Finite Group Databasebeta

← #10944141

Subgroups — #10944141

Order 768.

1372 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5572C211yesmaximal, characteristic, complemented
2C2×#5186C211yesmaximal, characteristic, complemented
3C2×#5185C211yesmaximal, characteristic, complemented
4C2×#4798C211yesmaximal, characteristic, complemented
5C2×#4806C211yesmaximal, characteristic
6#76640C211yesmaximal, characteristic
7C3×#1878C211yesmaximal, characteristic, complemented
8#71633C211yesmaximal, characteristic, complemented
9#70269C211yesmaximal, characteristic, complemented
10#70221C211yesmaximal, characteristic, complemented
11#69690C211yesmaximal, characteristic, complemented
12#68904C211yesmaximal, characteristic, complemented
13#68881C211yesmaximal, characteristic
14#68686C211yesmaximal, characteristic, complemented
15#68663C211yesmaximal, characteristic, complemented
16#32918—31nomaximal, Sylow
17C22×D3×Q8C2211yescharacteristic
18C22×C3×Q16C2211yescharacteristic
19C2×C3×C4×Q8C2211yescharacteristic
20C2×#947C2211yescharacteristic
21C2×#946C2211yescharacteristic
22C2×Q8×Dic3C2211yescharacteristic
23C22×#216C2211yescharacteristic
24C22×#215C2211yescharacteristic
25C22×#204C2211yescharacteristic
26#5572—24no—
27#5572—24no—
28C2×#895C2211yescharacteristic
29C2×#892—21no—
30C2×#892C2211yescharacteristic
31C2×#887—21no—
32C2×#887C2211yescharacteristic
33C2×#872—21no—
34C2×#872C2211yescharacteristic
35C2×C4×Dic6—21no—
36C2×C4×Dic6C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C3×#391C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#835C2211yescharacteristic
42#5186—24no—
43#5185—24no—
44C2×#821C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×(C2×D3)⋊C8C2211yescharacteristic
47C2×#816C2211yescharacteristic
48C2×Dic3⋊C8C2211yescharacteristic
49C2×Dic3⋊C8C2211yescharacteristic
50#4975C2211yescharacteristic
51C2×#810C2211yescharacteristic
52C2×#809C2211yescharacteristic
53#4939C2211yescharacteristic
54#4806—24no—
55#4798—24no—
56#4676—21no—
57#4676—21no—
58#4672—21no—
59#4672—21no—
60C3×#340C2211yescharacteristic
61C3×#336C2211yescharacteristic
62#4551C2211yescharacteristic
63#4529C2211yescharacteristic
64#4529C2211yescharacteristic
65#4524C2211yescharacteristic
66C2×#519—31no—
67C2×#464—31no—
68C2×#464—31no—
69C2×#451—31no—
70C2×#448—31no—
71#2620—31no—
72#1880—31no—
73#1880—31no—
74#1878—31no—
75#1878D311yescharacteristic, complemented
76#1875—31no—
77#1873—31no—
78#1803—31no—
79#1803—31no—
80#1798—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×D12—21no—
90C22×D12C2311yescharacteristic
91C22×C4×D3—21no—
92C22×C4×D3C2311yescharacteristic
93C22×Dic6—21no—
94C22×Dic6C2311yescharacteristic
95C2×C3×Q16—22no—
96C2×C3×Q16—22no—
97C2×C3×Q16—22no—
98C22×C3×C8C2311yescharacteristic
99C22×C3×C8C2311yescharacteristic
100C3×C4×Q8—22no—
101C3×C4×Q8—22no—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4C2311yescharacteristic
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C42—21no—
106C2×C3×C42C2311yescharacteristic
107#947—22no—
108#947—22no—
109#946—22no—
110#946—22no—
111Q8×Dic3—22no—
112Q8×Dic3D414yescomplemented
113C2×#216—22no—
114C2×#216—22no—
115C2×#216—22no—
116C2×#215—22no—
117C2×#215—22no—
118C2×#215—22no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4D411yescharacteristic
127C2×(C2×D3)⋊C4D411yescharacteristic
128C2×C4⋊Dic3—21no—
129C2×C4⋊Dic3C2311yescharacteristic
130C2×C4⋊Dic3C2311yescharacteristic
131C2×Dic3⋊C4—21no—
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4—21no—
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—21no—
136C2×Dic3⋊C4D411yescharacteristic
137C2×Dic3⋊C4D411yescharacteristic
138C2×C4×Dic3—21no—
139C2×C4×Dic3—21no—
140C2×C4×Dic3—21no—
141C2×C4×Dic3—21no—
142C2×C4×Dic3C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C2×#204—22no—
146C2×#204—22no—
147C2×#204—22no—
148#895—22no—
149#895—22no—
150#892—28no—
151#892—22no—
152#892—22no—
153#887—28no—
154#887—22no—
155#887D414yescomplemented
156#872—28no—
157#872—22no—
158#872—22no—
159C4×Dic6—28no—
160C4×Dic6—22no—
161C4×Dic6—22no—
162C3×#103—22no—
163C3×#103—22no—
164C3×#95—21no—
165C3×#95—21no—
166#835—22no—
167#835—22no—
168#821—22no—
169(C2×D3)⋊C8—22no—
170(C2×D3)⋊C8—22no—
171#816—22no—
172Dic3⋊C8—22no—
173Dic3⋊C8—22no—
174#810—22no—
175#809—22no—
176C23×Q8—31no—
177C22×Q16—31no—
178C22×Q16C2×D311yescharacteristic
179C22×SD16—31no—
180C22×SD16—31no—
181C2×#124—31no—
182C2×C22⋊Q8—31no—
183C2×#121—31no—
184#519—64no—
185#519—64no—
186C2×C4×Q8—31no—
187C2×C4×Q8—31no—
188C2×C4×Q8—31no—
189C2×C4×Q8—61no—
190C2×C4×Q8—61no—
191C2×C4×Q8C2×D311yescharacteristic
192C2×#117—31no—
193C2×#117—31no—
194C2×#117—61no—
195C2×#117—61no—
196#464—64no—
197#464—64no—
198#451—64no—
199#448—64no—
200C2×C4⋊C8—31no—
201C2×C4⋊C8—31no—
202C2×#103—31no—
203C2×#103—31no—
204C2×#103—31no—
205C2×#103—31no—
206C2×#103C2×D311yescharacteristic
207C2×#103C2×D311yescharacteristic
208C2×#102—31no—
209C2×#102—31no—
210C2×C22⋊C8—31no—
211C2×C22⋊C8—31no—
212#396—61no—
213#396—61no—
214#394—61no—
215#394—61no—
216#391C2×D311yescharacteristic
217#390—31no—
218#384—31no—
219#340—31no—
220#340—31no—
221#340—31no—
222#340C2×D311yescharacteristic
223#336—31no—
224#336C2×D311yescharacteristic
225C23×D3—21no—
226C23×D3C2×D411yescharacteristic
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×Q8—21no—
236C2×C3×Q8C2×D412yes—
237C2×C3×Q8C2×D412yes—
238C2×C3×Q8#4112yes—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4C2×D411yescharacteristic
244C22×C3×C4C2×D411yescharacteristic
245C22×C3×C4C2411yescharacteristic
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×D12—21no—
257C2×D12—21no—
258C2×D12—21no—
259C2×D12—21no—
260C2×D12—21no—
261C2×D12—21no—
262C2×D12—42no—
263C2×D12—81no—
264C2×D12—81no—
265C2×C4×D3—24no—
266C2×C4×D3—24no—
267C2×C4×D3—24no—
268C2×C4×D3—21no—
269C2×C4×D3—21no—
270C2×C4×D3—21no—
271C2×C4×D3—21no—
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×Dic6C2×D412yes—
281C2×Dic6C2×D412yes—
282C2×Dic6#4112yes—
283C3×Q16—44no—
284C2×C3×C8—21no—
285C2×C3×C8—21no—
286C2×C3×C8—21no—
287C2×C3×C8—21no—
288C2×C3×C8—21no—
289C2×C3×C8—21no—
290C3×C4⋊C4—24no—
291C3×C4⋊C4—21no—
292C3×C4⋊C4—21no—
293C3×C4⋊C4—21no—
294C3×C4⋊C4C2×D412yes—
295C3×C42—24no—
296C3×C42—21no—
297C3×C42—21no—
298#216—44no—
299#215—44no—
300(C2×D3)⋊C4—24no—
301(C2×D3)⋊C4—22no—
302(C2×D3)⋊C4—22no—
303(C2×D3)⋊C4—42no—
304(C2×D3)⋊C4—42no—
305(C2×D3)⋊C4—42no—
306(C2×D3)⋊C4—42no—
307(C2×D3)⋊C4—81no—
308(C2×D3)⋊C4—81no—
309C4⋊Dic3—21no—
310C4⋊Dic3—24no—
311C4⋊Dic3—21no—
312C4⋊Dic3—21no—
313C4⋊Dic3C2×D412yes—
314Dic3⋊C4—24no—
315Dic3⋊C4—22no—
316Dic3⋊C4—22no—
317Dic3⋊C4—24no—
318Dic3⋊C4—42no—
319Dic3⋊C4—81no—
320Dic3⋊C4—81no—
321C4×Dic3—24no—
322C4×Dic3—24no—
323C4×Dic3—24no—
324C4×Dic3—24no—
325C4×Dic3C2×D412yes—
326C4×Dic3C2×D412yes—
327C2×C3⋊C8—21no—
328C2×C3⋊C8—21no—
329C2×C3⋊C8—21no—
330C2×C3⋊C8—21no—
331C2×C3⋊C8—21no—
332C2×C3⋊C8—21no—
333#204—44no—
334C22×Q8—34no—
335C22×Q8—31no—
336C22×Q8—61no—
337C22×Q8—62no—
338C22×Q8—62no—
339C22×Q8—62no—
340C22×Q8—62no—
341C22×Q8—62no—
342C22×Q8C22×D311yescharacteristic
343C22×Q8C22×D311yescharacteristic
344C22×D4—31no—
345C22×D4—61no—
346C23×C4—31no—
347C23×C4—61no—
348C2×Q16—22no—
349C2×Q16—22no—
350C2×Q16—22no—
351C2×Q16—62no—
352C2×Q16—62no—
353C2×Q16—62no—
354C2×SD16—62no—
355C2×SD16—62no—
356C2×SD16—62no—
357C2×SD16—62no—
358C2×SD16—62no—
359C2×SD16—62no—
360C22×C8—31no—
361C22×C8—31no—
362C22×C8C22×D311yescharacteristic
363C22×C8C22×D311yescharacteristic
364#124—62no—
365#124—62no—
366C22⋊Q8—62no—
367C22⋊Q8—62no—
368#121—62no—
369#121—62no—
370C4×Q8—22no—
371C4×Q8—22no—
372C4×Q8—34no—
373C4×Q8—34no—
374C4×Q8—62no—
375C4×Q8—62no—
376C4×Q8—68no—
377C4×Q8—62no—
378C4×Q8—62no—
379C4×Q8—68no—
380#117—62no—
381#117—62no—
382#117—68no—
383#117—62no—
384#117—68no—
385#117—62no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—31no—
388C2×C4⋊C4—31no—
389C2×C4⋊C4—31no—
390C2×C4⋊C4—31no—
391C2×C4⋊C4—61no—
392C2×C4⋊C4—61no—
393C2×C4⋊C4—61no—
394C2×C4⋊C4—61no—
395C2×C4⋊C4—61no—
396C2×C4⋊C4—61no—
397C2×C4⋊C4C22×D311yescharacteristic
398C2×C4⋊C4C22×D311yescharacteristic
399C2×C22⋊C4—31no—
400C2×C22⋊C4—31no—
401C2×C22⋊C4—61no—
402C2×C22⋊C4—61no—
403C2×C22⋊C4—61no—
404C2×C22⋊C4—61no—
405C2×C22⋊C4—61no—
406C2×C22⋊C4—61no—
407C2×C22⋊C4—61no—
408C2×C42—21no—
409C2×C42—31no—
410C2×C42—61no—
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#102—62no—
424#102—62no—
425C22⋊C8—62no—
426C22⋊C8—62no—
427#95—21no—
428#95—21no—
429C23×C3C22×D411yescharacteristic
430C22×D3—21no—
431C22×D3—21no—
432C22×D3—21no—
433C22×D3—21no—
434C22×D3—21no—
435C22×D3—21no—
436C22×D3—41no—
437C22×D3—41no—
438C22×D3—41no—
439C22×D3—41no—
440C22×D3—41no—
441C22×D3—41no—
442C22×D3—41no—
443C22×D3#12112yes—
444C3×Q8—22no—
445C3×Q8—22no—
446C3×Q8—22no—
447C3×Q8—41no—
448C3×Q8—41no—
449C3×Q8—41no—
450C3×Q8—41no—
451C3×Q8#12114yes—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—21no—
456C2×C3×C4—22no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4C22×D411yescharacteristic
471C2×C3×C4C22×D411yescharacteristic
472C2×C3×C4C22×D411yescharacteristic
473C2×C3×C4C2×#4111yescharacteristic
474C2×C3×C4C2×#4111yescharacteristic
475C2×C3×C4C2×#4111yescharacteristic
476C2×Dic3—21no—
477C2×Dic3—22no—
478C2×Dic3—22no—
479C2×Dic3—21no—
480C2×Dic3—22no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—22no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3#12012yes—
492C2×Dic3#12012yes—
493C2×Dic3#12112yes—
494D12—41no—
495D12—41no—
496D12—41no—
497D12—41no—
498D12—84no—
499C4×D3—216no—
500C4×D3—22no—
501C4×D3—22no—
502C4×D3—22no—
503C4×D3—22no—
504Dic6—216no—
505Dic6—22no—
506Dic6—22no—
507Dic6—22no—
508Dic6#12114yes—
509C3×C8—41no—
510C3×C8—41no—
511C3⋊C8—41no—
512C3⋊C8—41no—
513C24—31no—
514C24—61no—
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—21no—
524C2×Q8—32no—
525C2×Q8—32no—
526C2×Q8—32no—
527C2×Q8—64no—
528C2×Q8—64no—
529C2×Q8—64no—
530C2×Q8—68no—
531C2×Q8—68no—
532C2×Q8—68no—
533C2×Q8—68no—
534C2×Q8—61no—
535C2×Q8—61no—
536C2×Q8—61no—
537C2×Q8#23512yes—
538C2×Q8D3×D412yes—
539C2×Q8D3×D412yes—
540C2×D4—61no—
541C2×D4—61no—
542C2×D4—61no—
543C2×D4—61no—
544C2×D4—61no—
545C2×D4—61no—
546C2×D4—122no—
547C2×D4—241no—
548C2×D4—241no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—31no—
554C22×C4—31no—
555C22×C4—31no—
556C22×C4—32no—
557C22×C4—32no—
558C22×C4—64no—
559C22×C4—64no—
560C22×C4—64no—
561C22×C4—61no—
562C22×C4—61no—
563C22×C4—61no—
564C22×C4—61no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4—61no—
568C22×C4D3×D411yescharacteristic
569C22×C4D3×D411yescharacteristic
570C22×C4C23×D311yescharacteristic
571Q16—44no—
572Q16—124no—
573SD16—124no—
574SD16—124no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—61no—
582C2×C8—61no—
583C2×C8—61no—
584C2×C8—61no—
585C2×C8—61no—
586C2×C8—61no—
587C4⋊C4—24no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—32no—
592C4⋊C4—62no—
593C4⋊C4—62no—
594C4⋊C4—64no—
595C4⋊C4—64no—
596C4⋊C4—64no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—122no—
601C4⋊C4—241no—
602C4⋊C4—241no—
603C4⋊C4D3×D412yes—
604C22⋊C4—62no—
605C22⋊C4—62no—
606C22⋊C4—64no—
607C22⋊C4—122no—
608C22⋊C4—122no—
609C22⋊C4—122no—
610C22⋊C4—122no—
611C22⋊C4—241no—
612C22⋊C4—241no—
613C42—24no—
614C42—21no—
615C42—21no—
616C42—32no—
617C42—32no—
618C42—64no—
619C42—64no—
620C42—64no—
621C42—64no—
622C22×C3C2×#12011yescharacteristic
623C22×C3C2×#12111yescharacteristic
624C22×C3#52511yescharacteristic
625C22×C3#57711yescharacteristic
626C22×C3#57711yescharacteristic
627C22×C3#57811yescharacteristic
628C22×C3#57811yescharacteristic
629C2×D3—22no—
630C2×D3—22no—
631C2×D3—22no—
632C2×D3—41no—
633C2×D3—41no—
634C2×D3—41no—
635C2×D3—41no—
636C2×D3—81no—
637C2×D3—81no—
638C2×D3—81no—
639C2×D3—81no—
640C2×D3—81no—
641C2×D3—81no—
642C2×D3—81no—
643C3×C4—24no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—42no—
647C3×C4—81no—
648C3×C4—81no—
649C3×C4C2×#12111yescharacteristic
650C3×C4C2×#12111yescharacteristic
651C3×C4#52511yescharacteristic
652C3×C4#52511yescharacteristic
653Dic3—22no—
654Dic3—24no—
655Dic3—22no—
656Dic3—22no—
657Dic3—42no—
658Dic3—81no—
659C23—32no—
660C23—61no—
661C23—61no—
662C23—61no—
663C23—61no—
664C23—61no—
665C23—61no—
666C23—121no—
667C23—121no—
668C23—121no—
669C23—121no—
670C23—121no—
671C23—121no—
672C23—121no—
673C23C2×D3×D411yescharacteristic
674Q8—22no—
675Q8—22no—
676Q8—22no—
677Q8—34no—
678Q8—41no—
679Q8—41no—
680Q8—41no—
681Q8—41no—
682Q8—616no—
683Q8—62no—
684Q8—62no—
685Q8—62no—
686Q8#88414yes—
687D4—121no—
688D4—121no—
689D4—121no—
690D4—121no—
691D4—244no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—32no—
703C2×C4—32no—
704C2×C4—32no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—616no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—62no—
720C2×C4—61no—
721C2×C4—62no—
722C2×C4—62no—
723C2×C4—62no—
724C2×C4—62no—
725C2×C4—62no—
726C2×C4—62no—
727C2×C4—62no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—121no—
731C2×C4—121no—
732C2×C4—121no—
733C2×C4C2×#23511yescharacteristic
734C2×C4C2×D3×D411yescharacteristic
735C2×C4C2×D3×D411yescharacteristic
736C2×C4C2×D3×D411yescharacteristic
737C2×C4D3×#4111yescharacteristic
738C2×C4D3×#4111yescharacteristic
739C8—41no—
740C8—41no—
741C8—121no—
742C8—121no—
743C2×C3#284711yescharacteristic
744C2×C3#301311yescharacteristic
745C2×C3#301311yescharacteristic
746C2×C3#304311yescharacteristic
747C2×C3#304411yescharacteristic
748C2×C3#312111yescharacteristic
749C2×C3#312111yescharacteristic
750D3—42no—
751D3—161no—
752C22—62no—
753C22—62no—
754C22—62no—
755C22—121no—
756C22—121no—
757C22—121no—
758C22—121no—
759C22—241no—
760C22—241no—
761C22—241no—
762C22—241no—
763C22—241no—
764C22—241no—
765C22—241no—
766C22#554711yescharacteristic
767C22D3×#12011yescharacteristic
768C22D3×#12111yescharacteristic
769C22#576611yescharacteristic
770C22#577011yescharacteristic
771C22#577811yescharacteristic
772C22#577911yescharacteristic
773C4—24no—
774C4—41no—
775C4—41no—
776C4—42no—
777C4—62no—
778C4—62no—
779C4—62no—
780C4—64no—
781C4—81no—
782C4—81no—
783C4—122no—
784C4—241no—
785C4C2×#88411yescharacteristic
786C4#554711yescharacteristic
787C4D3×#12111yescharacteristic
788C4#565611yescharacteristic
789C3#3291811yescharacteristic, complemented, Sylow
790C2—122no—
791C2—481no—
792C2#7493511yescharacteristic
793C2#7975011yescharacteristic
794C2#7983511yescharacteristic
795C2#8018611yescharacteristic
796C2#8023211yescharacteristic
797C2#8047811yescharacteristic
798C2#8060011yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1878C2
socleC23×C3C22×D4
prime radicalC2×#895C22
hypercenter#1878D3
hypocenterC3#32918
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
1. C2×#5572C2semidirect
2. C2×#5186C2semidirect
3. C2×#5185C2semidirect
4. C2×#4798C2semidirect
7. C3×#1878C2semidirect
8. #71633C2semidirect
9. #70269C2semidirect
10. #70221C2semidirect
11. #69690C2semidirect
12. #68904C2semidirect
14. #68686C2semidirect
15. #68663C2semidirect
75. #1878D3semidirect
112. Q8×Dic3D4semidirect
155. #887D4semidirect
789. C3#32918semidirect

Maximal subgroups

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

subgroupindex
C2×#55722
C2×#51862
C2×#51852
C2×#47982
C2×#48062
#766402
C3×#18782
#716332
#702692
#702212
#696902
#689042
#688812
#686862
#686632
#329183