Finite Group Databasebeta

← #10718039

Subgroups — #10718039

Order 768.

1802 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4987C211yesmaximal, characteristic
2C2×#4987C211yesmaximal, characteristic
3C2×#4972C211yesmaximal, characteristic, complemented
4C2×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
5C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
6C2×#4669C212yesmaximal
7C3×C4⋊#95C211yesmaximal, characteristic, complemented
8#71535C211yesmaximal, characteristic, complemented
9#69429C212yesmaximal
10#69417C212yesmaximal, complemented
11#69406C212yesmaximal, complemented
12#13974—31nomaximal, Sylow
13C23×C4×D3C2211yescharacteristic
14C22×C3×C4⋊C4C2211yescharacteristic
15C22×C3×C4⋊C4C2211yescharacteristic
16C22×C3×C42C2211yescharacteristic
17C22×(C2×D3)⋊C4C2211yescharacteristic
18C22×(C2×D3)⋊C4C2212yes—
19C22×(C2×D3)⋊C4C2212yes—
20C22×(C2×D3)⋊C4C2211yescharacteristic
21C22×C4⋊Dic3C2211yescharacteristic
22C22×C4⋊Dic3C2211yescharacteristic
23C22×Dic3⋊C4C2212yes—
24C22×C4×Dic3C2212yes—
25C22×C4×Dic3C2211yescharacteristic
26C2×C3×#95C2212yes—
27C2×C3×#95C2212yes—
28C2×C3⋊#95C2212yes—
29C2×C3⋊#95C2211yescharacteristic
30C2×C3⋊#95C2212yes—
31C2×C3⋊#95C2211yescharacteristic
32C2×C3⋊#95C2212yes—
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2212yes—
36#4987—24no—
37#4987C418yescomplemented
38Dic3×C4⋊C4—24no—
39#4972—24no—
40C4×(C2×D3)⋊C4—24no—
41#4669—28no—
42C2×#389—31no—
43C2×#388—32no—
44C2×#380—31no—
45C2×#380—31no—
46C2×C4×C4⋊C4—31no—
47C2×C4×C22⋊C4—31no—
48#1443—32no—
49#1440—32no—
50#1436—32no—
51C4⋊#95—31no—
52C4⋊#95D311yescharacteristic, complemented
53C24×D3C2311yescharacteristic
54C23×C3×C4C2312yes—
55C23×C3×C4C2312yes—
56C23×C3×C4C2311yescharacteristic
57C23×C3×C4C2311yescharacteristic
58C23×C3×C4C2311yescharacteristic
59C23×Dic3C2311yescharacteristic
60C23×Dic3C2312yes—
61C23×Dic3C2311yescharacteristic
62C23×Dic3C2312yes—
63C23×Dic3C2311yescharacteristic
64C22×C4×D3—22no—
65C22×C4×D3—22no—
66C22×C4×D3—22no—
67C22×C4×D3—22no—
68C22×C4×D3—22no—
69C22×C4×D3—22no—
70C22×C4×D3C2×C414yes—
71C2×C3×C4⋊C4—22no—
72C2×C3×C4⋊C4—22no—
73C2×C3×C4⋊C4—22no—
74C2×C3×C4⋊C4—22no—
75C2×C3×C4⋊C4—22no—
76C2×C3×C4⋊C4C2×C414yes—
77C2×C3×C42—22no—
78C2×C3×C42—22no—
79C2×C3×C42—22no—
80C2×(C2×D3)⋊C4—24no—
81C2×(C2×D3)⋊C4—22no—
82C2×(C2×D3)⋊C4—24no—
83C2×(C2×D3)⋊C4—22no—
84C2×(C2×D3)⋊C4—22no—
85C2×(C2×D3)⋊C4—22no—
86C2×(C2×D3)⋊C4—22no—
87C2×(C2×D3)⋊C4—24no—
88C2×(C2×D3)⋊C4—24no—
89C2×(C2×D3)⋊C4—42no—
90C2×(C2×D3)⋊C4C2×C418yes—
91C2×(C2×D3)⋊C4D414yes—
92C2×C4⋊Dic3—22no—
93C2×C4⋊Dic3—22no—
94C2×C4⋊Dic3—22no—
95C2×C4⋊Dic3—22no—
96C2×C4⋊Dic3C2×C414yes—
97C2×C4⋊Dic3D414yes—
98C2×Dic3⋊C4—24no—
99C2×Dic3⋊C4—24no—
100C2×Dic3⋊C4—24no—
101C2×C4×Dic3—22no—
102C2×C4×Dic3—22no—
103C2×C4×Dic3—24no—
104C2×C4×Dic3—24no—
105C2×C4×Dic3—42no—
106C2×C4×Dic3D414yes—
107C3×#95—24no—
108C3×#95—42no—
109C3⋊#95—24no—
110C3⋊#95—24no—
111C3⋊#95—22no—
112C3⋊#95—22no—
113C3⋊#95—24no—
114C3⋊#95—24no—
115C3⋊#95—24no—
116C3⋊#95C2×C418yes—
117C24×C4—31no—
118C22×C4⋊C4—31no—
119C22×C4⋊C4—31no—
120C22×C4⋊C4—32no—
121C22×C4⋊C4C2×D311yescharacteristic
122C22×C4⋊C4C2×D311yescharacteristic
123C22×C22⋊C4—32no—
124C22×C22⋊C4—31no—
125C22×C22⋊C4—31no—
126C22×C22⋊C4—32no—
127C22×C42—31no—
128C22×C42—32no—
129C22×C42C2×D311yescharacteristic
130#389—64no—
131#388—68no—
132#380—38no—
133#380—64no—
134C4×C4⋊C4—64no—
135C4×C22⋊C4—64no—
136C2×#95—32no—
137C2×#95—32no—
138C2×#95—32no—
139C2×#95—31no—
140C2×#95—32no—
141C2×#95—32no—
142C2×#95—32no—
143C2×#95—31no—
144C2×#95C2×D312yes—
145C2×#95C2×D312yes—
146C24×C3C2411yescharacteristic
147C23×D3—21no—
148C23×D3—21no—
149C23×D3—21no—
150C23×D3—21no—
151C23×D3—21no—
152C23×D3—21no—
153C23×D3—21no—
154C23×D3—21no—
155C23×D3—21no—
156C23×D3—21no—
157C23×D3—21no—
158C23×D3—21no—
159C23×D3C22×C412yes—
160C23×D3C2×D412yes—
161C23×D3#4112yes—
162C22×C3×C4—22no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—22no—
166C22×C3×C4—22no—
167C22×C3×C4—21no—
168C22×C3×C4—21no—
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4—22no—
174C22×C3×C4—21no—
175C22×C3×C4—22no—
176C22×C3×C4—21no—
177C22×C3×C4—22no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—22no—
181C22×C3×C4—22no—
182C22×C3×C4—22no—
183C22×C3×C4—22no—
184C22×C3×C4—22no—
185C22×C3×C4—22no—
186C22×C3×C4—22no—
187C22×C3×C4C22×C414yes—
188C22×C3×C4C22×C412yes—
189C22×C3×C4C2×D412yes—
190C22×C3×C4C2×D412yes—
191C22×C3×C4C2×D412yes—
192C22×C3×C4#4112yes—
193C22×C3×C4#4112yes—
194C22×C3×C4#4112yes—
195C22×C3×C4#4112yes—
196C22×C3×C4#4112yes—
197C22×Dic3—21no—
198C22×Dic3—21no—
199C22×Dic3—21no—
200C22×Dic3—21no—
201C22×Dic3—21no—
202C22×Dic3—21no—
203C22×Dic3—21no—
204C22×Dic3—22no—
205C22×Dic3—22no—
206C22×Dic3—22no—
207C22×Dic3—22no—
208C22×Dic3—22no—
209C22×Dic3—21no—
210C22×Dic3—22no—
211C22×Dic3—22no—
212C22×Dic3—22no—
213C22×Dic3—22no—
214C22×Dic3—21no—
215C22×Dic3—22no—
216C22×Dic3—21no—
217C22×Dic3—21no—
218C22×Dic3—21no—
219C22×Dic3—21no—
220C22×Dic3—21no—
221C22×Dic3—22no—
222C22×Dic3—21no—
223C22×Dic3—22no—
224C22×Dic3—21no—
225C22×Dic3C22×C412yes—
226C22×Dic3C22×C414yes—
227C22×Dic3C2×D412yes—
228C22×Dic3C2×D414yes—
229C22×Dic3C2×D412yes—
230C22×Dic3C2×D412yes—
231C22×Dic3#4112yes—
232C2×C4×D3—28no—
233C2×C4×D3—28no—
234C2×C4×D3—28no—
235C2×C4×D3—44no—
236C2×C4×D3—44no—
237C2×C4×D3—44no—
238C2×C4×D3—44no—
239C3×C4⋊C4—28no—
240C3×C4⋊C4—44no—
241C3×C42—44no—
242(C2×D3)⋊C4—28no—
243(C2×D3)⋊C4—216no—
244(C2×D3)⋊C4—28no—
245(C2×D3)⋊C4—48no—
246C4⋊Dic3—28no—
247C4⋊Dic3—28no—
248Dic3⋊C4—48no—
249C4×Dic3—28no—
250C4×Dic3—48no—
251C25—31no—
252C23×C4—31no—
253C23×C4—32no—
254C23×C4—32no—
255C23×C4—31no—
256C23×C4—31no—
257C23×C4—34no—
258C23×C4—62no—
259C23×C4—62no—
260C23×C4—62no—
261C23×C4—62no—
262C23×C4—62no—
263C23×C4—62no—
264C23×C4C22×D312yes—
265C23×C4C22×D312yes—
266C23×C4C22×D311yescharacteristic
267C23×C4C22×D311yescharacteristic
268C23×C4C22×D311yescharacteristic
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—34no—
275C2×C4⋊C4—34no—
276C2×C4⋊C4—62no—
277C2×C4⋊C4—62no—
278C2×C4⋊C4—62no—
279C2×C4⋊C4—62no—
280C2×C4⋊C4—64no—
281C2×C4⋊C4—64no—
282C2×C4⋊C4—64no—
283C2×C4⋊C4C4×D314yes—
284C2×C22⋊C4—38no—
285C2×C22⋊C4—34no—
286C2×C22⋊C4—62no—
287C2×C22⋊C4—62no—
288C2×C22⋊C4—62no—
289C2×C22⋊C4—64no—
290C2×C22⋊C4—64no—
291C2×C22⋊C4—62no—
292C2×C22⋊C4—62no—
293C2×C22⋊C4—64no—
294C2×C22⋊C4—64no—
295C2×C22⋊C4—122no—
296C2×C42—22no—
297C2×C42—22no—
298C2×C42—22no—
299C2×C42—34no—
300C2×C42—62no—
301C2×C42—62no—
302C2×C42—64no—
303C2×C42—64no—
304C2×C42—122no—
305#95—24no—
306#95—38no—
307#95—42no—
308#95—62no—
309#95—62no—
310#95—64no—
311#95—64no—
312#95—64no—
313#95—64no—
314#95—64no—
315C23×C3C23×C411yescharacteristic
316C23×C3C22×D411yescharacteristic
317C23×C3C22×D411yescharacteristic
318C23×C3C22×D411yescharacteristic
319C23×C3C2×#4111yescharacteristic
320C23×C3C2×#4111yescharacteristic
321C23×C3C2×#4111yescharacteristic
322C23×C3C2×#4111yescharacteristic
323C23×C3C2×#4111yescharacteristic
324C23×C3C2×#4111yescharacteristic
325C23×C3C2×#4111yescharacteristic
326C23×C3H(5,𝔽2)11yescharacteristic
327C23×C32−1+411yescharacteristic
328C23×C32−1+411yescharacteristic
329C23×C32−1+411yescharacteristic
330C22×D3—22no—
331C22×D3—22no—
332C22×D3—22no—
333C22×D3—22no—
334C22×D3—22no—
335C22×D3—22no—
336C22×D3—22no—
337C22×D3—22no—
338C22×D3—22no—
339C22×D3—22no—
340C22×D3—22no—
341C22×D3—22no—
342C22×D3—22no—
343C22×D3—22no—
344C22×D3—22no—
345C22×D3—22no—
346C22×D3—22no—
347C22×D3—22no—
348C22×D3—41no—
349C22×D3—41no—
350C22×D3—41no—
351C22×D3—41no—
352C22×D3—41no—
353C22×D3—41no—
354C22×D3—41no—
355C22×D3—41no—
356C22×D3—41no—
357C22×D3—41no—
358C22×D3—41no—
359C22×D3—41no—
360C22×D3—41no—
361C22×D3—41no—
362C22×D3—41no—
363C22×D3—41no—
364C22×D3C4×D414yes—
365C2×C3×C4—24no—
366C2×C3×C4—24no—
367C2×C3×C4—24no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—41no—
375C2×C3×C4—41no—
376C2×C3×C4—41no—
377C2×C3×C4—41no—
378C2×C3×C4—42no—
379C2×C3×C4—42no—
380C2×C3×C4—42no—
381C2×C3×C4—41no—
382C2×C3×C4—41no—
383C2×C3×C4—42no—
384C2×C3×C4—41no—
385C2×C3×C4—41no—
386C2×C3×C4—42no—
387C2×C3×C4—42no—
388C2×C3×C4—42no—
389C2×C3×C4—42no—
390C2×C3×C4—42no—
391C2×C3×C4—42no—
392C2×C3×C4—42no—
393C2×C3×C4#11714yes—
394C2×C3×C4C4×D414yes—
395C2×C3×C4C4×D414yes—
396C2×C3×C4#12114yes—
397C2×C3×C4#12314yes—
398C2×C3×C4#12414yes—
399C2×C3×C4#12614yes—
400C2×Dic3—22no—
401C2×Dic3—22no—
402C2×Dic3—22no—
403C2×Dic3—22no—
404C2×Dic3—22no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—24no—
408C2×Dic3—24no—
409C2×Dic3—22no—
410C2×Dic3—22no—
411C2×Dic3—24no—
412C2×Dic3—22no—
413C2×Dic3—24no—
414C2×Dic3—22no—
415C2×Dic3—22no—
416C2×Dic3—24no—
417C2×Dic3—24no—
418C2×Dic3—42no—
419C2×Dic3—41no—
420C2×Dic3—41no—
421C2×Dic3—42no—
422C2×Dic3—41no—
423C2×Dic3—41no—
424C2×Dic3—42no—
425C2×Dic3—42no—
426C2×Dic3—42no—
427C2×Dic3—42no—
428C2×Dic3—41no—
429C2×Dic3—42no—
430C2×Dic3—41no—
431C2×Dic3—41no—
432C2×Dic3—42no—
433C2×Dic3—41no—
434C2×Dic3#12114yes—
435C4×D3—416no—
436C24—32no—
437C24—32no—
438C24—32no—
439C24—61no—
440C24—61no—
441C24—61no—
442C24—61no—
443C24—61no—
444C24—61no—
445C24—61no—
446C24—61no—
447C24—61no—
448C24—61no—
449C24—61no—
450C24—61no—
451C24C23×D311yescharacteristic
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—32no—
478C22×C4—32no—
479C22×C4—32no—
480C22×C4—32no—
481C22×C4—34no—
482C22×C4—32no—
483C22×C4—34no—
484C22×C4—61no—
485C22×C4—61no—
486C22×C4—61no—
487C22×C4—61no—
488C22×C4—61no—
489C22×C4—62no—
490C22×C4—61no—
491C22×C4—61no—
492C22×C4—61no—
493C22×C4—61no—
494C22×C4—61no—
495C22×C4—62no—
496C22×C4—62no—
497C22×C4—62no—
498C22×C4—61no—
499C22×C4—62no—
500C22×C4—62no—
501C22×C4—62no—
502C22×C4—61no—
503C22×C4—62no—
504C22×C4—62no—
505C22×C4—61no—
506C22×C4—62no—
507C22×C4—61no—
508C22×C4—62no—
509C22×C4—61no—
510C22×C4—62no—
511C22×C4—61no—
512C22×C4—68no—
513C22×C4—68no—
514C22×C4—68no—
515C22×C4—124no—
516C22×C4—124no—
517C22×C4—124no—
518C22×C4—124no—
519C22×C4C2×C4×D314yes—
520C22×C4C2×C4×D312yes—
521C22×C4#23512yes—
522C22×C4#23512yes—
523C22×C4D3×D412yes—
524C22×C4D3×D412yes—
525C22×C4D3×D412yes—
526C22×C4#23712yes—
527C22×C4#23912yes—
528C22×C4#23912yes—
529C4⋊C4—28no—
530C4⋊C4—44no—
531C4⋊C4—68no—
532C4⋊C4—68no—
533C4⋊C4—128no—
534C22⋊C4—68no—
535C22⋊C4—616no—
536C22⋊C4—68no—
537C22⋊C4—128no—
538C42—44no—
539C42—68no—
540C42—128no—
541C22×C3C2×#11711yescharacteristic
542C22×C3C2×C4×D411yescharacteristic
543C22×C3C2×C4×D411yescharacteristic
544C22×C3C2×C4×D411yescharacteristic
545C22×C3C4×#4111yescharacteristic
546C22×C3#51911yescharacteristic
547C22×C3#52011yescharacteristic
548C22×C3C2×#12111yescharacteristic
549C22×C3C2×#12111yescharacteristic
550C22×C3C2×#12311yescharacteristic
551C22×C3#52511yescharacteristic
552C22×C3C2×#12411yescharacteristic
553C22×C3C2×#12611yescharacteristic
554C22×C3#52911yescharacteristic
555C22×C3#53211yescharacteristic
556C22×C3#53611yescharacteristic
557C22×C3#53711yescharacteristic
558C22×C3#54111yescharacteristic
559C22×C3#54211yescharacteristic
560C22×C3D4211yescharacteristic
561C22×C3#54711yescharacteristic
562C22×C3#54711yescharacteristic
563C22×C3#54711yescharacteristic
564C22×C3#54711yescharacteristic
565C22×C3#54811yescharacteristic
566C22×C3#54811yescharacteristic
567C22×C3#55211yescharacteristic
568C22×C3#55211yescharacteristic
569C22×C3#55211yescharacteristic
570C22×C3#55311yescharacteristic
571C22×C3#55311yescharacteristic
572C22×C3#55311yescharacteristic
573C22×C3#55611yescharacteristic
574C22×C3#55611yescharacteristic
575C22×C3#55611yescharacteristic
576C2×D3—24no—
577C2×D3—24no—
578C2×D3—24no—
579C2×D3—42no—
580C2×D3—42no—
581C2×D3—42no—
582C2×D3—42no—
583C2×D3—42no—
584C2×D3—42no—
585C2×D3—42no—
586C2×D3—42no—
587C2×D3—42no—
588C2×D3—42no—
589C2×D3—42no—
590C2×D3—42no—
591C3×C4—42no—
592C3×C4—44no—
593C3×C4—42no—
594C3×C4—82no—
595C3×C4#38818yescomplemented
596Dic3—24no—
597Dic3—42no—
598Dic3—44no—
599Dic3—42no—
600Dic3—44no—
601C23—34no—
602C23—62no—
603C23—62no—
604C23—62no—
605C23—62no—
606C23—62no—
607C23—62no—
608C23—62no—
609C23—62no—
610C23—62no—
611C23—62no—
612C23—62no—
613C23—62no—
614C23—62no—
615C23—62no—
616C23—62no—
617C23—62no—
618C23—62no—
619C23—62no—
620C23—121no—
621C23—121no—
622C23—121no—
623C23—121no—
624C23—121no—
625C23—121no—
626C23—121no—
627C23—121no—
628C23—121no—
629C23—121no—
630C23—121no—
631C23—121no—
632C23—121no—
633C23—121no—
634C23—121no—
635C23—121no—
636C23C22×C4×D311yescharacteristic
637C23C2×#23511yescharacteristic
638C23C2×#23511yescharacteristic
639C23C2×D3×D411yescharacteristic
640C23C2×D3×D411yescharacteristic
641C23C2×D3×D411yescharacteristic
642C23C2×#23711yescharacteristic
643C23#100411yescharacteristic
644C23C2×#23911yescharacteristic
645C23C2×#23911yescharacteristic
646C23#100711yescharacteristic
647C23D3×#4111yescharacteristic
648C23D3×#4111yescharacteristic
649C23#101011yescharacteristic
650C23#101011yescharacteristic
651C2×C4—22no—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—34no—
661C2×C4—41no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—62no—
681C2×C4—62no—
682C2×C4—62no—
683C2×C4—62no—
684C2×C4—62no—
685C2×C4—62no—
686C2×C4—64no—
687C2×C4—64no—
688C2×C4—62no—
689C2×C4—62no—
690C2×C4—62no—
691C2×C4—64no—
692C2×C4—62no—
693C2×C4—64no—
694C2×C4—64no—
695C2×C4—64no—
696C2×C4—62no—
697C2×C4—62no—
698C2×C4—121no—
699C2×C4—122no—
700C2×C4—122no—
701C2×C4—122no—
702C2×C4—121no—
703C2×C4—122no—
704C2×C4—121no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4—122no—
708C2×C4—121no—
709C2×C4—122no—
710C2×C4—121no—
711C2×C4—121no—
712C2×C4—122no—
713C2×C4—122no—
714C2×C4—1216no—
715C2×C4#87214yes—
716C2×C4#67⋊C414yes—
717C2×C4#88414yes—
718C2×C4#88514yes—
719C2×C4#89314yes—
720C2×C4#89414yes—
721C2×C4#89814yes—
722C2×C3C2×#38811yescharacteristic
723C2×C3C4×#12111yescharacteristic
724C2×C3#232311yescharacteristic
725C2×C3#234411yescharacteristic
726C2×C3#234711yescharacteristic
727C2×C3#236111yescharacteristic
728C2×C3#236211yescharacteristic
729C2×C3#241511yescharacteristic
730C2×C3#241611yescharacteristic
731C2×C3#242111yescharacteristic
732C2×C3#242211yescharacteristic
733C2×C3#249411yescharacteristic
734C2×C3#249611yescharacteristic
735C2×C3#254711yescharacteristic
736C2×C3#256211yescharacteristic
737D3—44no—
738C22—64no—
739C22—64no—
740C22—64no—
741C22—122no—
742C22—122no—
743C22—122no—
744C22—122no—
745C22—122no—
746C22—122no—
747C22—122no—
748C22—122no—
749C22—122no—
750C22—122no—
751C22—122no—
752C22—122no—
753C22C2×#87211yescharacteristic
754C22C2×#67⋊C411yescharacteristic
755C22C2×#88411yescharacteristic
756C22C2×#88511yescharacteristic
757C22C2×#89311yescharacteristic
758C22C2×#89411yescharacteristic
759C22#550711yescharacteristic
760C22C2×#89811yescharacteristic
761C22#551411yescharacteristic
762C22#552911yescharacteristic
763C22#553311yescharacteristic
764C22C4×D3×D411yescharacteristic
765C22#554611yescharacteristic
766C22#555111yescharacteristic
767C22#555811yescharacteristic
768C22#557211yescharacteristic
769C22C4×#23911yescharacteristic
770C22#558111yescharacteristic
771C22#558411yescharacteristic
772C22D3×#12111yescharacteristic
773C22#560811yescharacteristic
774C22#561111yescharacteristic
775C22#561411yescharacteristic
776C22#562711yescharacteristic
777C22#562811yescharacteristic
778C22#564111yescharacteristic
779C22#564211yescharacteristic
780C22#567711yescharacteristic
781C22#567711yescharacteristic
782C22#569111yescharacteristic
783C22#569811yescharacteristic
784C22#571711yescharacteristic
785C22#572511yescharacteristic
786C22#572611yescharacteristic
787C22#573311yescharacteristic
788C4—44no—
789C4—42no—
790C4—42no—
791C4—64no—
792C4—82no—
793C4—122no—
794C4—122no—
795C4—124no—
796C4—124no—
797C4#466918yescomplemented
798C3#1397411yescharacteristic, complemented, Sylow
799C2—124no—
800C2C2×#466911yescharacteristic
801C2#7363411yescharacteristic
802C2#7376711yescharacteristic
803C2#7393711yescharacteristic
804C2#7394111yescharacteristic
805C2#7423211yescharacteristic
806C2#7436211yescharacteristic
807C2#7596411yescharacteristic
808C2#7619711yescharacteristic
809C2#7623411yescharacteristic
810C2#7623811yescharacteristic
811C2#7643311yescharacteristic
812C2#7643911yescharacteristic
813C2#7649111yescharacteristic
814C2#7662011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×C4⋊#95C2
socle, cosocleC24×C3C24
prime radicalC24×D3C23
hypercenterC4⋊#95D3
hypocenterC3#13974
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#4972C2semidirect
4. C2×Dic3×C4⋊C4C2semidirect
7. C3×C4⋊#95C2semidirect
8. #71535C2semidirect
10. #69417C2semidirect
11. #69406C2semidirect
37. #4987C4semidirect
52. C4⋊#95D3semidirect
595. C3×C4#388semidirect
797. C4#4669semidirect
798. C3#13974semidirect

Maximal subgroups

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

subgroupindex
C2×#49872
C2×#49722
C2×Dic3×C4⋊C42
C2×C4×(C2×D3)⋊C42
C2×#46692
C3×C4⋊#952
#715352
#694292
#694172
#694062
#139743