Finite Group Databasebeta

← #10720119

Subgroups — #10720119

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×C3×#389C211yesmaximal, characteristic, complemented
3C2×#4989C212yesmaximal
4C2×#4987C211yesmaximal, characteristic
5C2×#4928C211yesmaximal, characteristic, complemented
6C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
7#71568C212yesmaximal, complemented
8#71563C211yesmaximal, characteristic, complemented
9#71563C211yesmaximal, characteristic, complemented
10(C2×D3)⋊#95C212yesmaximal
11#69414C212yesmaximal, complemented
12#14130—31nomaximal, Sylow
13C23×C4×D3C2212yes—
14C23×C4×D3C2211yescharacteristic
15C22×C3×C4⋊C4C2212yes—
16C22×C3×C4⋊C4C2211yescharacteristic
17C22×C3×C4⋊C4C2211yescharacteristic
18C22×C3×C42C2211yescharacteristic
19C22×(C2×D3)⋊C4C2212yes—
20C22×(C2×D3)⋊C4C2211yescharacteristic
21C22×(C2×D3)⋊C4C2211yescharacteristic
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—
30C3×#389—24no—
31C2×C3×#95C2212yes—
32C2×C3⋊#95C2212yes—
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2211yescharacteristic
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2211yescharacteristic
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2212yes—
40#4989—28no—
41#4987C418yescomplemented
42C4×(C2×D3)⋊C4—24no—
43#4928—24no—
44C23×C4⋊C4—31no—
45C2×#389—31no—
46C2×#389D311yescharacteristic, complemented
47C2×#385—32no—
48C2×#380—31no—
49C2×C4×C22⋊C4—31no—
50#1444—32no—
51#1442—32no—
52C4⋊#95—31no—
53C4⋊#95—31no—
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⋊C4—24no—
85C2×C3×C4⋊C4—24no—
86C2×C3×C4⋊C4—42no—
87C2×C3×C4⋊C4C2×C414yescomplemented
88C2×C3×C4⋊C4D414yes—
89C2×C3×C42—22no—
90C2×C3×C42—22no—
91C2×C3×C42—22no—
92C2×(C2×D3)⋊C4—22no—
93C2×(C2×D3)⋊C4—22no—
94C2×(C2×D3)⋊C4—24no—
95C2×(C2×D3)⋊C4—24no—
96C2×(C2×D3)⋊C4—22no—
97C2×(C2×D3)⋊C4—22no—
98C2×(C2×D3)⋊C4C2×C418yes—
99C2×(C2×D3)⋊C4D414yes—
100C2×(C2×D3)⋊C4Q814yes—
101C2×C4⋊Dic3—22no—
102C2×C4⋊Dic3—22no—
103C2×C4⋊Dic3—22no—
104C2×C4⋊Dic3—22no—
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—24no—
119C3⋊#95—22no—
120C3⋊#95—22no—
121C3⋊#95—24no—
122C3⋊#95—24no—
123C3⋊#95—42no—
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—64no—
133C22×C4⋊C4—64no—
134C22×C4⋊C4—64no—
135C22×C4⋊C4C2×D312yes—
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—24no—
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×#95—32no—
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—21no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—22no—
177C22×C3×C4—22no—
178C22×C3×C4—21no—
179C22×C3×C4—22no—
180C22×C3×C4—21no—
181C22×C3×C4—22no—
182C22×C3×C4—22no—
183C22×C3×C4—21no—
184C22×C3×C4—22no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—22no—
188C22×C3×C4—22no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
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×D412yes—
200C22×C3×C4C2×D412yes—
201C22×C3×C4C2×D412yes—
202C22×C3×C4C2×D414yes—
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—22no—
215C22×Dic3—22no—
216C22×Dic3—22no—
217C22×Dic3—22no—
218C22×Dic3—22no—
219C22×Dic3—21no—
220C22×Dic3—21no—
221C22×Dic3—21no—
222C22×Dic3—21no—
223C22×Dic3—22no—
224C22×Dic3—22no—
225C22×Dic3—21no—
226C22×Dic3—21no—
227C22×Dic3—22no—
228C22×Dic3—21no—
229C22×Dic3—21no—
230C22×Dic3—22no—
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3—22no—
234C22×Dic3—21no—
235C22×Dic3—21no—
236C22×Dic3C22×C414yes—
237C22×Dic3C22×C412yes—
238C22×Dic3C2×D412yes—
239C22×Dic3C2×D414yes—
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×C4⋊C4—48no—
260C3×C42—44no—
261(C2×D3)⋊C4—216no—
262(C2×D3)⋊C4—28no—
263(C2×D3)⋊C4—28no—
264C4⋊Dic3—28no—
265C4⋊Dic3—28no—
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—32no—
275C23×C4—31no—
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×D311yescharacteristic
291C23×C4C22×D311yescharacteristic
292C23×C4C22×D312yes—
293C23×C4C22×D311yescharacteristic
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—34no—
301C2×C4⋊C4—34no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—632no—
304C2×C4⋊C4—64no—
305C2×C4⋊C4—64no—
306C2×C4⋊C4—62no—
307C2×C4⋊C4—62no—
308C2×C4⋊C4—62no—
309C2×C4⋊C4—64no—
310C2×C4⋊C4—62no—
311C2×C4⋊C4—64no—
312C2×C4⋊C4—64no—
313C2×C4⋊C4—122no—
314C2×C4⋊C4C4×D314yescomplemented
315C2×C4⋊C4#6714yes—
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—62no—
334#95—62no—
335#95—64no—
336#95—64no—
337#95—64no—
338#95—122no—
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—22no—
397C2×C3×C4—22no—
398C2×C3×C4—24no—
399C2×C3×C4—24no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—41no—
403C2×C3×C4—41no—
404C2×C3×C4—42no—
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—41no—
412C2×C3×C4—41no—
413C2×C3×C4—42no—
414C2×C3×C4—41no—
415C2×C3×C4—42no—
416C2×C3×C4—41no—
417C2×C3×C4—42no—
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—24no—
438C2×Dic3—24no—
439C2×Dic3—22no—
440C2×Dic3—22no—
441C2×Dic3—22no—
442C2×Dic3—22no—
443C2×Dic3—42no—
444C2×Dic3—41no—
445C2×Dic3—41no—
446C2×Dic3—42no—
447C2×Dic3—41no—
448C2×Dic3—41no—
449C2×Dic3—42no—
450C2×Dic3—42no—
451C2×Dic3—42no—
452C2×Dic3—42no—
453C2×Dic3—42no—
454C2×Dic3—41no—
455C2×Dic3—41no—
456C2×Dic3—42no—
457C2×Dic3—41no—
458C2×Dic3—41no—
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—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—32no—
503C22×C4—32no—
504C22×C4—32no—
505C22×C4—316no—
506C22×C4—34no—
507C22×C4—32no—
508C22×C4—34no—
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—61no—
523C22×C4—61no—
524C22×C4—61no—
525C22×C4—62no—
526C22×C4—62no—
527C22×C4—62no—
528C22×C4—62no—
529C22×C4—61no—
530C22×C4—62no—
531C22×C4—61no—
532C22×C4—61no—
533C22×C4—62no—
534C22×C4—61no—
535C22×C4—62no—
536C22×C4—62no—
537C22×C4—61no—
538C22×C4—61no—
539C22×C4—62no—
540C22×C4—61no—
541C22×C4—62no—
542C22×C4—62no—
543C22×C4—61no—
544C22×C4—62no—
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×C4#23512yes—
554C22×C4D3×D412yes—
555C22×C4D3×D412yes—
556C22×C4D3×D412yes—
557C22×C4D3×Q812yes—
558C22×C4D3×Q812yes—
559C22×C4#23912yes—
560C22×C4C2×#6714yes—
561C22×C4C2×#6712yes—
562C4⋊C4—28no—
563C4⋊C4—28no—
564C4⋊C4—48no—
565C4⋊C4—616no—
566C4⋊C4—68no—
567C4⋊C4—68no—
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
670C23C2×#23511yescharacteristic
671C23C2×D3×D411yescharacteristic
672C23C2×D3×D411yescharacteristic
673C23C2×D3×D411yescharacteristic
674C23#100411yescharacteristic
675C23C2×D3×Q811yescharacteristic
676C23C2×D3×Q811yescharacteristic
677C23C2×#23911yescharacteristic
678C23#100711yescharacteristic
679C23D3×#4111yescharacteristic
680C23D3×#4111yescharacteristic
681C23#100911yescharacteristic
682C23#101011yescharacteristic
683C23C22×#6711yescharacteristic
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—34no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—42no—
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—62no—
721C2×C4—62no—
722C2×C4—64no—
723C2×C4—64no—
724C2×C4—64no—
725C2×C4—62no—
726C2×C4—64no—
727C2×C4—62no—
728C2×C4—62no—
729C2×C4—64no—
730C2×C4—64no—
731C2×C4—62no—
732C2×C4—1232no—
733C2×C4—122no—
734C2×C4—121no—
735C2×C4—122no—
736C2×C4—121no—
737C2×C4—122no—
738C2×C4—121no—
739C2×C4—121no—
740C2×C4—122no—
741C2×C4—121no—
742C2×C4—122no—
743C2×C4—121no—
744C2×C4—122no—
745C2×C4—122no—
746C2×C4—121no—
747C2×C4—122no—
748C2×C4—121no—
749C2×C4D3×C4⋊C414yes—
750C2×C4#89314yes—
751C2×C4#89414yes—
752C2×C4#89614yes—
753C2×C4C4×#6714yes—
754C2×C4#93714yes—
755C2×C4#94614yes—
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×D3×C4⋊C411yescharacteristic
788C22C2×#89311yescharacteristic
789C22C2×#89411yescharacteristic
790C22C2×#89611yescharacteristic
791C22C4×D3×D411yescharacteristic
792C22#554611yescharacteristic
793C22#555111yescharacteristic
794C22#555811yescharacteristic
795C22C4×D3×Q811yescharacteristic
796C22#557411yescharacteristic
797C22#557911yescharacteristic
798C22#558111yescharacteristic
799C22D3×#12111yescharacteristic
800C22#560711yescharacteristic
801C22#560911yescharacteristic
802C22#561211yescharacteristic
803C22D3×C22⋊Q811yescharacteristic
804C22#562811yescharacteristic
805C22#563211yescharacteristic
806C22#563311yescharacteristic
807C22D3×#12511yescharacteristic
808C22#568911yescharacteristic
809C22#569411yescharacteristic
810C22#569511yescharacteristic
811C22D3×C4⋊Q811yescharacteristic
812C22#572611yescharacteristic
813C22#572911yescharacteristic
814C22#573011yescharacteristic
815C22C2×C4×#6711yescharacteristic
816C22C2×#93711yescharacteristic
817C22D4×#6711yescharacteristic
818C22C2×#94611yescharacteristic
819C22Q8×#6711yescharacteristic
820C22#582911yescharacteristic
821C22#583111yescharacteristic
822C4—42no—
823C4—44no—
824C4—42no—
825C4—44no—
826C4—64no—
827C4—124no—
828C4—122no—
829C4—122no—
830C4—124no—
831C4#498918yescomplemented
832C3#1413011yescharacteristic, complemented, Sylow
833C2—68no—
834C2#7596811yescharacteristic
835C2#7599811yescharacteristic
836C2#7600211yescharacteristic
837C2D3×#38911yescharacteristic
838C2#7620511yescharacteristic
839C2#7620611yescharacteristic
840C2#7623111yescharacteristic
841C2#7623211yescharacteristic
842C2C2×#498911yescharacteristic
843C2#8239911yescharacteristic
844C2#8249011yescharacteristic
845C2#8264011yescharacteristic
846C2#8275111yescharacteristic
847C2#8302811yescharacteristic
848C2#8323311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC2×C3×#389C2
socle, cosocleC24×C3C24
prime radicalC24×D3C23
hypercenterC2×#389D3
hypocenterC3#14130
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C2×C3×#389C2semidirect
5. C2×#4928C2semidirect
7. #71568C2semidirect
8. #71563C2semidirect
9. #71563C2semidirect
11. #69414C2semidirect
41. #4987C4semidirect
46. C2×#389D3semidirect
87. 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#4989semidirect
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×C3×#3892
C2×#49892
C2×#49872
C2×#49282
C2×C4×(C2×D3)⋊C42
#715682
#715632
(C2×D3)⋊#952
#694142
#141303