Finite Group Databasebeta

← #10717839

Subgroups — #10717839

Order 768.

2006 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#892C211yesmaximal, characteristic
2C2×C3×#389C211yesmaximal, characteristic, complemented
3C2×#4987C211yesmaximal, characteristic
4C2×#4984C211yesmaximal, characteristic, complemented
5C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
6#71570C212yesmaximal
7#71563C212yesmaximal, complemented
8#71563C211yesmaximal, characteristic, complemented
9#71535C211yesmaximal, characteristic, complemented
10#69427C212yesmaximal
11#69402C212yesmaximal, complemented
12#13951—31nomaximal, Sylow
13C23×C4×D3C2211yescharacteristic
14C22×C3×C4⋊C4C2211yescharacteristic
15C22×C3×C4⋊C4C2212yes—
16C22×C3×C4⋊C4C2211yescharacteristic
17C22×C3×C42C2211yescharacteristic
18C22×(C2×D3)⋊C4C2211yescharacteristic
19C22×(C2×D3)⋊C4C2211yescharacteristic
20C22×(C2×D3)⋊C4C2212yes—
21C22×(C2×D3)⋊C4C2212yes—
22C22×C4⋊Dic3C2211yescharacteristic
23C22×C4⋊Dic3C2212yes—
24C22×C4⋊Dic3C2211yescharacteristic
25C22×C4×Dic3C2211yescharacteristic
26C22×C4×Dic3C2212yes—
27C2×#892—24no—
28C2×#892—24no—
29C2×#892C418yescomplemented
30C3×#389—24no—
31C2×C3×#95C2212yes—
32C2×C3⋊#95C2212yes—
33C2×C3⋊#95C2211yescharacteristic
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2211yescharacteristic
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2212yes—
40#4987—24no—
41#4984—24no—
42C4×(C2×D3)⋊C4—24no—
43C22×#117—31no—
44C2×#389—31no—
45C2×#389D311yescharacteristic, complemented
46C2×#380—31no—
47C2×C4×C22⋊C4—31no—
48#1439—32no—
49#1439—32no—
50C4⋊#95—31no—
51C4⋊#95—31no—
52C4⋊#95—32no—
53#1434—32no—
54C24×D3C2311yescharacteristic
55C23×C3×C4C2312yes—
56C23×C3×C4C2311yescharacteristic
57C23×C3×C4C2311yescharacteristic
58C23×C3×C4C2312yes—
59C23×C3×C4C2311yescharacteristic
60C23×Dic3C2312yes—
61C23×Dic3C2312yes—
62C23×Dic3C2311yescharacteristic
63C23×Dic3C2311yescharacteristic
64C23×Dic3C2311yescharacteristic
65C22×C4×D3—22no—
66C22×C4×D3—22no—
67C22×C4×D3—22no—
68C22×C4×D3—22no—
69C22×C4×D3C2×C414yes—
70C22×C4×D3D414yes—
71C22×C4×D3Q814yes—
72C2×C3×C4⋊C4—22no—
73C2×C3×C4⋊C4—24no—
74C2×C3×C4⋊C4—22no—
75C2×C3×C4⋊C4—24no—
76C2×C3×C4⋊C4—22no—
77C2×C3×C4⋊C4—42no—
78C2×C3×C4⋊C4C2×C414yes—
79C2×C3×C4⋊C4D414yes—
80C2×C3×C4⋊C4D414yes—
81C2×C3×C42—22no—
82C2×C3×C42—22no—
83C2×C3×C42—22no—
84C2×(C2×D3)⋊C4—22no—
85C2×(C2×D3)⋊C4—22no—
86C2×(C2×D3)⋊C4—24no—
87C2×(C2×D3)⋊C4—24no—
88C2×(C2×D3)⋊C4—22no—
89C2×(C2×D3)⋊C4—22no—
90C2×(C2×D3)⋊C4—22no—
91C2×(C2×D3)⋊C4—22no—
92C2×(C2×D3)⋊C4—24no—
93C2×(C2×D3)⋊C4—42no—
94C2×(C2×D3)⋊C4—42no—
95C2×(C2×D3)⋊C4C2×C418yes—
96C2×C4⋊Dic3—22no—
97C2×C4⋊Dic3—22no—
98C2×C4⋊Dic3—24no—
99C2×C4⋊Dic3—22no—
100C2×C4⋊Dic3—22no—
101C2×C4⋊Dic3—22no—
102C2×C4⋊Dic3—24no—
103C2×C4⋊Dic3—42no—
104C2×C4⋊Dic3C2×C414yes—
105C2×C4×Dic3—24no—
106C2×C4×Dic3—24no—
107C2×C4×Dic3—22no—
108C2×C4×Dic3—22no—
109C2×C4×Dic3—22no—
110C2×C4×Dic3C2×C418yes—
111#892—232no—
112C3×#95—24no—
113C3⋊#95—24no—
114C3⋊#95—24no—
115C3⋊#95—22no—
116C3⋊#95—22no—
117C3⋊#95—24no—
118C3⋊#95—24no—
119C3⋊#95—42no—
120C3⋊#95—42no—
121C24×C4—31no—
122C2×#117—38no—
123C2×#117—64no—
124C2×#117—64no—
125C22×C4⋊C4—31no—
126C22×C4⋊C4—31no—
127C22×C4⋊C4—32no—
128C22×C4⋊C4C2×D311yescharacteristic
129C22×C4⋊C4C2×D312yes—
130C22×C4⋊C4C2×D311yescharacteristic
131C22×C22⋊C4—32no—
132C22×C22⋊C4—31no—
133C22×C22⋊C4—31no—
134C22×C22⋊C4—32no—
135C22×C42—32no—
136C22×C42—31no—
137C22×C42C2×D311yescharacteristic
138#389—24no—
139#389—64no—
140#380—64no—
141C4×C22⋊C4—64no—
142C2×#95—31no—
143C2×#95—32no—
144C2×#95—32no—
145C2×#95—32no—
146C2×#95—32no—
147C2×#95—31no—
148C2×#95—32no—
149C2×#95—32no—
150C2×#95C2×D312yes—
151C24×C3C2411yescharacteristic
152C23×D3—21no—
153C23×D3—21no—
154C23×D3—21no—
155C23×D3—21no—
156C23×D3—21no—
157C23×D3—21no—
158C23×D3—21no—
159C23×D3—21no—
160C23×D3—21no—
161C23×D3—21no—
162C23×D3—21no—
163C23×D3—21no—
164C23×D3C22×C412yes—
165C23×D3C2×D412yes—
166C23×D3C2×Q812yes—
167C22×C3×C4—22no—
168C22×C3×C4—22no—
169C22×C3×C4—22no—
170C22×C3×C4—22no—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—22no—
184C22×C3×C4—22no—
185C22×C3×C4—22no—
186C22×C3×C4—22no—
187C22×C3×C4—22no—
188C22×C3×C4—22no—
189C22×C3×C4—22no—
190C22×C3×C4C22×C414yes—
191C22×C3×C4C22×C412yes—
192C22×C3×C4C2×D414yes—
193C22×C3×C4C2×D412yes—
194C22×C3×C4C2×D412yes—
195C22×C3×C4C2×D414yes—
196C22×C3×C4C2×D412yes—
197C22×C3×C4C2×Q812yes—
198C22×C3×C4#4112yes—
199C22×C3×C4#4112yes—
200C22×C3×C4#4112yes—
201C22×C3×C4#4112yes—
202C22×Dic3—21no—
203C22×Dic3—21no—
204C22×Dic3—21no—
205C22×Dic3—21no—
206C22×Dic3—21no—
207C22×Dic3—21no—
208C22×Dic3—21no—
209C22×Dic3—21no—
210C22×Dic3—22no—
211C22×Dic3—22no—
212C22×Dic3—22no—
213C22×Dic3—22no—
214C22×Dic3—21no—
215C22×Dic3—21no—
216C22×Dic3—21no—
217C22×Dic3—21no—
218C22×Dic3—22no—
219C22×Dic3—21no—
220C22×Dic3—21no—
221C22×Dic3—22no—
222C22×Dic3—21no—
223C22×Dic3—21no—
224C22×Dic3—22no—
225C22×Dic3—22no—
226C22×Dic3—22no—
227C22×Dic3—22no—
228C22×Dic3—22no—
229C22×Dic3—22no—
230C22×Dic3—22no—
231C22×Dic3C22×C414yes—
232C22×Dic3C22×C412yes—
233C22×Dic3C2×D412yes—
234C22×Dic3C2×Q812yes—
235C22×Dic3#4112yes—
236C22×Dic3#4112yes—
237C2×C4×D3—28no—
238C2×C4×D3—28no—
239C2×C4×D3—28no—
240C2×C4×D3—28no—
241C2×C4×D3—28no—
242C2×C4×D3—28no—
243C2×C4×D3C4⋊C4116yescomplemented
244C3×C4⋊C4—48no—
245C3×C4⋊C4—44no—
246C3×C4⋊C4C22⋊C4116yescomplemented
247C3×C42—44no—
248(C2×D3)⋊C4—28no—
249(C2×D3)⋊C4—28no—
250(C2×D3)⋊C4—216no—
251(C2×D3)⋊C4—48no—
252C4⋊Dic3—28no—
253C4⋊Dic3—48no—
254C4⋊Dic3—44no—
255C4×Dic3—216no—
256C4×Dic3—44no—
257C25—31no—
258C23×C4—31no—
259C23×C4—34no—
260C23×C4—34no—
261C23×C4—34no—
262C23×C4—31no—
263C23×C4—32no—
264C23×C4—31no—
265C23×C4—32no—
266C23×C4—62no—
267C23×C4—62no—
268C23×C4—62no—
269C23×C4—62no—
270C23×C4C22×D312yes—
271C23×C4C22×D311yescharacteristic
272C23×C4C22×D311yescharacteristic
273C23×C4C22×D312yes—
274C23×C4C22×D311yescharacteristic
275#117—632no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—34no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—62no—
284C2×C4⋊C4—62no—
285C2×C4⋊C4—64no—
286C2×C4⋊C4—64no—
287C2×C4⋊C4—62no—
288C2×C4⋊C4—62no—
289C2×C4⋊C4—62no—
290C2×C4⋊C4—122no—
291C2×C4⋊C4C4×D314yes—
292C2×C4⋊C4D1214yes—
293C2×C4⋊C4#6714yes—
294C2×C22⋊C4—38no—
295C2×C22⋊C4—62no—
296C2×C22⋊C4—62no—
297C2×C22⋊C4—62no—
298C2×C22⋊C4—62no—
299C2×C22⋊C4—64no—
300C2×C22⋊C4—62no—
301C2×C22⋊C4—62no—
302C2×C22⋊C4—64no—
303C2×C22⋊C4—64no—
304C2×C22⋊C4—122no—
305C2×C22⋊C4—122no—
306C2×C42—22no—
307C2×C42—22no—
308C2×C42—22no—
309C2×C42—38no—
310C2×C42—64no—
311C2×C42—64no—
312C2×C42—62no—
313C2×C42—62no—
314C2×C42—62no—
315#95—24no—
316#95—64no—
317#95—62no—
318#95—62no—
319#95—64no—
320#95—64no—
321#95—64no—
322#95—122no—
323#95—122no—
324C23×C3C23×C411yescharacteristic
325C23×C3C22×D411yescharacteristic
326C23×C3C22×D411yescharacteristic
327C23×C3C22×D411yescharacteristic
328C23×C3C22×Q811yescharacteristic
329C23×C3C2×#4111yescharacteristic
330C23×C3C2×#4111yescharacteristic
331C23×C3C2×#4111yescharacteristic
332C23×C3C2×#4111yescharacteristic
333C23×C3C2×#4111yescharacteristic
334C23×C3C2×#4111yescharacteristic
335C23×C3H(5,𝔽2)11yescharacteristic
336C23×C3H(5,𝔽2)11yescharacteristic
337C23×C32−1+411yescharacteristic
338C23×C32−1+411yescharacteristic
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—22no—
349C22×D3—22no—
350C22×D3—22no—
351C22×D3—22no—
352C22×D3—22no—
353C22×D3—22no—
354C22×D3—22no—
355C22×D3—22no—
356C22×D3—22no—
357C22×D3—41no—
358C22×D3—41no—
359C22×D3—41no—
360C22×D3—41no—
361C22×D3—41no—
362C22×D3—41no—
363C22×D3—41no—
364C22×D3—41no—
365C22×D3—41no—
366C22×D3—41no—
367C22×D3—41no—
368C22×D3—41no—
369C22×D3—41no—
370C22×D3—41no—
371C22×D3—41no—
372C22×D3—41no—
373C22×D3C2×C4⋊C414yes—
374C2×C3×C4—24no—
375C2×C3×C4—24no—
376C2×C3×C4—24no—
377C2×C3×C4—24no—
378C2×C3×C4—24no—
379C2×C3×C4—24no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—41no—
387C2×C3×C4—41no—
388C2×C3×C4—41no—
389C2×C3×C4—41no—
390C2×C3×C4—41no—
391C2×C3×C4—41no—
392C2×C3×C4—41no—
393C2×C3×C4—41no—
394C2×C3×C4—42no—
395C2×C3×C4—42no—
396C2×C3×C4—42no—
397C2×C3×C4—42no—
398C2×C3×C4—42no—
399C2×C3×C4—42no—
400C2×C3×C4—42no—
401C2×C3×C4C2×C22⋊C418yes—
402C2×C3×C4C2×C22⋊C414yes—
403C2×C3×C4C2×C4⋊C414yes—
404C2×C3×C4#11714yes—
405C2×C3×C4#12114yes—
406C2×C3×C4#12114yes—
407C2×C3×C4C22⋊Q814yes—
408C2×C3×C4C22⋊Q814yes—
409C2×Dic3—22no—
410C2×Dic3—22no—
411C2×Dic3—22no—
412C2×Dic3—22no—
413C2×Dic3—22no—
414C2×Dic3—22no—
415C2×Dic3—24no—
416C2×Dic3—24no—
417C2×Dic3—24no—
418C2×Dic3—22no—
419C2×Dic3—22no—
420C2×Dic3—22no—
421C2×Dic3—22no—
422C2×Dic3—22no—
423C2×Dic3—22no—
424C2×Dic3—41no—
425C2×Dic3—41no—
426C2×Dic3—41no—
427C2×Dic3—41no—
428C2×Dic3—41no—
429C2×Dic3—42no—
430C2×Dic3—42no—
431C2×Dic3—42no—
432C2×Dic3—41no—
433C2×Dic3—42no—
434C2×Dic3—41no—
435C2×Dic3—41no—
436C2×Dic3—42no—
437C2×Dic3—42no—
438C2×Dic3—42no—
439C2×Dic3—42no—
440C2×Dic3—42no—
441C2×Dic3—42no—
442C2×Dic3—42no—
443C2×Dic3C2×C4⋊C414yes—
444C4×D3—232no—
445C24—32no—
446C24—32no—
447C24—32no—
448C24—61no—
449C24—61no—
450C24—61no—
451C24—61no—
452C24—61no—
453C24—61no—
454C24—61no—
455C24—61no—
456C24—61no—
457C24—61no—
458C24—61no—
459C24—61no—
460C24C23×D311yescharacteristic
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—32no—
485C22×C4—32no—
486C22×C4—32no—
487C22×C4—316no—
488C22×C4—34no—
489C22×C4—32no—
490C22×C4—32no—
491C22×C4—61no—
492C22×C4—61no—
493C22×C4—61no—
494C22×C4—61no—
495C22×C4—68no—
496C22×C4—68no—
497C22×C4—68no—
498C22×C4—68no—
499C22×C4—68no—
500C22×C4—68no—
501C22×C4—61no—
502C22×C4—62no—
503C22×C4—61no—
504C22×C4—61no—
505C22×C4—61no—
506C22×C4—61no—
507C22×C4—61no—
508C22×C4—62no—
509C22×C4—61no—
510C22×C4—61no—
511C22×C4—61no—
512C22×C4—62no—
513C22×C4—61no—
514C22×C4—62no—
515C22×C4—61no—
516C22×C4—62no—
517C22×C4—61no—
518C22×C4—62no—
519C22×C4—62no—
520C22×C4—62no—
521C22×C4—62no—
522C22×C4—62no—
523C22×C4—62no—
524C22×C4—62no—
525C22×C4—62no—
526C22×C4C2×C4×D314yes—
527C22×C4C2×C4×D312yes—
528C22×C4C2×D1214yes—
529C22×C4C2×D1212yes—
530C22×C4D3×D412yes—
531C22×C4#23712yes—
532C22×C4#23712yes—
533C22×C4D3×Q812yes—
534C22×C4#23912yes—
535C22×C4#23912yes—
536C22×C4C2×#6714yes—
537C22×C4C2×#6712yes—
538C4⋊C4—48no—
539C4⋊C4—44no—
540C4⋊C4—68no—
541C4⋊C4—128no—
542C4⋊C4—124no—
543C4⋊C4(C2×D3)⋊C4116yescomplemented
544C22⋊C4—68no—
545C22⋊C4—68no—
546C22⋊C4—616no—
547C22⋊C4—128no—
548C42—44no—
549C42—616no—
550C42—124no—
551C22×C3C22×C22⋊C411yescharacteristic
552C22×C3C22×C4⋊C411yescharacteristic
553C22×C3C2×#11711yescharacteristic
554C22×C3C4×#4111yescharacteristic
555C22×C3C4×#4111yescharacteristic
556C22×C3#52011yescharacteristic
557C22×C3#52011yescharacteristic
558C22×C3C2×#12111yescharacteristic
559C22×C3C2×#12111yescharacteristic
560C22×C3C2×C22⋊Q811yescharacteristic
561C22×C3C2×C22⋊Q811yescharacteristic
562C22×C3#52511yescharacteristic
563C22×C3#52511yescharacteristic
564C22×C3#53311yescharacteristic
565C22×C3#53311yescharacteristic
566C22×C3#53511yescharacteristic
567C22×C3#53611yescharacteristic
568C22×C3#54411yescharacteristic
569C22×C3#54411yescharacteristic
570C22×C3#54611yescharacteristic
571C22×C3#54611yescharacteristic
572C22×C3#54711yescharacteristic
573C22×C3#54711yescharacteristic
574C22×C3#54811yescharacteristic
575C22×C3#54811yescharacteristic
576C22×C3#55011yescharacteristic
577C22×C3#55011yescharacteristic
578C22×C3#55211yescharacteristic
579C22×C3#55211yescharacteristic
580C22×C3#55311yescharacteristic
581C22×C3#55311yescharacteristic
582C22×C3#55511yescharacteristic
583C22×C3#55511yescharacteristic
584C22×C3#55611yescharacteristic
585C22×C3#55611yescharacteristic
586C2×D3—24no—
587C2×D3—24no—
588C2×D3—24no—
589C2×D3—42no—
590C2×D3—42no—
591C2×D3—42no—
592C2×D3—42no—
593C2×D3—42no—
594C2×D3—42no—
595C2×D3—42no—
596C2×D3—42no—
597C2×D3—42no—
598C2×D3—42no—
599C2×D3—42no—
600C2×D3—42no—
601C3×C4—28no—
602C3×C4—42no—
603C3×C4—42no—
604C3×C4—82no—
605C3×C4#38018yes—
606Dic3—24no—
607Dic3—44no—
608Dic3—42no—
609Dic3—42no—
610Dic3—82no—
611C23—34no—
612C23—62no—
613C23—62no—
614C23—62no—
615C23—62no—
616C23—62no—
617C23—62no—
618C23—62no—
619C23—62no—
620C23—62no—
621C23—62no—
622C23—62no—
623C23—62no—
624C23—62no—
625C23—62no—
626C23—62no—
627C23—62no—
628C23—62no—
629C23—62no—
630C23—121no—
631C23—121no—
632C23—121no—
633C23—121no—
634C23—121no—
635C23—121no—
636C23—121no—
637C23—121no—
638C23—121no—
639C23—121no—
640C23—121no—
641C23—121no—
642C23—121no—
643C23—121no—
644C23—121no—
645C23—121no—
646C23C22×C4×D311yescharacteristic
647C23C22×D1211yescharacteristic
648C23C2×D3×D411yescharacteristic
649C23C2×#23711yescharacteristic
650C23C2×#23711yescharacteristic
651C23#100411yescharacteristic
652C23C2×D3×Q811yescharacteristic
653C23C2×#23911yescharacteristic
654C23C2×#23911yescharacteristic
655C23#100711yescharacteristic
656C23D3×#4111yescharacteristic
657C23D3×#4111yescharacteristic
658C23#100911yescharacteristic
659C23#101011yescharacteristic
660C23C22×#6711yescharacteristic
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—34no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—62no—
690C2×C4—62no—
691C2×C4—62no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—62no—
695C2×C4—632no—
696C2×C4—62no—
697C2×C4—62no—
698C2×C4—64no—
699C2×C4—62no—
700C2×C4—64no—
701C2×C4—64no—
702C2×C4—62no—
703C2×C4—62no—
704C2×C4—62no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4—122no—
711C2×C4—122no—
712C2×C4—122no—
713C2×C4—121no—
714C2×C4—122no—
715C2×C4—121no—
716C2×C4—121no—
717C2×C4—122no—
718C2×C4—122no—
719C2×C4—122no—
720C2×C4—122no—
721C2×C4—122no—
722C2×C4—122no—
723C2×C4—122no—
724C2×C4D3×C4⋊C414yes—
725C2×C4#89214yes—
726C2×C4#89514yes—
727C2×C4#89714yes—
728C2×C4C2×(C2×D3)⋊C418yes—
729C2×C4C2×(C2×D3)⋊C414yes—
730C2×C4#93814yes—
731C2×C4#94614yes—
732C2×C3C2×#38011yescharacteristic
733C2×C3#229611yescharacteristic
734C2×C3#231711yescharacteristic
735C2×C3#233911yescharacteristic
736C2×C3#234111yescharacteristic
737C2×C3#234611yescharacteristic
738C2×C3#234711yescharacteristic
739C2×C3#241411yescharacteristic
740C2×C3#241411yescharacteristic
741C2×C3#241511yescharacteristic
742C2×C3#241511yescharacteristic
743C2×C3#243911yescharacteristic
744C2×C3#243911yescharacteristic
745C2×C3#244111yescharacteristic
746C2×C3#244111yescharacteristic
747D3—44no—
748C22—64no—
749C22—64no—
750C22—64no—
751C22—122no—
752C22—122no—
753C22—122no—
754C22—122no—
755C22—122no—
756C22—122no—
757C22—122no—
758C22—122no—
759C22—122no—
760C22—122no—
761C22—122no—
762C22—122no—
763C22C2×D3×C4⋊C411yescharacteristic
764C22C2×#89211yescharacteristic
765C22C2×#89511yescharacteristic
766C22C2×#89711yescharacteristic
767C22C4×#23711yescharacteristic
768C22#554611yescharacteristic
769C22#555411yescharacteristic
770C22#555511yescharacteristic
771C22C4×#23911yescharacteristic
772C22#557411yescharacteristic
773C22#557611yescharacteristic
774C22#557711yescharacteristic
775C22#560611yescharacteristic
776C22#560711yescharacteristic
777C22#561611yescharacteristic
778C22#561811yescharacteristic
779C22#562711yescharacteristic
780C22#562811yescharacteristic
781C22#564111yescharacteristic
782C22#564211yescharacteristic
783C22#568811yescharacteristic
784C22#568911yescharacteristic
785C22#569411yescharacteristic
786C22#569511yescharacteristic
787C22#572811yescharacteristic
788C22#572911yescharacteristic
789C22#573211yescharacteristic
790C22#573411yescharacteristic
791C22C22×(C2×D3)⋊C411yescharacteristic
792C22C2×#93811yescharacteristic
793C22#580611yescharacteristic
794C22C2×#94611yescharacteristic
795C22#581711yescharacteristic
796C22#582411yescharacteristic
797C22#583411yescharacteristic
798C4—28no—
799C4—42no—
800C4—42no—
801C4—64no—
802C4—82no—
803C4—124no—
804C4—122no—
805C4—122no—
806C4—242no—
807C4#498718yes—
808C3#1395111yescharacteristic, complemented, Sylow
809C2—124no—
810C2#7596311yescharacteristic
811C2#7596811yescharacteristic
812C2#7597911yescharacteristic
813C2#7598011yescharacteristic
814C2#7599711yescharacteristic
815C2#7600011yescharacteristic
816C2#7620911yescharacteristic
817C2#7621011yescharacteristic
818C2C2×#498711yescharacteristic
819C2#8233011yescharacteristic
820C2#8245711yescharacteristic
821C2#8270311yescharacteristic
822C2#8281311yescharacteristic
823C2#8305811yescharacteristic
824C2#8325611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC2×C3×#389C2
socle, cosocleC24×C3C24
prime radicalC24×D3C23
hypercenterC2×#389D3
hypocenterC3#13951
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
4. C2×#4984C2semidirect
7. #71563C2semidirect
8. #71563C2semidirect
9. #71535C2semidirect
11. #69402C2semidirect
29. C2×#892C4semidirect
45. C2×#389D3semidirect
243. C2×C4×D3C4⋊C4semidirect
246. C3×C4⋊C4C22⋊C4semidirect
543. C4⋊C4(C2×D3)⋊C4semidirect
808. C3#13951semidirect

Maximal subgroups

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

subgroupindex
C22×#8922
C2×C3×#3892
C2×#49872
C2×#49842
C2×C4×(C2×D3)⋊C42
#715702
#715632
#715352
#694272
#694022
#139513