Finite Group Databasebeta

← #10731933

Subgroups — #10731933

Order 768.

1778 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
1C2×#4988C211yesmaximal, characteristic
2C2×#4988C211yesmaximal, characteristic
3C2×#4939C211yesmaximal, characteristic
4C2×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
5C2×#4675C212yesmaximal, complemented
6C3×C4⋊#95C211yesmaximal, characteristic, complemented
7#71563C211yesmaximal, characteristic, complemented
8#71563C211yesmaximal, characteristic, complemented
9#69429C212yesmaximal, complemented
10#69429C212yesmaximal, complemented
11#69428C212yesmaximal, complemented
12#15147—31nomaximal, Sylow
13C23×D12C2211yescharacteristic
14C22×C3×C4⋊C4C2211yescharacteristic
15C22×C3×C4⋊C4C2211yescharacteristic
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×Dic3⋊C4C2211yescharacteristic
25C22×Dic3⋊C4C2211yescharacteristic
26C22×C4×Dic3C2211yescharacteristic
27C22×C4×Dic3C2211yescharacteristic
28C2×C3×#95C2212yes—
29C2×C3×#95C2212yes—
30C2×C3⋊#95C2212yes—
31C2×C3⋊#95C2211yescharacteristic
32C2×C3⋊#95C2211yescharacteristic
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2212yes—
36#4988—24no—
37#4988—24no—
38#4939—24no—
39C4×Dic3⋊C4—24no—
40#4675—28no—
41C2×#397—32no—
42C2×#390—31no—
43C2×#390—31no—
44C2×#390—31no—
45C2×C4×C4⋊C4—31no—
46#1440—32no—
47#1440—32no—
48#1439—32no—
49C4⋊#95—31no—
50C4⋊#95—31no—
51C4⋊#95D311yescharacteristic, complemented
52C24×D3C2312yes—
53C23×C3×C4C2312yes—
54C23×C3×C4C2312yes—
55C23×C3×C4C2311yescharacteristic
56C23×C3×C4C2311yescharacteristic
57C23×C3×C4C2311yescharacteristic
58C23×Dic3C2312yes—
59C23×Dic3C2311yescharacteristic
60C23×Dic3C2311yescharacteristic
61C23×Dic3C2311yescharacteristic
62C23×Dic3C2311yescharacteristic
63C22×D12—22no—
64C22×D12—22no—
65C22×D12—22no—
66C22×D12—22no—
67C22×D12—22no—
68C22×D12—22no—
69C22×D12D414yes—
70C2×C3×C4⋊C4—22no—
71C2×C3×C4⋊C4—22no—
72C2×C3×C4⋊C4—22no—
73C2×C3×C4⋊C4—22no—
74C2×C3×C4⋊C4—22no—
75C2×C3×C4⋊C4—22no—
76C2×C3×C42—22no—
77C2×C3×C42—22no—
78C2×C3×C42—22no—
79C2×(C2×D3)⋊C4—24no—
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—24no—
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)⋊C4—42no—
97C2×C4⋊Dic3—22no—
98C2×C4⋊Dic3—22no—
99C2×C4⋊Dic3—22no—
100C2×Dic3⋊C4—22no—
101C2×Dic3⋊C4—22no—
102C2×Dic3⋊C4—22no—
103C2×Dic3⋊C4—22no—
104C2×Dic3⋊C4—22no—
105C2×Dic3⋊C4D414yescomplemented
106C2×C4×Dic3—22no—
107C2×C4×Dic3—22no—
108C2×C4×Dic3—22no—
109C2×C4×Dic3—22no—
110C2×C4×Dic3—22no—
111C2×C4×Dic3D414yes—
112C3×#95—24no—
113C3×#95—42no—
114C3⋊#95—24no—
115C3⋊#95—24no—
116C3⋊#95—22no—
117C3⋊#95—22no—
118C3⋊#95—42no—
119C3⋊#95—42no—
120C23×D4—31no—
121C22×C4⋊C4—31no—
122C22×C4⋊C4—31no—
123C22×C4⋊C4—31no—
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×D311yescharacteristic
135#397—68no—
136#390—64no—
137#390—64no—
138#390—64no—
139C4×C4⋊C4—64no—
140C2×#95—32no—
141C2×#95—32no—
142C2×#95—31no—
143C2×#95—31no—
144C2×#95—32no—
145C2×#95—32no—
146C2×#95C2×D312yes—
147C2×#95C2×D312yes—
148C24×C3C2411yescharacteristic
149C23×D3—22no—
150C23×D3—22no—
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×D3C2×D414yes—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
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—22no—
177C22×C3×C4—22no—
178C22×C3×C4—22no—
179C22×C3×C4—22no—
180C22×C3×C4—22no—
181C22×C3×C4—22no—
182C22×C3×C4—22no—
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×C4C2×D412yes—
191C22×C3×C4C2×D412yes—
192C22×C3×C4C2×D412yes—
193C22×C3×C4#4112yes—
194C22×C3×C4#4112yes—
195C22×C3×C4#4112yes—
196C22×C3×C4#4112yes—
197C22×C3×C4#4112yes—
198C22×C3×C4#4112yes—
199C22×Dic3—21no—
200C22×Dic3—21no—
201C22×Dic3—21no—
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—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—21no—
220C22×Dic3—21no—
221C22×Dic3—22no—
222C22×Dic3—22no—
223C22×Dic3—22no—
224C22×Dic3—22no—
225C22×Dic3—22no—
226C22×Dic3—22no—
227C22×Dic3—22no—
228C22×Dic3C2×D412yes—
229C22×Dic3C2×D412yes—
230C22×Dic3C2×D412yes—
231C22×Dic3C2×D412yes—
232C22×Dic3#4112yes—
233C22×Dic3#4112yes—
234C2×D12—28no—
235C2×D12—28no—
236C2×D12—28no—
237C2×D12—44no—
238C2×D12—44no—
239C2×D12—44no—
240C2×D12—44no—
241C3×C4⋊C4—44no—
242C3×C4⋊C4—44no—
243C3×C42—44no—
244(C2×D3)⋊C4—48no—
245(C2×D3)⋊C4—48no—
246(C2×D3)⋊C4—48no—
247(C2×D3)⋊C4—48no—
248(C2×D3)⋊C4—48no—
249(C2×D3)⋊C4—48no—
250C4⋊Dic3—44no—
251Dic3⋊C4—28no—
252Dic3⋊C4—28no—
253C4×Dic3—28no—
254C4×Dic3—44no—
255C25—32no—
256C22×D4—34no—
257C22×D4—62no—
258C22×D4—62no—
259C22×D4—62no—
260C22×D4—62no—
261C22×D4—62no—
262C22×D4—62no—
263C23×C4—31no—
264C23×C4—31no—
265C23×C4—31no—
266C23×C4—31no—
267C23×C4—32no—
268C23×C4C22×D312yes—
269C23×C4C22×D312yes—
270C23×C4C22×D311yescharacteristic
271C23×C4C22×D311yescharacteristic
272C23×C4C22×D311yescharacteristic
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
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—62no—
283C2×C4⋊C4—62no—
284C2×C4⋊C4—62no—
285C2×C4⋊C4—62no—
286C2×C4⋊C4—62no—
287C2×C4⋊C4—62no—
288C2×C22⋊C4—64no—
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—64no—
300C2×C22⋊C4—122no—
301C2×C22⋊C4—122no—
302C2×C22⋊C4—122no—
303C2×C22⋊C4—122no—
304C2×C22⋊C4—122no—
305C2×C22⋊C4—122no—
306C2×C42—22no—
307C2×C42—22no—
308C2×C42—22no—
309C2×C42—34no—
310C2×C42—62no—
311C2×C42—62no—
312C2×C42—62no—
313C2×C42—62no—
314C2×C42—62no—
315#95—24no—
316#95—42no—
317#95—62no—
318#95—62no—
319#95—64no—
320#95—64no—
321#95—122no—
322#95—122no—
323C23×C3C22×D411yescharacteristic
324C23×C3C22×D411yescharacteristic
325C23×C3C22×D411yescharacteristic
326C23×C3C2×#4111yescharacteristic
327C23×C3C2×#4111yescharacteristic
328C23×C3C2×#4111yescharacteristic
329C23×C3C2×#4111yescharacteristic
330C23×C3C2×#4111yescharacteristic
331C23×C3C2×#4111yescharacteristic
332C23×C3C2×#4111yescharacteristic
333C23×C3C2×#4111yescharacteristic
334C23×C3H(5,𝔽2)11yescharacteristic
335C23×C3H(5,𝔽2)11yescharacteristic
336C23×C3H(5,𝔽2)11yescharacteristic
337C23×C32−1+411yescharacteristic
338C22×D3—24no—
339C22×D3—24no—
340C22×D3—24no—
341C22×D3—24no—
342C22×D3—24no—
343C22×D3—24no—
344C22×D3—24no—
345C22×D3—42no—
346C22×D3—42no—
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—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—41no—
380C2×C3×C4—41no—
381C2×C3×C4—41no—
382C2×C3×C4—41no—
383C2×C3×C4—41no—
384C2×C3×C4—41no—
385C2×C3×C4—41no—
386C2×C3×C4—41no—
387C2×C3×C4—42no—
388C2×C3×C4—42no—
389C2×C3×C4—42no—
390C2×C3×C4—42no—
391C2×C3×C4—42no—
392C2×C3×C4—42no—
393C2×C3×C4—42no—
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×C4#12114yes—
402C2×C3×C4#12314yes—
403C2×C3×C4#12314yes—
404C2×C3×C4#12314yes—
405C2×C3×C4#12414yes—
406C2×C3×C4#12614yes—
407C2×C3×C4#12614yes—
408C2×Dic3—22no—
409C2×Dic3—22no—
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—22no—
420C2×Dic3—22no—
421C2×Dic3—22no—
422C2×Dic3—22no—
423C2×Dic3—41no—
424C2×Dic3—41no—
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—41no—
434C2×Dic3—41no—
435C2×Dic3—42no—
436C2×Dic3—42no—
437C2×Dic3—42no—
438C2×Dic3—42no—
439C2×Dic3—42no—
440C2×Dic3—42no—
441C2×Dic3—42no—
442C2×Dic3#12114yes—
443D12—416no—
444C24—34no—
445C24—62no—
446C24—62no—
447C24—62no—
448C24—62no—
449C24—62no—
450C24—62no—
451C24—62no—
452C24—62no—
453C24—62no—
454C24—62no—
455C24—62no—
456C24—62no—
457C24—62no—
458C24—62no—
459C24C23×D311yescharacteristic
460C2×D4—68no—
461C2×D4—68no—
462C2×D4—68no—
463C2×D4—124no—
464C2×D4—124no—
465C2×D4—124no—
466C2×D4—124no—
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—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—32no—
494C22×C4—32no—
495C22×C4—32no—
496C22×C4—32no—
497C22×C4—32no—
498C22×C4—32no—
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—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—61no—
517C22×C4—61no—
518C22×C4—61no—
519C22×C4—61no—
520C22×C4—61no—
521C22×C4—62no—
522C22×C4—62no—
523C22×C4—62no—
524C22×C4—62no—
525C22×C4—62no—
526C22×C4—62no—
527C22×C4—62no—
528C22×C4#23512yes—
529C22×C4#23512yes—
530C22×C4#23512yes—
531C22×C4D3×D412yes—
532C22×C4D3×D412yes—
533C22×C4D3×D412yes—
534C22×C4#23712yes—
535C22×C4#23912yes—
536C22×C4#23912yes—
537C4⋊C4—44no—
538C4⋊C4—44no—
539C4⋊C4—68no—
540C4⋊C4—68no—
541C4⋊C4—124no—
542C22⋊C4—128no—
543C22⋊C4—128no—
544C22⋊C4—128no—
545C22⋊C4—128no—
546C22⋊C4—128no—
547C22⋊C4—128no—
548C42—44no—
549C42—68no—
550C42—124no—
551C22×C3C2×#12111yescharacteristic
552C22×C3C2×#12111yescharacteristic
553C22×C3C2×#12311yescharacteristic
554C22×C3C2×#12311yescharacteristic
555C22×C3C2×#12311yescharacteristic
556C22×C3#52511yescharacteristic
557C22×C3C2×#12411yescharacteristic
558C22×C3C2×#12611yescharacteristic
559C22×C3C2×#12611yescharacteristic
560C22×C3#52911yescharacteristic
561C22×C3#52911yescharacteristic
562C22×C3#53211yescharacteristic
563C22×C3#53211yescharacteristic
564C22×C3#53511yescharacteristic
565C22×C3#53711yescharacteristic
566C22×C3#54011yescharacteristic
567C22×C3#54011yescharacteristic
568C22×C3#54211yescharacteristic
569C22×C3#54211yescharacteristic
570C22×C3D4211yescharacteristic
571C22×C3#54611yescharacteristic
572C22×C3#54611yescharacteristic
573C22×C3#54711yescharacteristic
574C22×C3#54711yescharacteristic
575C22×C3#55011yescharacteristic
576C22×C3#55011yescharacteristic
577C22×C3#55311yescharacteristic
578C22×C3#55311yescharacteristic
579C22×C3#55511yescharacteristic
580C22×C3#55611yescharacteristic
581C22×C3#55611yescharacteristic
582C22×C3#55911yescharacteristic
583C22×C3#55911yescharacteristic
584C22×C3#55911yescharacteristic
585C22×C3#55911yescharacteristic
586C2×D3—44no—
587C2×D3—44no—
588C2×D3—44no—
589C2×D3—44no—
590C2×D3—44no—
591C2×D3—44no—
592C2×D3—44no—
593C2×D3—82no—
594C2×D3—82no—
595C2×D3—82no—
596C2×D3—82no—
597C2×D3—82no—
598C2×D3—82no—
599C2×D3—82no—
600C2×D3—82no—
601C3×C4—42no—
602C3×C4—42no—
603C3×C4—82no—
604C3×C4—82no—
605C3×C4#39718yescomplemented
606Dic3—24no—
607Dic3—42no—
608Dic3—42no—
609Dic3—42no—
610Dic3—82no—
611C23—64no—
612C23—64no—
613C23—64no—
614C23—64no—
615C23—64no—
616C23—64no—
617C23—64no—
618C23—122no—
619C23—122no—
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—
646C23C2×#23511yescharacteristic
647C23C2×#23511yescharacteristic
648C23C2×#23511yescharacteristic
649C23C2×D3×D411yescharacteristic
650C23C2×D3×D411yescharacteristic
651C23C2×D3×D411yescharacteristic
652C23C2×#23711yescharacteristic
653C23#100411yescharacteristic
654C23C2×#23911yescharacteristic
655C23C2×#23911yescharacteristic
656C23#100711yescharacteristic
657C23D3×#4111yescharacteristic
658C23D3×#4111yescharacteristic
659C23#100911yescharacteristic
660C23#100911yescharacteristic
661D4—1216no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—34no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—62no—
692C2×C4—62no—
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—62no—
705C2×C4—62no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4—121no—
711C2×C4—121no—
712C2×C4—121no—
713C2×C4—121no—
714C2×C4—121no—
715C2×C4—121no—
716C2×C4—121no—
717C2×C4—121no—
718C2×C4—122no—
719C2×C4—122no—
720C2×C4—122no—
721C2×C4—122no—
722C2×C4—122no—
723C2×C4—122no—
724C2×C4—122no—
725C2×C4#87614yes—
726C2×C4#88314yes—
727C2×C4#88414yes—
728C2×C4#88514yes—
729C2×C4#89414yes—
730C2×C4#89414yes—
731C2×C4#89814yes—
732C2×C3C2×#39711yescharacteristic
733C2×C3#244511yescharacteristic
734C2×C3#244511yescharacteristic
735C2×C3#244711yescharacteristic
736C2×C3#244711yescharacteristic
737C2×C3#251211yescharacteristic
738C2×C3#251211yescharacteristic
739C2×C3#251311yescharacteristic
740C2×C3#251311yescharacteristic
741C2×C3#253511yescharacteristic
742C2×C3#253711yescharacteristic
743C2×C3#254811yescharacteristic
744C2×C3#259211yescharacteristic
745C2×C3#262411yescharacteristic
746C2×C3#285411yescharacteristic
747D3—84no—
748C22—124no—
749C22—124no—
750C22—124no—
751C22—124no—
752C22—124no—
753C22—124no—
754C22—124no—
755C22—242no—
756C22—242no—
757C22—242no—
758C22—242no—
759C22—242no—
760C22—242no—
761C22—242no—
762C22—242no—
763C22C2×#87611yescharacteristic
764C22C2×#88311yescharacteristic
765C22C2×#88411yescharacteristic
766C22C2×#88511yescharacteristic
767C22C2×#89411yescharacteristic
768C22C2×#89411yescharacteristic
769C22#550711yescharacteristic
770C22C2×#89811yescharacteristic
771C22#551411yescharacteristic
772C22#553011yescharacteristic
773C22#553211yescharacteristic
774C22#554811yescharacteristic
775C22#555311yescharacteristic
776C22#555911yescharacteristic
777C22#556211yescharacteristic
778C22#556811yescharacteristic
779C22#558011yescharacteristic
780C22#558211yescharacteristic
781C22#558511yescharacteristic
782C22D3×#12111yescharacteristic
783C22#560711yescharacteristic
784C22#560911yescharacteristic
785C22#561211yescharacteristic
786C22#562711yescharacteristic
787C22#562911yescharacteristic
788C22#563011yescharacteristic
789C22#563111yescharacteristic
790C22#568111yescharacteristic
791C22#568111yescharacteristic
792C22#569111yescharacteristic
793C22#569711yescharacteristic
794C22#571811yescharacteristic
795C22#572511yescharacteristic
796C22#573211yescharacteristic
797C22#573311yescharacteristic
798C4—42no—
799C4—42no—
800C4—64no—
801C4—82no—
802C4—82no—
803C4—122no—
804C4—122no—
805C4—122no—
806C4—242no—
807C4#467518yescomplemented
808C3#1514711yescharacteristic, complemented, Sylow
809C2—244no—
810C2C2×#467511yescharacteristic
811C2#7369311yescharacteristic
812C2#7369511yescharacteristic
813C2#7393311yescharacteristic
814C2#7393511yescharacteristic
815C2#7417211yescharacteristic
816C2#7433311yescharacteristic
817C2#7600411yescharacteristic
818C2#7600611yescharacteristic
819C2#7624911yescharacteristic
820C2#7628611yescharacteristic
821C2#7631611yescharacteristic
822C2#7635311yescharacteristic
823C2#7650511yescharacteristic
824C2#7655511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×C4⋊#95C2
prime radicalC23×D12C22
hypercenterC4⋊#95D3
hypocenterC3#15147
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×C4×Dic3⋊C4C2semidirect
5. C2×#4675C2semidirect
6. C3×C4⋊#95C2semidirect
7. #71563C2semidirect
8. #71563C2semidirect
9. #69429C2semidirect
10. #69429C2semidirect
11. #69428C2semidirect
51. C4⋊#95D3semidirect
105. C2×Dic3⋊C4D4semidirect
605. C3×C4#397semidirect
807. C4#4675semidirect
808. C3#15147semidirect

Maximal subgroups

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

subgroupindex
C2×#49882
C2×#49392
C2×C4×Dic3⋊C42
C2×#46752
C3×C4⋊#952
#715632
#694292
#694282
#151473