Finite Group Databasebeta

← #10801013

Subgroups — #10801013

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×C4×#216C211yesmaximal, characteristic, complemented
3C2×#4808C211yesmaximal, characteristic
4C2×#4710C211yesmaximal, characteristic, complemented
5#73762C211yesmaximal, characteristic, complemented
6C3×#1763C211yesmaximal, characteristic, complemented
7#70267C211yesmaximal, characteristic
8#70239C211yesmaximal, characteristic, complemented
9#70236C211yesmaximal, characteristic, complemented
10#69830C211yesmaximal, characteristic, complemented
11C4×#809C211yesmaximal, characteristic, complemented
12#68896C211yesmaximal, characteristic, complemented
13#68894C211yesmaximal, characteristic, complemented
14#68878C211yesmaximal, characteristic, complemented
15#68874C211yesmaximal, characteristic, complemented
16#21465—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C2×C3×C4×Q8C2211yescharacteristic
19C2×Q8×Dic3C2211yescharacteristic
20C22×#216C2211yescharacteristic
21C22×#204C2211yescharacteristic
22#5574—24no—
23#5574—24no—
24C2×#897C2211yescharacteristic
25C2×#893—21no—
26C2×#893C2211yescharacteristic
27C2×D3×C4⋊C4—21no—
28C2×D3×C4⋊C4C2211yescharacteristic
29C2×C4×D12—21no—
30C2×C4×D12C2211yescharacteristic
31C2×#872—21no—
32C2×#872C2211yescharacteristic
33C2×C4×Dic6C2211yescharacteristic
34C2×C3×#103C2211yescharacteristic
35C2×C3×#103C2211yescharacteristic
36C2×C3×#97C2211yescharacteristic
37C3×C4×C4⋊C4C2211yescharacteristic
38C2×#835C2211yescharacteristic
39C2×#821C2211yescharacteristic
40C2×(C2×D3)⋊C8C2211yescharacteristic
41C2×(C2×D3)⋊C8C2211yescharacteristic
42C2×#818C2211yescharacteristic
43C2×#816C2211yescharacteristic
44C4×#216—24no—
45#4987C2211yescharacteristic
46#4984C2211yescharacteristic
47#4973C2211yescharacteristic
48C2×#810C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#807C2211yescharacteristic
52#4940—21no—
53#4928—21no—
54C2×C4×C3⋊C8C2211yescharacteristic
55#4808C418yescomplemented
56#4710—24no—
57#4670—21no—
58#4653—21no—
59C3×#340C2211yescharacteristic
60C3×#340C2211yescharacteristic
61#4550C2211yescharacteristic
62#4550C2211yescharacteristic
63#4529C2211yescharacteristic
64#4529C2211yescharacteristic
65C2×#520—31no—
66C2×#452—31no—
67C2×#440—31no—
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#1763D311yescharacteristic, complemented
78C4×#102—31no—
79#1750—31no—
80C22×C3×Q8C2311yescharacteristic
81C2×#239—22no—
82C2×#239—22no—
83C2×#239—22no—
84C2×#239—22no—
85C2×#239—22no—
86C2×#239C2×C414yes—
87C22×D12—21no—
88C22×D12C2311yescharacteristic
89C22×C4×D3—21no—
90C22×C4×D3—21no—
91C22×C4×D3—21no—
92C22×C4×D3—21no—
93C22×C4×D3C2311yescharacteristic
94C22×Dic6C2311yescharacteristic
95C22×C3×C8C2311yescharacteristic
96C22×C3×C8C2311yescharacteristic
97C3×C4×Q8—22no—
98C3×C4×Q8D414yes—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4C2311yescharacteristic
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C4⋊C4C2311yescharacteristic
103C2×C3×C42—21no—
104C2×C3×C42—21no—
105C2×C3×C42C2311yescharacteristic
106Q8×Dic3—22no—
107Q8×Dic3—22no—
108C2×#216—22no—
109C2×#216—22no—
110C2×#216C2×C414yescomplemented
111C2×(C2×D3)⋊C4—21no—
112C2×(C2×D3)⋊C4—21no—
113C2×(C2×D3)⋊C4—21no—
114C2×(C2×D3)⋊C4—21no—
115C2×(C2×D3)⋊C4D411yescharacteristic
116C2×(C2×D3)⋊C4D411yescharacteristic
117C2×C4⋊Dic3—21no—
118C2×C4⋊Dic3—21no—
119C2×C4⋊Dic3—21no—
120C2×C4⋊Dic3C2311yescharacteristic
121C2×C4⋊Dic3C2311yescharacteristic
122C2×Dic3⋊C4—21no—
123C2×Dic3⋊C4—21no—
124C2×Dic3⋊C4D411yescharacteristic
125C2×Dic3⋊C4D411yescharacteristic
126C2×C4×Dic3—21no—
127C2×C4×Dic3—21no—
128C2×C4×Dic3C2311yescharacteristic
129C22×C3⋊C8C2311yescharacteristic
130C22×C3⋊C8C2311yescharacteristic
131C2×#204—22no—
132C2×#204—22no—
133C2×#204C2×C414yescomplemented
134#897—22no—
135#897C2×C414yescomplemented
136#893—28no—
137#893—22no—
138#893—22no—
139D3×C4⋊C4—28no—
140D3×C4⋊C4—22no—
141D3×C4⋊C4—22no—
142C4×D12—28no—
143C4×D12—22no—
144C4×D12D414yes—
145#872—28no—
146#872—22no—
147#872—22no—
148C4×Dic6—22no—
149C4×Dic6—22no—
150C3×#103—22no—
151C3×#103C2×C414yescomplemented
152C3×#97—22no—
153C3×#95—21no—
154#835—22no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159#821—22no—
160(C2×D3)⋊C8—22no—
161(C2×D3)⋊C8C2×C414yescomplemented
162#818—22no—
163#816—22no—
164#810—22no—
165#809—22no—
166#809C2×C414yescomplemented
167#807—22no—
168C4×C3⋊C8—22no—
169C22×#41—31no—
170C22×Q16—31no—
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×#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⋊C4C2×D311yescharacteristic
211#340—31no—
212#340—31no—
213#340C2×D311yescharacteristic
214#340C2×D311yescharacteristic
215#336—31no—
216#336—31no—
217C23×D3—21no—
218C23×D3C2×D411yescharacteristic
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8C22×C412yes—
223C2×C3×Q8C2×D412yes—
224C2×C3×Q8#4112yes—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4C2×D411yescharacteristic
230C22×C3×C4C2×D411yescharacteristic
231C22×C3×C4C2411yescharacteristic
232C22×Dic3—21no—
233C22×Dic3—21no—
234C22×Dic3—21no—
235C22×Dic3C2×D411yescharacteristic
236C22×Dic3C2×D411yescharacteristic
237C22×Dic3C2×D411yescharacteristic
238#239—28no—
239#239—28no—
240#239—28no—
241#239—28no—
242C2×D12—24no—
243C2×D12—24no—
244C2×D12—24no—
245C2×D12—21no—
246C2×D12—21no—
247C2×D12—21no—
248C2×D12C22×C412yes—
249C2×D12C2×D412yes—
250C2×D12#4112yes—
251C2×C4×D3—24no—
252C2×C4×D3—24no—
253C2×C4×D3—21no—
254C2×C4×D3—21no—
255C2×C4×D3—21no—
256C2×C4×D3—21no—
257C2×C4×D3—24no—
258C2×C4×D3—24no—
259C2×C4×D3—24no—
260C2×C4×D3—24no—
261C2×C4×D3—81no—
262C2×C4×D3—81no—
263C2×C4×D3—81no—
264C2×C4×D3—81no—
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×Dic6—21no—
273C2×Dic6—21no—
274C2×Dic6C22×C412yes—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8C22×C412yes—
281C3×C4⋊C4—24no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4C22×C412yes—
287C3×C4⋊C4C2×D412yes—
288C3×C42—24no—
289C3×C42—81no—
290C3×C42C2×D412yes—
291C3×C42C2×D412yes—
292#216—28no—
293(C2×D3)⋊C4—24no—
294(C2×D3)⋊C4—24no—
295(C2×D3)⋊C4—22no—
296(C2×D3)⋊C4—24no—
297(C2×D3)⋊C4—22no—
298(C2×D3)⋊C4—81no—
299C4⋊Dic3—24no—
300C4⋊Dic3—21no—
301C4⋊Dic3—24no—
302C4⋊Dic3—21no—
303C4⋊Dic3—21no—
304C4⋊Dic3—81no—
305C4⋊Dic3C2×D412yes—
306Dic3⋊C4—24no—
307Dic3⋊C4—22no—
308Dic3⋊C4—22no—
309Dic3⋊C4—42no—
310C4×Dic3—24no—
311C4×Dic3—21no—
312C4×Dic3—21no—
313C4×Dic3—42no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8C22×C412yes—
320#204—28no—
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—31no—
330C22×D4—61no—
331C23×C4—31no—
332C23×C4—61no—
333C23×C4—61no—
334C23×C4—61no—
335C23×C4—61no—
336C2×Q16—34no—
337C2×Q16—62no—
338C2×Q16—62no—
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—62no—
350C4×Q8—62no—
351C4×Q8—62no—
352C4×Q8—62no—
353C4×Q8D1214yes—
354C4×D4—34no—
355C4×D4—68no—
356C4×D4—62no—
357C4×D4—68no—
358C4×D4—62no—
359C4×D4—62no—
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—62no—
369C2×C4⋊C4—68no—
370C2×C4⋊C4—61no—
371C2×C4⋊C4—61no—
372C2×C4⋊C4—61no—
373C2×C4⋊C4—62no—
374C2×C4⋊C4—61no—
375C2×C4⋊C4—61no—
376C2×C4⋊C4C22×D311yescharacteristic
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—21no—
387C2×C42—31no—
388C2×C42—61no—
389C2×C42—61no—
390C2×C42C22×D311yescharacteristic
391#107—62no—
392#107—62no—
393#103—22no—
394#103—62no—
395#103—62no—
396#103—62no—
397#103C4×D314yescomplemented
398#102—34no—
399#102—62no—
400#102—62no—
401C22⋊C8—34no—
402C22⋊C8—62no—
403#97—22no—
404C4×C8—62no—
405#95—21no—
406#95—61no—
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×Q8C4×D414yes—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—41no—
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#12012yes—
446C2×C3×C4#12012yes—
447C2×C3×C4C23×C411yescharacteristic
448C2×C3×C4C22×D411yescharacteristic
449C2×C3×C4C22×D411yescharacteristic
450C2×C3×C4C2×#4111yescharacteristic
451C2×C3×C4C2×#4111yescharacteristic
452C2×C3×C4C2×#4111yescharacteristic
453C2×Dic3—21no—
454C2×Dic3—21no—
455C2×Dic3—22no—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—22no—
459C2×Dic3—21no—
460C2×Dic3—21no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—41no—
464C2×Dic3—41no—
465C2×Dic3—41no—
466C2×Dic3—41no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3C4×D412yes—
471D12—216no—
472D12—22no—
473D12—22no—
474D12—22no—
475D12C4×D414yes—
476C4×D3—216no—
477C4×D3—22no—
478C4×D3—22no—
479C4×D3—22no—
480C4×D3—22no—
481C4×D3—84no—
482C4×D3—84no—
483C4×D3—84no—
484Dic6—22no—
485Dic6—22no—
486Dic6—41no—
487Dic6—41no—
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—32no—
502C2×Q8—61no—
503C2×Q8—61no—
504C2×Q8—61no—
505C2×Q8—61no—
506C2×Q8—61no—
507C2×Q8C2×C4×D312yes—
508C2×Q8C2×D1212yes—
509C2×Q8#23512yes—
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—32no—
525C22×C4—32no—
526C22×C4—31no—
527C22×C4—31no—
528C22×C4—64no—
529C22×C4—64no—
530C22×C4—64no—
531C22×C4—64no—
532C22×C4—64no—
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—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—68no—
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—21no—
569C4⋊C4—32no—
570C4⋊C4—64no—
571C4⋊C4—64no—
572C4⋊C4—64no—
573C4⋊C4—62no—
574C4⋊C4—62no—
575C4⋊C4—61no—
576C4⋊C4—61no—
577C4⋊C4—61no—
578C4⋊C4—122no—
579C4⋊C4—241no—
580C4⋊C4C2×C4×D312yes—
581C4⋊C4C2×D1212yes—
582C22⋊C4—64no—
583C22⋊C4—64no—
584C22⋊C4—62no—
585C22⋊C4—62no—
586C22⋊C4—64no—
587C22⋊C4—241no—
588C42—24no—
589C42—64no—
590C42—61no—
591C42—61no—
592C42—81no—
593C42—122no—
594C42C2×D1212yes—
595C42D3×D412yes—
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—22no—
618C3×C4—22no—
619C3×C4—24no—
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—41no—
629Dic3—41no—
630Dic3—42no—
631Dic3—42no—
632Dic3—81no—
633C23—32no—
634C23—62no—
635C23—61no—
636C23—61no—
637C23—61no—
638C23—61no—
639C23—61no—
640C23—62no—
641C23—62no—
642C23—61no—
643C23—121no—
644C23—121no—
645C23—121no—
646C23—121no—
647C23C2×D3×D411yescharacteristic
648Q8—22no—
649Q8—22no—
650Q8—22no—
651Q8—62no—
652Q8—62no—
653Q8—121no—
654Q8—121no—
655Q8C4×D1214yes—
656D4—34no—
657D4—616no—
658D4—62no—
659D4—62no—
660D4—62no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—32no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—616no—
679C2×C4—61no—
680C2×C4—61no—
681C2×C4—62no—
682C2×C4—62no—
683C2×C4—62no—
684C2×C4—62no—
685C2×C4—61no—
686C2×C4—62no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—62no—
693C2×C4—121no—
694C2×C4—121no—
695C2×C4—121no—
696C2×C4—121no—
697C2×C4—121no—
698C2×C4—121no—
699C2×C4—121no—
700C2×C4—244no—
701C2×C4—244no—
702C2×C4—244no—
703C2×C4#88212yes—
704C2×C4#88212yes—
705C2×C4C22×C4×D311yescharacteristic
706C2×C4C22×D1211yescharacteristic
707C2×C4C2×#23511yescharacteristic
708C2×C4C2×D3×D411yescharacteristic
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—64no—
725C22—62no—
726C22—62no—
727C22—62no—
728C22—121no—
729C22—122no—
730C22—121no—
731C22—122no—
732C22—122no—
733C22—121no—
734C22—122no—
735C22—122no—
736C22—121no—
737C22—122no—
738C22C2×#88211yescharacteristic
739C22C4×D3×D411yescharacteristic
740C22#554711yescharacteristic
741C22#577411yescharacteristic
742C22#577811yescharacteristic
743C22#577911yescharacteristic
744C22#577911yescharacteristic
745C4—22no—
746C4—24no—
747C4—22no—
748C4—42no—
749C4—42no—
750C4—62no—
751C4—81no—
752C4—121no—
753C4—122no—
754C4—122no—
755C4—121no—
756C4—241no—
757C4C2×C4×D1211yescharacteristic
758C4#552411yescharacteristic
759C4C4×D3×D411yescharacteristic
760C4#554711yescharacteristic
761C3#2146511yescharacteristic, complemented, Sylow
762C2—122no—
763C2—124no—
764C2C4×#88211yescharacteristic
765C2#7888611yescharacteristic
766C2#7896111yescharacteristic
767C2#7977811yescharacteristic
768C2#7981311yescharacteristic
769C2#7983011yescharacteristic
770C2#7984911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1763C2
socleC23×C3C22×D4
prime radicalC22×#239C22
cosocleC22×C3×C4C24
hypercenter#1763D3
hypocenterC3#21465
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
2. C2×C4×#216C2semidirect
4. C2×#4710C2semidirect
5. #73762C2semidirect
6. C3×#1763C2semidirect
8. #70239C2semidirect
9. #70236C2semidirect
10. #69830C2semidirect
11. C4×#809C2semidirect
12. #68896C2semidirect
13. #68894C2semidirect
14. #68878C2semidirect
15. #68874C2semidirect
55. #4808C4semidirect
77. #1763D3semidirect
110. C2×#216C2×C4semidirect
133. C2×#204C2×C4semidirect
135. #897C2×C4semidirect
151. C3×#103C2×C4semidirect
161. (C2×D3)⋊C8C2×C4semidirect
166. #809C2×C4semidirect
397. #103C4×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×C4×#2162
C2×#48082
C2×#47102
#737622
C3×#17632
#702672
#702392
#702362
#698302
C4×#8092
#688962
#688942
#688782
#688742
#214653