Finite Group Databasebeta

← #10726668

Subgroups — #10726668

Order 768.

3494 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#217C211yesmaximal, characteristic
2C2×C3×#379C211yesmaximal, characteristic
3C2×#5247C211yesmaximal, characteristic
4C2×#4948C212yesmaximal, complemented
5C2×#4950C211yesmaximal, characteristic, complemented
6C2×#4946C211yesmaximal, characteristic, complemented
7C2×#4942C211yesmaximal, characteristic, complemented
8#71547C212yesmaximal, complemented
9#71547C212yesmaximal, complemented
10#71546C212yesmaximal, complemented
11#71544C211yesmaximal, characteristic, complemented
12#14726—31nomaximal, Sylow
13C26×C3C2211yescharacteristic
14C24×Dic3C2211yescharacteristic
15C24×Dic3C2211yescharacteristic
16C22×C3×C22⋊C4C2211yescharacteristic
17C22×C3×C22⋊C4C2212yes—
18C22×C3×C22⋊C4C2212yes—
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×#217—24no—
21C22×#217—28no—
22C22×#217C2212yes—
23C22×#217C2211yescharacteristic
24C22×#217C2212yes—
25C22×#217C2212yes—
26C22×#217C2212yes—
27C22×#217C2211yescharacteristic
28C22×C4⋊Dic3C2212yescomplemented
29C22×Dic3⋊C4C2211yescharacteristic, complemented
30C22×Dic3⋊C4C2212yescomplemented
31C22×Dic3⋊C4C2211yescharacteristic, complemented
32C3×#379—24no—
33#5247—24no—
34C2×C3⋊#95C2212yescomplemented
35C2×C3⋊#95C2211yescharacteristic, complemented
36C2×C3⋊#95C2212yescomplemented
37C2×C3⋊#95C2211yescharacteristic, complemented
38C2×C3⋊#95C2212yescomplemented
39C2×C3⋊#95C2212yescomplemented
40#4950—24no—
41#4948—28no—
42#4946—24no—
43#4942—24no—
44C23×C22⋊C4—31no—
45C2×#396—32no—
46C2×#385—31no—
47C2×#385—31no—
48C2×#380—31no—
49C2×#379—31no—
50C2×#379D311yescharacteristic
51#1439—32no—
52#1439—32no—
53#1439—32no—
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×C3Q814yes—
66C25×C3C2312yes—
67C25×C3C2311yescharacteristic
68C23×C3×C4C2311yescharacteristic
69C23×C3×C4C2311yescharacteristic
70C23×C3×C4C2312yes—
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
87C2×C3×C22⋊C4—22no—
88C2×C3×C22⋊C4—22no—
89C2×C3×C22⋊C4—22no—
90C2×C3×C22⋊C4—24no—
91C2×C3×C22⋊C4—22no—
92C2×C3×C22⋊C4—24no—
93C2×C3×C22⋊C4—22no—
94C2×C3×C22⋊C4—24no—
95C2×C3×C22⋊C4—24no—
96C2×C3×C22⋊C4—42no—
97C2×C3×C22⋊C4—42no—
98C2×C3×C22⋊C4D414yes—
99C2×#217—232no—
100C2×#217—22no—
101C2×#217—24no—
102C2×#217—22no—
103C2×#217—24no—
104C2×#217—24no—
105C2×#217—24no—
106C2×#217—24no—
107C2×#217—22no—
108C2×#217—24no—
109C2×#217—22no—
110C2×#217—24no—
111C2×#217—22no—
112C2×#217—24no—
113C2×#217—24no—
114C2×#217—42no—
115C2×#217—42no—
116C2×#217D418yes—
117C2×#217D414yes—
118C2×C4⋊Dic3—24no—
119C2×C4⋊Dic3—24no—
120C2×C4⋊Dic3—42no—
121C2×Dic3⋊C4—24no—
122C2×Dic3⋊C4—22no—
123C2×Dic3⋊C4—22no—
124C2×Dic3⋊C4—24no—
125C2×Dic3⋊C4—24no—
126C2×Dic3⋊C4—42no—
127C2×Dic3⋊C4—42no—
128C3⋊#95—24no—
129C3⋊#95—22no—
130C3⋊#95—22no—
131C3⋊#95—24no—
132C3⋊#95—24no—
133C3⋊#95—42no—
134C26C2×D311yescharacteristic
135C24×C4—31no—
136C24×C4—31no—
137C22×C4⋊C4—31no—
138C22×C4⋊C4—32no—
139C22×C4⋊C4—32no—
140C22×C4⋊C4—31no—
141C22×C22⋊C4—32no—
142C22×C22⋊C4—31no—
143C22×C22⋊C4—32no—
144C22×C22⋊C4—31no—
145C22×C22⋊C4—32no—
146C22×C22⋊C4—32no—
147C22×C22⋊C4—68no—
148C22×C22⋊C4—64no—
149C22×C22⋊C4C2×D311yescharacteristic
150C22×C22⋊C4C2×D312yes—
151C22×C22⋊C4C2×D312yes—
152C22×C22⋊C4C2×D311yescharacteristic
153#396—68no—
154#385—64no—
155#385—64no—
156#380—64no—
157#379—24no—
158#379—64no—
159C2×#95—32no—
160C2×#95—32no—
161C2×#95—31no—
162C2×#95—31no—
163C2×#95—32no—
164C2×#95—32no—
165C24×C3—22no—
166C24×C3—22no—
167C24×C3—22no—
168C24×C3—22no—
169C24×C3—28no—
170C24×C3—216no—
171C24×C3—28no—
172C24×C3—216no—
173C24×C3—28no—
174C24×C3—22no—
175C24×C3—22no—
176C24×C3—22no—
177C24×C3—22no—
178C24×C3—22no—
179C24×C3—22no—
180C24×C3—22no—
181C24×C3—22no—
182C24×C3—22no—
183C24×C3—22no—
184C24×C3—22no—
185C24×C3—22no—
186C24×C3—28no—
187C24×C3—28no—
188C24×C3—48no—
189C24×C3—48no—
190C24×C3—48no—
191C24×C3—48no—
192C24×C3—48no—
193C24×C3—48no—
194C24×C3—48no—
195C24×C3—48no—
196C24×C3—48no—
197C24×C3—44no—
198C24×C3—44no—
199C24×C3—48no—
200C24×C3—44no—
201C24×C3—44no—
202C24×C3—44no—
203C24×C3—44no—
204C24×C3C2×D414yes—
205C24×C3C2×D412yes—
206C24×C3C2×D412yes—
207C24×C3C2×D412yes—
208C24×C3C2×Q814yes—
209C24×C3C2×Q812yes—
210C24×C3#4112yes—
211C24×C3#4114yes—
212C24×C3#4112yes—
213C24×C3#4112yes—
214C24×C3C2411yescharacteristic
215C22×C3×C4—22no—
216C22×C3×C4—22no—
217C22×C3×C4—22no—
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—22no—
221C22×C3×C4—21no—
222C22×C3×C4—22no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—22no—
229C22×C3×C4—22no—
230C22×C3×C4—22no—
231C22×C3×C4C2×D414yes—
232C22×Dic3—21no—
233C22×Dic3—21no—
234C22×Dic3—22no—
235C22×Dic3—28no—
236C22×Dic3—28no—
237C22×Dic3—21no—
238C22×Dic3—21no—
239C22×Dic3—21no—
240C22×Dic3—22no—
241C22×Dic3—22no—
242C22×Dic3—22no—
243C22×Dic3—22no—
244C22×Dic3—22no—
245C22×Dic3—21no—
246C22×Dic3—21no—
247C22×Dic3—22no—
248C22×Dic3—22no—
249C22×Dic3—21no—
250C22×Dic3—22no—
251C22×Dic3—22no—
252C22×Dic3—22no—
253C22×Dic3—22no—
254C22×Dic3—22no—
255C22×Dic3—28no—
256C22×Dic3—22no—
257C22×Dic3—22no—
258C22×Dic3—22no—
259C22×Dic3—22no—
260C22×Dic3—22no—
261C22×Dic3—22no—
262C22×Dic3—22no—
263C22×Dic3—44no—
264C22×Dic3—48no—
265C22×Dic3—48no—
266C22×Dic3—48no—
267C22×Dic3—48no—
268C22×Dic3—44no—
269C22×Dic3—44no—
270C22×Dic3C2×D412yes—
271C22×Dic3C2×D412yes—
272C22×Dic3C2×D414yes—
273C22×Dic3C2×D412yes—
274C22×Dic3C2×D412yes—
275C22×Dic3C2×D414yes—
276C3×C22⋊C4—28no—
277C3×C22⋊C4—48no—
278C3×C22⋊C4—48no—
279C3×C22⋊C4—44no—
280#217—216no—
281#217—28no—
282#217—216no—
283#217—48no—
284#217—48no—
285#217—44no—
286C4⋊Dic3—48no—
287Dic3⋊C4—48no—
288Dic3⋊C4—44no—
289Dic3⋊C4—44no—
290C25—24no—
291C25—22no—
292C25—24no—
293C25—22no—
294C25—22no—
295C25—22no—
296C25—22no—
297C25—22no—
298C25—42no—
299C25—42no—
300C25Dic614yes—
301C25C22×D312yes—
302C25C22×D311yescharacteristic
303C23×C4—31no—
304C23×C4—31no—
305C23×C4—31no—
306C23×C4—32no—
307C23×C4—31no—
308C23×C4—34no—
309C23×C4—32no—
310C23×C4—64no—
311C23×C4—64no—
312C23×C4—62no—
313C23×C4—62no—
314C23×C4—62no—
315C23×C4—62no—
316C23×C4—62no—
317C23×C4—122no—
318C23×C4—122no—
319C23×C4C22×D311yescharacteristic
320C23×C4C22×D311yescharacteristic
321C23×C4C22×D312yes—
322C2×C4⋊C4—62no—
323C2×C4⋊C4—62no—
324C2×C4⋊C4—64no—
325C2×C4⋊C4—64no—
326C2×C4⋊C4—64no—
327C2×C4⋊C4—64no—
328C2×C4⋊C4—64no—
329C2×C4⋊C4—122no—
330C2×C4⋊C4—122no—
331C2×C4⋊C4—122no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—38no—
342C2×C22⋊C4—34no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—64no—
346C2×C22⋊C4—64no—
347C2×C22⋊C4—64no—
348C2×C22⋊C4—64no—
349C2×C22⋊C4—632no—
350C2×C22⋊C4—62no—
351C2×C22⋊C4—64no—
352C2×C22⋊C4—62no—
353C2×C22⋊C4—64no—
354C2×C22⋊C4—64no—
355C2×C22⋊C4—62no—
356C2×C22⋊C4—64no—
357C2×C22⋊C4—64no—
358C2×C22⋊C4—62no—
359C2×C22⋊C4—62no—
360C2×C22⋊C4—122no—
361C2×C22⋊C4—122no—
362C2×C22⋊C4#6714yes—
363#95—64no—
364#95—62no—
365#95—62no—
366#95—64no—
367#95—64no—
368#95—122no—
369C23×C3—22no—
370C23×C3—24no—
371C23×C3—22no—
372C23×C3—24no—
373C23×C3—22no—
374C23×C3—22no—
375C23×C3—24no—
376C23×C3—24no—
377C23×C3—24no—
378C23×C3—24no—
379C23×C3—24no—
380C23×C3—24no—
381C23×C3—24no—
382C23×C3—24no—
383C23×C3—24no—
384C23×C3—24no—
385C23×C3—232no—
386C23×C3—24no—
387C23×C3—24no—
388C23×C3—24no—
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—24no—
400C23×C3—24no—
401C23×C3—24no—
402C23×C3—24no—
403C23×C3—24no—
404C23×C3—432no—
405C23×C3—432no—
406C23×C3—416no—
407C23×C3—416no—
408C23×C3—416no—
409C23×C3—416no—
410C23×C3—432no—
411C23×C3—432no—
412C23×C3—416no—
413C23×C3—42no—
414C23×C3—42no—
415C23×C3—42no—
416C23×C3—42no—
417C23×C3—42no—
418C23×C3—42no—
419C23×C3—42no—
420C23×C3—42no—
421C23×C3—42no—
422C23×C3—42no—
423C23×C3—42no—
424C23×C3—42no—
425C23×C3—42no—
426C23×C3—42no—
427C23×C3—42no—
428C23×C3—42no—
429C23×C3—416no—
430C23×C3#12114yes—
431C23×C3#12114yes—
432C23×C3#12114yes—
433C23×C3C22⋊Q818yes—
434C23×C3C22⋊Q814yes—
435C23×C3C22⋊Q814yes—
436C23×C3C22⋊Q814yes—
437C23×C3#12614yes—
438C23×C3C22×D411yescharacteristic
439C23×C3C22×D412yes—
440C23×C3C22×D411yescharacteristic
441C23×C3C22×D411yescharacteristic
442C23×C3C22×Q811yescharacteristic
443C23×C3C2×#4111yescharacteristic
444C23×C3C2×#4111yescharacteristic
445C23×C3C2×#4111yescharacteristic
446C23×C3C2×#4112yes—
447C23×C3H(5,𝔽2)12yes—
448C23×C3H(5,𝔽2)12yes—
449C2×C3×C4—24no—
450C2×C3×C4—24no—
451C2×C3×C4—24no—
452C2×C3×C4—42no—
453C2×C3×C4—42no—
454C2×C3×C4—42no—
455C2×C3×C4—42no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—42no—
463C2×C3×C4—42no—
464C2×C3×C4—42no—
465C2×C3×C4—42no—
466C2×Dic3—22no—
467C2×Dic3—22no—
468C2×Dic3—24no—
469C2×Dic3—24no—
470C2×Dic3—24no—
471C2×Dic3—22no—
472C2×Dic3—22no—
473C2×Dic3—22no—
474C2×Dic3—22no—
475C2×Dic3—22no—
476C2×Dic3—24no—
477C2×Dic3—24no—
478C2×Dic3—24no—
479C2×Dic3—24no—
480C2×Dic3—416no—
481C2×Dic3—416no—
482C2×Dic3—41no—
483C2×Dic3—42no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—42no—
488C2×Dic3—42no—
489C2×Dic3—42no—
490C2×Dic3—42no—
491C2×Dic3—42no—
492C2×Dic3—42no—
493C2×Dic3—42no—
494C2×Dic3—42no—
495C2×Dic3—42no—
496C2×Dic3—42no—
497C2×Dic3—42no—
498C2×Dic3—42no—
499C2×Dic3—42no—
500C2×Dic3—42no—
501C2×Dic3#12014yes—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—28no—
507C24—28no—
508C24—216no—
509C24—216no—
510C24—28no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—28no—
524C24—28no—
525C24—48no—
526C24—48no—
527C24—48no—
528C24—48no—
529C24—48no—
530C24—48no—
531C24—48no—
532C24—48no—
533C24—48no—
534C24—44no—
535C24—44no—
536C24—48no—
537C24—44no—
538C24—44no—
539C24—44no—
540C24—44no—
541C24C2×Dic614yes—
542C24C2×Dic612yes—
543C24#23512yes—
544C24D3×D414yes—
545C24D3×D412yes—
546C24D3×D412yes—
547C24#23714yes—
548C24#23712yes—
549C24#23712yes—
550C24C2×#6712yes—
551C24C23×D311yescharacteristic
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—32no—
569C22×C4—34no—
570C22×C4—32no—
571C22×C4—34no—
572C22×C4—32no—
573C22×C4—32no—
574C22×C4—68no—
575C22×C4—61no—
576C22×C4—62no—
577C22×C4—61no—
578C22×C4—68no—
579C22×C4—68no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—62no—
583C22×C4—61no—
584C22×C4—61no—
585C22×C4—62no—
586C22×C4—62no—
587C22×C4—62no—
588C22×C4—62no—
589C22×C4—62no—
590C22×C4—62no—
591C22×C4—61no—
592C22×C4—62no—
593C22×C4—62no—
594C22×C4—62no—
595C22×C4—62no—
596C22×C4—62no—
597C22×C4—61no—
598C22×C4—62no—
599C22×C4—62no—
600C22×C4—62no—
601C22×C4—62no—
602C22×C4—62no—
603C22×C4—62no—
604C22×C4—62no—
605C22×C4—124no—
606C22×C4—128no—
607C22×C4—128no—
608C22×C4—128no—
609C22×C4—128no—
610C22×C4—124no—
611C22×C4—124no—
612C22×C4C2×#6714yes—
613C4⋊C4—128no—
614C4⋊C4—124no—
615C4⋊C4—128no—
616C4⋊C4—124no—
617C22⋊C4—28no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—44no—
621C22⋊C4—616no—
622C22⋊C4—616no—
623C22⋊C4—68no—
624C22⋊C4—128no—
625C22⋊C4—128no—
626C22⋊C4—124no—
627C22×C3—24no—
628C22×C3—24no—
629C22×C3—24no—
630C22×C3—24no—
631C22×C3—24no—
632C22×C3—28no—
633C22×C3—28no—
634C22×C3—28no—
635C22×C3—28no—
636C22×C3—24no—
637C22×C3—28no—
638C22×C3—28no—
639C22×C3—28no—
640C22×C3—464no—
641C22×C3—44no—
642C22×C3—44no—
643C22×C3—44no—
644C22×C3—44no—
645C22×C3—44no—
646C22×C3—44no—
647C22×C3—44no—
648C22×C3—44no—
649C22×C3—44no—
650C22×C3—44no—
651C22×C3—44no—
652C22×C3—44no—
653C22×C3#39618yescomplemented
654C22×C3C2×#12011yescharacteristic
655C22×C3C2×#12111yescharacteristic
656C22×C3C2×#12111yescharacteristic
657C22×C3C2×#12111yescharacteristic
658C22×C3C2×C22⋊Q811yescharacteristic
659C22×C3C2×C22⋊Q812yes—
660C22×C3C2×C22⋊Q811yescharacteristic
661C22×C3C2×C22⋊Q811yescharacteristic
662C22×C3#52511yescharacteristic
663C22×C3#52512yes—
664C22×C3C2×#12611yescharacteristic
665C22×C3#53411yescharacteristic
666C22×C3#53511yescharacteristic
667C22×C3#53812yes—
668C22×C3#54312yes—
669C22×C3D4212yes—
670C22×C3D4212yes—
671C22×C3#54612yes—
672C22×C3#54612yes—
673C22×C3#54612yes—
674C22×C3#54612yes—
675C22×C3#55112yes—
676C22×C3#55112yes—
677C3×C4—44no—
678C3×C4—81no—
679C3×C4—81no—
680Dic3—24no—
681Dic3—42no—
682Dic3—44no—
683Dic3—42no—
684Dic3—42no—
685Dic3—82no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—22no—
693C23—24no—
694C23—24no—
695C23—22no—
696C23—22no—
697C23—24no—
698C23—24no—
699C23—24no—
700C23—22no—
701C23—24no—
702C23—232no—
703C23—24no—
704C23—24no—
705C23—24no—
706C23—24no—
707C23—24no—
708C23—24no—
709C23—24no—
710C23—24no—
711C23—24no—
712C23—24no—
713C23—24no—
714C23—24no—
715C23—24no—
716C23—24no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—432no—
722C23—432no—
723C23—416no—
724C23—432no—
725C23—416no—
726C23—416no—
727C23—416no—
728C23—432no—
729C23—416no—
730C23—416no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23#87818yes—
748C23#87814yes—
749C23#87814yes—
750C23#87914yes—
751C23#88414yes—
752C23#92414yes—
753C23#93814yes—
754C23#93914yes—
755C23C22×Dic611yescharacteristic
756C23C2×#23511yescharacteristic
757C23C2×D3×D411yescharacteristic
758C23C2×D3×D411yescharacteristic
759C23C2×D3×D412yes—
760C23C2×#23711yescharacteristic
761C23C2×#23711yescharacteristic
762C23C2×#23712yes—
763C23#100412yes—
764C23#100412yes—
765C23C22×#6711yescharacteristic
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—34no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—62no—
785C2×C4—64no—
786C2×C4—62no—
787C2×C4—64no—
788C2×C4—62no—
789C2×C4—62no—
790C2×C4—64no—
791C2×C4—62no—
792C2×C4—64no—
793C2×C4—62no—
794C2×C4—62no—
795C2×C4—64no—
796C2×C4—64no—
797C2×C4—64no—
798C2×C4—1216no—
799C2×C4—1216no—
800C2×C4—122no—
801C2×C4—122no—
802C2×C4—122no—
803C2×C4—122no—
804C2×C4—122no—
805C2×C4—121no—
806C2×C4—121no—
807C2×C4—121no—
808C2×C4—122no—
809C2×C4—122no—
810C2×C4—122no—
811C2×C4—121no—
812C2×C4—122no—
813C2×C4—122no—
814C2×C4—122no—
815C2×C4—122no—
816C2×C4—122no—
817C2×C4—122no—
818C2×C4—122no—
819C2×C3—28no—
820C2×C3—48no—
821C2×C3C2×#39611yescharacteristic
822C2×C3#240811yescharacteristic
823C2×C3#241011yescharacteristic
824C2×C3#241111yescharacteristic
825C2×C3#242412yes—
826C2×C3#243712yes—
827C2×C3#243712yes—
828C2×C3#248012yes—
829C2×C3#253411yescharacteristic
830C2×C3#262611yescharacteristic
831C2×C3#284811yescharacteristic
832C22—24no—
833C22—28no—
834C22—28no—
835C22—24no—
836C22—24no—
837C22—24no—
838C22—24no—
839C22—28no—
840C22—24no—
841C22—28no—
842C22—28no—
843C22—28no—
844C22—28no—
845C22—464no—
846C22—44no—
847C22—44no—
848C22—44no—
849C22—44no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—44no—
854C22—44no—
855C22—44no—
856C22—44no—
857C22—44no—
858C22#494818yescomplemented
859C22C2×#87811yescharacteristic
860C22C2×#87812yes—
861C22C2×#87811yescharacteristic
862C22C2×#87911yescharacteristic
863C22#548312yes—
864C22C2×#88411yescharacteristic
865C22#549012yes—
866C22#549512yes—
867C22#558612yes—
868C22#558611yescharacteristic
869C22#558712yes—
870C22D3×#12011yescharacteristic
871C22#558911yescharacteristic
872C22#559012yes—
873C22#559112yes—
874C22#559112yes—
875C22#559211yescharacteristic
876C22#559312yes—
877C22C2×#92411yescharacteristic
878C22C2×#93811yescharacteristic
879C22D4×#6712yes—
880C22C2×#93911yescharacteristic
881C22#580612yes—
882C4—44no—
883C4—64no—
884C4—81no—
885C4—81no—
886C4—124no—
887C4—122no—
888C4—122no—
889C4—122no—
890C4—242no—
891C3#1472611yescharacteristic, complemented, Sylow
892C2—28no—
893C2—48no—
894C2#7382411yescharacteristic
895C2#7382812yes—
896C2#7383112yes—
897C2#7383411yescharacteristic
898C2#7383611yescharacteristic
899C2#7384611yescharacteristic
900C2C2×#494811yescharacteristic
901C2#8211012yes—
902C2#8258311yescharacteristic
903C2#8258712yes—
904C2#8260511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#379C2
prime radicalC26×C3C22
hypercenterC2×#379D3
hypocenterC3#14726
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
4. C2×#4948C2semidirect
5. C2×#4950C2semidirect
6. C2×#4946C2semidirect
7. C2×#4942C2semidirect
8. #71547C2semidirect
9. #71547C2semidirect
10. #71546C2semidirect
11. #71544C2semidirect
28. C22×C4⋊Dic3C22semidirect
29. C22×Dic3⋊C4C22semidirect
30. C22×Dic3⋊C4C22semidirect
31. C22×Dic3⋊C4C22semidirect
34. C2×C3⋊#95C22semidirect
35. C2×C3⋊#95C22semidirect
36. C2×C3⋊#95C22semidirect
37. C2×C3⋊#95C22semidirect
38. C2×C3⋊#95C22semidirect
39. C2×C3⋊#95C22semidirect
653. C22×C3#396semidirect
858. C22#4948semidirect
891. C3#14726semidirect

Maximal subgroups

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

subgroupindex
C23×#2172
C2×C3×#3792
C2×#52472
C2×#49482
C2×#49502
C2×#49462
C2×#49422
#715472
#715462
#715442
#147263