Finite Group Databasebeta

← #10720096

Subgroups — #10720096

Order 768.

4046 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×C22⋊C4C212yesmaximal
2C2×#4989C212yesmaximal, complemented
3C2×#4955C211yesmaximal, characteristic
4C2×#4668C212yesmaximal, complemented
5C3×#1439C211yesmaximal, characteristic, complemented
6#71547C212yesmaximal, complemented
7#71546C211yesmaximal, characteristic, complemented
8(C2×D3)⋊#95C212yesmaximal, complemented
9(C2×D3)⋊#95C212yesmaximal, complemented
10#14127—31nomaximal, Sylow
11C25×D3C2211yescharacteristic
12C23×C4×D3C2212yes—
13C23×C4×D3C2212yes—
14C22×C3×C4⋊C4C2211yescharacteristic, complemented
15C22×C3×C22⋊C4C2212yes—
16C22×C3×C22⋊C4C2211yescharacteristic
17C22×#217C2212yes—
18C22×#217C2211yescharacteristic
19C22×(C2×D3)⋊C4C2212yes—
20C22×(C2×D3)⋊C4C2212yes—
21C22×(C2×D3)⋊C4C2212yes—
22C22×(C2×D3)⋊C4C2212yes—
23C22×C4⋊Dic3C2211yescharacteristic, complemented
24C22×Dic3⋊C4C2212yescomplemented
25C2×D3×C22⋊C4—28no—
26C2×D3×C22⋊C4—28no—
27C2×D3×C22⋊C4—28no—
28C2×C3×#95C2212yescomplemented
29C2×C3×#95C2211yescharacteristic, complemented
30C2×C3⋊#95C2212yescomplemented
31C2×C3⋊#95C2212yescomplemented
32C2×C3⋊#95C2212yescomplemented
33C2×C3⋊#95C2211yescharacteristic, complemented
34C2×C3⋊#95C2212yescomplemented
35#4989—28no—
36#4955C418yescomplemented
37#4668—28no—
38C23×C22⋊C4—32no—
39C2×#385—32no—
40C2×#385—32no—
41C2×#379—31no—
42#1439—31no—
43#1439—32no—
44#1439D311yescharacteristic, complemented
45C22⋊#95—32no—
46C22⋊#95—32no—
47C25×C3C2311yescharacteristic
48C24×D3—24no—
49C24×D3—24no—
50C24×D3—24no—
51C24×D3—24no—
52C24×D3—41no—
53C24×D3—41no—
54C24×D3—41no—
55C24×D3—41no—
56C24×D3C2×C414yes—
57C24×D3D414yes—
58C24×D3Q814yes—
59C24×D3C2312yes—
60C23×C3×C4C2311yescharacteristic
61C23×C3×C4C2311yescharacteristic
62C23×C3×C4C2312yes—
63C23×C3×C4C2312yes—
64C23×Dic3C2312yes—
65C23×Dic3C2312yes—
66C23×Dic3C2312yes—
67C22×C4×D3—24no—
68C22×C4×D3—24no—
69C22×C4×D3—24no—
70C22×C4×D3—24no—
71C22×C4×D3—24no—
72C22×C4×D3—24no—
73C22×C4×D3—24no—
74C22×C4×D3—24no—
75C22×C4×D3—24no—
76C22×C4×D3—24no—
77C22×C4×D3—42no—
78C22×C4×D3—42no—
79C22×C4×D3—42no—
80C22×C4×D3—42no—
81C2×C3×C4⋊C4—24no—
82C2×C3×C4⋊C4—41no—
83C2×C3×C22⋊C4—24no—
84C2×C3×C22⋊C4—24no—
85C2×C3×C22⋊C4—24no—
86C2×C3×C22⋊C4—41no—
87C2×C3×C22⋊C4—41no—
88C2×C3×C22⋊C4C2×C414yescomplemented
89C2×#217—24no—
90C2×#217—24no—
91C2×#217—24no—
92C2×#217—41no—
93C2×#217—41no—
94C2×#217C2×C414yescomplemented
95C2×(C2×D3)⋊C4—24no—
96C2×(C2×D3)⋊C4—24no—
97C2×(C2×D3)⋊C4—24no—
98C2×(C2×D3)⋊C4—24no—
99C2×(C2×D3)⋊C4—24no—
100C2×(C2×D3)⋊C4—24no—
101C2×(C2×D3)⋊C4—24no—
102C2×(C2×D3)⋊C4—24no—
103C2×(C2×D3)⋊C4C2×C418yescomplemented
104C2×(C2×D3)⋊C4C2×C418yescomplemented
105C2×(C2×D3)⋊C4D418yes—
106C2×(C2×D3)⋊C4D418yes—
107C2×C4⋊Dic3—24no—
108C2×C4⋊Dic3—41no—
109C2×Dic3⋊C4—24no—
110C2×Dic3⋊C4—24no—
111C2×Dic3⋊C4—42no—
112D3×C22⋊C4—264no—
113C3×#95—24no—
114C3×#95—41no—
115C3⋊#95—24no—
116C3⋊#95—24no—
117C3⋊#95—24no—
118C3⋊#95—42no—
119C3⋊#95—41no—
120C26—31no—
121C24×C4—32no—
122C24×C4—32no—
123C22×C4⋊C4—32no—
124C22×C4⋊C4—31no—
125C22×C4⋊C4C2×D311yescharacteristic, complemented
126C22×C22⋊C4—32no—
127C22×C22⋊C4—32no—
128C22×C22⋊C4—32no—
129C22×C22⋊C4—32no—
130C22×C22⋊C4—31no—
131C22×C22⋊C4—32no—
132C22×C22⋊C4—68no—
133C22×C22⋊C4—68no—
134C22×C22⋊C4—68no—
135C22×C22⋊C4C2×D312yes—
136C22×C22⋊C4C2×D311yescharacteristic
137#385—68no—
138#385—68no—
139#379—38no—
140C2×#95—32no—
141C2×#95—32no—
142C2×#95—32no—
143C2×#95—32no—
144C2×#95—31no—
145C2×#95C2×D312yescomplemented
146C2×#95C2×D311yescharacteristic, complemented
147C24×C3—22no—
148C24×C3—22no—
149C24×C3—22no—
150C24×C3—22no—
151C24×C3—21no—
152C24×C3—21no—
153C24×C3—21no—
154C24×C3—21no—
155C24×C3C22×C412yes—
156C24×C3C2×D412yes—
157C24×C3C2×Q812yes—
158C24×C3C2411yescharacteristic
159C23×D3—22no—
160C23×D3—22no—
161C23×D3—22no—
162C23×D3—22no—
163C23×D3—22no—
164C23×D3—22no—
165C23×D3—22no—
166C23×D3—22no—
167C23×D3—216no—
168C23×D3—216no—
169C23×D3—216no—
170C23×D3—216no—
171C23×D3—216no—
172C23×D3—216no—
173C23×D3—44no—
174C23×D3—44no—
175C23×D3—44no—
176C23×D3—44no—
177C23×D3—44no—
178C23×D3—44no—
179C23×D3—44no—
180C23×D3—44no—
181C23×D3—48no—
182C23×D3—48no—
183C23×D3—48no—
184C23×D3—48no—
185C23×D3—48no—
186C23×D3—44no—
187C23×D3—44no—
188C23×D3—48no—
189C23×D3C4⋊C4116yescomplemented
190C23×D3C22×C414yes—
191C23×D3C2×D414yes—
192C23×D3C2×D414yes—
193C23×D3C2×D414yes—
194C23×D3C2×Q814yes—
195C23×D3#4114yes—
196C23×D3#4114yes—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—22no—
205C22×C3×C4—22no—
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—21no—
210C22×C3×C4—22no—
211C22×C3×C4—21no—
212C22×C3×C4—22no—
213C22×C3×C4—22no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—22no—
217C22×C3×C4C22×C412yes—
218C22×C3×C4C22×C412yes—
219C22×C3×C4C2×D414yes—
220C22×C3×C4C2×D414yes—
221C22×Dic3—22no—
222C22×Dic3—22no—
223C22×Dic3—22no—
224C22×Dic3—22no—
225C22×Dic3—22no—
226C22×Dic3—22no—
227C22×Dic3—22no—
228C22×Dic3—22no—
229C22×Dic3—22no—
230C22×Dic3—22no—
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3—22no—
234C22×Dic3—22no—
235C22×Dic3—22no—
236C22×Dic3—22no—
237C22×Dic3—22no—
238C22×Dic3—22no—
239C22×Dic3C22×C414yes—
240C22×Dic3C2×D414yes—
241C22×Dic3C2×D414yes—
242C2×C4×D3—216no—
243C2×C4×D3—216no—
244C2×C4×D3—48no—
245C2×C4×D3—48no—
246C2×C4×D3—48no—
247C2×C4×D3—48no—
248C2×C4×D3—48no—
249C2×C4×D3—48no—
250C2×C4×D3—48no—
251C2×C4×D3—48no—
252C2×C4×D3—48no—
253C2×C4×D3—48no—
254C2×C4×D3—48no—
255C2×C4×D3—48no—
256C3×C4⋊C4—44no—
257C3×C22⋊C4—216no—
258C3×C22⋊C4—44no—
259#217—216no—
260#217—44no—
261(C2×D3)⋊C4—216no—
262(C2×D3)⋊C4—216no—
263(C2×D3)⋊C4—216no—
264(C2×D3)⋊C4—216no—
265C4⋊Dic3—44no—
266Dic3⋊C4—48no—
267C25—32no—
268C25—34no—
269C25—34no—
270C25—34no—
271C25—64no—
272C25—64no—
273C25—64no—
274C25—64no—
275C25—121no—
276C25—121no—
277C25—121no—
278C25—121no—
279C25C22×D311yescharacteristic
280C23×C4—32no—
281C23×C4—32no—
282C23×C4—32no—
283C23×C4—64no—
284C23×C4—64no—
285C23×C4—64no—
286C23×C4—64no—
287C23×C4—64no—
288C23×C4—64no—
289C23×C4—64no—
290C23×C4—64no—
291C23×C4—64no—
292C23×C4—64no—
293C23×C4—122no—
294C23×C4—122no—
295C23×C4—122no—
296C23×C4—122no—
297C23×C4C22×D311yescharacteristic
298C23×C4C22×D311yescharacteristic
299C23×C4C22×D312yes—
300C23×C4C22×D312yes—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—41no—
303C2×C4⋊C4—64no—
304C2×C4⋊C4—64no—
305C2×C4⋊C4—64no—
306C2×C4⋊C4—122no—
307C2×C4⋊C4—121no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—38no—
312C2×C22⋊C4—38no—
313C2×C22⋊C4—38no—
314C2×C22⋊C4—38no—
315C2×C22⋊C4—34no—
316C2×C22⋊C4—41no—
317C2×C22⋊C4—41no—
318C2×C22⋊C4—664no—
319C2×C22⋊C4—64no—
320C2×C22⋊C4—64no—
321C2×C22⋊C4—64no—
322C2×C22⋊C4—64no—
323C2×C22⋊C4—64no—
324C2×C22⋊C4—64no—
325C2×C22⋊C4—64no—
326C2×C22⋊C4—64no—
327C2×C22⋊C4—64no—
328C2×C22⋊C4—64no—
329C2×C22⋊C4—64no—
330C2×C22⋊C4—121no—
331C2×C22⋊C4—121no—
332C2×C22⋊C4C4×D314yescomplemented
333#95—24no—
334#95—41no—
335#95—64no—
336#95—64no—
337#95—64no—
338#95—121no—
339#95—122no—
340C23×C3—24no—
341C23×C3—24no—
342C23×C3—22no—
343C23×C3—22no—
344C23×C3—24no—
345C23×C3—24no—
346C23×C3—24no—
347C23×C3—24no—
348C23×C3—22no—
349C23×C3—22no—
350C23×C3—22no—
351C23×C3—22no—
352C23×C3—41no—
353C23×C3—41no—
354C23×C3—42no—
355C23×C3—42no—
356C23×C3—42no—
357C23×C3—42no—
358C23×C3—42no—
359C23×C3—41no—
360C23×C3—41no—
361C23×C3—42no—
362C23×C3C2×C4⋊C414yes—
363C23×C3C23×C411yescharacteristic
364C23×C3C22×D411yescharacteristic
365C23×C3C22×D412yes—
366C23×C3C22×D412yes—
367C23×C3C22×Q811yescharacteristic
368C23×C3C2×#4112yes—
369C23×C3C2×#4112yes—
370C23×C3H(5,𝔽2)11yescharacteristic
371C23×C3H(5,𝔽2)11yescharacteristic
372C23×C3H(5,𝔽2)11yescharacteristic
373C23×C3H(5,𝔽2)11yescharacteristic
374C22×D3—24no—
375C22×D3—24no—
376C22×D3—24no—
377C22×D3—24no—
378C22×D3—24no—
379C22×D3—24no—
380C22×D3—24no—
381C22×D3—24no—
382C22×D3—24no—
383C22×D3—24no—
384C22×D3—24no—
385C22×D3—24no—
386C22×D3—24no—
387C22×D3—24no—
388C22×D3—24no—
389C22×D3—24no—
390C22×D3—24no—
391C22×D3—24no—
392C22×D3—24no—
393C22×D3—24no—
394C22×D3—24no—
395C22×D3—24no—
396C22×D3—24no—
397C22×D3—24no—
398C22×D3—24no—
399C22×D3—24no—
400C22×D3—24no—
401C22×D3—24no—
402C22×D3—264no—
403C22×D3—416no—
404C22×D3—432no—
405C22×D3—416no—
406C22×D3—416no—
407C22×D3—416no—
408C22×D3—432no—
409C22×D3—416no—
410C22×D3—416no—
411C22×D3—432no—
412C22×D3—416no—
413C22×D3C2×C4⋊C418yes—
414C22×D3C4×D418yes—
415C22×D3C4×D418yes—
416C22×D3#12018yes—
417C22×D3C22⋊Q818yes—
418C22×D3C22⋊Q818yes—
419C22×D3#12318yes—
420C2×C3×C4—24no—
421C2×C3×C4—24no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—24no—
425C2×C3×C4—24no—
426C2×C3×C4—24no—
427C2×C3×C4—24no—
428C2×C3×C4—24no—
429C2×C3×C4—24no—
430C2×C3×C4—42no—
431C2×C3×C4—42no—
432C2×C3×C4—42no—
433C2×C3×C4—42no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—42no—
437C2×C3×C4—42no—
438C2×C3×C4—42no—
439C2×C3×C4—42no—
440C2×C3×C4—42no—
441C2×C3×C4—42no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×Dic3—24no—
445C2×Dic3—24no—
446C2×Dic3—24no—
447C2×Dic3—24no—
448C2×Dic3—24no—
449C2×Dic3—24no—
450C2×Dic3—24no—
451C2×Dic3—24no—
452C2×Dic3—24no—
453C2×Dic3—42no—
454C2×Dic3—42no—
455C2×Dic3—42no—
456C2×Dic3—42no—
457C2×Dic3—42no—
458C2×Dic3—42no—
459C2×Dic3—42no—
460C2×Dic3—42no—
461C2×Dic3—42no—
462C2×Dic3—42no—
463C2×Dic3—42no—
464C2×Dic3—42no—
465C4×D3—432no—
466C4×D3—432no—
467C24—22no—
468C24—22no—
469C24—21no—
470C24—21no—
471C24—22no—
472C24—22no—
473C24—21no—
474C24—21no—
475C24—34no—
476C24—34no—
477C24—34no—
478C24—34no—
479C24—34no—
480C24—34no—
481C24—34no—
482C24—316no—
483C24—616no—
484C24—616no—
485C24—616no—
486C24—616no—
487C24—616no—
488C24—616no—
489C24—62no—
490C24—62no—
491C24—62no—
492C24—62no—
493C24—62no—
494C24—62no—
495C24—62no—
496C24—62no—
497C24—124no—
498C24—124no—
499C24—124no—
500C24—124no—
501C24—124no—
502C24—124no—
503C24—128no—
504C24—124no—
505C24—128no—
506C24—124no—
507C24—128no—
508C24—124no—
509C24—124no—
510C24—128no—
511C24—128no—
512C24—128no—
513C24C2×C4×D312yes—
514C24D3×D412yes—
515C24D3×Q812yes—
516C24C23×D311yescharacteristic
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—34no—
538C22×C4—34no—
539C22×C4—34no—
540C22×C4—616no—
541C22×C4—616no—
542C22×C4—62no—
543C22×C4—62no—
544C22×C4—62no—
545C22×C4—62no—
546C22×C4—62no—
547C22×C4—62no—
548C22×C4—62no—
549C22×C4—62no—
550C22×C4—62no—
551C22×C4—62no—
552C22×C4—62no—
553C22×C4—62no—
554C22×C4—62no—
555C22×C4—62no—
556C22×C4—62no—
557C22×C4—62no—
558C22×C4—62no—
559C22×C4—62no—
560C22×C4—128no—
561C22×C4—128no—
562C22×C4—128no—
563C22×C4—128no—
564C22×C4—128no—
565C22×C4—128no—
566C22×C4—128no—
567C22×C4—128no—
568C22×C4—128no—
569C22×C4—128no—
570C22×C4—128no—
571C22×C4—128no—
572C22×C4C2×C4×D312yes—
573C22×C4C2×C4×D312yes—
574C22×C4D3×D414yes—
575C22×C4D3×D414yes—
576C4⋊C4—44no—
577C4⋊C4—128no—
578C4⋊C4—124no—
579C22⋊C4—216no—
580C22⋊C4—44no—
581C22⋊C4—616no—
582C22⋊C4—616no—
583C22⋊C4—616no—
584C22⋊C4—616no—
585C22⋊C4—616no—
586C22⋊C4—124no—
587C22×C3—24no—
588C22×C3—28no—
589C22×C3—44no—
590C22×C3—42no—
591C22×C3—42no—
592C22×C3—42no—
593C22×C3—44no—
594C22×C3—42no—
595C22×C3—42no—
596C22×C3—44no—
597C22×C3—42no—
598C22×C3C22×C4⋊C411yescharacteristic
599C22×C3C2×C4×D412yes—
600C22×C3C2×C4×D412yes—
601C22×C3#51811yescharacteristic
602C22×C3#51811yescharacteristic
603C22×C3C2×#12012yes—
604C22×C3C2×C22⋊Q812yes—
605C22×C3C2×C22⋊Q812yes—
606C22×C3C2×#12312yes—
607C22×C3#53411yescharacteristic
608C22×C3#53411yescharacteristic
609C22×C3#54311yescharacteristic
610C22×C3#54311yescharacteristic
611C22×C3D4211yescharacteristic
612C22×C3D4211yescharacteristic
613C22×C3D4212yes—
614C22×C3#54612yes—
615C22×C3#54612yes—
616C22×C3#54612yes—
617C22×C3#54612yes—
618C22×C3#55111yescharacteristic
619C22×C3#55111yescharacteristic
620C22×C3#55112yes—
621C2×D3—28no—
622C2×D3—28no—
623C2×D3—28no—
624C2×D3—28no—
625C2×D3—28no—
626C2×D3—28no—
627C2×D3—28no—
628C2×D3—28no—
629C2×D3—28no—
630C2×D3—28no—
631C2×D3—28no—
632C2×D3—28no—
633C2×D3—28no—
634C2×D3—28no—
635C2×D3—464no—
636C2×D3#385116yescomplemented
637C3×C4—42no—
638C3×C4—42no—
639C3×C4—44no—
640C3×C4—44no—
641Dic3—44no—
642Dic3—44no—
643Dic3—44no—
644C23—22no—
645C23—22no—
646C23—24no—
647C23—22no—
648C23—22no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—22no—
653C23—22no—
654C23—24no—
655C23—24no—
656C23—38no—
657C23—38no—
658C23—38no—
659C23—38no—
660C23—38no—
661C23—38no—
662C23—38no—
663C23—42no—
664C23—41no—
665C23—42no—
666C23—41no—
667C23—42no—
668C23—41no—
669C23—41no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—664no—
674C23—64no—
675C23—64no—
676C23—64no—
677C23—64no—
678C23—64no—
679C23—64no—
680C23—64no—
681C23—64no—
682C23—64no—
683C23—64no—
684C23—64no—
685C23—64no—
686C23—64no—
687C23—64no—
688C23—64no—
689C23—64no—
690C23—64no—
691C23—64no—
692C23—64no—
693C23—64no—
694C23—64no—
695C23—64no—
696C23—64no—
697C23—64no—
698C23—64no—
699C23—64no—
700C23—64no—
701C23—64no—
702C23—1216no—
703C23—1216no—
704C23—1232no—
705C23—1232no—
706C23—1216no—
707C23—1232no—
708C23—1216no—
709C23—1216no—
710C23—1216no—
711C23—1216no—
712C23D3×C4⋊C414yes—
713C23C22×C4×D311yescharacteristic
714C23C2×D3×D411yescharacteristic
715C23C2×D3×D412yes—
716C23C2×D3×D412yes—
717C23#100411yescharacteristic
718C23#100411yescharacteristic
719C23C2×D3×Q811yescharacteristic
720C23D3×#4112yes—
721C23D3×#4112yes—
722C23#100911yescharacteristic
723C23#100911yescharacteristic
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—42no—
735C2×C4—41no—
736C2×C4—42no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—64no—
749C2×C4—64no—
750C2×C4—64no—
751C2×C4—64no—
752C2×C4—64no—
753C2×C4—64no—
754C2×C4—64no—
755C2×C4—64no—
756C2×C4—64no—
757C2×C4—1232no—
758C2×C4—1232no—
759C2×C4—122no—
760C2×C4—122no—
761C2×C4—122no—
762C2×C4—122no—
763C2×C4—122no—
764C2×C4—122no—
765C2×C4—122no—
766C2×C4—122no—
767C2×C4—122no—
768C2×C4—122no—
769C2×C4—122no—
770C2×C4—122no—
771C2×C3—44no—
772C2×C3C2×#38512yes—
773C2×C3#231511yescharacteristic
774C2×C3#235812yes—
775C2×C3#235811yescharacteristic
776C2×C3#235811yescharacteristic
777C2×C3#240311yescharacteristic
778C2×C3#240512yes—
779C2×C3#243711yescharacteristic
780C2×C3#243711yescharacteristic
781C2×C3#243712yes—
782C2×C3#248311yescharacteristic
783D3—216no—
784C22—24no—
785C22—28no—
786C22—316no—
787C22—42no—
788C22—44no—
789C22—44no—
790C22—42no—
791C22—44no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—68no—
797C22—68no—
798C22—68no—
799C22—68no—
800C22—68no—
801C22—68no—
802C22—68no—
803C22—68no—
804C22—68no—
805C22—68no—
806C22—68no—
807C22—68no—
808C22—68no—
809C22—68no—
810C22—1264no—
811C22#548611yescharacteristic
812C22C2×D3×C4⋊C411yescharacteristic
813C22#552111yescharacteristic
814C22C4×D3×D412yes—
815C22C4×D3×D412yes—
816C22D3×#12012yes—
817C22#559011yescharacteristic
818C22#560511yescharacteristic
819C22#560511yescharacteristic
820C22#560912yes—
821C22#561012yes—
822C22#561212yes—
823C22D3×C22⋊Q812yes—
824C22D3×C22⋊Q812yes—
825C22#563411yescharacteristic
826C22#563411yescharacteristic
827C22D3×#12312yes—
828C22#565412yes—
829C22#565911yescharacteristic
830C22#567612yes—
831C22#567911yescharacteristic
832C22#570512yes—
833C22#571711yescharacteristic
834C4—44no—
835C4—42no—
836C4—42no—
837C4—44no—
838C4—124no—
839C4—124no—
840C4—124no—
841C3#1412711yescharacteristic, complemented, Sylow
842C2—44no—
843C2—616no—
844C2#7400511yescharacteristic
845C2D3×#38512yes—
846C2#7488011yescharacteristic
847C2#7583612yes—
848C2#7643211yescharacteristic
849C2#7675311yescharacteristic
850C2#7686511yescharacteristic
851C2#7710612yes—
852C2#7741812yes—
853C2#7767711yescharacteristic
854C2#7810211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1439C2
socle, cosocleC24×C3C24
prime radicalC25×D3C22
hypercenter#1439D3
hypocenterC3#14127
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#4989C2semidirect
4. C2×#4668C2semidirect
5. C3×#1439C2semidirect
6. #71547C2semidirect
7. #71546C2semidirect
8. (C2×D3)⋊#95C2semidirect
9. (C2×D3)⋊#95C2semidirect
14. C22×C3×C4⋊C4C22semidirect
23. C22×C4⋊Dic3C22semidirect
24. C22×Dic3⋊C4C22semidirect
28. C2×C3×#95C22semidirect
29. C2×C3×#95C22semidirect
30. C2×C3⋊#95C22semidirect
31. C2×C3⋊#95C22semidirect
32. C2×C3⋊#95C22semidirect
33. C2×C3⋊#95C22semidirect
34. C2×C3⋊#95C22semidirect
36. #4955C4semidirect
44. #1439D3semidirect
88. C2×C3×C22⋊C4C2×C4semidirect
94. C2×#217C2×C4semidirect
103. C2×(C2×D3)⋊C4C2×C4semidirect
104. C2×(C2×D3)⋊C4C2×C4semidirect
125. C22×C4⋊C4C2×D3semidirect
145. C2×#95C2×D3semidirect
146. C2×#95C2×D3semidirect
189. C23×D3C4⋊C4semidirect
332. C2×C22⋊C4C4×D3semidirect
636. C2×D3#385semidirect
841. C3#14127semidirect

Maximal subgroups

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

subgroupindex
C22×D3×C22⋊C42
C2×#49892
C2×#49552
C2×#46682
C3×#14392
#715472
#715462
(C2×D3)⋊#952
#141273