Finite Group Databasebeta

← #11667271

Subgroups — #11667271

Order 768.

1800 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86219C211yesmaximal, characteristic
2C2×#5728C211yesmaximal, characteristic, complemented
3C3×#3226C211yesmaximal, characteristic, complemented
4#83271C211yesmaximal, characteristic, complemented
5#83223C211yesmaximal, characteristic, complemented
6#81944C212yesmaximal, complemented
7#81938C212yesmaximal, complemented
8#81573C212yesmaximal, complemented
9#81562C212yesmaximal, complemented
10#81281C214yesmaximal, complemented
11#81275C214yesmaximal, complemented
12#80970C214yesmaximal, complemented
13#80964C214yesmaximal, complemented
14D3×#431C211yesmaximal, characteristic, complemented
15#79272C211yesmaximal, characteristic, complemented
16#60846—31nomaximal, Sylow
17C3×#532C2211yescharacteristic
18C2×C3×C4⋊Q8C2211yescharacteristic
19#5828—21no—
20Dic3×#41—21no—
21C2×#946—21no—
22C2×Q8×Dic3—21no—
23#5728—21no—
24#5728—21no—
25#5728—21no—
26#5728—21no—
27#5728C2211yescharacteristic
28#5728C2212yes—
29#5728C2212yes—
30#5728C2212yes—
31#5728C2212yes—
32#5728C2211yescharacteristic
33#5716C2211yescharacteristic
34#5716C2211yescharacteristic
35#5680—21no—
36#5680—21no—
37#5606—21no—
38#5606C2212yes—
39#5600—21no—
40#5600C2212yes—
41#5557—21no—
42#5557C2212yes—
43C4×#237—21no—
44C4×#237C2212yes—
45C2×#897—21no—
46C2×#892C2212yes—
47C2×#890C2212yes—
48C2×#887—21no—
49C2×C42×D3C2211yescharacteristic
50#5470C2211yescharacteristic
51C2×#869C2211yescharacteristic
52C3×#500C2212yescomplemented
53C3×#486C2212yescomplemented
54C3×#480C2214yes—
55C3×#474C2214yescomplemented
56C3×#431C2211yescharacteristic
57#5094C2214yescomplemented
58#5093C2212yescomplemented
59#5080C2212yescomplemented
60#5080C2212yescomplemented
61#5070C2212yescomplemented
62#5034C2214yes—
63#5008C2214yescomplemented
64#4971C2214yes—
65#4925C2211yescharacteristic
66#4888C2218yes—
67#4880C2218yes—
68#4878C2218yescomplemented
69#4877C2218yescomplemented
70#4850C2214yescomplemented
71#4833C2212yes—
72D3×C4⋊C8C2212yes—
73#4784C2218yes—
74#4772C2218yes—
75#4768C2218yescomplemented
76#4766C2218yescomplemented
77D3×C22⋊C8C2212yes—
78#4722C2214yes—
79#4718C2212yes—
80#4685C2212yes—
81C4×D3×C8C2212yes—
82#4682C2212yescomplemented
83#4681C2212yescomplemented
84#3444—31no—
85C2×#533—31no—
86#3233—34no—
87#3232—34no—
88#3231—32no—
89#3230—31no—
90#3229—31no—
91#3228—32no—
92#3227—31no—
93#3226D311yescharacteristic, complemented
94#3160—32no—
95#3131—32no—
96#3091—34no—
97#3076—34no—
98C2×#431—31no—
99C2×C3×#41—21no—
100C22×C3×Q8—21no—
101C2×#237—21no—
102C2×#237C2312yes—
103C22×C4×D3D411yescharacteristic
104C22×C4×D3D411yescharacteristic
105C22×C4×D3C2311yescharacteristic
106C22×Dic6—21no—
107C3×C4⋊Q8—21no—
108C3×C4⋊Q8—21no—
109C3×C4⋊Q8C2311yescharacteristic
110C3×C4⋊Q8C2312yes—
111C3×C4⋊Q8C2312yes—
112C3×#127C2311yescharacteristic
113C3×#124—21no—
114C3×#121—21no—
115C3×#121C2312yes—
116C3×C4×D4—21no—
117C3×C4×D4C2312yes—
118C2×C3×C4⋊C4—21no—
119C2×C3×C4⋊C4C2312yes—
120C2×C3×C42C2311yescharacteristic
121#946—21no—
122#946—21no—
123#946—22no—
124#946—22no—
125#946—22no—
126#946—22no—
127Q8×Dic3—21no—
128Q8×Dic3—21no—
129Q8×Dic3—22no—
130Q8×Dic3—22no—
131Q8×Dic3—22no—
132Q8×Dic3—22no—
133#938—21no—
134#938—21no—
135#938—21no—
136#938C2312yes—
137#937—22no—
138#936—21no—
139#936C2312yes—
140#935—22no—
141D4×Dic3—22no—
142D4×Dic3—22no—
143D4×Dic3—21no—
144D4×Dic3—21no—
145D4×Dic3—21no—
146D4×Dic3C2312yes—
147C4×#67—22no—
148C4×#67—22no—
149C2×(C2×D3)⋊C4—22no—
150#926—21no—
151#926—22no—
152C2×C4⋊Dic3—21no—
153C2×C4⋊Dic3—22no—
154C2×C4⋊Dic3C2312yes—
155#924—21no—
156#924C2312yes—
157C2×Dic3⋊C4—22no—
158C2×C4×Dic3—22no—
159C2×C4×Dic3—22no—
160C2×C4×Dic3D411yescharacteristic
161C2×C4×Dic3D411yescharacteristic
162C2×C4×Dic3C2311yescharacteristic
163C2×D3×C8C2314yes—
164#897—22no—
165#897—22no—
166#897—22no—
167#897—22no—
168#897—21no—
169#897C2312yes—
170#892—22no—
171#892—22no—
172#892—21no—
173#892C2312yes—
174#892C2314yes—
175#892C2314yes—
176#890—22no—
177#890—22no—
178#890—21no—
179#890C2314yes—
180#890C2312yes—
181#890C2314yes—
182#887—22no—
183#887—22no—
184#887—22no—
185#887—22no—
186#887—21no—
187#887C2312yes—
188#883—22no—
189#883—22no—
190#67⋊C4—22no—
191#67⋊C4—22no—
192#879—22no—
193#879—22no—
194#877—22no—
195#877—22no—
196C42×D3D411yescharacteristic
197C42×D3D411yescharacteristic
198C42×D3D411yescharacteristic
199C42×D3D411yescharacteristic
200C42×D3C2311yescharacteristic
201C42×D3C2311yescharacteristic
202C42×D3C2311yescharacteristic
203C42×D3C2311yescharacteristic
204#870—21no—
205#869—21no—
206#869—21no—
207#869C2311yescharacteristic
208#869C2312yes—
209#869C2311yescharacteristic
210#869C2312yes—
211C4×Dic6—21no—
212C4×Dic6C2312yes—
213C3×#107C2318yes—
214C3×C4⋊C8C2312yes—
215C3×#102C2318yes—
216C3×C22⋊C8C2312yes—
217C3×C4×C8C2312yes—
218#832C2318yes—
219#830C2312yes—
220(C2×D3)⋊C8C2314yes—
221#818C2318yes—
222#816C2318yes—
223Dic3⋊C8C2314yes—
224C8×Dic3C2314yes—
225#810C2318yes—
226#808C2318yes—
227#808C2318yes—
228C4⋊(C3⋊C8)C2312yes—
229C4×C3⋊C8C2312yes—
230#533—32no—
231#533—32no—
232#533—31no—
233#533—32no—
234#533—32no—
235#533—31no—
236#533—31no—
237#533—61no—
238#533—61no—
239#533—61no—
240#533—61no—
241#532—31no—
242#532—31no—
243#532C2×D311yescharacteristic
244C2×C4⋊Q8—31no—
245C2×C4⋊Q8C2×D311yescharacteristic
246#529—32no—
247#529—32no—
248#529—61no—
249#529—61no—
250#529—61no—
251#529—61no—
252C2×#125—32no—
253#525—32no—
254#525—61no—
255#525—61no—
256C2×C22⋊Q8—61no—
257C2×C22⋊Q8—61no—
258C4×#41—32no—
259C4×#41—61no—
260C4×#41—61no—
261C2×C4×Q8—61no—
262C2×C4×Q8—61no—
263C2×#117—32no—
264C22×C42—31no—
265#500—32no—
266#500C2×D312yescomplemented
267#499—38no—
268#498—32no—
269#498—32no—
270#488—38no—
271#487—32no—
272#487—32no—
273#486—32no—
274#486C2×D312yescomplemented
275#485—38no—
276#484—34no—
277#483—34no—
278#482—38no—
279#481—34no—
280#480C2×D314yes—
281#479—38no—
282#478—38no—
283#477—34no—
284#476—34no—
285#475—34no—
286#474C2×D314yescomplemented
287#431—31no—
288#431—32no—
289#431—32no—
290#431—32no—
291#431C2×D311yescharacteristic
292#427—38no—
293C2×C4⋊C8—32no—
294#416—38no—
295C2×C22⋊C8—32no—
296C2×C4×C8—32no—
297C23×D3C2×D411yescharacteristic
298C3×#41—44no—
299C2×C3×Q8—21no—
300C2×C3×Q8—22no—
301C2×C3×Q8—22no—
302C2×C3×Q8—44no—
303C2×C3×D4—22no—
304C2×C3×D4—21no—
305C2×C3×D4—21no—
306C2×C3×D4C2412yes—
307C22×C3×C4—22no—
308C22×C3×C4—22no—
309C22×C3×C4C2×D411yescharacteristic
310C22×C3×C4C2×D411yescharacteristic
311C22×C3×C4C2411yescharacteristic
312C2×#67—22no—
313C2×#67—22no—
314C22×Dic3—22no—
315C22×Dic3—22no—
316C22×Dic3—22no—
317C22×Dic3C2×D411yescharacteristic
318C22×Dic3C2×D411yescharacteristic
319C22×Dic3C2×D411yescharacteristic
320#237—28no—
321#237—44no—
322C2×C4×D3—24no—
323C2×C4×D3—24no—
324C2×C4×D3—42no—
325C2×C4×D3C2×D411yescharacteristic
326C2×C4×D3C2×D411yescharacteristic
327C2×C4×D3C2×D411yescharacteristic
328C2×C4×D3C2×D411yescharacteristic
329C2×C4×D3C2×D411yescharacteristic
330C2×C4×D3C2×D411yescharacteristic
331C2×C4×D3C2×D411yescharacteristic
332C2×C4×D3C2×D411yescharacteristic
333C2×C4×D3C2×D411yescharacteristic
334C2×C4×D3C2×D411yescharacteristic
335C2×C4×D3C2411yescharacteristic
336C2×C4×D3C2411yescharacteristic
337C2×Dic6—21no—
338C2×Dic6—22no—
339C2×Dic6—22no—
340C2×Dic6—44no—
341C2×Dic6C2412yes—
342C2×C3×C8C2414yes—
343C3×C4⋊C4—22no—
344C3×C4⋊C4—22no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—22no—
347C3×C4⋊C4C2412yes—
348C3×C4⋊C4C2414yes—
349C3×C22⋊C4—22no—
350C3×C22⋊C4—22no—
351C3×C42C2×D411yescharacteristic
352C3×C42C2×D411yescharacteristic
353C3×C42C2411yescharacteristic
354C3×C42C2411yescharacteristic
355#217—22no—
356#217—22no—
357#217—22no—
358#217—22no—
359#217—22no—
360(C2×D3)⋊C4—22no—
361(C2×D3)⋊C4—22no—
362(C2×D3)⋊C4—24no—
363(C2×D3)⋊C4—24no—
364C4⋊Dic3—21no—
365C4⋊Dic3—22no—
366C4⋊Dic3—22no—
367C4⋊Dic3—22no—
368C4⋊Dic3—21no—
369C4⋊Dic3—21no—
370C4⋊Dic3—22no—
371C4⋊Dic3—22no—
372C4⋊Dic3—24no—
373C4⋊Dic3—24no—
374C4⋊Dic3C2412yes—
375C4⋊Dic3C2414yes—
376Dic3⋊C4—22no—
377Dic3⋊C4—22no—
378Dic3⋊C4—22no—
379Dic3⋊C4—22no—
380Dic3⋊C4—24no—
381Dic3⋊C4—24no—
382C4×Dic3—22no—
383C4×Dic3—22no—
384C4×Dic3—22no—
385C4×Dic3—24no—
386C4×Dic3—24no—
387C4×Dic3C2×D411yescharacteristic
388C4×Dic3C2×D411yescharacteristic
389C4×Dic3C2×D411yescharacteristic
390C4×Dic3C2×D411yescharacteristic
391C4×Dic3C2×D411yescharacteristic
392C4×Dic3C2×D411yescharacteristic
393C4×Dic3C2×D411yescharacteristic
394C4×Dic3C2×D411yescharacteristic
395C4×Dic3C2×D411yescharacteristic
396C4×Dic3C2×D411yescharacteristic
397C4×Dic3C2411yescharacteristic
398C4×Dic3C2411yescharacteristic
399C2×C3⋊C8C2414yes—
400D3×C8—28no—
401C2×#41—21no—
402C2×#41—32no—
403C2×#41—61no—
404C22×Q8—21no—
405C22×Q8—61no—
406C23×C4—31no—
407C23×C4—31no—
408C23×C4—31no—
409C22×C8—34no—
410C4⋊Q8—21no—
411C4⋊Q8—21no—
412C4⋊Q8—32no—
413C4⋊Q8—32no—
414C4⋊Q8—31no—
415C4⋊Q8—31no—
416C4⋊Q8—61no—
417C4⋊Q8—61no—
418C4⋊Q8C22×D312yes—
419C4⋊Q8C22×D312yes—
420C4⋊Q8C22×D311yescharacteristic
421#127C22×D311yescharacteristic
422#126—62no—
423#126—62no—
424#125—34no—
425#125—34no—
426#125—32no—
427#125—62no—
428#125—62no—
429#125—61no—
430#125—61no—
431#124—21no—
432#124—32no—
433#124—61no—
434#123—62no—
435#123—62no—
436#123—62no—
437C22⋊Q8—32no—
438C22⋊Q8—32no—
439C22⋊Q8—62no—
440C22⋊Q8—62no—
441C22⋊Q8—62no—
442C22⋊Q8—62no—
443C22⋊Q8—61no—
444C22⋊Q8—62no—
445C22⋊Q8—62no—
446C22⋊Q8—62no—
447C22⋊Q8—62no—
448C22⋊Q8—61no—
449C22⋊Q8—61no—
450C22⋊Q8—61no—
451#121—21no—
452#121—32no—
453#121—61no—
454#121—61no—
455#121—61no—
456#121C22×D312yes—
457#120—62no—
458C4×Q8—32no—
459C4×Q8—32no—
460C4×Q8—62no—
461C4×Q8—62no—
462C4×Q8—62no—
463C4×Q8—62no—
464C4×Q8—61no—
465C4×Q8—62no—
466C4×Q8—62no—
467C4×Q8—62no—
468C4×Q8—62no—
469C4×Q8—61no—
470C4×Q8—61no—
471C4×Q8—61no—
472C4×D4—21no—
473C4×D4—32no—
474C4×D4—61no—
475C4×D4—61no—
476C4×D4—61no—
477C4×D4—62no—
478C4×D4—62no—
479C4×D4—62no—
480C4×D4—62no—
481C4×D4—62no—
482C4×D4—62no—
483C4×D4C22×D312yes—
484#117—34no—
485#117—34no—
486#117—32no—
487#117—62no—
488#117—62no—
489#117—62no—
490#117—62no—
491#117—62no—
492#117—61no—
493#117—61no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—32no—
496C2×C4⋊C4—62no—
497C2×C4⋊C4—62no—
498C2×C4⋊C4—61no—
499C2×C4⋊C4C22×D312yes—
500C2×C22⋊C4—62no—
501C2×C42—31no—
502C2×C42—31no—
503C2×C42—31no—
504C2×C42—31no—
505C2×C42—31no—
506C2×C42—31no—
507C2×C42—31no—
508C2×C42—31no—
509C2×C42—31no—
510C2×C42—31no—
511C2×C42—31no—
512C2×C42—62no—
513C2×C42—62no—
514C2×C42C22×D311yescharacteristic
515#107—38no—
516#107C22×D318yes—
517#106—38no—
518#106—38no—
519C4⋊C8—34no—
520C4⋊C8—32no—
521C4⋊C8C22×D312yes—
522#103—38no—
523#103—38no—
524#102—38no—
525#102C22×D318yes—
526C22⋊C8—32no—
527C22⋊C8—34no—
528C22⋊C8C22×D312yes—
529C4×C8—34no—
530C4×C8—32no—
531C4×C8C22×D312yes—
532C23×C3—22no—
533C23×C3C22×D411yescharacteristic
534C22×D3—22no—
535C22×D3—22no—
536C22×D3—41no—
537C22×D3C22×D411yescharacteristic
538C22×D3C22×D411yescharacteristic
539C3×Q8—44no—
540C3×Q8—44no—
541C3×Q8—42no—
542C3×D4—24no—
543C3×D4—44no—
544C3×D4—42no—
545C3×D4—42no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—24no—
550C2×C3×C4—44no—
551C2×C3×C4—44no—
552C2×C3×C4#13514yes—
553C2×C3×C4C22×D411yescharacteristic
554C2×C3×C4C22×D411yescharacteristic
555C2×C3×C4C22×D411yescharacteristic
556C2×C3×C4C22×D411yescharacteristic
557C2×C3×C4C22×D411yescharacteristic
558C2×C3×C4C2511yescharacteristic
559#67—44no—
560#67—44no—
561C2×Dic3—22no—
562C2×Dic3—22no—
563C2×Dic3—22no—
564C2×Dic3—22no—
565C2×Dic3—24no—
566C2×Dic3—41no—
567C2×Dic3—44no—
568C2×Dic3—44no—
569C2×Dic3—44no—
570C2×Dic3C22×D411yescharacteristic
571C2×Dic3C22×D411yescharacteristic
572C2×Dic3C22×D411yescharacteristic
573C2×Dic3C22×D411yescharacteristic
574C2×Dic3C22×D411yescharacteristic
575C2×Dic3C22×D411yescharacteristic
576C4×D3—22no—
577C4×D3—22no—
578C4×D3—22no—
579C4×D3—22no—
580C4×D3—22no—
581C4×D3—22no—
582C4×D3—22no—
583C4×D3—22no—
584C4×D3—22no—
585C4×D3—41no—
586C4×D3—41no—
587C4×D32−1+414yes—
588Dic6—24no—
589Dic6—44no—
590Dic6—44no—
591Dic6—42no—
592C3×C8—24no—
593C3⋊C8—24no—
594C24—31no—
595#41—44no—
596#41—68no—
597#41—124no—
598C2×Q8—21no—
599C2×Q8—22no—
600C2×Q8—22no—
601C2×Q8—32no—
602C2×Q8—44no—
603C2×Q8—61no—
604C2×Q8—62no—
605C2×Q8—62no—
606C2×Q8—124no—
607C2×D4—22no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—62no—
611C2×D4—62no—
612C2×D4C23×D312yes—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—31no—
616C22×C4—31no—
617C22×C4—31no—
618C22×C4—31no—
619C22×C4—31no—
620C22×C4—31no—
621C22×C4—31no—
622C22×C4—31no—
623C22×C4—31no—
624C22×C4—31no—
625C22×C4—31no—
626C22×C4—31no—
627C22×C4—31no—
628C22×C4—31no—
629C22×C4—31no—
630C22×C4—64no—
631C22×C4—62no—
632C22×C4—62no—
633C22×C4—64no—
634C22×C4—62no—
635C22×C4—122no—
636C22×C4D3×D411yescharacteristic
637C22×C4D3×D411yescharacteristic
638C22×C4C23×D311yescharacteristic
639C2×C8—34no—
640C2×C8—68no—
641C2×C8C23×D314yes—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—21no—
646C4⋊C4—34no—
647C4⋊C4—32no—
648C4⋊C4—64no—
649C4⋊C4—64no—
650C4⋊C4—64no—
651C4⋊C4—64no—
652C4⋊C4—62no—
653C4⋊C4—62no—
654C4⋊C4—62no—
655C4⋊C4—62no—
656C4⋊C4—62no—
657C4⋊C4—62no—
658C4⋊C4—62no—
659C4⋊C4—62no—
660C4⋊C4—61no—
661C4⋊C4—61no—
662C4⋊C4—61no—
663C4⋊C4—62no—
664C4⋊C4C23×D314yes—
665C4⋊C4C23×D312yes—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—64no—
669C22⋊C4—64no—
670C22⋊C4—62no—
671C22⋊C4—62no—
672C22⋊C4—62no—
673C22⋊C4—62no—
674C22⋊C4—62no—
675C22⋊C4—62no—
676C22⋊C4—62no—
677C42—31no—
678C42—31no—
679C42—31no—
680C42—31no—
681C42—31no—
682C42—31no—
683C42—31no—
684C42—31no—
685C42—31no—
686C42—31no—
687C42—31no—
688C42—31no—
689C42—62no—
690C42—64no—
691C42—64no—
692C42—62no—
693C42—62no—
694C42D3×D411yescharacteristic
695C42D3×D411yescharacteristic
696C42C23×D311yescharacteristic
697C42C23×D311yescharacteristic
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—42no—
701C22×C3—42no—
702C22×C3—42no—
703C22×C3C2×#13512yes—
704C22×C3C23×D411yescharacteristic
705C2×D3—21no—
706C2×D3—21no—
707C2×D3—21no—
708C2×D3—21no—
709C2×D3—21no—
710C2×D3—44no—
711C2×D3#53612yes—
712C3×C4—21no—
713C3×C4—21no—
714C3×C4—42no—
715C3×C4—44no—
716C3×C4C2×#13512yes—
717C3×C4C2×#13512yes—
718C3×C4#57512yes—
719C3×C4C2×2−1+412yes—
720Dic3—21no—
721Dic3—21no—
722Dic3—21no—
723Dic3—21no—
724Dic3—21no—
725Dic3—42no—
726Dic3—44no—
727Dic3—42no—
728Dic3#53612yes—
729C23—22no—
730C23—31no—
731C23—31no—
732C23—62no—
733C23—62no—
734C23—121no—
735C23C2×D3×D411yescharacteristic
736Q8—44no—
737Q8—44no—
738Q8—42no—
739Q8—64no—
740Q8—124no—
741Q8—124no—
742Q8—122no—
743D4—24no—
744D4—44no—
745D4—42no—
746D4—42no—
747D4—124no—
748D4—124no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—31no—
754C2×C4—34no—
755C2×C4—31no—
756C2×C4—31no—
757C2×C4—31no—
758C2×C4—31no—
759C2×C4—31no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—62no—
763C2×C4—62no—
764C2×C4—62no—
765C2×C4—62no—
766C2×C4—62no—
767C2×C4—62no—
768C2×C4—62no—
769C2×C4—62no—
770C2×C4—62no—
771C2×C4—62no—
772C2×C4—62no—
773C2×C4—62no—
774C2×C4—62no—
775C2×C4—64no—
776C2×C4—121no—
777C2×C4—121no—
778C2×C4—124no—
779C2×C4—121no—
780C2×C4—124no—
781C2×C4—124no—
782C2×C4#91214yes—
783C2×C4C2×D3×D411yescharacteristic
784C2×C4C2×D3×D411yescharacteristic
785C2×C4C2×D3×D411yescharacteristic
786C2×C4C2×D3×D411yescharacteristic
787C2×C4C2×D3×D411yescharacteristic
788C2×C4C24×D311yescharacteristic
789C8—24no—
790C8—64no—
791C2×C3—22no—
792C2×C3—82no—
793C2×C3C2×#53611yescharacteristic
794C2×C3C22×#13511yescharacteristic
795C2×C3C2×#57511yescharacteristic
796D3—22no—
797D3—41no—
798C22—21no—
799C22—21no—
800C22—32no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—61no—
805C22—61no—
806C22—61no—
807C22—61no—
808C22—61no—
809C22—124no—
810C22C2×#91212yes—
811C22C22×D3×D411yescharacteristic
812C4—21no—
813C4—21no—
814C4—32no—
815C4—42no—
816C4—44no—
817C4—61no—
818C4—61no—
819C4—61no—
820C4—61no—
821C4—61no—
822C4—122no—
823C4—122no—
824C4—124no—
825C4C2×#91212yes—
826C4C2×#91212yes—
827C4#577712yes—
828C4D3×2−1+412yes—
829C3#6084611yescharacteristic, complemented, Sylow
830C2—22no—
831C2—62no—
832C2—82no—
833C2—121no—
834C2D3×#53611yescharacteristic
835C2C22×#91211yescharacteristic
836C2C2×#577711yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3226C2
socleC22×C3C23×D4
prime radical#86219C2
hypercenter#3226D3
hypocenterC3#60846
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3226

Complements

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

NH ≅ G/Ntype
2. C2×#5728C2semidirect
3. C3×#3226C2semidirect
4. #83271C2semidirect
5. #83223C2semidirect
6. #81944C2semidirect
7. #81938C2semidirect
8. #81573C2semidirect
9. #81562C2semidirect
10. #81281C2semidirect
11. #81275C2semidirect
12. #80970C2semidirect
13. #80964C2semidirect
14. D3×#431C2semidirect
15. #79272C2semidirect
52. C3×#500C22semidirect
53. C3×#486C22semidirect
55. C3×#474C22semidirect
57. #5094C22semidirect
58. #5093C22semidirect
59. #5080C22semidirect
60. #5080C22semidirect
61. #5070C22semidirect
63. #5008C22semidirect
68. #4878C22semidirect
69. #4877C22semidirect
70. #4850C22semidirect
75. #4768C22semidirect
76. #4766C22semidirect
82. #4682C22semidirect
83. #4681C22semidirect
93. #3226D3semidirect
266. #500C2×D3semidirect
274. #486C2×D3semidirect
286. #474C2×D3semidirect
829. C3#60846semidirect

Maximal subgroups

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

subgroupindex
#862192
C2×#57282
C3×#32262
#832712
#832232
#819442
#819382
#815732
#815622
#812812
#812752
#809702
#809642
D3×#4312
#792722
#608463