Finite Group Databasebeta

← #10720221

Subgroups — #10720221

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×C4×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×#4988C211yesmaximal, characteristic
3C2×#4988C211yesmaximal, characteristic
4C2×#4972C211yesmaximal, characteristic, complemented
5C2×#4939C211yesmaximal, characteristic
6C2×#4940C212yesmaximal, complemented
7#71563C211yesmaximal, characteristic, complemented
8#71537C212yesmaximal, complemented
9C4×C3⋊#95C211yesmaximal, characteristic, complemented
10#69429C212yesmaximal, complemented
11#69428C212yesmaximal, complemented
12#14141—31nomaximal, Sylow
13C23×D12C2211yescharacteristic
14C22×C3×C4⋊C4C2211yescharacteristic
15C22×C3×C4⋊C4C2211yescharacteristic
16C22×C3×C42C2212yes—
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×Dic3⋊C4C2212yes—
26C22×C4×Dic3C2211yescharacteristic
27C22×C4×Dic3C2211yescharacteristic
28C3×C4×C4⋊C4—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#4988—24no—
38#4988—24no—
39#4972—24no—
40#4940—28no—
41#4939C418yescomplemented
42C2×#390—31no—
43C2×#390—31no—
44C2×#390—31no—
45C2×#389—31no—
46C2×#388—32no—
47C2×C4×C4⋊C4D311yescharacteristic, complemented
48#1440—32no—
49#1439—32no—
50#1437—32no—
51C4⋊#95—31no—
52C4×#95—31no—
53C24×D3C2312yes—
54C23×C3×C4C2311yescharacteristic
55C23×C3×C4C2312yes—
56C23×C3×C4C2312yes—
57C23×C3×C4C2311yescharacteristic
58C23×C3×C4C2311yescharacteristic
59C23×Dic3C2312yes—
60C23×Dic3C2311yescharacteristic
61C23×Dic3C2311yescharacteristic
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⋊C4D414yes—
76C2×C3×C4⋊C4D414yes—
77C2×C3×C42—22no—
78C2×C3×C42—22no—
79C2×C3×C42—24no—
80C2×C3×C42—24no—
81C2×C3×C42—42no—
82C2×C3×C42C2×C414yes—
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⋊Dic3C2×C414yes—
104C2×Dic3⋊C4—24no—
105C2×Dic3⋊C4—24no—
106C2×Dic3⋊C4—42no—
107C2×C4×Dic3—22no—
108C2×C4×Dic3—22no—
109C2×C4×Dic3—22no—
110C2×C4×Dic3—22no—
111C2×C4×Dic3—22no—
112C2×C4×Dic3—22no—
113C3×#95—24no—
114C3⋊#95—24no—
115C3⋊#95—22no—
116C3⋊#95—24no—
117C3⋊#95—22no—
118C3⋊#95—22no—
119C3⋊#95—42no—
120C3⋊#95D414yescomplemented
121C23×D4—31no—
122C22×C4⋊C4—31no—
123C22×C4⋊C4—32no—
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×C42C2×D312yes—
135C22×C42C2×D311yescharacteristic
136#390—38no—
137#390—64no—
138#390—64no—
139#389—64no—
140#388—68no—
141C4×C4⋊C4—24no—
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—21no—
167C22×C3×C4—21no—
168C22×C3×C4—21no—
169C22×C3×C4—21no—
170C22×C3×C4—22no—
171C22×C3×C4—21no—
172C22×C3×C4—22no—
173C22×C3×C4—22no—
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—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×C4C22×C412yes—
189C22×C3×C4C22×C412yes—
190C22×C3×C4C22×C412yes—
191C22×C3×C4C2×D414yes—
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—22no—
203C22×Dic3—22no—
204C22×Dic3—21no—
205C22×Dic3—21no—
206C22×Dic3—21no—
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—21no—
219C22×Dic3—22no—
220C22×Dic3—22no—
221C22×Dic3—21no—
222C22×Dic3—22no—
223C22×Dic3—21no—
224C22×Dic3—22no—
225C22×Dic3—21no—
226C22×Dic3—21no—
227C22×Dic3—21no—
228C22×Dic3—21no—
229C22×Dic3—21no—
230C22×Dic3—21no—
231C22×Dic3C22×C414yes—
232C22×Dic3C2×D412yes—
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×C42—28no—
246C3×C42—48no—
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—
254Dic3⋊C4—48no—
255C4×Dic3—44no—
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—32no—
266C23×C4—31no—
267C23×C4—31no—
268C23×C4—31no—
269C23×C4—31no—
270C23×C4C22×D311yescharacteristic
271C23×C4C22×D312yes—
272C23×C4C22×D312yes—
273C23×C4C22×D311yescharacteristic
274C23×C4C22×D311yescharacteristic
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—34no—
280C2×C4⋊C4—62no—
281C2×C4⋊C4—62no—
282C2×C4⋊C4—64no—
283C2×C4⋊C4—64no—
284C2×C4⋊C4—122no—
285C2×C4⋊C4D1214yes—
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—24no—
308C2×C42—24no—
309C2×C42—42no—
310C2×C42—62no—
311C2×C42—62no—
312C2×C42—62no—
313C2×C42—62no—
314C2×C42—62no—
315C2×C42—62no—
316C2×C42C4×D314yes—
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—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—24no—
385C2×C3×C4—24no—
386C2×C3×C4—24no—
387C2×C3×C4—24no—
388C2×C3×C4—24no—
389C2×C3×C4—24no—
390C2×C3×C4—42no—
391C2×C3×C4—42no—
392C2×C3×C4—42no—
393C2×C3×C4—42no—
394C2×C3×C4—42no—
395C2×C3×C4—41no—
396C2×C3×C4—42no—
397C2×C3×C4—41no—
398C2×C3×C4—42no—
399C2×C3×C4—41no—
400C2×C3×C4—41no—
401C2×C3×C4—42no—
402C2×C3×C4#11714yes—
403C2×C3×C4C4×D414yes—
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—24no—
411C2×Dic3—24no—
412C2×Dic3—24no—
413C2×Dic3—22no—
414C2×Dic3—22no—
415C2×Dic3—22no—
416C2×Dic3—22no—
417C2×Dic3—22no—
418C2×Dic3—22no—
419C2×Dic3—22no—
420C2×Dic3—22no—
421C2×Dic3—22no—
422C2×Dic3—22no—
423C2×Dic3—22no—
424C2×Dic3—22no—
425C2×Dic3—41no—
426C2×Dic3—41no—
427C2×Dic3—41no—
428C2×Dic3—41no—
429C2×Dic3—41no—
430C2×Dic3—41no—
431C2×Dic3—41no—
432C2×Dic3—41no—
433C2×Dic3—42no—
434C2×Dic3—41no—
435C2×Dic3—41no—
436C2×Dic3—41no—
437C2×Dic3—42no—
438C2×Dic3—42no—
439C2×Dic3—41no—
440C2×Dic3—41no—
441C2×Dic3—41no—
442C2×Dic3—41no—
443C2×Dic3—41no—
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—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—34no—
492C22×C4—32no—
493C22×C4—32no—
494C22×C4—32no—
495C22×C4—32no—
496C22×C4—61no—
497C22×C4—62no—
498C22×C4—61no—
499C22×C4—61no—
500C22×C4—61no—
501C22×C4—61no—
502C22×C4—61no—
503C22×C4—61no—
504C22×C4—61no—
505C22×C4—61no—
506C22×C4—61no—
507C22×C4—62no—
508C22×C4—62no—
509C22×C4—61no—
510C22×C4—61no—
511C22×C4—61no—
512C22×C4—61no—
513C22×C4—62no—
514C22×C4—61no—
515C22×C4—61no—
516C22×C4—61no—
517C22×C4—61no—
518C22×C4—61no—
519C22×C4—62no—
520C22×C4—61no—
521C22×C4—61no—
522C22×C4—62no—
523C22×C4—61no—
524C22×C4—61no—
525C22×C4—61no—
526C22×C4C2×C4×D312yes—
527C22×C4C2×C4×D312yes—
528C22×C4C2×C4×D312yes—
529C22×C4C2×D1214yes—
530C22×C4C2×D1212yes—
531C22×C4#23512yes—
532C22×C4#23512yes—
533C22×C4#23512yes—
534C22×C4#23512yes—
535C22×C4D3×D412yes—
536C22×C4#23912yes—
537C22×C4C2×#6714yes—
538C22×C4C2×#6712yes—
539C4⋊C4—28no—
540C4⋊C4—28no—
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—48no—
551C42—124no—
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—24no—
604C3×C4—42no—
605C3×C4—44no—
606C3×C4—44no—
607C3×C4#38818yescomplemented
608Dic3—44no—
609Dic3—42no—
610Dic3—42no—
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
649C23C22×D1211yescharacteristic
650C23C2×#23511yescharacteristic
651C23C2×#23511yescharacteristic
652C23C2×#23511yescharacteristic
653C23C2×#23511yescharacteristic
654C23C2×D3×D411yescharacteristic
655C23#100411yescharacteristic
656C23C2×#23911yescharacteristic
657C23#100711yescharacteristic
658C23D3×#4111yescharacteristic
659C23D3×#4111yescharacteristic
660C23#100911yescharacteristic
661C23#100911yescharacteristic
662C23C22×#6711yescharacteristic
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—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—42no—
691C2×C4—64no—
692C2×C4—64no—
693C2×C4—62no—
694C2×C4—64no—
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—62no—
705C2×C4—62no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4—121no—
711C2×C4—121no—
712C2×C4—122no—
713C2×C4—122no—
714C2×C4—121no—
715C2×C4—121no—
716C2×C4—121no—
717C2×C4—121no—
718C2×C4—121no—
719C2×C4—121no—
720C2×C4—121no—
721C2×C4—122no—
722C2×C4—121no—
723C2×C4—121no—
724C2×C4—121no—
725C2×C4—122no—
726C2×C4#87214yes—
727C2×C4C4×D1214yes—
728C2×C4#87514yes—
729C2×C4#87614yes—
730C2×C4#89314yes—
731C2×C4C4×#6714yes—
732C2×C4#92914yes—
733C2×C4#93014yes—
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
767C22C2×#87511yescharacteristic
768C22C2×#87611yescharacteristic
769C22C2×#89311yescharacteristic
770C22#550411yescharacteristic
771C22#550711yescharacteristic
772C22#551411yescharacteristic
773C22#552111yescharacteristic
774C22#552211yescharacteristic
775C22#553011yescharacteristic
776C22#553211yescharacteristic
777C22#554811yescharacteristic
778C22#554811yescharacteristic
779C22D4×D1211yescharacteristic
780C22#555311yescharacteristic
781C22#555411yescharacteristic
782C22#555911yescharacteristic
783C22#556211yescharacteristic
784C22#556211yescharacteristic
785C22#556811yescharacteristic
786C22#557611yescharacteristic
787C22#557711yescharacteristic
788C22#558011yescharacteristic
789C22#558011yescharacteristic
790C22#558211yescharacteristic
791C22#558211yescharacteristic
792C22#558511yescharacteristic
793C22C2×C4×#6711yescharacteristic
794C22C2×#92911yescharacteristic
795C22C2×#93011yescharacteristic
796C22D4×#6711yescharacteristic
797C22#581711yescharacteristic
798C22#582911yescharacteristic
799C22#583411yescharacteristic
800C4—24no—
801C4—42no—
802C4—44no—
803C4—44no—
804C4—122no—
805C4—122no—
806C4—122no—
807C4—124no—
808C4—122no—
809C4#494018yescomplemented
810C3#1414111yescharacteristic, complemented, Sylow
811C2—244no—
812C2#7361711yescharacteristic
813C2#7365311yescharacteristic
814C2#7365411yescharacteristic
815C2#7369311yescharacteristic
816C2#7369511yescharacteristic
817C2#7376111yescharacteristic
818C2#7378711yescharacteristic
819C2#7378811yescharacteristic
820C2C2×#494011yescharacteristic
821C2#8216311yescharacteristic
822C2#8224411yescharacteristic
823C2#8235811yescharacteristic
824C2#8240911yescharacteristic
825C2#8246911yescharacteristic
826C2#8249511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC2×C3×C4×C4⋊C4C2
socle, cosocleC24×C3C24
prime radicalC23×D12C22
hypercenterC2×C4×C4⋊C4D3
hypocenterC3#14141
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×C4⋊C4C2semidirect
4. C2×#4972C2semidirect
6. C2×#4940C2semidirect
7. #71563C2semidirect
8. #71537C2semidirect
9. C4×C3⋊#95C2semidirect
10. #69429C2semidirect
11. #69428C2semidirect
41. #4939C4semidirect
47. C2×C4×C4⋊C4D3semidirect
120. C3⋊#95D4semidirect
607. C3×C4#388semidirect
809. C4#4940semidirect
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×C4×C4⋊C42
C2×#49882
C2×#49722
C2×#49392
C2×#49402
#715632
#715372
C4×C3⋊#952
#694292
#694282
#141413