Finite Group Databasebeta

← #10720121

Subgroups — #10720121

Order 768.

2366 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×C4⋊C4C211yesmaximal, characteristic
2C2×#4987C211yesmaximal, characteristic
3C2×#4984C211yesmaximal, characteristic, complemented
4C2×#4972C211yesmaximal, characteristic, complemented
5C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
6C2×#4668C212yesmaximal
7C3×C4⋊#95C211yesmaximal, characteristic, complemented
8#71535C211yesmaximal, characteristic, complemented
9(C2×D3)⋊#95C212yesmaximal
10#69420C212yesmaximal, complemented
11#69413C212yesmaximal, complemented
12#14130—31nomaximal, Sylow
13C23×C4×D3C2212yes—
14C23×C4×D3C2211yescharacteristic
15C22×C3×C4⋊C4C2211yescharacteristic
16C22×C3×C4⋊C4C2211yescharacteristic
17C22×C3×C42C2211yescharacteristic
18C22×(C2×D3)⋊C4C2212yes—
19C22×(C2×D3)⋊C4C2211yescharacteristic
20C22×(C2×D3)⋊C4C2211yescharacteristic
21C22×C4⋊Dic3C2212yes—
22C22×C4⋊Dic3C2211yescharacteristic
23C22×C4⋊Dic3C2211yescharacteristic
24C22×Dic3⋊C4C2212yes—
25C22×Dic3⋊C4C2212yes—
26C22×C4×Dic3C2211yescharacteristic
27C2×D3×C4⋊C4—24no—
28C2×D3×C4⋊C4—24no—
29C2×D3×C4⋊C4—24no—
30C2×C3×#95C2212yes—
31C2×C3×#95C2212yes—
32C2×C3⋊#95C2211yescharacteristic
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2211yescharacteristic
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39#4987C418yescomplemented
40#4984—24no—
41#4972—24no—
42C4×(C2×D3)⋊C4—24no—
43#4668—28no—
44C23×C4⋊C4—31no—
45C2×#389—31no—
46C2×#389—31no—
47C2×#385—32no—
48C2×#380—31no—
49C2×C4×C22⋊C4—31no—
50#1444—32no—
51#1442—32no—
52C4⋊#95—31no—
53C4⋊#95D311yescharacteristic, complemented
54C22⋊#95—32no—
55C24×D3C2311yescharacteristic
56C23×C3×C4C2312yes—
57C23×C3×C4C2312yes—
58C23×C3×C4C2311yescharacteristic
59C23×C3×C4C2311yescharacteristic
60C23×C3×C4C2311yescharacteristic
61C23×Dic3C2312yes—
62C23×Dic3C2312yes—
63C23×Dic3C2311yescharacteristic
64C23×Dic3C2311yescharacteristic
65C23×Dic3C2311yescharacteristic
66C22×C4×D3—22no—
67C22×C4×D3—22no—
68C22×C4×D3—22no—
69C22×C4×D3—22no—
70C22×C4×D3—24no—
71C22×C4×D3—24no—
72C22×C4×D3—24no—
73C22×C4×D3—24no—
74C22×C4×D3—24no—
75C22×C4×D3—42no—
76C22×C4×D3—42no—
77C22×C4×D3C2×C414yes—
78C22×C4×D3D414yes—
79C22×C4×D3Q814yes—
80C2×C3×C4⋊C4—22no—
81C2×C3×C4⋊C4—22no—
82C2×C3×C4⋊C4—22no—
83C2×C3×C4⋊C4—22no—
84C2×C3×C4⋊C4C2×C414yescomplemented
85C2×C3×C4⋊C4D414yes—
86C2×C3×C42—22no—
87C2×C3×C42—22no—
88C2×C3×C42—22no—
89C2×(C2×D3)⋊C4—24no—
90C2×(C2×D3)⋊C4—22no—
91C2×(C2×D3)⋊C4—22no—
92C2×(C2×D3)⋊C4—24no—
93C2×(C2×D3)⋊C4—22no—
94C2×(C2×D3)⋊C4—22no—
95C2×(C2×D3)⋊C4C2×C418yes—
96C2×(C2×D3)⋊C4D414yes—
97C2×(C2×D3)⋊C4Q814yes—
98C2×C4⋊Dic3—22no—
99C2×C4⋊Dic3—22no—
100C2×C4⋊Dic3—22no—
101C2×C4⋊Dic3—22no—
102C2×C4⋊Dic3—24no—
103C2×C4⋊Dic3—24no—
104C2×C4⋊Dic3—42no—
105C2×C4⋊Dic3C2×C414yescomplemented
106C2×C4⋊Dic3D414yes—
107C2×Dic3⋊C4—24no—
108C2×Dic3⋊C4—24no—
109C2×Dic3⋊C4—24no—
110C2×Dic3⋊C4—24no—
111C2×Dic3⋊C4—24no—
112C2×Dic3⋊C4—42no—
113C2×C4×Dic3—22no—
114C2×C4×Dic3—22no—
115C2×C4×Dic3—22no—
116D3×C4⋊C4—232no—
117C3×#95—24no—
118C3×#95—42no—
119C3⋊#95—24no—
120C3⋊#95—24no—
121C3⋊#95—22no—
122C3⋊#95—22no—
123C3⋊#95—24no—
124C3⋊#95—42no—
125C3⋊#95C2×C418yescomplemented
126C24×C4—31no—
127C24×C4—32no—
128C22×C4⋊C4—31no—
129C22×C4⋊C4—31no—
130C22×C4⋊C4—32no—
131C22×C4⋊C4—32no—
132C22×C4⋊C4—32no—
133C22×C4⋊C4—64no—
134C22×C4⋊C4—64no—
135C22×C4⋊C4—64no—
136C22×C4⋊C4C2×D311yescharacteristic
137C22×C4⋊C4C2×D311yescharacteristic
138C22×C22⋊C4—31no—
139C22×C22⋊C4—32no—
140C22×C22⋊C4—31no—
141C22×C42—31no—
142C22×C42C2×D311yescharacteristic
143#389—64no—
144#389—64no—
145#385—68no—
146#380—38no—
147C4×C22⋊C4—64no—
148C2×#95—32no—
149C2×#95—32no—
150C2×#95—32no—
151C2×#95—32no—
152C2×#95—31no—
153C2×#95—31no—
154C2×#95—32no—
155C2×#95C2×D312yes—
156C2×#95C2×D312yes—
157C24×C3C2411yescharacteristic
158C23×D3—21no—
159C23×D3—21no—
160C23×D3—21no—
161C23×D3—21no—
162C23×D3—21no—
163C23×D3—21no—
164C23×D3—21no—
165C23×D3—21no—
166C23×D3C22×C412yes—
167C23×D3C2×D412yes—
168C23×D3C2×D412yes—
169C23×D3C2×Q812yes—
170C23×D3C2×Q812yes—
171C23×D3#4112yes—
172C23×D3#4112yes—
173C22×C3×C4—22no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—22no—
177C22×C3×C4—22no—
178C22×C3×C4—22no—
179C22×C3×C4—22no—
180C22×C3×C4—22no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—22no—
188C22×C3×C4—22no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—21no—
195C22×C3×C4—22no—
196C22×C3×C4—21no—
197C22×C3×C4C22×C414yes—
198C22×C3×C4C22×C412yes—
199C22×C3×C4C2×D414yes—
200C22×C3×C4C2×D412yes—
201C22×C3×C4C2×D412yes—
202C22×C3×C4C2×D412yes—
203C22×C3×C4C2×D412yes—
204C22×C3×C4C2×Q812yes—
205C22×C3×C4C2×Q812yes—
206C22×C3×C4#4112yes—
207C22×C3×C4#4112yes—
208C22×Dic3—21no—
209C22×Dic3—21no—
210C22×Dic3—21no—
211C22×Dic3—21no—
212C22×Dic3—21no—
213C22×Dic3—21no—
214C22×Dic3—21no—
215C22×Dic3—21no—
216C22×Dic3—22no—
217C22×Dic3—22no—
218C22×Dic3—22no—
219C22×Dic3—21no—
220C22×Dic3—21no—
221C22×Dic3—22no—
222C22×Dic3—22no—
223C22×Dic3—22no—
224C22×Dic3—22no—
225C22×Dic3—21no—
226C22×Dic3—21no—
227C22×Dic3—22no—
228C22×Dic3—22no—
229C22×Dic3—22no—
230C22×Dic3—21no—
231C22×Dic3—21no—
232C22×Dic3—22no—
233C22×Dic3—22no—
234C22×Dic3—21no—
235C22×Dic3—21no—
236C22×Dic3C22×C414yes—
237C22×Dic3C22×C412yes—
238C22×Dic3C2×D414yes—
239C22×Dic3C2×D412yes—
240C22×Dic3C2×D412yes—
241C22×Dic3C2×Q812yes—
242C22×Dic3C2×Q812yes—
243C2×C4×D3—28no—
244C2×C4×D3—28no—
245C2×C4×D3—28no—
246C2×C4×D3—28no—
247C2×C4×D3—28no—
248C2×C4×D3—28no—
249C2×C4×D3—216no—
250C2×C4×D3—48no—
251C2×C4×D3—48no—
252C2×C4×D3—48no—
253C2×C4×D3—48no—
254C2×C4×D3—48no—
255C2×C4×D3—48no—
256C2×C4×D3C4⋊C4116yescomplemented
257C3×C4⋊C4—28no—
258C3×C4⋊C4—28no—
259C3×C42—44no—
260(C2×D3)⋊C4—216no—
261(C2×D3)⋊C4—28no—
262(C2×D3)⋊C4—28no—
263C4⋊Dic3—28no—
264C4⋊Dic3—28no—
265C4⋊Dic3—48no—
266Dic3⋊C4—216no—
267Dic3⋊C4—48no—
268C4×Dic3—44no—
269C25—31no—
270C23×C4—31no—
271C23×C4—34no—
272C23×C4—34no—
273C23×C4—34no—
274C23×C4—31no—
275C23×C4—32no—
276C23×C4—31no—
277C23×C4—32no—
278C23×C4—64no—
279C23×C4—64no—
280C23×C4—64no—
281C23×C4—64no—
282C23×C4—62no—
283C23×C4—62no—
284C23×C4—62no—
285C23×C4—62no—
286C23×C4—64no—
287C23×C4—122no—
288C23×C4—122no—
289C23×C4C22×D312yes—
290C23×C4C22×D312yes—
291C23×C4C22×D311yescharacteristic
292C23×C4C22×D311yescharacteristic
293C23×C4C22×D311yescharacteristic
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—34no—
299C2×C4⋊C4—34no—
300C2×C4⋊C4—632no—
301C2×C4⋊C4—64no—
302C2×C4⋊C4—64no—
303C2×C4⋊C4—64no—
304C2×C4⋊C4—62no—
305C2×C4⋊C4—62no—
306C2×C4⋊C4—62no—
307C2×C4⋊C4—62no—
308C2×C4⋊C4—64no—
309C2×C4⋊C4—64no—
310C2×C4⋊C4—64no—
311C2×C4⋊C4—64no—
312C2×C4⋊C4—122no—
313C2×C4⋊C4—122no—
314C2×C4⋊C4C4×D314yescomplemented
315C2×C4⋊C4D1214yes—
316C2×C22⋊C4—38no—
317C2×C22⋊C4—34no—
318C2×C22⋊C4—34no—
319C2×C22⋊C4—62no—
320C2×C22⋊C4—62no—
321C2×C22⋊C4—64no—
322C2×C22⋊C4—62no—
323C2×C22⋊C4—64no—
324C2×C22⋊C4—62no—
325C2×C42—22no—
326C2×C42—22no—
327C2×C42—22no—
328C2×C42—62no—
329C2×C42—62no—
330C2×C42—62no—
331#95—24no—
332#95—38no—
333#95—42no—
334#95—62no—
335#95—62no—
336#95—64no—
337#95—64no—
338#95—64no—
339#95—122no—
340C23×C3C23×C411yescharacteristic
341C23×C3C22×D411yescharacteristic
342C23×C3C22×D411yescharacteristic
343C23×C3C22×D411yescharacteristic
344C23×C3C22×D411yescharacteristic
345C23×C3C22×Q811yescharacteristic
346C23×C3C22×Q811yescharacteristic
347C23×C3C2×#4111yescharacteristic
348C23×C3C2×#4111yescharacteristic
349C23×C3C2×#4111yescharacteristic
350C23×C3C2×#4111yescharacteristic
351C23×C3H(5,𝔽2)11yescharacteristic
352C23×C3H(5,𝔽2)11yescharacteristic
353C23×C32−1+411yescharacteristic
354C23×C32−1+411yescharacteristic
355C22×D3—22no—
356C22×D3—22no—
357C22×D3—22no—
358C22×D3—22no—
359C22×D3—22no—
360C22×D3—22no—
361C22×D3—22no—
362C22×D3—22no—
363C22×D3—22no—
364C22×D3—22no—
365C22×D3—22no—
366C22×D3—22no—
367C22×D3—22no—
368C22×D3—22no—
369C22×D3—22no—
370C22×D3—22no—
371C22×D3—22no—
372C22×D3—22no—
373C22×D3—22no—
374C22×D3—22no—
375C22×D3—22no—
376C22×D3—22no—
377C22×D3—22no—
378C22×D3—22no—
379C22×D3—22no—
380C22×D3—22no—
381C22×D3—22no—
382C22×D3—22no—
383C22×D3C2×C4⋊C414yes—
384C22×D3C4×D414yes—
385C22×D3C4×Q814yes—
386C22×D3#12114yes—
387C22×D3C22⋊Q814yes—
388C22×D3#12514yes—
389C22×D3C4⋊Q814yes—
390C2×C3×C4—24no—
391C2×C3×C4—24no—
392C2×C3×C4—24no—
393C2×C3×C4—24no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—24no—
397C2×C3×C4—24no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—42no—
403C2×C3×C4—41no—
404C2×C3×C4—41no—
405C2×C3×C4—42no—
406C2×C3×C4—41no—
407C2×C3×C4—41no—
408C2×C3×C4—42no—
409C2×C3×C4—42no—
410C2×C3×C4—42no—
411C2×C3×C4—42no—
412C2×C3×C4—42no—
413C2×C3×C4—41no—
414C2×C3×C4—41no—
415C2×C3×C4—41no—
416C2×C3×C4—42no—
417C2×C3×C4—41no—
418C2×C3×C4C2×C4⋊C414yes—
419C2×C3×C4C4×D414yes—
420C2×C3×C4C4×D414yes—
421C2×C3×C4#12014yes—
422C2×C3×C4C22⋊Q814yes—
423C2×C3×C4C22⋊Q814yes—
424C2×C3×C4#12314yes—
425C2×Dic3—22no—
426C2×Dic3—22no—
427C2×Dic3—22no—
428C2×Dic3—22no—
429C2×Dic3—22no—
430C2×Dic3—22no—
431C2×Dic3—24no—
432C2×Dic3—24no—
433C2×Dic3—24no—
434C2×Dic3—24no—
435C2×Dic3—22no—
436C2×Dic3—22no—
437C2×Dic3—22no—
438C2×Dic3—22no—
439C2×Dic3—24no—
440C2×Dic3—24no—
441C2×Dic3—22no—
442C2×Dic3—22no—
443C2×Dic3—41no—
444C2×Dic3—41no—
445C2×Dic3—42no—
446C2×Dic3—42no—
447C2×Dic3—41no—
448C2×Dic3—41no—
449C2×Dic3—42no—
450C2×Dic3—42no—
451C2×Dic3—42no—
452C2×Dic3—41no—
453C2×Dic3—41no—
454C2×Dic3—42no—
455C2×Dic3—41no—
456C2×Dic3—42no—
457C2×Dic3—41no—
458C2×Dic3—42no—
459C2×Dic3C2×C4⋊C414yes—
460C4×D3—232no—
461C4×D3—432no—
462C24—32no—
463C24—32no—
464C24—32no—
465C24—32no—
466C24—32no—
467C24—32no—
468C24—32no—
469C24—61no—
470C24—61no—
471C24—61no—
472C24—61no—
473C24—61no—
474C24—61no—
475C24—61no—
476C24—61no—
477C24C23×D311yescharacteristic
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—32no—
503C22×C4—32no—
504C22×C4—32no—
505C22×C4—316no—
506C22×C4—34no—
507C22×C4—34no—
508C22×C4—32no—
509C22×C4—32no—
510C22×C4—616no—
511C22×C4—61no—
512C22×C4—61no—
513C22×C4—61no—
514C22×C4—61no—
515C22×C4—68no—
516C22×C4—68no—
517C22×C4—68no—
518C22×C4—68no—
519C22×C4—68no—
520C22×C4—68no—
521C22×C4—61no—
522C22×C4—62no—
523C22×C4—61no—
524C22×C4—62no—
525C22×C4—62no—
526C22×C4—61no—
527C22×C4—61no—
528C22×C4—61no—
529C22×C4—62no—
530C22×C4—62no—
531C22×C4—61no—
532C22×C4—62no—
533C22×C4—61no—
534C22×C4—62no—
535C22×C4—61no—
536C22×C4—62no—
537C22×C4—62no—
538C22×C4—61no—
539C22×C4—61no—
540C22×C4—62no—
541C22×C4—62no—
542C22×C4—62no—
543C22×C4—61no—
544C22×C4—61no—
545C22×C4—128no—
546C22×C4—128no—
547C22×C4—128no—
548C22×C4—128no—
549C22×C4—128no—
550C22×C4—128no—
551C22×C4C2×C4×D314yes—
552C22×C4C2×C4×D312yes—
553C22×C4C2×D1214yes—
554C22×C4C2×D1212yes—
555C22×C4#23512yes—
556C22×C4D3×D412yes—
557C22×C4D3×D412yes—
558C22×C4D3×D412yes—
559C22×C4#23712yes—
560C22×C4D3×Q812yes—
561C22×C4D3×Q812yes—
562C4⋊C4—28no—
563C4⋊C4—28no—
564C4⋊C4—616no—
565C4⋊C4—68no—
566C4⋊C4—68no—
567C4⋊C4—128no—
568C4⋊C4—128no—
569C22⋊C4—616no—
570C22⋊C4—68no—
571C22⋊C4—68no—
572C42—44no—
573C42—124no—
574C22×C3C22×C4⋊C411yescharacteristic
575C22×C3C2×C4×D411yescharacteristic
576C22×C3C2×C4×D411yescharacteristic
577C22×C3C2×C4×D411yescharacteristic
578C22×C3C2×C4×Q811yescharacteristic
579C22×C3#52011yescharacteristic
580C22×C3#52011yescharacteristic
581C22×C3C2×#12011yescharacteristic
582C22×C3C2×#12111yescharacteristic
583C22×C3C2×C22⋊Q811yescharacteristic
584C22×C3C2×C22⋊Q811yescharacteristic
585C22×C3C2×C22⋊Q811yescharacteristic
586C22×C3C2×#12311yescharacteristic
587C22×C3C2×#12511yescharacteristic
588C22×C3C2×C4⋊Q811yescharacteristic
589C22×C3#53511yescharacteristic
590C22×C3#53611yescharacteristic
591C22×C3#54411yescharacteristic
592C22×C3#54411yescharacteristic
593C22×C3D4211yescharacteristic
594C22×C3D4211yescharacteristic
595C22×C3#54611yescharacteristic
596C22×C3#54611yescharacteristic
597C22×C3#54711yescharacteristic
598C22×C3#54711yescharacteristic
599C22×C3#54811yescharacteristic
600C22×C3#54811yescharacteristic
601C22×C3D4×Q811yescharacteristic
602C22×C3D4×Q811yescharacteristic
603C22×C3#55211yescharacteristic
604C22×C3#55211yescharacteristic
605C22×C3#55311yescharacteristic
606C22×C3#55311yescharacteristic
607C22×C3#55411yescharacteristic
608C22×C3#55411yescharacteristic
609C2×D3—24no—
610C2×D3—24no—
611C2×D3—24no—
612C2×D3—24no—
613C2×D3—24no—
614C2×D3—24no—
615C2×D3—24no—
616C2×D3—24no—
617C2×D3—24no—
618C2×D3—24no—
619C2×D3—24no—
620C2×D3—24no—
621C2×D3—24no—
622C2×D3—24no—
623C2×D3#38918yescomplemented
624C3×C4—44no—
625C3×C4—44no—
626C3×C4—42no—
627C3×C4—42no—
628C3×C4#38518yescomplemented
629Dic3—24no—
630Dic3—44no—
631Dic3—44no—
632Dic3—42no—
633Dic3—42no—
634C23—34no—
635C23—34no—
636C23—34no—
637C23—34no—
638C23—34no—
639C23—34no—
640C23—34no—
641C23—62no—
642C23—62no—
643C23—62no—
644C23—62no—
645C23—62no—
646C23—62no—
647C23—62no—
648C23—62no—
649C23—62no—
650C23—62no—
651C23—62no—
652C23—62no—
653C23—62no—
654C23—62no—
655C23—62no—
656C23—62no—
657C23—62no—
658C23—62no—
659C23—62no—
660C23—62no—
661C23—62no—
662C23—62no—
663C23—62no—
664C23—62no—
665C23—62no—
666C23—62no—
667C23—62no—
668C23—62no—
669C23C22×C4×D311yescharacteristic
670C23C22×D1211yescharacteristic
671C23C2×#23511yescharacteristic
672C23C2×D3×D411yescharacteristic
673C23C2×D3×D411yescharacteristic
674C23C2×D3×D411yescharacteristic
675C23C2×#23711yescharacteristic
676C23#100411yescharacteristic
677C23C2×D3×Q811yescharacteristic
678C23C2×D3×Q811yescharacteristic
679C23#100711yescharacteristic
680C23D3×#4111yescharacteristic
681C23D3×#4111yescharacteristic
682C23#100911yescharacteristic
683C23#101011yescharacteristic
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—34no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—62no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—632no—
720C2×C4—64no—
721C2×C4—62no—
722C2×C4—64no—
723C2×C4—62no—
724C2×C4—64no—
725C2×C4—64no—
726C2×C4—64no—
727C2×C4—62no—
728C2×C4—64no—
729C2×C4—62no—
730C2×C4—62no—
731C2×C4—62no—
732C2×C4—1232no—
733C2×C4—121no—
734C2×C4—121no—
735C2×C4—121no—
736C2×C4—121no—
737C2×C4—122no—
738C2×C4—122no—
739C2×C4—122no—
740C2×C4—122no—
741C2×C4—122no—
742C2×C4—121no—
743C2×C4—122no—
744C2×C4—121no—
745C2×C4—122no—
746C2×C4—122no—
747C2×C4—121no—
748C2×C4—121no—
749C2×C4C4×D1214yes—
750C2×C4#67⋊C414yes—
751C2×C4#88214yes—
752C2×C4#88314yes—
753C2×C4D3×C4⋊C414yes—
754C2×C4#89614yes—
755C2×C4#89714yes—
756C2×C3C2×#38511yescharacteristic
757C2×C3C2×#38911yescharacteristic
758C2×C3#231711yescharacteristic
759C2×C3#236011yescharacteristic
760C2×C3#236011yescharacteristic
761C2×C3#236111yescharacteristic
762C2×C3#236111yescharacteristic
763C2×C3#240811yescharacteristic
764C2×C3#240911yescharacteristic
765C2×C3#244011yescharacteristic
766C2×C3#244011yescharacteristic
767C2×C3#244211yescharacteristic
768C2×C3#244211yescharacteristic
769C2×C3#248611yescharacteristic
770C2×C3#248711yescharacteristic
771D3—28no—
772C22—38no—
773C22—64no—
774C22—64no—
775C22—64no—
776C22—64no—
777C22—64no—
778C22—64no—
779C22—64no—
780C22—64no—
781C22—64no—
782C22—64no—
783C22—64no—
784C22—64no—
785C22—64no—
786C22—64no—
787C22C2×C4×D1211yescharacteristic
788C22C2×#67⋊C411yescharacteristic
789C22C2×#88211yescharacteristic
790C22C2×#88311yescharacteristic
791C22C2×D3×C4⋊C411yescharacteristic
792C22#550711yescharacteristic
793C22C2×#89611yescharacteristic
794C22C2×#89711yescharacteristic
795C22#551111yescharacteristic
796C22#552911yescharacteristic
797C22#553011yescharacteristic
798C22C4×D3×D411yescharacteristic
799C22#554611yescharacteristic
800C22D4×D1211yescharacteristic
801C22#555411yescharacteristic
802C22C4×D3×Q811yescharacteristic
803C22#557411yescharacteristic
804C22Q8×D1211yescharacteristic
805C22#557611yescharacteristic
806C22D3×#12111yescharacteristic
807C22#560711yescharacteristic
808C22#561111yescharacteristic
809C22#561411yescharacteristic
810C22D3×C22⋊Q811yescharacteristic
811C22#562811yescharacteristic
812C22#563511yescharacteristic
813C22#563911yescharacteristic
814C22#567611yescharacteristic
815C22#567711yescharacteristic
816C22D3×#12511yescharacteristic
817C22#568911yescharacteristic
818C22#571711yescharacteristic
819C22D3×C4⋊Q811yescharacteristic
820C22#572711yescharacteristic
821C22#572911yescharacteristic
822C4—44no—
823C4—44no—
824C4—42no—
825C4—42no—
826C4—64no—
827C4—124no—
828C4—122no—
829C4—124no—
830C4—122no—
831C4#466818yescomplemented
832C3#1413011yescharacteristic, complemented, Sylow
833C2—68no—
834C2C2×#466811yescharacteristic
835C2#7377311yescharacteristic
836C2#7377411yescharacteristic
837C2#7391111yescharacteristic
838C2#7391211yescharacteristic
839C2#7416311yescharacteristic
840C2#7432611yescharacteristic
841C2#7596811yescharacteristic
842C2#7599911yescharacteristic
843C2#7600311yescharacteristic
844C2D3×#38911yescharacteristic
845C2#7643311yescharacteristic
846C2#7643611yescharacteristic
847C2#7661511yescharacteristic
848C2#7661911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×C4⋊#95C2
socle, cosocleC24×C3C24
prime radicalC24×D3C23
hypercenterC4⋊#95D3
hypocenterC3#14130
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#4984C2semidirect
4. C2×#4972C2semidirect
7. C3×C4⋊#95C2semidirect
8. #71535C2semidirect
10. #69420C2semidirect
11. #69413C2semidirect
39. #4987C4semidirect
53. C4⋊#95D3semidirect
84. C2×C3×C4⋊C4C2×C4semidirect
105. C2×C4⋊Dic3C2×C4semidirect
125. C3⋊#95C2×C4semidirect
256. C2×C4×D3C4⋊C4semidirect
314. C2×C4⋊C4C4×D3semidirect
623. C2×D3#389semidirect
628. C3×C4#385semidirect
831. C4#4668semidirect
832. C3#14130semidirect

Maximal subgroups

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

subgroupindex
C22×D3×C4⋊C42
C2×#49872
C2×#49842
C2×#49722
C2×C4×(C2×D3)⋊C42
C2×#46682
C3×C4⋊#952
#715352
(C2×D3)⋊#952
#694202
#694132
#141303