Finite Group Databasebeta

← #10720227

Subgroups — #10720227

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×#4939C211yesmaximal, characteristic
2C2×#4939C211yesmaximal, characteristic
3C2×#4939C211yesmaximal, characteristic
4C2×#4928C211yesmaximal, characteristic, complemented
5C2×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
6C2×#4669C212yesmaximal, complemented
7C3×C4×#95C211yesmaximal, characteristic, complemented
8#71535C211yesmaximal, characteristic, complemented
9#69429C212yesmaximal, complemented
10#69428C212yesmaximal, complemented
11#69408C212yesmaximal, complemented
12#14141—31nomaximal, Sylow
13C23×D12C2211yescharacteristic
14C22×C3×C42C2211yescharacteristic
15C22×C3×C42C2211yescharacteristic
16C22×C3×C42C2211yescharacteristic
17C22×(C2×D3)⋊C4C2212yes—
18C22×(C2×D3)⋊C4C2212yes—
19C22×(C2×D3)⋊C4C2212yes—
20C22×(C2×D3)⋊C4C2212yes—
21C22×(C2×D3)⋊C4C2212yes—
22C22×(C2×D3)⋊C4C2212yes—
23C22×C4⋊Dic3C2211yescharacteristic
24C22×C4⋊Dic3C2211yescharacteristic
25C22×C4⋊Dic3C2211yescharacteristic
26C22×Dic3⋊C4C2212yes—
27C22×C4×Dic3C2212yes—
28C2×C3×#95C2211yescharacteristic
29C2×C3×#95C2211yescharacteristic
30C2×C3×#95C2211yescharacteristic
31C2×C3×#95C2211yescharacteristic
32C2×C3⋊#95C2212yes—
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2212yes—
36#4939—24no—
37#4939—24no—
38#4939C418yescomplemented
39C4×C4⋊Dic3—24no—
40#4928—24no—
41#4669—28no—
42C2×#390—31no—
43C2×#390—31no—
44C2×#390—31no—
45C2×#389—31no—
46C2×#388—32no—
47C2×C4×C4⋊C4—31no—
48#1440—32no—
49#1439—32no—
50#1437—32no—
51C4⋊#95—31no—
52C4×#95D311yescharacteristic, complemented
53C24×D3C2312yes—
54C23×C3×C4C2311yescharacteristic
55C23×C3×C4C2311yescharacteristic
56C23×C3×C4C2311yescharacteristic
57C23×C3×C4C2311yescharacteristic
58C23×C3×C4C2311yescharacteristic
59C23×C3×C4C2311yescharacteristic
60C23×C3×C4C2311yescharacteristic
61C23×Dic3C2312yes—
62C23×Dic3C2312yes—
63C23×Dic3C2312yes—
64C22×D12—22no—
65C22×D12—22no—
66C22×D12—22no—
67C22×D12—22no—
68C22×D12—22no—
69C22×D12—22no—
70C22×D12C2×C414yes—
71C2×C3×C42—22no—
72C2×C3×C42—22no—
73C2×C3×C42—22no—
74C2×C3×C42—22no—
75C2×C3×C42—22no—
76C2×C3×C42—22no—
77C2×C3×C42—22no—
78C2×C3×C42—22no—
79C2×C3×C42C2×C414yes—
80C2×(C2×D3)⋊C4—24no—
81C2×(C2×D3)⋊C4—24no—
82C2×(C2×D3)⋊C4—24no—
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—42no—
91C2×(C2×D3)⋊C4—42no—
92C2×(C2×D3)⋊C4—42no—
93C2×(C2×D3)⋊C4—42no—
94C2×(C2×D3)⋊C4—42no—
95C2×(C2×D3)⋊C4—42no—
96C2×(C2×D3)⋊C4C2×C418yes—
97C2×(C2×D3)⋊C4C2×C418yes—
98C2×C4⋊Dic3—22no—
99C2×C4⋊Dic3—22no—
100C2×C4⋊Dic3—22no—
101C2×C4⋊Dic3—22no—
102C2×C4⋊Dic3—22no—
103C2×C4⋊Dic3—22no—
104C2×C4⋊Dic3C2×C414yes—
105C2×C4⋊Dic3D414yes—
106C2×C4⋊Dic3D414yes—
107C2×Dic3⋊C4—24no—
108C2×Dic3⋊C4—24no—
109C2×Dic3⋊C4—42no—
110C2×C4×Dic3—24no—
111C2×C4×Dic3—24no—
112C2×C4×Dic3—42no—
113C3×#95—22no—
114C3×#95—22no—
115C3×#95—22no—
116C3×#95D414yescomplemented
117C3⋊#95—24no—
118C3⋊#95—24no—
119C3⋊#95—24no—
120C3⋊#95—42no—
121C23×D4—31no—
122C22×C4⋊C4—31no—
123C22×C4⋊C4—31no—
124C22×C4⋊C4—31no—
125C22×C4⋊C4—32no—
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—32no—
133C22×C42C2×D311yescharacteristic
134C22×C42C2×D311yescharacteristic
135C22×C42C2×D311yescharacteristic
136#390—38no—
137#390—64no—
138#390—64no—
139#389—64no—
140#388—68no—
141C4×C4⋊C4—64no—
142C2×#95—32no—
143C2×#95—32no—
144C2×#95—32no—
145C2×#95—32no—
146C2×#95C2×D311yescharacteristic
147C2×#95C2×D311yescharacteristic
148C2×#95C2×D311yescharacteristic
149C2×#95C2×D311yescharacteristic
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—21no—
167C22×C3×C4—21no—
168C22×C3×C4—21no—
169C22×C3×C4—21no—
170C22×C3×C4—21no—
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—21no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4C22×C412yes—
201C22×C3×C4C22×C412yes—
202C22×C3×C4C22×C412yes—
203C22×C3×C4C2×D412yes—
204C22×C3×C4C2×D412yes—
205C22×C3×C4C2×D412yes—
206C22×C3×C4C2×D412yes—
207C22×C3×C4C2×D412yes—
208C22×C3×C4#4112yes—
209C22×C3×C4#4112yes—
210C22×C3×C4#4112yes—
211C22×C3×C4#4112yes—
212C22×C3×C4#4112yes—
213C22×C3×C4#4112yes—
214C22×C3×C4#4112yes—
215C22×Dic3—22no—
216C22×Dic3—22no—
217C22×Dic3—22no—
218C22×Dic3—22no—
219C22×Dic3—22no—
220C22×Dic3—22no—
221C22×Dic3—22no—
222C22×Dic3—22no—
223C22×Dic3—22no—
224C22×Dic3—22no—
225C22×Dic3—22no—
226C22×Dic3—22no—
227C22×Dic3—22no—
228C22×Dic3—22no—
229C22×Dic3—22no—
230C22×Dic3—22no—
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3C22×C414yes—
234C22×Dic3C2×D414yes—
235C22×Dic3C2×D414yes—
236C2×D12—28no—
237C2×D12—28no—
238C2×D12—28no—
239C2×D12—44no—
240C2×D12—44no—
241C2×D12—44no—
242C2×D12—44no—
243C3×C42—28no—
244C3×C42—44no—
245C3×C42—44no—
246(C2×D3)⋊C4—216no—
247(C2×D3)⋊C4—48no—
248(C2×D3)⋊C4—48no—
249(C2×D3)⋊C4—48no—
250(C2×D3)⋊C4—48no—
251(C2×D3)⋊C4—48no—
252C4⋊Dic3—28no—
253C4⋊Dic3—28no—
254C4⋊Dic3—28no—
255Dic3⋊C4—48no—
256C4×Dic3—48no—
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—32no—
266C23×C4—32no—
267C23×C4—32no—
268C23×C4C22×D311yescharacteristic
269C23×C4C22×D311yescharacteristic
270C23×C4C22×D311yescharacteristic
271C23×C4C22×D311yescharacteristic
272C23×C4C22×D311yescharacteristic
273C23×C4C22×D311yescharacteristic
274C23×C4C22×D311yescharacteristic
275C2×C4⋊C4—34no—
276C2×C4⋊C4—34no—
277C2×C4⋊C4—34no—
278C2×C4⋊C4—62no—
279C2×C4⋊C4—62no—
280C2×C4⋊C4—62no—
281C2×C4⋊C4—62no—
282C2×C4⋊C4—62no—
283C2×C4⋊C4—62no—
284C2×C4⋊C4—64no—
285C2×C4⋊C4—64no—
286C2×C4⋊C4—122no—
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—22no—
309C2×C42—22no—
310C2×C42—22no—
311C2×C42—22no—
312C2×C42—22no—
313C2×C42—64no—
314C2×C42—64no—
315C2×C42—122no—
316C2×C42C4×D314yes—
317#95—22no—
318#95—22no—
319#95—22no—
320#95—64no—
321#95—64no—
322#95—64no—
323#95—122no—
324#95D1214yescomplemented
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—22no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
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—22no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—41no—
397C2×C3×C4—41no—
398C2×C3×C4—41no—
399C2×C3×C4—41no—
400C2×C3×C4—41no—
401C2×C3×C4—41no—
402C2×C3×C4—41no—
403C2×C3×C4—41no—
404C2×C3×C4—41no—
405C2×C3×C4—41no—
406C2×C3×C4—41no—
407C2×C3×C4—41no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4—41no—
411C2×C3×C4—41no—
412C2×C3×C4—41no—
413C2×C3×C4—41no—
414C2×C3×C4—41no—
415C2×C3×C4—41no—
416C2×C3×C4#11714yes—
417C2×C3×C4C4×D414yes—
418C2×C3×C4C4×D414yes—
419C2×C3×C4C4×D414yes—
420C2×C3×C4#12114yes—
421C2×C3×C4#12314yes—
422C2×C3×C4#12414yes—
423C2×C3×C4#12614yes—
424C2×Dic3—24no—
425C2×Dic3—24no—
426C2×Dic3—24no—
427C2×Dic3—24no—
428C2×Dic3—24no—
429C2×Dic3—24no—
430C2×Dic3—24no—
431C2×Dic3—24no—
432C2×Dic3—24no—
433C2×Dic3—42no—
434C2×Dic3—42no—
435C2×Dic3—42no—
436C2×Dic3—42no—
437C2×Dic3—42no—
438C2×Dic3—42no—
439C2×Dic3—42no—
440C2×Dic3—42no—
441C2×Dic3—42no—
442C2×Dic3—42no—
443C2×Dic3—42no—
444C2×Dic3—42no—
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—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—34no—
504C22×C4—34no—
505C22×C4—34no—
506C22×C4—62no—
507C22×C4—62no—
508C22×C4—62no—
509C22×C4—62no—
510C22×C4—62no—
511C22×C4—62no—
512C22×C4—62no—
513C22×C4—62no—
514C22×C4—62no—
515C22×C4—62no—
516C22×C4—62no—
517C22×C4—62no—
518C22×C4—62no—
519C22×C4—62no—
520C22×C4—62no—
521C22×C4—62no—
522C22×C4—62no—
523C22×C4—62no—
524C22×C4C2×C4×D312yes—
525C22×C4C2×C4×D312yes—
526C22×C4C2×C4×D312yes—
527C22×C4C2×D1212yes—
528C22×C4C2×D1212yes—
529C22×C4C2×D1212yes—
530C22×C4#23512yes—
531C22×C4#23512yes—
532C22×C4#23512yes—
533C22×C4#23512yes—
534C22×C4#23512yes—
535C22×C4D3×D412yes—
536C22×C4D3×D412yes—
537C22×C4#23712yes—
538C22×C4#23912yes—
539C4⋊C4—68no—
540C4⋊C4—68no—
541C4⋊C4—68no—
542C4⋊C4—128no—
543C22⋊C4—616no—
544C22⋊C4—128no—
545C22⋊C4—128no—
546C22⋊C4—128no—
547C22⋊C4—128no—
548C22⋊C4—128no—
549C42—28no—
550C42—44no—
551C42—44no—
552C42—128no—
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—24no—
604C3×C4—42no—
605C3×C4—42no—
606C3×C4—42no—
607C3×C4—42no—
608C3×C4—42no—
609C3×C4#38818yescomplemented
610Dic3—44no—
611Dic3—44no—
612Dic3—44no—
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
649C23C22×D1211yescharacteristic
650C23C2×#23511yescharacteristic
651C23C2×#23511yescharacteristic
652C23C2×#23511yescharacteristic
653C23C2×#23511yescharacteristic
654C23C2×#23511yescharacteristic
655C23C2×D3×D411yescharacteristic
656C23C2×D3×D411yescharacteristic
657C23C2×#23711yescharacteristic
658C23C2×#23911yescharacteristic
659C23#100911yescharacteristic
660C23#100911yescharacteristic
661C23#100911yescharacteristic
662C23#101011yescharacteristic
663D4—1216no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—64no—
706C2×C4—64no—
707C2×C4—64no—
708C2×C4—64no—
709C2×C4—64no—
710C2×C4—64no—
711C2×C4—64no—
712C2×C4—64no—
713C2×C4—64no—
714C2×C4—122no—
715C2×C4—122no—
716C2×C4—122no—
717C2×C4—122no—
718C2×C4—122no—
719C2×C4—122no—
720C2×C4—122no—
721C2×C4—122no—
722C2×C4—122no—
723C2×C4—122no—
724C2×C4—122no—
725C2×C4—122no—
726C2×C4#87214yes—
727C2×C4C4×D1214yes—
728C2×C4#67⋊C414yes—
729C2×C4#88414yes—
730C2×C4#88514yes—
731C2×C4#89314yes—
732C2×C4#89414yes—
733C2×C4#89814yes—
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×#87211yescharacteristic
766C22C2×C4×D1211yescharacteristic
767C22C4×#23511yescharacteristic
768C22#547711yescharacteristic
769C22#547711yescharacteristic
770C22#547911yescharacteristic
771C22#547911yescharacteristic
772C22C2×#67⋊C411yescharacteristic
773C22C2×#88411yescharacteristic
774C22C2×#88511yescharacteristic
775C22C2×#89311yescharacteristic
776C22C2×#89411yescharacteristic
777C22C2×#89811yescharacteristic
778C22#552111yescharacteristic
779C22#552311yescharacteristic
780C22#553411yescharacteristic
781C22#553411yescharacteristic
782C22#553511yescharacteristic
783C22#553511yescharacteristic
784C22D4×D1211yescharacteristic
785C22D4×D1211yescharacteristic
786C22#555011yescharacteristic
787C22#555011yescharacteristic
788C22#555211yescharacteristic
789C22#555211yescharacteristic
790C22#555311yescharacteristic
791C22#555311yescharacteristic
792C22#555511yescharacteristic
793C22#556311yescharacteristic
794C22#556511yescharacteristic
795C22#556511yescharacteristic
796C22#557711yescharacteristic
797C22#558411yescharacteristic
798C22#558511yescharacteristic
799C22#558511yescharacteristic
800C4—24no—
801C4—42no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—124no—
807C4—124no—
808C4—124no—
809C4#466918yescomplemented
810C3#1414111yescharacteristic, complemented, Sylow
811C2—244no—
812C2#7329911yescharacteristic
813C2C2×#466911yescharacteristic
814C2#7341511yescharacteristic
815C2#7346711yescharacteristic
816C2#7346911yescharacteristic
817C2#7348511yescharacteristic
818C2#7348711yescharacteristic
819C2#7350611yescharacteristic
820C2#7350711yescharacteristic
821C2#7365311yescharacteristic
822C2#7365511yescharacteristic
823C2#7367311yescharacteristic
824C2#7369211yescharacteristic
825C2#7369411yescharacteristic
826C2#7378011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×C4×#95C2
socle, cosocleC24×C3C24
prime radicalC23×D12C22
hypercenterC4×#95D3
hypocenterC3#14141
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
4. C2×#4928C2semidirect
5. C2×C4×C4⋊Dic3C2semidirect
6. C2×#4669C2semidirect
7. C3×C4×#95C2semidirect
8. #71535C2semidirect
9. #69429C2semidirect
10. #69428C2semidirect
11. #69408C2semidirect
38. #4939C4semidirect
52. C4×#95D3semidirect
116. C3×#95D4semidirect
324. #95D12semidirect
609. C3×C4#388semidirect
809. C4#4669semidirect
810. C3#14141semidirect

Maximal subgroups

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

subgroupindex
C2×#49392
C2×#49282
C2×C4×C4⋊Dic32
C2×#46692
C3×C4×#952
#715352
#694292
#694282
#694082
#141413