Finite Group Databasebeta

← #10726637

Subgroups — #10726637

Order 768.

2558 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
1C22×C3×C22⋊Q8C211yesmaximal, characteristic, complemented
2C22×C4×#67C211yesmaximal, characteristic
3C2×#5231C211yesmaximal, characteristic, complemented
4C2×#5230C211yesmaximal, characteristic, complemented
5C2×#4989C212yesmaximal, complemented
6#72127C211yesmaximal, characteristic, complemented
7#71570C211yesmaximal, characteristic, complemented
8#71566C211yesmaximal, characteristic, complemented
9#71564C212yesmaximal, complemented
10#71550C212yesmaximal
11#71547C212yesmaximal, complemented
12#14723—31nomaximal, Sylow
13C23×C3×Q8C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C23×#67C2211yescharacteristic
16C23×C4×D3C2211yescharacteristic
17C2×C3×C22⋊Q8—24no—
18C2×C3×C22⋊Q8—28no—
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C4⋊C4C2212yes—
21C22×C3×C22⋊C4C2212yes—
22C22×#217C2211yescharacteristic
23C22×#217C2212yes—
24C2×C4×#67—24no—
25C2×C4×#67—24no—
26C2×C4×#67—24no—
27C22×(C2×D3)⋊C4C2212yes—
28C22×(C2×D3)⋊C4C2212yes—
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×Dic3⋊C4C2212yes—
31C22×Dic3⋊C4C2211yescharacteristic
32C22×C4×Dic3C2211yescharacteristic
33#5231—24no—
34#5230—24no—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2211yescharacteristic
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2211yescharacteristic
41C2×C3⋊#95C2212yes—
42C2×C3⋊#95C2212yes—
43#4989—28no—
44C22×C22⋊Q8D311yescharacteristic, complemented
45C22×C4×D4—31no—
46C2×#395—31no—
47C2×#393—31no—
48C2×#385—32no—
49#1441—31no—
50#1439—31no—
51#1439—32no—
52#1438—32no—
53#1436—32no—
54C22⋊#95—31no—
55C25×C3C2311yescharacteristic
56C24×D3C2311yescharacteristic
57C22×C3×Q8—24no—
58C22×C3×Q8—22no—
59C22×C3×Q8—22no—
60C22×C3×Q8—22no—
61C22×C3×Q8—42no—
62C23×C3×C4—22no—
63C23×C3×C4—22no—
64C23×C3×C4—24no—
65C23×C3×C4—42no—
66C23×C3×C4D414yes—
67C23×C3×C4C2312yes—
68C23×C3×C4C2312yes—
69C23×C3×C4C2311yescharacteristic
70C23×C3×C4C2311yescharacteristic
71C22×#67—22no—
72C22×#67—22no—
73C22×#67—22no—
74C22×#67—22no—
75C22×#67—22no—
76C22×#67—22no—
77C22×#67Q814yescomplemented
78C23×Dic3C2312yes—
79C23×Dic3C2311yescharacteristic
80C23×Dic3C2311yescharacteristic
81C23×Dic3C2312yes—
82C23×Dic3C2311yescharacteristic
83C22×C4×D3—22no—
84C22×C4×D3—22no—
85C22×C4×D3—22no—
86C22×C4×D3—24no—
87C22×C4×D3—42no—
88C3×C22⋊Q8—232no—
89C2×C3×C4⋊C4—24no—
90C2×C3×C4⋊C4—22no—
91C2×C3×C4⋊C4—24no—
92C2×C3×C4⋊C4—24no—
93C2×C3×C4⋊C4D418yescomplemented
94C2×C3×C22⋊C4—24no—
95C2×C3×C22⋊C4—24no—
96C2×C3×C22⋊C4—24no—
97C2×#217—22no—
98C2×#217—22no—
99C2×#217—22no—
100C2×#217—24no—
101C2×#217—24no—
102C2×#217—42no—
103C4×#67—232no—
104C2×(C2×D3)⋊C4—24no—
105C2×(C2×D3)⋊C4—24no—
106C2×(C2×D3)⋊C4—22no—
107C2×(C2×D3)⋊C4—22no—
108C2×(C2×D3)⋊C4—24no—
109C2×(C2×D3)⋊C4—24no—
110C2×(C2×D3)⋊C4—24no—
111C2×(C2×D3)⋊C4—42no—
112C2×(C2×D3)⋊C4D414yes—
113C2×Dic3⋊C4—22no—
114C2×Dic3⋊C4—22no—
115C2×Dic3⋊C4—24no—
116C2×Dic3⋊C4—24no—
117C2×Dic3⋊C4—42no—
118C2×Dic3⋊C4D414yes—
119C2×C4×Dic3—22no—
120C2×C4×Dic3—22no—
121C2×C4×Dic3—22no—
122C3⋊#95—22no—
123C3⋊#95—22no—
124C3⋊#95—24no—
125C3⋊#95—24no—
126C3⋊#95—24no—
127C3⋊#95—24no—
128C3⋊#95—24no—
129C3⋊#95—24no—
130C23×Q8C2×D311yescharacteristic
131C23×D4—31no—
132C24×C4—31no—
133C24×C4C2×D311yescharacteristic
134C2×C22⋊Q8—24no—
135C2×C22⋊Q8—28no—
136C2×C4×D4—64no—
137C2×C4×D4—64no—
138C2×C4×D4—64no—
139C22×C4⋊C4—31no—
140C22×C4⋊C4—32no—
141C22×C4⋊C4C2×D311yescharacteristic
142C22×C4⋊C4C2×D312yes—
143C22×C22⋊C4—31no—
144C22×C22⋊C4—31no—
145C22×C22⋊C4—32no—
146C22×C22⋊C4—32no—
147C22×C22⋊C4—32no—
148C22×C22⋊C4C2×D312yes—
149C22×C42—31no—
150#395—64no—
151#393—64no—
152#385—68no—
153C2×#95—31no—
154C2×#95—32no—
155C2×#95—31no—
156C2×#95—32no—
157C2×#95—32no—
158C2×#95—32no—
159C2×#95—32no—
160C2×#95—32no—
161C24×C3—21no—
162C24×C3—21no—
163C24×C3—22no—
164C24×C3—22no—
165C24×C3—21no—
166C24×C3—21no—
167C24×C3—22no—
168C24×C3—22no—
169C24×C3C2×D412yes—
170C24×C3C2×Q812yes—
171C24×C3#4112yes—
172C24×C3C2411yescharacteristic
173C23×D3—22no—
174C23×D3—21no—
175C23×D3—21no—
176C23×D3—22no—
177C23×D3—21no—
178C23×D3—21no—
179C23×D3—22no—
180C23×D3—22no—
181C23×D3C2×D412yes—
182C23×D3C2×Q812yes—
183C23×D3#4112yes—
184C2×C3×Q8—28no—
185C2×C3×Q8—48no—
186C2×C3×Q8—48no—
187C2×C3×Q8—44no—
188C2×C3×Q8—44no—
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—22no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—22no—
205C22×C3×C4—22no—
206C22×C3×C4—28no—
207C22×C3×C4—28no—
208C22×C3×C4—44no—
209C22×C3×C4—48no—
210C22×C3×C4—48no—
211C22×C3×C4C2×D412yes—
212C22×C3×C4C2×D412yes—
213C22×C3×C4C2×D414yes—
214C22×C3×C4C2×D414yes—
215C22×C3×C4C2×D414yes—
216C22×C3×C4C2×D412yes—
217C22×C3×C4C2×D412yes—
218C2×#67—28no—
219C2×#67—28no—
220C2×#67—28no—
221C2×#67—28no—
222C2×#67—28no—
223C2×#67—28no—
224C2×#67—28no—
225C22×Dic3—21no—
226C22×Dic3—21no—
227C22×Dic3—21no—
228C22×Dic3—21no—
229C22×Dic3—22no—
230C22×Dic3—22no—
231C22×Dic3—22no—
232C22×Dic3—21no—
233C22×Dic3—21no—
234C22×Dic3—21no—
235C22×Dic3—21no—
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×Dic3—22no—
246C22×Dic3—22no—
247C22×Dic3—22no—
248C22×Dic3—22no—
249C22×Dic3—22no—
250C22×Dic3C2×D412yes—
251C22×Dic3C2×D412yes—
252C22×Dic3C2×D412yes—
253C22×Dic3C2×Q812yes—
254C22×Dic3#4114yes—
255C22×Dic3#4112yes—
256C2×C4×D3—28no—
257C2×C4×D3—48no—
258C2×C4×D3—48no—
259C2×C4×D3—44no—
260C2×C4×D3—44no—
261C3×C4⋊C4—28no—
262C3×C4⋊C4—216no—
263C3×C22⋊C4—216no—
264#217—28no—
265#217—48no—
266(C2×D3)⋊C4—216no—
267(C2×D3)⋊C4—28no—
268(C2×D3)⋊C4—48no—
269Dic3⋊C4—28no—
270Dic3⋊C4—48no—
271C4×Dic3—28no—
272C25—31no—
273C25C22×D311yescharacteristic
274C22×Q8—22no—
275C22×Q8—22no—
276C22×Q8—24no—
277C22×Q8—22no—
278C22×Q8—42no—
279C22×D4—34no—
280C22×D4—62no—
281C22×D4—62no—
282C22×D4—62no—
283C22×D4—62no—
284C22×D4—62no—
285C22×D4—62no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—24no—
289C23×C4—31no—
290C23×C4—32no—
291C23×C4—31no—
292C23×C4—31no—
293C23×C4—32no—
294C23×C4—42no—
295C23×C4—62no—
296C23×C4—62no—
297C23×C4—62no—
298C23×C4—64no—
299C23×C4—122no—
300C23×C4#6714yes—
301C23×C4C22×D312yes—
302C23×C4C22×D312yes—
303C23×C4C22×D311yescharacteristic
304C23×C4C22×D311yescharacteristic
305C22⋊Q8—232no—
306C4×D4—632no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—34no—
312C2×C4⋊C4—62no—
313C2×C4⋊C4—62no—
314C2×C4⋊C4—64no—
315C2×C4⋊C4—64no—
316C2×C4⋊C4—122no—
317C2×C4⋊C4#6718yescomplemented
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—34no—
322C2×C22⋊C4—64no—
323C2×C22⋊C4—64no—
324C2×C22⋊C4—62no—
325C2×C22⋊C4—62no—
326C2×C22⋊C4—62no—
327C2×C22⋊C4—62no—
328C2×C22⋊C4—62no—
329C2×C22⋊C4—64no—
330C2×C22⋊C4—64no—
331C2×C22⋊C4—64no—
332C2×C22⋊C4—64no—
333C2×C22⋊C4—64no—
334C2×C22⋊C4—122no—
335C2×C22⋊C4—122no—
336C2×C42—62no—
337C2×C42—62no—
338C2×C42—62no—
339#95—64no—
340#95—64no—
341#95—64no—
342#95—64no—
343#95—62no—
344#95—62no—
345#95—64no—
346#95—64no—
347C23×C3—22no—
348C23×C3—22no—
349C23×C3—22no—
350C23×C3—22no—
351C23×C3—22no—
352C23×C3—22no—
353C23×C3—22no—
354C23×C3—22no—
355C23×C3—22no—
356C23×C3—22no—
357C23×C3—24no—
358C23×C3—24no—
359C23×C3—24no—
360C23×C3—24no—
361C23×C3—42no—
362C23×C3—42no—
363C23×C3—42no—
364C23×C3—42no—
365C23×C3—42no—
366C23×C3—42no—
367C23×C3—42no—
368C23×C3—42no—
369C23×C3C22⋊Q814yes—
370C23×C3C22×D411yescharacteristic
371C23×C3C22×D411yescharacteristic
372C23×C3C22×D411yescharacteristic
373C23×C3C22×D412yes—
374C23×C3C22×Q811yescharacteristic
375C23×C3C2×#4111yescharacteristic
376C23×C3C2×#4111yescharacteristic
377C23×C3C2×#4111yescharacteristic
378C23×C3C2×#4112yes—
379C23×C3H(5,𝔽2)12yes—
380C23×C32−1+412yes—
381C22×D3—22no—
382C22×D3—22no—
383C22×D3—22no—
384C22×D3—24no—
385C22×D3—22no—
386C22×D3—22no—
387C22×D3—22no—
388C22×D3—24no—
389C22×D3—24no—
390C22×D3—24no—
391C22×D3—24no—
392C22×D3—24no—
393C22×D3—41no—
394C22×D3—41no—
395C22×D3—42no—
396C22×D3—41no—
397C22×D3—41no—
398C22×D3—42no—
399C22×D3—42no—
400C22×D3—42no—
401C22×D3—42no—
402C22×D3—42no—
403C22×D3C22⋊Q814yescomplemented
404C3×Q8—416no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—24no—
410C2×C3×C4—24no—
411C2×C3×C4—24no—
412C2×C3×C4—24no—
413C2×C3×C4—24no—
414C2×C3×C4—24no—
415C2×C3×C4—24no—
416C2×C3×C4—24no—
417C2×C3×C4—24no—
418C2×C3×C4—24no—
419C2×C3×C4—416no—
420C2×C3×C4—42no—
421C2×C3×C4—42no—
422C2×C3×C4—42no—
423C2×C3×C4—42no—
424C2×C3×C4—42no—
425C2×C3×C4—42no—
426C2×C3×C4—42no—
427C2×C3×C4—42no—
428C2×C3×C4#12014yes—
429C2×C3×C4#12014yes—
430#67—232no—
431C2×Dic3—22no—
432C2×Dic3—22no—
433C2×Dic3—22no—
434C2×Dic3—22no—
435C2×Dic3—22no—
436C2×Dic3—22no—
437C2×Dic3—22no—
438C2×Dic3—22no—
439C2×Dic3—24no—
440C2×Dic3—24no—
441C2×Dic3—24no—
442C2×Dic3—24no—
443C2×Dic3—24no—
444C2×Dic3—41no—
445C2×Dic3—42no—
446C2×Dic3—41no—
447C2×Dic3—41no—
448C2×Dic3—41no—
449C2×Dic3—42no—
450C2×Dic3—42no—
451C2×Dic3—42no—
452C2×Dic3—42no—
453C2×Dic3—42no—
454C2×Dic3—42no—
455C2×Dic3—42no—
456C2×Dic3—42no—
457C2×Dic3—42no—
458C2×Dic3—42no—
459C2×Dic3—42no—
460C2×Dic3—42no—
461C2×Dic3C22⋊Q814yescomplemented
462C4×D3—416no—
463C24—21no—
464C24—21no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—21no—
469C24—21no—
470C24—22no—
471C24—32no—
472C24—32no—
473C24—32no—
474C24—61no—
475C24—62no—
476C24—61no—
477C24—62no—
478C24—62no—
479C24—61no—
480C24—62no—
481C24—61no—
482C24D3×Q812yes—
483C24#23912yes—
484C24C2×#6712yes—
485C24C23×D311yescharacteristic
486C2×Q8—28no—
487C2×Q8—48no—
488C2×Q8—48no—
489C2×Q8—44no—
490C2×Q8—44no—
491C2×D4—68no—
492C2×D4—68no—
493C2×D4—68no—
494C2×D4—68no—
495C2×D4—68no—
496C2×D4—68no—
497C2×D4—68no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—28no—
516C22×C4—28no—
517C22×C4—32no—
518C22×C4—32no—
519C22×C4—32no—
520C22×C4—32no—
521C22×C4—32no—
522C22×C4—34no—
523C22×C4—44no—
524C22×C4—48no—
525C22×C4—48no—
526C22×C4—68no—
527C22×C4—61no—
528C22×C4—61no—
529C22×C4—61no—
530C22×C4—61no—
531C22×C4—62no—
532C22×C4—61no—
533C22×C4—61no—
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—61no—
544C22×C4—61no—
545C22×C4—62no—
546C22×C4—62no—
547C22×C4—62no—
548C22×C4—62no—
549C22×C4—62no—
550C22×C4—62no—
551C22×C4—62no—
552C22×C4—128no—
553C22×C4—128no—
554C22×C4—124no—
555C22×C4—124no—
556C22×C4D3×D412yes—
557C22×C4D3×D412yes—
558C22×C4C2×#6714yes—
559C22×C4C2×#6714yes—
560C22×C4C2×#6712yes—
561C22×C4C2×#6714yes—
562C22×C4C2×#6712yes—
563C4⋊C4—28no—
564C4⋊C4—216no—
565C4⋊C4—68no—
566C4⋊C4—128no—
567C22⋊C4—216no—
568C22⋊C4—616no—
569C22⋊C4—68no—
570C22⋊C4—68no—
571C22⋊C4—128no—
572C22⋊C4—128no—
573C42—68no—
574C22×C3—24no—
575C22×C3—24no—
576C22×C3—24no—
577C22×C3—42no—
578C22×C3—42no—
579C22×C3—42no—
580C22×C3—42no—
581C22×C3—44no—
582C22×C3—44no—
583C22×C3—44no—
584C22×C3—44no—
585C22×C3C2×#12011yescharacteristic
586C22×C3C2×#12011yescharacteristic
587C22×C3C2×C22⋊Q811yescharacteristic
588C22×C3C2×C22⋊Q811yescharacteristic
589C22×C3C2×C22⋊Q811yescharacteristic
590C22×C3#52511yescharacteristic
591C22×C3#52512yes—
592C22×C3#52511yescharacteristic
593C22×C3#52511yescharacteristic
594C22×C3#53211yescharacteristic
595C22×C3#53212yes—
596C22×C3#53411yescharacteristic
597C22×C3#53611yescharacteristic
598C22×C3#53912yes—
599C22×C3#54212yes—
600C22×C3D4212yes—
601C22×C3D4212yes—
602C22×C3#54712yes—
603C22×C3#54812yes—
604C22×C3#54812yes—
605C22×C3D4×Q812yes—
606C22×C3#55112yes—
607C22×C3#55412yes—
608C2×D3—24no—
609C2×D3—28no—
610C2×D3—42no—
611C2×D3—42no—
612C2×D3—42no—
613C2×D3—42no—
614C2×D3—42no—
615C2×D3—42no—
616C2×D3—44no—
617C2×D3—44no—
618C2×D3—44no—
619C3×C4—24no—
620C3×C4—24no—
621C3×C4—44no—
622C3×C4—44no—
623Dic3—24no—
624Dic3—42no—
625Dic3—42no—
626Dic3—44no—
627Dic3—82no—
628C23—24no—
629C23—24no—
630C23—22no—
631C23—22no—
632C23—24no—
633C23—22no—
634C23—24no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—34no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—64no—
652C23—64no—
653C23—62no—
654C23—64no—
655C23—62no—
656C23—64no—
657C23—64no—
658C23—62no—
659C23—62no—
660C23—62no—
661C23—62no—
662C23—64no—
663C23—122no—
664C23—122no—
665C23—122no—
666C23—122no—
667C23—121no—
668C23—121no—
669C23—122no—
670C23—121no—
671C23—122no—
672C23—121no—
673C23#94614yes—
674C23C2×D3×D411yescharacteristic
675C23C2×D3×D411yescharacteristic
676C23#100412yes—
677C23C2×D3×Q811yescharacteristic
678C23C2×#23911yescharacteristic
679C23#100712yes—
680C23D3×#4112yes—
681C23D3×#4111yescharacteristic
682C23D3×#4111yescharacteristic
683C23C22×#6711yescharacteristic
684C23C22×#6712yes—
685Q8—416no—
686D4—632no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—34no—
702C2×C4—416no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—62no—
712C2×C4—62no—
713C2×C4—62no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—64no—
718C2×C4—64no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—64no—
722C2×C4—64no—
723C2×C4—64no—
724C2×C4—1216no—
725C2×C4—122no—
726C2×C4—122no—
727C2×C4—122no—
728C2×C4—122no—
729C2×C4—121no—
730C2×C4—121no—
731C2×C4—122no—
732C2×C4—121no—
733C2×C4—121no—
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#93714yes—
743C2×C4#95314yes—
744C2×C3—44no—
745C2×C3#238811yescharacteristic
746C2×C3#240311yescharacteristic
747C2×C3#240911yescharacteristic
748C2×C3#243211yescharacteristic
749C2×C3#244912yes—
750C2×C3#245212yes—
751C2×C3#246112yes—
752C2×C3#246312yes—
753C2×C3#256411yescharacteristic
754C2×C3#263811yescharacteristic
755C2×C3#284811yescharacteristic
756D3—44no—
757C22—24no—
758C22—24no—
759C22—24no—
760C22—42no—
761C22—44no—
762C22—44no—
763C22—42no—
764C22—42no—
765C22—44no—
766C22—44no—
767C22—42no—
768C22—68no—
769C22—64no—
770C22—122no—
771C22—124no—
772C22—124no—
773C22—122no—
774C22—122no—
775C22—122no—
776C22—122no—
777C22—124no—
778C22—122no—
779C22D3×C22⋊Q811yescharacteristic
780C22D3×C22⋊Q811yescharacteristic
781C22#562711yescharacteristic
782C22#562711yescharacteristic
783C22#563112yes—
784C22#563312yes—
785C22#563612yes—
786C22#563712yes—
787C22#563812yes—
788C22#564012yes—
789C22C2×#93711yescharacteristic
790C22D4×#6712yes—
791C22D4×#6712yes—
792C22#580411yescharacteristic
793C22C2×#94611yescharacteristic
794C22Q8×#6712yes—
795C22#581611yescharacteristic
796C22#581712yes—
797C22#582812yes—
798C22#582811yescharacteristic
799C22#583211yescharacteristic
800C22#583212yes—
801C22C2×#95311yescharacteristic
802C4—24no—
803C4—24no—
804C4—44no—
805C4—44no—
806C4—64no—
807C4—122no—
808C4—122no—
809C4—124no—
810C4—242no—
811C3#1472311yescharacteristic, complemented, Sylow
812C2—44no—
813C2—124no—
814C2#8275911yescharacteristic
815C2#8276612yes—
816C2#8276712yes—
817C2#8278411yescharacteristic
818C2#8281712yes—
819C2#8281812yes—
820C2#8282311yescharacteristic
821C2#8283411yescharacteristic
822C2#8405211yescharacteristic
823C2#8406811yescharacteristic
824C2#8409511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC22×C3×C22⋊Q8C2
prime radicalC23×#67C22
hypercenterC22×C22⋊Q8D3
hypocenterC3#14723
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×C22⋊Q8C2semidirect
3. C2×#5231C2semidirect
4. C2×#5230C2semidirect
5. C2×#4989C2semidirect
6. #72127C2semidirect
7. #71570C2semidirect
8. #71566C2semidirect
9. #71564C2semidirect
11. #71547C2semidirect
44. C22×C22⋊Q8D3semidirect
77. C22×#67Q8semidirect
93. C2×C3×C4⋊C4D4semidirect
317. C2×C4⋊C4#67semidirect
403. C22×D3C22⋊Q8semidirect
461. C2×Dic3C22⋊Q8semidirect
811. C3#14723semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C22⋊Q82
C22×C4×#672
C2×#52312
C2×#52302
C2×#49892
#721272
#715702
#715662
#715642
#715502
#715472
#147233