Finite Group Databasebeta

← #10720177

Subgroups — #10720177

Order 768.

2742 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#939C211yesmaximal, characteristic
2C22×#877C211yesmaximal, characteristic, complemented
3C2×#4957C212yesmaximal, complemented
4C2×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
5C3×#1438C211yesmaximal, characteristic, complemented
6#72131C211yesmaximal, characteristic, complemented
7#71550C211yesmaximal, characteristic, complemented
8#71550C211yesmaximal, characteristic, complemented
9#71545C212yesmaximal, complemented
10#69408C212yesmaximal, complemented
11Dic3⋊#95C212yesmaximal, complemented
12#14136—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C23×#67C2211yescharacteristic
15C23×#67C2211yescharacteristic
16C24×Dic3C2211yescharacteristic
17C22×C3×C22⋊C4C2211yescharacteristic
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×C3×C22⋊C4C2212yes—
20C22×#217C2211yescharacteristic
21C22×#217C2211yescharacteristic
22C22×#217C2212yes—
23C22×#217C2211yescharacteristic
24C2×#939—24no—
25C2×#939—24no—
26C2×#939C418yescomplemented
27C22×(C2×D3)⋊C4C2212yes—
28C22×(C2×D3)⋊C4C2212yes—
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×Dic3⋊C4C2211yescharacteristic
31C22×Dic3⋊C4C2212yes—
32C22×C4×Dic3C2212yes—
33C22×C4×Dic3C2212yes—
34C2×#877—24no—
35C2×#877—28no—
36C2×C3×#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2212yes—
41#4957—28no—
42Dic3×C22⋊C4—24no—
43C22×#121—31no—
44C22×#117—31no—
45C2×#390—32no—
46C2×C4×C22⋊C4—31no—
47#1438—31no—
48#1438—31no—
49#1438—31no—
50#1438D311yescharacteristic, complemented
51#1437—32no—
52#1437—32no—
53C4⋊#95—32no—
54C25×C3C2311yescharacteristic
55C25×C3C2311yescharacteristic
56C24×D3C2311yescharacteristic
57C22×C3×D4—22no—
58C22×C3×D4—22no—
59C22×C3×D4—42no—
60C22×C3×D4—42no—
61C22×C3×D4C2×C414yes—
62C23×C3×C4C2311yescharacteristic
63C23×C3×C4C2312yes—
64C23×C3×C4C2312yes—
65C22×#67—22no—
66C22×#67—22no—
67C22×#67—24no—
68C22×#67—22no—
69C22×#67—22no—
70C22×#67—24no—
71C22×#67—42no—
72C22×#67—42no—
73C22×#67C2×C414yes—
74C22×#67C2×C414yes—
75C23×Dic3—24no—
76C23×Dic3—24no—
77C23×Dic3C2×C414yes—
78C23×Dic3D414yes—
79C23×Dic3D414yes—
80C23×Dic3C2311yescharacteristic
81C23×Dic3C2312yes—
82C23×Dic3C2312yes—
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C2×C3×C22⋊C4—22no—
86C2×C3×C22⋊C4—22no—
87C2×C3×C22⋊C4—24no—
88C2×C3×C22⋊C4—24no—
89C2×C3×C22⋊C4—24no—
90C2×C3×C22⋊C4—24no—
91C2×C3×C22⋊C4—42no—
92C2×#217—22no—
93C2×#217—22no—
94C2×#217—24no—
95C2×#217—22no—
96C2×#217—22no—
97C2×#217—24no—
98C2×#217—24no—
99C2×#217—24no—
100C2×#217—42no—
101C2×#217C2×C414yes—
102#939—232no—
103C2×(C2×D3)⋊C4—22no—
104C2×(C2×D3)⋊C4—22no—
105C2×(C2×D3)⋊C4—24no—
106C2×(C2×D3)⋊C4—24no—
107C2×(C2×D3)⋊C4—24no—
108C2×(C2×D3)⋊C4—24no—
109C2×(C2×D3)⋊C4—42no—
110C2×(C2×D3)⋊C4—42no—
111C2×(C2×D3)⋊C4C2×C414yes—
112C2×Dic3⋊C4—24no—
113C2×Dic3⋊C4—24no—
114C2×Dic3⋊C4—22no—
115C2×Dic3⋊C4—22no—
116C2×Dic3⋊C4C2×C414yes—
117C2×Dic3⋊C4D418yescomplemented
118C2×C4×Dic3—24no—
119C2×C4×Dic3—24no—
120C2×C4×Dic3—24no—
121C2×C4×Dic3—24no—
122C2×C4×Dic3—24no—
123C2×C4×Dic3—24no—
124#877—232no—
125C3×#95—42no—
126C3⋊#95—24no—
127C3⋊#95—42no—
128C3⋊#95—42no—
129C3⋊#95—42no—
130C23×D4—31no—
131C23×D4—31no—
132C23×D4C2×D311yescharacteristic
133C24×C4—31no—
134C2×#121—38no—
135C2×#121—64no—
136C2×#121—64no—
137C2×#117—68no—
138C2×#117—64no—
139C22×C4⋊C4—32no—
140C22×C4⋊C4—31no—
141C22×C22⋊C4—31no—
142C22×C22⋊C4—31no—
143C22×C22⋊C4—31no—
144C22×C22⋊C4—31no—
145C22×C22⋊C4—32no—
146C22×C22⋊C4—32no—
147C22×C22⋊C4—32no—
148C22×C22⋊C4C2×D311yescharacteristic
149C22×C22⋊C4C2×D311yescharacteristic
150C22×C22⋊C4C2×D312yes—
151C22×C42—32no—
152C22×C42—32no—
153#390—68no—
154C4×C22⋊C4—64no—
155C2×#95—32no—
156C2×#95—32no—
157C2×#95—32no—
158C2×#95—32no—
159C2×#95C2×D312yes—
160C24×C3—22no—
161C24×C3—22no—
162C24×C3—22no—
163C24×C3—22no—
164C24×C3—22no—
165C24×C3—22no—
166C24×C3—22no—
167C24×C3—21no—
168C24×C3—21no—
169C24×C3—22no—
170C24×C3—22no—
171C24×C3—22no—
172C24×C3—22no—
173C24×C3—22no—
174C24×C3C22×C412yes—
175C24×C3C22×C412yes—
176C24×C3C2×D412yes—
177C24×C3C2×D412yes—
178C24×C3C2411yescharacteristic
179C23×D3—22no—
180C23×D3—21no—
181C23×D3—21no—
182C23×D3—22no—
183C23×D3—22no—
184C23×D3—22no—
185C23×D3—22no—
186C23×D3—22no—
187C23×D3C22×C412yes—
188C2×C3×D4—28no—
189C2×C3×D4—44no—
190C2×C3×D4—44no—
191C2×C3×D4—48no—
192C2×C3×D4—48no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
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—22no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4C22×C412yes—
210C22×C3×C4C2×D414yes—
211C22×C3×C4#4114yes—
212C2×#67—28no—
213C2×#67—28no—
214C2×#67—216no—
215C2×#67—44no—
216C2×#67—44no—
217C2×#67—48no—
218C2×#67—48no—
219C2×#67—44no—
220C2×#67—48no—
221C2×#67—44no—
222C22×Dic3—22no—
223C22×Dic3—22no—
224C22×Dic3—216no—
225C22×Dic3—28no—
226C22×Dic3—216no—
227C22×Dic3—28no—
228C22×Dic3—22no—
229C22×Dic3—22no—
230C22×Dic3—22no—
231C22×Dic3—22no—
232C22×Dic3—21no—
233C22×Dic3—21no—
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×Dic3C22⋊C4116yescomplemented
245C22×Dic3C22×C412yes—
246C22×Dic3C22×C412yes—
247C22×Dic3C22×C412yes—
248C22×Dic3C2×D414yes—
249C22×Dic3C2×D412yes—
250C22×Dic3C2×D412yes—
251C22×Dic3C2×D412yes—
252C22×Dic3C2×D412yes—
253C22×Dic3C2×D414yes—
254C22×Dic3#4114yes—
255C22×Dic3#4114yes—
256C3×C22⋊C4—28no—
257C3×C22⋊C4—28no—
258C3×C22⋊C4—48no—
259#217—28no—
260#217—28no—
261#217—28no—
262#217—48no—
263(C2×D3)⋊C4—28no—
264(C2×D3)⋊C4—48no—
265(C2×D3)⋊C4—48no—
266Dic3⋊C4—28no—
267Dic3⋊C4—216no—
268C4×Dic3—216no—
269C4×Dic3—48no—
270C25—31no—
271C25C22×D311yescharacteristic
272C25C22×D311yescharacteristic
273C22×D4—22no—
274C22×D4—22no—
275C22×D4—34no—
276C22×D4—34no—
277C22×D4—42no—
278C22×D4—42no—
279C22×D4—62no—
280C22×D4—62no—
281C22×D4—64no—
282C22×D4—64no—
283C22×D4—62no—
284C22×D4—62no—
285C22×D4—122no—
286C22×D4—122no—
287C22×D4C4×D314yes—
288C23×C4—31no—
289C23×C4—34no—
290C23×C4—34no—
291C23×C4—34no—
292C23×C4—31no—
293C23×C4—32no—
294C23×C4—32no—
295C23×C4—31no—
296C23×C4—64no—
297C23×C4—64no—
298C23×C4C22×D311yescharacteristic
299C23×C4C22×D312yes—
300C23×C4C22×D312yes—
301#121—632no—
302#117—632no—
303C2×C4⋊C4—34no—
304C2×C4⋊C4—38no—
305C2×C4⋊C4—64no—
306C2×C4⋊C4—64no—
307C2×C4⋊C4—62no—
308C2×C4⋊C4—62no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—34no—
316C2×C22⋊C4—34no—
317C2×C22⋊C4—42no—
318C2×C22⋊C4—62no—
319C2×C22⋊C4—62no—
320C2×C22⋊C4—64no—
321C2×C22⋊C4—62no—
322C2×C22⋊C4—62no—
323C2×C22⋊C4—64no—
324C2×C22⋊C4—62no—
325C2×C22⋊C4—62no—
326C2×C22⋊C4—64no—
327C2×C22⋊C4—64no—
328C2×C22⋊C4—64no—
329C2×C22⋊C4—64no—
330C2×C22⋊C4—64no—
331C2×C22⋊C4—64no—
332C2×C22⋊C4—122no—
333C2×C22⋊C4—122no—
334C2×C22⋊C4—122no—
335C2×C42—64no—
336C2×C42—64no—
337C2×C42—64no—
338C2×C42—64no—
339C2×C42—64no—
340C2×C42—64no—
341#95—42no—
342#95—64no—
343#95—122no—
344#95—122no—
345#95—122no—
346C23×C3—24no—
347C23×C3—24no—
348C23×C3—22no—
349C23×C3—22no—
350C23×C3—22no—
351C23×C3—24no—
352C23×C3—22no—
353C23×C3—22no—
354C23×C3—22no—
355C23×C3—24no—
356C23×C3—24no—
357C23×C3—24no—
358C23×C3—22no—
359C23×C3—24no—
360C23×C3—24no—
361C23×C3—22no—
362C23×C3—22no—
363C23×C3—42no—
364C23×C3—42no—
365C23×C3—42no—
366C23×C3—42no—
367C23×C3—42no—
368C23×C3—42no—
369C23×C3—42no—
370C23×C3—42no—
371C23×C3—41no—
372C23×C3—42no—
373C23×C3—41no—
374C23×C3—41no—
375C23×C3—41no—
376C23×C3—42no—
377C23×C3—42no—
378C23×C3—42no—
379C23×C3—42no—
380C23×C3—42no—
381C23×C3—42no—
382C23×C3—42no—
383C23×C3—42no—
384C23×C3—42no—
385C23×C3—42no—
386C23×C3—42no—
387C23×C3C2×C22⋊C414yes—
388C23×C3C23×C411yescharacteristic
389C23×C3C22×D411yescharacteristic
390C23×C3C22×D411yescharacteristic
391C23×C3C22×D412yes—
392C23×C3C2×#4112yes—
393C23×C3C2×#4112yes—
394C23×C3C2×#4112yes—
395C23×C3H(5,𝔽2)12yes—
396C23×C3H(5,𝔽2)12yes—
397C22×D3—22no—
398C22×D3—24no—
399C22×D3—24no—
400C22×D3—22no—
401C22×D3—22no—
402C22×D3—41no—
403C22×D3—42no—
404C22×D3—41no—
405C22×D3—41no—
406C22×D3—41no—
407C22×D3—42no—
408C22×D3—42no—
409C22×D3—42no—
410C22×D3—42no—
411C22×D3—42no—
412C22×D3—42no—
413C22×D3—42no—
414C22×D3—42no—
415C22×D3—42no—
416C22×D3—42no—
417C22×D3—42no—
418C3×D4—416no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—24no—
423C2×C3×C4—24no—
424C2×C3×C4—24no—
425C2×C3×C4—24no—
426C2×C3×C4—24no—
427C2×C3×C4—24no—
428C2×C3×C4—42no—
429C2×C3×C4—42no—
430C2×C3×C4—42no—
431C2×C3×C4—42no—
432C2×C3×C4—42no—
433C2×C3×C4—42no—
434C2×C3×C4—42no—
435C2×C3×C4—42no—
436C2×C3×C4—42no—
437C2×C3×C4—42no—
438#67—416no—
439#67—416no—
440C2×Dic3—24no—
441C2×Dic3—22no—
442C2×Dic3—24no—
443C2×Dic3—22no—
444C2×Dic3—232no—
445C2×Dic3—22no—
446C2×Dic3—22no—
447C2×Dic3—22no—
448C2×Dic3—24no—
449C2×Dic3—24no—
450C2×Dic3—24no—
451C2×Dic3—24no—
452C2×Dic3—24no—
453C2×Dic3—24no—
454C2×Dic3—42no—
455C2×Dic3—42no—
456C2×Dic3—42no—
457C2×Dic3—42no—
458C2×Dic3—42no—
459C2×Dic3—42no—
460C2×Dic3—42no—
461C2×Dic3—42no—
462C2×Dic3—42no—
463C2×Dic3—42no—
464C2×Dic3C2×C22⋊C414yes—
465C2×Dic3C2×C22⋊C414yes—
466C2×Dic3C4×D418yes—
467C2×Dic3#12014yes—
468C2×Dic3#12118yes—
469C2×Dic3#12314yes—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—21no—
478C24—21no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—32no—
485C24—62no—
486C24—61no—
487C24—61no—
488C24—62no—
489C24—62no—
490C24—62no—
491C24—62no—
492C24—62no—
493C24C2×C4×D312yes—
494C24C2×C4×D312yes—
495C24D3×D412yes—
496C24D3×D412yes—
497C24C23×D311yescharacteristic
498C2×D4—28no—
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—48no—
502C2×D4—48no—
503C2×D4—68no—
504C2×D4—616no—
505C2×D4—68no—
506C2×D4—124no—
507C2×D4—124no—
508C2×D4—128no—
509C2×D4—124no—
510C2×D4—124no—
511C2×D4—128no—
512C2×D4—128no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—32no—
530C22×C4—32no—
531C22×C4—34no—
532C22×C4—32no—
533C22×C4—34no—
534C22×C4—316no—
535C22×C4—32no—
536C22×C4—32no—
537C22×C4—32no—
538C22×C4—32no—
539C22×C4—34no—
540C22×C4—34no—
541C22×C4—68no—
542C22×C4—68no—
543C22×C4—616no—
544C22×C4—616no—
545C22×C4—62no—
546C22×C4—62no—
547C22×C4—62no—
548C22×C4—62no—
549C22×C4—62no—
550C22×C4—62no—
551C22×C4—61no—
552C22×C4—61no—
553C22×C4—62no—
554C22×C4—62no—
555C22×C4—62no—
556C22×C4—62no—
557C22×C4—62no—
558C22×C4—62no—
559C22×C4—62no—
560C22×C4—62no—
561C22×C4—62no—
562C22×C4—62no—
563C22×C4C2×C4×D312yes—
564C22×C4D3×D414yes—
565C22×C4#23714yes—
566C4⋊C4—616no—
567C4⋊C4—68no—
568C22⋊C4—28no—
569C22⋊C4—28no—
570C22⋊C4—48no—
571C22⋊C4—68no—
572C22⋊C4—68no—
573C22⋊C4—68no—
574C22⋊C4—68no—
575C22⋊C4—128no—
576C22⋊C4—128no—
577C22⋊C4—128no—
578C42—616no—
579C42—128no—
580C22×C3—24no—
581C22×C3—24no—
582C22×C3—24no—
583C22×C3—44no—
584C22×C3—44no—
585C22×C3—44no—
586C22×C3—44no—
587C22×C3—44no—
588C22×C3—44no—
589C22×C3—42no—
590C22×C3—44no—
591C22×C3—44no—
592C22×C3—42no—
593C22×C3—42no—
594C22×C3—82no—
595C22×C3—82no—
596C22×C3—82no—
597C22×C3—82no—
598C22×C3C22×C22⋊C411yescharacteristic
599C22×C3C2×C4×D412yes—
600C22×C3C4×#4112yes—
601C22×C3#51811yescharacteristic
602C22×C3#51811yescharacteristic
603C22×C3C2×#12011yescharacteristic
604C22×C3C2×#12112yes—
605C22×C3C2×#12311yescharacteristic
606C22×C3#52511yescharacteristic
607C22×C3#52511yescharacteristic
608C22×C3#53212yes—
609C22×C3#53512yes—
610C22×C3#53512yes—
611C22×C3#54612yes—
612C22×C3#54612yes—
613C22×C3#55012yes—
614C22×C3#55012yes—
615C22×C3#55312yes—
616C22×C3#55312yes—
617C22×C3#55512yes—
618C22×C3#55512yes—
619C2×D3—42no—
620C2×D3—44no—
621C2×D3—44no—
622C2×D3—42no—
623C2×D3—42no—
624C2×D3—82no—
625C2×D3—82no—
626C2×D3—82no—
627C2×D3—82no—
628C3×C4—42no—
629C3×C4—44no—
630C3×C4—44no—
631Dic3—24no—
632Dic3—42no—
633Dic3—44no—
634Dic3—44no—
635Dic3#38618yes—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—24no—
641C23—24no—
642C23—22no—
643C23—22no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—24no—
652C23—24no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—41no—
662C23—41no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—41no—
667C23—41no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—62no—
678C23—62no—
679C23—62no—
680C23—64no—
681C23—64no—
682C23—121no—
683C23—121no—
684C23—122no—
685C23—122no—
686C23—122no—
687C23—121no—
688C23—121no—
689C23—122no—
690C23—122no—
691C23—122no—
692C23—122no—
693C23—122no—
694C23—122no—
695C23—122no—
696C23—122no—
697C23—122no—
698C23D3×C22⋊C414yes—
699C23C22×C4×D311yescharacteristic
700C23C2×D3×D411yescharacteristic
701C23C2×D3×D411yescharacteristic
702C23C2×D3×D412yes—
703C23C2×#23712yes—
704C23#100412yes—
705C23#100412yes—
706C23D3×#4112yes—
707C23D3×#4112yes—
708D4—416no—
709D4—1216no—
710D4—1216no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—34no—
721C2×C4—34no—
722C2×C4—38no—
723C2×C4—34no—
724C2×C4—38no—
725C2×C4—34no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—632no—
737C2×C4—62no—
738C2×C4—64no—
739C2×C4—62no—
740C2×C4—64no—
741C2×C4—64no—
742C2×C4—64no—
743C2×C4—62no—
744C2×C4—62no—
745C2×C4—62no—
746C2×C4—64no—
747C2×C4—64no—
748C2×C4—64no—
749C2×C4—64no—
750C2×C4—122no—
751C2×C4—122no—
752C2×C4—122no—
753C2×C4—122no—
754C2×C4—122no—
755C2×C4—122no—
756C2×C4—122no—
757C2×C4—122no—
758C2×C4—122no—
759C2×C4—122no—
760C2×C3—44no—
761C2×C3—82no—
762C2×C3C2×#38611yescharacteristic
763C2×C3#229711yescharacteristic
764C2×C3#230911yescharacteristic
765C2×C3#236312yes—
766C2×C3#236312yes—
767C2×C3#241412yes—
768C2×C3#241412yes—
769C2×C3#243112yes—
770C2×C3#250012yes—
771D3—82no—
772C22—24no—
773C22—24no—
774C22—24no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—44no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—44no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—124no—
791C22—122no—
792C22—122no—
793C22—122no—
794C22—124no—
795C22—242no—
796C22—242no—
797C22—242no—
798C22—242no—
799C22C2×D3×C22⋊C411yescharacteristic
800C22#548611yescharacteristic
801C22#548611yescharacteristic
802C22C4×#23712yes—
803C22C4×D3×D412yes—
804C22#558611yescharacteristic
805C22D3×#12011yescharacteristic
806C22#559112yes—
807C22#559212yes—
808C22#559212yes—
809C22#559612yes—
810C22#559912yes—
811C22#560112yes—
812C22D3×#12112yes—
813C22#561012yes—
814C22#561612yes—
815C22D3×#12311yescharacteristic
816C22#565611yescharacteristic
817C22#566112yes—
818C22#567012yes—
819C22#571812yes—
820C4—38no—
821C4—42no—
822C4—44no—
823C4—44no—
824C4—64no—
825C4—122no—
826C4—124no—
827C4—124no—
828C3#1413611yescharacteristic, complemented, Sylow
829C2—44no—
830C2—82no—
831C2—242no—
832C2#7381911yescharacteristic
833C2#7465811yescharacteristic
834C2#7467712yes—
835C2D3×#38611yescharacteristic
836C2#7630512yes—
837C2#7667012yes—
838C2#7667212yes—
839C2#7689612yes—
840C2#7693612yes—
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1438C2
socle, cosocleC24×C3C24
prime radicalC22×#939C2
hypercenter#1438D3
hypocenterC3#14136
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C22×#877C2semidirect
3. C2×#4957C2semidirect
4. C2×Dic3×C22⋊C4C2semidirect
5. C3×#1438C2semidirect
6. #72131C2semidirect
7. #71550C2semidirect
8. #71550C2semidirect
9. #71545C2semidirect
10. #69408C2semidirect
11. Dic3⋊#95C2semidirect
26. C2×#939C4semidirect
50. #1438D3semidirect
117. C2×Dic3⋊C4D4semidirect
244. C22×Dic3C22⋊C4semidirect
828. C3#14136semidirect

Maximal subgroups

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

subgroupindex
C22×#9392
C22×#8772
C2×#49572
C2×Dic3×C22⋊C42
C3×#14382
#721312
#715502
#715452
#694082
Dic3⋊#952
#141363