Finite Group Databasebeta

← #10729195

Subgroups — #10729195

Order 768.

3030 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#935C211yesmaximal, characteristic, complemented
2C22×#939C211yesmaximal, characteristic
3C22×#886C211yesmaximal, characteristic, complemented
4C2×C3×#386C211yesmaximal, characteristic, complemented
5C2×#5213C211yesmaximal, characteristic, complemented
6C22×C3⋊#95C211yesmaximal, characteristic, complemented
7#71550C212yesmaximal, complemented
8#71546C212yesmaximal, complemented
9#71544C211yesmaximal, characteristic, complemented
10#69428C212yesmaximal, complemented
11#69420C212yesmaximal, complemented
12#14926—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C23×#67C2211yescharacteristic
16C23×#67C2211yescharacteristic
17C24×Dic3C2211yescharacteristic
18C24×Dic3C2211yescharacteristic
19C22×C3×C22⋊C4C2212yes—
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×#217C2211yescharacteristic
22C22×#217C2212yes—
23C22×#217C2211yescharacteristic
24C2×#939—24no—
25C2×#939—24no—
26C2×#939—24no—
27C2×#935—24no—
28C2×#935—24no—
29C2×#935—24no—
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2212yes—
32C22×(C2×D3)⋊C4C2212yes—
33C22×C4⋊Dic3C2212yes—
34C22×Dic3⋊C4C2211yescharacteristic
35C22×Dic3⋊C4C2212yes—
36C2×#886—24no—
37C2×#886—24no—
38C2×#886—24no—
39C3×#386—24no—
40C2×C3×#95C2212yes—
41#5213—24no—
42C2×C3⋊#95—24no—
43C2×C3⋊#95C2212yes—
44C2×C3⋊#95C2212yes—
45C2×C3⋊#95C2212yes—
46C2×C3⋊#95C2212yes—
47C2×C3⋊#95C2212yes—
48C22×#123—31no—
49C22×#123—31no—
50C22×#121—31no—
51C2×#386—31no—
52C2×#386D311yescharacteristic, complemented
53C22×#95—31no—
54#1444—32no—
55#1439—32no—
56#1439—32no—
57#1438—32no—
58C22⋊#95—31no—
59C25×C3C2311yescharacteristic
60C25×C3C2311yescharacteristic
61C24×D3C2311yescharacteristic
62C22×C3×D4—22no—
63C22×C3×D4—22no—
64C22×C3×D4—22no—
65C22×C3×D4—22no—
66C22×C3×D4—22no—
67C22×C3×D4—22no—
68C22×C3×D4D414yes—
69C23×C3×C4—22no—
70C23×C3×C4—24no—
71C23×C3×C4—22no—
72C23×C3×C4—22no—
73C23×C3×C4—42no—
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2312yes—
76C23×C3×C4C2312yes—
77C22×#67—22no—
78C22×#67—22no—
79C22×#67—22no—
80C22×#67—22no—
81C22×#67—22no—
82C22×#67—22no—
83C22×#67—22no—
84C22×#67—22no—
85C22×#67—22no—
86C22×#67—24no—
87C22×#67—42no—
88C22×#67D414yes—
89C23×Dic3—22no—
90C23×Dic3—22no—
91C23×Dic3—22no—
92C23×Dic3—22no—
93C23×Dic3—22no—
94C23×Dic3—22no—
95C23×Dic3—22no—
96C23×Dic3—22no—
97C23×Dic3—24no—
98C23×Dic3—42no—
99C23×Dic3D414yes—
100C23×Dic3D414yescomplemented
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2312yes—
103C23×Dic3C2311yescharacteristic
104C23×Dic3C2312yes—
105C23×Dic3C2311yescharacteristic
106C2×C3×C22⋊C4—22no—
107C2×C3×C22⋊C4—22no—
108C2×C3×C22⋊C4—24no—
109C2×C3×C22⋊C4—24no—
110C2×C3×C22⋊C4—42no—
111C2×C3×C22⋊C4D414yescomplemented
112C2×#217—24no—
113C2×#217—22no—
114C2×#217—22no—
115C2×#217—22no—
116C2×#217—24no—
117C2×#217—24no—
118C2×#217—22no—
119C2×#217—22no—
120C2×#217D414yescomplemented
121#939—232no—
122#935—232no—
123C2×(C2×D3)⋊C4—24no—
124C2×(C2×D3)⋊C4—22no—
125C2×(C2×D3)⋊C4—24no—
126C2×(C2×D3)⋊C4—22no—
127C2×(C2×D3)⋊C4—24no—
128C2×(C2×D3)⋊C4—22no—
129C2×(C2×D3)⋊C4—24no—
130C2×(C2×D3)⋊C4—24no—
131C2×(C2×D3)⋊C4—42no—
132C2×C4⋊Dic3—24no—
133C2×C4⋊Dic3—24no—
134C2×C4⋊Dic3—24no—
135C2×Dic3⋊C4—24no—
136C2×Dic3⋊C4—22no—
137C2×Dic3⋊C4—24no—
138C2×Dic3⋊C4—24no—
139C2×Dic3⋊C4—22no—
140C2×Dic3⋊C4—22no—
141#886—232no—
142C3×#95—24no—
143C3⋊#95—24no—
144C3⋊#95—24no—
145C3⋊#95—24no—
146C3⋊#95—24no—
147C3⋊#95—42no—
148C23×D4—31no—
149C23×D4—31no—
150C23×D4C2×D311yescharacteristic
151C24×C4—31no—
152C24×C4—31no—
153C24×C4C2×D311yescharacteristic
154C2×#123—64no—
155C2×#123—64no—
156C2×#123—64no—
157C2×#123—64no—
158C2×#123—64no—
159C2×#123—64no—
160C2×#121—64no—
161C2×#121—64no—
162C2×#121—64no—
163C22×C4⋊C4—31no—
164C22×C4⋊C4—32no—
165C22×C4⋊C4—32no—
166C22×C22⋊C4—31no—
167C22×C22⋊C4—31no—
168C22×C22⋊C4—32no—
169C22×C22⋊C4—31no—
170C22×C22⋊C4—32no—
171C22×C22⋊C4—32no—
172C22×C22⋊C4C2×D312yes—
173C22×C22⋊C4C2×D311yescharacteristic
174#386—24no—
175#386—64no—
176C2×#95—32no—
177C2×#95—32no—
178C2×#95—32no—
179C2×#95—32no—
180C2×#95—32no—
181C2×#95—64no—
182C2×#95C2×D312yes—
183C24×C3—22no—
184C24×C3—22no—
185C24×C3—22no—
186C24×C3—22no—
187C24×C3—21no—
188C24×C3—21no—
189C24×C3—21no—
190C24×C3—21no—
191C24×C3—21no—
192C24×C3—22no—
193C24×C3—22no—
194C24×C3—21no—
195C24×C3—22no—
196C24×C3—22no—
197C24×C3C2×D412yes—
198C24×C3C2×D412yes—
199C24×C3C2×D412yes—
200C24×C3C2×D412yes—
201C24×C3C2×D412yes—
202C24×C3C2×D412yes—
203C24×C3C2×D412yes—
204C24×C3#4112yes—
205C24×C3C2411yescharacteristic
206C23×D3—21no—
207C23×D3—21no—
208C23×D3—21no—
209C23×D3—21no—
210C23×D3—21no—
211C23×D3—22no—
212C23×D3—21no—
213C23×D3—22no—
214C23×D3—22no—
215C23×D3—22no—
216C23×D3C2×D412yes—
217C2×C3×D4—28no—
218C2×C3×D4—28no—
219C2×C3×D4—28no—
220C2×C3×D4—44no—
221C2×C3×D4—44no—
222C2×C3×D4—44no—
223C2×C3×D4—44no—
224C22×C3×C4—28no—
225C22×C3×C4—22no—
226C22×C3×C4—22no—
227C22×C3×C4—21no—
228C22×C3×C4—22no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—22no—
234C22×C3×C4—22no—
235C22×C3×C4—22no—
236C22×C3×C4—22no—
237C22×C3×C4—22no—
238C22×C3×C4—21no—
239C22×C3×C4—22no—
240C22×C3×C4—22no—
241C22×C3×C4—22no—
242C22×C3×C4—22no—
243C22×C3×C4—48no—
244C22×C3×C4—48no—
245C22×C3×C4—44no—
246C22×C3×C4—44no—
247C22×C3×C4C2×D412yes—
248C22×C3×C4C2×D414yes—
249C22×C3×C4#4114yes—
250C2×#67—28no—
251C2×#67—28no—
252C2×#67—28no—
253C2×#67—28no—
254C2×#67—48no—
255C2×#67—48no—
256C2×#67—44no—
257C2×#67—44no—
258C2×#67—44no—
259C2×#67—44no—
260C2×#67—44no—
261C2×#67—44no—
262C22×Dic3—21no—
263C22×Dic3—21no—
264C22×Dic3—22no—
265C22×Dic3—28no—
266C22×Dic3—28no—
267C22×Dic3—28no—
268C22×Dic3—28no—
269C22×Dic3—22no—
270C22×Dic3—21no—
271C22×Dic3—22no—
272C22×Dic3—22no—
273C22×Dic3—22no—
274C22×Dic3—22no—
275C22×Dic3—21no—
276C22×Dic3—21no—
277C22×Dic3—21no—
278C22×Dic3—21no—
279C22×Dic3—22no—
280C22×Dic3—22no—
281C22×Dic3—21no—
282C22×Dic3—21no—
283C22×Dic3—22no—
284C22×Dic3—22no—
285C22×Dic3—22no—
286C22×Dic3—22no—
287C22×Dic3—21no—
288C22×Dic3—22no—
289C22×Dic3—22no—
290C22×Dic3—22no—
291C22×Dic3—28no—
292C22×Dic3—44no—
293C22×Dic3—48no—
294C22×Dic3—48no—
295C22×Dic3—44no—
296C22×Dic3—44no—
297C22×Dic3—44no—
298C22×Dic3—44no—
299C22×Dic3C2×D412yes—
300C22×Dic3C2×D414yes—
301C22×Dic3C2×D412yes—
302C22×Dic3C2×D414yes—
303C22×Dic3C2×D412yes—
304C22×Dic3#4114yes—
305C3×C22⋊C4—28no—
306C3×C22⋊C4—48no—
307#217—216no—
308#217—28no—
309#217—28no—
310(C2×D3)⋊C4—216no—
311(C2×D3)⋊C4—28no—
312(C2×D3)⋊C4—48no—
313C4⋊Dic3—216no—
314Dic3⋊C4—216no—
315Dic3⋊C4—28no—
316C25—31no—
317C25C22×D311yescharacteristic
318C25C22×D311yescharacteristic
319C22×D4—22no—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4—22no—
325C22×D4—34no—
326C22×D4—62no—
327C22×D4—64no—
328C22×D4—62no—
329C22×D4—62no—
330C22×D4—62no—
331C22×D4—62no—
332C22×D4—62no—
333C22×D4—62no—
334C22×D4—62no—
335C22×D4—62no—
336C22×D4—122no—
337C22×D4D1214yes—
338C23×C4—22no—
339C23×C4—24no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—31no—
343C23×C4—34no—
344C23×C4—32no—
345C23×C4—32no—
346C23×C4—31no—
347C23×C4—31no—
348C23×C4—34no—
349C23×C4—42no—
350C23×C4—64no—
351C23×C4—62no—
352C23×C4—62no—
353C23×C4—62no—
354C23×C4—62no—
355C23×C4—62no—
356C23×C4—62no—
357C23×C4—62no—
358C23×C4—62no—
359C23×C4—122no—
360C23×C4C22×D311yescharacteristic
361C23×C4C22×D312yes—
362C23×C4C22×D312yes—
363#123—632no—
364#123—632no—
365#121—632no—
366C2×C4⋊C4—62no—
367C2×C4⋊C4—62no—
368C2×C4⋊C4—64no—
369C2×C4⋊C4—64no—
370C2×C4⋊C4—64no—
371C2×C4⋊C4—64no—
372C2×C4⋊C4—62no—
373C2×C4⋊C4—64no—
374C2×C4⋊C4—64no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—34no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—62no—
382C2×C22⋊C4—64no—
383C2×C22⋊C4—62no—
384C2×C22⋊C4—64no—
385C2×C22⋊C4—62no—
386C2×C22⋊C4—62no—
387C2×C22⋊C4—64no—
388C2×C22⋊C4—64no—
389C2×C22⋊C4—62no—
390C2×C22⋊C4—64no—
391C2×C22⋊C4—62no—
392C2×C22⋊C4—62no—
393C2×C22⋊C4—62no—
394C2×C22⋊C4—64no—
395C2×C22⋊C4—64no—
396C2×C22⋊C4—64no—
397C2×C22⋊C4—122no—
398C2×C22⋊C4#6714yescomplemented
399#95—24no—
400#95—64no—
401#95—64no—
402#95—64no—
403#95—64no—
404#95—122no—
405C23×C3—22no—
406C23×C3—22no—
407C23×C3—24no—
408C23×C3—24no—
409C23×C3—22no—
410C23×C3—22no—
411C23×C3—24no—
412C23×C3—24no—
413C23×C3—24no—
414C23×C3—24no—
415C23×C3—24no—
416C23×C3—24no—
417C23×C3—24no—
418C23×C3—24no—
419C23×C3—24no—
420C23×C3—24no—
421C23×C3—22no—
422C23×C3—22no—
423C23×C3—22no—
424C23×C3—24no—
425C23×C3—24no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3—42no—
432C23×C3—41no—
433C23×C3—42no—
434C23×C3—41no—
435C23×C3—41no—
436C23×C3—42no—
437C23×C3—42no—
438C23×C3—42no—
439C23×C3—42no—
440C23×C3—42no—
441C23×C3—42no—
442C23×C3—42no—
443C23×C3—42no—
444C23×C3#12014yes—
445C23×C3#12014yes—
446C23×C3#12014yes—
447C23×C3#12114yes—
448C23×C3#12114yes—
449C23×C3#12114yes—
450C23×C3#12714yes—
451C23×C3C22×D411yescharacteristic
452C23×C3C22×D411yescharacteristic
453C23×C3C22×D411yescharacteristic
454C23×C3C22×D411yescharacteristic
455C23×C3C22×D411yescharacteristic
456C23×C3C22×D411yescharacteristic
457C23×C3C2×#4111yescharacteristic
458C23×C3C2×#4112yes—
459C23×C3C2×#4112yes—
460C23×C3H(5,𝔽2)12yes—
461C23×C32−1+412yes—
462C22×D3—22no—
463C22×D3—22no—
464C22×D3—22no—
465C22×D3—24no—
466C22×D3—24no—
467C22×D3—41no—
468C22×D3—41no—
469C22×D3—41no—
470C22×D3—41no—
471C22×D3—41no—
472C22×D3—42no—
473C22×D3—41no—
474C22×D3—42no—
475C22×D3—41no—
476C22×D3—41no—
477C22×D3—42no—
478C22×D3—42no—
479C22×D3—42no—
480C22×D3—42no—
481C22×D3—42no—
482C22×D3—42no—
483C22×D3—42no—
484C22×D3—42no—
485C3×D4—416no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—24no—
489C2×C3×C4—22no—
490C2×C3×C4—24no—
491C2×C3×C4—24no—
492C2×C3×C4—24no—
493C2×C3×C4—24no—
494C2×C3×C4—24no—
495C2×C3×C4—416no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—42no—
500C2×C3×C4—41no—
501C2×C3×C4—42no—
502C2×C3×C4—42no—
503C2×C3×C4—42no—
504C2×C3×C4—42no—
505C2×C3×C4—42no—
506C2×C3×C4—42no—
507C2×C3×C4—42no—
508#67—416no—
509#67—416no—
510C2×Dic3—22no—
511C2×Dic3—22no—
512C2×Dic3—24no—
513C2×Dic3—24no—
514C2×Dic3—24no—
515C2×Dic3—24no—
516C2×Dic3—22no—
517C2×Dic3—22no—
518C2×Dic3—24no—
519C2×Dic3—22no—
520C2×Dic3—24no—
521C2×Dic3—22no—
522C2×Dic3—22no—
523C2×Dic3—22no—
524C2×Dic3—24no—
525C2×Dic3—24no—
526C2×Dic3—416no—
527C2×Dic3—42no—
528C2×Dic3—41no—
529C2×Dic3—42no—
530C2×Dic3—42no—
531C2×Dic3—41no—
532C2×Dic3—41no—
533C2×Dic3—42no—
534C2×Dic3—41no—
535C2×Dic3—42no—
536C2×Dic3—42no—
537C2×Dic3—42no—
538C2×Dic3—42no—
539C2×Dic3—42no—
540C2×Dic3—42no—
541C2×Dic3—416no—
542C2×Dic3#12314yescomplemented
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—21no—
548C24—21no—
549C24—21no—
550C24—21no—
551C24—21no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—21no—
557C24—32no—
558C24—61no—
559C24—61no—
560C24—61no—
561C24—61no—
562C24—61no—
563C24—62no—
564C24—62no—
565C24—62no—
566C24—62no—
567C24—61no—
568C24C2×D1212yes—
569C24C2×D1212yes—
570C24#23512yes—
571C24D3×D412yes—
572C24D3×D412yes—
573C24D3×D412yes—
574C24D3×D412yes—
575C24C2×#6712yes—
576C24C23×D311yescharacteristic
577C2×D4—28no—
578C2×D4—28no—
579C2×D4—28no—
580C2×D4—44no—
581C2×D4—44no—
582C2×D4—44no—
583C2×D4—44no—
584C2×D4—68no—
585C2×D4—68no—
586C2×D4—68no—
587C2×D4—68no—
588C2×D4—124no—
589C2×D4—128no—
590C2×D4—128no—
591C2×D4—124no—
592C2×D4—124no—
593C2×D4—124no—
594C2×D4—124no—
595C2×D4—124no—
596C22×C4—28no—
597C22×C4—21no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—21no—
614C22×C4—22no—
615C22×C4—32no—
616C22×C4—34no—
617C22×C4—32no—
618C22×C4—34no—
619C22×C4—34no—
620C22×C4—32no—
621C22×C4—48no—
622C22×C4—48no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—68no—
626C22×C4—61no—
627C22×C4—61no—
628C22×C4—62no—
629C22×C4—68no—
630C22×C4—68no—
631C22×C4—68no—
632C22×C4—68no—
633C22×C4—62no—
634C22×C4—61no—
635C22×C4—62no—
636C22×C4—61no—
637C22×C4—62no—
638C22×C4—61no—
639C22×C4—62no—
640C22×C4—61no—
641C22×C4—62no—
642C22×C4—61no—
643C22×C4—62no—
644C22×C4—62no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4—62no—
648C22×C4—62no—
649C22×C4—62no—
650C22×C4—62no—
651C22×C4—62no—
652C22×C4—62no—
653C22×C4—62no—
654C22×C4—61no—
655C22×C4—124no—
656C22×C4—128no—
657C22×C4—128no—
658C22×C4—124no—
659C22×C4—124no—
660C22×C4—124no—
661C22×C4—124no—
662C22×C4C2×D1212yes—
663C22×C4#23714yes—
664C22×C4C2×#6714yes—
665C4⋊C4—68no—
666C4⋊C4—616no—
667C4⋊C4—616no—
668C22⋊C4—28no—
669C22⋊C4—48no—
670C22⋊C4—68no—
671C22⋊C4—616no—
672C22⋊C4—68no—
673C22⋊C4—616no—
674C22⋊C4—68no—
675C22⋊C4—128no—
676C22×C3—24no—
677C22×C3—24no—
678C22×C3—24no—
679C22×C3—24no—
680C22×C3—28no—
681C22×C3—28no—
682C22×C3—28no—
683C22×C3—28no—
684C22×C3—24no—
685C22×C3—24no—
686C22×C3—42no—
687C22×C3—42no—
688C22×C3—42no—
689C22×C3—44no—
690C22×C3—44no—
691C22×C3—81no—
692C22×C3—81no—
693C22×C3—82no—
694C22×C3—82no—
695C22×C3—81no—
696C22×C3—81no—
697C22×C3#39218yes—
698C22×C3C2×#12011yescharacteristic
699C22×C3C2×#12011yescharacteristic
700C22×C3C2×#12011yescharacteristic
701C22×C3C2×#12111yescharacteristic
702C22×C3C2×#12111yescharacteristic
703C22×C3C2×#12111yescharacteristic
704C22×C3C2×#12311yescharacteristic
705C22×C3#52511yescharacteristic
706C22×C3#52912yes—
707C22×C3C2×#12711yescharacteristic
708C22×C3#53212yes—
709C22×C3#53411yescharacteristic
710C22×C3#53611yescharacteristic
711C22×C3#53712yes—
712C22×C3#53912yes—
713C22×C3#54612yes—
714C22×C3#54612yes—
715C22×C3#54612yes—
716C22×C3#54612yes—
717C22×C3#54712yes—
718C22×C3#54712yes—
719C22×C3#54712yes—
720C22×C3#54712yes—
721C2×D3—42no—
722C2×D3—42no—
723C2×D3—42no—
724C2×D3—44no—
725C2×D3—44no—
726C2×D3—81no—
727C2×D3—81no—
728C2×D3—82no—
729C2×D3—82no—
730C2×D3—81no—
731C2×D3—81no—
732C3×C4—42no—
733C3×C4—44no—
734C3×C4—44no—
735Dic3—24no—
736Dic3—44no—
737Dic3—42no—
738Dic3—42no—
739Dic3—44no—
740C23—22no—
741C23—22no—
742C23—24no—
743C23—24no—
744C23—24no—
745C23—24no—
746C23—24no—
747C23—24no—
748C23—24no—
749C23—22no—
750C23—22no—
751C23—24no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—24no—
760C23—24no—
761C23—41no—
762C23—41no—
763C23—42no—
764C23—41no—
765C23—41no—
766C23—42no—
767C23—41no—
768C23—41no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—41no—
773C23—41no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—62no—
780C23—62no—
781C23—62no—
782C23—64no—
783C23—64no—
784C23—121no—
785C23—121no—
786C23—122no—
787C23—121no—
788C23—121no—
789C23—121no—
790C23—122no—
791C23—121no—
792C23—122no—
793C23—122no—
794C23—122no—
795C23—122no—
796C23—122no—
797C23—121no—
798C23—121no—
799C23—122no—
800C23—122no—
801C23—122no—
802C23#88214yes—
803C23#88214yes—
804C23#88414yes—
805C23#88414yes—
806C23#93014yes—
807C23#93714yes—
808C23#94014yes—
809C23C22×D1211yescharacteristic
810C23C2×#23511yescharacteristic
811C23C2×D3×D411yescharacteristic
812C23C2×D3×D411yescharacteristic
813C23C2×D3×D411yescharacteristic
814C23C2×D3×D411yescharacteristic
815C23C2×#23712yes—
816C23#100412yes—
817C23D3×#4112yes—
818C23#101012yes—
819C23C22×#6711yescharacteristic
820D4—416no—
821D4—1216no—
822D4—1216no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—24no—
831C2×C4—24no—
832C2×C4—34no—
833C2×C4—416no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—42no—
838C2×C4—41no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—62no—
847C2×C4—64no—
848C2×C4—62no—
849C2×C4—64no—
850C2×C4—62no—
851C2×C4—64no—
852C2×C4—64no—
853C2×C4—62no—
854C2×C4—64no—
855C2×C4—62no—
856C2×C4—64no—
857C2×C4—62no—
858C2×C4—64no—
859C2×C4—62no—
860C2×C4—62no—
861C2×C4—64no—
862C2×C4—1216no—
863C2×C4—1216no—
864C2×C4—122no—
865C2×C4—121no—
866C2×C4—122no—
867C2×C4—121no—
868C2×C4—122no—
869C2×C4—121no—
870C2×C4—122no—
871C2×C4—121no—
872C2×C4—122no—
873C2×C4—122no—
874C2×C4—122no—
875C2×C4—122no—
876C2×C4—122no—
877C2×C4—122no—
878C2×C3—28no—
879C2×C3—82no—
880C2×C3C2×#39211yescharacteristic
881C2×C3#240511yescharacteristic
882C2×C3#240611yescharacteristic
883C2×C3#242512yes—
884C2×C3#242512yes—
885C2×C3#243012yes—
886C2×C3#243012yes—
887C2×C3#250111yescharacteristic
888C2×C3#253911yescharacteristic
889C2×C3#261811yescharacteristic
890C2×C3#285411yescharacteristic
891D3—82no—
892C22—24no—
893C22—24no—
894C22—24no—
895C22—24no—
896C22—28no—
897C22—24no—
898C22—24no—
899C22—28no—
900C22—28no—
901C22—28no—
902C22—44no—
903C22—42no—
904C22—42no—
905C22—44no—
906C22—42no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—82no—
912C22—82no—
913C22—122no—
914C22—122no—
915C22—124no—
916C22—122no—
917C22—124no—
918C22—241no—
919C22—241no—
920C22—241no—
921C22—241no—
922C22—242no—
923C22—242no—
924C22#496018yes—
925C22C2×#88211yescharacteristic
926C22C2×#88211yescharacteristic
927C22C2×#88411yescharacteristic
928C22C2×#88411yescharacteristic
929C22#553812yes—
930C22#555412yes—
931C22#555512yes—
932C22#556412yes—
933C22#558611yescharacteristic
934C22#558911yescharacteristic
935C22#559112yes—
936C22#559612yes—
937C22#559712yes—
938C22#561012yes—
939C22#561112yes—
940C22#564811yescharacteristic
941C22D3×#12311yescharacteristic
942C22#565512yes—
943C22C2×#93011yescharacteristic
944C22C2×#93711yescharacteristic
945C22C2×#94011yescharacteristic
946C22#580612yes—
947C22#582412yes—
948C4—44no—
949C4—42no—
950C4—44no—
951C4—64no—
952C4—122no—
953C4—124no—
954C4—124no—
955C4—122no—
956C3#1492611yescharacteristic, complemented, Sylow
957C2—28no—
958C2—82no—
959C2—242no—
960C2#7468611yescharacteristic
961C2#7468711yescharacteristic
962C2#7469612yes—
963C2#7469912yes—
964C2#7478111yescharacteristic
965C2#7487211yescharacteristic
966C2C2×#496011yescharacteristic
967C2#8235512yes—
968C2#8259111yescharacteristic
969C2#8265112yes—
970C2#8285911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#386C2
prime radicalC22×#939C2
hypercenterC2×#386D3
hypocenterC3#14926
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#935C2semidirect
3. C22×#886C2semidirect
4. C2×C3×#386C2semidirect
5. C2×#5213C2semidirect
6. C22×C3⋊#95C2semidirect
7. #71550C2semidirect
8. #71546C2semidirect
9. #71544C2semidirect
10. #69428C2semidirect
11. #69420C2semidirect
52. C2×#386D3semidirect
100. C23×Dic3D4semidirect
111. C2×C3×C22⋊C4D4semidirect
120. C2×#217D4semidirect
398. C2×C22⋊C4#67semidirect
542. C2×Dic3#123semidirect
956. C3#14926semidirect

Maximal subgroups

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

subgroupindex
C22×#9352
C22×#9392
C22×#8862
C2×C3×#3862
C2×#52132
C22×C3⋊#952
#715502
#715462
#715442
#694282
#694202
#149263