Finite Group Databasebeta

← #10801014

Subgroups — #10801014

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×#5574C211yesmaximal, characteristic
2C2×#5187C211yesmaximal, characteristic
3C2×Dic3×Q16C211yesmaximal, characteristic, complemented
4C2×#4817C211yesmaximal, characteristic, complemented
5#76611C211yesmaximal, characteristic, complemented
6C3×#1878C211yesmaximal, characteristic, complemented
7#71628C211yesmaximal, characteristic, complemented
8#70268C211yesmaximal, characteristic, complemented
9#70267C211yesmaximal, characteristic
10#70220C211yesmaximal, characteristic, complemented
11#69687C211yesmaximal, characteristic, complemented
12#68874C211yesmaximal, characteristic, complemented
13#68780C211yesmaximal, characteristic, complemented
14#68670C211yesmaximal, characteristic, complemented
15#68601C211yesmaximal, characteristic, complemented
16#21465—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C22×C3×Q16C2211yescharacteristic
19C2×C3×C4×Q8C2211yescharacteristic
20C2×#946C2211yescharacteristic
21C2×Q8×Dic3C2211yescharacteristic
22C2×Q8×Dic3C2211yescharacteristic
23C22×#215C2211yescharacteristic
24#5574—24no—
25#5574—24no—
26C2×#893—21no—
27C2×#893C2211yescharacteristic
28C2×D3×C4⋊C4—21no—
29C2×D3×C4⋊C4C2211yescharacteristic
30C2×C4×D12—21no—
31C2×C4×D12C2211yescharacteristic
32C2×#872—21no—
33C2×#872C2211yescharacteristic
34C2×C3×#103C2211yescharacteristic
35C2×C3×#103C2211yescharacteristic
36C3×#391C2211yescharacteristic
37C2×#835C2211yescharacteristic
38C2×#835C2211yescharacteristic
39C2×#835C2211yescharacteristic
40#5187C418yescomplemented
41Dic3×Q16—24no—
42C2×#821C2211yescharacteristic
43C2×#821C2211yescharacteristic
44C2×(C2×D3)⋊C8C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×#818C2211yescharacteristic
47C2×#815C2211yescharacteristic
48C2×C8×Dic3C2211yescharacteristic
49#4987C2211yescharacteristic
50Dic3×C4⋊C4C2211yescharacteristic
51C2×#809C2211yescharacteristic
52C2×#807C2211yescharacteristic
53#4928C2211yescharacteristic
54#4817—24no—
55#4670—21no—
56#4669—21no—
57#4652—21no—
58#4647—21no—
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61#4551C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64#4524C2211yescharacteristic
65C2×#520—31no—
66C2×#452—31no—
67C2×#440—31no—
68C2×C4×Q16—31no—
69#2323—31no—
70#1878D311yescharacteristic, complemented
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×Q8C2311yescharacteristic
82C2×#239—22no—
83C2×#239—22no—
84C2×#239—22no—
85C2×#239—22no—
86C2×#239—22no—
87C2×#239C2×C414yes—
88C22×D12—21no—
89C22×D12C2311yescharacteristic
90C22×C4×D3—21no—
91C22×C4×D3—21no—
92C22×C4×D3—21no—
93C22×C4×D3—21no—
94C22×C4×D3C2311yescharacteristic
95C2×C3×Q16—22no—
96C2×C3×Q16—22no—
97C2×C3×Q16C2×C414yescomplemented
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#946—22no—
108#946C2×C414yescomplemented
109Q8×Dic3—22no—
110Q8×Dic3—22no—
111Q8×Dic3—22no—
112Q8×Dic3D414yes—
113C2×#215—22no—
114C2×#215—22no—
115C2×#215C2×C414yescomplemented
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4—21no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4D411yescharacteristic
121C2×(C2×D3)⋊C4D411yescharacteristic
122C2×C4⋊Dic3—21no—
123C2×C4⋊Dic3—21no—
124C2×C4⋊Dic3C2311yescharacteristic
125C2×C4⋊Dic3C2311yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127C2×Dic3⋊C4—21no—
128C2×Dic3⋊C4—21no—
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4D411yescharacteristic
131C2×Dic3⋊C4D411yescharacteristic
132C2×C4×Dic3—21no—
133C2×C4×Dic3—21no—
134C2×C4×Dic3—21no—
135C2×C4×Dic3C2311yescharacteristic
136C22×C3⋊C8C2311yescharacteristic
137C22×C3⋊C8C2311yescharacteristic
138#893—28no—
139#893—22no—
140#893D414yes—
141D3×C4⋊C4—28no—
142D3×C4⋊C4—22no—
143D3×C4⋊C4—22no—
144C4×D12—28no—
145C4×D12—22no—
146C4×D12—22no—
147#872—28no—
148#872—22no—
149#872—22no—
150C3×#103—22no—
151C3×#103—22no—
152C3×#95—21no—
153C3×#95—21no—
154#835—22no—
155#835—22no—
156#835C2×C414yescomplemented
157C3⋊#95—21no—
158C3⋊#95—21no—
159C3⋊#95—21no—
160#821—22no—
161#821C2×C414yescomplemented
162(C2×D3)⋊C8—22no—
163(C2×D3)⋊C8C2×C414yescomplemented
164#818—22no—
165#815—22no—
166C8×Dic3—22no—
167#809—22no—
168#807—22no—
169C22×#41—31no—
170C22×Q16C2×D311yescharacteristic
171C22×SD16—31no—
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—31no—
180C2×C4×D4—61no—
181C2×C4×D4—61no—
182C2×#117—31no—
183C2×#117—61no—
184C22×C4⋊C4—31no—
185C22×C4⋊C4—61no—
186#452—38no—
187#440—64no—
188C4×Q16—64no—
189C2×#107—31no—
190C2×#107—31no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103C2×D311yescharacteristic
195C2×#103C2×D311yescharacteristic
196C2×#102—31no—
197C2×#102—31no—
198C2×#102—31no—
199C2×C22⋊C8—31no—
200C2×C22⋊C8—31no—
201C2×#97—31no—
202C2×C4×C8—31no—
203#391C2×D311yescharacteristic
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#340C2×D311yescharacteristic
215#336—31no—
216#336C2×D311yescharacteristic
217C23×D3—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×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8C22×C412yes—
228C2×C3×Q8C22×C412yes—
229C2×C3×Q8C2×D412yes—
230C2×C3×Q8#4112yes—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2411yescharacteristic
238C22×Dic3—21no—
239C22×Dic3—21no—
240C22×Dic3—21no—
241C22×Dic3C2×D411yescharacteristic
242C22×Dic3C2×D411yescharacteristic
243C22×Dic3C2×D411yescharacteristic
244#239—28no—
245#239—28no—
246#239—28no—
247#239—28no—
248C2×D12—24no—
249C2×D12—24no—
250C2×D12—24no—
251C2×D12—21no—
252C2×D12—21no—
253C2×D12—21no—
254C2×D12C22×C412yes—
255C2×D12C2×D412yes—
256C2×D12#4112yes—
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—24no—
264C2×C4×D3—24no—
265C2×C4×D3—24no—
266C2×C4×D3—24no—
267C2×C4×D3—81no—
268C2×C4×D3—81no—
269C2×C4×D3—81no—
270C2×C4×D3—81no—
271C2×C4×D3—81no—
272C2×C4×D3—81no—
273C2×C4×D3C22×C412yes—
274C2×C4×D3#4112yes—
275C3×Q16—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—24no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4C2×D412yes—
287C3×C42—24no—
288C3×C42—21no—
289C3×C42—21no—
290#215—28no—
291(C2×D3)⋊C4—24no—
292(C2×D3)⋊C4—24no—
293(C2×D3)⋊C4—22no—
294(C2×D3)⋊C4—22no—
295(C2×D3)⋊C4—24no—
296(C2×D3)⋊C4—81no—
297C4⋊Dic3—21no—
298C4⋊Dic3—21no—
299C4⋊Dic3—24no—
300C4⋊Dic3—21no—
301C4⋊Dic3—21no—
302C4⋊Dic3—42no—
303C4⋊Dic3C22×C412yes—
304C4⋊Dic3C2×D412yes—
305Dic3⋊C4—24no—
306Dic3⋊C4—24no—
307Dic3⋊C4—22no—
308Dic3⋊C4—22no—
309Dic3⋊C4—81no—
310C4×Dic3—24no—
311C4×Dic3—42no—
312C4×Dic3—81no—
313C4×Dic3C2×D412yes—
314C4×Dic3C2×D412yes—
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×Q8C22×D311yescharacteristic
328C22×Q8C22×D311yescharacteristic
329C22×D4—31no—
330C22×D4—61no—
331C23×C4—31no—
332C23×C4—61no—
333C23×C4—61no—
334C23×C4—61no—
335C23×C4—61no—
336C2×Q16—22no—
337C2×Q16—22no—
338C2×Q16C4×D314yescomplemented
339C2×SD16—34no—
340C2×SD16—62no—
341C2×SD16—62no—
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—34no—
355C4×D4—62no—
356C4×D4—62no—
357C4×D4—68no—
358C4×D4—62no—
359C4×D4—68no—
360#117—62no—
361#117—62no—
362#117—68no—
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—68no—
371C2×C4⋊C4—61no—
372C2×C4⋊C4—61no—
373C2×C4⋊C4—61no—
374C2×C4⋊C4—62no—
375C2×C4⋊C4—61no—
376C2×C4⋊C4—61no—
377C2×C4⋊C4C22×D311yescharacteristic
378C2×C4⋊C4C22×D311yescharacteristic
379C2×C22⋊C4—31no—
380C2×C22⋊C4—31no—
381C2×C22⋊C4—61no—
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—62no—
392#107—62no—
393#103—22no—
394#103—22no—
395#103—34no—
396#103—62no—
397#103—62no—
398#102—34no—
399#102—62no—
400#102—62no—
401C22⋊C8—34no—
402C22⋊C8—62no—
403#97—62no—
404C4×C8—62no—
405#95—21no—
406#95—21no—
407#95—61no—
408#95—61no—
409#95—61no—
410C23×C3C22×D411yescharacteristic
411C22×D3—22no—
412C22×D3—21no—
413C22×D3—22no—
414C22×D3—21no—
415C22×D3—22no—
416C22×D3—21no—
417C22×D3—21no—
418C22×D3—21no—
419C22×D3—21no—
420C22×D3—41no—
421C22×D3—41no—
422C22×D3—41no—
423C22×D3—41no—
424C22×D3C4×D412yes—
425C3×Q8—22no—
426C3×Q8—22no—
427C3×Q8—22no—
428C3×Q8—22no—
429C3×Q8—22no—
430C3×Q8—41no—
431C3×Q8—41no—
432C3×Q8C4×D414yes—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—22no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4C23×C411yescharacteristic
452C2×C3×C4C22×D411yescharacteristic
453C2×C3×C4C22×D411yescharacteristic
454C2×C3×C4C2×#4111yescharacteristic
455C2×C3×C4C2×#4111yescharacteristic
456C2×C3×C4C2×#4111yescharacteristic
457C2×Dic3—21no—
458C2×Dic3—21no—
459C2×Dic3—21no—
460C2×Dic3—21no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—22no—
464C2×Dic3—22no—
465C2×Dic3—41no—
466C2×Dic3—41no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3C4×D412yes—
473C2×Dic3#12012yes—
474C2×Dic3#12012yes—
475D12—216no—
476D12—22no—
477D12—22no—
478D12—22no—
479D12C4×D414yes—
480C4×D3—216no—
481C4×D3—22no—
482C4×D3—22no—
483C4×D3—22no—
484C4×D3—22no—
485C4×D3—84no—
486C4×D3—84no—
487C4×D3—84no—
488C3×C8—22no—
489C3×C8—41no—
490C3⋊C8—22no—
491C3⋊C8—41no—
492C24—31no—
493C24—61no—
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—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8C2×C4×D312yes—
507C2×Q8C2×C4×D312yes—
508C2×Q8D3×D412yes—
509C2×Q8#23712yes—
510C2×D4—32no—
511C2×D4—32no—
512C2×D4—32no—
513C2×D4—64no—
514C2×D4—64no—
515C2×D4—64no—
516C2×D4—61no—
517C2×D4—61no—
518C2×D4—61no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—31no—
524C22×C4—31no—
525C22×C4—31no—
526C22×C4—32no—
527C22×C4—32no—
528C22×C4—64no—
529C22×C4—64no—
530C22×C4—64no—
531C22×C4—64no—
532C22×C4—64no—
533C22×C4—64no—
534C22×C4—61no—
535C22×C4—61no—
536C22×C4—61no—
537C22×C4—61no—
538C22×C4—61no—
539C22×C4—61no—
540C22×C4—61no—
541C22×C4—241no—
542C22×C4—241no—
543C22×C4—241no—
544C22×C4—241no—
545C22×C4—241no—
546C22×C4—241no—
547C22×C4D3×D411yescharacteristic
548C22×C4D3×D411yescharacteristic
549C22×C4C23×D311yescharacteristic
550Q16—28no—
551SD16—68no—
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—24no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—32no—
569C4⋊C4—32no—
570C4⋊C4—62no—
571C4⋊C4—62no—
572C4⋊C4—64no—
573C4⋊C4—64no—
574C4⋊C4—64no—
575C4⋊C4—61no—
576C4⋊C4—61no—
577C4⋊C4—61no—
578C4⋊C4—61no—
579C4⋊C4—122no—
580C4⋊C4—241no—
581C4⋊C4D3×D412yes—
582C22⋊C4—62no—
583C22⋊C4—62no—
584C22⋊C4—64no—
585C22⋊C4—64no—
586C22⋊C4—64no—
587C22⋊C4—241no—
588C42—24no—
589C42—21no—
590C42—21no—
591C42—32no—
592C42—32no—
593C42—64no—
594C42—122no—
595C42—241no—
596C22×C3C2×C4×D411yescharacteristic
597C22×C3C2×#12011yescharacteristic
598C22×C3#52511yescharacteristic
599C22×C3#57611yescharacteristic
600C22×C3#57711yescharacteristic
601C22×C3#57811yescharacteristic
602C22×C3#57811yescharacteristic
603C2×D3—22no—
604C2×D3—22no—
605C2×D3—22no—
606C2×D3—24no—
607C2×D3—41no—
608C2×D3—42no—
609C2×D3—41no—
610C2×D3—42no—
611C2×D3—42no—
612C2×D3—42no—
613C2×D3—41no—
614C2×D3—42no—
615C2×D3—41no—
616C2×D3—42no—
617C3×C4—24no—
618C3×C4—41no—
619C3×C4—41no—
620C3×C4—42no—
621C3×C4—42no—
622C3×C4—81no—
623C3×C4C2×C4×D411yescharacteristic
624C3×C4C2×C4×D411yescharacteristic
625C3×C4#52511yescharacteristic
626C3×C4#52511yescharacteristic
627Dic3—22no—
628Dic3—22no—
629Dic3—22no—
630Dic3—42no—
631Dic3—42no—
632Dic3—81no—
633C23—32no—
634C23—61no—
635C23—61no—
636C23—61no—
637C23—61no—
638C23—62no—
639C23—62no—
640C23—61no—
641C23—62no—
642C23—61no—
643C23—121no—
644C23—121no—
645C23—121no—
646C23—121no—
647C23C2×D3×D411yescharacteristic
648Q8—22no—
649Q8—22no—
650Q8—22no—
651Q8—22no—
652Q8—22no—
653Q8—41no—
654Q8—41no—
655Q8#67⋊C414yes—
656D4—34no—
657D4—616no—
658D4—62no—
659D4—62no—
660D4—62no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—32no—
673C2×C4—32no—
674C2×C4—32no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—616no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—62no—
690C2×C4—62no—
691C2×C4—62no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—62no—
695C2×C4—121no—
696C2×C4—121no—
697C2×C4—121no—
698C2×C4—121no—
699C2×C4—121no—
700C2×C4—121no—
701C2×C4—121no—
702C2×C4—244no—
703C2×C4—244no—
704C2×C4—244no—
705C2×C4C22×C4×D311yescharacteristic
706C2×C4C2×D3×D411yescharacteristic
707C2×C4C2×D3×D411yescharacteristic
708C2×C4C2×#23711yescharacteristic
709C2×C4D3×#4111yescharacteristic
710C2×C4D3×#4111yescharacteristic
711C8—22no—
712C8—41no—
713C8—62no—
714C8—121no—
715C2×C3C4×#12011yescharacteristic
716C2×C3#294711yescharacteristic
717C2×C3#295111yescharacteristic
718C2×C3#301111yescharacteristic
719C2×C3#301211yescharacteristic
720C2×C3#312011yescharacteristic
721C2×C3#312411yescharacteristic
722D3—42no—
723D3—44no—
724C22—62no—
725C22—64no—
726C22—62no—
727C22—62no—
728C22—121no—
729C22—122no—
730C22—121no—
731C22—122no—
732C22—121no—
733C22—122no—
734C22—122no—
735C22—121no—
736C22—122no—
737C22—122no—
738C22C4×D3×D411yescharacteristic
739C22D3×#12011yescharacteristic
740C22#560611yescharacteristic
741C22#576611yescharacteristic
742C22#576911yescharacteristic
743C22#577811yescharacteristic
744C22#577911yescharacteristic
745C4—24no—
746C4—41no—
747C4—41no—
748C4—42no—
749C4—42no—
750C4—62no—
751C4—62no—
752C4—62no—
753C4—81no—
754C4—122no—
755C4—122no—
756C4—241no—
757C4C2×#67⋊C411yescharacteristic
758C4C4×D3×D411yescharacteristic
759C4#560611yescharacteristic
760C4#565611yescharacteristic
761C3#2146511yescharacteristic, complemented, Sylow
762C2—122no—
763C2—124no—
764C2#7465911yescharacteristic
765C2#7972111yescharacteristic
766C2#7983011yescharacteristic
767C2#8018511yescharacteristic
768C2#8023111yescharacteristic
769C2#8046011yescharacteristic
770C2#8057411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1878C2
socleC23×C3C22×D4
prime radicalC22×#239C22
cosocleC22×C3×C4C24
hypercenter#1878D3
hypocenterC3#21465
LCSG ▷ C2×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×Dic3×Q16C2semidirect
4. C2×#4817C2semidirect
5. #76611C2semidirect
6. C3×#1878C2semidirect
7. #71628C2semidirect
8. #70268C2semidirect
10. #70220C2semidirect
11. #69687C2semidirect
12. #68874C2semidirect
13. #68780C2semidirect
14. #68670C2semidirect
15. #68601C2semidirect
40. #5187C4semidirect
70. #1878D3semidirect
97. C2×C3×Q16C2×C4semidirect
108. #946C2×C4semidirect
115. C2×#215C2×C4semidirect
156. #835C2×C4semidirect
161. #821C2×C4semidirect
163. (C2×D3)⋊C8C2×C4semidirect
338. C2×Q16C4×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×#55742
C2×#51872
C2×Dic3×Q162
C2×#48172
#766112
C3×#18782
#716282
#702682
#702672
#702202
#696872
#688742
#687802
#686702
#686012
#214653