Finite Group Databasebeta

← #10732216

Subgroups — #10732216

Order 768.

1946 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#924C211yesmaximal, characteristic
2C2×C3×C4×C22⋊C4C211yesmaximal, characteristic
3C2×#5212C211yesmaximal, characteristic
4C2×#4929C211yesmaximal, characteristic, complemented
5C2×#4929C211yesmaximal, characteristic, complemented
6C2×#4928C211yesmaximal, characteristic, complemented
7#71548C212yesmaximal
8#71547C212yesmaximal
9#71535C211yesmaximal, characteristic, complemented
10#69414C212yesmaximal, complemented
11#69409C212yesmaximal, complemented
12#15179—31nomaximal, Sylow
13C24×C3×C4C2211yescharacteristic
14C23×Dic6C2211yescharacteristic
15C22×C3×C22⋊C4C2211yescharacteristic
16C22×C3×C22⋊C4C2211yescharacteristic
17C22×C3×C42C2211yescharacteristic
18C22×C3×C42C2211yescharacteristic
19C22×#217C2212yes—
20C22×#217C2212yes—
21C22×C4⋊Dic3C2211yescharacteristic
22C22×C4⋊Dic3C2211yescharacteristic
23C22×C4⋊Dic3C2211yescharacteristic
24C2×#924—24no—
25C2×#924—24no—
26C2×#924—24no—
27C22×Dic3⋊C4C2212yes—
28C22×Dic3⋊C4C2212yes—
29C3×C4×C22⋊C4—24no—
30C2×C3×#95C2211yescharacteristic
31C2×C3×#95C2211yescharacteristic
32#5212—24no—
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2212yes—
41#4929—24no—
42#4929—24no—
43#4928—24no—
44C22×C22⋊Q8—31no—
45C2×#391—31no—
46C2×#391—31no—
47C2×#389—31no—
48C2×#380—31no—
49C2×C4×C22⋊C4D311yescharacteristic
50#1442—32no—
51#1441—32no—
52#1440—32no—
53#1439—32no—
54C4⋊#95—31no—
55C25×C3C2311yescharacteristic
56C23×C3×C4—22no—
57C23×C3×C4—22no—
58C23×C3×C4—22no—
59C23×C3×C4—22no—
60C23×C3×C4—22no—
61C23×C3×C4—22no—
62C23×C3×C4D414yes—
63C23×C3×C4C2311yescharacteristic
64C23×C3×C4C2311yescharacteristic
65C23×C3×C4C2311yescharacteristic
66C23×C3×C4C2311yescharacteristic
67C23×C3×C4C2311yescharacteristic
68C23×C3×C4C2311yescharacteristic
69C23×Dic3C2312yes—
70C23×Dic3C2312yes—
71C23×Dic3C2312yes—
72C23×Dic3C2312yes—
73C22×Dic6—22no—
74C22×Dic6—22no—
75C22×Dic6—22no—
76C22×Dic6—22no—
77C22×Dic6—22no—
78C22×Dic6—22no—
79C22×Dic6D414yes—
80C2×C3×C22⋊C4—22no—
81C2×C3×C22⋊C4—22no—
82C2×C3×C22⋊C4—22no—
83C2×C3×C22⋊C4—22no—
84C2×C3×C22⋊C4—22no—
85C2×C3×C22⋊C4Q814yescomplemented
86C2×C3×C42—22no—
87C2×C3×C42—22no—
88C2×C3×C42—22no—
89C2×C3×C42—22no—
90C2×C3×C42—22no—
91C2×C3×C42—22no—
92C2×#217—24no—
93C2×#217—24no—
94C2×#217—24no—
95C2×#217—24no—
96C2×#217—24no—
97C2×#217—42no—
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⋊Dic3—22no—
105C2×C4⋊Dic3D414yes—
106C2×C4⋊Dic3D414yes—
107#924—232no—
108C2×Dic3⋊C4—24no—
109C2×Dic3⋊C4—24no—
110C2×Dic3⋊C4—24no—
111C2×Dic3⋊C4—24no—
112C2×Dic3⋊C4—24no—
113C2×Dic3⋊C4—42no—
114C3×#95—22no—
115C3×#95—22no—
116C3⋊#95—24no—
117C3⋊#95—24no—
118C3⋊#95—24no—
119C3⋊#95—24no—
120C3⋊#95—24no—
121C3⋊#95—24no—
122C3⋊#95—24no—
123C3⋊#95—42no—
124C23×Q8—31no—
125C24×C4C2×D311yescharacteristic
126C2×C22⋊Q8—64no—
127C2×C22⋊Q8—64no—
128C2×C22⋊Q8—64no—
129C22×C4⋊C4—31no—
130C22×C4⋊C4—31no—
131C22×C4⋊C4—32no—
132C22×C4⋊C4—31no—
133C22×C4⋊C4—32no—
134C22×C22⋊C4—32no—
135C22×C22⋊C4—32no—
136C22×C22⋊C4C2×D311yescharacteristic
137C22×C22⋊C4C2×D311yescharacteristic
138C22×C42C2×D311yescharacteristic
139C22×C42C2×D311yescharacteristic
140#391—64no—
141#391—64no—
142#389—64no—
143#380—64no—
144C4×C22⋊C4—24no—
145C2×#95—32no—
146C2×#95—32no—
147C2×#95—32no—
148C2×#95—32no—
149C2×#95—32no—
150C2×#95—32no—
151C2×#95—32no—
152C2×#95—32no—
153C2×#95C2×D311yescharacteristic
154C2×#95C2×D311yescharacteristic
155C24×C3—21no—
156C24×C3—21no—
157C24×C3—21no—
158C24×C3—21no—
159C24×C3—21no—
160C24×C3—21no—
161C24×C3—21no—
162C24×C3—21no—
163C24×C3—21no—
164C24×C3—21no—
165C24×C3—21no—
166C24×C3—21no—
167C24×C3C2×D412yes—
168C24×C3C2×Q812yes—
169C24×C3#4112yes—
170C24×C3C2411yescharacteristic
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×C4—21no—
201C22×C3×C4—28no—
202C22×C3×C4—28no—
203C22×C3×C4—28no—
204C22×C3×C4—44no—
205C22×C3×C4—44no—
206C22×C3×C4—44no—
207C22×C3×C4—44no—
208C22×C3×C4C2×D412yes—
209C22×C3×C4C2×D412yes—
210C22×C3×C4C2×D412yes—
211C22×C3×C4C2×D412yes—
212C22×C3×C4C2×D412yes—
213C22×C3×C4C2×Q812yes—
214C22×C3×C4C2×Q812yes—
215C22×C3×C4#4112yes—
216C22×C3×C4#4112yes—
217C22×C3×C4#4112yes—
218C22×C3×C4#4112yes—
219C22×C3×C4#4112yes—
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×Dic3—22no—
238C22×Dic3—22no—
239C22×Dic3—22no—
240C22×Dic3—22no—
241C22×Dic3—22no—
242C22×Dic3—22no—
243C22×Dic3—22no—
244C22×Dic3—22no—
245C22×Dic3C2×D414yes—
246C22×Dic3C2×D414yes—
247C22×Dic3C2×D414yes—
248C2×Dic6—28no—
249C2×Dic6—28no—
250C2×Dic6—28no—
251C2×Dic6—44no—
252C2×Dic6—44no—
253C2×Dic6—44no—
254C2×Dic6—44no—
255C3×C22⋊C4—28no—
256C3×C22⋊C4—28no—
257C3×C42—44no—
258C3×C42—44no—
259#217—216no—
260#217—48no—
261C4⋊Dic3—28no—
262C4⋊Dic3—28no—
263C4⋊Dic3—44no—
264Dic3⋊C4—216no—
265Dic3⋊C4—48no—
266C25C22×D311yescharacteristic
267C22×Q8—34no—
268C22×Q8—62no—
269C22×Q8—62no—
270C22×Q8—62no—
271C22×Q8—62no—
272C22×Q8—62no—
273C22×Q8—62no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—32no—
281C23×C4—32no—
282C23×C4—32no—
283C23×C4—32no—
284C23×C4#6714yes—
285C23×C4C22×D311yescharacteristic
286C23×C4C22×D311yescharacteristic
287C23×C4C22×D311yescharacteristic
288C23×C4C22×D311yescharacteristic
289C23×C4C22×D311yescharacteristic
290C23×C4C22×D311yescharacteristic
291C22⋊Q8—632no—
292C2×C4⋊C4—34no—
293C2×C4⋊C4—34no—
294C2×C4⋊C4—64no—
295C2×C4⋊C4—64no—
296C2×C4⋊C4—62no—
297C2×C4⋊C4—62no—
298C2×C4⋊C4—62no—
299C2×C4⋊C4—64no—
300C2×C4⋊C4—62no—
301C2×C4⋊C4—64no—
302C2×C4⋊C4—64no—
303C2×C4⋊C4—62no—
304C2×C4⋊C4—62no—
305C2×C4⋊C4—62no—
306C2×C4⋊C4—122no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—64no—
313C2×C22⋊C4—64no—
314C2×C22⋊C4—64no—
315C2×C22⋊C4—64no—
316C2×C22⋊C4—64no—
317C2×C22⋊C4—122no—
318C2×C22⋊C4Dic614yescomplemented
319C2×C42—22no—
320C2×C42—22no—
321C2×C42—22no—
322C2×C42—22no—
323C2×C42—22no—
324C2×C42—22no—
325#95—22no—
326#95—22no—
327#95—64no—
328#95—64no—
329#95—64no—
330#95—64no—
331#95—64no—
332#95—64no—
333#95—64no—
334#95—122no—
335C23×C3—22no—
336C23×C3—22no—
337C23×C3—22no—
338C23×C3—22no—
339C23×C3—22no—
340C23×C3—22no—
341C23×C3—22no—
342C23×C3—22no—
343C23×C3—22no—
344C23×C3—22no—
345C23×C3—22no—
346C23×C3—22no—
347C23×C3—22no—
348C23×C3—22no—
349C23×C3—22no—
350C23×C3—22no—
351C23×C3—22no—
352C23×C3—22no—
353C23×C3—41no—
354C23×C3—41no—
355C23×C3—41no—
356C23×C3—41no—
357C23×C3—41no—
358C23×C3—41no—
359C23×C3—41no—
360C23×C3—41no—
361C23×C3—41no—
362C23×C3—41no—
363C23×C3—41no—
364C23×C3—41no—
365C23×C3—41no—
366C23×C3—41no—
367C23×C3—41no—
368C23×C3—41no—
369C23×C3C22⋊Q814yes—
370C23×C3C22×D411yescharacteristic
371C23×C3C22×D411yescharacteristic
372C23×C3C22×D411yescharacteristic
373C23×C3C22×D411yescharacteristic
374C23×C3C22×Q811yescharacteristic
375C23×C3C2×#4111yescharacteristic
376C23×C3C2×#4111yescharacteristic
377C23×C3C2×#4111yescharacteristic
378C23×C3C2×#4111yescharacteristic
379C23×C3C2×#4111yescharacteristic
380C23×C3C2×#4111yescharacteristic
381C23×C3H(5,𝔽2)11yescharacteristic
382C23×C32−1+411yescharacteristic
383C23×C32−1+411yescharacteristic
384C23×C32−1+411yescharacteristic
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—22no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
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—41no—
417C2×C3×C4—41no—
418C2×C3×C4—41no—
419C2×C3×C4—41no—
420C2×C3×C4—416no—
421C2×C3×C4#12014yes—
422C2×C3×C4#12114yes—
423C2×C3×C4#12114yes—
424C2×C3×C4#12114yes—
425C2×C3×C4#12314yes—
426C2×C3×C4#12314yes—
427C2×C3×C4#12414yes—
428C2×Dic3—24no—
429C2×Dic3—24no—
430C2×Dic3—24no—
431C2×Dic3—24no—
432C2×Dic3—24no—
433C2×Dic3—24no—
434C2×Dic3—24no—
435C2×Dic3—24no—
436C2×Dic3—24no—
437C2×Dic3—42no—
438C2×Dic3—42no—
439C2×Dic3—42no—
440C2×Dic3—42no—
441C2×Dic3—42no—
442C2×Dic3—42no—
443C2×Dic3—42no—
444C2×Dic3—42no—
445C2×Dic3—42no—
446C2×Dic3—42no—
447C2×Dic3—42no—
448C2×Dic3—42no—
449C2×Dic3—42no—
450C2×Dic3—42no—
451C2×Dic3—42no—
452C2×Dic3—42no—
453C2×Dic3—42no—
454C2×Dic3—42no—
455C2×Dic3—42no—
456Dic6—416no—
457C24—21no—
458C24—21no—
459C24—21no—
460C24—21no—
461C24—21no—
462C24—21no—
463C24—21no—
464C24—21no—
465C24—21no—
466C24—21no—
467C24—21no—
468C24—21no—
469C24C2×Dic612yes—
470C24#23512yes—
471C24C2×#6712yes—
472C24C23×D311yescharacteristic
473C2×Q8—68no—
474C2×Q8—68no—
475C2×Q8—68no—
476C2×Q8—124no—
477C2×Q8—124no—
478C2×Q8—124no—
479C2×Q8—124no—
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—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—28no—
511C22×C4—28no—
512C22×C4—28no—
513C22×C4—34no—
514C22×C4—34no—
515C22×C4—34no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4—44no—
519C22×C4—44no—
520C22×C4—62no—
521C22×C4—62no—
522C22×C4—62no—
523C22×C4—62no—
524C22×C4—62no—
525C22×C4—62no—
526C22×C4—62no—
527C22×C4—62no—
528C22×C4—62no—
529C22×C4—62no—
530C22×C4—62no—
531C22×C4—62no—
532C22×C4—62no—
533C22×C4—62no—
534C22×C4—62no—
535C22×C4—62no—
536C22×C4—62no—
537C22×C4—62no—
538C22×C4—62no—
539C22×C4—62no—
540C22×C4—62no—
541C22×C4—62no—
542C22×C4—62no—
543C22×C4—62no—
544C22×C4—62no—
545C22×C4C2×Dic612yes—
546C22×C4C2×Dic612yes—
547C22×C4#23512yes—
548C22×C4#23512yes—
549C22×C4#23512yes—
550C22×C4#23512yes—
551C22×C4D3×D412yes—
552C22×C4D3×D412yes—
553C22×C4D3×D412yes—
554C22×C4#23712yes—
555C22×C4C2×#6712yes—
556C22×C4C2×#6712yes—
557C4⋊C4—616no—
558C4⋊C4—68no—
559C4⋊C4—68no—
560C4⋊C4—128no—
561C4⋊C4—124no—
562C22⋊C4—28no—
563C22⋊C4—28no—
564C22⋊C4—616no—
565C22⋊C4—128no—
566C42—44no—
567C42—44no—
568C22×C3—24no—
569C22×C3—24no—
570C22×C3—24no—
571C22×C3—42no—
572C22×C3—42no—
573C22×C3—42no—
574C22×C3—42no—
575C22×C3—42no—
576C22×C3—42no—
577C22×C3—42no—
578C22×C3—42no—
579C22×C3—42no—
580C22×C3—42no—
581C22×C3—42no—
582C22×C3—42no—
583C22×C3C2×#12011yescharacteristic
584C22×C3C2×#12111yescharacteristic
585C22×C3C2×#12111yescharacteristic
586C22×C3C2×#12111yescharacteristic
587C22×C3C2×C22⋊Q811yescharacteristic
588C22×C3C2×#12311yescharacteristic
589C22×C3C2×#12311yescharacteristic
590C22×C3#52511yescharacteristic
591C22×C3C2×#12411yescharacteristic
592C22×C3#52911yescharacteristic
593C22×C3#52911yescharacteristic
594C22×C3#53311yescharacteristic
595C22×C3#53311yescharacteristic
596C22×C3#53611yescharacteristic
597C22×C3#53711yescharacteristic
598C22×C3#54111yescharacteristic
599C22×C3#54111yescharacteristic
600C22×C3#54211yescharacteristic
601C22×C3#54211yescharacteristic
602C22×C3#54611yescharacteristic
603C22×C3#54611yescharacteristic
604C22×C3#54711yescharacteristic
605C22×C3#54711yescharacteristic
606C22×C3#54811yescharacteristic
607C22×C3#54811yescharacteristic
608C22×C3#54811yescharacteristic
609C22×C3#54811yescharacteristic
610C22×C3D4×Q811yescharacteristic
611C22×C3D4×Q811yescharacteristic
612C22×C3D4×Q811yescharacteristic
613C22×C3#55011yescharacteristic
614C22×C3#55211yescharacteristic
615C22×C3#55211yescharacteristic
616C22×C3#55411yescharacteristic
617C22×C3#55611yescharacteristic
618C3×C4—42no—
619C3×C4—42no—
620C3×C4—42no—
621C3×C4—42no—
622C3×C4—42no—
623C3×C4#39418yes—
624Dic3—44no—
625Dic3—44no—
626Dic3—44no—
627Dic3—82no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23#92414yes—
663C23C22×Dic611yescharacteristic
664C23C2×#23511yescharacteristic
665C23C2×#23511yescharacteristic
666C23C2×#23511yescharacteristic
667C23C2×#23511yescharacteristic
668C23C2×#23511yescharacteristic
669C23C2×D3×D411yescharacteristic
670C23C2×D3×D411yescharacteristic
671C23C2×D3×D411yescharacteristic
672C23C2×#23711yescharacteristic
673C23#100911yescharacteristic
674C23#101011yescharacteristic
675C23#101011yescharacteristic
676C23#101011yescharacteristic
677C23C22×#6711yescharacteristic
678Q8—1216no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
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—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—416no—
715C2×C4—64no—
716C2×C4—64no—
717C2×C4—64no—
718C2×C4—64no—
719C2×C4—64no—
720C2×C4—64no—
721C2×C4—64no—
722C2×C4—64no—
723C2×C4—64no—
724C2×C4—122no—
725C2×C4—122no—
726C2×C4—122no—
727C2×C4—122no—
728C2×C4—122no—
729C2×C4—122no—
730C2×C4—122no—
731C2×C4—122no—
732C2×C4—122no—
733C2×C4—122no—
734C2×C4—122no—
735C2×C4—122no—
736C2×C4—122no—
737C2×C4—122no—
738C2×C4—122no—
739C2×C4—122no—
740C2×C4—122no—
741C2×C4—122no—
742C2×C4—122no—
743C2×C4#88314yes—
744C2×C4#88414yes—
745C2×C4#88414yes—
746C2×C4#88514yes—
747C2×C4#92914yes—
748C2×C4#93714yes—
749C2×C4#93914yes—
750C2×C3—44no—
751C2×C3C2×#39411yescharacteristic
752C2×C3#240711yescharacteristic
753C2×C3#240911yescharacteristic
754C2×C3#241511yescharacteristic
755C2×C3#241711yescharacteristic
756C2×C3#242111yescharacteristic
757C2×C3#242311yescharacteristic
758C2×C3#242611yescharacteristic
759C2×C3#242711yescharacteristic
760C2×C3#242911yescharacteristic
761C2×C3#242911yescharacteristic
762C2×C3#248911yescharacteristic
763C2×C3#249211yescharacteristic
764C2×C3#262511yescharacteristic
765C2×C3#285511yescharacteristic
766C22—24no—
767C22—24no—
768C22—24no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22#547011yescharacteristic
782C22#547011yescharacteristic
783C22#547911yescharacteristic
784C22#547911yescharacteristic
785C22C2×#88311yescharacteristic
786C22C2×#88411yescharacteristic
787C22C2×#88411yescharacteristic
788C22C2×#88511yescharacteristic
789C22#551811yescharacteristic
790C22#551811yescharacteristic
791C22#553411yescharacteristic
792C22#553411yescharacteristic
793C22D4×Dic611yescharacteristic
794C22D4×Dic611yescharacteristic
795C22D4×Dic611yescharacteristic
796C22#554111yescharacteristic
797C22#554111yescharacteristic
798C22#554211yescharacteristic
799C22#554311yescharacteristic
800C22#555011yescharacteristic
801C22#555011yescharacteristic
802C22#555111yescharacteristic
803C22#555111yescharacteristic
804C22#555211yescharacteristic
805C22#555211yescharacteristic
806C22#555211yescharacteristic
807C22#555211yescharacteristic
808C22#555311yescharacteristic
809C22C2×#92411yescharacteristic
810C22C2×#92911yescharacteristic
811C22#579111yescharacteristic
812C22C2×#93711yescharacteristic
813C22C2×#93911yescharacteristic
814C22#582511yescharacteristic
815C22#583311yescharacteristic
816C4—42no—
817C4—42no—
818C4—42no—
819C4—42no—
820C4—42no—
821C4—124no—
822C4—124no—
823C4—124no—
824C4—242no—
825C4#495918yes—
826C3#1517911yescharacteristic, complemented, Sylow
827C2—44no—
828C2#7348311yescharacteristic
829C2#7348411yescharacteristic
830C2#7348511yescharacteristic
831C2#7348611yescharacteristic
832C2#7348811yescharacteristic
833C2#7348811yescharacteristic
834C2#7350511yescharacteristic
835C2#7350811yescharacteristic
836C2#8207511yescharacteristic
837C2C2×#495911yescharacteristic
838C2#8226311yescharacteristic
839C2#8234911yescharacteristic
840C2#8235111yescharacteristic
841C2#8235311yescharacteristic
842C2#8240211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×C4×C22⋊C4C2
prime radicalC25×C3C23
hypercenterC2×C4×C22⋊C4D3
hypocenterC3#15179
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×#4929C2semidirect
5. C2×#4929C2semidirect
6. C2×#4928C2semidirect
9. #71535C2semidirect
10. #69414C2semidirect
11. #69409C2semidirect
85. C2×C3×C22⋊C4Q8semidirect
318. C2×C22⋊C4Dic6semidirect
826. C3#15179semidirect

Maximal subgroups

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

subgroupindex
C22×#9242
C2×C3×C4×C22⋊C42
C2×#52122
C2×#49292
C2×#49282
#715482
#715472
#715352
#694142
#694092
#151793