Finite Group Databasebeta

← #10801007

Subgroups — #10801007

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×#5523C211yesmaximal, characteristic
2C3×#2323C211yesmaximal, characteristic, complemented
3C2×#5047C211yesmaximal, characteristic
4C2×#5026C211yesmaximal, characteristic, complemented
5C2×C4×#216C211yesmaximal, characteristic, complemented
6#71692C211yesmaximal, characteristic, complemented
7#71582C211yesmaximal, characteristic, complemented
8#69690C211yesmaximal, characteristic, complemented
9#69687C211yesmaximal, characteristic, complemented
10#69631C211yesmaximal, characteristic, complemented
11#69625C211yesmaximal, characteristic, complemented
12#69522C211yesmaximal, characteristic
13#69504C211yesmaximal, characteristic, complemented
14#69475C211yesmaximal, characteristic, complemented
15C4×#809C211yesmaximal, characteristic, complemented
16#21465—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C2×C3×C22⋊Q8C2211yescharacteristic
19C2×C3×C4×Q8C2211yescharacteristic
20C2×C3×#117C2211yescharacteristic
21C22×#216C2211yescharacteristic
22C22×#215C2211yescharacteristic
23C22×C4⋊Dic3C2211yescharacteristic
24#5523—24no—
25#5523—24no—
26C2×#892—21no—
27C2×D3×C4⋊C4—21no—
28C2×#67⋊C4—21no—
29C2×#67⋊C4—21no—
30C2×C4×D12C2211yescharacteristic
31C2×C4×D12C2211yescharacteristic
32C2×C4×Dic6C2211yescharacteristic
33C2×C4×Dic6C2211yescharacteristic
34C3×#391C2211yescharacteristic
35C3×#389—21no—
36C3×#389C2211yescharacteristic
37C3×#388—21no—
38C3×#388—21no—
39C3×#387—21no—
40C3×#380C2211yescharacteristic
41C3×C4×C4⋊C4C2211yescharacteristic
42C2×#835C2211yescharacteristic
43C2×#835C2211yescharacteristic
44C2×#830C2211yescharacteristic
45C2×#830C2211yescharacteristic
46#5047C418yescomplemented
47C4×#216—24no—
48#5026—24no—
49C2×#810C2211yescharacteristic
50C2×#810C2211yescharacteristic
51C2×#810C2211yescharacteristic
52C2×#809C2211yescharacteristic
53C2×#809C2211yescharacteristic
54C2×#809C2211yescharacteristic
55C2×#807C2211yescharacteristic
56C2×#807C2211yescharacteristic
57C2×#803C2211yescharacteristic
58C2×C4×C3⋊C8C2211yescharacteristic
59#4529C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4524C2211yescharacteristic
64#4524C2211yescharacteristic
65C2×#520—31no—
66C2×#452—31no—
67C2×#440—31no—
68C2×C4×Q16—31no—
69#2323D311yescharacteristic, complemented
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
81C23×C3×C4C2311yescharacteristic
82C22×#67—21no—
83C23×Dic3—21no—
84C2×#235—22no—
85C2×#235—22no—
86C2×#235—22no—
87C2×#235—22no—
88C2×#235—22no—
89C2×#235C2×C414yes—
90C22×D12C2311yescharacteristic
91C22×C4×D3—21no—
92C22×C4×D3—21no—
93C22×C4×D3—21no—
94C22×Dic6C2311yescharacteristic
95C3×C22⋊Q8—22no—
96C3×C22⋊Q8C2×C414yescomplemented
97C3×C4×Q8—22no—
98C3×C4×Q8—22no—
99C3×#117—22no—
100C3×#117—22no—
101C2×C3×C4⋊C4—21no—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4D411yescharacteristic
105C2×C3×C4⋊C4D411yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C22⋊C4—21no—
110C2×C3×C22⋊C4—21no—
111C2×C3×C22⋊C4D411yescharacteristic
112C2×C3×C22⋊C4D411yescharacteristic
113C2×C3×C42—21no—
114C2×C3×C42—21no—
115C2×C3×C42C2311yescharacteristic
116C2×C3×C42C2311yescharacteristic
117C2×#216—22no—
118C2×#216—22no—
119C2×#216C2×C414yescomplemented
120C2×#215—22no—
121C2×#215—22no—
122C2×#215C2×C414yescomplemented
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×C4⋊Dic3—21no—
126C2×C4⋊Dic3—22no—
127C2×C4⋊Dic3—22no—
128C2×C4⋊Dic3C2311yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130C2×Dic3⋊C4—21no—
131C2×Dic3⋊C4—21no—
132C2×C4×Dic3—21no—
133C2×C4×Dic3—21no—
134C22×C3⋊C8C2311yescharacteristic
135C22×C3⋊C8C2311yescharacteristic
136C22×C3⋊C8C2311yescharacteristic
137C22×C3⋊C8C2311yescharacteristic
138#892—28no—
139D3×C4⋊C4—28no—
140#67⋊C4—28no—
141#67⋊C4—28no—
142C4×D12—22no—
143C4×D12—22no—
144C4×D12—22no—
145C4×D12D414yes—
146C4×Dic6—22no—
147C4×Dic6—22no—
148C4×Dic6—22no—
149C4×Dic6D414yes—
150C3×#95—21no—
151C3×#95—21no—
152C3×#95—21no—
153C3×#95—21no—
154C3×#95—21no—
155#835—22no—
156#835—22no—
157#830—22no—
158#830C2×C414yescomplemented
159#810—22no—
160#810—22no—
161#810C2×C414yescomplemented
162#809—22no—
163#809—22no—
164#809C2×C414yescomplemented
165#807—22no—
166#807—22no—
167#803—22no—
168C4×C3⋊C8—22no—
169C22×#41—31no—
170C22×Q16—31no—
171C22×SD16—31no—
172C2×C22⋊Q8C2×D311yescharacteristic
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—61no—
183C2×#117C2×D311yescharacteristic
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×#103—31no—
195C2×#103—31no—
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—21no—
205#389C2×D311yescharacteristic
206#388—21no—
207#388—21no—
208#387—21no—
209#380C2×D311yescharacteristic
210C4×C4⋊C4C2×D311yescharacteristic
211#340—31no—
212#340—31no—
213#340—31no—
214#340—31no—
215#336—31no—
216#336—31no—
217C24×C3C2×D411yescharacteristic
218C23×D3—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8C22×C412yes—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4C22×C412yes—
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2×D411yescharacteristic
238C22×C3×C4C2×D411yescharacteristic
239C22×C3×C4#4112yes—
240C22×C3×C4C2411yescharacteristic
241C2×#67—24no—
242C2×#67—24no—
243C2×#67—24no—
244C22×Dic3—21no—
245C22×Dic3—21no—
246C22×Dic3—21no—
247C22×Dic3—24no—
248C22×Dic3—81no—
249C22×Dic3—81no—
250#235—28no—
251#235—28no—
252#235—28no—
253#235—28no—
254C2×D12—21no—
255C2×D12—21no—
256C2×D12—21no—
257C2×D12C22×C412yes—
258C2×D12C2×D412yes—
259C2×D12#4112yes—
260C2×C4×D3—24no—
261C2×C4×D3—24no—
262C2×C4×D3—24no—
263C2×C4×D3—24no—
264C2×C4×D3—24no—
265C2×C4×D3—81no—
266C2×C4×D3—81no—
267C2×C4×D3—81no—
268C2×C4×D3—81no—
269C2×Dic6—21no—
270C2×Dic6—21no—
271C2×Dic6—21no—
272C2×Dic6C22×C412yes—
273C2×Dic6C2×D412yes—
274C2×Dic6#4112yes—
275C3×C4⋊C4—24no—
276C3×C4⋊C4—22no—
277C3×C4⋊C4—22no—
278C3×C4⋊C4—21no—
279C3×C4⋊C4—21no—
280C3×C4⋊C4—21no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—42no—
284C3×C4⋊C4—81no—
285C3×C4⋊C4C22×C412yes—
286C3×C22⋊C4—24no—
287C3×C22⋊C4—22no—
288C3×C22⋊C4—22no—
289C3×C22⋊C4—81no—
290C3×C42—21no—
291C3×C42—21no—
292C3×C42—42no—
293C3×C42—81no—
294C3×C42C2×D412yes—
295C3×C42C2×D412yes—
296#216—28no—
297#215—28no—
298(C2×D3)⋊C4—24no—
299(C2×D3)⋊C4—24no—
300C4⋊Dic3—24no—
301C4⋊Dic3—21no—
302C4⋊Dic3—21no—
303C4⋊Dic3C2×D412yes—
304C4⋊Dic3C2×D412yes—
305Dic3⋊C4—24no—
306Dic3⋊C4—24no—
307C4×Dic3—24no—
308C4×Dic3—24no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8C22×C412yes—
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—31no—
330C22×D4—61no—
331C23×C4—61no—
332C23×C4—61no—
333C23×C4—61no—
334C23×C4—61no—
335C23×C4C22×D311yescharacteristic
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×C8—31no—
345C22×C8—31no—
346C22⋊Q8—22no—
347C22⋊Q8C4×D314yescomplemented
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—68no—
359C4×D4—62no—
360#117—22no—
361#117—22no—
362#117—68no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—68no—
369C2×C4⋊C4—62no—
370C2×C4⋊C4—62no—
371C2×C4⋊C4—61no—
372C2×C4⋊C4—61no—
373C2×C4⋊C4—61no—
374C2×C4⋊C4#6711yescharacteristic
375C2×C4⋊C4#6711yescharacteristic
376C2×C4⋊C4C22×D311yescharacteristic
377C2×C4⋊C4C22×D311yescharacteristic
378C2×C4⋊C4C22×D311yescharacteristic
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—61no—
382C2×C22⋊C4—61no—
383C2×C22⋊C4#6711yescharacteristic
384C2×C22⋊C4#6711yescharacteristic
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—61no—
388C2×C42—61no—
389C2×C42C22×D311yescharacteristic
390C2×C42C22×D311yescharacteristic
391#107—62no—
392#107—62no—
393#103—34no—
394#103—62no—
395#103—62no—
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—21no—
408#95—21no—
409#95—21no—
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3C4×D412yes—
417C23×C3C22×D411yescharacteristic
418C22×D3—22no—
419C22×D3—22no—
420C22×D3—22no—
421C22×D3—41no—
422C22×D3—41no—
423C22×D3—41no—
424C22×D3—41no—
425C3×Q8—22no—
426C3×Q8—22no—
427C3×Q8—41no—
428C3×Q8—41no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4C4×D412yes—
458C2×C3×C4#12012yes—
459C2×C3×C4#12012yes—
460C2×C3×C4C23×C411yescharacteristic
461C2×C3×C4C22×D411yescharacteristic
462C2×C3×C4C22×D411yescharacteristic
463C2×C3×C4C2×#4111yescharacteristic
464C2×C3×C4C2×#4111yescharacteristic
465C2×C3×C4C2×#4111yescharacteristic
466#67—216no—
467C2×Dic3—22no—
468C2×Dic3—22no—
469C2×Dic3—22no—
470C2×Dic3—22no—
471C2×Dic3—22no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—84no—
477D12—22no—
478D12—22no—
479D12—22no—
480D12C4×D414yes—
481C4×D3—216no—
482C4×D3—84no—
483C4×D3—84no—
484Dic6—22no—
485Dic6—22no—
486Dic6—22no—
487Dic6C4×D414yes—
488C3⋊C8—22no—
489C3⋊C8—22no—
490C3⋊C8—41no—
491C3⋊C8—41no—
492C24—61no—
493C24C2×#6711yescharacteristic
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—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—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—64no—
528C22×C4—64no—
529C22×C4—64no—
530C22×C4—61no—
531C22×C4—64no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—64no—
535C22×C4—64no—
536C22×C4—241no—
537C22×C4—241no—
538C22×C4—241no—
539C22×C4—241no—
540C22×C4—241no—
541C22×C4—241no—
542C22×C4C2×C4×D312yes—
543C22×C4#23512yes—
544C22×C4C2×#6711yescharacteristic
545C22×C4C2×#6711yescharacteristic
546C22×C4C2×#6711yescharacteristic
547C22×C4C2×#6711yescharacteristic
548C22×C4C2×#6711yescharacteristic
549C22×C4C23×D311yescharacteristic
550Q16—68no—
551SD16—68no—
552C2×C8—32no—
553C2×C8—32no—
554C2×C8—61no—
555C2×C8—61no—
556C2×C8—61no—
557C2×C8—61no—
558C2×C8—61no—
559C2×C8—61no—
560C2×C8—61no—
561C2×C8—61no—
562C2×C8—61no—
563C2×C8—61no—
564C4⋊C4—24no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—32no—
573C4⋊C4—32no—
574C4⋊C4—42no—
575C4⋊C4—64no—
576C4⋊C4—64no—
577C4⋊C4—64no—
578C4⋊C4—61no—
579C4⋊C4—61no—
580C4⋊C4—81no—
581C4⋊C4C2×C4×D312yes—
582C22⋊C4—24no—
583C22⋊C4—22no—
584C22⋊C4—22no—
585C22⋊C4—64no—
586C22⋊C4—64no—
587C22⋊C4—81no—
588C42—21no—
589C42—21no—
590C42—42no—
591C42—64no—
592C42—64no—
593C42—81no—
594C42D3×D412yes—
595C42D3×D412yes—
596C22×C3—22no—
597C22×C3—22no—
598C22×C3—22no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3C2×C4×D411yescharacteristic
604C22×C3C2×#12011yescharacteristic
605C22×C3#52511yescharacteristic
606C22×C3#57611yescharacteristic
607C22×C3#57711yescharacteristic
608C22×C3#57811yescharacteristic
609C22×C3#57811yescharacteristic
610C2×D3—24no—
611C2×D3—42no—
612C2×D3—42no—
613C2×D3—42no—
614C2×D3—42no—
615C2×D3—42no—
616C2×D3—42no—
617C3×C4—22no—
618C3×C4—22no—
619C3×C4—22no—
620C3×C4—42no—
621C3×C4—41no—
622C3×C4—41no—
623C3×C4—42no—
624C3×C4—81no—
625C3×C4—81no—
626C3×C4C2×C4×D411yescharacteristic
627C3×C4C2×C4×D411yescharacteristic
628C3×C4#52511yescharacteristic
629C3×C4#52511yescharacteristic
630Dic3—24no—
631Dic3—42no—
632Dic3—42no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—62no—
640C23—62no—
641C23—62no—
642C23—121no—
643C23—121no—
644C23—121no—
645C23—121no—
646C23C4×#6712yes—
647C23C22×#6711yescharacteristic
648Q8—22no—
649Q8—22no—
650Q8—34no—
651Q8—41no—
652Q8—41no—
653Q8—62no—
654Q8—62no—
655Q8—62no—
656D4—34no—
657D4—616no—
658D4—62no—
659D4—62no—
660D4—62no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—616no—
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—244no—
700C2×C4—244no—
701C2×C4—244no—
702C2×C4C4×#6712yes—
703C2×C4#93712yes—
704C2×C4#93712yes—
705C2×C4C22×C4×D311yescharacteristic
706C2×C4C2×#23511yescharacteristic
707C2×C4C2×D3×D411yescharacteristic
708C2×C4C2×D3×D411yescharacteristic
709C2×C4D3×#4111yescharacteristic
710C2×C4D3×#4111yescharacteristic
711C8—62no—
712C8—62no—
713C8—121no—
714C8—121no—
715C2×C3—42no—
716C2×C3C4×#12011yescharacteristic
717C2×C3#294711yescharacteristic
718C2×C3#295111yescharacteristic
719C2×C3#301111yescharacteristic
720C2×C3#301211yescharacteristic
721C2×C3#312011yescharacteristic
722C2×C3#312411yescharacteristic
723D3—44no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—64no—
732C22—122no—
733C22—122no—
734C22—122no—
735C22—122no—
736C22—122no—
737C22—122no—
738C22C2×C4×#6711yescharacteristic
739C22C2×#93711yescharacteristic
740C22#582811yescharacteristic
741C22#583511yescharacteristic
742C22#583711yescharacteristic
743C22#583811yescharacteristic
744C22#583811yescharacteristic
745C4—22no—
746C4—22no—
747C4—22no—
748C4—42no—
749C4—41no—
750C4—42no—
751C4—41no—
752C4—64no—
753C4—81no—
754C4—81no—
755C4—122no—
756C4—122no—
757C4C4×D3×D411yescharacteristic
758C4C4×D3×D411yescharacteristic
759C4#554711yescharacteristic
760C4#554711yescharacteristic
761C3#2146511yescharacteristic, complemented, Sylow
762C2—42no—
763C2—124no—
764C2C4×#93711yescharacteristic
765C2#8254711yescharacteristic
766C2#8255711yescharacteristic
767C2#8341111yescharacteristic
768C2#8342411yescharacteristic
769C2#8344611yescharacteristic
770C2#8346111yescharacteristic
subgroupG/H
centerC23C22×#67
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#2323C2
socleC23×C3C22×D4
prime radicalC22×#235C22
cosocleC22×C3×C4C24
hypercenter#2323D3
hypocenterC3#21465
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2323

Complements

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

NH ≅ G/Ntype
2. C3×#2323C2semidirect
4. C2×#5026C2semidirect
5. C2×C4×#216C2semidirect
6. #71692C2semidirect
7. #71582C2semidirect
8. #69690C2semidirect
9. #69687C2semidirect
10. #69631C2semidirect
11. #69625C2semidirect
13. #69504C2semidirect
14. #69475C2semidirect
15. C4×#809C2semidirect
46. #5047C4semidirect
69. #2323D3semidirect
96. C3×C22⋊Q8C2×C4semidirect
119. C2×#216C2×C4semidirect
122. C2×#215C2×C4semidirect
158. #830C2×C4semidirect
161. #810C2×C4semidirect
164. #809C2×C4semidirect
347. C22⋊Q8C4×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×#55232
C3×#23232
C2×#50472
C2×#50262
C2×C4×#2162
#716922
#715822
#696902
#696872
#696312
#696252
#695222
#695042
#694752
C4×#8092
#214653