×#949C2212yescomplemented
40#5816C2212yes—
41#5812C2212yescomplemented
42C2×#942C2212yes—
43#5805C2212yes—
44#5804—22no—
45#5798—22no—
46#5798C2212yescomplemented
47C2×#932C2212yes—
48#5791—22no—
49C2×#926—22no—
50C2×#926C2211yescharacteristic
51C2×#926C2211yescharacteristic
52C22×#208C2211yescharacteristic
53#5233C2214yescomplemented
54#5232C2214yescomplemented
55#5225C2212yescomplemented
56#5215C2212yescomplemented
57#5185C2218yescomplemented
58#5182C2218yescomplemented
59#5166C2218yescomplemented
60#5165C2218yescomplemented
61#5163C2218yescomplemented
62#5162C2218yescomplemented
63#5153C2218yescomplemented
64#5150C2218yescomplemented
65#5113C2212yes—
66#5113C2212yes—
67#5113C2214yescomplemented
68C2×#821C2212yescomplemented
69C2×#816C2212yescomplemented
70#5102C2212yescomplemented
71#5102C2212yescomplemented
72#5102C2214yescomplemented
73C2×Dic3⋊C8C2214yescomplemented
74C2×#575—31no—
75C22×#135D311yescharacteristic, complemented
76#3449—31no—
77#3428—31no—
78#3046—34no—
79#3045—34no—
80#3044—32no—
81#3043—32no—
82#3042—32no—
83#3041—32no—
84#3035—38no—
85C2×#424—31no—
86#2896—31no—
87C2×#416—31no—
88C2×C3×#41—21no—
89C2×C3×#41—21no—
90C2×C3×#41—21no—
91C2×C3×#41—21no—
92C2×C3×#41—24no—
93C2×C3×#41—24no—
94C2×C3×#41—24no—
95C2×C3×#41D418yescomplemented
96C2×C3×#41C2312yes—
97C2×C3×#41C2312yes—
98C2×C3×#41C2312yes—
99C2×C3×#41C2312yes—
100C22×C3×Q8C2311yescharacteristic
101C22×C3×Q8C2311yescharacteristic
102C22×C3×D4—21no—
103C22×C3×D4—21no—
104C22×C3×D4C2311yescharacteristic
105C22×C3×D4C2311yescharacteristic
106C23×C3×C4—21no—
107C23×C3×C4—21no—
108C23×C3×C4C2311yescharacteristic
109C22×#67—21no—
110C2×#235—21no—
111C2×#235—21no—
112C2×#235—24no—
113C2×#235—24no—
114C2×#235C2312yes—
115C2×#235C2312yes—
116C22×D12C2311yescharacteristic
117C22×C4×D3—21no—
118C22×Dic6C2311yescharacteristic
119C3×#135—216no—
120C3×#135—216no—
121C2×C3×Q16—24no—
122C2×C3×Q16C2314yes—
123C2×C3×SD16—24no—
124C2×C3×SD16—24no—
125C2×C3×SD16C2314yes—
126C2×C3×SD16C2314yes—
127C2×C3×D8—24no—
128C2×C3×D8C2314yes—
129C22×C3×C8—24no—
130C22×C3×C8C2311yescharacteristic
131C22×C3×C8C2311yescharacteristic
132C22×C3×C8C2312yes—
133C22×C3×C8C2312yes—
134#953—24no—
135C2×#217—21no—
136C2×#217—24no—
137C2×#217D412yes—
138#951—28no—
139#950—216no—
140#949—28no—
141#947C2314yes—
142#946—24no—
143Q8×Dic3—24no—
144Q8×Dic3C2318yes—
145#944C2314yes—
146C2×#216C2314yes—
147#942—28no—
148C2×#215C2314yes—
149#940C2314yes—
150#939—28no—
151#938—24no—
152#937—24no—
153#936C2314yes—
154#935—24no—
155D4×Dic3—28no—
156D4×Dic3—28no—
157D4×Dic3—24no—
158D4×Dic3C2318yes—
159C2×#214C2314yes—
160#932—28no—
161C2×#213C2314yes—
162#930—24no—
163#929—24no—
164C4×#67—28no—
165#926—21no—
166#926—21no—
167#926—24no—
168#926—24no—
169#926—24no—
170#926D412yes—
171#926D412yes—
172#926C2312yes—
173#926C2312yes—
174#926C2312yes—
175#926C2312yes—
176C2×C4⋊Dic3—24no—
177C2×C4⋊Dic3D412yes—
178C2×C4⋊Dic3C2312yes—
179#924—24no—
180C2×C4×Dic3—21no—
181C2×C4×Dic3—24no—
182C2×C4×Dic3C2312yes—
183C2×#208—24no—
184C2×#208C2312yes—
185C2×#208C2312yes—
186C22×C3⋊C8C2312yes—
187#835C2318yes—
188#832C2318yes—
189#821C2314yes—
190#821C2314yes—
191#816C2314yes—
192#816C2314yes—
193Dic3⋊C8C2318yes—
194Dic3⋊C8C2318yes—
195C22×#41—31no—
196C22×#41C2×D311yescharacteristic
197C22×#41C2×D311yescharacteristic
198#575—68no—
199C2×#137—32no—
200C2×#137—32no—
201C2×AGL(1,ℤ/8)—32no—
202C2×AGL(1,ℤ/8)—32no—
203C2×#135—28no—
204C2×#135—34no—
205C2×#135C2×D314yes—
206C2×#135C2×D314yescomplemented
207C22×Q16C2×D311yescharacteristic, complemented
208C22×SD16C2×D311yescharacteristic, complemented
209C22×SD16C2×D311yescharacteristic, complemented
210C22×D8C2×D311yescharacteristic, complemented
211C22×M16—31no—
212C23×C8C2×D311yescharacteristic
213#537—62no—
214#536—32no—
215#536—32no—
216#535—32no—
217#535—32no—
218#534—62no—
219#532—34no—
220#525—62no—
221#525—62no—
222#520—34no—
223#520—62no—
224#519—32no—
225#518—32no—
226#518—62no—
227C4×#41—34no—
228C4×#41—62no—
229C2×#117—31no—
230C2×#117—31no—
231C2×#117—62no—
232#464—38no—
233#464—38no—
234#463—38no—
235#463—38no—
236#462—38no—
237#461—38no—
238#460—38no—
239#459—38no—
240#424—32no—
241#424—32no—
242#424—34no—
243C2×C4⋊C8—34no—
244#419—32no—
245#418—32no—
246#417—34no—
247#416—34no—
248#416—34no—
249#416—32no—
250#416—32no—
251C2×#103—32no—
252C2×#102—32no—
253C24×C3—21no—
254C24×C3—21no—
255C24×C3C2×D411yescharacteristic
256C23×D3—21no—
257C3×#41—28no—
258C3×#41—28no—
259C3×#41—24no—
260C3×#41—24no—
261C3×#41—24no—
262C3×#41—24no—
263C3×#41—24no—
264C3×#41—24no—
265C3×#41—44no—
266C3×#41—44no—
267C3×#41C2×D418yes—
268C3×#41C2×D418yes—
269C2×C3×Q8—21no—
270C2×C3×Q8—21no—
271C2×C3×Q8—22no—
272C2×C3×Q8—22no—
273C2×C3×Q8—22no—
274C2×C3×Q8C2×D414yes—
275C2×C3×Q8C2412yes—
276C2×C3×Q8C2412yes—
277C2×C3×D4—28no—
278C2×C3×D4—22no—
279C2×C3×D4—22no—
280C2×C3×D4—22no—
281C2×C3×D4—22no—
282C2×C3×D4—21no—
283C2×C3×D4—22no—
284C2×C3×D4—21no—
285C2×C3×D4—22no—
286C2×C3×D4—22no—
287C2×C3×D4—44no—
288C2×C3×D4C2×D414yes—
289C2×C3×D4C2412yes—
290C2×C3×D4C2412yes—
291C22×C3×C4—21no—
292C22×C3×C4—28no—
293C22×C3×C4—22no—
294C22×C3×C4—22no—
295C22×C3×C4—21no—
296C22×C3×C4—22no—
297C22×C3×C4—22no—
298C22×C3×C4—44no—
299C22×C3×C4C2×D411yescharacteristic
300C22×C3×C4C2×D411yescharacteristic
301C22×C3×C4C2×D411yescharacteristic
302C22×C3×C4C2×D414yes—
303C22×C3×C4#4114yes—
304C22×C3×C4C2411yescharacteristic
305C22×C3×C4C2411yescharacteristic
306C22×C3×C4C2411yescharacteristic
307C2×#67—22no—
308C2×#67—22no—
309C2×#67—28no—
310C2×#67—44no—
311C22×Dic3—21no—
312C22×Dic3—22no—
313C22×Dic3—28no—
314C22×Dic3C2×D414yes—
315#235—24no—
316#235—24no—
317#235—24no—
318#235—24no—
319#235—44no—
320#235—44no—
321C2×D12—22no—
322C2×D12—22no—
323C2×D12—21no—
324C2×D12C2412yes—
325C2×C4×D3—22no—
326C2×C4×D3—22no—
327C2×C4×D3—44no—
328C2×Dic6—22no—
329C2×Dic6—22no—
330C2×Dic6—21no—
331C2×Dic6C2412yes—
332C3×Q16—28no—
333C3×SD16—28no—
334C3×SD16—28no—
335C3×D8—28no—
336C2×C3×C8—22no—
337C2×C3×C8—22no—
338C2×C3×C8—24no—
339C2×C3×C8—24no—
340C2×C3×C8C2412yes—
341C2×C3×C8C2412yes—
342#217—22no—
343#217—22no—
344#217—28no—
345#217—28no—
346#217C2×D414yes—
347#217C2×D414yes—
348#216—28no—
349#215—28no—
350#214—28no—
351#213—28no—
352(C2×D3)⋊C4—28no—
353C4⋊Dic3—22no—
354C4⋊Dic3—28no—
355C4⋊Dic3C2×D414yes—
356C4⋊Dic3C2×D414yes—
357C4⋊Dic3C2414yes—
358Dic3⋊C4—28no—
359C4×Dic3—22no—
360C4×Dic3—22no—
361C4×Dic3—28no—
362C4×Dic3C2×D414yes—
363C4×Dic3C2414yes—
364#208—24no—
365#208—24no—
366C2×C3⋊C8—24no—
367C2×C3⋊C8C2414yes—
368C2×#41—21no—
369C2×#41—21no—
370C2×#41—21no—
371C2×#41—21no—
372C2×#41—24no—
373C2×#41—24no—
374C2×#41—24no—
375C2×#41—32no—
376C2×#41—32no—
377C2×#41—61no—
378C2×#41—61no—
379C2×#41—64no—
380C2×#41—64no—
381C2×#41#6718yescomplemented
382C2×#41C22×D312yes—
383C2×#41C22×D312yes—
384C2×#41C22×D312yes—
385C2×#41C22×D312yes—
386C22×Q8—31no—
387C22×Q8C22×D311yescharacteristic
388C22×Q8C22×D311yescharacteristic
389C22×D4—21no—
390C22×D4—21no—
391C22×D4—31no—
392C22×D4—61no—
393C22×D4C22×D311yescharacteristic
394C22×D4C22×D311yescharacteristic
395C23×C4—21no—
396C23×C4—21no—
397C23×C4—61no—
398C23×C4C22×D311yescharacteristic
399#137—68no—
400#137—68no—
401AGL(1,ℤ/8)—68no—
402AGL(1,ℤ/8)—68no—
403#135—216no—
404#135—216no—
405#135—616no—
406C2×Q16—24no—
407C2×Q16—34no—
408C2×Q16C22×D314yes—
409C2×SD16—24no—
410C2×SD16—24no—
411C2×SD16—34no—
412C2×SD16—34no—
413C2×SD16C22×D314yes—
414C2×SD16C22×D314yes—
415C2×D8—24no—
416C2×D8—34no—
417C2×D8C22×D314yes—
418C2×M16—32no—
419C2×M16—32no—
420C2×M16—64no—
421C22×C8—24no—
422C22×C8—32no—
423C22×C8C22×D311yescharacteristic
424C22×C8C22×D311yescharacteristic
425C22×C8C22×D312yes—
426C22×C8C22×D312yes—
427C4⋊Q8—34no—
428#127—34no—
429#124—34no—
430#124—34no—
431#123—64no—
432#123—64no—
433C22⋊Q8—64no—
434C22⋊Q8—64no—
435#121—64no—
436#121—64no—
437#121—68no—
438#120—64no—
439#120—64no—
440C4×Q8—38no—
441C4×Q8—64no—
442C4×D4—38no—
443C4×D4—68no—
444C4×D4—68no—
445C4×D4—64no—
446C4×D4—68no—
447#117—32no—
448#117—32no—
449#117—32no—
450#117—32no—
451#117—32no—
452#117—32no—
453#117—64no—
454#117—64no—
455#117—64no—
456#117—61no—
457#117—61no—
458C2×C4⋊C4—32no—
459C2×C4⋊C4—32no—
460C2×C4⋊C4—64no—
461C2×C22⋊C4—32no—
462C2×C22⋊C4—64no—
463C2×C22⋊C4—61no—
464C2×C42—32no—
465C2×C42—64no—
466C2×C42—61no—
467C4⋊C8—38no—
468C4⋊C8—38no—
469#103—38no—
470#103—34no—
471#103—34no—
472#102—38no—
473#102—34no—
474#102—34no—
475C23×C3—22no—
476C23×C3—24no—
477C23×C3—22no—
478C23×C3—42no—
479C23×C3—42no—
480C23×C3—82no—
481C23×C3—82no—
482C23×C3#12114yes—
483C23×C3C22×D411yescharacteristic
484C23×C3C22×D411yescharacteristic
485C23×C3C22×D411yescharacteristic
486C22×D3—22no—
487C22×D3—42no—
488C22×D3—82no—
489C3×Q8—24no—
490C3×Q8—22no—
491C3×Q8—22no—
492C3×Q8—22no—
493C3×Q8—42no—
494C3×Q8C22×D414yes—
495C3×D4—28no—
496C3×D4—28no—
497C3×D4—24no—
498C3×D4—22no—
499C3×D4—22no—
500C3×D4—22no—
501C3×D4—44no—
502C3×D4—44no—
503C3×D4—42no—
504C3×D4C22×D414yes—
505C2×C3×C4—24no—
506C2×C3×C4—22no—
507C2×C3×C4—28no—
508C2×C3×C4—28no—
509C2×C3×C4—22no—
510C2×C3×C4—42no—
511C2×C3×C4—44no—
512C2×C3×C4—44no—
513C2×C3×C4#12114yes—
514C2×C3×C4#12114yes—
515C2×C3×C4#12114yes—
516C2×C3×C4C22×D411yescharacteristic
517C2×C3×C4C22×D411yescharacteristic
518C2×C3×C4C22×D411yescharacteristic
519C2×C3×C4C22×D412yes—
520C2×C3×C4C22×D412yes—
521C2×C3×C4C22×D412yes—
522C2×C3×C4C2×#4112yes—
523C2×C3×C4C2×#4112yes—
524C2×C3×C4C2×#4112yes—
525C2×C3×C4C2511yescharacteristic
526#67—44no—
527#67—44no—
528#67—88no—
529C2×Dic3—24no—
530C2×Dic3—22no—
531C2×Dic3—44no—
532C2×Dic3—42no—
533C2×Dic3—88no—
534C2×Dic3—82no—
535C2×Dic3C22×D418yes—
536D12—22no—
537D12—22no—
538D12—42no—
539C4×D3—44no—
540C4×D3—44no—
541Dic6—22no—
542Dic6—22no—
543Dic6—42no—
544C3×C8—22no—
545C3×C8—22no—
546C3⋊C8—24no—
547C24—21no—
548C24—21no—
549C24—61no—
550C24D3×D411yescharacteristic
551#41—28no—
552#41—28no—
553#41—24no—
554#41—24no—
555#41—24no—
556#41—24no—
557#41—24no—
558#41—24no—
559#41—44no—
560#41—44no—
561#41—64no—
562#41—64no—
563#41—64no—
564#41—64no—
565#41—124no—
566#41—124no—
567#41C2×#6718yes—
568#41C2×#6718yes—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—22no—
572C2×Q8—22no—
573C2×Q8—22no—
574C2×Q8—32no—
575C2×Q8—61no—
576C2×Q8—62no—
577C2×Q8—62no—
578C2×Q8C2×#6714yes—
579C2×Q8C23×D312yes—
580C2×Q8C23×D312yes—
581C2×D4—28no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—32no—
592C2×D4—44no—
593C2×D4—68no—
594C2×D4—62no—
595C2×D4—62no—
596C2×D4—61no—
597C2×D4—62no—
598C2×D4—62no—
599C2×D4—124no—
600C2×D4C2×#6714yes—
601C2×D4C23×D312yes—
602C2×D4C23×D312yes—
603C22×C4—21no—
604C22×C4—28no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—21no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—34no—
611C22×C4—44no—
612C22×C4—68no—
613C22×C4—61no—
614C22×C4—62no—
615C22×C4—62no—
616C22×C4—62no—
617C22×C4—124no—
618C22×C4D3×D411yescharacteristic
619C22×C4D3×D411yescharacteristic
620C22×C4D3×D411yescharacteristic
621C22×C4#23714yes—
622C22×C4C2×#6714yes—
623C22×C4C23×D311yescharacteristic
624C22×C4C23×D311yescharacteristic
625C22×C4C23×D311yescharacteristic
626Q16—28no—
627Q16—68no—
628SD16—28no—
629SD16—28no—
630SD16—68no—
631SD16—68no—
632D8—28no—
633D8—68no—
634M16—64no—
635M16—64no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—24no—
639C2×C8—24no—
640C2×C8—34no—
641C2×C8—64no—
642C2×C8C23×D312yes—
643C2×C8C23×D312yes—
644C4⋊C4—34no—
645C4⋊C4—34no—
646C4⋊C4—34no—
647C4⋊C4—68no—
648C4⋊C4—68no—
649C4⋊C4—62no—
650C22⋊C4—34no—
651C22⋊C4—34no—
652C22⋊C4—68no—
653C22⋊C4—68no—
654C22⋊C4—68no—
655C22⋊C4—62no—
656C22⋊C4—62no—
657C42—34no—
658C42—34no—
659C42—68no—
660C42—62no—
661C42—62no—
662C22×C3—22no—
663C22×C3—22no—
664C22×C3—22no—
665C22×C3—24no—
666C22×C3—44no—
667C22×C3—44no—
668C22×C3—44no—
669C22×C3—42no—
670C22×C3—84no—
671C22×C3—84no—
672C22×C3C2×#12112yes—
673C22×C3C2×#12112yes—
674C22×C3C2×#12112yes—
675C22×C3C23×D411yescharacteristic
676C2×D3—44no—
677C2×D3—42no—
678C2×D3—84no—
679C3×C4—24no—
680C3×C4—42no—
681C3×C4C2×#12112yes—
682C3×C4C2×#12112yes—
683C3×C4C2×#12112yes—
684C3×C4C23×D411yescharacteristic
685C3×C4C22×#4111yescharacteristic
686Dic3—28no—
687Dic3—44no—
688Dic3—42no—
689C23—22no—
690C23—24no—
691C23—22no—
692C23—42no—
693C23—42no—
694C23—62no—
695C23—82no—
696C23—82no—
697C23—122no—
698C23—242no—
699C23#93914yes—
700C23C2×D3×D411yescharacteristic
701C23C2×D3×D411yescharacteristic
702C23C2×D3×D411yescharacteristic
703Q8—22no—
704Q8—24no—
705Q8—22no—
706Q8—22no—
707Q8—42no—
708Q8—62no—
709Q8—62no—
710Q8—122no—
711Q8C22×#6714yes—
712D4—28no—
713D4—28no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—24no—
718D4—44no—
719D4—44no—
720D4—42no—
721D4—62no—
722D4—62no—
723D4—124no—
724D4—124no—
725D4—122no—
726D4—248no—
727D4C22×#6714yes—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—28no—
731C2×C4—28no—
732C2×C4—22no—
733C2×C4—38no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—64no—
738C2×C4—62no—
739C2×C4—124no—
740C2×C4—122no—
741C2×C4—124no—
742C2×C4—124no—
743C2×C4—248no—
744C2×C4—242no—
745C2×C4#93914yes—
746C2×C4#93914yes—
747C2×C4#93914yes—
748C2×C4C2×D3×D411yescharacteristic
749C2×C4C2×D3×D411yescharacteristic
750C2×C4C2×D3×D411yescharacteristic
751C2×C4C2×#23712yes—
752C2×C4C2×#23712yes—
753C2×C4C2×#23712yes—
754C2×C4C22×#6712yes—
755C2×C4C22×#6712yes—
756C2×C4C22×#6712yes—
757C2×C4C24×D311yescharacteristic
758C8—22no—
759C8—22no—
760C8—64no—
761C2×C3—22no—
762C2×C3—22no—
763C2×C3—22no—
764C2×C3—44no—
765C2×C3—82no—
766C2×C3C22×#12111yescharacteristic
767C2×C3#358412yes—
768D3—82no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—24no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—42no—
777C22—84no—
778C22—84no—
779C22—124no—
780C22—122no—
781C22—244no—
782C22C2×#93912yes—
783C22C2×#93912yes—
784C22C2×#93912yes—
785C22C22×D3×D411yescharacteristic
786C4—24no—
787C4—42no—
788C4—68no—
789C4—124no—
790C4—122no—
791C4C2×#93912yes—
792C4C2×#93912yes—
793C4C2×#93912yes—
794C4C22×#23711yescharacteristic
795C4C23×#6711yescharacteristic
796C3#6042211yescharacteristic, complemented, Sylow
797C2—22no—
798C2—22no—
799C2—22no—
800C2—44no—
801C2—82no—
802C2—242no—
803C2#8718712yes—
804C2C22×#93911yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC22×C3×#135C2
socleC22×C3C23×D4
hypercenterC22×#135D3
hypocenterC3#60422
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#135

Complements

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

NH ≅ G/Ntype
1. C22×C3×#135C2semidirect
2. #87268C2semidirect
3. #87260C2semidirect
4. C2×#5822C2semidirect
5. #84072C2semidirect
6. #83902C2semidirect
7. #83901C2semidirect
8. #83900C2semidirect
9. #83877C2semidirect
10. #83849C2semidirect
11. #83848C2semidirect
12. #83826C2semidirect
13. C2×#5113C2semidirect
14. C2×#5102C2semidirect
21. C2×C3×#135C22semidirect
22. C22×C3×Q16C22semidirect
23. C22×C3×SD16C22semidirect
24. C22×C3×SD16C22semidirect
25. C22×C3×D8C22semidirect
28. #5832C22semidirect
29. #5830C22semidirect
32. #5827C22semidirect
34. Dic3×#41C22semidirect
35. #5825C22semidirect
36. C2×#951C22semidirect
38. C2×#950C22semidirect
39. C2×#949C22semidirect
41. #5812C22semidirect
46. #5798C22semidirect
53. #5233C22semidirect
54. #5232C22semidirect
55. #5225C22semidirect
56. #5215C22semidirect
57. #5185C22semidirect
58. #5182C22semidirect
59. #5166C22semidirect
60. #5165C22semidirect
61. #5163C22semidirect
62. #5162C22semidirect
63. #5153C22semidirect
64. #5150C22semidirect
67. #5113C22semidirect
68. C2×#821C22semidirect
69. C2×#816C22semidirect
70. #5102C22semidirect
71. #5102C22semidirect
72. #5102C22semidirect
73. C2×Dic3⋊C8C22semidirect
75. C22×#135D3semidirect
95. C2×C3×#41D4semidirect
206. C2×#135C2×D3semidirect
207. C22×Q16C2×D3semidirect
208. C22×SD16C2×D3semidirect
209. C22×SD16C2×D3semidirect
210. C22×D8C2×D3semidirect
381. C2×#41#67semidirect
796. C3#60422semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#1352
#872682
#872602
C2×#58222
#840722
#839022
#839012
#839002
#838772
#838492
#838482
#838262
C2×#51132
C2×#51022
#604223