Finite Group Databasebeta

← #10717954

Subgroups — #10717954

Order 768.

4478 conjugacy classes of subgroups.

The subgroup lattice has 1062 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#953C211yesmaximal, characteristic
2C23×#217C211yesmaximal, characteristic, complemented
3C22×#67⋊C4C211yesmaximal, characteristic, complemented
4C2×C3×#379C211yesmaximal, characteristic, complemented
5C2×#4956C212yesmaximal, complemented
6C2×#4958C211yesmaximal, characteristic, complemented
7#71550C212yesmaximal, complemented
8#71547C212yesmaximal, complemented
9#71545C212yesmaximal, complemented
10#71544C211yesmaximal, characteristic, complemented
11#71544C211yesmaximal, characteristic, complemented
12#13967—31nomaximal, Sylow
13C26×C3C2211yescharacteristic
14C23×#67C2212yes—
15C23×#67C2211yescharacteristic
16C24×Dic3C2211yescharacteristic
17C24×Dic3C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic, complemented
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2212yes—
21C22×C3×C22⋊C4C2212yes—
22C22×C3×C22⋊C4C2211yescharacteristic
23C2×#953—24no—
24C2×#953—24no—
25C2×#953C418yescomplemented
26C22×#217—24no—
27C22×#217—28no—
28C22×#217C2212yes—
29C22×#217C2211yescharacteristic
30C22×#217C2212yes—
31C22×#217C2212yes—
32C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
33C22×(C2×D3)⋊C4C2212yescomplemented
34C22×Dic3⋊C4C2211yescharacteristic, complemented
35C22×C4×Dic3C2211yescharacteristic, complemented
36C2×#67⋊C4—24no—
37C2×#67⋊C4—24no—
38C2×#67⋊C4—24no—
39C3×#379—24no—
40C2×C3⋊#95C2212yescomplemented
41C2×C3⋊#95C2212yescomplemented
42C2×C3⋊#95C2212yescomplemented
43C2×C3⋊#95C2212yescomplemented
44C2×C3⋊#95C2212yescomplemented
45#4958—24no—
46#4956—28no—
47C22×#120—31no—
48C22×C4×D4—31no—
49C23×C22⋊C4—31no—
50C2×#386—31no—
51C2×#386—32no—
52C2×#379D311yescharacteristic, complemented
53#1439—32no—
54#1438—32no—
55#1437—32no—
56C22⋊#95—31no—
57C22⋊#95—31no—
58C25×C3—24no—
59C25×C3—22no—
60C25×C3—24no—
61C25×C3—22no—
62C25×C3—22no—
63C25×C3—22no—
64C25×C3—22no—
65C25×C3—22no—
66C25×C3—42no—
67C25×C3—42no—
68C25×C3C2×C414yescomplemented
69C25×C3C2312yes—
70C25×C3C2311yescharacteristic
71C24×D3C2311yescharacteristic
72C23×C3×C4C2312yes—
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C22×#67—22no—
76C22×#67—22no—
77C22×#67—22no—
78C22×#67—22no—
79C22×#67—24no—
80C22×#67—24no—
81C22×#67—24no—
82C22×#67—24no—
83C22×#67—42no—
84C22×#67—42no—
85C22×#67C2×C414yes—
86C22×#67C2×C418yescomplemented
87C22×#67D414yes—
88C22×#67D414yes—
89C23×Dic3—22no—
90C23×Dic3—22no—
91C23×Dic3—22no—
92C23×Dic3—24no—
93C23×Dic3—24no—
94C23×Dic3—22no—
95C23×Dic3—22no—
96C23×Dic3—42no—
97C23×Dic3—42no—
98C23×Dic3D414yescomplemented
99C23×Dic3C2312yes—
100C23×Dic3C2312yes—
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C22×C4×D3—22no—
105C22×C4×D3—22no—
106C22×C4×D3—22no—
107C22×C4×D3—24no—
108C22×C4×D3—42no—
109C2×C3×C22⋊C4—22no—
110C2×C3×C22⋊C4—22no—
111C2×C3×C22⋊C4—24no—
112C2×C3×C22⋊C4—22no—
113C2×C3×C22⋊C4—22no—
114C2×C3×C22⋊C4—24no—
115C2×C3×C22⋊C4—22no—
116C2×C3×C22⋊C4—24no—
117C2×C3×C22⋊C4—24no—
118C2×C3×C22⋊C4—42no—
119C2×C3×C22⋊C4—42no—
120C2×C3×C22⋊C4D414yescomplemented
121#953—232no—
122C2×#217—232no—
123C2×#217—24no—
124C2×#217—22no—
125C2×#217—22no—
126C2×#217—24no—
127C2×#217—24no—
128C2×#217—24no—
129C2×#217—24no—
130C2×#217—24no—
131C2×#217—24no—
132C2×#217C2×C414yescomplemented
133C2×#217C2×C418yescomplemented
134C2×#217D418yescomplemented
135C2×(C2×D3)⋊C4—22no—
136C2×(C2×D3)⋊C4—22no—
137C2×(C2×D3)⋊C4—22no—
138C2×(C2×D3)⋊C4—24no—
139C2×(C2×D3)⋊C4—24no—
140C2×(C2×D3)⋊C4—42no—
141C2×Dic3⋊C4—22no—
142C2×Dic3⋊C4—22no—
143C2×Dic3⋊C4—22no—
144C2×C4×Dic3—22no—
145C2×C4×Dic3—22no—
146C2×C4×Dic3—22no—
147#67⋊C4—232no—
148C3⋊#95—24no—
149C3⋊#95—24no—
150C3⋊#95—24no—
151C3⋊#95—42no—
152C3⋊#95—42no—
153C26C2×D311yescharacteristic
154C23×D4—31no—
155C23×D4—32no—
156C24×C4—31no—
157C24×C4—31no—
158C24×C4—31no—
159C2×#120—38no—
160C2×#120—64no—
161C2×#120—64no—
162C2×C4×D4—64no—
163C2×C4×D4—64no—
164C2×C4×D4—64no—
165C22×C4⋊C4—31no—
166C22×C22⋊C4—32no—
167C22×C22⋊C4—31no—
168C22×C22⋊C4—32no—
169C22×C22⋊C4—32no—
170C22×C22⋊C4—31no—
171C22×C22⋊C4—32no—
172C22×C22⋊C4—68no—
173C22×C22⋊C4—64no—
174C22×C22⋊C4C2×D311yescharacteristic
175C22×C22⋊C4C2×D312yes—
176C22×C22⋊C4C2×D312yes—
177C22×C22⋊C4C2×D311yescharacteristic
178C22×C42—31no—
179#386—68no—
180#386—64no—
181#379—24no—
182C2×#95—32no—
183C2×#95—32no—
184C2×#95—32no—
185C2×#95—32no—
186C2×#95—32no—
187C24×C3—22no—
188C24×C3—22no—
189C24×C3—22no—
190C24×C3—22no—
191C24×C3—28no—
192C24×C3—216no—
193C24×C3—28no—
194C24×C3—28no—
195C24×C3—216no—
196C24×C3—22no—
197C24×C3—22no—
198C24×C3—22no—
199C24×C3—22no—
200C24×C3—22no—
201C24×C3—22no—
202C24×C3—22no—
203C24×C3—22no—
204C24×C3—22no—
205C24×C3—22no—
206C24×C3—22no—
207C24×C3—22no—
208C24×C3—28no—
209C24×C3—28no—
210C24×C3—48no—
211C24×C3—48no—
212C24×C3—48no—
213C24×C3—48no—
214C24×C3—48no—
215C24×C3—48no—
216C24×C3—48no—
217C24×C3—48no—
218C24×C3—48no—
219C24×C3—44no—
220C24×C3—44no—
221C24×C3—48no—
222C24×C3—44no—
223C24×C3—44no—
224C24×C3—44no—
225C24×C3—44no—
226C24×C3C22×C414yes—
227C24×C3C22×C412yes—
228C24×C3C2×D414yes—
229C24×C3C2×D412yes—
230C24×C3C2×D412yes—
231C24×C3C2×D412yes—
232C24×C3C2×D412yes—
233C24×C3#4112yes—
234C24×C3#4114yes—
235C24×C3#4112yes—
236C24×C3C2411yescharacteristic
237C23×D3—21no—
238C23×D3—22no—
239C23×D3—21no—
240C23×D3—21no—
241C23×D3—21no—
242C23×D3—22no—
243C23×D3—22no—
244C23×D3—22no—
245C23×D3C22×C412yes—
246C23×D3C2×D412yes—
247C23×D3C2×D412yes—
248C22×C3×C4—22no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—22no—
254C22×C3×C4—22no—
255C22×C3×C4—22no—
256C22×C3×C4—22no—
257C22×C3×C4—22no—
258C22×C3×C4—22no—
259C22×C3×C4—22no—
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4—22no—
263C22×C3×C4C2×D412yes—
264C22×C3×C4C2×D412yes—
265C2×#67—28no—
266C2×#67—28no—
267C2×#67—28no—
268C2×#67—28no—
269C2×#67—28no—
270C2×#67—28no—
271C2×#67—216no—
272C2×#67—216no—
273C2×#67—48no—
274C2×#67—48no—
275C2×#67—48no—
276C2×#67—48no—
277C2×#67—48no—
278C2×#67C22⋊C4116yescomplemented
279C22×Dic3—21no—
280C22×Dic3—21no—
281C22×Dic3—21no—
282C22×Dic3—21no—
283C22×Dic3—21no—
284C22×Dic3—21no—
285C22×Dic3—22no—
286C22×Dic3—28no—
287C22×Dic3—28no—
288C22×Dic3—22no—
289C22×Dic3—22no—
290C22×Dic3—21no—
291C22×Dic3—21no—
292C22×Dic3—22no—
293C22×Dic3—22no—
294C22×Dic3—22no—
295C22×Dic3—22no—
296C22×Dic3—22no—
297C22×Dic3—22no—
298C22×Dic3—22no—
299C22×Dic3—22no—
300C22×Dic3—22no—
301C22×Dic3—22no—
302C22×Dic3—22no—
303C22×Dic3—22no—
304C22×Dic3—28no—
305C22×Dic3—44no—
306C22×Dic3—48no—
307C22×Dic3—48no—
308C22×Dic3—48no—
309C22×Dic3—48no—
310C22×Dic3—44no—
311C22×Dic3—44no—
312C22×Dic3C22×C414yes—
313C22×Dic3C22×C412yes—
314C22×Dic3C2×D414yes—
315C22×Dic3C2×D412yes—
316C22×Dic3C2×D412yes—
317C22×Dic3C2×D412yes—
318C22×Dic3C2×D414yes—
319C22×Dic3C2×D412yes—
320C2×C4×D3—28no—
321C2×C4×D3—48no—
322C2×C4×D3—48no—
323C2×C4×D3—44no—
324C2×C4×D3—44no—
325C3×C22⋊C4—28no—
326C3×C22⋊C4—48no—
327C3×C22⋊C4—48no—
328C3×C22⋊C4—44no—
329#217—216no—
330#217—28no—
331#217—216no—
332#217—216no—
333(C2×D3)⋊C4—28no—
334(C2×D3)⋊C4—48no—
335Dic3⋊C4—28no—
336C4×Dic3—28no—
337C25—24no—
338C25—22no—
339C25—24no—
340C25—22no—
341C25—22no—
342C25—22no—
343C25—22no—
344C25—22no—
345C25—31no—
346C25—42no—
347C25—42no—
348C25C4×D314yescomplemented
349C25C22×D312yes—
350C25C22×D311yescharacteristic
351C22×D4—34no—
352C22×D4—34no—
353C22×D4—34no—
354C22×D4—38no—
355C22×D4—62no—
356C22×D4—62no—
357C22×D4—62no—
358C22×D4—62no—
359C22×D4—64no—
360C22×D4—64no—
361C22×D4—64no—
362C22×D4—64no—
363C22×D4—122no—
364C22×D4—122no—
365C23×C4—31no—
366C23×C4—31no—
367C23×C4—31no—
368C23×C4—32no—
369C23×C4—32no—
370C23×C4—34no—
371C23×C4—62no—
372C23×C4—64no—
373C23×C4—62no—
374C23×C4—64no—
375C23×C4—64no—
376C23×C4—62no—
377C23×C4—62no—
378C23×C4—62no—
379C23×C4—62no—
380C23×C4—62no—
381C23×C4—62no—
382C23×C4—122no—
383C23×C4—122no—
384C23×C4—122no—
385C23×C4C22×D312yes—
386C23×C4C22×D311yescharacteristic
387C23×C4C22×D311yescharacteristic
388#120—632no—
389C4×D4—632no—
390C2×C4⋊C4—62no—
391C2×C4⋊C4—62no—
392C2×C4⋊C4—62no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—38no—
403C2×C22⋊C4—34no—
404C2×C22⋊C4—38no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—62no—
408C2×C22⋊C4—62no—
409C2×C22⋊C4—64no—
410C2×C22⋊C4—64no—
411C2×C22⋊C4—64no—
412C2×C22⋊C4—64no—
413C2×C22⋊C4—64no—
414C2×C22⋊C4—64no—
415C2×C22⋊C4—632no—
416C2×C22⋊C4—64no—
417C2×C22⋊C4—62no—
418C2×C22⋊C4—62no—
419C2×C22⋊C4—62no—
420C2×C22⋊C4—64no—
421C2×C22⋊C4—64no—
422C2×C22⋊C4—122no—
423C2×C22⋊C4#6714yescomplemented
424C2×C42—62no—
425C2×C42—62no—
426C2×C42—62no—
427#95—64no—
428#95—64no—
429#95—64no—
430#95—122no—
431#95—122no—
432C23×C3—24no—
433C23×C3—24no—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—24no—
437C23×C3—22no—
438C23×C3—22no—
439C23×C3—24no—
440C23×C3—24no—
441C23×C3—24no—
442C23×C3—24no—
443C23×C3—24no—
444C23×C3—24no—
445C23×C3—24no—
446C23×C3—24no—
447C23×C3—24no—
448C23×C3—232no—
449C23×C3—24no—
450C23×C3—24no—
451C23×C3—24no—
452C23×C3—24no—
453C23×C3—24no—
454C23×C3—24no—
455C23×C3—24no—
456C23×C3—24no—
457C23×C3—24no—
458C23×C3—24no—
459C23×C3—24no—
460C23×C3—24no—
461C23×C3—24no—
462C23×C3—24no—
463C23×C3—24no—
464C23×C3—24no—
465C23×C3—24no—
466C23×C3—24no—
467C23×C3—432no—
468C23×C3—432no—
469C23×C3—416no—
470C23×C3—416no—
471C23×C3—416no—
472C23×C3—416no—
473C23×C3—432no—
474C23×C3—432no—
475C23×C3—416no—
476C23×C3—42no—
477C23×C3—42no—
478C23×C3—42no—
479C23×C3—42no—
480C23×C3—42no—
481C23×C3—42no—
482C23×C3—42no—
483C23×C3—42no—
484C23×C3—42no—
485C23×C3—42no—
486C23×C3—42no—
487C23×C3—42no—
488C23×C3—42no—
489C23×C3—42no—
490C23×C3—42no—
491C23×C3—42no—
492C23×C3—416no—
493C23×C3C2×C22⋊C414yes—
494C23×C3C4×D414yes—
495C23×C3C4×D414yes—
496C23×C3C4×D418yescomplemented
497C23×C3#12014yes—
498C23×C3#12114yes—
499C23×C3#12114yes—
500C23×C3#12314yes—
501C23×C3C23×C411yescharacteristic
502C23×C3C22×D411yescharacteristic
503C23×C3C22×D411yescharacteristic
504C23×C3C22×D411yescharacteristic
505C23×C3C22×D412yes—
506C23×C3C22×D411yescharacteristic
507C23×C3C2×#4111yescharacteristic
508C23×C3C2×#4111yescharacteristic
509C23×C3C2×#4112yes—
510C23×C3H(5,𝔽2)12yes—
511C23×C3H(5,𝔽2)12yes—
512C22×D3—24no—
513C22×D3—22no—
514C22×D3—22no—
515C22×D3—24no—
516C22×D3—22no—
517C22×D3—22no—
518C22×D3—22no—
519C22×D3—22no—
520C22×D3—24no—
521C22×D3—24no—
522C22×D3—24no—
523C22×D3—24no—
524C22×D3—41no—
525C22×D3—41no—
526C22×D3—42no—
527C22×D3—41no—
528C22×D3—41no—
529C22×D3—42no—
530C22×D3—42no—
531C22×D3—42no—
532C22×D3—42no—
533C22×D3—42no—
534C22×D3C2×C22⋊C414yescomplemented
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—24no—
538C2×C3×C4—24no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—42no—
544C2×C3×C4—42no—
545C2×C3×C4—42no—
546C2×C3×C4—42no—
547C2×C3×C4—42no—
548C2×C3×C4—42no—
549C2×C3×C4—42no—
550C2×C3×C4—42no—
551C2×C3×C4—42no—
552#67—232no—
553#67—432no—
554C2×Dic3—22no—
555C2×Dic3—22no—
556C2×Dic3—22no—
557C2×Dic3—22no—
558C2×Dic3—22no—
559C2×Dic3—22no—
560C2×Dic3—22no—
561C2×Dic3—22no—
562C2×Dic3—24no—
563C2×Dic3—24no—
564C2×Dic3—24no—
565C2×Dic3—24no—
566C2×Dic3—24no—
567C2×Dic3—22no—
568C2×Dic3—22no—
569C2×Dic3—24no—
570C2×Dic3—22no—
571C2×Dic3—24no—
572C2×Dic3—24no—
573C2×Dic3—416no—
574C2×Dic3—416no—
575C2×Dic3—42no—
576C2×Dic3—42no—
577C2×Dic3—42no—
578C2×Dic3—42no—
579C2×Dic3—42no—
580C2×Dic3—42no—
581C2×Dic3—42no—
582C2×Dic3—42no—
583C2×Dic3—42no—
584C2×Dic3—42no—
585C2×Dic3C2×C22⋊C414yescomplemented
586C2×Dic3#12014yescomplemented
587C4×D3—416no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—28no—
593C24—28no—
594C24—216no—
595C24—28no—
596C24—216no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—28no—
610C24—28no—
611C24—32no—
612C24—32no—
613C24—32no—
614C24—48no—
615C24—48no—
616C24—48no—
617C24—48no—
618C24—48no—
619C24—48no—
620C24—48no—
621C24—48no—
622C24—48no—
623C24—44no—
624C24—44no—
625C24—48no—
626C24—44no—
627C24—44no—
628C24—44no—
629C24—44no—
630C24—61no—
631C24—61no—
632C24—62no—
633C24—61no—
634C24—62no—
635C24—62no—
636C24—62no—
637C24—61no—
638C24C2×C4×D314yes—
639C24C2×C4×D312yes—
640C24#23512yes—
641C24D3×D414yes—
642C24D3×D412yes—
643C24D3×D412yes—
644C24D3×D412yes—
645C24#23714yes—
646C24#23712yes—
647C24C2×#6712yes—
648C24C23×D311yescharacteristic
649C2×D4—316no—
650C2×D4—68no—
651C2×D4—68no—
652C2×D4—68no—
653C2×D4—68no—
654C2×D4—68no—
655C2×D4—68no—
656C2×D4—616no—
657C2×D4—616no—
658C2×D4—128no—
659C2×D4—128no—
660C2×D4—128no—
661C2×D4—128no—
662C2×D4—128no—
663C22×C4—22no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—32no—
679C22×C4—32no—
680C22×C4—34no—
681C22×C4—32no—
682C22×C4—32no—
683C22×C4—34no—
684C22×C4—34no—
685C22×C4—32no—
686C22×C4—68no—
687C22×C4—68no—
688C22×C4—61no—
689C22×C4—61no—
690C22×C4—61no—
691C22×C4—61no—
692C22×C4—62no—
693C22×C4—61no—
694C22×C4—61no—
695C22×C4—68no—
696C22×C4—68no—
697C22×C4—62no—
698C22×C4—62no—
699C22×C4—62no—
700C22×C4—62no—
701C22×C4—62no—
702C22×C4—62no—
703C22×C4—62no—
704C22×C4—62no—
705C22×C4—61no—
706C22×C4—62no—
707C22×C4—62no—
708C22×C4—62no—
709C22×C4—62no—
710C22×C4—62no—
711C22×C4—62no—
712C22×C4—61no—
713C22×C4—128no—
714C22×C4—124no—
715C22×C4—128no—
716C22×C4—124no—
717C22×C4—124no—
718C22×C4—128no—
719C22×C4—128no—
720C22×C4—128no—
721C22×C4—128no—
722C22×C4—124no—
723C22×C4—124no—
724C22×C4C2×#6712yes—
725C22×C4C2×#6712yes—
726C4⋊C4—68no—
727C22⋊C4—28no—
728C22⋊C4—48no—
729C22⋊C4—48no—
730C22⋊C4—44no—
731C22⋊C4—68no—
732C22⋊C4—616no—
733C22⋊C4—616no—
734C22⋊C4—616no—
735C22⋊C4—68no—
736C22⋊C4—128no—
737C42—68no—
738C22×C3—24no—
739C22×C3—28no—
740C22×C3—28no—
741C22×C3—24no—
742C22×C3—24no—
743C22×C3—24no—
744C22×C3—28no—
745C22×C3—28no—
746C22×C3—24no—
747C22×C3—24no—
748C22×C3—28no—
749C22×C3—28no—
750C22×C3—28no—
751C22×C3—464no—
752C22×C3—44no—
753C22×C3—44no—
754C22×C3—44no—
755C22×C3—44no—
756C22×C3—44no—
757C22×C3—44no—
758C22×C3—44no—
759C22×C3—44no—
760C22×C3—44no—
761C22×C3—44no—
762C22×C3—44no—
763C22×C3—44no—
764C22×C3#38618yescomplemented
765C22×C3C22×C22⋊C411yescharacteristic
766C22×C3C2×C4×D411yescharacteristic
767C22×C3C2×C4×D412yes—
768C22×C3C2×C4×D411yescharacteristic
769C22×C3#51812yes—
770C22×C3C2×#12011yescharacteristic
771C22×C3C2×#12011yescharacteristic
772C22×C3C2×#12111yescharacteristic
773C22×C3C2×#12111yescharacteristic
774C22×C3C2×#12311yescharacteristic
775C22×C3#52511yescharacteristic
776C22×C3#52512yes—
777C22×C3#53411yescharacteristic
778C22×C3#53511yescharacteristic
779C22×C3#53812yes—
780C22×C3D4212yes—
781C22×C3D4212yes—
782C22×C3D4212yes—
783C22×C3#54612yes—
784C22×C3#54612yes—
785C22×C3#54612yes—
786C22×C3#54612yes—
787C22×C3#55112yes—
788C2×D3—28no—
789C2×D3—24no—
790C2×D3—42no—
791C2×D3—44no—
792C2×D3—42no—
793C2×D3—42no—
794C2×D3—42no—
795C2×D3—44no—
796C2×D3—44no—
797C2×D3—42no—
798C2×D3—42no—
799C3×C4—42no—
800C3×C4—42no—
801C3×C4—82no—
802Dic3—24no—
803Dic3—24no—
804Dic3—44no—
805Dic3—42no—
806Dic3—44no—
807C23—24no—
808C23—24no—
809C23—24no—
810C23—24no—
811C23—24no—
812C23—24no—
813C23—22no—
814C23—24no—
815C23—22no—
816C23—22no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—24no—
821C23—22no—
822C23—24no—
823C23—232no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—24no—
839C23—24no—
840C23—24no—
841C23—24no—
842C23—34no—
843C23—432no—
844C23—432no—
845C23—416no—
846C23—416no—
847C23—432no—
848C23—416no—
849C23—416no—
850C23—432no—
851C23—416no—
852C23—416no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—42no—
862C23—42no—
863C23—42no—
864C23—42no—
865C23—42no—
866C23—42no—
867C23—42no—
868C23—42no—
869C23—64no—
870C23—62no—
871C23—64no—
872C23—62no—
873C23—62no—
874C23—62no—
875C23—62no—
876C23—62no—
877C23—64no—
878C23—64no—
879C23—64no—
880C23—64no—
881C23—122no—
882C23—122no—
883C23—122no—
884C23—122no—
885C23—122no—
886C23—121no—
887C23—121no—
888C23—121no—
889C23—121no—
890C23—122no—
891C23D3×C22⋊C414yes—
892C23#67⋊C414yes—
893C23#67⋊C418yescomplemented
894C23#88314yes—
895C23#88414yes—
896C23C4×#6714yes—
897C23#93714yes—
898C23#93814yes—
899C23C22×C4×D311yescharacteristic
900C23C2×#23511yescharacteristic
901C23C2×D3×D411yescharacteristic
902C23C2×D3×D411yescharacteristic
903C23C2×D3×D411yescharacteristic
904C23C2×D3×D412yes—
905C23C2×#23711yescharacteristic
906C23C2×#23712yes—
907C23#100412yes—
908C23#100412yes—
909C23C22×#6711yescharacteristic
910D4—632no—
911D4—1232no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—34no—
917C2×C4—34no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—41no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—42no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—62no—
932C2×C4—62no—
933C2×C4—62no—
934C2×C4—62no—
935C2×C4—62no—
936C2×C4—62no—
937C2×C4—62no—
938C2×C4—64no—
939C2×C4—62no—
940C2×C4—64no—
941C2×C4—64no—
942C2×C4—64no—
943C2×C4—64no—
944C2×C4—64no—
945C2×C4—62no—
946C2×C4—64no—
947C2×C4—62no—
948C2×C4—62no—
949C2×C4—64no—
950C2×C4—1216no—
951C2×C4—1216no—
952C2×C4—1216no—
953C2×C4—122no—
954C2×C4—122no—
955C2×C4—122no—
956C2×C4—122no—
957C2×C4—122no—
958C2×C4—122no—
959C2×C4—122no—
960C2×C4—122no—
961C2×C4—122no—
962C2×C4—122no—
963C2×C3—28no—
964C2×C3—48no—
965C2×C3C2×#38611yescharacteristic
966C2×C3C4×#12011yescharacteristic
967C2×C3#232111yescharacteristic
968C2×C3D4×C22⋊C412yes—
969C2×C3#235812yes—
970C2×C3#240311yescharacteristic
971C2×C3#240411yescharacteristic
972C2×C3#240811yescharacteristic
973C2×C3#241812yes—
974C2×C3#242412yes—
975C2×C3#253411yescharacteristic
976D3—44no—
977C22—24no—
978C22—24no—
979C22—24no—
980C22—28no—
981C22—24no—
982C22—28no—
983C22—24no—
984C22—28no—
985C22—24no—
986C22—28no—
987C22—28no—
988C22—28no—
989C22—28no—
990C22—464no—
991C22—44no—
992C22—44no—
993C22—44no—
994C22—44no—
995C22—44no—
996C22—44no—
997C22—44no—
998C22—44no—
999C22—44no—
1000C22—44no—
1001C22—44no—
1002C22—44no—
1003C22—68no—
1004C22—64no—
1005C22—122no—
1006C22—122no—
1007C22—122no—
1008C22—124no—
1009C22—122no—
1010C22—122no—
1011C22—124no—
1012C22—122no—
1013C22—124no—
1014C22#495618yescomplemented
1015C22C2×D3×C22⋊C411yescharacteristic
1016C22C2×#67⋊C411yescharacteristic
1017C22C2×#67⋊C412yes—
1018C22#548612yes—
1019C22C2×#88311yescharacteristic
1020C22C2×#88411yescharacteristic
1021C22#549012yes—
1022C22#549512yes—
1023C22#558612yes—
1024C22#558611yescharacteristic
1025C22D3×#12011yescharacteristic
1026C22#558911yescharacteristic
1027C22#559012yes—
1028C22#559012yes—
1029C22#559112yes—
1030C22#559112yes—
1031C22#559211yescharacteristic
1032C22#559312yes—
1033C22C2×C4×#6711yescharacteristic
1034C22C2×#93711yescharacteristic
1035C22C2×#93811yescharacteristic
1036C22D4×#6712yes—
1037C22#580612yes—
1038C4—42no—
1039C4—42no—
1040C4—64no—
1041C4—64no—
1042C4—82no—
1043C4—124no—
1044C4—124no—
1045C4—122no—
1046C3#1396711yescharacteristic, complemented, Sylow
1047C2—28no—
1048C2—48no—
1049C2—124no—
1050C2#7381811yescharacteristic
1051C2#7382111yescharacteristic
1052C2#7382411yescharacteristic
1053C2#7382612yes—
1054C2#7383411yescharacteristic
1055C2#7385012yes—
1056C2#8209912yes—
1057C2C2×#495611yescharacteristic
1058C2#8258111yescharacteristic
1059C2#8258612yes—
1060C2#8260411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC2×C3×#379C2
socle, cosocleC24×C3C24
prime radicalC22×#953C2
hypercenterC2×#379D3
hypocenterC3#13967
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
2. C23×#217C2semidirect
3. C22×#67⋊C4C2semidirect
4. C2×C3×#379C2semidirect
5. C2×#4956C2semidirect
6. C2×#4958C2semidirect
7. #71550C2semidirect
8. #71547C2semidirect
9. #71545C2semidirect
10. #71544C2semidirect
11. #71544C2semidirect
18. C23×C4×D3C22semidirect
25. C2×#953C4semidirect
32. C22×(C2×D3)⋊C4C22semidirect
33. C22×(C2×D3)⋊C4C22semidirect
34. C22×Dic3⋊C4C22semidirect
35. C22×C4×Dic3C22semidirect
40. C2×C3⋊#95C22semidirect
41. C2×C3⋊#95C22semidirect
42. C2×C3⋊#95C22semidirect
43. C2×C3⋊#95C22semidirect
44. C2×C3⋊#95C22semidirect
52. C2×#379D3semidirect
68. C25×C3C2×C4semidirect
86. C22×#67C2×C4semidirect
98. C23×Dic3D4semidirect
120. C2×C3×C22⋊C4D4semidirect
132. C2×#217C2×C4semidirect
133. C2×#217C2×C4semidirect
134. C2×#217D4semidirect
278. C2×#67C22⋊C4semidirect
348. C25C4×D3semidirect
423. C2×C22⋊C4#67semidirect
496. C23×C3C4×D4semidirect
534. C22×D3C2×C22⋊C4semidirect
585. C2×Dic3C2×C22⋊C4semidirect
586. C2×Dic3#120semidirect
764. C22×C3#386semidirect
893. C23#67⋊C4semidirect
1014. C22#4956semidirect
1046. C3#13967semidirect

Maximal subgroups

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

subgroupindex
C22×#9532
C23×#2172
C22×#67⋊C42
C2×C3×#3792
C2×#49562
C2×#49582
#715502
#715472
#715452
#715442
#139673