Finite Group Databasebeta

← #10801009

Subgroups — #10801009

Order 768.

1420 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5546C211yesmaximal, characteristic
2C2×C3×#440C211yesmaximal, characteristic, complemented
3C2×#5173C211yesmaximal, characteristic
4#82488C211yesmaximal, characteristic, complemented
5C2×C4×#216C211yesmaximal, characteristic, complemented
6#72047C211yesmaximal, characteristic, complemented
7C4×#832C211yesmaximal, characteristic, complemented
8#70642C211yesmaximal, characteristic, complemented
9#70632C211yesmaximal, characteristic, complemented
10#70281C211yesmaximal, characteristic, complemented
11#70268C211yesmaximal, characteristic, complemented
12#70199C211yesmaximal, characteristic
13#70167C211yesmaximal, characteristic, complemented
14#69830C211yesmaximal, characteristic, complemented
15#69813C211yesmaximal, characteristic, complemented
16#21465—31nomaximal, Sylow
17C22×#237C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C2×C3×C4×Q8C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21C2×#946C2211yescharacteristic
22C22×#216C2211yescharacteristic
23C2×D4×Dic3C2211yescharacteristic
24C2×C4×#67—21no—
25C22×Dic3⋊C4—21no—
26#5546—24no—
27#5546—24no—
28C2×D3×C4⋊C4C2211yescharacteristic
29C2×#887C2211yescharacteristic
30C2×#67⋊C4—21no—
31C2×#877—21no—
32C2×#872C2211yescharacteristic
33C2×C4×Dic6C2211yescharacteristic
34C3×#440—24no—
35C2×C3×#107C2211yescharacteristic
36C2×C3×#103C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×#97C2211yescharacteristic
39#5229C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#832C2211yescharacteristic
42C2×#832C2211yescharacteristic
43#5173C418yescomplemented
44C2×(C2×D3)⋊C8C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×#816C2211yescharacteristic
47C2×#816C2211yescharacteristic
48C4×#216—24no—
49#4990—21no—
50#4987C2211yescharacteristic
51#4976—21no—
52#4972C2211yescharacteristic
53C2×#810C2211yescharacteristic
54C2×#807C2211yescharacteristic
55#4940—21no—
56C4×C4⋊Dic3C2211yescharacteristic
57#4933—21no—
58C2×C4×C3⋊C8C2211yescharacteristic
59#4551C2211yescharacteristic
60#4551C2211yescharacteristic
61#4550C2211yescharacteristic
62#4550C2211yescharacteristic
63#4529C2211yescharacteristic
64#4529C2211yescharacteristic
65C2×#520—31no—
66C2×#452—31no—
67C2×#440D311yescharacteristic, complemented
68C2×C4×Q16—31no—
69#2323—31no—
70#1878—31no—
71#1877—31no—
72#1872—31no—
73#1863—31no—
74#1862—31no—
75#1852—31no—
76#1788—31no—
77#1763—31no—
78C4×#102—31no—
79#1750—31no—
80C22×C3×Q8C2311yescharacteristic
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4—21no—
83C22×#67—21no—
84C23×Dic3—21no—
85C23×Dic3—21no—
86C2×#237—22no—
87C2×#237—22no—
88C2×#237—22no—
89C2×#237—22no—
90C2×#237—22no—
91C2×#237C2×C414yes—
92C22×C4×D3—21no—
93C22×C4×D3C2311yescharacteristic
94C22×Dic6C2311yescharacteristic
95C2×C3×SD16—22no—
96C2×C3×SD16—22no—
97C2×C3×SD16C2×C414yescomplemented
98C22×C3×C8C2311yescharacteristic
99C22×C3×C8C2311yescharacteristic
100C3×C4×Q8—22no—
101C3×C4×Q8—22no—
102C3×C4×D4—22no—
103C3×C4×D4D414yes—
104C2×C3×C4⋊C4—21no—
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C22⋊C4—21no—
108C2×C3×C42—21no—
109C2×C3×C42C2311yescharacteristic
110C2×#217—21no—
111#946—22no—
112#946C2×C414yescomplemented
113C2×#216—22no—
114C2×#216—22no—
115C2×#216C2×C414yescomplemented
116D4×Dic3—22no—
117D4×Dic3—22no—
118C4×#67—28no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4D411yescharacteristic
122C2×(C2×D3)⋊C4D411yescharacteristic
123C2×C4⋊Dic3C2311yescharacteristic
124C2×C4⋊Dic3C2311yescharacteristic
125C2×C4⋊Dic3C2311yescharacteristic
126C2×Dic3⋊C4—28no—
127C2×Dic3⋊C4—21no—
128C2×Dic3⋊C4—21no—
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4—21no—
131C2×Dic3⋊C4—21no—
132C2×Dic3⋊C4D411yescharacteristic
133C2×Dic3⋊C4D411yescharacteristic
134C2×C4×Dic3—21no—
135C2×C4×Dic3—21no—
136C2×C4×Dic3—21no—
137C2×C4×Dic3C2311yescharacteristic
138C22×C3⋊C8C2311yescharacteristic
139C22×C3⋊C8C2311yescharacteristic
140D3×C4⋊C4—22no—
141D3×C4⋊C4—22no—
142#887—22no—
143#887—22no—
144#67⋊C4—28no—
145#877—28no—
146#872—22no—
147#872—22no—
148C4×Dic6—22no—
149C4×Dic6D414yes—
150C3×#107—22no—
151C3×#103—22no—
152C3×#102—22no—
153C3×#97—22no—
154#835—22no—
155#832—22no—
156#832C2×C414yescomplemented
157C3⋊#95—21no—
158C3⋊#95—21no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162(C2×D3)⋊C8—22no—
163(C2×D3)⋊C8C2×C414yescomplemented
164#816—22no—
165#816C2×C414yescomplemented
166#810—22no—
167#807—22no—
168C4×C3⋊C8—22no—
169C22×#41—31no—
170C22×Q16—31no—
171C22×SD16C2×D311yescharacteristic
172C2×C22⋊Q8—31no—
173#520—64no—
174#520—64no—
175C2×C4×Q8—31no—
176C2×C4×Q8—31no—
177C2×C4×Q8C2×D311yescharacteristic
178C2×C4×D4—31no—
179C2×C4×D4—61no—
180C2×C4×D4—61no—
181C2×C4×D4C2×D311yescharacteristic
182C2×#117—31no—
183C2×#117—61no—
184C22×C4⋊C4—31no—
185C22×C4⋊C4—61no—
186#452—38no—
187#440—24no—
188C4×Q16—64no—
189C2×#107—31no—
190C2×#107C2×D311yescharacteristic
191C2×#103—31no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103—31no—
195C2×#103C2×D311yescharacteristic
196C2×#102—31no—
197C2×#102—31no—
198C2×#102C2×D311yescharacteristic
199C2×C22⋊C8—31no—
200C2×C22⋊C8—31no—
201C2×#97C2×D311yescharacteristic
202C2×C4×C8—31no—
203#391—31no—
204#389—31no—
205#389—61no—
206#388—61no—
207#388—61no—
208#387—61no—
209#380—31no—
210C4×C4⋊C4—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340—31no—
215#336—31no—
216#336—31no—
217C24×C3—21no—
218C23×D3C2×D411yescharacteristic
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8C22×C412yes—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4C22×C412yes—
229C2×C3×D4C2×D412yes—
230C2×C3×D4#4112yes—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—24no—
234C22×C3×C4—21no—
235C22×C3×C4—81no—
236C22×C3×C4—81no—
237C22×C3×C4C2×D411yescharacteristic
238C22×C3×C4C2×D411yescharacteristic
239C22×C3×C4C2411yescharacteristic
240C2×#67—24no—
241C2×#67—24no—
242C2×#67—24no—
243C22×Dic3—24no—
244C22×Dic3—24no—
245C22×Dic3—21no—
246C22×Dic3—24no—
247C22×Dic3—21no—
248C22×Dic3—21no—
249C22×Dic3—24no—
250C22×Dic3—21no—
251C22×Dic3—81no—
252C22×Dic3—81no—
253C22×Dic3C2×D411yescharacteristic
254C22×Dic3C2×D411yescharacteristic
255C22×Dic3C2×D411yescharacteristic
256#237—28no—
257#237—28no—
258#237—28no—
259#237—28no—
260C2×C4×D3—21no—
261C2×C4×D3—21no—
262C2×C4×D3—21no—
263C2×C4×D3—21no—
264C2×C4×D3—24no—
265C2×C4×D3—81no—
266C2×C4×D3—81no—
267C2×C4×D3C22×C412yes—
268C2×C4×D3#4112yes—
269C2×Dic6—21no—
270C2×Dic6—21no—
271C2×Dic6—21no—
272C2×Dic6C22×C412yes—
273C2×Dic6C2×D412yes—
274C2×Dic6#4112yes—
275C3×SD16—28no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8C22×C412yes—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—42no—
286C3×C4⋊C4C2×D412yes—
287C3×C22⋊C4—24no—
288C3×C42—42no—
289C3×C42C2×D412yes—
290C3×C42C2×D412yes—
291#217—24no—
292#216—28no—
293(C2×D3)⋊C4—24no—
294(C2×D3)⋊C4—22no—
295(C2×D3)⋊C4—22no—
296(C2×D3)⋊C4—81no—
297C4⋊Dic3—21no—
298C4⋊Dic3—21no—
299C4⋊Dic3—21no—
300C4⋊Dic3—21no—
301C4⋊Dic3C22×C412yes—
302C4⋊Dic3C2×D412yes—
303Dic3⋊C4—24no—
304Dic3⋊C4—24no—
305Dic3⋊C4—24no—
306Dic3⋊C4—22no—
307Dic3⋊C4—22no—
308Dic3⋊C4—24no—
309Dic3⋊C4—81no—
310C4×Dic3—24no—
311C4×Dic3—24no—
312C4×Dic3—21no—
313C4×Dic3—21no—
314C4×Dic3—81no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8C22×C412yes—
321C2×#41—34no—
322C2×#41—62no—
323C2×#41—62no—
324C2×#41—62no—
325C2×#41—62no—
326C2×#41—62no—
327C22×Q8—31no—
328C22×Q8C22×D311yescharacteristic
329C22×D4—61no—
330C22×D4C22×D311yescharacteristic
331C23×C4—21no—
332C23×C4—31no—
333C23×C4—61no—
334C23×C4—61no—
335C23×C4—61no—
336C2×Q16—34no—
337C2×Q16—62no—
338C2×Q16—62no—
339C2×SD16—22no—
340C2×SD16—22no—
341C2×SD16C4×D314yescomplemented
342C22×C8—31no—
343C22×C8—31no—
344C22×C8C22×D311yescharacteristic
345C22×C8C22×D311yescharacteristic
346C22⋊Q8—34no—
347C22⋊Q8—62no—
348C4×Q8—22no—
349C4×Q8—22no—
350C4×Q8—34no—
351C4×Q8—62no—
352C4×Q8—62no—
353C4×Q8—62no—
354C4×D4—22no—
355C4×D4—68no—
356C4×D4—62no—
357C4×D4—68no—
358C4×D4—62no—
359C4×D4#6714yes—
360#117—68no—
361#117—62no—
362#117—62no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—62no—
370C2×C4⋊C4—61no—
371C2×C4⋊C4—61no—
372C2×C4⋊C4—61no—
373C2×C4⋊C4—68no—
374C2×C4⋊C4—61no—
375C2×C4⋊C4—62no—
376C2×C4⋊C4—61no—
377C2×C4⋊C4C22×D311yescharacteristic
378C2×C4⋊C4C22×D311yescharacteristic
379C2×C22⋊C4—21no—
380C2×C22⋊C4—31no—
381C2×C22⋊C4—31no—
382C2×C22⋊C4—61no—
383C2×C22⋊C4—61no—
384C2×C22⋊C4—61no—
385C2×C42—21no—
386C2×C42—31no—
387C2×C42—61no—
388C2×C42—61no—
389C2×C42—61no—
390C2×C42C22×D311yescharacteristic
391#107—22no—
392#107—62no—
393#103—22no—
394#103—34no—
395#103—62no—
396#103—62no—
397#103—62no—
398#102—22no—
399#102—34no—
400#102—62no—
401C22⋊C8—34no—
402C22⋊C8—62no—
403#97—22no—
404C4×C8—62no—
405#95—61no—
406#95—61no—
407#95—61no—
408#95—61no—
409#95—61no—
410C23×C3—22no—
411C23×C3—22no—
412C23×C3—22no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3C22×D411yescharacteristic
418C22×D3—21no—
419C22×D3—21no—
420C22×D3—21no—
421C22×D3—21no—
422C22×D3—21no—
423C22×D3—21no—
424C22×D3C4×D412yes—
425C3×Q8—22no—
426C3×Q8—22no—
427C3×Q8—41no—
428C3×Q8—41no—
429C3×D4—22no—
430C3×D4—22no—
431C3×D4—22no—
432C3×D4C4×D414yes—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—84no—
447C2×C3×C4#12012yes—
448C2×C3×C4#12012yes—
449C2×C3×C4C23×C411yescharacteristic
450C2×C3×C4C22×D411yescharacteristic
451C2×C3×C4C22×D411yescharacteristic
452C2×C3×C4C2×#4111yescharacteristic
453C2×C3×C4C2×#4111yescharacteristic
454C2×C3×C4C2×#4111yescharacteristic
455#67—216no—
456C2×Dic3—216no—
457C2×Dic3—22no—
458C2×Dic3—22no—
459C2×Dic3—21no—
460C2×Dic3—22no—
461C2×Dic3—21no—
462C2×Dic3—22no—
463C2×Dic3—21no—
464C2×Dic3—21no—
465C2×Dic3—22no—
466C2×Dic3—21no—
467C2×Dic3—21no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477C2×Dic3—84no—
478C2×Dic3C4×D412yes—
479C4×D3—22no—
480C4×D3—22no—
481C4×D3—22no—
482C4×D3—22no—
483C4×D3—84no—
484Dic6—22no—
485Dic6—22no—
486Dic6—22no—
487Dic6C4×D414yes—
488C3×C8—22no—
489C3×C8—41no—
490C3⋊C8—22no—
491C3⋊C8—41no—
492C24—21no—
493C24—31no—
494#41—68no—
495#41—68no—
496#41—68no—
497#41—68no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—32no—
504C2×Q8—32no—
505C2×Q8—32no—
506C2×Q8—61no—
507C2×Q8—61no—
508C2×Q8—61no—
509C2×Q8C2×C4×D312yes—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—64no—
514C2×D4—64no—
515C2×D4—64no—
516C2×D4C2×C4×D312yes—
517C2×D4#23512yes—
518C2×D4C2×#6712yes—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—24no—
522C22×C4—21no—
523C22×C4—31no—
524C22×C4—32no—
525C22×C4—32no—
526C22×C4—31no—
527C22×C4—31no—
528C22×C4—64no—
529C22×C4—64no—
530C22×C4—64no—
531C22×C4—64no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4—61no—
536C22×C4—61no—
537C22×C4—61no—
538C22×C4—61no—
539C22×C4—64no—
540C22×C4—61no—
541C22×C4—81no—
542C22×C4—81no—
543C22×C4—241no—
544C22×C4—241no—
545C22×C4—241no—
546C22×C4—241no—
547C22×C4D3×D411yescharacteristic
548C22×C4D3×D411yescharacteristic
549C22×C4C23×D311yescharacteristic
550Q16—68no—
551SD16—28no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—32no—
558C2×C8—61no—
559C2×C8—61no—
560C2×C8—61no—
561C2×C8—61no—
562C2×C8—61no—
563C2×C8C2×C4×D312yes—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—32no—
568C4⋊C4—32no—
569C4⋊C4—42no—
570C4⋊C4—64no—
571C4⋊C4—64no—
572C4⋊C4—64no—
573C4⋊C4—62no—
574C4⋊C4—62no—
575C4⋊C4—64no—
576C4⋊C4—61no—
577C4⋊C4—61no—
578C4⋊C4—61no—
579C4⋊C4—61no—
580C4⋊C4—241no—
581C4⋊C4C2×#6712yes—
582C22⋊C4—24no—
583C22⋊C4—64no—
584C22⋊C4—64no—
585C22⋊C4—62no—
586C22⋊C4—62no—
587C22⋊C4—241no—
588C42—42no—
589C42—64no—
590C42—64no—
591C42—61no—
592C42—61no—
593C42—241no—
594C42D3×D412yes—
595C42C2×#6712yes—
596C22×C3—24no—
597C22×C3—42no—
598C22×C3—42no—
599C22×C3—42no—
600C22×C3—42no—
601C22×C3—42no—
602C22×C3—42no—
603C22×C3C2×C4×D411yescharacteristic
604C22×C3C2×#12011yescharacteristic
605C22×C3#52511yescharacteristic
606C22×C3#57611yescharacteristic
607C22×C3#57711yescharacteristic
608C22×C3#57811yescharacteristic
609C22×C3#57811yescharacteristic
610C2×D3—22no—
611C2×D3—22no—
612C2×D3—22no—
613C2×D3—41no—
614C2×D3—41no—
615C2×D3—41no—
616C2×D3—41no—
617C3×C4—22no—
618C3×C4—22no—
619C3×C4—42no—
620C3×C4—42no—
621C3×C4—81no—
622C3×C4C2×C4×D411yescharacteristic
623C3×C4C2×C4×D411yescharacteristic
624C3×C4#52511yescharacteristic
625C3×C4#52511yescharacteristic
626Dic3—24no—
627Dic3—22no—
628Dic3—42no—
629Dic3—41no—
630Dic3—42no—
631Dic3—41no—
632Dic3—81no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—32no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—61no—
642C23—61no—
643C23—61no—
644C23—61no—
645C23—61no—
646C23—61no—
647C23C2×D3×D411yescharacteristic
648Q8—22no—
649Q8—22no—
650Q8—34no—
651Q8—41no—
652Q8—41no—
653Q8—62no—
654Q8—62no—
655Q8—62no—
656D4—22no—
657D4—22no—
658D4—22no—
659D4—616no—
660D4C4×#6714yes—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—32no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—616no—
676C2×C4—62no—
677C2×C4—61no—
678C2×C4—62no—
679C2×C4—61no—
680C2×C4—62no—
681C2×C4—62no—
682C2×C4—62no—
683C2×C4—62no—
684C2×C4—62no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—62no—
691C2×C4—61no—
692C2×C4—62no—
693C2×C4—84no—
694C2×C4—121no—
695C2×C4—121no—
696C2×C4—121no—
697C2×C4—121no—
698C2×C4—121no—
699C2×C4—121no—
700C2×C4—121no—
701C2×C4—244no—
702C2×C4—244no—
703C2×C4#93712yes—
704C2×C4#93712yes—
705C2×C4C22×C4×D311yescharacteristic
706C2×C4C2×#23511yescharacteristic
707C2×C4C2×D3×D411yescharacteristic
708C2×C4D3×#4111yescharacteristic
709C2×C4D3×#4111yescharacteristic
710C2×C4C22×#6711yescharacteristic
711C8—22no—
712C8—41no—
713C8—62no—
714C8—121no—
715C2×C3—44no—
716C2×C3C4×#12011yescharacteristic
717C2×C3#294711yescharacteristic
718C2×C3#295111yescharacteristic
719C2×C3#301111yescharacteristic
720C2×C3#301211yescharacteristic
721C2×C3#312011yescharacteristic
722C2×C3#312411yescharacteristic
723D3—42no—
724C22—24no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—62no—
732C22—62no—
733C22—62no—
734C22—121no—
735C22—121no—
736C22—121no—
737C22—121no—
738C22C4×D3×D411yescharacteristic
739C22#554711yescharacteristic
740C22#577411yescharacteristic
741C22#577511yescharacteristic
742C22#577911yescharacteristic
743C22#577911yescharacteristic
744C22C2×#93711yescharacteristic
745C4—22no—
746C4—22no—
747C4—42no—
748C4—42no—
749C4—62no—
750C4—64no—
751C4—81no—
752C4—121no—
753C4—122no—
754C4—121no—
755C4—122no—
756C4—241no—
757C4C4×D3×D411yescharacteristic
758C4#554711yescharacteristic
759C4C2×C4×#6711yescharacteristic
760C4#582811yescharacteristic
761C3#2146511yescharacteristic, complemented, Sylow
762C2—44no—
763C2—122no—
764C2#7977611yescharacteristic
765C2#7977811yescharacteristic
766C2#7978611yescharacteristic
767C2#7978811yescharacteristic
768C2C4×#93711yescharacteristic
769C2#8394911yescharacteristic
770C2#8398311yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC2×C3×#440C2
socleC23×C3C22×D4
prime radicalC22×#237C22
cosocleC22×C3×C4C24
hypercenterC2×#440D3
hypocenterC3#21465
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×C3×#440C2semidirect
4. #82488C2semidirect
5. C2×C4×#216C2semidirect
6. #72047C2semidirect
7. C4×#832C2semidirect
8. #70642C2semidirect
9. #70632C2semidirect
10. #70281C2semidirect
11. #70268C2semidirect
13. #70167C2semidirect
14. #69830C2semidirect
15. #69813C2semidirect
43. #5173C4semidirect
67. C2×#440D3semidirect
97. C2×C3×SD16C2×C4semidirect
112. #946C2×C4semidirect
115. C2×#216C2×C4semidirect
156. #832C2×C4semidirect
163. (C2×D3)⋊C8C2×C4semidirect
165. #816C2×C4semidirect
341. C2×SD16C4×D3semidirect
761. C3#21465semidirect

Maximal subgroups

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

subgroupindex
C2×#55462
C2×C3×#4402
C2×#51732
#824882
C2×C4×#2162
#720472
C4×#8322
#706422
#706322
#702812
#702682
#701992
#701672
#698302
#698132
#214653