Finite Group Databasebeta

← #10943987

Subgroups — #10943987

Order 768.

1576 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D3×Q8C211yesmaximal, characteristic, complemented
2C2×#5170C211yesmaximal, characteristic, complemented
3C2×#5163C211yesmaximal, characteristic, complemented
4C2×#4806C211yesmaximal, characteristic, complemented
5C2×#4762C211yesmaximal, characteristic, complemented
6#76476C211yesmaximal, characteristic
7C3×#1880C211yesmaximal, characteristic, complemented
8#71633C211yesmaximal, characteristic, complemented
9#70221C211yesmaximal, characteristic, complemented
10#70200C211yesmaximal, characteristic, complemented
11#69660C211yesmaximal, characteristic, complemented
12#68904C211yesmaximal, characteristic, complemented
13#68880C211yesmaximal, characteristic, complemented
14#68686C211yesmaximal, characteristic, complemented
15#68662C211yesmaximal, characteristic, complemented
16#32903—31nomaximal, Sylow
17C22×D3×Q8C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C2×C3×C4×Q8C2211yescharacteristic
20C2×Q8×Dic3C2211yescharacteristic
21C22×#215C2211yescharacteristic
22C2×#940C2211yescharacteristic
23C2×#938C2211yescharacteristic
24C22×#214C2211yescharacteristic
25C22×#204C2211yescharacteristic
26C4×D3×Q8—24no—
27C4×D3×Q8—24no—
28C2×#895C2211yescharacteristic
29C2×D3×C4⋊C4—21no—
30C2×D3×C4⋊C4C2211yescharacteristic
31C2×#887—21no—
32C2×#887C2211yescharacteristic
33C2×#884—21no—
34C2×#884—21no—
35C2×C42×D3—21no—
36C2×C42×D3C2211yescharacteristic
37C2×C4×Dic6—21no—
38C2×C4×Dic6C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×#102C2211yescharacteristic
41C3×#390C2211yescharacteristic
42C2×#835C2211yescharacteristic
43C2×#832C2211yescharacteristic
44#5170—24no—
45#5163—24no—
46C2×#821C2211yescharacteristic
47C2×(C2×D3)⋊C8C2211yescharacteristic
48C2×(C2×D3)⋊C8C2211yescharacteristic
49C2×#816C2211yescharacteristic
50C2×Dic3⋊C8C2211yescharacteristic
51C2×Dic3⋊C8C2211yescharacteristic
52#4975C2211yescharacteristic
53C2×#810C2211yescharacteristic
54C2×#809C2211yescharacteristic
55#4957—21no—
56#4957—21no—
57#4939C2211yescharacteristic
58#4806—24no—
59#4762—24no—
60C3×#340C2211yescharacteristic
61C3×#336C2211yescharacteristic
62#4551C2211yescharacteristic
63#4529C2211yescharacteristic
64#4529C2211yescharacteristic
65#4524C2211yescharacteristic
66C22×C4×Q8—31no—
67C2×#460—31no—
68C2×#460—31no—
69C2×#448—31no—
70C2×#448—31no—
71#2856—31no—
72#1880—31no—
73#1880—31no—
74#1880—31no—
75#1880D311yescharacteristic, complemented
76#1874—31no—
77#1874—31no—
78#1803—31no—
79#1803—31no—
80#1797—31no—
81C22×C3×Q8C2311yescharacteristic
82C22×C3×D4C2311yescharacteristic
83C22×#67—21no—
84C22×#67—21no—
85C22×#67—21no—
86C2×D3×Q8—22no—
87C2×D3×Q8—22no—
88C2×D3×Q8—22no—
89C2×D3×Q8—22no—
90C2×D3×Q8—22no—
91C2×D3×Q8D414yescomplemented
92C22×D12—21no—
93C22×D12C2311yescharacteristic
94C22×C4×D3—21no—
95C22×C4×D3—21no—
96C22×C4×D3D411yescharacteristic
97C22×C4×D3D411yescharacteristic
98C22×C4×D3C2311yescharacteristic
99C22×Dic6—21no—
100C22×Dic6C2311yescharacteristic
101C2×C3×SD16—22no—
102C2×C3×SD16—22no—
103C2×C3×SD16—22no—
104C22×C3×C8C2311yescharacteristic
105C22×C3×C8C2311yescharacteristic
106C3×C4×Q8—22no—
107C3×C4×Q8—22no—
108C2×C3×C4⋊C4—21no—
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C22⋊C4—21no—
112C2×C3×C22⋊C4—21no—
113C2×C3×C42—21no—
114C2×C3×C42C2311yescharacteristic
115C2×#217—21no—
116Q8×Dic3—22no—
117Q8×Dic3D414yescomplemented
118C2×#215—22no—
119C2×#215—22no—
120C2×#215—22no—
121#940—22no—
122#940—22no—
123#938—22no—
124#938—22no—
125C2×#214—22no—
126C2×#214—22no—
127C2×#214—22no—
128C2×(C2×D3)⋊C4—21no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4—21no—
131C2×C4⋊Dic3—21no—
132C2×C4⋊Dic3C2311yescharacteristic
133C2×C4⋊Dic3C2311yescharacteristic
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—21no—
136C2×Dic3⋊C4—21no—
137C2×Dic3⋊C4—21no—
138C2×Dic3⋊C4—21no—
139C2×C4×Dic3—21no—
140C2×C4×Dic3—21no—
141C2×C4×Dic3—21no—
142C2×C4×Dic3D411yescharacteristic
143C2×C4×Dic3D411yescharacteristic
144C2×C4×Dic3C2311yescharacteristic
145C22×C3⋊C8C2311yescharacteristic
146C22×C3⋊C8C2311yescharacteristic
147C2×#204—22no—
148C2×#204—22no—
149C2×#204—22no—
150#895—22no—
151#895—22no—
152D3×C4⋊C4—28no—
153D3×C4⋊C4—22no—
154D3×C4⋊C4—22no—
155#887—28no—
156#887—22no—
157#887D414yescomplemented
158#884—44no—
159#884—44no—
160C42×D3—28no—
161C42×D3—22no—
162C42×D3—22no—
163C4×Dic6—28no—
164C4×Dic6—22no—
165C4×Dic6—22no—
166C3×#103—22no—
167C3×#102—22no—
168#835—22no—
169#832—22no—
170#821—22no—
171(C2×D3)⋊C8—22no—
172(C2×D3)⋊C8—22no—
173#816—22no—
174Dic3⋊C8—22no—
175Dic3⋊C8—22no—
176#810—22no—
177#809—22no—
178C23×Q8—31no—
179C22×SD16—31no—
180C22×SD16—31no—
181C22×SD16—31no—
182C22×SD16C2×D311yescharacteristic
183C2×#127—31no—
184C2×#121—31no—
185C2×#121—31no—
186C2×#121—61no—
187C2×#121—61no—
188C2×C4×Q8—31no—
189C2×C4×Q8—31no—
190C2×C4×Q8—31no—
191C2×C4×Q8—61no—
192C2×C4×Q8—61no—
193C2×C4×Q8—64no—
194C2×C4×Q8—64no—
195C2×C4×Q8C2×D311yescharacteristic
196C22×C4⋊C4—31no—
197C22×C4⋊C4—61no—
198C22×C42—31no—
199C22×C42—61no—
200#460—64no—
201#460—64no—
202#448—64no—
203#448—64no—
204C2×C4⋊C8—31no—
205C2×C4⋊C8—31no—
206C2×#103—31no—
207C2×#103—31no—
208C2×#103—31no—
209C2×#103C2×D311yescharacteristic
210C2×#102—31no—
211C2×#102—31no—
212C2×#102—31no—
213C2×#102C2×D311yescharacteristic
214C2×C22⋊C8—31no—
215C2×C22⋊C8—31no—
216#390—31no—
217#390—61no—
218#390—61no—
219#390C2×D311yescharacteristic
220#384—31no—
221#340—31no—
222#340—31no—
223#340—31no—
224#340C2×D311yescharacteristic
225#336—31no—
226#336C2×D311yescharacteristic
227C24×C3—21no—
228C23×D3—21no—
229C23×D3C2×D411yescharacteristic
230C2×C3×Q8—21no—
231C2×C3×Q8—21no—
232C2×C3×Q8—21no—
233C2×C3×Q8C2×D412yes—
234C2×C3×Q8C2×D412yes—
235C2×C3×Q8#4112yes—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4C2×D411yescharacteristic
246C22×C3×C4C2×D411yescharacteristic
247C22×C3×C4C2411yescharacteristic
248C2×#67—42no—
249C2×#67—42no—
250C2×#67—42no—
251C2×#67—42no—
252C2×#67—42no—
253C2×#67—42no—
254C2×#67—42no—
255C2×#67—42no—
256C2×#67—42no—
257C22×Dic3—21no—
258C22×Dic3—21no—
259C22×Dic3—21no—
260C22×Dic3C2×D411yescharacteristic
261C22×Dic3C2×D411yescharacteristic
262C22×Dic3C2×D411yescharacteristic
263D3×Q8—28no—
264D3×Q8—28no—
265D3×Q8—28no—
266D3×Q8—28no—
267C2×D12—21no—
268C2×D12—21no—
269C2×D12—21no—
270C2×D12—21no—
271C2×D12—21no—
272C2×D12—21no—
273C2×D12—42no—
274C2×D12—42no—
275C2×D12—42no—
276C2×C4×D3—24no—
277C2×C4×D3—24no—
278C2×C4×D3—24no—
279C2×C4×D3—21no—
280C2×C4×D3—21no—
281C2×C4×D3—21no—
282C2×C4×D3—21no—
283C2×C4×D3—22no—
284C2×C4×D3—22no—
285C2×C4×D3—24no—
286C2×C4×D3—22no—
287C2×C4×D3—22no—
288C2×C4×D3—41no—
289C2×C4×D3—42no—
290C2×C4×D3—42no—
291C2×C4×D3SD1614yescomplemented
292C2×C4×D3C2×D412yes—
293C2×C4×D3#4112yes—
294C2×Dic6—24no—
295C2×Dic6—24no—
296C2×Dic6—21no—
297C2×Dic6—21no—
298C2×Dic6—21no—
299C2×Dic6—24no—
300C2×Dic6C2×D412yes—
301C2×Dic6C2×D412yes—
302C2×Dic6#4112yes—
303C3×SD16—44no—
304C2×C3×C8—21no—
305C2×C3×C8—21no—
306C2×C3×C8—21no—
307C2×C3×C8—21no—
308C2×C3×C8—21no—
309C2×C3×C8—21no—
310C3×C4⋊C4—24no—
311C3×C4⋊C4—21no—
312C3×C4⋊C4—21no—
313C3×C4⋊C4—21no—
314C3×C4⋊C4C2×D412yes—
315C3×C22⋊C4—42no—
316C3×C22⋊C4—42no—
317C3×C42—24no—
318C3×C42—21no—
319C3×C42—21no—
320#217—42no—
321#215—44no—
322#214—44no—
323(C2×D3)⋊C4—42no—
324(C2×D3)⋊C4—42no—
325(C2×D3)⋊C4—42no—
326C4⋊Dic3—21no—
327C4⋊Dic3—24no—
328C4⋊Dic3—21no—
329C4⋊Dic3—21no—
330C4⋊Dic3C2×D412yes—
331Dic3⋊C4—24no—
332Dic3⋊C4—24no—
333Dic3⋊C4—24no—
334Dic3⋊C4—42no—
335Dic3⋊C4—42no—
336C4×Dic3—24no—
337C4×Dic3—22no—
338C4×Dic3—22no—
339C4×Dic3—24no—
340C4×Dic3—24no—
341C4×Dic3C2×D412yes—
342C4×Dic3C2×D412yes—
343C2×C3⋊C8—21no—
344C2×C3⋊C8—21no—
345C2×C3⋊C8—21no—
346C2×C3⋊C8—21no—
347C2×C3⋊C8—21no—
348C2×C3⋊C8—21no—
349#204—44no—
350C22×Q8—34no—
351C22×Q8—31no—
352C22×Q8—61no—
353C22×Q8—62no—
354C22×Q8—62no—
355C22×Q8—62no—
356C22×Q8—62no—
357C22×Q8—62no—
358C22×Q8C22×D311yescharacteristic
359C22×D4—31no—
360C22×D4—61no—
361C22×D4—61no—
362C22×D4—61no—
363C22×D4—61no—
364C22×D4C22×D311yescharacteristic
365C23×C4—31no—
366C23×C4—31no—
367C23×C4—31no—
368C23×C4—61no—
369C23×C4—61no—
370C2×SD16—22no—
371C2×SD16—22no—
372C2×SD16—22no—
373C2×SD16—62no—
374C2×SD16—62no—
375C2×SD16—62no—
376C2×SD16—62no—
377C2×SD16—62no—
378C2×SD16—62no—
379C2×SD16—62no—
380C2×SD16—62no—
381C2×SD16—62no—
382C22×C8—31no—
383C22×C8—31no—
384C22×C8C22×D311yescharacteristic
385C22×C8C22×D311yescharacteristic
386#127—62no—
387#127—62no—
388#121—62no—
389#121—62no—
390#121—62no—
391#121—62no—
392#121—124no—
393#121—124no—
394C4×Q8—22no—
395C4×Q8—22no—
396C4×Q8—34no—
397C4×Q8—34no—
398C4×Q8—62no—
399C4×Q8—62no—
400C4×Q8—68no—
401C4×Q8—62no—
402C4×Q8—62no—
403C4×Q8—68no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—31no—
406C2×C4⋊C4—31no—
407C2×C4⋊C4—62no—
408C2×C4⋊C4—68no—
409C2×C4⋊C4—61no—
410C2×C4⋊C4—61no—
411C2×C4⋊C4—61no—
412C2×C4⋊C4—61no—
413C2×C4⋊C4—62no—
414C2×C4⋊C4—61no—
415C2×C4⋊C4—61no—
416C2×C4⋊C4C22×D311yescharacteristic
417C2×C4⋊C4C22×D311yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—61no—
421C2×C22⋊C4—61no—
422C2×C22⋊C4—61no—
423C2×C22⋊C4—61no—
424C2×C42—21no—
425C2×C42—31no—
426C2×C42—31no—
427C2×C42—31no—
428C2×C42—62no—
429C2×C42—62no—
430C2×C42—68no—
431C2×C42—61no—
432C2×C42—61no—
433C2×C42—61no—
434C2×C42C22×D311yescharacteristic
435C4⋊C8—62no—
436C4⋊C8—62no—
437#103—22no—
438#103—62no—
439#103—62no—
440#103—62no—
441#102—22no—
442#102—62no—
443#102—62no—
444#102—62no—
445C22⋊C8—62no—
446C22⋊C8—62no—
447C23×C3—41no—
448C23×C3—41no—
449C23×C3—41no—
450C23×C3—41no—
451C23×C3—41no—
452C23×C3—41no—
453C23×C3—41no—
454C23×C3C22×D411yescharacteristic
455C22×D3—21no—
456C22×D3—21no—
457C22×D3—21no—
458C22×D3—21no—
459C22×D3—41no—
460C22×D3—41no—
461C22×D3—41no—
462C22×D3—41no—
463C22×D3—41no—
464C22×D3—41no—
465C22×D3—41no—
466C22×D3#12112yes—
467C22×D3C2×SD1612yes—
468C22×D3AGL(1,ℤ/8)12yes—
469C3×Q8—22no—
470C3×Q8—22no—
471C3×Q8—22no—
472C3×Q8#12114yescomplemented
473C3×D4—41no—
474C3×D4—41no—
475C3×D4—41no—
476C3×D4—41no—
477C2×C3×C4—21no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—22no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4C2×SD1612yes—
492C2×C3×C4C22×D411yescharacteristic
493C2×C3×C4C22×D411yescharacteristic
494C2×C3×C4C22×D411yescharacteristic
495C2×C3×C4C2×#4111yescharacteristic
496C2×C3×C4C2×#4111yescharacteristic
497C2×C3×C4C2×#4111yescharacteristic
498#67—84no—
499#67—84no—
500#67—84no—
501C2×Dic3—21no—
502C2×Dic3—22no—
503C2×Dic3—22no—
504C2×Dic3—21no—
505C2×Dic3—22no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—22no—
509C2×Dic3—41no—
510C2×Dic3—41no—
511C2×Dic3—41no—
512C2×Dic3—41no—
513C2×Dic3—41no—
514C2×Dic3#12012yes—
515C2×Dic3#12012yes—
516C2×Dic3#12112yes—
517C2×Dic3C2×SD1612yes—
518C2×Dic3#13712yes—
519D12—41no—
520D12—41no—
521D12—41no—
522D12—41no—
523D12—84no—
524C4×D3—216no—
525C4×D3—22no—
526C4×D3—22no—
527C4×D3—22no—
528C4×D3—22no—
529C4×D3—28no—
530C4×D3—44no—
531C4×D3—48no—
532Dic6—216no—
533Dic6—22no—
534Dic6—22no—
535Dic6—22no—
536Dic6#12114yescomplemented
537C3×C8—41no—
538C3×C8—41no—
539C3⋊C8—41no—
540C3⋊C8—41no—
541C24—21no—
542C24—31no—
543C24—61no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—32no—
548C2×Q8—32no—
549C2×Q8—32no—
550C2×Q8—64no—
551C2×Q8—64no—
552C2×Q8—64no—
553C2×Q8—68no—
554C2×Q8—68no—
555C2×Q8—68no—
556C2×Q8—68no—
557C2×Q8—61no—
558C2×Q8—61no—
559C2×Q8—61no—
560C2×Q8#23512yes—
561C2×Q8D3×D412yes—
562C2×Q8D3×D412yes—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—61no—
570C2×D4—61no—
571C2×D4—61no—
572C2×D4—61no—
573C2×D4—61no—
574C2×D4—61no—
575C2×D4—122no—
576C2×D4—122no—
577C2×D4—122no—
578C2×D4—122no—
579C2×D4—122no—
580C2×D4—122no—
581C2×D4—122no—
582C2×D4—122no—
583C2×D4—122no—
584C2×D4—122no—
585C2×D4—122no—
586C2×D4—122no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—31no—
591C22×C4—31no—
592C22×C4—31no—
593C22×C4—34no—
594C22×C4—32no—
595C22×C4—32no—
596C22×C4—62no—
597C22×C4—62no—
598C22×C4—62no—
599C22×C4—64no—
600C22×C4—64no—
601C22×C4—64no—
602C22×C4—62no—
603C22×C4—64no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—121no—
612C22×C4—122no—
613C22×C4—122no—
614C22×C4D3×D411yescharacteristic
615C22×C4D3×D411yescharacteristic
616C22×C4C23×D311yescharacteristic
617SD16—44no—
618SD16—124no—
619SD16—124no—
620SD16—124no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—61no—
628C2×C8—61no—
629C2×C8—61no—
630C2×C8—61no—
631C2×C8—61no—
632C2×C8—61no—
633C4⋊C4—24no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—32no—
638C4⋊C4—64no—
639C4⋊C4—64no—
640C4⋊C4—64no—
641C4⋊C4—64no—
642C4⋊C4—61no—
643C4⋊C4—61no—
644C4⋊C4—61no—
645C4⋊C4—122no—
646C4⋊C4—122no—
647C4⋊C4D3×D412yes—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—122no—
651C22⋊C4—122no—
652C22⋊C4—122no—
653C22⋊C4—122no—
654C42—24no—
655C42—21no—
656C42—21no—
657C42—32no—
658C42—32no—
659C42—62no—
660C42—62no—
661C42—64no—
662C42—64no—
663C42—64no—
664C22×C3—81no—
665C22×C3—81no—
666C22×C3—81no—
667C22×C3—81no—
668C22×C3—81no—
669C22×C3—81no—
670C22×C3—81no—
671C22×C3C2×#12011yescharacteristic
672C22×C3C2×#12111yescharacteristic
673C22×C3#52511yescharacteristic
674C22×C3C22×SD1611yescharacteristic
675C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
676C22×C3C2×#13711yescharacteristic
677C22×C3#57511yescharacteristic
678C2×D3—22no—
679C2×D3—22no—
680C2×D3—22no—
681C2×D3—22no—
682C2×D3—22no—
683C2×D3—22no—
684C2×D3—81no—
685C2×D3—81no—
686C2×D3—81no—
687C2×D3—81no—
688C2×D3—81no—
689C2×D3—81no—
690C2×D3—81no—
691C2×D3#46014yescomplemented
692C3×C4—24no—
693C3×C4—22no—
694C3×C4—41no—
695C3×C4—42no—
696C3×C4—81no—
697C3×C4C2×#12111yescharacteristic
698C3×C4C2×#12111yescharacteristic
699C3×C4#52511yescharacteristic
700C3×C4#52511yescharacteristic
701Dic3—22no—
702Dic3—24no—
703Dic3—22no—
704Dic3—42no—
705Dic3—81no—
706Dic3#44814yescomplemented
707C23—32no—
708C23—32no—
709C23—32no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—61no—
718C23—61no—
719C23—61no—
720C23—61no—
721C23—121no—
722C23—121no—
723C23—121no—
724C23—121no—
725C23—121no—
726C23—121no—
727C23—121no—
728C23C2×D3×D411yescharacteristic
729Q8—22no—
730Q8—22no—
731Q8—22no—
732Q8—34no—
733Q8—616no—
734Q8—62no—
735Q8—62no—
736Q8—62no—
737Q8#88414yescomplemented
738D4—41no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—121no—
743D4—121no—
744D4—121no—
745D4—121no—
746D4—244no—
747D4—244no—
748D4—244no—
749D4—244no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—32no—
760C2×C4—32no—
761C2×C4—32no—
762C2×C4—32no—
763C2×C4—32no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—68no—
770C2×C4—616no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—62no—
775C2×C4—61no—
776C2×C4—62no—
777C2×C4—62no—
778C2×C4—62no—
779C2×C4—62no—
780C2×C4—62no—
781C2×C4—62no—
782C2×C4—62no—
783C2×C4—124no—
784C2×C4—128no—
785C2×C4—121no—
786C2×C4—121no—
787C2×C4—121no—
788C2×C4—121no—
789C2×C4—121no—
790C2×C4D3×SD1612yes—
791C2×C4C2×#23511yescharacteristic
792C2×C4C2×D3×D411yescharacteristic
793C2×C4C2×D3×D411yescharacteristic
794C2×C4C2×D3×D411yescharacteristic
795C2×C4D3×#4111yescharacteristic
796C2×C4D3×#4111yescharacteristic
797C8—41no—
798C8—41no—
799C8—121no—
800C8—121no—
801C2×C3—161no—
802C2×C3#284711yescharacteristic
803C2×C3C2×#44811yescharacteristic
804C2×C3#300611yescharacteristic
805C2×C3C2×#46011yescharacteristic
806C2×C3#303711yescharacteristic
807C2×C3#310311yescharacteristic
808C2×C3#311211yescharacteristic
809D3—24no—
810D3—161no—
811C22—34no—
812C22—62no—
813C22—62no—
814C22—62no—
815C22—62no—
816C22—62no—
817C22—62no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22—241no—
826C22—241no—
827C22—241no—
828C22—241no—
829C22—241no—
830C22—241no—
831C22—241no—
832C22#554711yescharacteristic
833C22D3×#12011yescharacteristic
834C22D3×#12111yescharacteristic
835C22C2×D3×SD1611yescharacteristic
836C22#576811yescharacteristic
837C22D3×AGL(1,ℤ/8)11yescharacteristic
838C22D3×#13711yescharacteristic
839C4—22no—
840C4—24no—
841C4—34no—
842C4—41no—
843C4—42no—
844C4—62no—
845C4—64no—
846C4—62no—
847C4—81no—
848C4—122no—
849C4—241no—
850C4C2×#88411yescharacteristic
851C4#554711yescharacteristic
852C4D3×#12111yescharacteristic
853C4#565611yescharacteristic
854C3#3290311yescharacteristic, complemented, Sylow
855C2—64no—
856C2—161no—
857C2—481no—
858C2#7493511yescharacteristic
859C2#7965311yescharacteristic
860C2#7978111yescharacteristic
861C2D3×#44811yescharacteristic
862C2#8008411yescharacteristic
863C2D3×#46011yescharacteristic
864C2#8059811yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1880C2
socleC23×C3C22×D4
prime radical#76476C2
hypercenter#1880D3
hypocenterC3#32903
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
1. C2×C4×D3×Q8C2semidirect
2. C2×#5170C2semidirect
3. C2×#5163C2semidirect
4. C2×#4806C2semidirect
5. C2×#4762C2semidirect
7. C3×#1880C2semidirect
8. #71633C2semidirect
9. #70221C2semidirect
10. #70200C2semidirect
11. #69660C2semidirect
12. #68904C2semidirect
13. #68880C2semidirect
14. #68686C2semidirect
15. #68662C2semidirect
75. #1880D3semidirect
91. C2×D3×Q8D4semidirect
117. Q8×Dic3D4semidirect
157. #887D4semidirect
291. C2×C4×D3SD16semidirect
472. C3×Q8#121semidirect
536. Dic6#121semidirect
691. C2×D3#460semidirect
706. Dic3#448semidirect
737. Q8#884semidirect
854. C3#32903semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D3×Q82
C2×#51702
C2×#51632
C2×#48062
C2×#47622
#764762
C3×#18802
#716332
#702212
#702002
#696602
#689042
#688802
#686862
#686622
#329033