Finite Group Databasebeta

← #11675106

Subgroups — #11675106

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
1Q8×#235C211yesmaximal, characteristic, complemented
2C2×#5584C211yesmaximal, characteristic, complemented
3C3×Q8×M16C211yesmaximal, characteristic, complemented
4#79985C214yesmaximal, complemented
5#79981C212yesmaximal, complemented
6#79974C214yesmaximal, complemented
7#79970C212yesmaximal, complemented
8#79934C212yesmaximal, complemented
9#79926C212yesmaximal, complemented
10#79068C212yesmaximal, complemented
11#79059C211yesmaximal, characteristic, complemented
12#79058C212yesmaximal
13#79057C211yesmaximal, characteristic, complemented
14#78537C211yesmaximal, characteristic, complemented
15C4×#909C212yesmaximal, complemented
16#78527C212yesmaximal, complemented
17C4×#908C211yesmaximal, characteristic
18#61323—31nomaximal, Sylow
19C2×C3×C4×Q8C2211yescharacteristic
20Q8×#67—21no—
21C2×#946—21no—
22C2×#909C2212yes—
23C2×#908C2211yescharacteristic
24#5584—21no—
25#5584—22no—
26#5584—21no—
27#5584C2212yes—
28#5584C2212yes—
29#5584C2214yes—
30#5579C2211yescharacteristic, complemented
31#5579C2212yescomplemented
32#5578—22no—
33#5578—21no—
34Q8×D12C2211yescharacteristic, complemented
35C4×D3×Q8—21no—
36#5567C2211yescharacteristic, complemented
37#5567C2212yescomplemented
38Q8×Dic6C2211yescharacteristic, complemented
39C2×#898—22no—
40#5511—21no—
41#5511—22no—
42C2×#892—21no—
43C2×#875C2212yes—
44C4×#235C2211yescharacteristic
45C4×#235C2212yes—
46C2×C4×D12C2211yescharacteristic
47#5470C2212yes—
48#5470C2211yescharacteristic
49C2×#869C2211yescharacteristic
50C2×C4×Dic6C2212yes—
51C3×#446C2212yescomplemented
52C3×#446C2214yescomplemented
53C3×C8×Q8C2212yescomplemented
54C3×#423C2211yescharacteristic
55C3×#423C2212yes—
56C3×C4×M16C2211yescharacteristic
57C3×C4×M16C2212yes—
58#5133C2211yescharacteristic
59#5131C2211yescharacteristic
60#5131C2212yes—
61#5121C2211yescharacteristic
62#5121C2212yes—
63#5120C2212yes—
64#5120C2212yes—
65#5120C2212yes—
66#4851C2214yescomplemented
67#4850C2214yescomplemented
68#4849C2212yescomplemented
69#4849C2212yescomplemented
70#4847C2214yes—
71#4846C2212yes—
72#4845C2214yes—
73#4845C2214yes—
74#4844C2214yes—
75#4844C2214yes—
76#4842C2212yes—
77#4841C2212yescomplemented
78#4841C2212yescomplemented
79#4829C2214yescomplemented
80#4829C2214yescomplemented
81#4716C2214yescomplemented
82#4714C2214yes—
83#4714C2214yes—
84#4711C2212yes—
85#4710C2212yes—
86#4710C2214yescomplemented
87#4703C2214yescomplemented
88C4×Dic12C2214yescomplemented
89#4697C2214yes—
90#4697C2214yes—
91C4×D24C2212yes—
92C4×#204C2212yes—
93C4×#204C2214yescomplemented
94#4681C2212yescomplemented
95#4681C2212yescomplemented
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×M16D311yescharacteristic, complemented
111C4×#137—32no—
112C4×AGL(1,ℤ/8)—31no—
113C22×C3×Q8D411yescharacteristic
114C2×D3×Q8—21no—
115C2×#235C2311yescharacteristic
116C22×D12C2311yescharacteristic
117C22×C4×D3—21no—
118C22×Dic6C2312yes—
119C2×C3×M16C2311yescharacteristic
120C2×C3×M16C2311yescharacteristic
121C2×C3×M16C2312yes—
122C3×C4×Q8D411yescharacteristic
123C3×C4×Q8D412yes—
124C3×C4×Q8D411yescharacteristic
125C3×C4×Q8C2311yescharacteristic
126C3×C4×Q8C2311yescharacteristic
127C3×C4×Q8C2312yes—
128C2×C3×C4⋊C4D411yescharacteristic
129C2×C3×C4⋊C4D412yes—
130C2×C3×C42C2312yes—
131C2×C3×C42C2311yescharacteristic
132#946—22no—
133#946—22no—
134#946—24no—
135#946—21no—
136#946—22no—
137Q8×Dic3—21no—
138#944—21no—
139#944—22no—
140C4×#67—22no—
141C4×#67—21no—
142C4×#67—21no—
143C4×#67—22no—
144C2×(C2×D3)⋊C4—21no—
145C2×(C2×D3)⋊C4—22no—
146C2×(C2×D3)⋊C4—22no—
147#926C2312yes—
148#926C2311yescharacteristic
149C2×C4⋊Dic3—21no—
150C2×C4⋊Dic3—21no—
151C2×C4⋊Dic3C2311yescharacteristic
152#924—22no—
153#924—21no—
154#924—21no—
155#924—22no—
156C2×Dic3⋊C4—22no—
157C2×C4×Dic3—22no—
158#909—28no—
159#908—24no—
160C2×Dic12C2314yes—
161C2×D24C2312yes—
162C2×#204C2312yes—
163C2×#204C2314yes—
164#898—24no—
165#898—24no—
166#898—24no—
167#898—24no—
168#897—21no—
169#897—22no—
170#896—22no—
171#896—22no—
172#896—22no—
173#892—22no—
174#892—22no—
175#892—24no—
176D3×C4⋊C4—21no—
177D3×C4⋊C4—22no—
178#889—22no—
179#889—22no—
180#889—22no—
181#888—21no—
182#888—22no—
183#887—21no—
184#887—22no—
185#875—22no—
186#875—22no—
187#875C2314yes—
188#875C2314yes—
189C4×D12—21no—
190C4×D12—21no—
191C4×D12C2312yes—
192C4×D12C2312yes—
193C4×D12C2311yescharacteristic
194C4×D12C2312yes—
195C4×D12C2312yes—
196C4×D12C2311yescharacteristic
197#872—22no—
198#872—21no—
199C42×D3—22no—
200C42×D3—21no—
201#870C2312yes—
202#870C2312yes—
203#870C2312yes—
204#869—21no—
205#869—21no—
206#869C2312yes—
207#869C2312yes—
208#869C2311yescharacteristic
209#869C2311yescharacteristic
210#869C2312yes—
211#869C2312yes—
212C4×Dic6—22no—
213C4×Dic6—22no—
214C4×Dic6—22no—
215C4×Dic6—21no—
216C4×Dic6—22no—
217C4×Dic6—21no—
218C4×Dic6C2311yescharacteristic
219C4×Dic6C2314yes—
220C4×Dic6C2312yes—
221C4×Dic6C2314yes—
222C4×Dic6C2311yescharacteristic
223C4×Dic6C2312yes—
224C3×C4⋊C8C2314yes—
225C3×C4⋊C8C2312yes—
226C3×C4⋊C8C2312yes—
227C3×C4⋊C8C2314yes—
228C3×#97C2312yes—
229C3×#97C2314yes—
230C3×C4×C8C2312yes—
231C3×C4×C8C2314yes—
232#821C2312yes—
233#821C2312yes—
234#821C2314yes—
235#821C2314yes—
236#821C2312yes—
237#818C2312yes—
238#818C2314yes—
239#817C2312yes—
240#817C2314yes—
241#816C2314yes—
242#816C2314yes—
243#816C2314yes—
244#816C2314yes—
245#816C2314yes—
246#816C2314yes—
247#816C2312yes—
248C2×#137—32no—
249C2×AGL(1,ℤ/8)—31no—
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—61no—
262#554—62no—
263D4×Q8—31no—
264D4×Q8—61no—
265#533—31no—
266#533—32no—
267#533—61no—
268#533—62no—
269C2×C4⋊Q8—31no—
270C2×#126—62no—
271C2×#124—32no—
272C2×C22⋊Q8—61no—
273C4×#41—31no—
274C4×#41—32no—
275C2×C4×Q8—32no—
276C2×C4×Q8—61no—
277C2×C4×Q8C2×D311yescharacteristic
278C2×C4×D4—31no—
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#446C2×D312yescomplemented
303#446C2×D314yescomplemented
304C8×Q8C2×D312yescomplemented
305#442—32no—
306#441—34no—
307#440—34no—
308#440—32no—
309C4×Q16—34no—
310C4×SD16—34no—
311C4×SD16—32no—
312C4×D8—32no—
313#428—32no—
314#428—31no—
315#423C2×D311yescharacteristic
316#423C2×D312yes—
317#419—32no—
318#419—32no—
319#419—32no—
320#418—32no—
321#418—31no—
322#417—31no—
323C4×M16C2×D311yescharacteristic
324C4×M16C2×D312yes—
325C23×D3—21no—
326C2×C3×Q8—42no—
327C2×C3×Q8C2×D411yescharacteristic
328C2×C3×Q8C2×D411yescharacteristic
329C2×C3×Q8C2×D412yes—
330C22×C3×C4C2×D411yescharacteristic
331C22×C3×C4C2×D412yes—
332C22×C3×C4C2×D412yes—
333C22×C3×C4C2×D411yescharacteristic
334C22×C3×C4C2411yescharacteristic
335C2×#67—21no—
336C22×Dic3—21no—
337C22×Dic3—22no—
338D3×Q8—44no—
339#235—22no—
340#235#4114yes—
341C2×D12—22no—
342C2×D12—22no—
343C2×D12—21no—
344C2×D12C2412yes—
345C2×D12C2411yescharacteristic
346C2×C4×D3—21no—
347C2×C4×D3—22no—
348C2×C4×D3—21no—
349C2×C4×D3—22no—
350C2×C4×D3—22no—
351C2×C4×D3—22no—
352C2×C4×D3—21no—
353C2×C4×D3—44no—
354C2×Dic6—24no—
355C2×Dic6—24no—
356C2×Dic6—22no—
357C2×Dic6—22no—
358C2×Dic6—21no—
359C2×Dic6—22no—
360C2×Dic6—21no—
361C2×Dic6C2414yes—
362C2×Dic6C2411yescharacteristic
363C3×M16—22no—
364C3×M16—24no—
365C3×M16—22no—
366C2×C3×C8C2412yes—
367C2×C3×C8C2412yes—
368C2×C3×C8C2414yes—
369C3×C4⋊C4C2×D411yescharacteristic
370C3×C4⋊C4C2×D412yes—
371C3×C4⋊C4C2×D411yescharacteristic
372C3×C4⋊C4C2×D412yes—
373C3×C4⋊C4C2×D412yes—
374C3×C4⋊C4C2×D412yes—
375C3×C4⋊C4C2×D412yes—
376C3×C42C2×D412yes—
377C3×C42C2×D412yes—
378C3×C42C2×D411yescharacteristic
379C3×C42C2×D411yescharacteristic
380C3×C42C2412yes—
381C3×C42C2411yescharacteristic
382C3×C42C2412yes—
383C3×C42C2411yescharacteristic
384#217—21no—
385#217—22no—
386(C2×D3)⋊C4—22no—
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4—22no—
389(C2×D3)⋊C4—21no—
390(C2×D3)⋊C4—22no—
391(C2×D3)⋊C4—22no—
392(C2×D3)⋊C4—24no—
393(C2×D3)⋊C4—24no—
394(C2×D3)⋊C4—24no—
395(C2×D3)⋊C4—24no—
396C4⋊Dic3—21no—
397C4⋊Dic3—22no—
398C4⋊Dic3—21no—
399C4⋊Dic3—22no—
400C4⋊Dic3—21no—
401C4⋊Dic3—22no—
402C4⋊Dic3—22no—
403C4⋊Dic3—22no—
404C4⋊Dic3—22no—
405C4⋊Dic3C2412yes—
406C4⋊Dic3C2411yescharacteristic
407C4⋊Dic3C2412yes—
408C4⋊Dic3C2411yescharacteristic
409C4⋊Dic3C2412yes—
410Dic3⋊C4—24no—
411Dic3⋊C4—24no—
412Dic3⋊C4—22no—
413Dic3⋊C4—22no—
414Dic3⋊C4—22no—
415Dic3⋊C4—22no—
416Dic3⋊C4—22no—
417Dic3⋊C4—22no—
418Dic3⋊C4—22no—
419Dic3⋊C4—21no—
420Dic3⋊C4—22no—
421Dic3⋊C4—21no—
422C4×Dic3—21no—
423C4×Dic3—22no—
424C4×Dic3—24no—
425C4×Dic3—24no—
426C4×Dic3—22no—
427C4×Dic3—21no—
428C4×Dic3—22no—
429C4×Dic3—21no—
430Dic12—28no—
431D24—24no—
432#204—28no—
433#204—24no—
434C2×#41—31no—
435C22×Q8—32no—
436C22×Q8—61no—
437C22×Q8D1211yescharacteristic
438C22×D4—31no—
439C23×C4—61no—
440#137—68no—
441AGL(1,ℤ/8)—64no—
442C2×Q16—34no—
443C2×SD16—32no—
444C2×SD16—34no—
445C2×D8—32no—
446C2×M16C22×D311yescharacteristic
447C2×M16C22×D312yes—
448C2×M16C22×D311yescharacteristic
449C4⋊Q8—31no—
450C4⋊Q8—32no—
451C4⋊Q8—32no—
452C4⋊Q8—31no—
453C4⋊Q8—32no—
454C4⋊Q8—32no—
455C4⋊Q8—61no—
456C4⋊Q8—62no—
457C4⋊Q8—61no—
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—64no—
478C22⋊Q8—61no—
479C22⋊Q8—62no—
480C22⋊Q8—61no—
481C22⋊Q8—62no—
482C22⋊Q8—62no—
483C22⋊Q8—61no—
484C22⋊Q8—61no—
485C22⋊Q8—62no—
486C22⋊Q8—62no—
487C22⋊Q8—62no—
488C22⋊Q8—62no—
489C4×Q8—34no—
490C4×Q8—34no—
491C4×Q8—32no—
492C4×Q8—31no—
493C4×Q8—31no—
494C4×Q8—32no—
495C4×Q8—61no—
496C4×Q8—61no—
497C4×Q8—62no—
498C4×Q8—62no—
499C4×Q8—62no—
500C4×Q8—61no—
501C4×Q8—62no—
502C4×Q8—61no—
503C4×Q8—62no—
504C4×Q8D1211yescharacteristic
505C4×Q8D1211yescharacteristic
506C4×Q8D1212yes—
507C4×Q8C22×D311yescharacteristic
508C4×Q8C22×D311yescharacteristic
509C4×Q8C22×D312yes—
510C4×D4—32no—
511C4×D4—32no—
512C4×D4—31no—
513C4×D4—32no—
514C4×D4—32no—
515C4×D4—31no—
516C4×D4—61no—
517C4×D4—62no—
518C4×D4—62no—
519C4×D4—61no—
520C4×D4—61no—
521C4×D4—61no—
522#117—31no—
523#117—32no—
524#117—62no—
525#117—64no—
526#117—62no—
527#117—61no—
528#117—62no—
529C2×C4⋊C4—31no—
530C2×C4⋊C4—61no—
531C2×C4⋊C4—62no—
532C2×C4⋊C4—61no—
533C2×C4⋊C4—61no—
534C2×C4⋊C4—62no—
535C2×C4⋊C4D1211yescharacteristic
536C2×C4⋊C4D1212yes—
537C2×C22⋊C4—62no—
538C2×C22⋊C4—61no—
539C2×C22⋊C4—62no—
540C2×C42—62no—
541C2×C42—61no—
542C2×C42—62no—
543C2×C42C22×D311yescharacteristic
544C2×C42C22×D312yes—
545#107—32no—
546#107—34no—
547#106—34no—
548#106—32no—
549C4⋊C8C22×D312yes—
550C4⋊C8C22×D314yes—
551C4⋊C8C22×D312yes—
552C4⋊C8C22×D314yes—
553#103—32no—
554#103—34no—
555#103—34no—
556#103—34no—
557#103—34no—
558#103—34no—
559#103—34no—
560#102—32no—
561#102—32no—
562#102—32no—
563#102—34no—
564#102—34no—
565#97C22×D314yes—
566#97C22×D312yes—
567C4×C8C22×D312yes—
568C4×C8C22×D314yes—
569C23×C3C22×D411yescharacteristic
570C22×D3—21no—
571C22×D3—22no—
572C22×D3—42no—
573C22×D3—42no—
574C22×D3—42no—
575C3×Q8—22no—
576C3×Q8—22no—
577C3×Q8—42no—
578C2×C3×C4—22no—
579C2×C3×C4—42no—
580C2×C3×C4—41no—
581C2×C3×C4—42no—
582C2×C3×C4C22×D412yes—
583C2×C3×C4C22×D412yes—
584C2×C3×C4C22×D411yescharacteristic
585C2×C3×C4C22×D412yes—
586C2×C3×C4C22×D412yes—
587C2×C3×C4C22×D411yescharacteristic
588C2×C3×C4C22×D411yescharacteristic
589C2×C3×C4C22×D411yescharacteristic
590C2×C3×C4C22×D411yescharacteristic
591C2×C3×C4C2×#4112yes—
592C2×C3×C42−1+412yes—
593C2×C3×C4C2511yescharacteristic
594#67—24no—
595C2×Dic3—21no—
596C2×Dic3—22no—
597C2×Dic3—22no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—22no—
601C2×Dic3—24no—
602C2×Dic3—42no—
603C2×Dic3—44no—
604D12—22no—
605D12—21no—
606D12—22no—
607D12—42no—
608D12C2×#4112yes—
609C4×D3—24no—
610C4×D3—44no—
611C4×D3—44no—
612C4×D3—44no—
613C4×D3—42no—
614C4×D3—82no—
615C4×D3—81no—
616Dic6—21no—
617Dic6—24no—
618Dic6—24no—
619Dic6—44no—
620Dic6—44no—
621Dic6—42no—
622Dic6—82no—
623Dic6—81no—
624Dic6C2×#4112yes—
625C3×C8—22no—
626C3×C8—24no—
627C3×C8—22no—
628C24—61no—
629#41—34no—
630#41—62no—
631C2×Q8—31no—
632C2×Q8—34no—
633C2×Q8—42no—
634C2×Q8—62no—
635C2×Q8—61no—
636C2×Q8—62no—
637C2×Q8—62no—
638C2×Q8—61no—
639C2×Q8—64no—
640C2×Q8—64no—
641C2×Q8—124no—
642C2×Q8C2×D1211yescharacteristic
643C2×Q8C2×D1211yescharacteristic
644C2×Q8C2×D1212yes—
645C2×D4—31no—
646C2×D4—32no—
647C2×D4—61no—
648C2×D4—61no—
649C2×D4—62no—
650C2×D4—62no—
651C22×C4—61no—
652C22×C4—61no—
653C22×C4—62no—
654C22×C4—62no—
655C22×C4—61no—
656C22×C4—62no—
657C22×C4—62no—
658C22×C4—62no—
659C22×C4—61no—
660C22×C4—124no—
661C22×C4C2×D1211yescharacteristic
662C22×C4C2×D1212yes—
663C22×C4C2×D1211yescharacteristic
664C22×C4C2×D1212yes—
665C22×C4C23×D311yescharacteristic
666Q16—68no—
667SD16—68no—
668SD16—64no—
669D8—64no—
670M16—22no—
671M16—22no—
672M16—24no—
673C2×C8C23×D312yes—
674C2×C8C23×D314yes—
675C2×C8C23×D312yes—
676C4⋊C4—31no—
677C4⋊C4—32no—
678C4⋊C4—31no—
679C4⋊C4—32no—
680C4⋊C4—32no—
681C4⋊C4—61no—
682C4⋊C4—62no—
683C4⋊C4—62no—
684C4⋊C4—64no—
685C4⋊C4—64no—
686C4⋊C4—62no—
687C4⋊C4—62no—
688C4⋊C4—62no—
689C4⋊C4—62no—
690C4⋊C4—61no—
691C4⋊C4—62no—
692C4⋊C4—62no—
693C4⋊C4—62no—
694C4⋊C4—62no—
695C4⋊C4—61no—
696C4⋊C4—61no—
697C4⋊C4—62no—
698C4⋊C4—62no—
699C4⋊C4—62no—
700C4⋊C4—62no—
701C4⋊C4—61no—
702C4⋊C4C2×D1211yescharacteristic
703C4⋊C4C2×D1212yes—
704C4⋊C4C2×D1212yes—
705C4⋊C4C2×D1211yescharacteristic
706C4⋊C4C2×D1212yes—
707C4⋊C4C2×D1212yes—
708C4⋊C4C2×D1212yes—
709C22⋊C4—61no—
710C22⋊C4—62no—
711C22⋊C4—64no—
712C22⋊C4—64no—
713C22⋊C4—62no—
714C22⋊C4—62no—
715C22⋊C4—64no—
716C22⋊C4—64no—
717C22⋊C4—62no—
718C22⋊C4—62no—
719C22⋊C4—61no—
720C22⋊C4—61no—
721C42—61no—
722C42—62no—
723C42—64no—
724C42—64no—
725C42—62no—
726C42—61no—
727C42—62no—
728C42—61no—
729C42C2×D1211yescharacteristic
730C42C2×D1212yes—
731C42C2×D1211yescharacteristic
732C42C2×D1212yes—
733C42C23×D311yescharacteristic
734C42C23×D312yes—
735C42C23×D311yescharacteristic
736C42C23×D312yes—
737C22×C3—21no—
738C22×C3—21no—
739C22×C3#54812yes—
740C22×C3C23×D411yescharacteristic
741C2×D3—22no—
742C2×D3—41no—
743C2×D3—41no—
744C2×D3—42no—
745C2×D3—42no—
746C2×D3—42no—
747C2×D3—84no—
748C3×C4—22no—
749C3×C4—21no—
750C3×C4—22no—
751C3×C4—21no—
752C3×C4—22no—
753C3×C4—21no—
754C3×C4—22no—
755C3×C4#54812yes—
756C3×C4#57512yes—
757C3×C4C22×#4111yescharacteristic
758C3×C4C2×2−1+411yescharacteristic
759Dic3—22no—
760Dic3—41no—
761Dic3—42no—
762Dic3—44no—
763Dic3—41no—
764Dic3—42no—
765Dic3—42no—
766C23—61no—
767C23—62no—
768C23—122no—
769C23—122no—
770C23—122no—
771C23C22×D1211yescharacteristic
772Q8—22no—
773Q8—22no—
774Q8—32no—
775Q8—42no—
776Q8—61no—
777Q8—64no—
778Q8—64no—
779Q8—124no—
780Q8—122no—
781Q8—124no—
782Q8—242no—
783Q8—241no—
784D4—32no—
785D4—64no—
786D4—61no—
787D4—62no—
788D4—62no—
789D4—122no—
790C2×C4—22no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—61no—
795C2×C4—64no—
796C2×C4—62no—
797C2×C4—64no—
798C2×C4—62no—
799C2×C4—61no—
800C2×C4—62no—
801C2×C4—61no—
802C2×C4—124no—
803C2×C4—124no—
804C2×C4—122no—
805C2×C4—124no—
806C2×C4—124no—
807C2×C4—122no—
808C2×C4—242no—
809C2×C4—241no—
810C2×C4C22×D1212yes—
811C2×C4C22×D1212yes—
812C2×C4C22×D1211yescharacteristic
813C2×C4C22×D1212yes—
814C2×C4C22×D1212yes—
815C2×C4C22×D1211yescharacteristic
816C2×C4C22×D1211yescharacteristic
817C2×C4C22×D1211yescharacteristic
818C2×C4C22×D1211yescharacteristic
819C2×C4#100712yes—
820C2×C4D3×#4112yes—
821C2×C4C24×D311yescharacteristic
822C8—22no—
823C8—22no—
824C8—24no—
825C2×C3—22no—
826C2×C3C2×#54811yescharacteristic
827C2×C3C2×#57511yescharacteristic
828C2×C3#358611yescharacteristic
829D3—42no—
830D3—82no—
831C22—21no—
832C22—21no—
833C22—62no—
834C22—121no—
835C22—121no—
836C22—122no—
837C22—122no—
838C22—122no—
839C22—244no—
840C22#557612yes—
841C22C23×D1211yescharacteristic
842C4—21no—
843C4—22no—
844C4—22no—
845C4—22no—
846C4—21no—
847C4—22no—
848C4—21no—
849C4—62no—
850C4—124no—
851C4—122no—
852C4—122no—
853C4—121no—
854C4—122no—
855C4—121no—
856C4#557612yes—
857C4#574812yes—
858C4C2×#100711yescharacteristic
859C4C2×D3×#4111yescharacteristic
860C3#6132311yescharacteristic, complemented, Sylow
861C2—22no—
862C2—122no—
863C2—242no—
864C2C2×#557611yescharacteristic
865C2C2×#574811yescharacteristic
866C2#8716811yescharacteristic
subgroupG/H
centerC22C23×D12
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×Q8×M16C2
socleC22×C3C23×D4
prime radicalC2×#908C22
hypercenterQ8×M16D3
hypocenterC3#61323
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
1. Q8×#235C2semidirect
2. C2×#5584C2semidirect
3. C3×Q8×M16C2semidirect
4. #79985C2semidirect
5. #79981C2semidirect
6. #79974C2semidirect
7. #79970C2semidirect
8. #79934C2semidirect
9. #79926C2semidirect
10. #79068C2semidirect
11. #79059C2semidirect
13. #79057C2semidirect
14. #78537C2semidirect
15. C4×#909C2semidirect
16. #78527C2semidirect
30. #5579C22semidirect
31. #5579C22semidirect
34. Q8×D12C22semidirect
36. #5567C22semidirect
37. #5567C22semidirect
38. Q8×Dic6C22semidirect
51. C3×#446C22semidirect
52. C3×#446C22semidirect
53. C3×C8×Q8C22semidirect
66. #4851C22semidirect
67. #4850C22semidirect
68. #4849C22semidirect
69. #4849C22semidirect
77. #4841C22semidirect
78. #4841C22semidirect
79. #4829C22semidirect
80. #4829C22semidirect
81. #4716C22semidirect
86. #4710C22semidirect
87. #4703C22semidirect
88. C4×Dic12C22semidirect
93. C4×#204C22semidirect
94. #4681C22semidirect
95. #4681C22semidirect
110. Q8×M16D3semidirect
302. #446C2×D3semidirect
303. #446C2×D3semidirect
304. C8×Q8C2×D3semidirect
860. C3#61323semidirect

Maximal subgroups

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

subgroupindex
Q8×#2352
C2×#55842
C3×Q8×M162
#799852
#799812
#799742
#799702
#799342
#799262
#790682
#790592
#790582
#790572
#785372
C4×#9092
#785272
C4×#9082
#613233