Finite Group Databasebeta

← #10732210

Subgroups — #10732210

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×C3×C22⋊Q8C211yesmaximal, characteristic
2C2×#5229C211yesmaximal, characteristic, complemented
3C2×#5229C211yesmaximal, characteristic, complemented
4C2×#5212C211yesmaximal, characteristic
5C2×C4×#217C211yesmaximal, characteristic
6C2×#4972C211yesmaximal, characteristic, complemented
7#71567C212yesmaximal, complemented
8#71566C212yesmaximal, complemented
9#71563C211yesmaximal, characteristic, complemented
10#71549C212yesmaximal
11#71547C212yesmaximal
12#15179—31nomaximal, Sylow
13C23×C3×Q8C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C2×C3×C22⋊Q8—24no—
16C2×C3×C22⋊Q8—24no—
17C2×C3×C22⋊Q8—24no—
18C22×C3×C4⋊C4C2212yes—
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2212yes—
21C22×#217C2211yescharacteristic
22C22×#217C2212yes—
23C22×#217C2211yescharacteristic
24C22×C4⋊Dic3C2211yescharacteristic
25C22×C4⋊Dic3C2211yescharacteristic
26C22×Dic3⋊C4C2212yes—
27C22×C4×Dic3C2211yescharacteristic
28C22×C4×Dic3C2211yescharacteristic
29#5229—24no—
30#5229—24no—
31#5212—24no—
32C4×#217—24no—
33C2×C3⋊#95C2211yescharacteristic
34C2×C3⋊#95C2211yescharacteristic
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2212yes—
41C2×C3⋊#95C2212yes—
42C2×C3⋊#95C2212yes—
43#4972—24no—
44C22×C22⋊Q8D311yescharacteristic
45C2×#391—31no—
46C2×#391—31no—
47C2×#389—31no—
48C2×#380—31no—
49C2×C4×C22⋊C4—31no—
50#1442—32no—
51#1441—32no—
52#1440—32no—
53#1439—32no—
54C4⋊#95—31no—
55C25×C3C2311yescharacteristic
56C22×C3×Q8—22no—
57C22×C3×Q8—22no—
58C22×C3×Q8—22no—
59C22×C3×Q8—22no—
60C22×C3×Q8—22no—
61C22×C3×Q8—22no—
62C22×C3×Q8D414yes—
63C23×C3×C4—22no—
64C23×C3×C4—22no—
65C23×C3×C4—22no—
66C23×C3×C4—22no—
67C23×C3×C4—22no—
68C23×C3×C4—22no—
69C23×C3×C4D414yes—
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2312yes—
72C23×C3×C4C2312yes—
73C23×C3×C4C2311yescharacteristic
74C23×Dic3C2312yes—
75C23×Dic3C2312yes—
76C23×Dic3C2311yescharacteristic
77C23×Dic3C2311yescharacteristic
78C23×Dic3C2311yescharacteristic
79C23×Dic3C2311yescharacteristic
80C3×C22⋊Q8—232no—
81C2×C3×C4⋊C4—24no—
82C2×C3×C4⋊C4—24no—
83C2×C3×C4⋊C4—24no—
84C2×C3×C4⋊C4—22no—
85C2×C3×C4⋊C4—22no—
86C2×C3×C4⋊C4D414yes—
87C2×C3×C22⋊C4—24no—
88C2×C3×C22⋊C4—24no—
89C2×C3×C22⋊C4—24no—
90C2×#217—22no—
91C2×#217—22no—
92C2×#217—22no—
93C2×#217—22no—
94C2×#217—22no—
95C2×#217—24no—
96C2×#217—24no—
97C2×#217—42no—
98C2×#217Q814yescomplemented
99C2×C4⋊Dic3—22no—
100C2×C4⋊Dic3—22no—
101C2×C4⋊Dic3—22no—
102C2×C4⋊Dic3—22no—
103C2×C4⋊Dic3—22no—
104C2×C4⋊Dic3D414yes—
105C2×Dic3⋊C4—24no—
106C2×Dic3⋊C4—24no—
107C2×Dic3⋊C4—42no—
108C2×C4×Dic3—22no—
109C2×C4×Dic3—22no—
110C2×C4×Dic3—22no—
111C2×C4×Dic3—22no—
112C2×C4×Dic3—22no—
113C2×C4×Dic3—22no—
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×Q8C2×D311yescharacteristic
125C24×C4C2×D311yescharacteristic
126C2×C22⋊Q8—24no—
127C2×C22⋊Q8—24no—
128C2×C22⋊Q8—24no—
129C22×C4⋊C4—31no—
130C22×C4⋊C4—31no—
131C22×C4⋊C4—32no—
132C22×C4⋊C4C2×D312yes—
133C22×C4⋊C4C2×D311yescharacteristic
134C22×C22⋊C4—31no—
135C22×C22⋊C4—31no—
136C22×C22⋊C4—32no—
137C22×C22⋊C4C2×D312yes—
138C22×C42—31no—
139C22×C42—31no—
140#391—64no—
141#391—64no—
142#389—64no—
143#380—64no—
144C4×C22⋊C4—64no—
145C2×#95—32no—
146C2×#95—32no—
147C2×#95—32no—
148C2×#95—32no—
149C2×#95—32no—
150C2×#95—32no—
151C2×#95—31no—
152C2×#95—32no—
153C2×#95—31no—
154C2×#95—32no—
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
171C2×C3×Q8—28no—
172C2×C3×Q8—28no—
173C2×C3×Q8—28no—
174C2×C3×Q8—44no—
175C2×C3×Q8—44no—
176C2×C3×Q8—44no—
177C2×C3×Q8—44no—
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×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—28no—
197C22×C3×C4—28no—
198C22×C3×C4—28no—
199C22×C3×C4—44no—
200C22×C3×C4—44no—
201C22×C3×C4—44no—
202C22×C3×C4—44no—
203C22×C3×C4C2×D412yes—
204C22×C3×C4C2×D414yes—
205C22×C3×C4C2×D412yes—
206C22×C3×C4C2×D414yes—
207C22×C3×C4C2×D412yes—
208C22×C3×C4C2×D412yes—
209C22×C3×C4C2×D412yes—
210C22×C3×C4#4112yes—
211C22×C3×C4#4112yes—
212C22×C3×C4#4112yes—
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—21no—
222C22×Dic3—22no—
223C22×Dic3—21no—
224C22×Dic3—21no—
225C22×Dic3—21no—
226C22×Dic3—22no—
227C22×Dic3—22no—
228C22×Dic3—21no—
229C22×Dic3—21no—
230C22×Dic3—22no—
231C22×Dic3—21no—
232C22×Dic3—21no—
233C22×Dic3—21no—
234C22×Dic3—21no—
235C22×Dic3—22no—
236C22×Dic3—22no—
237C22×Dic3—21no—
238C22×Dic3—21no—
239C22×Dic3—21no—
240C22×Dic3—21no—
241C22×Dic3—21no—
242C22×Dic3—21no—
243C22×Dic3—22no—
244C22×Dic3—22no—
245C22×Dic3—22no—
246C22×Dic3—22no—
247C22×Dic3—22no—
248C22×Dic3—22no—
249C22×Dic3—22no—
250C22×Dic3C2×D414yes—
251C22×Dic3C2×Q812yes—
252C22×Dic3C2×Q812yes—
253C22×Dic3#4112yes—
254C22×Dic3#4112yes—
255C3×C4⋊C4—216no—
256C3×C4⋊C4—28no—
257C3×C22⋊C4—216no—
258#217—28no—
259#217—28no—
260#217—48no—
261C4⋊Dic3—28no—
262C4⋊Dic3—44no—
263Dic3⋊C4—48no—
264C4×Dic3—44no—
265C4×Dic3—44no—
266C25C22×D311yescharacteristic
267C22×Q8—22no—
268C22×Q8—22no—
269C22×Q8—22no—
270C22×Q8—22no—
271C22×Q8—22no—
272C22×Q8—22no—
273C22×Q8#6714yes—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—32no—
281C23×C4—31no—
282C23×C4—31no—
283C23×C4—31no—
284C23×C4—31no—
285C23×C4—32no—
286C23×C4#6714yes—
287C23×C4C22×D312yes—
288C23×C4C22×D312yes—
289C23×C4C22×D311yescharacteristic
290C23×C4C22×D311yescharacteristic
291C22⋊Q8—232no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—34no—
298C2×C4⋊C4—62no—
299C2×C4⋊C4—62no—
300C2×C4⋊C4—64no—
301C2×C4⋊C4—62no—
302C2×C4⋊C4—62no—
303C2×C4⋊C4—64no—
304C2×C4⋊C4—62no—
305C2×C4⋊C4—122no—
306C2×C4⋊C4#6714yes—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—34no—
311C2×C22⋊C4—62no—
312C2×C22⋊C4—62no—
313C2×C22⋊C4—62no—
314C2×C22⋊C4—62no—
315C2×C22⋊C4—62no—
316C2×C22⋊C4—64no—
317C2×C22⋊C4—64no—
318C2×C22⋊C4—122no—
319C2×C42—62no—
320C2×C42—62no—
321C2×C42—62no—
322C2×C42—62no—
323C2×C42—62no—
324C2×C42—62no—
325#95—64no—
326#95—64no—
327#95—64no—
328#95—64no—
329#95—62no—
330#95—62no—
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
385C3×Q8—416no—
386C2×C3×C4—24no—
387C2×C3×C4—24no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—24no—
391C2×C3×C4—22no—
392C2×C3×C4—24no—
393C2×C3×C4—24no—
394C2×C3×C4—24no—
395C2×C3×C4—41no—
396C2×C3×C4—41no—
397C2×C3×C4—42no—
398C2×C3×C4—42no—
399C2×C3×C4—41no—
400C2×C3×C4—42no—
401C2×C3×C4—42no—
402C2×C3×C4—41no—
403C2×C3×C4—42no—
404C2×C3×C4—42no—
405C2×C3×C4—42no—
406C2×C3×C4—42no—
407C2×C3×C4—416no—
408C2×C3×C4#12014yes—
409C2×C3×C4#12114yes—
410C2×C3×C4#12114yes—
411C2×C3×C4#12114yes—
412C2×C3×C4#12314yes—
413C2×C3×C4#12314yes—
414C2×C3×C4#12414yes—
415C2×Dic3—24no—
416C2×Dic3—22no—
417C2×Dic3—22no—
418C2×Dic3—22no—
419C2×Dic3—22no—
420C2×Dic3—22no—
421C2×Dic3—24no—
422C2×Dic3—24no—
423C2×Dic3—22no—
424C2×Dic3—22no—
425C2×Dic3—22no—
426C2×Dic3—22no—
427C2×Dic3—22no—
428C2×Dic3—22no—
429C2×Dic3—22no—
430C2×Dic3—41no—
431C2×Dic3—41no—
432C2×Dic3—41no—
433C2×Dic3—41no—
434C2×Dic3—42no—
435C2×Dic3—41no—
436C2×Dic3—41no—
437C2×Dic3—41no—
438C2×Dic3—41no—
439C2×Dic3—42no—
440C2×Dic3—42no—
441C2×Dic3—41no—
442C2×Dic3—41no—
443C2×Dic3—41no—
444C2×Dic3—41no—
445C2×Dic3—41no—
446C2×Dic3—42no—
447C2×Dic3—41no—
448C2×Dic3—41no—
449C2×Dic3—41no—
450C2×Dic3—42no—
451C2×Dic3—42no—
452C2×Dic3—42no—
453C2×Dic3—42no—
454C2×Dic3—42no—
455C2×Dic3—42no—
456C2×Dic3—42no—
457C24—21no—
458C24—21no—
459C24—21no—
460C24—21no—
461C24—21no—
462C24—21no—
463C24—21no—
464C24—21no—
465C24—21no—
466C24—21no—
467C24—21no—
468C24—21no—
469C24D3×Q812yes—
470C24#23912yes—
471C24C2×#6712yes—
472C24C23×D311yescharacteristic
473C2×Q8—28no—
474C2×Q8—28no—
475C2×Q8—28no—
476C2×Q8—44no—
477C2×Q8—44no—
478C2×Q8—44no—
479C2×Q8—44no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
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—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—28no—
499C22×C4—28no—
500C22×C4—28no—
501C22×C4—34no—
502C22×C4—32no—
503C22×C4—32no—
504C22×C4—32no—
505C22×C4—32no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—44no—
510C22×C4—61no—
511C22×C4—61no—
512C22×C4—61no—
513C22×C4—61no—
514C22×C4—62no—
515C22×C4—61no—
516C22×C4—61no—
517C22×C4—62no—
518C22×C4—61no—
519C22×C4—61no—
520C22×C4—61no—
521C22×C4—61no—
522C22×C4—62no—
523C22×C4—61no—
524C22×C4—61no—
525C22×C4—62no—
526C22×C4—61no—
527C22×C4—62no—
528C22×C4—61no—
529C22×C4—61no—
530C22×C4—61no—
531C22×C4—61no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4—61no—
536C22×C4—61no—
537C22×C4—61no—
538C22×C4—62no—
539C22×C4—61no—
540C22×C4—62no—
541C22×C4—62no—
542C22×C4—62no—
543C22×C4—62no—
544C22×C4—62no—
545C22×C4—62no—
546C22×C4—62no—
547C22×C4D3×D412yes—
548C22×C4#23712yes—
549C22×C4#23712yes—
550C22×C4#23712yes—
551C22×C4C2×#6714yes—
552C22×C4C2×#6712yes—
553C22×C4C2×#6714yes—
554C22×C4C2×#6712yes—
555C22×C4C2×#6712yes—
556C22×C4C2×#6712yes—
557C4⋊C4—216no—
558C4⋊C4—28no—
559C4⋊C4—68no—
560C4⋊C4—128no—
561C4⋊C4—124no—
562C22⋊C4—216no—
563C22⋊C4—68no—
564C22⋊C4—68no—
565C22⋊C4—128no—
566C42—124no—
567C42—124no—
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—44no—
620C3×C4—44no—
621C3×C4#39418yes—
622Dic3—42no—
623Dic3—42no—
624Dic3—42no—
625Dic3—42no—
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#94614yes—
663C23C2×D3×D411yescharacteristic
664C23C2×#23711yescharacteristic
665C23C2×#23711yescharacteristic
666C23C2×#23711yescharacteristic
667C23C2×D3×Q811yescharacteristic
668C23C2×#23911yescharacteristic
669C23#100711yescharacteristic
670C23#100711yescharacteristic
671C23D3×#4111yescharacteristic
672C23D3×#4111yescharacteristic
673C23#100911yescharacteristic
674C23#101011yescharacteristic
675C23C22×#6711yescharacteristic
676C23C22×#6711yescharacteristic
677C23C22×#6711yescharacteristic
678Q8—416no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—416no—
701C2×C4—62no—
702C2×C4—62no—
703C2×C4—62no—
704C2×C4—62no—
705C2×C4—64no—
706C2×C4—62no—
707C2×C4—62no—
708C2×C4—62no—
709C2×C4—62no—
710C2×C4—62no—
711C2×C4—62no—
712C2×C4—62no—
713C2×C4—62no—
714C2×C4—64no—
715C2×C4—64no—
716C2×C4—121no—
717C2×C4—121no—
718C2×C4—122no—
719C2×C4—121no—
720C2×C4—121no—
721C2×C4—121no—
722C2×C4—121no—
723C2×C4—122no—
724C2×C4—121no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—122no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—121no—
731C2×C4—121no—
732C2×C4—121no—
733C2×C4—122no—
734C2×C4—121no—
735C2×C4—121no—
736C2×C4—122no—
737C2×C4—122no—
738C2×C4—122no—
739C2×C4—122no—
740C2×C4—122no—
741C2×C4—122no—
742C2×C4—122no—
743C2×C4#93514yes—
744C2×C4#93514yes—
745C2×C4#93614yes—
746C2×C4#93814yes—
747C2×C4#93914yes—
748C2×C4#93914yes—
749C2×C4#95314yes—
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#562211yescharacteristic
782C22#562211yescharacteristic
783C22#562411yescharacteristic
784C22#562411yescharacteristic
785C22#562511yescharacteristic
786C22#562511yescharacteristic
787C22#563011yescharacteristic
788C22#563111yescharacteristic
789C22#563211yescharacteristic
790C22#563311yescharacteristic
791C22#563511yescharacteristic
792C22#563911yescharacteristic
793C22#564111yescharacteristic
794C22#564211yescharacteristic
795C22#564311yescharacteristic
796C22#564311yescharacteristic
797C22C2×#93511yescharacteristic
798C22C2×#93511yescharacteristic
799C22C2×#93611yescharacteristic
800C22C2×#93811yescharacteristic
801C22C2×#93911yescharacteristic
802C22C2×#93911yescharacteristic
803C22C2×#94611yescharacteristic
804C22Q8×#6711yescharacteristic
805C22Q8×#6711yescharacteristic
806C22#581611yescharacteristic
807C22#581711yescharacteristic
808C22#581711yescharacteristic
809C22#582411yescharacteristic
810C22#582811yescharacteristic
811C22#582911yescharacteristic
812C22#583111yescharacteristic
813C22#583311yescharacteristic
814C22#583411yescharacteristic
815C22C2×#95311yescharacteristic
816C4—42no—
817C4—44no—
818C4—44no—
819C4—124no—
820C4—122no—
821C4—122no—
822C4—122no—
823C4—122no—
824C4—242no—
825C4#522218yes—
826C3#1517911yescharacteristic, complemented, Sylow
827C2—44no—
828C2#8275311yescharacteristic
829C2#8275411yescharacteristic
830C2#8275511yescharacteristic
831C2#8275611yescharacteristic
832C2#8275711yescharacteristic
833C2#8275811yescharacteristic
834C2#8277211yescharacteristic
835C2#8277311yescharacteristic
836C2#8278711yescharacteristic
837C2#8281011yescharacteristic
838C2#8281411yescharacteristic
839C2#8281511yescharacteristic
840C2C2×#522211yescharacteristic
841C2#8406811yescharacteristic
842C2#8409711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC22×C3×C22⋊Q8C2
prime radicalC25×C3C23
hypercenterC22×C22⋊Q8D3
hypocenterC3#15179
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#5229C2semidirect
3. C2×#5229C2semidirect
6. C2×#4972C2semidirect
7. #71567C2semidirect
8. #71566C2semidirect
9. #71563C2semidirect
98. C2×#217Q8semidirect
826. C3#15179semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C22⋊Q82
C2×#52292
C2×#52122
C2×C4×#2172
C2×#49722
#715672
#715662
#715632
#715492
#715472
#151793