Finite Group Databasebeta

← #10944014

Subgroups — #10944014

Order 768.

1436 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D3×Q8C211yesmaximal, characteristic
2C2×#5186C211yesmaximal, characteristic
3C2×#5182C211yesmaximal, characteristic, complemented
4C2×#4795C211yesmaximal, characteristic, complemented
5C2×#4809C211yesmaximal, characteristic
6#76664C211yesmaximal, characteristic
7C3×#1878C211yesmaximal, characteristic, complemented
8#71632C211yesmaximal, characteristic, complemented
9#70268C211yesmaximal, characteristic
10#70221C211yesmaximal, characteristic, complemented
11#69690C211yesmaximal, characteristic, complemented
12#68904C211yesmaximal, characteristic, complemented
13#68878C211yesmaximal, characteristic
14#68685C211yesmaximal, characteristic, complemented
15#68662C211yesmaximal, characteristic
16#32906—31nomaximal, Sylow
17C22×D3×Q8C2211yescharacteristic
18C22×C3×Q16C2211yescharacteristic
19C2×C3×C4×Q8C2211yescharacteristic
20C2×#946C2211yescharacteristic
21C2×Q8×Dic3C2211yescharacteristic
22C2×#944C2211yescharacteristic
23C22×#216C2211yescharacteristic
24C22×#216C2211yescharacteristic
25C22×Dic12C2211yescharacteristic
26C4×D3×Q8—24no—
27C4×D3×Q8—24no—
28C2×#897C2211yescharacteristic
29C2×D3×C4⋊C4—21no—
30C2×D3×C4⋊C4C2211yescharacteristic
31C2×#887—21no—
32C2×#887C2211yescharacteristic
33C2×C42×D3—21no—
34C2×C42×D3C2211yescharacteristic
35C2×C4×Dic6—21no—
36C2×C4×Dic6C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C3×#391C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#835C2211yescharacteristic
42#5186—24no—
43#5182—24no—
44C2×(C2×D3)⋊C8C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×#816C2211yescharacteristic
47C2×#816C2211yescharacteristic
48C2×Dic3⋊C8C2211yescharacteristic
49C2×Dic3⋊C8C2211yescharacteristic
50#4975C2211yescharacteristic
51C2×#810C2211yescharacteristic
52C2×#810C2211yescharacteristic
53#4929C2211yescharacteristic
54#4809—24no—
55#4795—24no—
56#4667—21no—
57#4667—21no—
58#4647—21no—
59#4647—21no—
60C3×#340C2211yescharacteristic
61C3×#336C2211yescharacteristic
62#4551C2211yescharacteristic
63#4529C2211yescharacteristic
64#4529C2211yescharacteristic
65#4524C2211yescharacteristic
66C22×C4×Q8—31no—
67C2×#462—31no—
68C2×#462—31no—
69C2×#451—31no—
70C2×#451—31no—
71#2857—31no—
72#1878—31no—
73#1878—31no—
74#1878—31no—
75#1878D311yescharacteristic, complemented
76#1872—31no—
77#1872—31no—
78#1803—31no—
79#1803—31no—
80#1797—31no—
81C22×C3×Q8C2311yescharacteristic
82C22×C3×Q8C2311yescharacteristic
83C2×D3×Q8—22no—
84C2×D3×Q8—22no—
85C2×D3×Q8—22no—
86C2×D3×Q8—22no—
87C2×D3×Q8—22no—
88C2×D3×Q8D414yes—
89C22×C4×D3—21no—
90C22×C4×D3—21no—
91C22×C4×D3D411yescharacteristic
92C22×C4×D3D411yescharacteristic
93C22×C4×D3C2311yescharacteristic
94C22×Dic6—21no—
95C22×Dic6C2311yescharacteristic
96C22×Dic6C2311yescharacteristic
97C2×C3×Q16—22no—
98C2×C3×Q16—22no—
99C2×C3×Q16—22no—
100C22×C3×C8C2311yescharacteristic
101C22×C3×C8C2311yescharacteristic
102C3×C4×Q8—22no—
103C3×C4×Q8—22no—
104C2×C3×C4⋊C4—21no—
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C42—21no—
108C2×C3×C42C2311yescharacteristic
109#946—22no—
110#946—22no—
111Q8×Dic3—22no—
112Q8×Dic3D414yes—
113#944—22no—
114#944—22no—
115C2×#216—22no—
116C2×#216—22no—
117C2×#216—22no—
118C2×#216—22no—
119C2×#216—22no—
120C2×#216—22no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×C4⋊Dic3—21no—
124C2×C4⋊Dic3—21no—
125C2×C4⋊Dic3C2311yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127C2×Dic3⋊C4—21no—
128C2×Dic3⋊C4—21no—
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4—21no—
131C2×Dic3⋊C4—21no—
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4—21no—
134C2×Dic3⋊C4—21no—
135C2×C4×Dic3—21no—
136C2×C4×Dic3—21no—
137C2×C4×Dic3—21no—
138C2×C4×Dic3D411yescharacteristic
139C2×C4×Dic3D411yescharacteristic
140C2×C4×Dic3C2311yescharacteristic
141C22×C3⋊C8C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C2×Dic12—22no—
144C2×Dic12—22no—
145C2×Dic12—22no—
146#897—22no—
147#897—22no—
148D3×C4⋊C4—28no—
149D3×C4⋊C4—22no—
150D3×C4⋊C4—22no—
151#887—28no—
152#887—22no—
153#887D414yes—
154C42×D3—28no—
155C42×D3—22no—
156C42×D3—22no—
157C4×Dic6—28no—
158C4×Dic6—22no—
159C4×Dic6—22no—
160C3×#103—22no—
161C3×#103—22no—
162C3×#95—21no—
163C3×#95—21no—
164#835—22no—
165#835—22no—
166C3⋊#95—21no—
167C3⋊#95—21no—
168(C2×D3)⋊C8—22no—
169(C2×D3)⋊C8—22no—
170#816—22no—
171#816—22no—
172Dic3⋊C8—22no—
173Dic3⋊C8—22no—
174#810—22no—
175#810—22no—
176C23×Q8—31no—
177C22×Q16—31no—
178C22×Q16—31no—
179C22×Q16—31no—
180C22×Q16C2×D311yescharacteristic
181C2×C4⋊Q8—31no—
182C2×C22⋊Q8—31no—
183C2×C22⋊Q8—31no—
184C2×C4×Q8—31no—
185C2×C4×Q8—31no—
186C2×C4×Q8—31no—
187C2×C4×Q8—61no—
188C2×C4×Q8—61no—
189C2×C4×Q8—64no—
190C2×C4×Q8—64no—
191C2×C4×Q8C2×D311yescharacteristic
192C22×C4⋊C4—31no—
193C22×C4⋊C4—61no—
194C22×C42—31no—
195C22×C42—61no—
196#462—64no—
197#462—64no—
198#451—64no—
199#451—64no—
200C2×C4⋊C8—31no—
201C2×C4⋊C8—31no—
202C2×#103—31no—
203C2×#103—31no—
204C2×#103—31no—
205C2×#103—31no—
206C2×#103—31no—
207C2×#103—31no—
208C2×#103C2×D311yescharacteristic
209C2×#103C2×D311yescharacteristic
210C2×C22⋊C8—31no—
211C2×C22⋊C8—31no—
212#391—31no—
213#391C2×D311yescharacteristic
214#389—61no—
215#389—61no—
216#384—31no—
217#380—61no—
218#380—61no—
219#340—31no—
220#340—31no—
221#340—31no—
222#340C2×D311yescharacteristic
223#336—31no—
224#336C2×D311yescharacteristic
225C23×D3C2×D411yescharacteristic
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8—21no—
229C2×C3×Q8—21no—
230C2×C3×Q8—21no—
231C2×C3×Q8—21no—
232C2×C3×Q8—21no—
233C2×C3×Q8—21no—
234C2×C3×Q8—21no—
235C2×C3×Q8C2×D412yes—
236C2×C3×Q8C2×D412yes—
237C2×C3×Q8#4112yes—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4C2×D411yescharacteristic
243C22×C3×C4C2×D411yescharacteristic
244C22×C3×C4C2411yescharacteristic
245C22×Dic3—21no—
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3—21no—
249C22×Dic3C2×D411yescharacteristic
250C22×Dic3C2×D411yescharacteristic
251C22×Dic3C2×D411yescharacteristic
252D3×Q8—28no—
253D3×Q8—28no—
254D3×Q8—28no—
255D3×Q8—28no—
256C2×C4×D3—24no—
257C2×C4×D3—24no—
258C2×C4×D3—24no—
259C2×C4×D3—21no—
260C2×C4×D3—21no—
261C2×C4×D3—21no—
262C2×C4×D3—21no—
263C2×C4×D3—22no—
264C2×C4×D3—22no—
265C2×C4×D3—24no—
266C2×C4×D3—22no—
267C2×C4×D3—22no—
268C2×C4×D3—41no—
269C2×C4×D3—42no—
270C2×C4×D3—42no—
271C2×C4×D3Q1614yescomplemented
272C2×C4×D3C2×D412yes—
273C2×C4×D3#4112yes—
274C2×Dic6—24no—
275C2×Dic6—24no—
276C2×Dic6—21no—
277C2×Dic6—21no—
278C2×Dic6—21no—
279C2×Dic6—24no—
280C2×Dic6—21no—
281C2×Dic6—21no—
282C2×Dic6—21no—
283C2×Dic6—21no—
284C2×Dic6—21no—
285C2×Dic6—21no—
286C2×Dic6C2×D412yes—
287C2×Dic6C2×D412yes—
288C2×Dic6#4112yes—
289C3×Q16—44no—
290C2×C3×C8—21no—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C3×C4⋊C4—24no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4C2×D412yes—
301C3×C42—24no—
302C3×C42—21no—
303C3×C42—21no—
304#216—44no—
305#216—44no—
306(C2×D3)⋊C4—42no—
307(C2×D3)⋊C4—42no—
308C4⋊Dic3—21no—
309C4⋊Dic3—24no—
310C4⋊Dic3—21no—
311C4⋊Dic3—21no—
312C4⋊Dic3—42no—
313C4⋊Dic3C2×D412yes—
314Dic3⋊C4—24no—
315Dic3⋊C4—24no—
316Dic3⋊C4—24no—
317Dic3⋊C4—42no—
318Dic3⋊C4—42no—
319Dic3⋊C4—42no—
320Dic3⋊C4—42no—
321Dic3⋊C4—42no—
322C4×Dic3—24no—
323C4×Dic3—22no—
324C4×Dic3—22no—
325C4×Dic3—24no—
326C4×Dic3—24no—
327C4×Dic3C2×D412yes—
328C4×Dic3C2×D412yes—
329C2×C3⋊C8—21no—
330C2×C3⋊C8—21no—
331C2×C3⋊C8—21no—
332C2×C3⋊C8—21no—
333C2×C3⋊C8—21no—
334C2×C3⋊C8—21no—
335Dic12—44no—
336C22×Q8—34no—
337C22×Q8—31no—
338C22×Q8—31no—
339C22×Q8—61no—
340C22×Q8—62no—
341C22×Q8—62no—
342C22×Q8—62no—
343C22×Q8—62no—
344C22×Q8—62no—
345C22×Q8C22×D311yescharacteristic
346C22×Q8C22×D311yescharacteristic
347C23×C4—31no—
348C23×C4—31no—
349C23×C4—31no—
350C23×C4—61no—
351C23×C4—61no—
352C2×Q16—22no—
353C2×Q16—22no—
354C2×Q16—22no—
355C2×Q16—62no—
356C2×Q16—62no—
357C2×Q16—62no—
358C2×Q16—62no—
359C2×Q16—62no—
360C2×Q16—62no—
361C2×Q16—62no—
362C2×Q16—62no—
363C2×Q16—62no—
364C22×C8—31no—
365C22×C8—31no—
366C22×C8C22×D311yescharacteristic
367C22×C8C22×D311yescharacteristic
368C4⋊Q8—62no—
369C4⋊Q8—62no—
370C22⋊Q8—62no—
371C22⋊Q8—62no—
372C22⋊Q8—62no—
373C22⋊Q8—62no—
374C4×Q8—22no—
375C4×Q8—22no—
376C4×Q8—34no—
377C4×Q8—34no—
378C4×Q8—62no—
379C4×Q8—62no—
380C4×Q8—68no—
381C4×Q8—62no—
382C4×Q8—62no—
383C4×Q8—68no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—31no—
386C2×C4⋊C4—31no—
387C2×C4⋊C4—62no—
388C2×C4⋊C4—68no—
389C2×C4⋊C4—61no—
390C2×C4⋊C4—61no—
391C2×C4⋊C4—61no—
392C2×C4⋊C4—61no—
393C2×C4⋊C4—62no—
394C2×C4⋊C4—61no—
395C2×C4⋊C4—61no—
396C2×C4⋊C4—61no—
397C2×C4⋊C4—61no—
398C2×C4⋊C4—61no—
399C2×C4⋊C4—61no—
400C2×C4⋊C4C22×D311yescharacteristic
401C2×C4⋊C4C22×D311yescharacteristic
402C2×C22⋊C4—61no—
403C2×C22⋊C4—61no—
404C2×C42—21no—
405C2×C42—31no—
406C2×C42—31no—
407C2×C42—31no—
408C2×C42—62no—
409C2×C42—62no—
410C2×C42—68no—
411C2×C42—61no—
412C2×C42—61no—
413C2×C42—61no—
414C2×C42C22×D311yescharacteristic
415C4⋊C8—62no—
416C4⋊C8—62no—
417#103—22no—
418#103—22no—
419#103—62no—
420#103—62no—
421#103—62no—
422#103—62no—
423#103—62no—
424#103—62no—
425C22⋊C8—62no—
426C22⋊C8—62no—
427#95—21no—
428#95—21no—
429#95—61no—
430#95—61no—
431C23×C3C22×D411yescharacteristic
432C22×D3—21no—
433C22×D3—21no—
434C22×D3—21no—
435C22×D3—21no—
436C22×D3#12112yes—
437C22×D3C2×Q1612yes—
438C22×D3#13712yes—
439C3×Q8—22no—
440C3×Q8—22no—
441C3×Q8—22no—
442C3×Q8—41no—
443C3×Q8—41no—
444C3×Q8—41no—
445C3×Q8—41no—
446C3×Q8#12114yes—
447C2×C3×C4—21no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—22no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4C2×Q1612yes—
465C2×C3×C4C22×D411yescharacteristic
466C2×C3×C4C22×D411yescharacteristic
467C2×C3×C4C22×D411yescharacteristic
468C2×C3×C4C2×#4111yescharacteristic
469C2×C3×C4C2×#4111yescharacteristic
470C2×C3×C4C2×#4111yescharacteristic
471C2×Dic3—21no—
472C2×Dic3—22no—
473C2×Dic3—22no—
474C2×Dic3—21no—
475C2×Dic3—22no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—22no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3#12012yes—
488C2×Dic3#12012yes—
489C2×Dic3#12112yes—
490C2×Dic3C2×Q1612yes—
491C2×Dic3#13712yes—
492C4×D3—216no—
493C4×D3—22no—
494C4×D3—22no—
495C4×D3—22no—
496C4×D3—22no—
497C4×D3—28no—
498C4×D3—44no—
499C4×D3—48no—
500Dic6—216no—
501Dic6—22no—
502Dic6—22no—
503Dic6—22no—
504Dic6—41no—
505Dic6—41no—
506Dic6—41no—
507Dic6—41no—
508Dic6#12114yes—
509C3×C8—41no—
510C3×C8—41no—
511C3⋊C8—41no—
512C3⋊C8—41no—
513C24—31no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—32no—
524C2×Q8—32no—
525C2×Q8—32no—
526C2×Q8—64no—
527C2×Q8—64no—
528C2×Q8—64no—
529C2×Q8—68no—
530C2×Q8—68no—
531C2×Q8—68no—
532C2×Q8—68no—
533C2×Q8—61no—
534C2×Q8—61no—
535C2×Q8—61no—
536C2×Q8—61no—
537C2×Q8—61no—
538C2×Q8—61no—
539C2×Q8—61no—
540C2×Q8—61no—
541C2×Q8—61no—
542C2×Q8#23512yes—
543C2×Q8D3×D412yes—
544C2×Q8D3×D412yes—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—31no—
550C22×C4—31no—
551C22×C4—31no—
552C22×C4—34no—
553C22×C4—32no—
554C22×C4—32no—
555C22×C4—62no—
556C22×C4—62no—
557C22×C4—62no—
558C22×C4—64no—
559C22×C4—64no—
560C22×C4—64no—
561C22×C4—62no—
562C22×C4—64no—
563C22×C4—61no—
564C22×C4—61no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4—61no—
568C22×C4—61no—
569C22×C4—61no—
570C22×C4—61no—
571C22×C4—121no—
572C22×C4—122no—
573C22×C4—122no—
574C22×C4D3×D411yescharacteristic
575C22×C4D3×D411yescharacteristic
576C22×C4C23×D311yescharacteristic
577Q16—44no—
578Q16—124no—
579Q16—124no—
580Q16—124no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—61no—
588C2×C8—61no—
589C2×C8—61no—
590C2×C8—61no—
591C2×C8—61no—
592C2×C8—61no—
593C4⋊C4—24no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—32no—
598C4⋊C4—64no—
599C4⋊C4—64no—
600C4⋊C4—64no—
601C4⋊C4—64no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—122no—
606C4⋊C4—122no—
607C4⋊C4—122no—
608C4⋊C4—122no—
609C4⋊C4—122no—
610C4⋊C4—122no—
611C4⋊C4D3×D412yes—
612C22⋊C4—122no—
613C22⋊C4—122no—
614C42—24no—
615C42—21no—
616C42—21no—
617C42—32no—
618C42—32no—
619C42—62no—
620C42—62no—
621C42—64no—
622C42—64no—
623C42—64no—
624C22×C3C2×#12011yescharacteristic
625C22×C3C2×#12111yescharacteristic
626C22×C3#52511yescharacteristic
627C22×C3C22×Q1611yescharacteristic
628C22×C3C2×#13711yescharacteristic
629C22×C3C2×#13711yescharacteristic
630C22×C3#57511yescharacteristic
631C2×D3—22no—
632C2×D3—22no—
633C2×D3—22no—
634C2×D3—22no—
635C2×D3—22no—
636C2×D3—22no—
637C2×D3#46214yescomplemented
638C3×C4—24no—
639C3×C4—22no—
640C3×C4—41no—
641C3×C4—42no—
642C3×C4—81no—
643C3×C4—81no—
644C3×C4C2×#12111yescharacteristic
645C3×C4C2×#12111yescharacteristic
646C3×C4#52511yescharacteristic
647C3×C4#52511yescharacteristic
648Dic3—22no—
649Dic3—24no—
650Dic3—22no—
651Dic3—42no—
652Dic3—81no—
653Dic3—81no—
654Dic3#45114yescomplemented
655C23—32no—
656C23—32no—
657C23—32no—
658C23—61no—
659C23—61no—
660C23—61no—
661C23—61no—
662C23C2×D3×D411yescharacteristic
663Q8—22no—
664Q8—22no—
665Q8—22no—
666Q8—34no—
667Q8—41no—
668Q8—41no—
669Q8—41no—
670Q8—41no—
671Q8—616no—
672Q8—62no—
673Q8—62no—
674Q8—62no—
675Q8—121no—
676Q8—121no—
677Q8—121no—
678Q8—121no—
679Q8#88414yes—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—32no—
690C2×C4—32no—
691C2×C4—32no—
692C2×C4—32no—
693C2×C4—32no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—68no—
703C2×C4—616no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—62no—
708C2×C4—61no—
709C2×C4—62no—
710C2×C4—62no—
711C2×C4—62no—
712C2×C4—62no—
713C2×C4—62no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—124no—
717C2×C4—128no—
718C2×C4—121no—
719C2×C4—121no—
720C2×C4—121no—
721C2×C4—121no—
722C2×C4—121no—
723C2×C4—121no—
724C2×C4—121no—
725C2×C4—121no—
726C2×C4D3×Q1612yes—
727C2×C4C2×#23511yescharacteristic
728C2×C4C2×D3×D411yescharacteristic
729C2×C4C2×D3×D411yescharacteristic
730C2×C4C2×D3×D411yescharacteristic
731C2×C4D3×#4111yescharacteristic
732C2×C4D3×#4111yescharacteristic
733C8—41no—
734C8—41no—
735C8—121no—
736C8—121no—
737C2×C3#284711yescharacteristic
738C2×C3C2×#45111yescharacteristic
739C2×C3#300711yescharacteristic
740C2×C3C2×#46211yescharacteristic
741C2×C3#303711yescharacteristic
742C2×C3#310411yescharacteristic
743C2×C3#311311yescharacteristic
744D3—24no—
745C22—34no—
746C22—62no—
747C22—62no—
748C22—62no—
749C22—62no—
750C22—62no—
751C22—62no—
752C22#554711yescharacteristic
753C22D3×#12011yescharacteristic
754C22D3×#12111yescharacteristic
755C22C2×D3×Q1611yescharacteristic
756C22#576811yescharacteristic
757C22D3×#13711yescharacteristic
758C22D3×#13711yescharacteristic
759C4—22no—
760C4—24no—
761C4—34no—
762C4—41no—
763C4—42no—
764C4—62no—
765C4—62no—
766C4—64no—
767C4—81no—
768C4—81no—
769C4—122no—
770C4—241no—
771C4—241no—
772C4C2×#88411yescharacteristic
773C4#554711yescharacteristic
774C4D3×#12111yescharacteristic
775C4#565611yescharacteristic
776C3#3290611yescharacteristic, complemented, Sylow
777C2—64no—
778C2#7493511yescharacteristic
779C2#7972211yescharacteristic
780C2#7983311yescharacteristic
781C2D3×#45111yescharacteristic
782C2#8022811yescharacteristic
783C2D3×#46211yescharacteristic
784C2#8059811yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1878C2
socleC23×C3C22×D4
prime radicalC23×D3C2×D4
hypercenter#1878D3
hypocenterC3#32906
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1878

Complements

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

NH ≅ G/Ntype
3. C2×#5182C2semidirect
4. C2×#4795C2semidirect
7. C3×#1878C2semidirect
8. #71632C2semidirect
10. #70221C2semidirect
11. #69690C2semidirect
12. #68904C2semidirect
14. #68685C2semidirect
75. #1878D3semidirect
271. C2×C4×D3Q16semidirect
637. C2×D3#462semidirect
654. Dic3#451semidirect
776. C3#32906semidirect

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×#51862
C2×#51822
C2×#47952
C2×#48092
#766642
C3×#18782
#716322
#702682
#702212
#696902
#689042
#688782
#686852
#686622
#329063