Finite Group Databasebeta

← #11675125

Subgroups — #11675125

Order 768.

1878 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5713C211yesmaximal, characteristic, complemented
2#41×Dic6C211yesmaximal, characteristic, complemented
3C3×#3038C211yesmaximal, characteristic
4#83933C212yesmaximal, complemented
5Dic3×AGL(1,ℤ/8)C212yesmaximal, complemented
6#83159C211yesmaximal, characteristic, complemented
7C4×#951C211yesmaximal, characteristic, complemented
8#80374C212yesmaximal, complemented
9#80373C214yesmaximal, complemented
10#80370C212yesmaximal, complemented
11#80323C212yesmaximal, complemented
12#80322C214yesmaximal, complemented
13#80319C212yesmaximal, complemented
14#79068C211yesmaximal, characteristic, complemented
15#79046C211yesmaximal, characteristic, complemented
16#78922C212yesmaximal, complemented
17#78917C212yesmaximal, complemented
18#61324—31nomaximal, Sylow
19C2×C3×AGL(1,ℤ/8)C2212yes—
20C2×C3×#127C2211yescharacteristic
21C3×C4×#41C2211yescharacteristic
22Dic3×#41C2212yes—
23C2×#951C2211yescharacteristic
24C2×#936—21no—
25C2×#936C2212yes—
26C2×#935—22no—
27C2×D4×Dic3—21no—
28C2×D4×Dic3C2212yes—
29#5713—21no—
30#5713—21no—
31#5713—22no—
32#5713C2212yes—
33#5713C2214yes—
34#5713C2212yes—
35#5570C2211yescharacteristic, complemented
36#5569C2212yescomplemented
37Q8×Dic6C2211yescharacteristic, complemented
38#5543—21no—
39#5543C2211yescharacteristic, complemented
40#5539—22no—
41#5539C2212yescomplemented
42D4×Dic6—21no—
43D4×Dic6C2211yescharacteristic, complemented
44#5517—22no—
45#5517C2212yes—
46#5470—21no—
47#5470C2211yescharacteristic
48C2×C4×Dic6—21no—
49C2×C4×Dic6C2211yescharacteristic
50C2×C4×Dic6C2211yescharacteristic
51C3×#460C2212yes—
52C3×#460C2212yes—
53C3×#459C2212yes—
54C3×#459C2212yes—
55C3×#423C2211yescharacteristic
56C3×#418C2212yes—
57#5232C2211yescharacteristic
58#5215C2212yes—
59#5215C2212yes—
60#5166C2214yescomplemented
61#5166C2214yescomplemented
62#5164C2214yescomplemented
63Dic3×SD16C2214yescomplemented
64#5153C2214yescomplemented
65#5153C2214yescomplemented
66#5152C2214yescomplemented
67Dic3×D8C2214yescomplemented
68#5121C2212yes—
69#5120C2212yes—
70#5118C2212yes—
71Dic3×M16C2212yes—
72#5071C2214yes—
73#5070C2212yes—
74#5070C2212yes—
75#5030C2212yescomplemented
76C4×#216C2212yescomplemented
77#5018C2212yescomplemented
78C4×#214C2212yescomplemented
79#5004C2211yescharacteristic
80#4995C2211yescharacteristic
81C4×#208C2211yescharacteristic
82#4851C2212yescomplemented
83#4850C2212yescomplemented
84#4831C2212yescomplemented
85#4830C2212yescomplemented
86#4829C2214yescomplemented
87#4828C2214yescomplemented
88#4768C2214yescomplemented
89#4768C2214yescomplemented
90#4766C2214yescomplemented
91#4765C2214yescomplemented
92#4765C2214yescomplemented
93#4763C2214yescomplemented
94#4761C2214yescomplemented
95#4759C2214yescomplemented
96C2×#559—31no—
97Q8×#41—31no—
98#3375—32no—
99#3373—32no—
100#3371—34no—
101#3370—34no—
102#3365—32no—
103#3361—32no—
104#3140—32no—
105#3138—31no—
106#3078—31no—
107#3077—32no—
108#3040—32no—
109#3038D311yescharacteristic
110Q8×M16—31no—
111C4×#137—31no—
112C4×AGL(1,ℤ/8)—32no—
113C2×C3×#41C2311yescharacteristic
114C22×C3×D4—21no—
115C22×C3×D4—21no—
116C22×C3×D4C2312yes—
117C23×Dic3—22no—
118C22×Dic6—21no—
119C22×Dic6D411yescharacteristic
120C22×Dic6C2311yescharacteristic
121C3×AGL(1,ℤ/8)—28no—
122C2×C3×SD16C2314yes—
123C2×C3×D8C2314yes—
124C2×C3×M16C2312yes—
125C3×#127—21no—
126C3×#127—21no—
127C3×#127C2312yes—
128C3×#127C2312yes—
129C3×C4×Q8C2311yescharacteristic
130C3×C4×Q8C2311yescharacteristic
131C3×C4×D4—21no—
132C3×C4×D4—21no—
133C3×C4×D4C2311yescharacteristic
134C3×C4×D4C2311yescharacteristic
135C3×#117—21no—
136C3×#117C2311yescharacteristic
137C2×C3×C42—21no—
138C2×C3×C42C2311yescharacteristic
139C2×#217—22no—
140C2×#217—22no—
141C2×#217—22no—
142#951—24no—
143Q8×Dic3C2312yes—
144Q8×Dic3C2312yes—
145C2×#216C2312yes—
146#936—22no—
147#936—22no—
148#936—24no—
149#936—22no—
150#936—22no—
151#936C2314yes—
152#936C2314yes—
153#935—24no—
154#935—24no—
155#935—24no—
156#935—24no—
157D4×Dic3—22no—
158D4×Dic3—22no—
159D4×Dic3—22no—
160D4×Dic3—22no—
161D4×Dic3—24no—
162D4×Dic3—22no—
163D4×Dic3—22no—
164D4×Dic3C2312yes—
165D4×Dic3C2314yes—
166D4×Dic3C2312yes—
167D4×Dic3C2314yes—
168C2×#214C2312yes—
169#926—22no—
170#926C2312yes—
171C2×C4⋊Dic3—21no—
172C2×C4⋊Dic3D411yescharacteristic
173C2×C4⋊Dic3C2311yescharacteristic
174#924—21no—
175#924—21no—
176#924—21no—
177#924—21no—
178#924—22no—
179C2×Dic3⋊C4—21no—
180C2×Dic3⋊C4—22no—
181C2×Dic3⋊C4D412yes—
182C2×C4×Dic3—21no—
183C2×C4×Dic3—22no—
184C2×C4×Dic3C2312yes—
185C2×#208C2311yescharacteristic
186C2×#208C2311yescharacteristic
187#890—22no—
188#890—22no—
189#890C2312yes—
190#890C2312yes—
191#888—22no—
192#888—22no—
193#888C2312yes—
194#888C2312yes—
195#878—22no—
196#878—22no—
197#878—22no—
198#878—22no—
199#878—22no—
200#878—22no—
201#870—22no—
202#870C2312yes—
203#869—21no—
204#869—21no—
205#869C2311yescharacteristic
206#869C2311yescharacteristic
207C4×Dic6—21no—
208C4×Dic6—21no—
209C4×Dic6—21no—
210C4×Dic6—21no—
211C4×Dic6—21no—
212C4×Dic6—21no—
213C4×Dic6—22no—
214C4×Dic6—22no—
215C4×Dic6—22no—
216C4×Dic6D411yescharacteristic
217C4×Dic6D411yescharacteristic
218C4×Dic6D412yes—
219C4×Dic6C2312yes—
220C4×Dic6C2312yes—
221C4×Dic6C2311yescharacteristic
222C4×Dic6C2312yes—
223C4×Dic6C2311yescharacteristic
224C3×C4⋊C8C2312yes—
225C3×C4⋊C8C2312yes—
226C3×#102C2314yes—
227C3×#102C2314yes—
228#835C2312yes—
229#832C2312yes—
230#832C2314yes—
231#832C2314yes—
232#832C2314yes—
233#832C2314yes—
234#818C2314yes—
235#817C2314yes—
236#816C2314yes—
237#816C2314yes—
238#815C2314yes—
239Dic3⋊C8C2314yes—
240Dic3⋊C8C2314yes—
241C8×Dic3C2314yes—
242#810C2312yes—
243#810C2312yes—
244#808C2312yes—
245#807C2312yes—
246#803C2312yes—
247C4×C3⋊C8C2312yes—
248C2×#137—31no—
249C2×AGL(1,ℤ/8)C2×D312yes—
250#559—32no—
251#559—34no—
252#559—32no—
253#559—61no—
254#559—62no—
255#559—61no—
256Q82—31no—
257#557—31no—
258#557—32no—
259#554—31no—
260#554—32no—
261#554—62no—
262#554—61no—
263D4×Q8—31no—
264D4×Q8—61no—
265#533—32no—
266#533—31no—
267#533—61no—
268#533—62no—
269C2×#127C2×D311yescharacteristic
270C2×#124—32no—
271C2×#124—61no—
272C2×#123—62no—
273C4×#41—32no—
274C4×#41C2×D311yescharacteristic
275C2×C4×Q8—31no—
276C2×C4×Q8—31no—
277C2×C4×Q8—61no—
278C2×C4×D4—32no—
279C2×C4×D4—61no—
280#490—34no—
281#489—34no—
282#489—34no—
283#488—34no—
284#488—34no—
285#486—32no—
286#486—32no—
287#479—34no—
288#478—34no—
289#478—34no—
290#477—32no—
291#476—34no—
292#475—32no—
293#474—34no—
294#464—34no—
295#464—34no—
296#463—34no—
297#463—34no—
298#460C2×D312yes—
299#460C2×D312yes—
300#459C2×D312yes—
301#459C2×D312yes—
302#446—34no—
303#446—32no—
304C8×Q8—32no—
305#442—34no—
306#441—32no—
307#440—34no—
308#440—32no—
309C4×Q16—32no—
310C4×SD16—34no—
311C4×SD16—32no—
312C4×D8—34no—
313#428—32no—
314#428—31no—
315#423—32no—
316#423C2×D311yescharacteristic
317#419—32no—
318#419—31no—
319#418—32no—
320#418—32no—
321#418C2×D312yes—
322#417—31no—
323C4×M16—32no—
324C4×M16—31no—
325C24×C3—22no—
326C3×#41—22no—
327C3×#41#4114yes—
328C2×C3×Q8C2411yescharacteristic
329C2×C3×D4—21no—
330C2×C3×D4—22no—
331C2×C3×D4—22no—
332C2×C3×D4—22no—
333C2×C3×D4—22no—
334C2×C3×D4—22no—
335C2×C3×D4—24no—
336C2×C3×D4—24no—
337C2×C3×D4—44no—
338C2×C3×D4—82no—
339C2×C3×D4C2414yes—
340C2×C3×D4C2411yescharacteristic
341C22×C3×C4—21no—
342C22×C3×C4—21no—
343C22×C3×C4—21no—
344C22×C3×C4C2×D411yescharacteristic
345C22×C3×C4C2×D411yescharacteristic
346C22×C3×C4C2411yescharacteristic
347C22×Dic3—21no—
348C22×Dic3—21no—
349C22×Dic3—22no—
350C22×Dic3—22no—
351C22×Dic3—24no—
352C22×Dic3—24no—
353C22×Dic3—84no—
354C22×Dic3C2×D412yes—
355C22×Dic3C2×D412yes—
356C2×Dic6—22no—
357C2×Dic6—22no—
358C2×Dic6—21no—
359C2×Dic6—21no—
360C2×Dic6—22no—
361C2×Dic6—21no—
362C2×Dic6—22no—
363C2×Dic6—42no—
364C2×Dic6—44no—
365C2×Dic6C2×D411yescharacteristic
366C2×Dic6C2×D411yescharacteristic
367C2×Dic6C2×D412yes—
368C2×Dic6C2412yes—
369C3×SD16—28no—
370C3×D8—28no—
371C3×M16—24no—
372C2×C3×C8C2414yes—
373C3×C4⋊C4—21no—
374C3×C4⋊C4—21no—
375C3×C4⋊C4C2411yescharacteristic
376C3×C4⋊C4C2411yescharacteristic
377C3×C22⋊C4—21no—
378C3×C22⋊C4—21no—
379C3×C22⋊C4—21no—
380C3×C42—21no—
381C3×C42—21no—
382C3×C42—21no—
383C3×C42C2×D411yescharacteristic
384C3×C42C2×D411yescharacteristic
385C3×C42C2411yescharacteristic
386C3×C42C2411yescharacteristic
387#217—22no—
388#217—22no—
389#217—22no—
390#217—24no—
391#217—24no—
392#217—24no—
393#217—24no—
394#217—24no—
395#217—24no—
396#216—24no—
397#214—24no—
398C4⋊Dic3—21no—
399C4⋊Dic3—21no—
400C4⋊Dic3—21no—
401C4⋊Dic3—22no—
402C4⋊Dic3—22no—
403C4⋊Dic3—22no—
404C4⋊Dic3—22no—
405C4⋊Dic3C2×D411yescharacteristic
406C4⋊Dic3C2×D411yescharacteristic
407C4⋊Dic3C2×D412yes—
408C4⋊Dic3C2412yes—
409C4⋊Dic3C2412yes—
410C4⋊Dic3C2412yes—
411Dic3⋊C4—22no—
412Dic3⋊C4—22no—
413Dic3⋊C4—22no—
414Dic3⋊C4—22no—
415Dic3⋊C4—22no—
416Dic3⋊C4—22no—
417Dic3⋊C4—22no—
418Dic3⋊C4—22no—
419Dic3⋊C4C2×D412yes—
420Dic3⋊C4C2×D412yes—
421Dic3⋊C4C2×D412yes—
422Dic3⋊C4C2×D412yes—
423C4×Dic3—22no—
424C4×Dic3—22no—
425C4×Dic3—22no—
426C4×Dic3—22no—
427C4×Dic3—22no—
428C4×Dic3C2×D412yes—
429C4×Dic3C2×D412yes—
430C4×Dic3C2412yes—
431C4×Dic3C2412yes—
432#208—22no—
433#208—22no—
434C2×C3⋊C8C2412yes—
435C2×C3⋊C8C2412yes—
436C2×#41C22×D311yescharacteristic
437C22×Q8—31no—
438C22×Q8—31no—
439C22×Q8—61no—
440C22×D4—21no—
441C22×D4—21no—
442C22×D4C22×D312yes—
443C23×C4—62no—
444#137—64no—
445AGL(1,ℤ/8)—28no—
446C2×Q16—32no—
447C2×SD16—32no—
448C2×SD16C22×D314yes—
449C2×D8C22×D314yes—
450C2×M16—31no—
451C2×M16—31no—
452C2×M16C22×D312yes—
453C4⋊Q8—32no—
454C4⋊Q8—32no—
455C4⋊Q8—31no—
456C4⋊Q8—31no—
457C4⋊Q8—61no—
458C4⋊Q8—61no—
459C4⋊Q8—62no—
460C4⋊Q8—62no—
461#127—21no—
462#127—21no—
463#127C22×D312yes—
464#127C22×D312yes—
465#125—32no—
466#125—32no—
467#125—32no—
468#125—62no—
469#125—62no—
470#125—62no—
471#124—34no—
472#124—34no—
473#124—62no—
474#124—62no—
475#124—62no—
476#124—62no—
477#124—64no—
478#123—64no—
479#123—64no—
480#123—64no—
481#123—64no—
482C22⋊Q8—62no—
483C22⋊Q8—62no—
484C22⋊Q8—62no—
485C22⋊Q8—62no—
486C22⋊Q8—62no—
487C22⋊Q8—62no—
488C22⋊Q8—61no—
489C22⋊Q8—62no—
490C22⋊Q8—61no—
491C22⋊Q8—61no—
492C22⋊Q8—61no—
493C4×Q8—31no—
494C4×Q8—32no—
495C4×Q8—31no—
496C4×Q8—31no—
497C4×Q8—31no—
498C4×Q8—32no—
499C4×Q8—32no—
500C4×Q8—32no—
501C4×Q8—32no—
502C4×Q8—32no—
503C4×Q8—62no—
504C4×Q8—62no—
505C4×Q8—62no—
506C4×Q8—61no—
507C4×Q8—61no—
508C4×Q8—61no—
509C4×Q8—61no—
510C4×Q8—61no—
511C4×Q8—61no—
512C4×Q8C22×D311yescharacteristic
513C4×Q8C22×D311yescharacteristic
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—34no—
517C4×D4—34no—
518C4×D4—32no—
519C4×D4—32no—
520C4×D4—62no—
521C4×D4—62no—
522C4×D4—62no—
523C4×D4—64no—
524C4×D4—62no—
525C4×D4—62no—
526C4×D4—62no—
527C4×D4C22×D311yescharacteristic
528C4×D4C22×D311yescharacteristic
529#117—21no—
530#117—32no—
531#117—62no—
532#117C22×D311yescharacteristic
533C2×C4⋊C4—31no—
534C2×C4⋊C4—32no—
535C2×C4⋊C4—31no—
536C2×C4⋊C4—62no—
537C2×C4⋊C4—61no—
538C2×C4⋊C4—61no—
539C2×C22⋊C4—62no—
540C2×C22⋊C4—62no—
541C2×C22⋊C4—62no—
542C2×C42—21no—
543C2×C42—32no—
544C2×C42—62no—
545C2×C42—61no—
546C2×C42C22×D311yescharacteristic
547#107—34no—
548#107—32no—
549#106—34no—
550#106—32no—
551C4⋊C8—34no—
552C4⋊C8—34no—
553C4⋊C8C22×D312yes—
554C4⋊C8C22×D312yes—
555#103—32no—
556#103—34no—
557#103—34no—
558#103—32no—
559#103—32no—
560#102—32no—
561#102—34no—
562#102—34no—
563#102—34no—
564#102—34no—
565#102C22×D314yes—
566#102C22×D314yes—
567#97—34no—
568#97—32no—
569C4×C8—34no—
570C4×C8—32no—
571C23×C3—21no—
572C23×C3—24no—
573C23×C3—44no—
574C23×C3—44no—
575C23×C3—44no—
576C23×C3C22×D411yescharacteristic
577C3×Q8—21no—
578C3×Q8C2×#4112yes—
579C3×D4—24no—
580C3×D4—24no—
581C3×D4—21no—
582C3×D4—24no—
583C3×D4—44no—
584C3×D4—44no—
585C3×D4—44no—
586C3×D4—82no—
587C3×D4—82no—
588C3×D4C2×#4112yes—
589C2×C3×C4—21no—
590C2×C3×C4—24no—
591C2×C3×C4—22no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—41no—
595C2×C3×C4—42no—
596C2×C3×C4—81no—
597C2×C3×C4C22×D411yescharacteristic
598C2×C3×C4C22×D411yescharacteristic
599C2×C3×C4C22×D411yescharacteristic
600C2×C3×C4C22×D411yescharacteristic
601C2×C3×C4C22×D411yescharacteristic
602C2×C3×C4C2×#4112yes—
603C2×C3×C42−1+412yes—
604C2×C3×C4C2511yescharacteristic
605C2×Dic3—22no—
606C2×Dic3—22no—
607C2×Dic3—22no—
608C2×Dic3—22no—
609C2×Dic3—42no—
610C2×Dic3—42no—
611C2×Dic3—44no—
612C2×Dic3—42no—
613C2×Dic3—42no—
614C2×Dic3—82no—
615C2×Dic3—84no—
616C2×Dic3—84no—
617C2×Dic3C22×D412yes—
618C2×Dic3C22×D412yes—
619C2×Dic3C22×D412yes—
620C2×Dic3C22×D412yes—
621Dic6—22no—
622Dic6—22no—
623Dic6—22no—
624Dic6—22no—
625Dic6—42no—
626Dic6—44no—
627Dic6—42no—
628Dic6—42no—
629Dic6—82no—
630Dic6—81no—
631C3×C8—24no—
632C3⋊C8—22no—
633C3⋊C8—22no—
634C24—22no—
635#41—22no—
636#41#23714yes—
637C2×Q8—31no—
638C2×Q8—31no—
639C2×Q8—32no—
640C2×Q8—32no—
641C2×Q8—62no—
642C2×Q8—62no—
643C2×Q8—61no—
644C2×Q8—61no—
645C2×Q8—61no—
646C2×Q8—62no—
647C2×Q8—62no—
648C2×Q8—122no—
649C2×Q8—124no—
650C2×Q8C23×D311yescharacteristic
651C2×D4—21no—
652C2×D4—22no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—22no—
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—44no—
660C2×D4—82no—
661C2×D4C23×D314yes—
662C2×D4C23×D311yescharacteristic
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—32no—
667C22×C4—32no—
668C22×C4—62no—
669C22×C4—62no—
670C22×C4—64no—
671C22×C4—64no—
672C22×C4—61no—
673C22×C4—61no—
674C22×C4—244no—
675C22×C4D3×D411yescharacteristic
676C22×C4D3×D411yescharacteristic
677C22×C4C23×D311yescharacteristic
678Q16—64no—
679SD16—28no—
680SD16—64no—
681D8—28no—
682M16—24no—
683M16—62no—
684M16—62no—
685C2×C8—32no—
686C2×C8—32no—
687C2×C8C23×D314yes—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—31no—
691C4⋊C4—32no—
692C4⋊C4—32no—
693C4⋊C4—31no—
694C4⋊C4—32no—
695C4⋊C4—32no—
696C4⋊C4—32no—
697C4⋊C4—32no—
698C4⋊C4—32no—
699C4⋊C4—32no—
700C4⋊C4—62no—
701C4⋊C4—62no—
702C4⋊C4—62no—
703C4⋊C4—62no—
704C4⋊C4—62no—
705C4⋊C4—62no—
706C4⋊C4—62no—
707C4⋊C4—62no—
708C4⋊C4—61no—
709C4⋊C4—62no—
710C4⋊C4—62no—
711C4⋊C4—62no—
712C4⋊C4—61no—
713C4⋊C4—62no—
714C4⋊C4—61no—
715C4⋊C4C23×D311yescharacteristic
716C4⋊C4C23×D311yescharacteristic
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—64no—
721C22⋊C4—64no—
722C22⋊C4—64no—
723C22⋊C4—64no—
724C22⋊C4—64no—
725C22⋊C4—64no—
726C22⋊C4—62no—
727C22⋊C4—62no—
728C22⋊C4—62no—
729C42—21no—
730C42—21no—
731C42—21no—
732C42—32no—
733C42—32no—
734C42—32no—
735C42—32no—
736C42—62no—
737C42—62no—
738C42—62no—
739C42—62no—
740C42—62no—
741C42D3×D411yescharacteristic
742C42D3×D411yescharacteristic
743C42C23×D311yescharacteristic
744C42C23×D311yescharacteristic
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—22no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—44no—
751C22×C3—44no—
752C22×C3—44no—
753C22×C3—88no—
754C22×C3#54812yes—
755C22×C3C23×D411yescharacteristic
756C3×C4—21no—
757C3×C4—21no—
758C3×C4—22no—
759C3×C4—21no—
760C3×C4—41no—
761C3×C4—41no—
762C3×C4#54812yes—
763C3×C4#57512yes—
764C3×C4C22×#4111yescharacteristic
765C3×C4C2×2−1+411yescharacteristic
766Dic3—22no—
767Dic3—22no—
768Dic3—22no—
769Dic3—22no—
770Dic3—42no—
771Dic3—42no—
772Dic3—42no—
773Dic3—42no—
774C23—21no—
775C23—24no—
776C23—44no—
777C23—44no—
778C23—44no—
779C23C2×D3×D411yescharacteristic
780Q8—21no—
781Q8—62no—
782Q8—62no—
783Q8—62no—
784Q8—62no—
785Q8—122no—
786Q8—124no—
787Q8—122no—
788Q8—122no—
789Q8—241no—
790Q8—242no—
791Q8C2×#23712yes—
792D4—24no—
793D4—24no—
794D4—21no—
795D4—24no—
796D4—44no—
797D4—44no—
798D4—44no—
799D4—82no—
800D4—82no—
801D4C2×#23712yes—
802C2×C4—21no—
803C2×C4—22no—
804C2×C4—24no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—32no—
808C2×C4—32no—
809C2×C4—32no—
810C2×C4—32no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—62no—
814C2×C4—62no—
815C2×C4—62no—
816C2×C4—62no—
817C2×C4—81no—
818C2×C4—122no—
819C2×C4—122no—
820C2×C4—124no—
821C2×C4—122no—
822C2×C4—122no—
823C2×C4—244no—
824C2×C4—244no—
825C2×C4—242no—
826C2×C4C2×D3×D411yescharacteristic
827C2×C4C2×D3×D411yescharacteristic
828C2×C4C2×D3×D411yescharacteristic
829C2×C4C2×D3×D411yescharacteristic
830C2×C4C2×D3×D411yescharacteristic
831C2×C4C2×#23712yes—
832C2×C4#101012yes—
833C2×C4C24×D311yescharacteristic
834C8—24no—
835C8—62no—
836C8—62no—
837C2×C3—22no—
838C2×C3—42no—
839C2×C3—84no—
840C2×C3C2×#54811yescharacteristic
841C2×C3C2×#57511yescharacteristic
842C2×C3#358511yescharacteristic
843C22—21no—
844C22—21no—
845C22—22no—
846C22—41no—
847C22—41no—
848C22—44no—
849C22—44no—
850C22—44no—
851C22—88no—
852C22#559812yes—
853C22C22×D3×D411yescharacteristic
854C4—21no—
855C4—21no—
856C4—21no—
857C4—22no—
858C4—41no—
859C4—41no—
860C4—62no—
861C4—62no—
862C4—62no—
863C4—62no—
864C4—122no—
865C4—122no—
866C4—122no—
867C4—122no—
868C4#559812yes—
869C4#577312yes—
870C4C22×#23711yescharacteristic
871C4C2×#101011yescharacteristic
872C3#6132411yescharacteristic, complemented, Sylow
873C2—22no—
874C2—42no—
875C2—84no—
876C2C2×#559811yescharacteristic
877C2C2×#577311yescharacteristic
878C2#8719211yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
Fitting, prime radicalC3×#3038C2
socleC22×C3C23×D4
hypercenter#3038D3
hypocenterC3#61324
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3038

Complements

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

NH ≅ G/Ntype
1. C2×#5713C2semidirect
2. #41×Dic6C2semidirect
4. #83933C2semidirect
5. Dic3×AGL(1,ℤ/8)C2semidirect
6. #83159C2semidirect
7. C4×#951C2semidirect
8. #80374C2semidirect
9. #80373C2semidirect
10. #80370C2semidirect
11. #80323C2semidirect
12. #80322C2semidirect
13. #80319C2semidirect
14. #79068C2semidirect
15. #79046C2semidirect
16. #78922C2semidirect
17. #78917C2semidirect
35. #5570C22semidirect
36. #5569C22semidirect
37. Q8×Dic6C22semidirect
39. #5543C22semidirect
41. #5539C22semidirect
43. D4×Dic6C22semidirect
60. #5166C22semidirect
61. #5166C22semidirect
62. #5164C22semidirect
63. Dic3×SD16C22semidirect
64. #5153C22semidirect
65. #5153C22semidirect
66. #5152C22semidirect
67. Dic3×D8C22semidirect
75. #5030C22semidirect
76. C4×#216C22semidirect
77. #5018C22semidirect
78. C4×#214C22semidirect
82. #4851C22semidirect
83. #4850C22semidirect
84. #4831C22semidirect
85. #4830C22semidirect
86. #4829C22semidirect
87. #4828C22semidirect
88. #4768C22semidirect
89. #4768C22semidirect
90. #4766C22semidirect
91. #4765C22semidirect
92. #4765C22semidirect
93. #4763C22semidirect
94. #4761C22semidirect
95. #4759C22semidirect
872. C3#61324semidirect

Maximal subgroups

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

subgroupindex
C2×#57132
#41×Dic62
C3×#30382
#839332
Dic3×AGL(1,ℤ/8)2
#831592
C4×#9512
#803742
#803732
#803702
#803232
#803222
#803192
#790682
#790462
#789222
#789172
#613243