Finite Group Databasebeta

← #11675808

Subgroups — #11675808

Order 768.

1750 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#235C211yesmaximal, characteristic
2C2×#5567C211yesmaximal, characteristic, complemented
3C3×Q8×M16C211yesmaximal, characteristic, complemented
4#79987C214yesmaximal, complemented
5#79986C212yesmaximal, complemented
6#79978C214yesmaximal, complemented
7#79977C212yesmaximal, complemented
8#79937C212yesmaximal, complemented
9#79931C212yesmaximal, complemented
10#79068C212yesmaximal, complemented
11#79068C211yesmaximal, characteristic, complemented
12#79061C212yesmaximal
13#79060C211yesmaximal, characteristic
14C4×#909C212yesmaximal
15C4×#909C211yesmaximal, characteristic
16#78507C212yesmaximal, complemented
17#78506C211yesmaximal, characteristic, complemented
18#61369—31nomaximal, Sylow
19C2×C3×C4×Q8C2211yescharacteristic
20Q8×#67—21no—
21C2×#944—21no—
22C2×#909C2211yescharacteristic
23#5579C2211yescharacteristic
24#5579C2212yes—
25#5578—21no—
26#5578—22no—
27Q8×D12C2211yescharacteristic
28C4×D3×Q8—21no—
29#5567—21no—
30#5567—22no—
31#5567—21no—
32#5567C2212yes—
33#5567C2212yes—
34#5567C2214yes—
35#5567C2211yescharacteristic
36#5567C2212yes—
37Q8×Dic6C2211yescharacteristic
38#5511—21no—
39#5511—22no—
40C2×#889—22no—
41C2×#887—21no—
42C4×#235C2211yescharacteristic
43C4×#235C2212yes—
44#5470C2211yescharacteristic
45#5470C2212yes—
46C2×#870C2212yes—
47C2×#869C2211yescharacteristic
48C2×C4×Dic6C2212yes—
49C2×C4×Dic6C2211yescharacteristic
50C3×#446C2212yes—
51C3×#446C2214yes—
52C3×C8×Q8C2212yes—
53C3×#423C2211yescharacteristic
54C3×#423C2212yes—
55C3×C4×M16C2211yescharacteristic
56C3×C4×M16C2212yes—
57#5133C2212yes—
58#5133C2211yescharacteristic
59#5121C2212yes—
60#5121C2212yes—
61#5121C2211yescharacteristic
62#5121C2212yes—
63#5121C2212yes—
64#5120C2211yescharacteristic
65#5120C2212yes—
66#4851C2212yes—
67#4851C2212yes—
68#4851C2214yes—
69#4850C2212yes—
70#4850C2214yes—
71#4850C2212yes—
72#4847C2214yes—
73#4847C2214yes—
74#4846C2212yes—
75#4842C2212yes—
76#4829C2214yes—
77#4829C2214yes—
78#4829C2214yes—
79#4829C2214yes—
80#4829C2214yes—
81#4716C2214yes—
82#4716C2212yes—
83#4710C2214yes—
84#4710C2212yes—
85#4702C2214yes—
86#4702C2214yes—
87#4702C2214yes—
88C4×Dic12C2212yes—
89C4×Dic12C2214yes—
90C4×#204C2212yes—
91C4×#204C2214yes—
92#4683C2214yes—
93#4683C2214yes—
94#4682C2212yes—
95#4680C2212yes—
96Q8×#41—31no—
97C2×#557—31no—
98#3390—34no—
99#3388—34no—
100#3387—32no—
101#3386—32no—
102#3383—32no—
103#3381—32no—
104#3166—32no—
105#3165—31no—
106#3080—32no—
107#3079—31no—
108#3078—31no—
109#3078—32no—
110Q8×M16D311yescharacteristic, complemented
111C4×#137—31no—
112C4×#137—32no—
113C22×C3×Q8D411yescharacteristic
114C2×D3×Q8—21no—
115C2×#235C2311yescharacteristic
116C22×Dic6—21no—
117C22×Dic6C2311yescharacteristic
118C2×C3×M16C2311yescharacteristic
119C2×C3×M16C2312yes—
120C2×C3×M16C2311yescharacteristic
121C3×C4×Q8D411yescharacteristic
122C3×C4×Q8D411yescharacteristic
123C3×C4×Q8D412yes—
124C3×C4×Q8C2311yescharacteristic
125C3×C4×Q8C2311yescharacteristic
126C3×C4×Q8C2312yes—
127C2×C3×C4⋊C4D411yescharacteristic
128C2×C3×C4⋊C4D412yes—
129C2×C3×C42C2311yescharacteristic
130C2×C3×C42C2312yes—
131#946—21no—
132#946—22no—
133Q8×Dic3—21no—
134#944—22no—
135#944—22no—
136#944—24no—
137#944—21no—
138#944—22no—
139C4×#67—22no—
140C4×#67—21no—
141C4×#67—21no—
142C4×#67—22no—
143#926C2312yes—
144#926C2311yescharacteristic
145C2×C4⋊Dic3—21no—
146C2×C4⋊Dic3C2312yes—
147C2×C4⋊Dic3C2311yescharacteristic
148#924—22no—
149#924—21no—
150#924—21no—
151#924—22no—
152C2×Dic3⋊C4—21no—
153C2×Dic3⋊C4—22no—
154C2×Dic3⋊C4—22no—
155C2×Dic3⋊C4—22no—
156C2×C4×Dic3—22no—
157C2×C4×Dic3—21no—
158#909Q818yescomplemented
159C2×Dic12C2312yes—
160C2×#204C2312yes—
161#897—21no—
162#897—22no—
163#896—22no—
164#896—22no—
165#896—22no—
166D3×C4⋊C4—21no—
167D3×C4⋊C4—22no—
168#889—24no—
169#889—24no—
170#889—24no—
171#889—24no—
172#889—22no—
173#889—22no—
174#889—22no—
175#888—21no—
176#888—22no—
177#887—22no—
178#887—22no—
179#887—24no—
180#887—21no—
181#887—22no—
182C4×D12C2311yescharacteristic
183C4×D12C2312yes—
184C4×D12C2312yes—
185C4×D12C2311yescharacteristic
186#872—21no—
187#872—22no—
188C42×D3—21no—
189C42×D3—22no—
190#870—22no—
191#870—22no—
192#870C2314yes—
193#870C2312yes—
194#870C2312yes—
195#870C2314yes—
196#870C2312yes—
197#869—21no—
198#869—21no—
199#869C2311yescharacteristic
200#869C2312yes—
201#869C2311yescharacteristic
202#869C2312yes—
203#869C2312yes—
204#869C2312yes—
205C4×Dic6—22no—
206C4×Dic6—22no—
207C4×Dic6—21no—
208C4×Dic6—21no—
209C4×Dic6—21no—
210C4×Dic6—22no—
211C4×Dic6—21no—
212C4×Dic6—22no—
213C4×Dic6C2314yes—
214C4×Dic6C2312yes—
215C4×Dic6C2311yescharacteristic
216C4×Dic6C2312yes—
217C4×Dic6C2312yes—
218C4×Dic6C2314yes—
219C4×Dic6C2312yes—
220C4×Dic6C2311yescharacteristic
221C3×C4⋊C8C2314yes—
222C3×C4⋊C8C2312yes—
223C3×C4⋊C8C2312yes—
224C3×C4⋊C8C2314yes—
225C3×#97C2314yes—
226C3×#97C2312yes—
227C3×C4×C8C2312yes—
228C3×C4×C8C2314yes—
229#821C2314yes—
230#821C2312yes—
231#818C2314yes—
232#818C2314yes—
233#818C2312yes—
234#818C2314yes—
235#818C2314yes—
236#817C2314yes—
237#817C2314yes—
238#817C2312yes—
239#817C2314yes—
240#817C2314yes—
241#816C2312yes—
242#816C2314yes—
243#816C2314yes—
244#816C2312yes—
245#816C2312yes—
246#816C2314yes—
247C2×#137—31no—
248Q82—31no—
249#557—32no—
250#557—31no—
251#557—32no—
252#557—34no—
253#557—32no—
254#557—61no—
255#557—62no—
256#557—61no—
257#554—31no—
258#554—32no—
259#554—61no—
260#554—62no—
261D4×Q8—31no—
262D4×Q8—61no—
263#533—31no—
264#533—32no—
265#533—62no—
266#533—61no—
267C2×C4⋊Q8—31no—
268C2×C4⋊Q8—61no—
269C2×#125—32no—
270C2×#125—62no—
271C4×#41—31no—
272C4×#41—32no—
273C2×C4×Q8—32no—
274C2×C4×Q8—31no—
275C2×C4×Q8—61no—
276C2×C4×Q8—61no—
277C2×C4×Q8C2×D311yescharacteristic
278#501—34no—
279#501—34no—
280#501—34no—
281#500—32no—
282#499—34no—
283#499—34no—
284#498—32no—
285#479—34no—
286#479—34no—
287#479—34no—
288#479—34no—
289#479—34no—
290#478—34no—
291#478—34no—
292#477—32no—
293#477—34no—
294#477—32no—
295#476—32no—
296#475—32no—
297#475—34no—
298#475—32no—
299#474—32no—
300#446C2×D312yes—
301#446C2×D314yes—
302C8×Q8C2×D312yes—
303#441—34no—
304#441—32no—
305#440—34no—
306#440—32no—
307C4×Q16—32no—
308C4×Q16—34no—
309C4×SD16—32no—
310C4×SD16—34no—
311#428—32no—
312#428—32no—
313#428—32no—
314#428—32no—
315#428—31no—
316#423C2×D311yescharacteristic
317#423C2×D312yes—
318#419—32no—
319#419—31no—
320#417—32no—
321#417—31no—
322C4×M16C2×D311yescharacteristic
323C4×M16C2×D312yes—
324C2×C3×Q8—42no—
325C2×C3×Q8C2×D411yescharacteristic
326C2×C3×Q8C2×D411yescharacteristic
327C2×C3×Q8C2×D412yes—
328C22×C3×C4C2×D411yescharacteristic
329C22×C3×C4C2×D412yes—
330C22×C3×C4C2×D412yes—
331C22×C3×C4C2×D411yescharacteristic
332C22×C3×C4C2411yescharacteristic
333C2×#67—21no—
334C22×Dic3—21no—
335C22×Dic3—21no—
336C22×Dic3—22no—
337D3×Q8—44no—
338#235—22no—
339#235C2×Q814yes—
340C2×D12C2411yescharacteristic
341C2×C4×D3—21no—
342C2×C4×D3—22no—
343C2×C4×D3—21no—
344C2×C4×D3—22no—
345C2×C4×D3—21no—
346C2×Dic6—21no—
347C2×Dic6—22no—
348C2×Dic6—22no—
349C2×Dic6—21no—
350C2×Dic6—22no—
351C2×Dic6—22no—
352C2×Dic6—22no—
353C2×Dic6—21no—
354C2×Dic6—44no—
355C2×Dic6C2×Q814yescomplemented
356C2×Dic6C2412yes—
357C2×Dic6C2411yescharacteristic
358C3×M16—22no—
359C3×M16—24no—
360C3×M16C2×Q814yescomplemented
361C2×C3×C8C2412yes—
362C2×C3×C8C2414yes—
363C2×C3×C8C2412yes—
364C3×C4⋊C4C2×D411yescharacteristic
365C3×C4⋊C4C2×D411yescharacteristic
366C3×C4⋊C4C2×D412yes—
367C3×C4⋊C4C2×D412yes—
368C3×C4⋊C4C2×D412yes—
369C3×C4⋊C4C2×D412yes—
370C3×C4⋊C4C2×D412yes—
371C3×C42C2×D411yescharacteristic
372C3×C42C2×D411yescharacteristic
373C3×C42C2×D412yes—
374C3×C42C2×D412yes—
375C3×C42C2411yescharacteristic
376C3×C42C2412yes—
377C3×C42C2412yes—
378C3×C42C2411yescharacteristic
379#217—21no—
380#217—22no—
381(C2×D3)⋊C4—22no—
382(C2×D3)⋊C4—21no—
383(C2×D3)⋊C4—21no—
384(C2×D3)⋊C4—22no—
385C4⋊Dic3—22no—
386C4⋊Dic3—21no—
387C4⋊Dic3—22no—
388C4⋊Dic3—21no—
389C4⋊Dic3—22no—
390C4⋊Dic3—21no—
391C4⋊Dic3—22no—
392C4⋊Dic3—22no—
393C4⋊Dic3C2412yes—
394C4⋊Dic3C2411yescharacteristic
395C4⋊Dic3C2411yescharacteristic
396C4⋊Dic3C2412yes—
397C4⋊Dic3C2414yes—
398C4⋊Dic3C2412yes—
399Dic3⋊C4—22no—
400Dic3⋊C4—22no—
401Dic3⋊C4—24no—
402Dic3⋊C4—24no—
403Dic3⋊C4—22no—
404Dic3⋊C4—22no—
405Dic3⋊C4—22no—
406Dic3⋊C4—22no—
407Dic3⋊C4—22no—
408Dic3⋊C4—22no—
409Dic3⋊C4—22no—
410Dic3⋊C4—21no—
411Dic3⋊C4—21no—
412Dic3⋊C4—22no—
413Dic3⋊C4—24no—
414Dic3⋊C4—24no—
415Dic3⋊C4—24no—
416Dic3⋊C4—24no—
417C4×Dic3—22no—
418C4×Dic3—21no—
419C4×Dic3—24no—
420C4×Dic3—24no—
421C4×Dic3—22no—
422C4×Dic3—22no—
423C4×Dic3—22no—
424C4×Dic3—21no—
425C4×Dic3—22no—
426C4×Dic3—21no—
427Dic12C2×Q818yescomplemented
428#204C2×Q818yescomplemented
429C2×#41—31no—
430C22×Q8—31no—
431C22×Q8—61no—
432C22×Q8—61no—
433C22×Q8D1211yescharacteristic
434#137—38no—
435C2×Q16—32no—
436C2×SD16—32no—
437C2×M16C22×D311yescharacteristic
438C2×M16C22×D312yes—
439C2×M16C22×D311yescharacteristic
440C4⋊Q8—32no—
441C4⋊Q8—32no—
442C4⋊Q8—31no—
443C4⋊Q8—32no—
444C4⋊Q8—32no—
445C4⋊Q8—31no—
446C4⋊Q8—62no—
447C4⋊Q8—62no—
448C4⋊Q8—64no—
449C4⋊Q8—61no—
450C4⋊Q8—62no—
451C4⋊Q8—61no—
452C4⋊Q8—62no—
453C4⋊Q8—61no—
454C4⋊Q8—61no—
455#125—34no—
456#125—34no—
457#125—32no—
458#125—32no—
459#125—32no—
460#125—64no—
461#125—64no—
462#125—64no—
463#125—64no—
464#125—62no—
465#125—62no—
466#125—62no—
467#125—62no—
468#125—62no—
469C22⋊Q8—61no—
470C22⋊Q8—62no—
471C22⋊Q8—61no—
472C22⋊Q8—62no—
473C22⋊Q8—62no—
474C22⋊Q8—61no—
475C22⋊Q8—61no—
476C22⋊Q8—62no—
477C22⋊Q8—62no—
478C22⋊Q8—62no—
479C22⋊Q8—62no—
480C4×Q8—32no—
481C4×Q8—34no—
482C4×Q8—34no—
483C4×Q8—32no—
484C4×Q8—32no—
485C4×Q8—31no—
486C4×Q8—31no—
487C4×Q8—32no—
488C4×Q8—61no—
489C4×Q8—61no—
490C4×Q8—62no—
491C4×Q8—62no—
492C4×Q8—64no—
493C4×Q8—62no—
494C4×Q8—62no—
495C4×Q8—62no—
496C4×Q8—61no—
497C4×Q8—61no—
498C4×Q8—62no—
499C4×Q8—61no—
500C4×Q8—62no—
501C4×Q8—61no—
502C4×Q8D1211yescharacteristic
503C4×Q8D1212yes—
504C4×Q8D1211yescharacteristic
505C4×Q8C22×D311yescharacteristic
506C4×Q8C22×D311yescharacteristic
507C4×Q8C22×D312yes—
508C4×D4—31no—
509C4×D4—32no—
510C4×D4—32no—
511C4×D4—31no—
512C4×D4—61no—
513C4×D4—62no—
514C4×D4—62no—
515C4×D4—61no—
516#117—31no—
517#117—32no—
518#117—62no—
519#117—61no—
520C2×C4⋊C4—31no—
521C2×C4⋊C4—32no—
522C2×C4⋊C4—61no—
523C2×C4⋊C4—62no—
524C2×C4⋊C4—62no—
525C2×C4⋊C4—62no—
526C2×C4⋊C4—61no—
527C2×C4⋊C4—61no—
528C2×C4⋊C4—62no—
529C2×C4⋊C4D1211yescharacteristic
530C2×C4⋊C4D1212yes—
531C2×C42—62no—
532C2×C42—61no—
533C2×C42—62no—
534C2×C42—61no—
535C2×C42C22×D312yes—
536C2×C42C22×D311yescharacteristic
537#107—32no—
538#107—34no—
539#107—34no—
540#107—34no—
541#107—34no—
542#106—34no—
543#106—32no—
544#106—34no—
545#106—34no—
546#106—34no—
547C4⋊C8C22×D312yes—
548C4⋊C8C22×D314yes—
549C4⋊C8C22×D314yes—
550C4⋊C8C22×D312yes—
551#103—34no—
552#103—32no—
553#103—34no—
554#103—32no—
555#103—32no—
556#103—34no—
557#102—34no—
558#102—32no—
559#97C22×D312yes—
560#97C22×D314yes—
561C4×C8C22×D312yes—
562C4×C8C22×D314yes—
563C23×C3C22×D411yescharacteristic
564C22×D3—21no—
565C3×Q8—22no—
566C3×Q8—22no—
567C3×Q8—42no—
568C2×C3×C4—22no—
569C2×C3×C4—42no—
570C2×C3×C4—41no—
571C2×C3×C4—42no—
572C2×C3×C4C22×D412yes—
573C2×C3×C4C22×D412yes—
574C2×C3×C4C22×D411yescharacteristic
575C2×C3×C4C22×D411yescharacteristic
576C2×C3×C4C22×D412yes—
577C2×C3×C4C22×D412yes—
578C2×C3×C4C22×D411yescharacteristic
579C2×C3×C4C22×D411yescharacteristic
580C2×C3×C4C22×D411yescharacteristic
581C2×C3×C4C22×Q812yes—
582C2×C3×C42−1+412yes—
583C2×C3×C4C2511yescharacteristic
584#67—24no—
585C2×Dic3—24no—
586C2×Dic3—22no—
587C2×Dic3—21no—
588C2×Dic3—22no—
589C2×Dic3—24no—
590C2×Dic3—22no—
591C2×Dic3—21no—
592C2×Dic3—21no—
593C2×Dic3—22no—
594C2×Dic3—44no—
595C2×Dic3—42no—
596D12—21no—
597D12C22×Q812yes—
598C4×D3—24no—
599C4×D3—44no—
600C4×D3—42no—
601C4×D3—82no—
602C4×D3—81no—
603Dic6—24no—
604Dic6—22no—
605Dic6—21no—
606Dic6—44no—
607Dic6—44no—
608Dic6—44no—
609Dic6—42no—
610Dic6—82no—
611Dic6—81no—
612Dic6C22×Q814yes—
613Dic6C22×Q812yes—
614C3×C8—22no—
615C3×C8—24no—
616C3×C8C22×Q814yes—
617#41—34no—
618#41—62no—
619C2×Q8—34no—
620C2×Q8—32no—
621C2×Q8—31no—
622C2×Q8—42no—
623C2×Q8—61no—
624C2×Q8—62no—
625C2×Q8—61no—
626C2×Q8—62no—
627C2×Q8—62no—
628C2×Q8—62no—
629C2×Q8—61no—
630C2×Q8—62no—
631C2×Q8—124no—
632C2×Q8—124no—
633C2×Q8C2×D1211yescharacteristic
634C2×Q8C2×D1211yescharacteristic
635C2×Q8C2×D1212yes—
636C2×D4—31no—
637C2×D4—61no—
638C22×C4—61no—
639C22×C4—61no—
640C22×C4—61no—
641C22×C4—62no—
642C22×C4—62no—
643C22×C4—61no—
644C22×C4—62no—
645C22×C4—61no—
646C22×C4C2×D1211yescharacteristic
647C22×C4C2×D1212yes—
648C22×C4C2×D1211yescharacteristic
649C22×C4C2×D1212yes—
650C22×C4C23×D311yescharacteristic
651Q16—38no—
652SD16—38no—
653M16—22no—
654M16—24no—
655M16D3×Q814yescomplemented
656C2×C8C23×D312yes—
657C2×C8C23×D314yes—
658C2×C8C23×D312yes—
659C4⋊C4—32no—
660C4⋊C4—34no—
661C4⋊C4—32no—
662C4⋊C4—31no—
663C4⋊C4—31no—
664C4⋊C4—32no—
665C4⋊C4—61no—
666C4⋊C4—62no—
667C4⋊C4—62no—
668C4⋊C4—62no—
669C4⋊C4—64no—
670C4⋊C4—64no—
671C4⋊C4—62no—
672C4⋊C4—62no—
673C4⋊C4—62no—
674C4⋊C4—62no—
675C4⋊C4—61no—
676C4⋊C4—64no—
677C4⋊C4—64no—
678C4⋊C4—64no—
679C4⋊C4—64no—
680C4⋊C4—62no—
681C4⋊C4—62no—
682C4⋊C4—62no—
683C4⋊C4—61no—
684C4⋊C4—62no—
685C4⋊C4—61no—
686C4⋊C4—62no—
687C4⋊C4—62no—
688C4⋊C4—62no—
689C4⋊C4—62no—
690C4⋊C4—61no—
691C4⋊C4C2×D1211yescharacteristic
692C4⋊C4C2×D1212yes—
693C4⋊C4C2×D1212yes—
694C4⋊C4C2×D1211yescharacteristic
695C4⋊C4C2×D1212yes—
696C4⋊C4C2×D1212yes—
697C4⋊C4C2×D1212yes—
698C22⋊C4—61no—
699C22⋊C4—62no—
700C22⋊C4—62no—
701C22⋊C4—61no—
702C22⋊C4—62no—
703C22⋊C4—61no—
704C42—62no—
705C42—61no—
706C42—62no—
707C42—61no—
708C42—62no—
709C42—61no—
710C42—64no—
711C42—64no—
712C42—62no—
713C42—62no—
714C42C2×D1212yes—
715C42C2×D1211yescharacteristic
716C42C2×D1212yes—
717C42C2×D1211yescharacteristic
718C42C23×D312yes—
719C42C23×D311yescharacteristic
720C42C23×D312yes—
721C42C23×D311yescharacteristic
722C22×C3—21no—
723C22×C3—21no—
724C22×C3D4×Q812yes—
725C22×C3C23×D411yescharacteristic
726C2×D3—22no—
727C2×D3—41no—
728C2×D3—41no—
729C3×C4—22no—
730C3×C4—21no—
731C3×C4—22no—
732C3×C4—21no—
733C3×C4—21no—
734C3×C4—22no—
735C3×C4—22no—
736C3×C4D4×Q812yes—
737C3×C4#57512yes—
738C3×C4C23×Q811yescharacteristic
739C3×C4C2×2−1+411yescharacteristic
740Dic3—24no—
741Dic3—22no—
742Dic3—41no—
743Dic3—42no—
744Dic3—42no—
745Dic3—41no—
746Dic3—42no—
747Dic3—44no—
748C23—61no—
749C23C22×D1211yescharacteristic
750Q8—22no—
751Q8—22no—
752Q8—34no—
753Q8—32no—
754Q8—42no—
755Q8—62no—
756Q8—61no—
757Q8—64no—
758Q8—124no—
759Q8—124no—
760Q8—122no—
761Q8—124no—
762Q8—242no—
763Q8—241no—
764D4—32no—
765D4—64no—
766D4—61no—
767C2×C4—22no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—41no—
771C2×C4—61no—
772C2×C4—62no—
773C2×C4—64no—
774C2×C4—64no—
775C2×C4—62no—
776C2×C4—61no—
777C2×C4—62no—
778C2×C4—61no—
779C2×C4—62no—
780C2×C4—64no—
781C2×C4—124no—
782C2×C4—124no—
783C2×C4—122no—
784C2×C4—122no—
785C2×C4—242no—
786C2×C4—241no—
787C2×C4C22×D1212yes—
788C2×C4C22×D1212yes—
789C2×C4C22×D1211yescharacteristic
790C2×C4C22×D1211yescharacteristic
791C2×C4C22×D1212yes—
792C2×C4C22×D1212yes—
793C2×C4C22×D1211yescharacteristic
794C2×C4C22×D1211yescharacteristic
795C2×C4C22×D1211yescharacteristic
796C2×C4C2×D3×Q812yes—
797C2×C4#101012yes—
798C2×C4C24×D311yescharacteristic
799C8—22no—
800C8—24no—
801C8C2×D3×Q814yes—
802C2×C3—22no—
803C2×C3C2×D4×Q811yescharacteristic
804C2×C3C2×#57511yescharacteristic
805C2×C3#358611yescharacteristic
806D3—42no—
807C22—21no—
808C22—21no—
809C22—62no—
810C22—121no—
811C22—121no—
812C22Q8×D1212yes—
813C22C23×D1211yescharacteristic
814C4—21no—
815C4—22no—
816C4—22no—
817C4—22no—
818C4—21no—
819C4—22no—
820C4—21no—
821C4—62no—
822C4—64no—
823C4—122no—
824C4—121no—
825C4—124no—
826C4—122no—
827C4—122no—
828C4—121no—
829C4Q8×D1212yes—
830C4#574812yes—
831C4C22×D3×Q811yescharacteristic
832C4C2×#101011yescharacteristic
833C3#6136911yescharacteristic, complemented, Sylow
834C2—22no—
835C2—122no—
836C2C2×Q8×D1211yescharacteristic
837C2C2×#574811yescharacteristic
838C2#8716811yescharacteristic
subgroupG/H
centerC22C23×D12
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×Q8×M16C2
socleC22×C3C23×D4
prime radicalC2×#235C23
hypercenterQ8×M16D3
hypocenterC3#61369
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ Q8×M16

Complements

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

NH ≅ G/Ntype
2. C2×#5567C2semidirect
3. C3×Q8×M16C2semidirect
4. #79987C2semidirect
5. #79986C2semidirect
6. #79978C2semidirect
7. #79977C2semidirect
8. #79937C2semidirect
9. #79931C2semidirect
10. #79068C2semidirect
11. #79068C2semidirect
16. #78507C2semidirect
17. #78506C2semidirect
110. Q8×M16D3semidirect
158. #909Q8semidirect
355. C2×Dic6C2×Q8semidirect
360. C3×M16C2×Q8semidirect
427. Dic12C2×Q8semidirect
428. #204C2×Q8semidirect
655. M16D3×Q8semidirect
833. C3#61369semidirect

Maximal subgroups

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

subgroupindex
Q8×#2352
C2×#55672
C3×Q8×M162
#799872
#799862
#799782
#799772
#799372
#799312
#790682
#790612
#790602
C4×#9092
#785072
#785062
#613693