Finite Group Databasebeta

← #11664118

Subgroups — #11664118

Order 768.

2134 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#85747C211yesmaximal, characteristic, complemented
2C2×#5523C211yesmaximal, characteristic, complemented
3C3×#2924C211yesmaximal, characteristic, complemented
4#79389C214yesmaximal, complemented
5#79384C214yesmaximal, complemented
6#79357C212yesmaximal, complemented
7#79343C212yesmaximal, complemented
8#79309C212yesmaximal, complemented
9#79300C212yesmaximal, complemented
10#79092C212yesmaximal, complemented
11#79088C212yesmaximal, complemented
12#78639C211yesmaximal, characteristic, complemented
13#78622C211yesmaximal, characteristic, complemented
14#78610C211yesmaximal, characteristic, complemented
15C2×#4735C211yesmaximal, characteristic, complemented
16#78574C212yesmaximal, complemented
17#78560C212yesmaximal, complemented
18#60588—31nomaximal, Sylow
19C22×#235C2211yescharacteristic
20C2×C3×#117C2211yescharacteristic
21#5791C2211yescharacteristic
22C2×#930C2211yescharacteristic
23C22×C4⋊Dic3C2211yescharacteristic
24C2×#908C2212yes—
25C2×#904C2212yes—
26#5535C2212yescomplemented
27#5534C2212yescomplemented
28#5532—21no—
29#5530—21no—
30#5527—22no—
31#5525C2211yescharacteristic, complemented
32#5523—22no—
33#5523—21no—
34#5523—21no—
35#5523C2212yes—
36#5523C2212yes—
37#5523C2214yescomplemented
38#5523C2211yescharacteristic, complemented
39#5521C2211yescharacteristic, complemented
40#5519C2211yescharacteristic, complemented
41#5514—21no—
42#5507—21no—
43C2×#892—21no—
44C2×D3×C4⋊C4—21no—
45#5490—22no—
46C2×#67⋊C4—22no—
47#5479C2212yes—
48#5477C2212yes—
49C2×C4×D12C2212yescomplemented
50C2×C4×Dic6C2212yescomplemented
51C3×#433C2214yescomplemented
52C3×#432C2212yescomplemented
53C3×#431C2212yescomplemented
54C3×#424C2212yescomplemented
55C3×#407C2211yescharacteristic
56C2×C3×C22⋊C8C2211yescharacteristic
57C3×#405C2212yescomplemented
58#5133C2212yes—
59#5133C2212yescomplemented
60#5121C2212yescomplemented
61#5113C2212yes—
62C2×#821C2212yescomplemented
63C2×#817C2212yescomplemented
64#4851C2214yescomplemented
65#4848C2214yescomplemented
66#4847C2214yescomplemented
67#4845C2214yescomplemented
68#4844C2214yescomplemented
69#4843C2214yescomplemented
70#4842C2214yescomplemented
71#4829C2214yescomplemented
72#4739C2211yescharacteristic, complemented
73#4738C2212yes—
74#4738C2211yescharacteristic, complemented
75#4736C2212yescomplemented
76#4735C2212yes—
77#4735C2212yes—
78#4735C2214yescomplemented
79#4735C2212yescomplemented
80#4734C2214yes—
81#4734C2212yescomplemented
82#4733C2212yescomplemented
83#4732C2212yes—
84#4732C2211yescharacteristic, complemented
85#4731C2211yescharacteristic, complemented
86#4722C2212yescomplemented
87#4721C2212yescomplemented
88#4716C2214yescomplemented
89#4711C2214yescomplemented
90#4711C2214yescomplemented
91#4710C2214yescomplemented
92C4×D24C2214yescomplemented
93C4×#204C2214yescomplemented
94C4×#204C2214yescomplemented
95C4×#204C2214yescomplemented
96#3494—31no—
97C2×#520—31no—
98#3125—34no—
99#3119—34no—
100#3117—32no—
101#3109—32no—
102#3105—32no—
103#3103—32no—
104#3092—31no—
105C2×#481—31no—
106#3084—32no—
107#3045—32no—
108#3006—31no—
109#3002—31no—
110#2952—32no—
111#2946—32no—
112#2924D311yescharacteristic, complemented
113C23×C3×C4C2311yescharacteristic
114C22×#67—21no—
115C22×#67—21no—
116C23×Dic3—21no—
117C2×#235—21no—
118C2×#235—21no—
119C2×#235—28no—
120C2×#235—22no—
121C2×#235C2311yescharacteristic
122C2×#235C2312yes—
123C2×#235C2312yes—
124C22×D12C2311yescharacteristic
125C22×D12C2311yescharacteristic
126C22×C4×D3—21no—
127C22×C4×D3—22no—
128C22×Dic6C2311yescharacteristic
129C2×C3×M16C2312yes—
130C22×C3×C8C2312yes—
131C3×#117D412yes—
132C3×#117D411yescharacteristic
133C3×#117D411yescharacteristic
134C3×#117C2311yescharacteristic
135C3×#117C2311yescharacteristic
136C3×#117C2312yes—
137C2×C3×C4⋊C4D411yescharacteristic
138C2×C3×C4⋊C4D411yescharacteristic
139C2×C3×C22⋊C4D412yes—
140C2×C3×C42C2312yes—
141#953—21no—
142#930—22no—
143#930—21no—
144#930—21no—
145#930C2311yescharacteristic
146#930C2312yes—
147#930C2312yes—
148#930C2311yescharacteristic
149#929—22no—
150#929—21no—
151C4×#67—22no—
152C4×#67—21no—
153C4×#67—21no—
154C2×(C2×D3)⋊C4—22no—
155C2×(C2×D3)⋊C4—21no—
156#926C2311yescharacteristic
157C2×C4⋊Dic3—21no—
158C2×C4⋊Dic3—21no—
159C2×C4⋊Dic3—21no—
160C2×C4⋊Dic3C2312yes—
161C2×C4⋊Dic3C2311yescharacteristic
162C2×C4⋊Dic3C2312yes—
163C2×C4⋊Dic3C2312yes—
164#924C2311yescharacteristic
165#924C2311yescharacteristic
166C2×Dic3⋊C4—22no—
167C2×C4×Dic3—22no—
168#908—28no—
169C2×Dic12C2312yes—
170#904—28no—
171C2×D24C2314yes—
172C2×D24C2312yes—
173C2×#204C2312yes—
174C2×#204C2312yes—
175C2×#204C2314yes—
176#898—22no—
177#896—22no—
178#895—21no—
179#895—21no—
180#894—22no—
181#894—22no—
182#893—21no—
183#893—21no—
184#892—22no—
185#892—22no—
186#892—24no—
187#892—21no—
188D3×C4⋊C4—22no—
189D3×C4⋊C4—22no—
190D3×C4⋊C4—24no—
191D3×C4⋊C4—21no—
192#890—21no—
193#888—21no—
194#885—22no—
195#884—22no—
196#884—22no—
197#883—22no—
198#882—22no—
199#67⋊C4—24no—
200#67⋊C4—24no—
201#67⋊C4—24no—
202#67⋊C4—24no—
203#67⋊C4—22no—
204D3×C22⋊C4—22no—
205#878—22no—
206#876—22no—
207#875—22no—
208#875C2312yes—
209#874C2312yes—
210C4×D12—22no—
211C4×D12—22no—
212C4×D12—22no—
213C4×D12C2312yes—
214C4×D12C2312yes—
215C4×D12C2314yes—
216C4×D12C2312yes—
217C4×D12C2314yes—
218#872—22no—
219#870C2312yes—
220#869C2312yes—
221C4×Dic6—22no—
222C4×Dic6—22no—
223C4×Dic6C2314yes—
224C4×Dic6C2312yes—
225C4×Dic6C2314yes—
226C3×C4⋊C8C2314yes—
227C3×C4⋊C8C2314yes—
228C3×C22⋊C8C2312yes—
229C3×C22⋊C8C2312yes—
230C3×C22⋊C8C2311yescharacteristic
231C3×C22⋊C8C2311yescharacteristic
232C3×C22⋊C8C2312yes—
233C3×#97C2314yes—
234C3×C4×C8C2314yes—
235#821C2314yes—
236#821C2314yes—
237#821C2314yes—
238#821C2312yes—
239#821C2314yes—
240#821C2312yes—
241#818C2314yes—
242#817C2314yes—
243#817C2314yes—
244#817C2314yes—
245#816C2314yes—
246#816C2314yes—
247#816C2312yes—
248#816C2312yes—
249C22×#41—31no—
250C2×AGL(1,ℤ/8)—32no—
251C2×#135—32no—
252#555—61no—
253#553—61no—
254#553—61no—
255#551—62no—
256#547—61no—
257#546—62no—
258#544—31no—
259#542—32no—
260#540—32no—
261#535—31no—
262#532—32no—
263#529—32no—
264#525—31no—
265C2×#121—31no—
266#520—32no—
267#520—34no—
268#520—32no—
269#520—31no—
270#520—62no—
271#520—61no—
272#520—61no—
273#518—31no—
274C2×C4×Q8—32no—
275C2×C4×D4—32no—
276C2×C4×D4—62no—
277C2×#117—61no—
278C2×#117C2×D311yescharacteristic
279C22×C4⋊C4—31no—
280C22×C4⋊C4—61no—
281#484—32no—
282#483—32no—
283#481—32no—
284#481—32no—
285#481—34no—
286#481—32no—
287#480—32no—
288#479—34no—
289#478—34no—
290#476—34no—
291#475—34no—
292#464—34no—
293#463—34no—
294#460—34no—
295#459—34no—
296#452—32no—
297#451—31no—
298#450—31no—
299#449—32no—
300#449—34no—
301#448—31no—
302#448—32no—
303#447—32no—
304#447—31no—
305#442—34no—
306#442—34no—
307#441—34no—
308#440—34no—
309C4×SD16—34no—
310C4×SD16—34no—
311C4×SD16—34no—
312C4×D8—34no—
313#433C2×D314yescomplemented
314#432C2×D312yescomplemented
315#431C2×D312yescomplemented
316#428—32no—
317C2×#106—32no—
318#424C2×D312yescomplemented
319#417—32no—
320#417—32no—
321#416—32no—
322C2×#102—32no—
323#407C2×D311yescharacteristic
324C2×C22⋊C8C2×D311yescharacteristic
325#405C2×D312yescomplemented
326C24×C3C2×D411yescharacteristic
327C23×D3—21no—
328C23×D3—21no—
329C22×C3×C4—24no—
330C22×C3×C4C2×D412yes—
331C22×C3×C4C2×D411yescharacteristic
332C22×C3×C4C2×D411yescharacteristic
333C22×C3×C4C2×D411yescharacteristic
334C22×C3×C4C2×D412yes—
335C22×C3×C4C2411yescharacteristic
336C22×C3×C4C2411yescharacteristic
337C22×C3×C4C2411yescharacteristic
338C2×#67—28no—
339C2×#67—22no—
340C2×#67—22no—
341C2×#67—21no—
342C2×#67—22no—
343C2×#67—21no—
344C2×#67—22no—
345C2×#67—21no—
346C2×#67—82no—
347C22×Dic3—21no—
348C22×Dic3—22no—
349C22×Dic3—21no—
350C22×Dic3—22no—
351C22×Dic3—22no—
352C22×Dic3—82no—
353#235—28no—
354#235—28no—
355#235—24no—
356#235—24no—
357#235—24no—
358#235—24no—
359#235—84no—
360#235#4118yescomplemented
361C2×D12—21no—
362C2×D12—24no—
363C2×D12—24no—
364C2×D12—21no—
365C2×D12—22no—
366C2×D12—22no—
367C2×D12C2411yescharacteristic
368C2×D12C2412yes—
369C2×D12C2412yes—
370C2×C4×D3—28no—
371C2×C4×D3—22no—
372C2×C4×D3—22no—
373C2×C4×D3—21no—
374C2×C4×D3—22no—
375C2×C4×D3—22no—
376C2×C4×D3—24no—
377C2×C4×D3—24no—
378C2×C4×D3—22no—
379C2×C4×D3—84no—
380C2×Dic6—21no—
381C2×Dic6—24no—
382C2×Dic6—22no—
383C2×Dic6C2411yescharacteristic
384C2×Dic6C2412yes—
385C3×M16—24no—
386C2×C3×C8—24no—
387C2×C3×C8C2414yes—
388C2×C3×C8C2412yes—
389C2×C3×C8C2412yes—
390C3×C4⋊C4C2×D411yescharacteristic
391C3×C4⋊C4C2×D411yescharacteristic
392C3×C4⋊C4C2×D411yescharacteristic
393C3×C4⋊C4C2×D412yes—
394C3×C4⋊C4C2×D411yescharacteristic
395C3×C4⋊C4C2×D412yes—
396C3×C22⋊C4C2×D412yes—
397C3×C22⋊C4C2×D412yes—
398C3×C22⋊C4C2×D412yes—
399C3×C22⋊C4C2×D412yes—
400C3×C42C2×D412yes—
401C3×C42C2×D412yes—
402C3×C42C2412yes—
403C3×C42C2412yes—
404#217—21no—
405#217—21no—
406#217—21no—
407(C2×D3)⋊C4—22no—
408(C2×D3)⋊C4—22no—
409(C2×D3)⋊C4—21no—
410(C2×D3)⋊C4—24no—
411(C2×D3)⋊C4—24no—
412(C2×D3)⋊C4—22no—
413(C2×D3)⋊C4—22no—
414(C2×D3)⋊C4—22no—
415(C2×D3)⋊C4—22no—
416(C2×D3)⋊C4—21no—
417(C2×D3)⋊C4—22no—
418C4⋊Dic3—22no—
419C4⋊Dic3—22no—
420C4⋊Dic3—21no—
421C4⋊Dic3—22no—
422C4⋊Dic3—22no—
423C4⋊Dic3C2412yes—
424C4⋊Dic3C2411yescharacteristic
425C4⋊Dic3C2411yescharacteristic
426C4⋊Dic3C2414yes—
427Dic3⋊C4—24no—
428Dic3⋊C4—24no—
429Dic3⋊C4—22no—
430Dic3⋊C4—22no—
431Dic3⋊C4—22no—
432Dic3⋊C4—21no—
433Dic3⋊C4—21no—
434C4×Dic3—24no—
435C4×Dic3—24no—
436C4×Dic3—22no—
437C4×Dic3—21no—
438Dic12—24no—
439D24—24no—
440D24—28no—
441#204—24no—
442#204—24no—
443#204—28no—
444C2×#41—32no—
445C2×#41—32no—
446C2×#41—31no—
447C2×#41—68no—
448C2×#41—61no—
449C2×#41—61no—
450C2×#41—62no—
451C22×Q8—31no—
452C22×D4—31no—
453C22×D4—31no—
454C22×D4—61no—
455C22×D4—61no—
456C23×C4—61no—
457C23×C4—61no—
458C23×C4—62no—
459C23×C4C22×D311yescharacteristic
460AGL(1,ℤ/8)—68no—
461#135—68no—
462C2×Q16—32no—
463C2×SD16—32no—
464C2×SD16—32no—
465C2×SD16—34no—
466C2×D8—32no—
467C2×D8—34no—
468C2×M16C22×D312yes—
469C22×C8C22×D312yes—
470C4⋊Q8—32no—
471C4⋊Q8—61no—
472#127—32no—
473#126—62no—
474#126—62no—
475#125—32no—
476#125—61no—
477#124—32no—
478#124—62no—
479#124—62no—
480#123—61no—
481#123—62no—
482#123—62no—
483#123—62no—
484#123—62no—
485C22⋊Q8—31no—
486C22⋊Q8—31no—
487C22⋊Q8—62no—
488C22⋊Q8—62no—
489#121—32no—
490#121—32no—
491#121—31no—
492#121—31no—
493#121—61no—
494#121—61no—
495#121—62no—
496#121—61no—
497#121—61no—
498#121—62no—
499#121—62no—
500#120—61no—
501#120—62no—
502C4×Q8—34no—
503C4×Q8—34no—
504C4×Q8—32no—
505C4×Q8—62no—
506C4×Q8—62no—
507C4×D4—34no—
508C4×D4—34no—
509C4×D4—32no—
510C4×D4—32no—
511C4×D4—32no—
512C4×D4—61no—
513C4×D4—61no—
514C4×D4—62no—
515C4×D4—61no—
516C4×D4—61no—
517C4×D4—64no—
518C4×D4—64no—
519C4×D4—64no—
520C4×D4—64no—
521C4×D4—62no—
522C4×D4—62no—
523C4×D4—62no—
524C4×D4—62no—
525#117—31no—
526#117—62no—
527#117—62no—
528#117—64no—
529#117—61no—
530#117—62no—
531#117D1212yes—
532#117D1211yescharacteristic
533#117D1211yescharacteristic
534#117C22×D311yescharacteristic
535#117C22×D311yescharacteristic
536#117C22×D312yes—
537C2×C4⋊C4—32no—
538C2×C4⋊C4—32no—
539C2×C4⋊C4—32no—
540C2×C4⋊C4—31no—
541C2×C4⋊C4—61no—
542C2×C4⋊C4—61no—
543C2×C4⋊C4—61no—
544C2×C4⋊C4—62no—
545C2×C4⋊C4—62no—
546C2×C4⋊C4—62no—
547C2×C4⋊C4—64no—
548C2×C4⋊C4—61no—
549C2×C4⋊C4D1211yescharacteristic
550C2×C4⋊C4D1211yescharacteristic
551C2×C22⋊C4—62no—
552C2×C22⋊C4—61no—
553C2×C22⋊C4—62no—
554C2×C22⋊C4D1212yes—
555C2×C42—62no—
556C2×C42C22×D312yes—
557#107—34no—
558#106—34no—
559#106—34no—
560#106—34no—
561C4⋊C8C22×D314yes—
562C4⋊C8C22×D314yes—
563#103—32no—
564#103—32no—
565#103—34no—
566#103—34no—
567#102—34no—
568#102—34no—
569#102—32no—
570#102—32no—
571#102—34no—
572#102—34no—
573C22⋊C8C22×D311yescharacteristic
574C22⋊C8C22×D311yescharacteristic
575C22⋊C8C22×D312yes—
576C22⋊C8C22×D312yes—
577C22⋊C8C22×D312yes—
578#97C22×D314yes—
579C4×C8C22×D314yes—
580C23×C3—22no—
581C23×C3—22no—
582C23×C3—41no—
583C23×C3C22×D411yescharacteristic
584C23×C3C22×D411yescharacteristic
585C23×C3C22×D411yescharacteristic
586C22×D3—24no—
587C22×D3—22no—
588C22×D3—22no—
589C22×D3—21no—
590C22×D3—42no—
591C22×D3—42no—
592C22×D3—42no—
593C22×D3—81no—
594C22×D3—81no—
595C2×C3×C4—22no—
596C2×C3×C4—24no—
597C2×C3×C4—22no—
598C2×C3×C4—22no—
599C2×C3×C4—22no—
600C2×C3×C4—22no—
601C2×C3×C4—42no—
602C2×C3×C4C22×D412yes—
603C2×C3×C4C22×D412yes—
604C2×C3×C4C22×D412yes—
605C2×C3×C4C22×D412yes—
606C2×C3×C4C22×D411yescharacteristic
607C2×C3×C4C22×D411yescharacteristic
608C2×C3×C4C22×D411yescharacteristic
609C2×C3×C4C2×#4114yes—
610C2×C3×C4C2511yescharacteristic
611#67—28no—
612#67—28no—
613#67—42no—
614#67—42no—
615#67—44no—
616#67—81no—
617#67—82no—
618C2×Dic3—24no—
619C2×Dic3—22no—
620C2×Dic3—21no—
621C2×Dic3—24no—
622C2×Dic3—21no—
623C2×Dic3—22no—
624C2×Dic3—21no—
625C2×Dic3—44no—
626C2×Dic3—82no—
627C2×Dic3—82no—
628C2×Dic3—81no—
629D12—24no—
630D12—22no—
631D12—24no—
632D12—22no—
633D12—42no—
634D12—82no—
635D12—82no—
636D12C2×#4114yes—
637C4×D3—28no—
638C4×D3—28no—
639C4×D3—42no—
640C4×D3—82no—
641C4×D3—84no—
642C4×D3—84no—
643C4×D3—82no—
644C4×D3—82no—
645Dic6—24no—
646Dic6—22no—
647Dic6—22no—
648Dic6—82no—
649Dic6C2×#4114yes—
650C3×C8—22no—
651C3×C8—24no—
652C3×C8—22no—
653C24—61no—
654C24—61no—
655C24C2×D1211yescharacteristic
656#41—38no—
657#41—64no—
658#41—64no—
659#41—68no—
660#41—68no—
661#41—64no—
662#41—64no—
663#41—244no—
664C2×Q8—32no—
665C2×Q8—31no—
666C2×Q8—64no—
667C2×Q8—61no—
668C2×Q8—62no—
669C2×D4—32no—
670C2×D4—32no—
671C2×D4—31no—
672C2×D4—64no—
673C2×D4—68no—
674C2×D4—62no—
675C2×D4—62no—
676C2×D4—61no—
677C2×D4—61no—
678C2×D4—62no—
679C2×D4—61no—
680C2×D4—62no—
681C2×D4—61no—
682C2×D4—61no—
683C2×D4—62no—
684C2×D4—62no—
685C2×D4—64no—
686C2×D4—242no—
687C22×C4—24no—
688C22×C4—68no—
689C22×C4—61no—
690C22×C4—62no—
691C22×C4—62no—
692C22×C4—62no—
693C22×C4—61no—
694C22×C4—62no—
695C22×C4—62no—
696C22×C4—61no—
697C22×C4—62no—
698C22×C4—62no—
699C22×C4—64no—
700C22×C4—64no—
701C22×C4—62no—
702C22×C4—244no—
703C22×C4—242no—
704C22×C4C2×D1212yes—
705C22×C4C2×D1211yescharacteristic
706C22×C4C2×D1211yescharacteristic
707C22×C4C2×D1211yescharacteristic
708C22×C4C2×D1212yes—
709C22×C4C23×D311yescharacteristic
710C22×C4C23×D311yescharacteristic
711C22×C4C23×D311yescharacteristic
712Q16—64no—
713SD16—64no—
714SD16—64no—
715SD16—68no—
716D8—64no—
717D8—68no—
718M16—24no—
719C2×C8—24no—
720C2×C8C23×D312yes—
721C2×C8C23×D314yes—
722C2×C8C23×D312yes—
723C4⋊C4—34no—
724C4⋊C4—32no—
725C4⋊C4—31no—
726C4⋊C4—31no—
727C4⋊C4—62no—
728C4⋊C4—62no—
729C4⋊C4—62no—
730C4⋊C4—61no—
731C4⋊C4—64no—
732C4⋊C4—64no—
733C4⋊C4—62no—
734C4⋊C4—61no—
735C4⋊C4—62no—
736C4⋊C4—62no—
737C4⋊C4—62no—
738C4⋊C4—61no—
739C4⋊C4C2×D1211yescharacteristic
740C4⋊C4C2×D1211yescharacteristic
741C4⋊C4C2×D1212yes—
742C4⋊C4C2×D1211yescharacteristic
743C4⋊C4C2×D1211yescharacteristic
744C4⋊C4C2×D1212yes—
745C22⋊C4—61no—
746C22⋊C4—61no—
747C22⋊C4—61no—
748C22⋊C4—64no—
749C22⋊C4—64no—
750C22⋊C4—62no—
751C22⋊C4—62no—
752C22⋊C4—62no—
753C22⋊C4—62no—
754C22⋊C4—62no—
755C22⋊C4—62no—
756C22⋊C4—61no—
757C22⋊C4—62no—
758C22⋊C4—61no—
759C22⋊C4C2×D1212yes—
760C22⋊C4C2×D1212yes—
761C22⋊C4C2×D1212yes—
762C22⋊C4C2×D1212yes—
763C42—64no—
764C42—64no—
765C42—61no—
766C42—62no—
767C42C2×D1212yes—
768C42C2×D1212yes—
769C42C23×D312yes—
770C42C23×D312yes—
771C22×C3—21no—
772C22×C3—21no—
773C22×C3—21no—
774C22×C3—21no—
775C22×C3—21no—
776C22×C3—21no—
777C22×C3—21no—
778C22×C3—44no—
779C22×C3#52512yes—
780C22×C3#57712yes—
781C22×C3C23×D411yescharacteristic
782C2×D3—24no—
783C2×D3—48no—
784C2×D3—42no—
785C2×D3—42no—
786C2×D3—42no—
787C2×D3—41no—
788C2×D3—41no—
789C2×D3—42no—
790C2×D3—41no—
791C2×D3—42no—
792C2×D3—162no—
793C3×C4—22no—
794C3×C4—22no—
795C3×C4—21no—
796C3×C4—21no—
797C3×C4—22no—
798C3×C4—22no—
799C3×C4#52512yes—
800C3×C4C22×#4112yes—
801Dic3—24no—
802Dic3—44no—
803Dic3—41no—
804Dic3—41no—
805Dic3—41no—
806Dic3—42no—
807C23—22no—
808C23—22no—
809C23—41no—
810C23—64no—
811C23—62no—
812C23—62no—
813C23—61no—
814C23—122no—
815C23—122no—
816C23—122no—
817C23—241no—
818C23—241no—
819C23C22×D1211yescharacteristic
820C23C22×D1211yescharacteristic
821C23C22×D1211yescharacteristic
822Q8—34no—
823Q8—64no—
824Q8—62no—
825Q8—62no—
826Q8—242no—
827D4—34no—
828D4—64no—
829D4—68no—
830D4—68no—
831D4—62no—
832D4—64no—
833D4—62no—
834D4—124no—
835D4—122no—
836D4—122no—
837D4—122no—
838D4—242no—
839D4—242no—
840D4—242no—
841D4—241no—
842C2×C4—24no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—42no—
849C2×C4—68no—
850C2×C4—64no—
851C2×C4—62no—
852C2×C4—68no—
853C2×C4—61no—
854C2×C4—64no—
855C2×C4—61no—
856C2×C4—61no—
857C2×C4—62no—
858C2×C4—124no—
859C2×C4—122no—
860C2×C4—244no—
861C2×C4—244no—
862C2×C4—242no—
863C2×C4—242no—
864C2×C4—242no—
865C2×C4—242no—
866C2×C4—242no—
867C2×C4—241no—
868C2×C4C22×D1212yes—
869C2×C4C22×D1212yes—
870C2×C4C22×D1212yes—
871C2×C4C22×D1211yescharacteristic
872C2×C4C22×D1212yes—
873C2×C4C22×D1211yescharacteristic
874C2×C4C22×D1211yescharacteristic
875C2×C4D3×#4114yes—
876C2×C4C24×D311yescharacteristic
877C8—22no—
878C8—22no—
879C8—24no—
880C2×C3—22no—
881C2×C3—22no—
882C2×C3—41no—
883C2×C3C2×#52511yescharacteristic
884C2×C3C2×#57711yescharacteristic
885C2×C3#358511yescharacteristic
886D3—44no—
887D3—81no—
888D3—82no—
889C22—21no—
890C22—21no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—21no—
895C22—21no—
896C22—44no—
897C22—64no—
898C22—128no—
899C22—122no—
900C22—122no—
901C22—121no—
902C22—122no—
903C22—122no—
904C22—121no—
905C22—121no—
906C22—122no—
907C22—482no—
908C22#552412yes—
909C22#575112yes—
910C22C23×D1211yescharacteristic
911C4—22no—
912C4—22no—
913C4—22no—
914C4—22no—
915C4—21no—
916C4—21no—
917C4—64no—
918C4—122no—
919C4—121no—
920C4—124no—
921C4—121no—
922C4—121no—
923C4#552412yes—
924C4C2×D3×#4112yes—
925C3#6058811yescharacteristic, complemented, Sylow
926C2—22no—
927C2—22no—
928C2—41no—
929C2—124no—
930C2—242no—
931C2—241no—
932C2C2×#552411yescharacteristic
933C2C2×#575111yescharacteristic
934C2#8716711yescharacteristic
subgroupG/H
centerC22C23×D12
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#2924C2
socleC22×C3C23×D4
hypercenter#2924D3
hypocenterC3#60588
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2924

Complements

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

NH ≅ G/Ntype
1. #85747C2semidirect
2. C2×#5523C2semidirect
3. C3×#2924C2semidirect
4. #79389C2semidirect
5. #79384C2semidirect
6. #79357C2semidirect
7. #79343C2semidirect
8. #79309C2semidirect
9. #79300C2semidirect
10. #79092C2semidirect
11. #79088C2semidirect
12. #78639C2semidirect
13. #78622C2semidirect
14. #78610C2semidirect
15. C2×#4735C2semidirect
16. #78574C2semidirect
17. #78560C2semidirect
26. #5535C22semidirect
27. #5534C22semidirect
31. #5525C22semidirect
37. #5523C22semidirect
38. #5523C22semidirect
39. #5521C22semidirect
40. #5519C22semidirect
49. C2×C4×D12C22semidirect
50. C2×C4×Dic6C22semidirect
51. C3×#433C22semidirect
52. C3×#432C22semidirect
53. C3×#431C22semidirect
54. C3×#424C22semidirect
57. C3×#405C22semidirect
59. #5133C22semidirect
60. #5121C22semidirect
62. C2×#821C22semidirect
63. C2×#817C22semidirect
64. #4851C22semidirect
65. #4848C22semidirect
66. #4847C22semidirect
67. #4845C22semidirect
68. #4844C22semidirect
69. #4843C22semidirect
70. #4842C22semidirect
71. #4829C22semidirect
72. #4739C22semidirect
74. #4738C22semidirect
75. #4736C22semidirect
78. #4735C22semidirect
79. #4735C22semidirect
81. #4734C22semidirect
82. #4733C22semidirect
84. #4732C22semidirect
85. #4731C22semidirect
86. #4722C22semidirect
87. #4721C22semidirect
88. #4716C22semidirect
89. #4711C22semidirect
90. #4711C22semidirect
91. #4710C22semidirect
92. C4×D24C22semidirect
93. C4×#204C22semidirect
94. C4×#204C22semidirect
95. C4×#204C22semidirect
112. #2924D3semidirect
313. #433C2×D3semidirect
314. #432C2×D3semidirect
315. #431C2×D3semidirect
318. #424C2×D3semidirect
325. #405C2×D3semidirect
360. #235#41semidirect
925. C3#60588semidirect

Maximal subgroups

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

subgroupindex
#857472
C2×#55232
C3×#29242
#793892
#793842
#793572
#793432
#793092
#793002
#790922
#790882
#786392
#786222
#786102
C2×#47352
#785742
#785602
#605883