Finite Group Databasebeta

← #10720229

Subgroups — #10720229

Order 768.

1938 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#389C211yesmaximal, characteristic, complemented
2C2×#4988C211yesmaximal, characteristic
3C2×#4988C211yesmaximal, characteristic
4C2×#4990C212yesmaximal, complemented
5C2×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
6C2×#4939C211yesmaximal, characteristic
7#71570C212yesmaximal, complemented
8#71563C211yesmaximal, characteristic, complemented
9C4×C3⋊#95C211yesmaximal, characteristic, complemented
10#69429C212yesmaximal, complemented
11#69408C212yesmaximal, complemented
12#14141—31nomaximal, Sylow
13C23×D12C2211yescharacteristic
14C22×C3×C4⋊C4C2212yes—
15C22×C3×C4⋊C4C2211yescharacteristic
16C22×C3×C4⋊C4C2211yescharacteristic
17C22×C3×C42C2211yescharacteristic
18C22×(C2×D3)⋊C4C2212yes—
19C22×(C2×D3)⋊C4C2212yes—
20C22×(C2×D3)⋊C4C2212yes—
21C22×(C2×D3)⋊C4C2212yes—
22C22×(C2×D3)⋊C4C2212yes—
23C22×(C2×D3)⋊C4C2212yes—
24C22×C4⋊Dic3C2211yescharacteristic
25C22×C4×Dic3C2211yescharacteristic
26C22×C4×Dic3C2212yes—
27C22×C4×Dic3C2211yescharacteristic
28C3×#389—24no—
29C2×C3×#95C2212yes—
30C2×C3⋊#95C2211yescharacteristic
31C2×C3⋊#95C2211yescharacteristic
32C2×C3⋊#95C2212yes—
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2211yescharacteristic
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2211yescharacteristic
37#4990—28no—
38#4988—24no—
39#4988C418yescomplemented
40Dic3×C4⋊C4—24no—
41#4939—24no—
42C2×#390—31no—
43C2×#390—31no—
44C2×#390—31no—
45C2×#389D311yescharacteristic, complemented
46C2×#388—32no—
47C2×C4×C4⋊C4—31no—
48#1440—32no—
49#1439—32no—
50#1437—32no—
51C4⋊#95—31no—
52C4×#95—31no—
53C24×D3C2312yes—
54C23×C3×C4C2312yes—
55C23×C3×C4C2311yescharacteristic
56C23×C3×C4C2312yes—
57C23×C3×C4C2311yescharacteristic
58C23×C3×C4C2311yescharacteristic
59C23×Dic3C2311yescharacteristic
60C23×Dic3C2311yescharacteristic
61C23×Dic3C2312yes—
62C23×Dic3C2311yescharacteristic
63C23×Dic3C2311yescharacteristic
64C22×D12—22no—
65C22×D12—22no—
66C22×D12—22no—
67C22×D12—22no—
68C22×D12—22no—
69C22×D12—22no—
70C22×D12C2×C414yes—
71C2×C3×C4⋊C4—22no—
72C2×C3×C4⋊C4—22no—
73C2×C3×C4⋊C4—22no—
74C2×C3×C4⋊C4—22no—
75C2×C3×C4⋊C4—24no—
76C2×C3×C4⋊C4—24no—
77C2×C3×C4⋊C4—42no—
78C2×C3×C4⋊C4C2×C414yes—
79C2×C3×C4⋊C4D414yes—
80C2×C3×C42—22no—
81C2×C3×C42—22no—
82C2×C3×C42—22no—
83C2×(C2×D3)⋊C4—24no—
84C2×(C2×D3)⋊C4—24no—
85C2×(C2×D3)⋊C4—24no—
86C2×(C2×D3)⋊C4—24no—
87C2×(C2×D3)⋊C4—24no—
88C2×(C2×D3)⋊C4—24no—
89C2×(C2×D3)⋊C4—24no—
90C2×(C2×D3)⋊C4—24no—
91C2×(C2×D3)⋊C4—24no—
92C2×(C2×D3)⋊C4—24no—
93C2×(C2×D3)⋊C4—42no—
94C2×(C2×D3)⋊C4—42no—
95C2×(C2×D3)⋊C4—42no—
96C2×(C2×D3)⋊C4—42no—
97C2×(C2×D3)⋊C4—42no—
98C2×(C2×D3)⋊C4—42no—
99C2×(C2×D3)⋊C4C2×C418yes—
100C2×(C2×D3)⋊C4C2×C418yes—
101C2×C4⋊Dic3—22no—
102C2×C4⋊Dic3—22no—
103C2×C4⋊Dic3D414yes—
104C2×C4×Dic3—22no—
105C2×C4×Dic3—22no—
106C2×C4×Dic3—22no—
107C2×C4×Dic3—22no—
108C2×C4×Dic3—22no—
109C2×C4×Dic3—24no—
110C2×C4×Dic3—24no—
111C2×C4×Dic3—42no—
112C2×C4×Dic3C2×C414yes—
113C3×#95—24no—
114C3⋊#95—22no—
115C3⋊#95—24no—
116C3⋊#95—24no—
117C3⋊#95—22no—
118C3⋊#95—22no—
119C3⋊#95—42no—
120C3⋊#95D414yescomplemented
121C23×D4—31no—
122C22×C4⋊C4—31no—
123C22×C4⋊C4C2×D312yes—
124C22×C4⋊C4C2×D311yescharacteristic
125C22×C4⋊C4C2×D311yescharacteristic
126C22×C22⋊C4—32no—
127C22×C22⋊C4—32no—
128C22×C22⋊C4—32no—
129C22×C22⋊C4—32no—
130C22×C22⋊C4—32no—
131C22×C22⋊C4—32no—
132C22×C42—31no—
133C22×C42—31no—
134C22×C42—32no—
135C22×C42C2×D311yescharacteristic
136#390—38no—
137#390—64no—
138#390—64no—
139#389—24no—
140#388—68no—
141C4×C4⋊C4—64no—
142C2×#95—31no—
143C2×#95—31no—
144C2×#95—31no—
145C2×#95—31no—
146C2×#95—32no—
147C2×#95—32no—
148C2×#95—32no—
149C2×#95C2×D312yes—
150C24×C3C2411yescharacteristic
151C23×D3—22no—
152C23×D3—22no—
153C23×D3—22no—
154C23×D3—22no—
155C23×D3—22no—
156C23×D3—22no—
157C23×D3—22no—
158C23×D3—22no—
159C23×D3—22no—
160C23×D3—22no—
161C23×D3—22no—
162C23×D3—22no—
163C23×D3—22no—
164C23×D3—22no—
165C23×D3C22×C414yes—
166C22×C3×C4—22no—
167C22×C3×C4—22no—
168C22×C3×C4—21no—
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—22no—
177C22×C3×C4—22no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—22no—
181C22×C3×C4—22no—
182C22×C3×C4—22no—
183C22×C3×C4—22no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—22no—
187C22×C3×C4—22no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4C22×C414yes—
191C22×C3×C4C22×C412yes—
192C22×C3×C4C2×D412yes—
193C22×C3×C4C2×D412yes—
194C22×C3×C4C2×D414yes—
195C22×C3×C4C2×D412yes—
196C22×C3×C4#4112yes—
197C22×C3×C4#4112yes—
198C22×C3×C4#4112yes—
199C22×C3×C4#4112yes—
200C22×C3×C4#4112yes—
201C22×Dic3—21no—
202C22×Dic3—21no—
203C22×Dic3—21no—
204C22×Dic3—21no—
205C22×Dic3—21no—
206C22×Dic3—22no—
207C22×Dic3—21no—
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—21no—
217C22×Dic3—21no—
218C22×Dic3—22no—
219C22×Dic3—22no—
220C22×Dic3—22no—
221C22×Dic3—21no—
222C22×Dic3—22no—
223C22×Dic3—22no—
224C22×Dic3—21no—
225C22×Dic3—21no—
226C22×Dic3—21no—
227C22×Dic3—21no—
228C22×Dic3—21no—
229C22×Dic3C22×C412yes—
230C22×Dic3C22×C412yes—
231C22×Dic3C2×D412yes—
232C22×Dic3C2×D414yes—
233C22×Dic3C2×D412yes—
234C22×Dic3#4112yes—
235C22×Dic3#4112yes—
236C2×D12—28no—
237C2×D12—28no—
238C2×D12—28no—
239C2×D12—44no—
240C2×D12—44no—
241C2×D12—44no—
242C2×D12—44no—
243C3×C4⋊C4—28no—
244C3×C4⋊C4—28no—
245C3×C4⋊C4—48no—
246C3×C42—44no—
247(C2×D3)⋊C4—216no—
248(C2×D3)⋊C4—48no—
249(C2×D3)⋊C4—48no—
250(C2×D3)⋊C4—48no—
251(C2×D3)⋊C4—48no—
252(C2×D3)⋊C4—48no—
253C4⋊Dic3—28no—
254C4×Dic3—28no—
255C4×Dic3—48no—
256C4×Dic3—44no—
257C25—32no—
258C22×D4—34no—
259C22×D4—62no—
260C22×D4—62no—
261C22×D4—62no—
262C22×D4—62no—
263C22×D4—62no—
264C22×D4—62no—
265C23×C4—31no—
266C23×C4—32no—
267C23×C4—31no—
268C23×C4—31no—
269C23×C4—31no—
270C23×C4C22×D312yes—
271C23×C4C22×D311yescharacteristic
272C23×C4C22×D311yescharacteristic
273C23×C4C22×D312yes—
274C23×C4C22×D311yescharacteristic
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—34no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—62no—
284C2×C4⋊C4—62no—
285C2×C4⋊C4C4×D314yes—
286C2×C4⋊C4#6714yes—
287C2×C22⋊C4—38no—
288C2×C22⋊C4—38no—
289C2×C22⋊C4—64no—
290C2×C22⋊C4—64no—
291C2×C22⋊C4—64no—
292C2×C22⋊C4—64no—
293C2×C22⋊C4—64no—
294C2×C22⋊C4—64no—
295C2×C22⋊C4—64no—
296C2×C22⋊C4—64no—
297C2×C22⋊C4—64no—
298C2×C22⋊C4—64no—
299C2×C22⋊C4—122no—
300C2×C22⋊C4—122no—
301C2×C22⋊C4—122no—
302C2×C22⋊C4—122no—
303C2×C22⋊C4—122no—
304C2×C22⋊C4—122no—
305C2×C42—22no—
306C2×C42—22no—
307C2×C42—22no—
308C2×C42—34no—
309C2×C42—62no—
310C2×C42—62no—
311C2×C42—64no—
312C2×C42—64no—
313C2×C42—62no—
314C2×C42—62no—
315C2×C42—62no—
316C2×C42—122no—
317#95—24no—
318#95—34no—
319#95—62no—
320#95—62no—
321#95—64no—
322#95—64no—
323#95—62no—
324#95—122no—
325C23×C3C23×C411yescharacteristic
326C23×C3C22×D411yescharacteristic
327C23×C3C22×D411yescharacteristic
328C23×C3C22×D411yescharacteristic
329C23×C3C2×#4111yescharacteristic
330C23×C3C2×#4111yescharacteristic
331C23×C3C2×#4111yescharacteristic
332C23×C3C2×#4111yescharacteristic
333C23×C3C2×#4111yescharacteristic
334C23×C3C2×#4111yescharacteristic
335C23×C3C2×#4111yescharacteristic
336C23×C3H(5,𝔽2)11yescharacteristic
337C23×C3H(5,𝔽2)11yescharacteristic
338C23×C3H(5,𝔽2)11yescharacteristic
339C23×C32−1+411yescharacteristic
340C22×D3—24no—
341C22×D3—24no—
342C22×D3—24no—
343C22×D3—24no—
344C22×D3—24no—
345C22×D3—24no—
346C22×D3—24no—
347C22×D3—42no—
348C22×D3—42no—
349C22×D3—42no—
350C22×D3—42no—
351C22×D3—42no—
352C22×D3—42no—
353C22×D3—42no—
354C22×D3—42no—
355C22×D3—42no—
356C22×D3—42no—
357C22×D3—42no—
358C22×D3—42no—
359C22×D3—42no—
360C22×D3—42no—
361C22×D3—42no—
362C22×D3—42no—
363C22×D3—42no—
364C22×D3—42no—
365C22×D3—42no—
366C22×D3—42no—
367C22×D3—42no—
368C22×D3—42no—
369C22×D3—42no—
370C22×D3—42no—
371C22×D3—42no—
372C22×D3—42no—
373C22×D3—42no—
374C22×D3—42no—
375C2×C3×C4—24no—
376C2×C3×C4—24no—
377C2×C3×C4—24no—
378C2×C3×C4—24no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—24no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—24no—
386C2×C3×C4—22no—
387C2×C3×C4—41no—
388C2×C3×C4—41no—
389C2×C3×C4—42no—
390C2×C3×C4—41no—
391C2×C3×C4—42no—
392C2×C3×C4—41no—
393C2×C3×C4—42no—
394C2×C3×C4—42no—
395C2×C3×C4—41no—
396C2×C3×C4—41no—
397C2×C3×C4—42no—
398C2×C3×C4—42no—
399C2×C3×C4—41no—
400C2×C3×C4—42no—
401C2×C3×C4—41no—
402C2×C3×C4—42no—
403C2×C3×C4#11714yes—
404C2×C3×C4C4×D414yes—
405C2×C3×C4C4×D414yes—
406C2×C3×C4#12114yes—
407C2×C3×C4#12314yes—
408C2×C3×C4#12414yes—
409C2×C3×C4#12614yes—
410C2×Dic3—22no—
411C2×Dic3—22no—
412C2×Dic3—22no—
413C2×Dic3—22no—
414C2×Dic3—22no—
415C2×Dic3—22no—
416C2×Dic3—22no—
417C2×Dic3—22no—
418C2×Dic3—22no—
419C2×Dic3—24no—
420C2×Dic3—22no—
421C2×Dic3—22no—
422C2×Dic3—24no—
423C2×Dic3—22no—
424C2×Dic3—22no—
425C2×Dic3—24no—
426C2×Dic3—22no—
427C2×Dic3—22no—
428C2×Dic3—41no—
429C2×Dic3—41no—
430C2×Dic3—42no—
431C2×Dic3—42no—
432C2×Dic3—41no—
433C2×Dic3—41no—
434C2×Dic3—41no—
435C2×Dic3—41no—
436C2×Dic3—42no—
437C2×Dic3—41no—
438C2×Dic3—41no—
439C2×Dic3—41no—
440C2×Dic3—41no—
441C2×Dic3—41no—
442C2×Dic3—41no—
443C2×Dic3—42no—
444C2×Dic3C4×D414yes—
445D12—416no—
446C24—34no—
447C24—62no—
448C24—62no—
449C24—62no—
450C24—62no—
451C24—62no—
452C24—62no—
453C24—62no—
454C24—62no—
455C24—62no—
456C24—62no—
457C24—62no—
458C24—62no—
459C24—62no—
460C24—62no—
461C24C23×D311yescharacteristic
462C2×D4—68no—
463C2×D4—68no—
464C2×D4—68no—
465C2×D4—124no—
466C2×D4—124no—
467C2×D4—124no—
468C2×D4—124no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—32no—
494C22×C4—32no—
495C22×C4—32no—
496C22×C4—32no—
497C22×C4—32no—
498C22×C4—34no—
499C22×C4—32no—
500C22×C4—61no—
501C22×C4—61no—
502C22×C4—61no—
503C22×C4—61no—
504C22×C4—62no—
505C22×C4—61no—
506C22×C4—62no—
507C22×C4—61no—
508C22×C4—61no—
509C22×C4—61no—
510C22×C4—61no—
511C22×C4—61no—
512C22×C4—61no—
513C22×C4—61no—
514C22×C4—61no—
515C22×C4—61no—
516C22×C4—62no—
517C22×C4—62no—
518C22×C4—61no—
519C22×C4—61no—
520C22×C4—61no—
521C22×C4—61no—
522C22×C4—62no—
523C22×C4—62no—
524C22×C4—61no—
525C22×C4—61no—
526C22×C4—61no—
527C22×C4—61no—
528C22×C4C2×C4×D314yes—
529C22×C4C2×C4×D312yes—
530C22×C4#23512yes—
531C22×C4D3×D412yes—
532C22×C4D3×D412yes—
533C22×C4#23712yes—
534C22×C4#23912yes—
535C22×C4#23912yes—
536C22×C4#23912yes—
537C22×C4C2×#6714yes—
538C22×C4C2×#6712yes—
539C4⋊C4—28no—
540C4⋊C4—28no—
541C4⋊C4—48no—
542C4⋊C4—68no—
543C22⋊C4—616no—
544C22⋊C4—128no—
545C22⋊C4—128no—
546C22⋊C4—128no—
547C22⋊C4—128no—
548C22⋊C4—128no—
549C42—44no—
550C42—68no—
551C42—128no—
552C42—124no—
553C22×C3C2×#11711yescharacteristic
554C22×C3C2×C4×D411yescharacteristic
555C22×C3C2×C4×D411yescharacteristic
556C22×C3C2×C4×D411yescharacteristic
557C22×C3C4×#4111yescharacteristic
558C22×C3#51811yescharacteristic
559C22×C3#52011yescharacteristic
560C22×C3C2×#12111yescharacteristic
561C22×C3C2×#12311yescharacteristic
562C22×C3C2×#12411yescharacteristic
563C22×C3C2×#12611yescharacteristic
564C22×C3#52911yescharacteristic
565C22×C3#52911yescharacteristic
566C22×C3#53211yescharacteristic
567C22×C3#53211yescharacteristic
568C22×C3#54011yescharacteristic
569C22×C3#54011yescharacteristic
570C22×C3#54211yescharacteristic
571C22×C3#54211yescharacteristic
572C22×C3D4211yescharacteristic
573C22×C3D4211yescharacteristic
574C22×C3#54611yescharacteristic
575C22×C3#54611yescharacteristic
576C22×C3#54711yescharacteristic
577C22×C3#54811yescharacteristic
578C22×C3#54811yescharacteristic
579C22×C3#55011yescharacteristic
580C22×C3#55011yescharacteristic
581C22×C3#55011yescharacteristic
582C22×C3#55311yescharacteristic
583C22×C3#55311yescharacteristic
584C22×C3#55511yescharacteristic
585C22×C3#55611yescharacteristic
586C22×C3#55911yescharacteristic
587C22×C3#55911yescharacteristic
588C2×D3—44no—
589C2×D3—44no—
590C2×D3—44no—
591C2×D3—44no—
592C2×D3—44no—
593C2×D3—44no—
594C2×D3—44no—
595C2×D3—82no—
596C2×D3—82no—
597C2×D3—82no—
598C2×D3—82no—
599C2×D3—82no—
600C2×D3—82no—
601C2×D3—82no—
602C2×D3—82no—
603C3×C4—44no—
604C3×C4—42no—
605C3×C4—44no—
606C3×C4—42no—
607C3×C4#38818yescomplemented
608Dic3—24no—
609Dic3—42no—
610Dic3—44no—
611Dic3—42no—
612Dic3—42no—
613C23—64no—
614C23—64no—
615C23—64no—
616C23—64no—
617C23—64no—
618C23—64no—
619C23—64no—
620C23—122no—
621C23—122no—
622C23—122no—
623C23—122no—
624C23—122no—
625C23—122no—
626C23—122no—
627C23—122no—
628C23—122no—
629C23—122no—
630C23—122no—
631C23—122no—
632C23—122no—
633C23—122no—
634C23—122no—
635C23—122no—
636C23—122no—
637C23—122no—
638C23—122no—
639C23—122no—
640C23—122no—
641C23—122no—
642C23—122no—
643C23—122no—
644C23—122no—
645C23—122no—
646C23—122no—
647C23—122no—
648C23C22×C4×D311yescharacteristic
649C23C2×#23511yescharacteristic
650C23C2×D3×D411yescharacteristic
651C23C2×D3×D411yescharacteristic
652C23C2×#23711yescharacteristic
653C23#100411yescharacteristic
654C23C2×#23911yescharacteristic
655C23C2×#23911yescharacteristic
656C23C2×#23911yescharacteristic
657C23#100711yescharacteristic
658C23D3×#4111yescharacteristic
659C23D3×#4111yescharacteristic
660C23#100911yescharacteristic
661C23#100911yescharacteristic
662C23C22×#6711yescharacteristic
663D4—1216no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—34no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—41no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—62no—
694C2×C4—62no—
695C2×C4—62no—
696C2×C4—62no—
697C2×C4—62no—
698C2×C4—62no—
699C2×C4—62no—
700C2×C4—62no—
701C2×C4—62no—
702C2×C4—62no—
703C2×C4—62no—
704C2×C4—64no—
705C2×C4—62no—
706C2×C4—62no—
707C2×C4—62no—
708C2×C4—62no—
709C2×C4—64no—
710C2×C4—64no—
711C2×C4—121no—
712C2×C4—121no—
713C2×C4—121no—
714C2×C4—122no—
715C2×C4—122no—
716C2×C4—121no—
717C2×C4—121no—
718C2×C4—121no—
719C2×C4—122no—
720C2×C4—121no—
721C2×C4—121no—
722C2×C4—121no—
723C2×C4—121no—
724C2×C4—122no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4#89214yes—
728C2×C4#89314yes—
729C2×C4#89414yes—
730C2×C4#89814yes—
731C2×C4C4×#6714yes—
732C2×C4#93914yes—
733C2×C4#94714yes—
734C2×C3C2×#38811yescharacteristic
735C2×C3#229311yescharacteristic
736C2×C3#231911yescharacteristic
737C2×C3#236111yescharacteristic
738C2×C3#236311yescharacteristic
739C2×C3#236611yescharacteristic
740C2×C3#236711yescharacteristic
741C2×C3#242611yescharacteristic
742C2×C3#242811yescharacteristic
743C2×C3#244511yescharacteristic
744C2×C3#244811yescharacteristic
745C2×C3#249011yescharacteristic
746C2×C3#249111yescharacteristic
747C2×C3#251211yescharacteristic
748C2×C3#251311yescharacteristic
749D3—84no—
750C22—124no—
751C22—124no—
752C22—124no—
753C22—124no—
754C22—124no—
755C22—124no—
756C22—124no—
757C22—242no—
758C22—242no—
759C22—242no—
760C22—242no—
761C22—242no—
762C22—242no—
763C22—242no—
764C22—242no—
765C22C2×#89211yescharacteristic
766C22C2×#89311yescharacteristic
767C22C2×#89411yescharacteristic
768C22C2×#89811yescharacteristic
769C22C4×D3×D411yescharacteristic
770C22#554511yescharacteristic
771C22#555311yescharacteristic
772C22#555911yescharacteristic
773C22#556811yescharacteristic
774C22C4×#23911yescharacteristic
775C22#557411yescharacteristic
776C22#558511yescharacteristic
777C22#559611yescharacteristic
778C22#559911yescharacteristic
779C22#560911yescharacteristic
780C22#561911yescharacteristic
781C22#562411yescharacteristic
782C22#563011yescharacteristic
783C22#563311yescharacteristic
784C22#564311yescharacteristic
785C22#569111yescharacteristic
786C22#569511yescharacteristic
787C22#569511yescharacteristic
788C22#569711yescharacteristic
789C22#572511yescharacteristic
790C22#572611yescharacteristic
791C22#573311yescharacteristic
792C22#573411yescharacteristic
793C22C2×C4×#6711yescharacteristic
794C22D4×#6711yescharacteristic
795C22C2×#93911yescharacteristic
796C22C2×#94711yescharacteristic
797C22#581711yescharacteristic
798C22#582911yescharacteristic
799C22#583411yescharacteristic
800C4—42no—
801C4—44no—
802C4—44no—
803C4—42no—
804C4—64no—
805C4—122no—
806C4—122no—
807C4—122no—
808C4—124no—
809C4#499018yescomplemented
810C3#1414111yescharacteristic, complemented, Sylow
811C2—244no—
812C2#7596111yescharacteristic
813C2#7596911yescharacteristic
814C2#7598511yescharacteristic
815C2#7600411yescharacteristic
816C2#7600711yescharacteristic
817C2#7604711yescharacteristic
818C2#7604811yescharacteristic
819C2#7620611yescharacteristic
820C2C2×#499011yescharacteristic
821C2#8234311yescharacteristic
822C2#8246611yescharacteristic
823C2#8264911yescharacteristic
824C2#8275511yescharacteristic
825C2#8306111yescharacteristic
826C2#8325711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC2×C3×#389C2
socle, cosocleC24×C3C24
prime radicalC23×D12C22
hypercenterC2×#389D3
hypocenterC3#14141
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C2×C3×#389C2semidirect
4. C2×#4990C2semidirect
5. C2×Dic3×C4⋊C4C2semidirect
7. #71570C2semidirect
8. #71563C2semidirect
9. C4×C3⋊#95C2semidirect
10. #69429C2semidirect
11. #69408C2semidirect
39. #4988C4semidirect
45. C2×#389D3semidirect
120. C3⋊#95D4semidirect
607. C3×C4#388semidirect
809. C4#4990semidirect
810. C3#14141semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3892
C2×#49882
C2×#49902
C2×Dic3×C4⋊C42
C2×#49392
#715702
#715632
C4×C3⋊#952
#694292
#694082
#141413