Finite Group Databasebeta

← #10726666

Subgroups — #10726666

Order 768.

3494 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×(C2×D3)⋊C4C211yesmaximal, characteristic
2C2×C3×#380C211yesmaximal, characteristic, complemented
3C2×#5210C211yesmaximal, characteristic, complemented
4C2×#4994C212yesmaximal, complemented
5C2×#4955C211yesmaximal, characteristic
6C2×#4955C211yesmaximal, characteristic
7C2×#4950C211yesmaximal, characteristic, complemented
8#71570C212yesmaximal, complemented
9#71544C211yesmaximal, characteristic, complemented
10#69428C212yesmaximal, complemented
11#69427C212yesmaximal, complemented
12#14726—31nomaximal, Sylow
13C25×D3C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C24×Dic3C2211yescharacteristic
16C22×C3×C4⋊C4C2212yescomplemented
17C22×C3×C22⋊C4C2211yescharacteristic
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×#217C2211yescharacteristic
20C22×#217C2211yescharacteristic
21C22×(C2×D3)⋊C4—24no—
22C22×(C2×D3)⋊C4—28no—
23C22×(C2×D3)⋊C4C2212yes—
24C22×(C2×D3)⋊C4C2212yes—
25C22×(C2×D3)⋊C4C2212yes—
26C22×(C2×D3)⋊C4C2212yes—
27C22×(C2×D3)⋊C4C2212yes—
28C22×(C2×D3)⋊C4C2212yes—
29C22×C4⋊Dic3C2212yescomplemented
30C22×Dic3⋊C4C2211yescharacteristic, complemented
31C22×Dic3⋊C4C2211yescharacteristic, complemented
32C3×#380—24no—
33C2×C3×#95C2212yescomplemented
34#5210—24no—
35C2×C3⋊#95C2212yescomplemented
36C2×C3⋊#95C2211yescharacteristic, complemented
37C2×C3⋊#95C2212yescomplemented
38C2×C3⋊#95C2211yescharacteristic, complemented
39C2×C3⋊#95C2212yescomplemented
40#4994—28no—
41#4955—24no—
42#4955—24no—
43#4950—24no—
44C23×C22⋊C4—31no—
45C2×#396—32no—
46C2×#385—31no—
47C2×#385—31no—
48C2×#380D311yescharacteristic, complemented
49C2×#379—31no—
50C2×#379—31no—
51#1439—32no—
52#1439—32no—
53#1439—32no—
54C22⋊#95—31no—
55C25×C3C2311yescharacteristic
56C24×D3—22no—
57C24×D3—22no—
58C24×D3—24no—
59C24×D3—24no—
60C24×D3—22no—
61C24×D3—22no—
62C24×D3—22no—
63C24×D3—22no—
64C24×D3—42no—
65C24×D3—42no—
66C24×D3Q814yes—
67C24×D3C2312yes—
68C23×C3×C4—22no—
69C23×C3×C4—22no—
70C23×C3×C4—24no—
71C23×C3×C4—42no—
72C23×C3×C4D414yes—
73C23×C3×C4C2312yes—
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2312yes—
76C23×C3×C4C2311yescharacteristic
77C23×Dic3—22no—
78C23×Dic3—24no—
79C23×Dic3—22no—
80C23×Dic3—22no—
81C23×Dic3—42no—
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2312yes—
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C2×C3×C4⋊C4—24no—
88C2×C3×C4⋊C4—24no—
89C2×C3×C4⋊C4—42no—
90C2×C3×C22⋊C4—22no—
91C2×C3×C22⋊C4—22no—
92C2×C3×C22⋊C4—22no—
93C2×C3×C22⋊C4—22no—
94C2×C3×C22⋊C4—22no—
95C2×C3×C22⋊C4D414yes—
96C2×#217—22no—
97C2×#217—22no—
98C2×#217—22no—
99C2×#217—22no—
100C2×#217—22no—
101C2×#217D414yes—
102C2×(C2×D3)⋊C4—232no—
103C2×(C2×D3)⋊C4—24no—
104C2×(C2×D3)⋊C4—24no—
105C2×(C2×D3)⋊C4—24no—
106C2×(C2×D3)⋊C4—24no—
107C2×(C2×D3)⋊C4—24no—
108C2×(C2×D3)⋊C4—24no—
109C2×(C2×D3)⋊C4—24no—
110C2×(C2×D3)⋊C4—24no—
111C2×(C2×D3)⋊C4—24no—
112C2×(C2×D3)⋊C4—24no—
113C2×(C2×D3)⋊C4—24no—
114C2×(C2×D3)⋊C4—24no—
115C2×(C2×D3)⋊C4—24no—
116C2×(C2×D3)⋊C4—42no—
117C2×(C2×D3)⋊C4—42no—
118C2×(C2×D3)⋊C4—42no—
119C2×(C2×D3)⋊C4—42no—
120C2×(C2×D3)⋊C4D418yes—
121C2×C4⋊Dic3—24no—
122C2×C4⋊Dic3—24no—
123C2×C4⋊Dic3—42no—
124C2×Dic3⋊C4—22no—
125C2×Dic3⋊C4—22no—
126C2×Dic3⋊C4—24no—
127C2×Dic3⋊C4—42no—
128C3×#95—24no—
129C3⋊#95—22no—
130C3⋊#95—22no—
131C3⋊#95—24no—
132C3⋊#95—24no—
133C3⋊#95—42no—
134C26—31no—
135C24×C4—31no—
136C24×C4C2×D311yescharacteristic
137C22×C4⋊C4—31no—
138C22×C4⋊C4—32no—
139C22×C4⋊C4—31no—
140C22×C4⋊C4C2×D312yescomplemented
141C22×C22⋊C4—31no—
142C22×C22⋊C4—32no—
143C22×C22⋊C4—31no—
144C22×C22⋊C4—32no—
145C22×C22⋊C4—32no—
146C22×C22⋊C4—32no—
147C22×C22⋊C4—32no—
148C22×C22⋊C4—32no—
149C22×C22⋊C4—68no—
150C22×C22⋊C4—64no—
151C22×C22⋊C4C2×D311yescharacteristic
152C22×C22⋊C4C2×D311yescharacteristic
153#396—68no—
154#385—64no—
155#385—64no—
156#380—24no—
157#379—64no—
158#379—64no—
159C2×#95—32no—
160C2×#95—32no—
161C2×#95—31no—
162C2×#95—31no—
163C2×#95—32no—
164C2×#95C2×D312yescomplemented
165C24×C3—22no—
166C24×C3—22no—
167C24×C3—22no—
168C24×C3—22no—
169C24×C3C2×D412yes—
170C24×C3C2×D412yes—
171C24×C3C2×D412yes—
172C24×C3C2×Q812yes—
173C24×C3#4112yes—
174C24×C3#4112yes—
175C24×C3#4112yes—
176C24×C3C2411yescharacteristic
177C23×D3—28no—
178C23×D3—216no—
179C23×D3—28no—
180C23×D3—28no—
181C23×D3—22no—
182C23×D3—22no—
183C23×D3—22no—
184C23×D3—22no—
185C23×D3—22no—
186C23×D3—22no—
187C23×D3—22no—
188C23×D3—22no—
189C23×D3—22no—
190C23×D3—22no—
191C23×D3—22no—
192C23×D3—22no—
193C23×D3—216no—
194C23×D3—28no—
195C23×D3—28no—
196C23×D3—48no—
197C23×D3—48no—
198C23×D3—48no—
199C23×D3—48no—
200C23×D3—48no—
201C23×D3—48no—
202C23×D3—48no—
203C23×D3—48no—
204C23×D3—48no—
205C23×D3—44no—
206C23×D3—44no—
207C23×D3—48no—
208C23×D3—44no—
209C23×D3—44no—
210C23×D3—44no—
211C23×D3—44no—
212C23×D3C2×D414yes—
213C23×D3C2×Q814yes—
214C23×D3#4114yes—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—22no—
218C22×C3×C4—28no—
219C22×C3×C4—22no—
220C22×C3×C4—21no—
221C22×C3×C4—22no—
222C22×C3×C4—22no—
223C22×C3×C4—22no—
224C22×C3×C4—22no—
225C22×C3×C4—21no—
226C22×C3×C4—22no—
227C22×C3×C4—22no—
228C22×C3×C4—22no—
229C22×C3×C4—28no—
230C22×C3×C4—22no—
231C22×C3×C4—22no—
232C22×C3×C4—22no—
233C22×C3×C4—22no—
234C22×C3×C4—22no—
235C22×C3×C4—22no—
236C22×C3×C4—22no—
237C22×C3×C4—44no—
238C22×C3×C4—48no—
239C22×C3×C4—48no—
240C22×C3×C4C2×D412yes—
241C22×C3×C4C2×D412yes—
242C22×C3×C4C2×D414yes—
243C22×C3×C4C2×D414yes—
244C22×Dic3—28no—
245C22×Dic3—21no—
246C22×Dic3—21no—
247C22×Dic3—22no—
248C22×Dic3—22no—
249C22×Dic3—22no—
250C22×Dic3—22no—
251C22×Dic3—22no—
252C22×Dic3—21no—
253C22×Dic3—21no—
254C22×Dic3—22no—
255C22×Dic3—22no—
256C22×Dic3—22no—
257C22×Dic3—22no—
258C22×Dic3—22no—
259C22×Dic3—21no—
260C22×Dic3—22no—
261C22×Dic3—21no—
262C22×Dic3—21no—
263C22×Dic3—21no—
264C22×Dic3—22no—
265C22×Dic3—21no—
266C22×Dic3—21no—
267C22×Dic3—22no—
268C22×Dic3—22no—
269C22×Dic3—48no—
270C22×Dic3—48no—
271C22×Dic3—44no—
272C22×Dic3—44no—
273C22×Dic3C2×D412yes—
274C22×Dic3C2×D414yes—
275C22×Dic3C2×D412yes—
276C3×C4⋊C4—48no—
277C3×C22⋊C4—28no—
278C3×C22⋊C4—44no—
279#217—28no—
280#217—44no—
281(C2×D3)⋊C4—216no—
282(C2×D3)⋊C4—216no—
283(C2×D3)⋊C4—48no—
284(C2×D3)⋊C4—48no—
285(C2×D3)⋊C4—48no—
286(C2×D3)⋊C4—48no—
287C4⋊Dic3—48no—
288Dic3⋊C4—44no—
289Dic3⋊C4—44no—
290C25—32no—
291C25—34no—
292C25—64no—
293C25—64no—
294C25—62no—
295C25—62no—
296C25—62no—
297C25—62no—
298C25—62no—
299C25—62no—
300C25—122no—
301C25—122no—
302C25C22×D311yescharacteristic
303C23×C4—22no—
304C23×C4—22no—
305C23×C4—24no—
306C23×C4—31no—
307C23×C4—31no—
308C23×C4—32no—
309C23×C4—31no—
310C23×C4—31no—
311C23×C4—42no—
312C23×C4—64no—
313C23×C4—62no—
314C23×C4—62no—
315C23×C4—62no—
316C23×C4—122no—
317C23×C4D1214yes—
318C23×C4C22×D312yes—
319C23×C4C22×D311yescharacteristic
320C23×C4C22×D312yes—
321C23×C4C22×D311yescharacteristic
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—64no—
326C2×C4⋊C4—64no—
327C2×C4⋊C4—62no—
328C2×C4⋊C4—62no—
329C2×C4⋊C4—64no—
330C2×C4⋊C4—122no—
331C2×C4⋊C4—122no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—34no—
338C2×C22⋊C4—38no—
339C2×C22⋊C4—64no—
340C2×C22⋊C4—64no—
341C2×C22⋊C4—632no—
342C2×C22⋊C4—62no—
343C2×C22⋊C4—62no—
344C2×C22⋊C4—64no—
345C2×C22⋊C4—64no—
346C2×C22⋊C4—64no—
347C2×C22⋊C4—64no—
348C2×C22⋊C4—64no—
349C2×C22⋊C4—64no—
350C2×C22⋊C4—64no—
351C2×C22⋊C4—64no—
352C2×C22⋊C4—64no—
353C2×C22⋊C4—62no—
354C2×C22⋊C4—62no—
355C2×C22⋊C4—62no—
356C2×C22⋊C4—64no—
357C2×C22⋊C4—64no—
358C2×C22⋊C4—122no—
359C2×C22⋊C4—122no—
360C2×C22⋊C4—122no—
361C2×C22⋊C4—122no—
362C2×C22⋊C4#6714yes—
363#95—24no—
364#95—64no—
365#95—64no—
366#95—62no—
367#95—62no—
368#95—122no—
369C23×C3—22no—
370C23×C3—24no—
371C23×C3—22no—
372C23×C3—24no—
373C23×C3—22no—
374C23×C3—22no—
375C23×C3—24no—
376C23×C3—24no—
377C23×C3—24no—
378C23×C3—24no—
379C23×C3—24no—
380C23×C3—24no—
381C23×C3—24no—
382C23×C3—24no—
383C23×C3—24no—
384C23×C3—24no—
385C23×C3#12114yes—
386C23×C3#12114yes—
387C23×C3#12114yes—
388C23×C3C22⋊Q814yes—
389C23×C3C22⋊Q814yes—
390C23×C3C22⋊Q814yes—
391C23×C3#12614yes—
392C23×C3C22×D411yescharacteristic
393C23×C3C22×D412yes—
394C23×C3C22×D411yescharacteristic
395C23×C3C22×D411yescharacteristic
396C23×C3C22×Q811yescharacteristic
397C23×C3C2×#4111yescharacteristic
398C23×C3C2×#4111yescharacteristic
399C23×C3C2×#4111yescharacteristic
400C23×C3C2×#4112yes—
401C23×C3H(5,𝔽2)12yes—
402C23×C3H(5,𝔽2)12yes—
403C22×D3—232no—
404C22×D3—24no—
405C22×D3—24no—
406C22×D3—24no—
407C22×D3—24no—
408C22×D3—24no—
409C22×D3—24no—
410C22×D3—24no—
411C22×D3—24no—
412C22×D3—24no—
413C22×D3—24no—
414C22×D3—24no—
415C22×D3—24no—
416C22×D3—24no—
417C22×D3—24no—
418C22×D3—24no—
419C22×D3—24no—
420C22×D3—24no—
421C22×D3—24no—
422C22×D3—432no—
423C22×D3—432no—
424C22×D3—416no—
425C22×D3—416no—
426C22×D3—416no—
427C22×D3—416no—
428C22×D3—432no—
429C22×D3—432no—
430C22×D3—416no—
431C22×D3—42no—
432C22×D3—42no—
433C22×D3—42no—
434C22×D3—42no—
435C22×D3—42no—
436C22×D3—42no—
437C22×D3—42no—
438C22×D3—42no—
439C22×D3—42no—
440C22×D3—42no—
441C22×D3—42no—
442C22×D3—42no—
443C22×D3—42no—
444C22×D3—42no—
445C22×D3—42no—
446C22×D3—42no—
447C22×D3—416no—
448C22×D3C22⋊Q818yes—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—24no—
452C2×C3×C4—24no—
453C2×C3×C4—22no—
454C2×C3×C4—24no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—24no—
458C2×C3×C4—24no—
459C2×C3×C4—416no—
460C2×C3×C4—42no—
461C2×C3×C4—42no—
462C2×C3×C4—42no—
463C2×C3×C4—42no—
464C2×C3×C4—42no—
465C2×C3×C4—42no—
466C2×C3×C4—42no—
467C2×C3×C4—42no—
468C2×C3×C4—42no—
469C2×C3×C4—42no—
470C2×C3×C4—42no—
471C2×C3×C4—42no—
472C2×C3×C4—42no—
473C2×C3×C4#12014yes—
474C2×Dic3—24no—
475C2×Dic3—22no—
476C2×Dic3—22no—
477C2×Dic3—24no—
478C2×Dic3—24no—
479C2×Dic3—24no—
480C2×Dic3—24no—
481C2×Dic3—416no—
482C2×Dic3—41no—
483C2×Dic3—42no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—42no—
488C2×Dic3—42no—
489C2×Dic3—42no—
490C2×Dic3—42no—
491C2×Dic3—42no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494C2×Dic3—41no—
495C2×Dic3—41no—
496C2×Dic3—41no—
497C2×Dic3—41no—
498C2×Dic3—42no—
499C2×Dic3—42no—
500C2×Dic3—42no—
501C2×Dic3—42no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—34no—
507C24—34no—
508C24—34no—
509C24—616no—
510C24—68no—
511C24—68no—
512C24—616no—
513C24—68no—
514C24—62no—
515C24—62no—
516C24—62no—
517C24—62no—
518C24—62no—
519C24—62no—
520C24—62no—
521C24—62no—
522C24—62no—
523C24—62no—
524C24—62no—
525C24—62no—
526C24—68no—
527C24—68no—
528C24—128no—
529C24—128no—
530C24—128no—
531C24—128no—
532C24—128no—
533C24—128no—
534C24—128no—
535C24—128no—
536C24—128no—
537C24—124no—
538C24—124no—
539C24—128no—
540C24—124no—
541C24—124no—
542C24—124no—
543C24—124no—
544C24C2×D1212yes—
545C24#23512yes—
546C24D3×D412yes—
547C24#23712yes—
548C24D3×Q812yes—
549C24#23912yes—
550C24C2×#6712yes—
551C24C23×D311yescharacteristic
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—28no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—28no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—32no—
575C22×C4—34no—
576C22×C4—32no—
577C22×C4—44no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—68no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—62no—
584C22×C4—62no—
585C22×C4—62no—
586C22×C4—62no—
587C22×C4—62no—
588C22×C4—61no—
589C22×C4—61no—
590C22×C4—62no—
591C22×C4—62no—
592C22×C4—62no—
593C22×C4—62no—
594C22×C4—62no—
595C22×C4—61no—
596C22×C4—61no—
597C22×C4—61no—
598C22×C4—61no—
599C22×C4—62no—
600C22×C4—62no—
601C22×C4—62no—
602C22×C4—62no—
603C22×C4—61no—
604C22×C4—61no—
605C22×C4—128no—
606C22×C4—128no—
607C22×C4—124no—
608C22×C4—124no—
609C22×C4C2×D1212yes—
610C22×C4C2×D1212yes—
611C22×C4D3×D414yes—
612C22×C4C2×#6714yes—
613C4⋊C4—48no—
614C4⋊C4—124no—
615C4⋊C4—128no—
616C4⋊C4—124no—
617C22⋊C4—28no—
618C22⋊C4—44no—
619C22⋊C4—616no—
620C22⋊C4—68no—
621C22⋊C4—616no—
622C22⋊C4—128no—
623C22⋊C4—128no—
624C22⋊C4—128no—
625C22⋊C4—128no—
626C22⋊C4—124no—
627C22×C3—24no—
628C22×C3—24no—
629C22×C3—24no—
630C22×C3—24no—
631C22×C3—24no—
632C22×C3—28no—
633C22×C3—28no—
634C22×C3—28no—
635C22×C3—28no—
636C22×C3—24no—
637C22×C3#39618yescomplemented
638C22×C3C2×#12011yescharacteristic
639C22×C3C2×#12111yescharacteristic
640C22×C3C2×#12111yescharacteristic
641C22×C3C2×#12111yescharacteristic
642C22×C3C2×C22⋊Q811yescharacteristic
643C22×C3C2×C22⋊Q811yescharacteristic
644C22×C3C2×C22⋊Q811yescharacteristic
645C22×C3C2×C22⋊Q812yes—
646C22×C3#52511yescharacteristic
647C22×C3#52512yes—
648C22×C3C2×#12611yescharacteristic
649C22×C3#53411yescharacteristic
650C22×C3#53511yescharacteristic
651C22×C3#53812yes—
652C22×C3#54312yes—
653C22×C3D4212yes—
654C22×C3D4212yes—
655C22×C3#54612yes—
656C22×C3#54612yes—
657C22×C3#54612yes—
658C22×C3#54612yes—
659C22×C3#55112yes—
660C22×C3#55112yes—
661C2×D3—28no—
662C2×D3—28no—
663C2×D3—28no—
664C2×D3—464no—
665C2×D3—44no—
666C2×D3—44no—
667C2×D3—44no—
668C2×D3—44no—
669C2×D3—44no—
670C2×D3—44no—
671C2×D3—44no—
672C2×D3—44no—
673C2×D3—44no—
674C2×D3—44no—
675C2×D3—44no—
676C2×D3—44no—
677C3×C4—24no—
678C3×C4—42no—
679C3×C4—44no—
680C3×C4—82no—
681Dic3—42no—
682Dic3—44no—
683Dic3—42no—
684Dic3—81no—
685Dic3—81no—
686C23—24no—
687C23—24no—
688C23—22no—
689C23—24no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—24no—
694C23—24no—
695C23—24no—
696C23—24no—
697C23—24no—
698C23—24no—
699C23—24no—
700C23—24no—
701C23—24no—
702C23—38no—
703C23—632no—
704C23—64no—
705C23—64no—
706C23—64no—
707C23—64no—
708C23—64no—
709C23—64no—
710C23—64no—
711C23—64no—
712C23—64no—
713C23—64no—
714C23—64no—
715C23—64no—
716C23—64no—
717C23—64no—
718C23—64no—
719C23—64no—
720C23—64no—
721C23—64no—
722C23—1232no—
723C23—1232no—
724C23—1232no—
725C23—1216no—
726C23—1216no—
727C23—1216no—
728C23—1232no—
729C23—1216no—
730C23—1216no—
731C23—122no—
732C23—122no—
733C23—122no—
734C23—1216no—
735C23—122no—
736C23—122no—
737C23—122no—
738C23—122no—
739C23—122no—
740C23—122no—
741C23—122no—
742C23—122no—
743C23—122no—
744C23—122no—
745C23—122no—
746C23—122no—
747C23—122no—
748C23#89514yes—
749C23#89614yes—
750C23#89714yes—
751C23#89814yes—
752C23#93014yes—
753C23#93914yes—
754C23#94614yes—
755C23C22×D1211yescharacteristic
756C23C2×#23511yescharacteristic
757C23C2×D3×D412yes—
758C23C2×D3×D411yescharacteristic
759C23C2×#23711yescharacteristic
760C23#100412yes—
761C23C2×D3×Q811yescharacteristic
762C23C2×#23911yescharacteristic
763C23D3×#4112yes—
764C23#100912yes—
765C23C22×#6711yescharacteristic
766C2×C4—24no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—24no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—416no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—64no—
791C2×C4—62no—
792C2×C4—62no—
793C2×C4—64no—
794C2×C4—64no—
795C2×C4—64no—
796C2×C4—64no—
797C2×C4—1216no—
798C2×C4—122no—
799C2×C4—121no—
800C2×C4—121no—
801C2×C4—122no—
802C2×C4—121no—
803C2×C4—122no—
804C2×C4—121no—
805C2×C4—122no—
806C2×C4—122no—
807C2×C4—122no—
808C2×C4—121no—
809C2×C4—122no—
810C2×C4—121no—
811C2×C4—121no—
812C2×C4—121no—
813C2×C4—122no—
814C2×C4—121no—
815C2×C4—121no—
816C2×C4—122no—
817C2×C4—122no—
818C2×C4#88214yes—
819C2×C3—28no—
820C2×C3C2×#39611yescharacteristic
821C2×C3#240811yescharacteristic
822C2×C3#241011yescharacteristic
823C2×C3#241111yescharacteristic
824C2×C3#242412yes—
825C2×C3#243712yes—
826C2×C3#243712yes—
827C2×C3#248012yes—
828C2×C3#253411yescharacteristic
829C2×C3#262611yescharacteristic
830C2×C3#284811yescharacteristic
831D3—48no—
832C22—28no—
833C22—24no—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—28no—
838C22—28no—
839C22—28no—
840C22—24no—
841C22—24no—
842C22—68no—
843C22—68no—
844C22—68no—
845C22—1264no—
846C22—124no—
847C22—124no—
848C22—124no—
849C22—124no—
850C22—124no—
851C22—124no—
852C22—124no—
853C22—124no—
854C22—124no—
855C22—124no—
856C22—124no—
857C22—124no—
858C22#499418yescomplemented
859C22C2×#88211yescharacteristic
860C22#549012yes—
861C22#549311yescharacteristic
862C22C2×#89511yescharacteristic
863C22C2×#89611yescharacteristic
864C22C2×#89711yescharacteristic
865C22C2×#89811yescharacteristic
866C22#552411yescharacteristic
867C22#552511yescharacteristic
868C22#552712yes—
869C22#560612yes—
870C22#560912yes—
871C22#561012yes—
872C22#561712yes—
873C22D3×C22⋊Q812yes—
874C22#563012yes—
875C22#563412yes—
876C22#563712yes—
877C22C2×#93011yescharacteristic
878C22D4×#6712yes—
879C22C2×#93911yescharacteristic
880C22C2×#94611yescharacteristic
881C22#582912yes—
882C4—24no—
883C4—44no—
884C4—42no—
885C4—82no—
886C4—124no—
887C4—122no—
888C4—122no—
889C4—241no—
890C4—241no—
891C3#1472611yescharacteristic, complemented, Sylow
892C2—28no—
893C2—128no—
894C2#7389612yes—
895C2#7390912yes—
896C2#7395211yescharacteristic
897C2#7401611yescharacteristic
898C2#7402911yescharacteristic
899C2#7404911yescharacteristic
900C2#8212711yescharacteristic
901C2C2×#499411yescharacteristic
902C2#8227511yescharacteristic
903C2#8270612yes—
904C2#8281612yes—
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#380C2
prime radicalC25×D3C22
hypercenterC2×#380D3
hypocenterC3#14726
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×C3×#380C2semidirect
3. C2×#5210C2semidirect
4. C2×#4994C2semidirect
7. C2×#4950C2semidirect
8. #71570C2semidirect
9. #71544C2semidirect
10. #69428C2semidirect
11. #69427C2semidirect
16. C22×C3×C4⋊C4C22semidirect
29. C22×C4⋊Dic3C22semidirect
30. C22×Dic3⋊C4C22semidirect
31. C22×Dic3⋊C4C22semidirect
33. C2×C3×#95C22semidirect
35. C2×C3⋊#95C22semidirect
36. C2×C3⋊#95C22semidirect
37. C2×C3⋊#95C22semidirect
38. C2×C3⋊#95C22semidirect
39. C2×C3⋊#95C22semidirect
48. C2×#380D3semidirect
140. C22×C4⋊C4C2×D3semidirect
164. C2×#95C2×D3semidirect
637. C22×C3#396semidirect
858. C22#4994semidirect
891. C3#14726semidirect

Maximal subgroups

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

subgroupindex
C23×(C2×D3)⋊C42
C2×C3×#3802
C2×#52102
C2×#49942
C2×#49552
C2×#49502
#715702
#715442
#694282
#694272
#147263