Finite Group Databasebeta

← #10732555

Subgroups — #10732555

Order 768.

1686 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C22⋊C4C211yesmaximal, characteristic
2C2×#5212C211yesmaximal, characteristic
3C2×#5212C211yesmaximal, characteristic
4C2×#4928C211yesmaximal, characteristic, complemented
5C2×#4928C211yesmaximal, characteristic, complemented
6C2×#4936C211yesmaximal, characteristic, complemented
7#71547C212yesmaximal
8#71547C212yesmaximal
9#71535C211yesmaximal, characteristic, complemented
10#69417C212yesmaximal, complemented
11#69409C212yesmaximal, complemented
12#15220—31nomaximal, Sylow
13C24×C3×C4C2211yescharacteristic
14C22×C3×C22⋊C4C2211yescharacteristic
15C22×C3×C22⋊C4C2211yescharacteristic
16C22×C3×C42C2211yescharacteristic
17C22×C3×C42C2211yescharacteristic
18C22×#217C2212yes—
19C22×#217C2212yes—
20C22×C4⋊Dic3C2211yescharacteristic
21C22×C4⋊Dic3C2211yescharacteristic
22C22×C4⋊Dic3C2211yescharacteristic
23C22×C4⋊Dic3C2211yescharacteristic
24C22×Dic3⋊C4C2212yes—
25C22×Dic3⋊C4C2212yes—
26C3×C4×C22⋊C4—24no—
27C2×C3×#95C2211yescharacteristic
28C2×C3×#95C2211yescharacteristic
29#5212—24no—
30#5212—24no—
31C2×C3⋊#95C2212yes—
32C2×C3⋊#95C2212yes—
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39#4936—24no—
40#4928—24no—
41#4928—24no—
42C2×#389—31no—
43C2×#389—31no—
44C2×#382—31no—
45C2×#380—31no—
46C2×#380—31no—
47C2×C4×C22⋊C4D311yescharacteristic
48#1443—32no—
49#1441—32no—
50#1439—32no—
51#1439—32no—
52C4⋊#95—31no—
53C25×C3C2311yescharacteristic
54C23×C3×C4—22no—
55C23×C3×C4—22no—
56C23×C3×C4—22no—
57C23×C3×C4—22no—
58C23×C3×C4—22no—
59C23×C3×C4—22no—
60C23×C3×C4Q814yes—
61C23×C3×C4C2311yescharacteristic
62C23×C3×C4C2311yescharacteristic
63C23×C3×C4C2311yescharacteristic
64C23×C3×C4C2311yescharacteristic
65C23×C3×C4C2311yescharacteristic
66C23×C3×C4C2311yescharacteristic
67C23×Dic3C2312yes—
68C23×Dic3C2312yes—
69C23×Dic3C2312yes—
70C23×Dic3C2312yes—
71C2×C3×C22⋊C4—22no—
72C2×C3×C22⋊C4—22no—
73C2×C3×C22⋊C4—22no—
74C2×C3×C22⋊C4—22no—
75C2×C3×C22⋊C4—22no—
76C2×C3×C22⋊C4—22no—
77C2×C3×C42—22no—
78C2×C3×C42—22no—
79C2×C3×C42—22no—
80C2×C3×C42—22no—
81C2×C3×C42—22no—
82C2×C3×C42D414yes—
83C2×#217—24no—
84C2×#217—24no—
85C2×#217—24no—
86C2×#217—24no—
87C2×#217—42no—
88C2×#217—42no—
89C2×C4⋊Dic3—22no—
90C2×C4⋊Dic3—22no—
91C2×C4⋊Dic3—22no—
92C2×C4⋊Dic3—22no—
93C2×C4⋊Dic3—22no—
94C2×C4⋊Dic3—22no—
95C2×C4⋊Dic3—22no—
96C2×C4⋊Dic3—22no—
97C2×C4⋊Dic3—22no—
98C2×C4⋊Dic3—22no—
99C2×C4⋊Dic3D414yes—
100C2×C4⋊Dic3D414yes—
101C2×Dic3⋊C4—24no—
102C2×Dic3⋊C4—24no—
103C2×Dic3⋊C4—24no—
104C2×Dic3⋊C4—42no—
105C2×Dic3⋊C4—42no—
106C2×Dic3⋊C4—42no—
107C3×#95—22no—
108C3×#95—22no—
109C3⋊#95—24no—
110C3⋊#95—24no—
111C3⋊#95—24no—
112C3⋊#95—24no—
113C3⋊#95—24no—
114C3⋊#95—24no—
115C3⋊#95—24no—
116C3⋊#95—42no—
117C24×C4C2×D311yescharacteristic
118C22×C4⋊C4—31no—
119C22×C4⋊C4—31no—
120C22×C4⋊C4—31no—
121C22×C4⋊C4—31no—
122C22×C4⋊C4—32no—
123C22×C4⋊C4—32no—
124C22×C22⋊C4—32no—
125C22×C22⋊C4—32no—
126C22×C22⋊C4C2×D311yescharacteristic
127C22×C22⋊C4C2×D311yescharacteristic
128C22×C42C2×D311yescharacteristic
129C22×C42C2×D311yescharacteristic
130#389—64no—
131#389—64no—
132#382—64no—
133#380—64no—
134#380—64no—
135C4×C22⋊C4—24no—
136C2×#95—32no—
137C2×#95—32no—
138C2×#95—32no—
139C2×#95—32no—
140C2×#95—32no—
141C2×#95—32no—
142C2×#95—32no—
143C2×#95—32no—
144C2×#95C2×D311yescharacteristic
145C2×#95C2×D311yescharacteristic
146C24×C3—21no—
147C24×C3—21no—
148C24×C3—21no—
149C24×C3—21no—
150C24×C3—21no—
151C24×C3—21no—
152C24×C3—21no—
153C24×C3—21no—
154C24×C3—21no—
155C24×C3—21no—
156C24×C3—21no—
157C24×C3—21no—
158C24×C3C2×Q812yes—
159C24×C3#4112yes—
160C24×C3#4112yes—
161C24×C3C2411yescharacteristic
162C22×C3×C4—21no—
163C22×C3×C4—21no—
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—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—28no—
193C22×C3×C4—28no—
194C22×C3×C4—28no—
195C22×C3×C4—44no—
196C22×C3×C4—44no—
197C22×C3×C4—44no—
198C22×C3×C4—44no—
199C22×C3×C4C2×D412yes—
200C22×C3×C4C2×D412yes—
201C22×C3×C4C2×D412yes—
202C22×C3×C4C2×D412yes—
203C22×C3×C4C2×D412yes—
204C22×C3×C4C2×Q812yes—
205C22×C3×C4C2×Q812yes—
206C22×C3×C4#4112yes—
207C22×C3×C4#4112yes—
208C22×C3×C4#4112yes—
209C22×C3×C4#4112yes—
210C22×C3×C4#4112yes—
211C22×Dic3—22no—
212C22×Dic3—22no—
213C22×Dic3—22no—
214C22×Dic3—22no—
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×Dic3—22no—
234C22×Dic3—22no—
235C22×Dic3—22no—
236C22×Dic3—22no—
237C22×Dic3C2×D414yes—
238C22×Dic3C2×D414yes—
239C3×C22⋊C4—28no—
240C3×C22⋊C4—28no—
241C3×C42—28no—
242C3×C42—44no—
243#217—48no—
244#217—48no—
245C4⋊Dic3—28no—
246C4⋊Dic3—28no—
247C4⋊Dic3—44no—
248C4⋊Dic3—44no—
249Dic3⋊C4—48no—
250Dic3⋊C4—48no—
251C25C22×D311yescharacteristic
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—32no—
259C23×C4—32no—
260C23×C4—32no—
261C23×C4—32no—
262C23×C4Dic614yes—
263C23×C4C22×D311yescharacteristic
264C23×C4C22×D311yescharacteristic
265C23×C4C22×D311yescharacteristic
266C23×C4C22×D311yescharacteristic
267C23×C4C22×D311yescharacteristic
268C23×C4C22×D311yescharacteristic
269C2×C4⋊C4—34no—
270C2×C4⋊C4—34no—
271C2×C4⋊C4—62no—
272C2×C4⋊C4—62no—
273C2×C4⋊C4—62no—
274C2×C4⋊C4—62no—
275C2×C4⋊C4—64no—
276C2×C4⋊C4—64no—
277C2×C4⋊C4—62no—
278C2×C4⋊C4—62no—
279C2×C4⋊C4—62no—
280C2×C4⋊C4—62no—
281C2×C4⋊C4—62no—
282C2×C4⋊C4—64no—
283C2×C4⋊C4—62no—
284C2×C4⋊C4—122no—
285C2×C4⋊C4—122no—
286C2×C4⋊C4—122no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—22no—
289C2×C22⋊C4—22no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—64no—
294C2×C22⋊C4—64no—
295C2×C22⋊C4—64no—
296C2×C22⋊C4—64no—
297C2×C22⋊C4—122no—
298C2×C22⋊C4—122no—
299C2×C42—22no—
300C2×C42—22no—
301C2×C42—22no—
302C2×C42—22no—
303C2×C42—22no—
304C2×C42#6714yes—
305#95—22no—
306#95—22no—
307#95—64no—
308#95—64no—
309#95—64no—
310#95—64no—
311#95—64no—
312#95—64no—
313#95—64no—
314#95—122no—
315C23×C3—22no—
316C23×C3—22no—
317C23×C3—22no—
318C23×C3—22no—
319C23×C3—22no—
320C23×C3—22no—
321C23×C3—22no—
322C23×C3—22no—
323C23×C3—22no—
324C23×C3—22no—
325C23×C3—22no—
326C23×C3—22no—
327C23×C3—22no—
328C23×C3—22no—
329C23×C3—22no—
330C23×C3—22no—
331C23×C3—22no—
332C23×C3—22no—
333C23×C3—41no—
334C23×C3—41no—
335C23×C3—41no—
336C23×C3—41no—
337C23×C3—41no—
338C23×C3—41no—
339C23×C3—41no—
340C23×C3—41no—
341C23×C3—41no—
342C23×C3—41no—
343C23×C3—41no—
344C23×C3—41no—
345C23×C3—41no—
346C23×C3—41no—
347C23×C3—41no—
348C23×C3—41no—
349C23×C3#12514yes—
350C23×C3C22×D411yescharacteristic
351C23×C3C22×D411yescharacteristic
352C23×C3C22×D411yescharacteristic
353C23×C3C22×Q811yescharacteristic
354C23×C3C2×#4111yescharacteristic
355C23×C3C2×#4111yescharacteristic
356C23×C3C2×#4111yescharacteristic
357C23×C3C2×#4111yescharacteristic
358C23×C3C2×#4111yescharacteristic
359C23×C3C2×#4111yescharacteristic
360C23×C3C2×#4111yescharacteristic
361C23×C3H(5,𝔽2)11yescharacteristic
362C23×C3H(5,𝔽2)11yescharacteristic
363C23×C32−1+411yescharacteristic
364C23×C32−1+411yescharacteristic
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
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—22no—
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—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—41no—
395C2×C3×C4—41no—
396C2×C3×C4—41no—
397C2×C3×C4—41no—
398C2×C3×C4—41no—
399C2×C3×C4—41no—
400C2×C3×C4—416no—
401C2×C3×C4#12114yes—
402C2×C3×C4#12114yes—
403C2×C3×C4#12114yes—
404C2×C3×C4C22⋊Q814yes—
405C2×C3×C4C22⋊Q814yes—
406C2×C3×C4C22⋊Q814yes—
407C2×C3×C4#12614yes—
408C2×Dic3—24no—
409C2×Dic3—24no—
410C2×Dic3—24no—
411C2×Dic3—24no—
412C2×Dic3—24no—
413C2×Dic3—24no—
414C2×Dic3—42no—
415C2×Dic3—42no—
416C2×Dic3—42no—
417C2×Dic3—42no—
418C2×Dic3—42no—
419C2×Dic3—42no—
420C2×Dic3—42no—
421C2×Dic3—42no—
422C2×Dic3—42no—
423C2×Dic3—42no—
424C2×Dic3—42no—
425C2×Dic3—42no—
426C2×Dic3—42no—
427C2×Dic3—42no—
428C2×Dic3—42no—
429C2×Dic3—42no—
430C2×Dic3—42no—
431C2×Dic3—42no—
432C2×Dic3—42no—
433C2×Dic3—42no—
434C2×Dic3—42no—
435C2×Dic3—42no—
436C24—21no—
437C24—21no—
438C24—21no—
439C24—21no—
440C24—21no—
441C24—21no—
442C24—21no—
443C24—21no—
444C24—21no—
445C24—21no—
446C24—21no—
447C24—21no—
448C24C2×Dic612yes—
449C24#23512yes—
450C24#23512yes—
451C24C23×D311yescharacteristic
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
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—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—34no—
486C22×C4—34no—
487C22×C4—44no—
488C22×C4—44no—
489C22×C4—44no—
490C22×C4—44no—
491C22×C4—62no—
492C22×C4—62no—
493C22×C4—62no—
494C22×C4—62no—
495C22×C4—62no—
496C22×C4—62no—
497C22×C4—62no—
498C22×C4—62no—
499C22×C4—62no—
500C22×C4—62no—
501C22×C4—62no—
502C22×C4—62no—
503C22×C4—62no—
504C22×C4—62no—
505C22×C4—62no—
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×C4C2×Dic612yes—
518C22×C4C2×Dic612yes—
519C22×C4#23512yes—
520C22×C4#23512yes—
521C22×C4#23512yes—
522C22×C4D3×D412yes—
523C22×C4D3×D412yes—
524C22×C4#23712yes—
525C22×C4#23712yes—
526C22×C4C2×#6712yes—
527C22×C4C2×#6712yes—
528C22×C4C2×#6712yes—
529C4⋊C4—68no—
530C4⋊C4—68no—
531C4⋊C4—128no—
532C4⋊C4—128no—
533C4⋊C4—124no—
534C4⋊C4—124no—
535C22⋊C4—28no—
536C22⋊C4—28no—
537C22⋊C4—128no—
538C22⋊C4—128no—
539C42—28no—
540C42—44no—
541C22×C3—24no—
542C22×C3—24no—
543C22×C3—24no—
544C22×C3—42no—
545C22×C3—42no—
546C22×C3—42no—
547C22×C3—42no—
548C22×C3—42no—
549C22×C3—42no—
550C22×C3—42no—
551C22×C3—42no—
552C22×C3—42no—
553C22×C3—42no—
554C22×C3—42no—
555C22×C3—42no—
556C22×C3C2×#12111yescharacteristic
557C22×C3C2×#12111yescharacteristic
558C22×C3C2×#12111yescharacteristic
559C22×C3C2×C22⋊Q811yescharacteristic
560C22×C3C2×C22⋊Q811yescharacteristic
561C22×C3C2×C22⋊Q811yescharacteristic
562C22×C3#52511yescharacteristic
563C22×C3#52511yescharacteristic
564C22×C3C2×#12511yescharacteristic
565C22×C3C2×#12611yescharacteristic
566C22×C3#52911yescharacteristic
567C22×C3#52911yescharacteristic
568C22×C3#53311yescharacteristic
569C22×C3#53511yescharacteristic
570C22×C3#53611yescharacteristic
571C22×C3#54211yescharacteristic
572C22×C3#54211yescharacteristic
573C22×C3#54411yescharacteristic
574C22×C3#54411yescharacteristic
575C22×C3#54611yescharacteristic
576C22×C3#54611yescharacteristic
577C22×C3#54611yescharacteristic
578C22×C3#54711yescharacteristic
579C22×C3#54811yescharacteristic
580C22×C3#54811yescharacteristic
581C22×C3#54811yescharacteristic
582C22×C3#55011yescharacteristic
583C22×C3#55211yescharacteristic
584C22×C3#55211yescharacteristic
585C22×C3#55211yescharacteristic
586C22×C3#55311yescharacteristic
587C22×C3#55311yescharacteristic
588C22×C3#55311yescharacteristic
589C22×C3#55511yescharacteristic
590C22×C3#55611yescharacteristic
591C3×C4—42no—
592C3×C4—42no—
593C3×C4—42no—
594C3×C4—42no—
595C3×C4—42no—
596C3×C4#39618yes—
597Dic3—44no—
598Dic3—44no—
599Dic3—82no—
600Dic3—82no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23#87014yes—
636C23C22×Dic611yescharacteristic
637C23C2×#23511yescharacteristic
638C23C2×#23511yescharacteristic
639C23C2×#23511yescharacteristic
640C23C2×#23511yescharacteristic
641C23C2×#23511yescharacteristic
642C23C2×D3×D411yescharacteristic
643C23C2×D3×D411yescharacteristic
644C23C2×#23711yescharacteristic
645C23C2×#23711yescharacteristic
646C23#100911yescharacteristic
647C23#100911yescharacteristic
648C23#101011yescharacteristic
649C23#101011yescharacteristic
650C23C22×#6711yescharacteristic
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
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—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—416no—
687C2×C4—64no—
688C2×C4—64no—
689C2×C4—64no—
690C2×C4—64no—
691C2×C4—64no—
692C2×C4—64no—
693C2×C4—122no—
694C2×C4—122no—
695C2×C4—122no—
696C2×C4—122no—
697C2×C4—122no—
698C2×C4—122no—
699C2×C4—122no—
700C2×C4—122no—
701C2×C4—122no—
702C2×C4—122no—
703C2×C4—122no—
704C2×C4—122no—
705C2×C4—122no—
706C2×C4—122no—
707C2×C4—122no—
708C2×C4—122no—
709C2×C4—122no—
710C2×C4—122no—
711C2×C4—122no—
712C2×C4—122no—
713C2×C4—122no—
714C2×C4—122no—
715C2×C4#87814yes—
716C2×C4#87814yes—
717C2×C4#87914yes—
718C2×C4#88414yes—
719C2×C4#92414yes—
720C2×C4#93814yes—
721C2×C4#93914yes—
722C2×C3—44no—
723C2×C3C2×#39611yescharacteristic
724C2×C3#241411yescharacteristic
725C2×C3#241511yescharacteristic
726C2×C3#242611yescharacteristic
727C2×C3#242711yescharacteristic
728C2×C3#243911yescharacteristic
729C2×C3#244111yescharacteristic
730C2×C3#244211yescharacteristic
731C2×C3#244211yescharacteristic
732C2×C3#249411yescharacteristic
733C2×C3#249511yescharacteristic
734C2×C3#253511yescharacteristic
735C2×C3#253611yescharacteristic
736C2×C3#262811yescharacteristic
737C2×C3#285111yescharacteristic
738C22—24no—
739C22—24no—
740C22—24no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22C2×#87011yescharacteristic
754C22#547011yescharacteristic
755C22#547911yescharacteristic
756C22#547911yescharacteristic
757C22C2×#87811yescharacteristic
758C22C2×#87811yescharacteristic
759C22C2×#87911yescharacteristic
760C22C2×#88411yescharacteristic
761C22#551911yescharacteristic
762C22#551911yescharacteristic
763C22#553411yescharacteristic
764C22#553411yescharacteristic
765C22#554111yescharacteristic
766C22#554111yescharacteristic
767C22#554111yescharacteristic
768C22#554211yescharacteristic
769C22#555011yescharacteristic
770C22#555011yescharacteristic
771C22#555011yescharacteristic
772C22#555111yescharacteristic
773C22#555211yescharacteristic
774C22#555211yescharacteristic
775C22#555211yescharacteristic
776C22#555311yescharacteristic
777C22#556311yescharacteristic
778C22#556511yescharacteristic
779C22#556511yescharacteristic
780C22#556511yescharacteristic
781C22C2×#92411yescharacteristic
782C22#579111yescharacteristic
783C22#579111yescharacteristic
784C22C2×#93811yescharacteristic
785C22C2×#93911yescharacteristic
786C22#582511yescharacteristic
787C22#583011yescharacteristic
788C4—42no—
789C4—42no—
790C4—42no—
791C4—42no—
792C4—42no—
793C4—124no—
794C4—124no—
795C4—242no—
796C4—242no—
797C4#494818yes—
798C3#1522011yescharacteristic, complemented, Sylow
799C2—44no—
800C2#7348511yescharacteristic
801C2#7348611yescharacteristic
802C2#7349211yescharacteristic
803C2#7349411yescharacteristic
804C2#7349511yescharacteristic
805C2#7349511yescharacteristic
806C2#7351011yescharacteristic
807C2#7351111yescharacteristic
808C2#8207411yescharacteristic
809C2C2×#494811yescharacteristic
810C2#8226411yescharacteristic
811C2#8235011yescharacteristic
812C2#8235111yescharacteristic
813C2#8237511yescharacteristic
814C2#8241511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×C4×C22⋊C4C2
prime radicalC25×C3C23
hypercenterC2×C4×C22⋊C4D3
hypocenterC3#15220
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×#4928C2semidirect
5. C2×#4928C2semidirect
6. C2×#4936C2semidirect
9. #71535C2semidirect
10. #69417C2semidirect
11. #69409C2semidirect
798. C3#15220semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×C22⋊C42
C2×#52122
C2×#49282
C2×#49362
#715472
#715352
#694172
#694092
#152203