Finite Group Databasebeta

← #11675100

Subgroups — #11675100

Order 768.

1814 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×Dic6C211yesmaximal, characteristic, complemented
2C2×#5542C211yesmaximal, characteristic, complemented
3C3×C4×AGL(1,ℤ/8)C211yesmaximal, characteristic
4#83933C212yesmaximal
5#82533C211yesmaximal, characteristic, complemented
6#82296C211yesmaximal, characteristic, complemented
7#79854C214yesmaximal, complemented
8#79758C214yesmaximal, complemented
9#79626C212yesmaximal, complemented
10#79623C212yesmaximal, complemented
11#79571C212yesmaximal, complemented
12#79568C212yesmaximal, complemented
13#79245C212yesmaximal, complemented
14#78922C212yesmaximal, complemented
15#78867C212yesmaximal, complemented
16#78537C211yesmaximal, characteristic, complemented
17M16×Dic6C211yesmaximal, characteristic, complemented
18#61323—31nomaximal, Sylow
19C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
20C3×C4×#41C2211yescharacteristic
21C2×C3×C4×D4C2211yescharacteristic
22Dic3×#41C2212yes—
23C2×#951C2212yes—
24C2×#936C2212yes—
25C2×#926—21no—
26C2×#924—21no—
27#5570C2211yescharacteristic, complemented
28#5569C2212yescomplemented
29Q8×Dic6C2211yescharacteristic, complemented
30#5543—21no—
31#5543C2211yescharacteristic, complemented
32#5542—21no—
33#5542—21no—
34#5542—22no—
35#5542C2212yes—
36#5542C2212yes—
37#5542C2214yes—
38#5539—22no—
39#5539C2212yescomplemented
40D4×Dic6—21no—
41D4×Dic6C2211yescharacteristic, complemented
42#5517—22no—
43#5517C2212yes—
44C2×#887C2212yes—
45C2×#879—22no—
46#5470—21no—
47#5470C2211yescharacteristic
48C2×#869C2211yescharacteristic
49C2×C4×Dic6—21no—
50C2×C4×Dic6C2211yescharacteristic
51C3×#442C2212yes—
52C3×#440C2212yes—
53C3×C4×SD16C2212yes—
54C3×C4×D8C2212yes—
55C3×#428C2211yescharacteristic
56C3×#418C2211yescharacteristic
57C3×#417C2211yescharacteristic
58C3×C4×M16C2211yescharacteristic
59#5215C2212yes—
60#5166C2214yes—
61#5166C2214yes—
62#5153C2214yes—
63#5153C2214yes—
64#5120C2212yes—
65#5120C2212yes—
66#5118C2212yes—
67Dic3×M16C2212yes—
68#5031C2212yescomplemented
69#5031C2212yescomplemented
70#5019C2212yescomplemented
71#5019C2212yescomplemented
72#5009C2214yes—
73#5008C2212yes—
74#5007C2212yes—
75#5004C2212yes—
76#4964C2212yes—
77#4924C2211yescharacteristic
78#4877C2214yescomplemented
79#4875C2214yescomplemented
80#4857C2214yescomplemented
81#4854C2214yescomplemented
82#4790C2214yescomplemented
83#4789C2214yescomplemented
84#4768C2214yes—
85#4768C2214yes—
86#4765C2214yes—
87#4765C2214yes—
88#4758C2214yescomplemented
89#4757C2214yescomplemented
90#4703C2214yescomplemented
91#4701C2214yescomplemented
92#4681C2212yescomplemented
93#4681C2212yescomplemented
94#4679C2212yescomplemented
95C8×Dic6C2212yescomplemented
96Q8×#41—31no—
97C2×#556—31no—
98#3377—34no—
99#3376—34no—
100#3369—32no—
101#3367—32no—
102#3364—32no—
103#3360—32no—
104#3140—32no—
105#3139—31no—
106#3078—32no—
107#3077—31no—
108#3040—32no—
109#3039—31no—
110Q8×M16—31no—
111C4×#137—32no—
112C4×AGL(1,ℤ/8)D311yescharacteristic
113C2×C3×#41C2311yescharacteristic
114C22×C3×D4C2311yescharacteristic
115C23×C3×C4—21no—
116C22×Dic6—21no—
117C22×Dic6D411yescharacteristic
118C22×Dic6C2312yes—
119C3×AGL(1,ℤ/8)—24no—
120C2×C3×SD16C2312yes—
121C2×C3×D8C2312yes—
122C2×C3×M16C2311yescharacteristic
123C2×C3×M16C2311yescharacteristic
124C3×C4×Q8C2311yescharacteristic
125C3×C4×Q8C2311yescharacteristic
126C3×C4×D4—21no—
127C3×C4×D4—21no—
128C3×C4×D4—21no—
129C3×C4×D4—21no—
130C3×C4×D4C2312yes—
131C3×C4×D4C2312yes—
132C3×C4×D4C2311yescharacteristic
133C3×C4×D4C2311yescharacteristic
134C3×#117—21no—
135C3×#117C2311yescharacteristic
136C2×C3×C4⋊C4C2311yescharacteristic
137C2×C3×C22⋊C4—21no—
138C2×C3×C42—21no—
139C2×C3×C42C2311yescharacteristic
140C2×#217—22no—
141C2×#217—22no—
142#951—28no—
143Q8×Dic3C2312yes—
144Q8×Dic3C2312yes—
145C2×#216C2314yes—
146#936—22no—
147#936—22no—
148#936C2314yes—
149#936C2314yes—
150D4×Dic3—22no—
151D4×Dic3—22no—
152D4×Dic3C2312yes—
153D4×Dic3C2312yes—
154C2×#214C2314yes—
155#926—22no—
156#926—22no—
157#926—24no—
158#926—22no—
159#926C2312yes—
160C2×C4⋊Dic3—21no—
161C2×C4⋊Dic3—21no—
162C2×C4⋊Dic3—21no—
163C2×C4⋊Dic3D411yescharacteristic
164#924—21no—
165#924—21no—
166#924—21no—
167#924—22no—
168#924—22no—
169#924—24no—
170#924—21no—
171#924—22no—
172C2×Dic3⋊C4—22no—
173C2×Dic3⋊C4—22no—
174C2×Dic3⋊C4D412yes—
175C2×C4×Dic3—22no—
176C2×C4×Dic3—22no—
177C2×C4×Dic3C2312yes—
178C2×#208C2312yes—
179#890—22no—
180#890—22no—
181#890C2312yes—
182#890C2312yes—
183#888—22no—
184#888—22no—
185#888C2312yes—
186#888C2312yes—
187#887—22no—
188#887—22no—
189#887C2314yes—
190#887C2314yes—
191#879—24no—
192#879—24no—
193#879—24no—
194#879—24no—
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#869—21no—
206#869—21no—
207#869C2312yes—
208#869C2312yes—
209#869C2311yescharacteristic
210#869C2311yescharacteristic
211C4×Dic6—21no—
212C4×Dic6—21no—
213C4×Dic6—21no—
214C4×Dic6—21no—
215C4×Dic6—22no—
216C4×Dic6—22no—
217C4×Dic6—22no—
218C4×Dic6D411yescharacteristic
219C4×Dic6D411yescharacteristic
220C4×Dic6D412yes—
221C4×Dic6C2311yescharacteristic
222C4×Dic6C2311yescharacteristic
223C4×Dic6C2312yes—
224C3×#107C2312yes—
225C3×#106C2312yes—
226C3×#103C2312yes—
227C3×#102C2312yes—
228C3×#102C2312yes—
229C3×#102C2312yes—
230C3×#97C2312yes—
231C3×C4×C8C2312yes—
232#832C2314yes—
233#832C2314yes—
234#816C2314yes—
235#816C2314yes—
236#816C2314yes—
237#816C2314yes—
238#815C2314yes—
239Dic3⋊C8C2314yes—
240Dic3⋊C8C2314yes—
241C8×Dic3C2314yes—
242#810C2314yes—
243#810C2314yes—
244#808C2314yes—
245#807C2314yes—
246C4⋊(C3⋊C8)C2312yes—
247C4⋊(C3⋊C8)C2312yes—
248C2×#137—32no—
249C2×AGL(1,ℤ/8)C2×D311yescharacteristic
250Q82—31no—
251#557—31no—
252#557—32no—
253#556—32no—
254#556—32no—
255#556—34no—
256#556—61no—
257#556—62no—
258#556—61no—
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×C4⋊Q8—31no—
270C2×#126—62no—
271C2×#124—32no—
272C2×C22⋊Q8—61no—
273C4×#41—32no—
274C4×#41C2×D311yescharacteristic
275C2×C4×Q8—31no—
276C2×C4×Q8—32no—
277C2×C4×Q8—61no—
278C2×C4×D4C2×D311yescharacteristic
279C2×#117—61no—
280#491—34no—
281#489—34no—
282#489—34no—
283#488—34no—
284#488—34no—
285#487—32no—
286#487—32no—
287#479—34no—
288#479—34no—
289#478—34no—
290#477—34no—
291#476—32no—
292#475—34no—
293#474—32no—
294#464—34no—
295#464—34no—
296#463—34no—
297#463—34no—
298#462—32no—
299#462—32no—
300#461—32no—
301#461—32no—
302#446—34no—
303#446—32no—
304C8×Q8—32no—
305#442C2×D312yes—
306#441—34no—
307#440—34no—
308#440C2×D312yes—
309C4×Q16—34no—
310C4×SD16—34no—
311C4×SD16C2×D312yes—
312C4×D8C2×D312yes—
313#428—32no—
314#428C2×D311yescharacteristic
315#423—32no—
316#423—31no—
317#419—32no—
318#419—32no—
319#419—32no—
320#418—32no—
321#418C2×D311yescharacteristic
322#417C2×D311yescharacteristic
323C4×M16—32no—
324C4×M16C2×D311yescharacteristic
325C24×C3—21no—
326C3×#41—22no—
327C3×#41#4114yes—
328C2×C3×Q8C2411yescharacteristic
329C2×C3×D4—21no—
330C2×C3×D4—21no—
331C2×C3×D4—22no—
332C2×C3×D4—22no—
333C2×C3×D4C2412yes—
334C2×C3×D4C2411yescharacteristic
335C22×C3×C4—21no—
336C22×C3×C4—21no—
337C22×C3×C4—21no—
338C22×C3×C4—22no—
339C22×C3×C4—22no—
340C22×C3×C4—21no—
341C22×C3×C4—44no—
342C22×C3×C4C2×D411yescharacteristic
343C22×C3×C4C2×D411yescharacteristic
344C22×C3×C4C2411yescharacteristic
345C22×Dic3—22no—
346C22×Dic3—22no—
347C22×Dic3—22no—
348C22×Dic3C2×D412yes—
349C22×Dic3C2×D412yes—
350C2×Dic6—24no—
351C2×Dic6—24no—
352C2×Dic6—21no—
353C2×Dic6—22no—
354C2×Dic6—22no—
355C2×Dic6—21no—
356C2×Dic6—22no—
357C2×Dic6—42no—
358C2×Dic6—44no—
359C2×Dic6C2×D411yescharacteristic
360C2×Dic6C2×D411yescharacteristic
361C2×Dic6C2×D412yes—
362C2×Dic6C2414yes—
363C3×SD16—24no—
364C3×D8—24no—
365C3×M16—22no—
366C3×M16—22no—
367C2×C3×C8C2412yes—
368C2×C3×C8C2412yes—
369C3×C4⋊C4—21no—
370C3×C4⋊C4—21no—
371C3×C4⋊C4—21no—
372C3×C4⋊C4C2412yes—
373C3×C4⋊C4C2411yescharacteristic
374C3×C4⋊C4C2411yescharacteristic
375C3×C22⋊C4—21no—
376C3×C22⋊C4—21no—
377C3×C22⋊C4—21no—
378C3×C22⋊C4—22no—
379C3×C22⋊C4—22no—
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#216—28no—
395#214—28no—
396C4⋊Dic3—21no—
397C4⋊Dic3—21no—
398C4⋊Dic3—22no—
399C4⋊Dic3—22no—
400C4⋊Dic3—22no—
401C4⋊Dic3—22no—
402C4⋊Dic3—22no—
403C4⋊Dic3—22no—
404C4⋊Dic3—22no—
405C4⋊Dic3—22no—
406C4⋊Dic3C2×D411yescharacteristic
407C4⋊Dic3C2×D411yescharacteristic
408C4⋊Dic3C2×D412yes—
409C4⋊Dic3C2412yes—
410C4⋊Dic3C2412yes—
411Dic3⋊C4—22no—
412Dic3⋊C4—22no—
413Dic3⋊C4—22no—
414Dic3⋊C4—22no—
415Dic3⋊C4—22no—
416Dic3⋊C4—22no—
417Dic3⋊C4—24no—
418Dic3⋊C4—24no—
419Dic3⋊C4C2×D412yes—
420Dic3⋊C4C2×D412yes—
421Dic3⋊C4C2×D412yes—
422Dic3⋊C4C2×D412yes—
423C4×Dic3—22no—
424C4×Dic3—22no—
425C4×Dic3—22no—
426C4×Dic3—24no—
427C4×Dic3—24no—
428C4×Dic3C2×D412yes—
429C4×Dic3C2×D412yes—
430C4×Dic3C2412yes—
431C4×Dic3C2412yes—
432#208—24no—
433C2×C3⋊C8C2414yes—
434C2×#41C22×D311yescharacteristic
435C22×Q8—31no—
436C22×Q8—32no—
437C22×Q8—61no—
438C22×D4C22×D311yescharacteristic
439C23×C4—21no—
440#137—68no—
441AGL(1,ℤ/8)—24no—
442C2×Q16—34no—
443C2×SD16—34no—
444C2×SD16C22×D312yes—
445C2×D8C22×D312yes—
446C2×M16—32no—
447C2×M16C22×D311yescharacteristic
448C2×M16C22×D311yescharacteristic
449C4⋊Q8—32no—
450C4⋊Q8—32no—
451C4⋊Q8—31no—
452C4⋊Q8—31no—
453C4⋊Q8—32no—
454C4⋊Q8—32no—
455C4⋊Q8—61no—
456C4⋊Q8—61no—
457C4⋊Q8—62no—
458C4⋊Q8—62no—
459C4⋊Q8—61no—
460C4⋊Q8—61no—
461#126—64no—
462#126—64no—
463#126—64no—
464#126—64no—
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—
475C22⋊Q8—62no—
476C22⋊Q8—62no—
477C22⋊Q8—62no—
478C22⋊Q8—62no—
479C22⋊Q8—62no—
480C22⋊Q8—62no—
481C22⋊Q8—61no—
482C22⋊Q8—62no—
483C22⋊Q8—62no—
484C22⋊Q8—62no—
485C22⋊Q8—64no—
486C22⋊Q8—61no—
487C22⋊Q8—61no—
488C22⋊Q8—61no—
489C4×Q8—31no—
490C4×Q8—32no—
491C4×Q8—31no—
492C4×Q8—31no—
493C4×Q8—31no—
494C4×Q8—32no—
495C4×Q8—32no—
496C4×Q8—32no—
497C4×Q8—34no—
498C4×Q8—34no—
499C4×Q8—62no—
500C4×Q8—62no—
501C4×Q8—62no—
502C4×Q8—61no—
503C4×Q8—61no—
504C4×Q8—62no—
505C4×Q8—62no—
506C4×Q8—61no—
507C4×Q8—61no—
508C4×Q8C22×D311yescharacteristic
509C4×Q8C22×D311yescharacteristic
510C4×D4—21no—
511C4×D4—21no—
512C4×D4—21no—
513C4×D4—21no—
514C4×D4—32no—
515C4×D4—32no—
516C4×D4—62no—
517C4×D4—62no—
518C4×D4C22×D312yes—
519C4×D4C22×D312yes—
520C4×D4C22×D311yescharacteristic
521C4×D4C22×D311yescharacteristic
522#117—21no—
523#117—32no—
524#117—62no—
525#117—62no—
526#117—64no—
527#117—62no—
528#117C22×D311yescharacteristic
529C2×C4⋊C4—31no—
530C2×C4⋊C4—32no—
531C2×C4⋊C4—62no—
532C2×C4⋊C4—61no—
533C2×C4⋊C4—62no—
534C2×C4⋊C4—61no—
535C2×C4⋊C4—61no—
536C2×C4⋊C4C22×D311yescharacteristic
537C2×C22⋊C4—21no—
538C2×C22⋊C4—62no—
539C2×C22⋊C4—62no—
540C2×C42—21no—
541C2×C42—32no—
542C2×C42—62no—
543C2×C42—62no—
544C2×C42C22×D311yescharacteristic
545#107—34no—
546#107C22×D312yes—
547#106—34no—
548#106C22×D312yes—
549C4⋊C8—34no—
550C4⋊C8—34no—
551C4⋊C8—32no—
552C4⋊C8—32no—
553#103—34no—
554#103—34no—
555#103—34no—
556#103—34no—
557#103—34no—
558#103—34no—
559#103C22×D312yes—
560#102—34no—
561#102—34no—
562#102C22×D312yes—
563#102C22×D312yes—
564#102C22×D312yes—
565#97—34no—
566#97C22×D312yes—
567C4×C8—34no—
568C4×C8C22×D312yes—
569C23×C3—21no—
570C23×C3—22no—
571C23×C3—42no—
572C23×C3—42no—
573C23×C3—42no—
574C23×C3C22×D411yescharacteristic
575C3×Q8—21no—
576C3×Q8C2×#4112yes—
577C3×D4—24no—
578C3×D4—22no—
579C3×D4—21no—
580C3×D4—22no—
581C3×D4—42no—
582C3×D4C2×#4112yes—
583C2×C3×C4—21no—
584C2×C3×C4—24no—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—41no—
590C2×C3×C4—44no—
591C2×C3×C4—42no—
592C2×C3×C4—42no—
593C2×C3×C4—44no—
594C2×C3×C4—81no—
595C2×C3×C4C22×D411yescharacteristic
596C2×C3×C4C22×D411yescharacteristic
597C2×C3×C4C22×D411yescharacteristic
598C2×C3×C4C22×D411yescharacteristic
599C2×C3×C4C22×D411yescharacteristic
600C2×C3×C4C2×#4112yes—
601C2×C3×C42−1+412yes—
602C2×C3×C4C2511yescharacteristic
603C2×Dic3—22no—
604C2×Dic3—22no—
605C2×Dic3—24no—
606C2×Dic3—42no—
607C2×Dic3—42no—
608C2×Dic3—44no—
609C2×Dic3—44no—
610C2×Dic3—82no—
611C2×Dic3C22×D412yes—
612C2×Dic3C22×D412yes—
613C2×Dic3C22×D412yes—
614C2×Dic3C22×D412yes—
615Dic6—22no—
616Dic6—22no—
617Dic6—24no—
618Dic6—24no—
619Dic6—42no—
620Dic6—44no—
621Dic6—44no—
622Dic6—42no—
623Dic6—82no—
624Dic6—81no—
625C3×C8—22no—
626C3×C8—22no—
627C3⋊C8—24no—
628C24—21no—
629#41—22no—
630#41#23514yes—
631C2×Q8—31no—
632C2×Q8—31no—
633C2×Q8—32no—
634C2×Q8—34no—
635C2×Q8—62no—
636C2×Q8—62no—
637C2×Q8—61no—
638C2×Q8—62no—
639C2×Q8—61no—
640C2×Q8—64no—
641C2×Q8—64no—
642C2×Q8—122no—
643C2×Q8—124no—
644C2×Q8C23×D311yescharacteristic
645C2×D4—21no—
646C2×D4—22no—
647C2×D4—21no—
648C2×D4—22no—
649C2×D4C23×D312yes—
650C2×D4C23×D311yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—21no—
657C22×C4—32no—
658C22×C4—32no—
659C22×C4—44no—
660C22×C4—62no—
661C22×C4—62no—
662C22×C4—62no—
663C22×C4D3×D411yescharacteristic
664C22×C4D3×D411yescharacteristic
665C22×C4C23×D311yescharacteristic
666Q16—68no—
667SD16—24no—
668SD16—68no—
669D8—24no—
670M16—22no—
671M16—22no—
672M16—64no—
673C2×C8—34no—
674C2×C8C23×D312yes—
675C2×C8C23×D312yes—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—31no—
680C4⋊C4—32no—
681C4⋊C4—32no—
682C4⋊C4—31no—
683C4⋊C4—32no—
684C4⋊C4—32no—
685C4⋊C4—32no—
686C4⋊C4—32no—
687C4⋊C4—32no—
688C4⋊C4—64no—
689C4⋊C4—64no—
690C4⋊C4—62no—
691C4⋊C4—62no—
692C4⋊C4—62no—
693C4⋊C4—62no—
694C4⋊C4—62no—
695C4⋊C4—62no—
696C4⋊C4—62no—
697C4⋊C4—62no—
698C4⋊C4—62no—
699C4⋊C4—62no—
700C4⋊C4—62no—
701C4⋊C4—61no—
702C4⋊C4—62no—
703C4⋊C4—62no—
704C4⋊C4—62no—
705C4⋊C4—61no—
706C4⋊C4C23×D311yescharacteristic
707C4⋊C4C23×D311yescharacteristic
708C4⋊C4C23×D312yes—
709C22⋊C4—21no—
710C22⋊C4—22no—
711C22⋊C4—22no—
712C22⋊C4—21no—
713C22⋊C4—21no—
714C22⋊C4—64no—
715C22⋊C4—64no—
716C22⋊C4—64no—
717C22⋊C4—64no—
718C22⋊C4—62no—
719C22⋊C4—62no—
720C22⋊C4—62no—
721C42—21no—
722C42—21no—
723C42—21no—
724C42—32no—
725C42—32no—
726C42—32no—
727C42—32no—
728C42—64no—
729C42—64no—
730C42—62no—
731C42—62no—
732C42—62no—
733C42D3×D411yescharacteristic
734C42D3×D411yescharacteristic
735C42C23×D311yescharacteristic
736C42C23×D311yescharacteristic
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—22no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—42no—
743C22×C3—42no—
744C22×C3—42no—
745C22×C3—84no—
746C22×C3#54812yes—
747C22×C3C23×D411yescharacteristic
748C3×C4—21no—
749C3×C4—21no—
750C3×C4—22no—
751C3×C4—21no—
752C3×C4—41no—
753C3×C4—41no—
754C3×C4—42no—
755C3×C4#54812yes—
756C3×C4#57512yes—
757C3×C4C22×#4111yescharacteristic
758C3×C4C2×2−1+411yescharacteristic
759Dic3—22no—
760Dic3—22no—
761Dic3—22no—
762Dic3—22no—
763Dic3—42no—
764Dic3—44no—
765Dic3—42no—
766C23—21no—
767C23—22no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23C2×D3×D411yescharacteristic
772Q8—21no—
773Q8—62no—
774Q8—62no—
775Q8—64no—
776Q8—64no—
777Q8—122no—
778Q8—124no—
779Q8—122no—
780Q8—124no—
781Q8—241no—
782Q8—242no—
783Q8C2×#23512yes—
784D4—24no—
785D4—22no—
786D4—21no—
787D4—22no—
788D4—42no—
789D4C2×#23512yes—
790C2×C4—21no—
791C2×C4—22no—
792C2×C4—24no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—22no—
796C2×C4—32no—
797C2×C4—32no—
798C2×C4—32no—
799C2×C4—32no—
800C2×C4—41no—
801C2×C4—44no—
802C2×C4—42no—
803C2×C4—44no—
804C2×C4—42no—
805C2×C4—64no—
806C2×C4—62no—
807C2×C4—62no—
808C2×C4—81no—
809C2×C4—122no—
810C2×C4—122no—
811C2×C4—124no—
812C2×C4—124no—
813C2×C4—242no—
814C2×C4C2×#23512yes—
815C2×C4C2×D3×D411yescharacteristic
816C2×C4C2×D3×D411yescharacteristic
817C2×C4C2×D3×D411yescharacteristic
818C2×C4C2×D3×D411yescharacteristic
819C2×C4C2×D3×D411yescharacteristic
820C2×C4#101012yes—
821C2×C4C24×D311yescharacteristic
822C8—22no—
823C8—22no—
824C8—64no—
825C2×C3—22no—
826C2×C3—42no—
827C2×C3—82no—
828C2×C3C2×#54811yescharacteristic
829C2×C3C2×#57511yescharacteristic
830C2×C3#358611yescharacteristic
831C22—21no—
832C22—21no—
833C22—22no—
834C22—41no—
835C22—41no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—84no—
840C22#555212yes—
841C22C22×D3×D411yescharacteristic
842C4—21no—
843C4—21no—
844C4—21no—
845C4—22no—
846C4—42no—
847C4—41no—
848C4—41no—
849C4—62no—
850C4—62no—
851C4—62no—
852C4—62no—
853C4—122no—
854C4—122no—
855C4—124no—
856C4#555212yes—
857C4#577312yes—
858C4C22×#23511yescharacteristic
859C4C2×#101011yescharacteristic
860C3#6132311yescharacteristic, complemented, Sylow
861C2—22no—
862C2—42no—
863C2—82no—
864C2C2×#555211yescharacteristic
865C2C2×#577311yescharacteristic
866C2#8720111yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×C4×AGL(1,ℤ/8)C2
socleC22×C3C23×D4
prime radicalC2×C3×AGL(1,ℤ/8)C22
hypercenterC4×AGL(1,ℤ/8)D3
hypocenterC3#61323
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #41×Dic6C2semidirect
2. C2×#5542C2semidirect
5. #82533C2semidirect
6. #82296C2semidirect
7. #79854C2semidirect
8. #79758C2semidirect
9. #79626C2semidirect
10. #79623C2semidirect
11. #79571C2semidirect
12. #79568C2semidirect
13. #79245C2semidirect
14. #78922C2semidirect
15. #78867C2semidirect
16. #78537C2semidirect
17. M16×Dic6C2semidirect
27. #5570C22semidirect
28. #5569C22semidirect
29. Q8×Dic6C22semidirect
31. #5543C22semidirect
39. #5539C22semidirect
41. D4×Dic6C22semidirect
68. #5031C22semidirect
69. #5031C22semidirect
70. #5019C22semidirect
71. #5019C22semidirect
78. #4877C22semidirect
79. #4875C22semidirect
80. #4857C22semidirect
81. #4854C22semidirect
82. #4790C22semidirect
83. #4789C22semidirect
88. #4758C22semidirect
89. #4757C22semidirect
90. #4703C22semidirect
91. #4701C22semidirect
92. #4681C22semidirect
93. #4681C22semidirect
94. #4679C22semidirect
95. C8×Dic6C22semidirect
860. C3#61323semidirect

Maximal subgroups

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

subgroupindex
#41×Dic62
C2×#55422
C3×C4×AGL(1,ℤ/8)2
#839332
#825332
#822962
#798542
#797582
#796262
#796232
#795712
#795682
#792452
#789222
#788672
#785372
M16×Dic62
#613233