Finite Group Databasebeta

← #10726577

Subgroups — #10726577

Order 768.

3654 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#217C211yesmaximal, characteristic
2C22×#878C211yesmaximal, characteristic, complemented
3C2×C3×#379C211yesmaximal, characteristic
4C2×#5247C211yesmaximal, characteristic
5C2×#4947C212yesmaximal, complemented
6#71547C212yesmaximal, complemented
7#71547C212yesmaximal, complemented
8#71546C212yesmaximal, complemented
9#71544C211yesmaximal, characteristic, complemented
10#71544C211yesmaximal, characteristic, complemented
11#71544C211yesmaximal, characteristic, complemented
12#14717—31nomaximal, Sylow
13C26×C3C2211yescharacteristic
14C24×Dic3C2211yescharacteristic
15C24×Dic3C2211yescharacteristic
16C23×Dic6C2211yescharacteristic, complemented
17C22×C3×C22⋊C4C2211yescharacteristic
18C22×C3×C22⋊C4C2212yes—
19C22×C3×C22⋊C4C2212yes—
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×#217—24no—
22C22×#217—28no—
23C22×#217C2212yes—
24C22×#217C2211yescharacteristic
25C22×#217C2212yes—
26C22×#217C2212yes—
27C22×#217C2212yes—
28C22×#217C2211yescharacteristic
29C22×C4⋊Dic3C2211yescharacteristic, complemented
30C22×Dic3⋊C4C2211yescharacteristic, complemented
31C22×Dic3⋊C4C2211yescharacteristic, complemented
32C2×#878—24no—
33C2×#878—24no—
34C2×#878—24no—
35C3×#379—24no—
36#5247—24no—
37C2×C3⋊#95C2212yescomplemented
38C2×C3⋊#95C2212yescomplemented
39C2×C3⋊#95C2212yescomplemented
40C2×C3⋊#95C2212yescomplemented
41C2×C3⋊#95C2212yescomplemented
42C2×C3⋊#95C2212yescomplemented
43#4947—28no—
44C22×C22⋊Q8—31no—
45C23×C22⋊C4—31no—
46C2×#393—32no—
47C2×#379—31no—
48C2×#379D311yescharacteristic
49#1439—32no—
50#1439—32no—
51#1439—32no—
52C22⋊#95—31no—
53C22⋊#95—31no—
54C22⋊#95—31no—
55C25×C3—24no—
56C25×C3—22no—
57C25×C3—24no—
58C25×C3—22no—
59C25×C3—22no—
60C25×C3—22no—
61C25×C3—22no—
62C25×C3—22no—
63C25×C3—42no—
64C25×C3—42no—
65C25×C3Q814yescomplemented
66C25×C3C2312yes—
67C25×C3C2311yescharacteristic
68C23×C3×C4C2312yes—
69C23×C3×C4C2311yescharacteristic
70C23×C3×C4C2311yescharacteristic
71C23×Dic3—22no—
72C23×Dic3—22no—
73C23×Dic3—22no—
74C23×Dic3—24no—
75C23×Dic3—24no—
76C23×Dic3—22no—
77C23×Dic3—22no—
78C23×Dic3—42no—
79C23×Dic3—42no—
80C23×Dic3D414yes—
81C23×Dic3C2312yes—
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2312yes—
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C22×Dic6—22no—
88C22×Dic6—22no—
89C22×Dic6—22no—
90C22×Dic6—24no—
91C22×Dic6—42no—
92C2×C3×C22⋊C4—22no—
93C2×C3×C22⋊C4—22no—
94C2×C3×C22⋊C4—24no—
95C2×C3×C22⋊C4—22no—
96C2×C3×C22⋊C4—24no—
97C2×C3×C22⋊C4—22no—
98C2×C3×C22⋊C4—22no—
99C2×C3×C22⋊C4—24no—
100C2×C3×C22⋊C4—24no—
101C2×C3×C22⋊C4—42no—
102C2×C3×C22⋊C4—42no—
103C2×C3×C22⋊C4D414yes—
104C2×#217—232no—
105C2×#217—22no—
106C2×#217—22no—
107C2×#217—24no—
108C2×#217—24no—
109C2×#217—24no—
110C2×#217—24no—
111C2×#217—24no—
112C2×#217—24no—
113C2×#217—22no—
114C2×#217—22no—
115C2×#217—24no—
116C2×#217—22no—
117C2×#217—24no—
118C2×#217—24no—
119C2×#217—42no—
120C2×#217—42no—
121C2×#217D418yes—
122C2×#217D414yes—
123C2×C4⋊Dic3—22no—
124C2×C4⋊Dic3—22no—
125C2×C4⋊Dic3—22no—
126C2×Dic3⋊C4—22no—
127C2×Dic3⋊C4—22no—
128C2×Dic3⋊C4—22no—
129C2×Dic3⋊C4—22no—
130C2×Dic3⋊C4—22no—
131C2×Dic3⋊C4—22no—
132#878—232no—
133C3⋊#95—24no—
134C3⋊#95—24no—
135C3⋊#95—24no—
136C3⋊#95—42no—
137C3⋊#95—42no—
138C3⋊#95—42no—
139C26C2×D311yescharacteristic
140C23×Q8—31no—
141C24×C4—31no—
142C24×C4—31no—
143C2×C22⋊Q8—64no—
144C2×C22⋊Q8—64no—
145C2×C22⋊Q8—64no—
146C22×C4⋊C4—31no—
147C22×C4⋊C4—31no—
148C22×C4⋊C4—31no—
149C22×C22⋊C4—32no—
150C22×C22⋊C4—31no—
151C22×C22⋊C4—32no—
152C22×C22⋊C4—31no—
153C22×C22⋊C4—32no—
154C22×C22⋊C4—32no—
155C22×C22⋊C4—68no—
156C22×C22⋊C4—64no—
157C22×C22⋊C4C2×D311yescharacteristic
158C22×C22⋊C4C2×D312yes—
159C22×C22⋊C4C2×D312yes—
160C22×C22⋊C4C2×D311yescharacteristic
161#393—68no—
162#379—24no—
163#379—64no—
164C2×#95—32no—
165C2×#95—32no—
166C2×#95—32no—
167C2×#95—32no—
168C2×#95—32no—
169C2×#95—32no—
170C24×C3—22no—
171C24×C3—22no—
172C24×C3—22no—
173C24×C3—22no—
174C24×C3—28no—
175C24×C3—216no—
176C24×C3—28no—
177C24×C3—28no—
178C24×C3—216no—
179C24×C3—22no—
180C24×C3—22no—
181C24×C3—22no—
182C24×C3—22no—
183C24×C3—22no—
184C24×C3—22no—
185C24×C3—22no—
186C24×C3—22no—
187C24×C3—22no—
188C24×C3—22no—
189C24×C3—22no—
190C24×C3—22no—
191C24×C3—28no—
192C24×C3—28no—
193C24×C3—48no—
194C24×C3—48no—
195C24×C3—48no—
196C24×C3—48no—
197C24×C3—48no—
198C24×C3—48no—
199C24×C3—48no—
200C24×C3—48no—
201C24×C3—48no—
202C24×C3—44no—
203C24×C3—44no—
204C24×C3—48no—
205C24×C3—44no—
206C24×C3—44no—
207C24×C3—44no—
208C24×C3—44no—
209C24×C3C2×D414yes—
210C24×C3C2×D412yes—
211C24×C3C2×D412yes—
212C24×C3C2×D412yes—
213C24×C3C2×Q814yes—
214C24×C3C2×Q812yes—
215C24×C3#4112yes—
216C24×C3#4114yes—
217C24×C3#4112yes—
218C24×C3#4112yes—
219C24×C3C2411yescharacteristic
220C22×C3×C4—22no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—22no—
226C22×C3×C4—22no—
227C22×C3×C4—22no—
228C22×C3×C4—22no—
229C22×C3×C4—22no—
230C22×C3×C4—22no—
231C22×C3×C4—22no—
232C22×C3×C4—22no—
233C22×C3×C4—22no—
234C22×C3×C4—22no—
235C22×C3×C4C2×D412yes—
236C22×C3×C4C2×D412yes—
237C22×Dic3—21no—
238C22×Dic3—21no—
239C22×Dic3—22no—
240C22×Dic3—28no—
241C22×Dic3—28no—
242C22×Dic3—22no—
243C22×Dic3—21no—
244C22×Dic3—21no—
245C22×Dic3—21no—
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3—21no—
249C22×Dic3—22no—
250C22×Dic3—22no—
251C22×Dic3—22no—
252C22×Dic3—22no—
253C22×Dic3—22no—
254C22×Dic3—22no—
255C22×Dic3—22no—
256C22×Dic3—22no—
257C22×Dic3—22no—
258C22×Dic3—22no—
259C22×Dic3—22no—
260C22×Dic3—28no—
261C22×Dic3—22no—
262C22×Dic3—22no—
263C22×Dic3—22no—
264C22×Dic3—22no—
265C22×Dic3—22no—
266C22×Dic3—22no—
267C22×Dic3—22no—
268C22×Dic3—44no—
269C22×Dic3—48no—
270C22×Dic3—48no—
271C22×Dic3—48no—
272C22×Dic3—48no—
273C22×Dic3—44no—
274C22×Dic3—44no—
275C22×Dic3C2×D414yes—
276C22×Dic3C2×D412yes—
277C22×Dic3C2×D412yes—
278C22×Dic3C2×D412yes—
279C22×Dic3C2×D414yes—
280C22×Dic3C2×D412yes—
281C2×Dic6—28no—
282C2×Dic6—48no—
283C2×Dic6—48no—
284C2×Dic6—44no—
285C2×Dic6—44no—
286C3×C22⋊C4—28no—
287C3×C22⋊C4—48no—
288C3×C22⋊C4—48no—
289C3×C22⋊C4—44no—
290#217—216no—
291#217—28no—
292#217—216no—
293#217—48no—
294#217—48no—
295#217—44no—
296C4⋊Dic3—28no—
297Dic3⋊C4—28no—
298Dic3⋊C4—28no—
299C25—24no—
300C25—22no—
301C25—24no—
302C25—22no—
303C25—22no—
304C25—22no—
305C25—22no—
306C25—22no—
307C25—42no—
308C25—42no—
309C25Dic614yescomplemented
310C25C22×D312yes—
311C25C22×D311yescharacteristic
312C22×Q8—62no—
313C22×Q8—62no—
314C22×Q8—64no—
315C22×Q8—62no—
316C22×Q8—122no—
317C23×C4—31no—
318C23×C4—31no—
319C23×C4—31no—
320C23×C4—31no—
321C23×C4—32no—
322C23×C4—34no—
323C23×C4—32no—
324C23×C4—64no—
325C23×C4—64no—
326C23×C4—62no—
327C23×C4—62no—
328C23×C4—62no—
329C23×C4—62no—
330C23×C4—62no—
331C23×C4—122no—
332C23×C4—122no—
333C23×C4C22×D312yes—
334C23×C4C22×D311yescharacteristic
335C23×C4C22×D311yescharacteristic
336C22⋊Q8—632no—
337C2×C4⋊C4—62no—
338C2×C4⋊C4—62no—
339C2×C4⋊C4—62no—
340C2×C4⋊C4—62no—
341C2×C4⋊C4—62no—
342C2×C4⋊C4—62no—
343C2×C4⋊C4—62no—
344C2×C4⋊C4—62no—
345C2×C4⋊C4—62no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—38no—
356C2×C22⋊C4—34no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—64no—
360C2×C22⋊C4—64no—
361C2×C22⋊C4—64no—
362C2×C22⋊C4—64no—
363C2×C22⋊C4—632no—
364C2×C22⋊C4—64no—
365C2×C22⋊C4—62no—
366C2×C22⋊C4—62no—
367C2×C22⋊C4—64no—
368C2×C22⋊C4—64no—
369C2×C22⋊C4—62no—
370C2×C22⋊C4—62no—
371C2×C22⋊C4—64no—
372C2×C22⋊C4—64no—
373C2×C22⋊C4—62no—
374C2×C22⋊C4—122no—
375C2×C22⋊C4—122no—
376C2×C22⋊C4#6714yes—
377#95—64no—
378#95—64no—
379#95—64no—
380#95—122no—
381#95—122no—
382#95—122no—
383C23×C3—22no—
384C23×C3—24no—
385C23×C3—22no—
386C23×C3—24no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—24no—
390C23×C3—24no—
391C23×C3—24no—
392C23×C3—24no—
393C23×C3—24no—
394C23×C3—24no—
395C23×C3—24no—
396C23×C3—24no—
397C23×C3—24no—
398C23×C3—24no—
399C23×C3—232no—
400C23×C3—24no—
401C23×C3—24no—
402C23×C3—24no—
403C23×C3—24no—
404C23×C3—24no—
405C23×C3—24no—
406C23×C3—24no—
407C23×C3—24no—
408C23×C3—24no—
409C23×C3—24no—
410C23×C3—24no—
411C23×C3—24no—
412C23×C3—24no—
413C23×C3—24no—
414C23×C3—24no—
415C23×C3—24no—
416C23×C3—24no—
417C23×C3—24no—
418C23×C3—432no—
419C23×C3—432no—
420C23×C3—416no—
421C23×C3—416no—
422C23×C3—416no—
423C23×C3—416no—
424C23×C3—416no—
425C23×C3—432no—
426C23×C3—432no—
427C23×C3—42no—
428C23×C3—42no—
429C23×C3—42no—
430C23×C3—42no—
431C23×C3—42no—
432C23×C3—42no—
433C23×C3—42no—
434C23×C3—42no—
435C23×C3—42no—
436C23×C3—42no—
437C23×C3—42no—
438C23×C3—42no—
439C23×C3—42no—
440C23×C3—42no—
441C23×C3—42no—
442C23×C3—42no—
443C23×C3—416no—
444C23×C3#12014yes—
445C23×C3C22⋊Q814yes—
446C23×C3C22⋊Q814yes—
447C23×C3C22⋊Q814yes—
448C23×C3C22⋊Q818yescomplemented
449C23×C3#12414yes—
450C23×C3#12414yes—
451C23×C3#12414yes—
452C23×C3C22×D411yescharacteristic
453C23×C3C22×D412yes—
454C23×C3C22×D411yescharacteristic
455C23×C3C22×D411yescharacteristic
456C23×C3C22×Q811yescharacteristic
457C23×C3C2×#4111yescharacteristic
458C23×C3C2×#4111yescharacteristic
459C23×C3C2×#4112yes—
460C23×C3C2×#4111yescharacteristic
461C23×C3H(5,𝔽2)12yes—
462C23×C3H(5,𝔽2)12yes—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—24no—
466C2×C3×C4—24no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—42no—
472C2×C3×C4—42no—
473C2×C3×C4—42no—
474C2×C3×C4—42no—
475C2×C3×C4—42no—
476C2×C3×C4—42no—
477C2×C3×C4—42no—
478C2×C3×C4—42no—
479C2×C3×C4—42no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—24no—
483C2×Dic3—24no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—22no—
487C2×Dic3—22no—
488C2×Dic3—24no—
489C2×Dic3—22no—
490C2×Dic3—24no—
491C2×Dic3—24no—
492C2×Dic3—24no—
493C2×Dic3—24no—
494C2×Dic3—416no—
495C2×Dic3—416no—
496C2×Dic3—41no—
497C2×Dic3—41no—
498C2×Dic3—42no—
499C2×Dic3—41no—
500C2×Dic3—41no—
501C2×Dic3—42no—
502C2×Dic3—42no—
503C2×Dic3—42no—
504C2×Dic3—42no—
505C2×Dic3—42no—
506C2×Dic3—42no—
507C2×Dic3—42no—
508C2×Dic3—42no—
509C2×Dic3—42no—
510C2×Dic3—42no—
511C2×Dic3—42no—
512C2×Dic3—42no—
513C2×Dic3—42no—
514C2×Dic3—42no—
515C2×Dic3#12014yes—
516Dic6—416no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—28no—
522C24—28no—
523C24—216no—
524C24—28no—
525C24—216no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—28no—
539C24—28no—
540C24—48no—
541C24—48no—
542C24—48no—
543C24—48no—
544C24—48no—
545C24—48no—
546C24—48no—
547C24—48no—
548C24—48no—
549C24—44no—
550C24—44no—
551C24—48no—
552C24—44no—
553C24—44no—
554C24—44no—
555C24—44no—
556C24C2×Dic614yes—
557C24C2×Dic612yes—
558C24#23512yes—
559C24D3×D414yes—
560C24D3×D412yes—
561C24D3×D412yes—
562C24#23714yes—
563C24#23712yes—
564C24#23712yes—
565C24C2×#6712yes—
566C24C23×D311yescharacteristic
567C2×Q8—68no—
568C2×Q8—128no—
569C2×Q8—124no—
570C2×Q8—128no—
571C2×Q8—124no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—34no—
588C22×C4—32no—
589C22×C4—34no—
590C22×C4—32no—
591C22×C4—32no—
592C22×C4—32no—
593C22×C4—68no—
594C22×C4—61no—
595C22×C4—62no—
596C22×C4—61no—
597C22×C4—68no—
598C22×C4—68no—
599C22×C4—62no—
600C22×C4—62no—
601C22×C4—62no—
602C22×C4—62no—
603C22×C4—62no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—62no—
608C22×C4—62no—
609C22×C4—62no—
610C22×C4—62no—
611C22×C4—62no—
612C22×C4—62no—
613C22×C4—62no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4—62no—
618C22×C4—62no—
619C22×C4—62no—
620C22×C4—62no—
621C22×C4—62no—
622C22×C4—62no—
623C22×C4—62no—
624C22×C4—124no—
625C22×C4—128no—
626C22×C4—128no—
627C22×C4—128no—
628C22×C4—128no—
629C22×C4—124no—
630C22×C4—124no—
631C22×C4C2×#6712yes—
632C22×C4C2×#6712yes—
633C4⋊C4—68no—
634C4⋊C4—68no—
635C4⋊C4—68no—
636C22⋊C4—28no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—44no—
640C22⋊C4—616no—
641C22⋊C4—616no—
642C22⋊C4—68no—
643C22⋊C4—128no—
644C22⋊C4—128no—
645C22⋊C4—124no—
646C22×C3—24no—
647C22×C3—24no—
648C22×C3—24no—
649C22×C3—24no—
650C22×C3—24no—
651C22×C3—24no—
652C22×C3—28no—
653C22×C3—28no—
654C22×C3—28no—
655C22×C3—28no—
656C22×C3—28no—
657C22×C3—28no—
658C22×C3—28no—
659C22×C3—464no—
660C22×C3—44no—
661C22×C3—44no—
662C22×C3—44no—
663C22×C3—44no—
664C22×C3—44no—
665C22×C3—44no—
666C22×C3—44no—
667C22×C3—44no—
668C22×C3—44no—
669C22×C3—44no—
670C22×C3—44no—
671C22×C3—44no—
672C22×C3#39318yescomplemented
673C22×C3C2×#12011yescharacteristic
674C22×C3C2×#12011yescharacteristic
675C22×C3C2×C22⋊Q811yescharacteristic
676C22×C3C2×C22⋊Q812yes—
677C22×C3C2×C22⋊Q811yescharacteristic
678C22×C3C2×C22⋊Q811yescharacteristic
679C22×C3#52511yescharacteristic
680C22×C3#52512yes—
681C22×C3C2×#12411yescharacteristic
682C22×C3C2×#12411yescharacteristic
683C22×C3C2×#12411yescharacteristic
684C22×C3#53411yescharacteristic
685C22×C3#53511yescharacteristic
686C22×C3#53812yes—
687C22×C3#54312yes—
688C22×C3D4212yes—
689C22×C3D4212yes—
690C22×C3#54612yes—
691C22×C3#54612yes—
692C22×C3#54612yes—
693C22×C3#54612yes—
694C22×C3#55112yes—
695C22×C3#55112yes—
696C3×C4—42no—
697C3×C4—42no—
698C3×C4—82no—
699Dic3—24no—
700Dic3—42no—
701Dic3—42no—
702Dic3—42no—
703Dic3—44no—
704Dic3—82no—
705C23—24no—
706C23—24no—
707C23—24no—
708C23—24no—
709C23—24no—
710C23—24no—
711C23—22no—
712C23—24no—
713C23—24no—
714C23—22no—
715C23—22no—
716C23—24no—
717C23—24no—
718C23—24no—
719C23—22no—
720C23—24no—
721C23—232no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—24no—
734C23—24no—
735C23—24no—
736C23—24no—
737C23—24no—
738C23—24no—
739C23—24no—
740C23—432no—
741C23—432no—
742C23—416no—
743C23—432no—
744C23—416no—
745C23—416no—
746C23—416no—
747C23—432no—
748C23—416no—
749C23—416no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23#87814yes—
767C23#87814yes—
768C23#87818yescomplemented
769C23#88514yes—
770C23#88514yes—
771C23#92414yes—
772C23#93614yes—
773C23#93714yes—
774C23C22×Dic611yescharacteristic
775C23C2×#23511yescharacteristic
776C23C2×D3×D412yes—
777C23C2×D3×D411yescharacteristic
778C23C2×D3×D411yescharacteristic
779C23C2×#23711yescharacteristic
780C23C2×#23711yescharacteristic
781C23C2×#23712yes—
782C23#100412yes—
783C23#100412yes—
784C23C22×#6711yescharacteristic
785Q8—1216no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—34no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—62no—
805C2×C4—64no—
806C2×C4—62no—
807C2×C4—64no—
808C2×C4—64no—
809C2×C4—62no—
810C2×C4—62no—
811C2×C4—62no—
812C2×C4—64no—
813C2×C4—62no—
814C2×C4—62no—
815C2×C4—64no—
816C2×C4—64no—
817C2×C4—64no—
818C2×C4—1216no—
819C2×C4—1216no—
820C2×C4—122no—
821C2×C4—122no—
822C2×C4—122no—
823C2×C4—122no—
824C2×C4—122no—
825C2×C4—121no—
826C2×C4—121no—
827C2×C4—121no—
828C2×C4—122no—
829C2×C4—122no—
830C2×C4—122no—
831C2×C4—121no—
832C2×C4—122no—
833C2×C4—122no—
834C2×C4—122no—
835C2×C4—122no—
836C2×C4—122no—
837C2×C4—122no—
838C2×C4—122no—
839C2×C3—28no—
840C2×C3—48no—
841C2×C3C2×#39311yescharacteristic
842C2×C3#240311yescharacteristic
843C2×C3#240411yescharacteristic
844C2×C3#243511yescharacteristic
845C2×C3#243712yes—
846C2×C3#243712yes—
847C2×C3#247212yes—
848C2×C3#247212yes—
849C2×C3#256111yescharacteristic
850C2×C3#262611yescharacteristic
851C2×C3#284811yescharacteristic
852C22—24no—
853C22—28no—
854C22—28no—
855C22—24no—
856C22—24no—
857C22—24no—
858C22—24no—
859C22—28no—
860C22—24no—
861C22—28no—
862C22—28no—
863C22—28no—
864C22—28no—
865C22—464no—
866C22—44no—
867C22—44no—
868C22—44no—
869C22—44no—
870C22—44no—
871C22—44no—
872C22—44no—
873C22—44no—
874C22—44no—
875C22—44no—
876C22—44no—
877C22—44no—
878C22#494718yescomplemented
879C22C2×#87811yescharacteristic
880C22C2×#87812yes—
881C22C2×#87811yescharacteristic
882C22#548312yes—
883C22#549012yes—
884C22C2×#88511yescharacteristic
885C22C2×#88511yescharacteristic
886C22#549512yes—
887C22#558612yes—
888C22#558611yescharacteristic
889C22#558712yes—
890C22D3×#12011yescharacteristic
891C22#558911yescharacteristic
892C22#559012yes—
893C22#559112yes—
894C22#559112yes—
895C22#559211yescharacteristic
896C22#559312yes—
897C22C2×#92411yescharacteristic
898C22C2×#93611yescharacteristic
899C22C2×#93711yescharacteristic
900C22D4×#6712yes—
901C22#580612yes—
902C4—42no—
903C4—42no—
904C4—64no—
905C4—82no—
906C4—124no—
907C4—122no—
908C4—122no—
909C4—122no—
910C4—242no—
911C3#1471711yescharacteristic, complemented, Sylow
912C2—28no—
913C2—48no—
914C2#7382711yescharacteristic
915C2#7382812yes—
916C2#7382912yes—
917C2#7383511yescharacteristic
918C2#7383611yescharacteristic
919C2#7384611yescharacteristic
920C2C2×#494711yescharacteristic
921C2#8211012yes—
922C2#8258111yescharacteristic
923C2#8258912yes—
924C2#8260411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#379C2
prime radicalC26×C3C22
hypercenterC2×#379D3
hypocenterC3#14717
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
2. C22×#878C2semidirect
5. C2×#4947C2semidirect
6. #71547C2semidirect
7. #71547C2semidirect
8. #71546C2semidirect
9. #71544C2semidirect
10. #71544C2semidirect
11. #71544C2semidirect
16. C23×Dic6C22semidirect
29. C22×C4⋊Dic3C22semidirect
30. C22×Dic3⋊C4C22semidirect
31. C22×Dic3⋊C4C22semidirect
37. C2×C3⋊#95C22semidirect
38. C2×C3⋊#95C22semidirect
39. C2×C3⋊#95C22semidirect
40. C2×C3⋊#95C22semidirect
41. C2×C3⋊#95C22semidirect
42. C2×C3⋊#95C22semidirect
65. C25×C3Q8semidirect
309. C25Dic6semidirect
448. C23×C3C22⋊Q8semidirect
672. C22×C3#393semidirect
768. C23#878semidirect
878. C22#4947semidirect
911. C3#14717semidirect

Maximal subgroups

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

subgroupindex
C23×#2172
C22×#8782
C2×C3×#3792
C2×#52472
C2×#49472
#715472
#715462
#715442
#147173