Finite Group Databasebeta

← #10727094

Subgroups — #10727094

Order 768.

3510 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#939C212yesmaximal, complemented
2C22×#930C211yesmaximal, characteristic, complemented
3C2×C3×#386C211yesmaximal, characteristic, complemented
4C22×C3⋊#95C211yesmaximal, characteristic, complemented
5C2×#4960C211yesmaximal, characteristic, complemented
6C2×#4958C212yesmaximal, complemented
7#71550C212yesmaximal, complemented
8#71546C211yesmaximal, characteristic, complemented
9#69428C212yesmaximal, complemented
10#69426C211yesmaximal, characteristic, complemented
11#69420C211yesmaximal, characteristic, complemented
12#14757—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C23×#67C2212yes—
16C23×#67C2212yes—
17C24×Dic3C2212yes—
18C23×D12C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×#217C2212yes—
23C2×#939—28no—
24C2×#939—28no—
25C2×#939—28no—
26C2×#930—24no—
27C2×#930—28no—
28C22×(C2×D3)⋊C4C2212yes—
29C22×(C2×D3)⋊C4C2212yes—
30C22×(C2×D3)⋊C4C2212yes—
31C22×(C2×D3)⋊C4C2212yes—
32C22×C4⋊Dic3C2211yescharacteristic
33C22×Dic3⋊C4C2212yes—
34C3×#386—24no—
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3⋊#95—24no—
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2211yescharacteristic
40C2×C3⋊#95C2212yes—
41C2×C3⋊#95C2212yes—
42C2×C3⋊#95C2211yescharacteristic
43#4960—24no—
44#4958—28no—
45C22×#121—32no—
46C22×#121—31no—
47C2×#392—31no—
48C2×#386—32no—
49C2×#386D311yescharacteristic, complemented
50C22×#95—31no—
51#1444—31no—
52#1439—32no—
53#1439—31no—
54#1438—31no—
55#1438—32no—
56C25×C3C2311yescharacteristic
57C25×C3C2311yescharacteristic
58C24×D3C2312yes—
59C22×C3×D4—22no—
60C22×C3×D4—24no—
61C22×C3×D4—24no—
62C22×C3×D4—22no—
63C22×C3×D4D414yescomplemented
64C23×C3×C4—24no—
65C23×C3×C4—22no—
66C23×C3×C4—22no—
67C23×C3×C4—42no—
68C23×C3×C4D414yescomplemented
69C23×C3×C4C2311yescharacteristic
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C22×#67—24no—
75C22×#67—24no—
76C22×#67—24no—
77C22×#67—24no—
78C22×#67—24no—
79C22×#67—24no—
80C22×#67—24no—
81C22×#67—24no—
82C22×#67—24no—
83C22×#67—24no—
84C22×#67—24no—
85C22×#67—42no—
86C22×#67—42no—
87C22×#67D418yescomplemented
88C23×Dic3—24no—
89C23×Dic3—24no—
90C23×Dic3—24no—
91C23×Dic3—24no—
92C23×Dic3—42no—
93C23×Dic3—42no—
94C23×Dic3D418yescomplemented
95C23×Dic3C2312yes—
96C23×Dic3C2312yes—
97C23×Dic3C2312yes—
98C22×D12—24no—
99C22×D12—22no—
100C22×D12—22no—
101C22×D12—22no—
102C22×D12—42no—
103C2×C3×C22⋊C4—24no—
104C2×C3×C22⋊C4—22no—
105C2×C3×C22⋊C4—22no—
106C2×C3×C22⋊C4—22no—
107C2×C3×C22⋊C4—22no—
108C2×C3×C22⋊C4—22no—
109C2×C3×C22⋊C4—42no—
110C2×#217—24no—
111C2×#217—24no—
112C2×#217—24no—
113#939—264no—
114#930—232no—
115C2×(C2×D3)⋊C4—24no—
116C2×(C2×D3)⋊C4—24no—
117C2×(C2×D3)⋊C4—24no—
118C2×(C2×D3)⋊C4—24no—
119C2×(C2×D3)⋊C4—24no—
120C2×(C2×D3)⋊C4—24no—
121C2×(C2×D3)⋊C4—24no—
122C2×(C2×D3)⋊C4—24no—
123C2×(C2×D3)⋊C4—24no—
124C2×(C2×D3)⋊C4—24no—
125C2×(C2×D3)⋊C4—42no—
126C2×(C2×D3)⋊C4—42no—
127C2×C4⋊Dic3—22no—
128C2×C4⋊Dic3—24no—
129C2×Dic3⋊C4—24no—
130C2×Dic3⋊C4—24no—
131C2×Dic3⋊C4—24no—
132C3×#95—22no—
133C3×#95—22no—
134C3⋊#95—22no—
135C3⋊#95—24no—
136C3⋊#95—24no—
137C3⋊#95—24no—
138C3⋊#95D414yescomplemented
139C23×D4—32no—
140C23×D4—32no—
141C23×D4—31no—
142C23×D4C2×D311yescharacteristic
143C24×C4—32no—
144C24×C4C2×D311yescharacteristic
145C2×#121—68no—
146C2×#121—68no—
147C2×#121—68no—
148C2×#121—68no—
149C2×#121—64no—
150C22×C4⋊C4—32no—
151C22×C4⋊C4—31no—
152C22×C22⋊C4—32no—
153C22×C22⋊C4—32no—
154C22×C22⋊C4—32no—
155C22×C22⋊C4—32no—
156C22×C22⋊C4—32no—
157C22×C22⋊C4C2×D311yescharacteristic
158C22×C22⋊C4C2×D311yescharacteristic
159C22×C22⋊C4C2×D311yescharacteristic
160#392—64no—
161#386—24no—
162#386—68no—
163C2×#95—31no—
164C2×#95—32no—
165C2×#95—31no—
166C2×#95—32no—
167C2×#95—32no—
168C2×#95—64no—
169C2×#95C2×D311yescharacteristic
170C2×#95C2×D311yescharacteristic
171C24×C3—21no—
172C24×C3—22no—
173C24×C3—21no—
174C24×C3—21no—
175C24×C3—22no—
176C24×C3—21no—
177C24×C3—22no—
178C24×C3—22no—
179C24×C3—21no—
180C24×C3—21no—
181C24×C3—21no—
182C24×C3—22no—
183C24×C3—21no—
184C24×C3—22no—
185C24×C3—21no—
186C24×C3—21no—
187C24×C3C2×D412yes—
188C24×C3C2×D412yes—
189C24×C3C2×D414yes—
190C24×C3C2×D414yes—
191C24×C3C2×D412yes—
192C24×C3#4112yes—
193C24×C3C2411yescharacteristic
194C23×D3—22no—
195C23×D3—22no—
196C23×D3—22no—
197C23×D3—22no—
198C23×D3—22no—
199C23×D3—22no—
200C23×D3—22no—
201C23×D3—22no—
202C23×D3—22no—
203C23×D3—22no—
204C23×D3—22no—
205C23×D3—22no—
206C23×D3—22no—
207C23×D3—22no—
208C23×D3C2×D414yes—
209C2×C3×D4—216no—
210C2×C3×D4—28no—
211C2×C3×D4—44no—
212C2×C3×D4—48no—
213C2×C3×D4—44no—
214C22×C3×C4—22no—
215C22×C3×C4—22no—
216C22×C3×C4—28no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—22no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—22no—
225C22×C3×C4—28no—
226C22×C3×C4—22no—
227C22×C3×C4—22no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—22no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—22no—
235C22×C3×C4—21no—
236C22×C3×C4—44no—
237C22×C3×C4—48no—
238C22×C3×C4—48no—
239C22×C3×C4C2×D412yes—
240C22×C3×C4C2×D412yes—
241C22×C3×C4C2×D412yes—
242C22×C3×C4C2×D412yes—
243C22×C3×C4#4112yes—
244C2×#67—216no—
245C2×#67—216no—
246C2×#67—216no—
247C2×#67—216no—
248C2×#67—48no—
249C2×#67—48no—
250C2×#67—48no—
251C2×#67—48no—
252C2×#67—48no—
253C2×#67—48no—
254C2×#67—48no—
255C2×#67—48no—
256C2×#67—48no—
257C2×#67—48no—
258C22×Dic3—22no—
259C22×Dic3—22no—
260C22×Dic3—22no—
261C22×Dic3—22no—
262C22×Dic3—216no—
263C22×Dic3—22no—
264C22×Dic3—22no—
265C22×Dic3—22no—
266C22×Dic3—22no—
267C22×Dic3—22no—
268C22×Dic3—22no—
269C22×Dic3—22no—
270C22×Dic3—22no—
271C22×Dic3—22no—
272C22×Dic3—22no—
273C22×Dic3—22no—
274C22×Dic3—22no—
275C22×Dic3—216no—
276C22×Dic3—48no—
277C22×Dic3—48no—
278C22×Dic3—48no—
279C22×Dic3—48no—
280C22×Dic3—48no—
281C22×Dic3C2×D414yes—
282C22×Dic3C2×D414yes—
283C22×Dic3C2×D414yes—
284C22×Dic3C2×D414yes—
285C22×Dic3#4114yes—
286C2×D12—28no—
287C2×D12—48no—
288C2×D12—48no—
289C2×D12—44no—
290C2×D12—44no—
291C3×C22⋊C4—44no—
292C3×C22⋊C4—44no—
293C3×C22⋊C4—44no—
294#217—216no—
295(C2×D3)⋊C4—216no—
296(C2×D3)⋊C4—216no—
297(C2×D3)⋊C4—48no—
298(C2×D3)⋊C4—48no—
299C4⋊Dic3—28no—
300Dic3⋊C4—216no—
301C25—32no—
302C25C22×D311yescharacteristic
303C25C22×D311yescharacteristic
304C22×D4—22no—
305C22×D4—24no—
306C22×D4—24no—
307C22×D4—22no—
308C22×D4—38no—
309C22×D4—64no—
310C22×D4—64no—
311C22×D4—64no—
312C22×D4—64no—
313C22×D4—64no—
314C22×D4—64no—
315C22×D4—64no—
316C22×D4—64no—
317C22×D4—64no—
318C22×D4—64no—
319C22×D4—64no—
320C22×D4—64no—
321C22×D4—62no—
322C22×D4—62no—
323C22×D4—62no—
324C22×D4—122no—
325C22×D4—122no—
326C22×D4—122no—
327C22×D4D1214yescomplemented
328C23×C4—24no—
329C23×C4—22no—
330C23×C4—22no—
331C23×C4—32no—
332C23×C4—32no—
333C23×C4—32no—
334C23×C4—38no—
335C23×C4—42no—
336C23×C4—64no—
337C23×C4—64no—
338C23×C4—64no—
339C23×C4—64no—
340C23×C4—122no—
341C23×C4—122no—
342C23×C4#6714yescomplemented
343C23×C4C22×D311yescharacteristic
344C23×C4C22×D311yescharacteristic
345C23×C4C22×D311yescharacteristic
346C23×C4C22×D311yescharacteristic
347C23×C4C22×D311yescharacteristic
348#121—632no—
349#121—664no—
350C2×C4⋊C4—64no—
351C2×C4⋊C4—64no—
352C2×C4⋊C4—64no—
353C2×C4⋊C4—64no—
354C2×C4⋊C4—62no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—64no—
363C2×C22⋊C4—64no—
364C2×C22⋊C4—64no—
365C2×C22⋊C4—64no—
366C2×C22⋊C4—64no—
367C2×C22⋊C4—64no—
368C2×C22⋊C4—64no—
369C2×C22⋊C4—64no—
370C2×C22⋊C4—64no—
371C2×C22⋊C4—64no—
372C2×C22⋊C4—64no—
373C2×C22⋊C4—64no—
374C2×C22⋊C4—64no—
375C2×C22⋊C4—122no—
376C2×C22⋊C4—122no—
377#95—22no—
378#95—22no—
379#95—34no—
380#95—64no—
381#95—64no—
382#95—64no—
383#95—62no—
384C23×C3—24no—
385C23×C3—22no—
386C23×C3—22no—
387C23×C3—24no—
388C23×C3—24no—
389C23×C3—22no—
390C23×C3—22no—
391C23×C3—24no—
392C23×C3—22no—
393C23×C3—24no—
394C23×C3—24no—
395C23×C3—24no—
396C23×C3—24no—
397C23×C3—24no—
398C23×C3—22no—
399C23×C3—22no—
400C23×C3—24no—
401C23×C3—22no—
402C23×C3—24no—
403C23×C3—22no—
404C23×C3—22no—
405C23×C3—24no—
406C23×C3—22no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3—42no—
410C23×C3—42no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—42no—
414C23×C3—41no—
415C23×C3—42no—
416C23×C3—41no—
417C23×C3—42no—
418C23×C3—42no—
419C23×C3—42no—
420C23×C3—42no—
421C23×C3—42no—
422C23×C3—41no—
423C23×C3—42no—
424C23×C3—41no—
425C23×C3#12018yes—
426C23×C3#12014yes—
427C23×C3#12118yes—
428C23×C3#12114yes—
429C23×C3#12714yes—
430C23×C3C22×D411yescharacteristic
431C23×C3C22×D412yes—
432C23×C3C22×D412yes—
433C23×C3C22×D411yescharacteristic
434C23×C3C22×D411yescharacteristic
435C23×C3C2×#4111yescharacteristic
436C23×C3C2×#4111yescharacteristic
437C23×C3C2×#4112yes—
438C23×C3H(5,𝔽2)12yes—
439C23×C3H(5,𝔽2)11yescharacteristic
440C23×C32−1+411yescharacteristic
441C22×D3—24no—
442C22×D3—24no—
443C22×D3—24no—
444C22×D3—24no—
445C22×D3—24no—
446C22×D3—24no—
447C22×D3—24no—
448C22×D3—42no—
449C22×D3—42no—
450C22×D3—42no—
451C22×D3—42no—
452C22×D3—42no—
453C22×D3—42no—
454C22×D3—42no—
455C22×D3—42no—
456C22×D3—42no—
457C22×D3—42no—
458C22×D3—42no—
459C22×D3—42no—
460C22×D3—42no—
461C22×D3—42no—
462C22×D3—42no—
463C22×D3—42no—
464C22×D3—42no—
465C22×D3—42no—
466C22×D3—42no—
467C22×D3—42no—
468C22×D3—42no—
469C22×D3—42no—
470C22×D3—42no—
471C22×D3—42no—
472C22×D3—42no—
473C22×D3—42no—
474C22×D3—42no—
475C22×D3—42no—
476C3×D4—416no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—24no—
480C2×C3×C4—24no—
481C2×C3×C4—24no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—416no—
487C2×C3×C4—41no—
488C2×C3×C4—42no—
489C2×C3×C4—41no—
490C2×C3×C4—42no—
491C2×C3×C4—42no—
492C2×C3×C4—42no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—42no—
498C2×C3×C4—42no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—42no—
502C2×C3×C4#12114yescomplemented
503#67—432no—
504#67—432no—
505C2×Dic3—24no—
506C2×Dic3—24no—
507C2×Dic3—24no—
508C2×Dic3—24no—
509C2×Dic3—24no—
510C2×Dic3—24no—
511C2×Dic3—24no—
512C2×Dic3—24no—
513C2×Dic3—24no—
514C2×Dic3—24no—
515C2×Dic3—24no—
516C2×Dic3—24no—
517C2×Dic3—432no—
518C2×Dic3—42no—
519C2×Dic3—42no—
520C2×Dic3—42no—
521C2×Dic3—42no—
522C2×Dic3—42no—
523C2×Dic3—42no—
524C2×Dic3—42no—
525C2×Dic3—42no—
526C2×Dic3#12118yescomplemented
527D12—416no—
528C24—21no—
529C24—21no—
530C24—22no—
531C24—22no—
532C24—21no—
533C24—21no—
534C24—21no—
535C24—21no—
536C24—22no—
537C24—22no—
538C24—21no—
539C24—22no—
540C24—22no—
541C24—21no—
542C24—21no—
543C24—21no—
544C24—34no—
545C24—62no—
546C24—62no—
547C24—62no—
548C24—62no—
549C24—62no—
550C24—62no—
551C24—62no—
552C24—62no—
553C24—62no—
554C24—62no—
555C24—62no—
556C24—62no—
557C24—62no—
558C24—62no—
559C24C2×D1212yes—
560C24C2×D1212yes—
561C24#23512yes—
562C24D3×D414yes—
563C24D3×D414yes—
564C24C2×#6712yes—
565C24C23×D311yescharacteristic
566C2×D4—216no—
567C2×D4—28no—
568C2×D4—48no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—68no—
572C2×D4—616no—
573C2×D4—616no—
574C2×D4—616no—
575C2×D4—616no—
576C2×D4—128no—
577C2×D4—128no—
578C2×D4—124no—
579C2×D4—128no—
580C2×D4—128no—
581C2×D4—128no—
582C2×D4—128no—
583C2×D4—128no—
584C2×D4—128no—
585C2×D4—128no—
586C2×D4—128no—
587C2×D4—128no—
588C2×D4—128no—
589C2×D4—124no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—28no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—28no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—34no—
613C22×C4—34no—
614C22×C4—34no—
615C22×C4—34no—
616C22×C4—34no—
617C22×C4—44no—
618C22×C4—48no—
619C22×C4—48no—
620C22×C4—616no—
621C22×C4—62no—
622C22×C4—62no—
623C22×C4—62no—
624C22×C4—62no—
625C22×C4—616no—
626C22×C4—62no—
627C22×C4—62no—
628C22×C4—62no—
629C22×C4—62no—
630C22×C4—62no—
631C22×C4—62no—
632C22×C4—62no—
633C22×C4—62no—
634C22×C4—62no—
635C22×C4—62no—
636C22×C4—62no—
637C22×C4—62no—
638C22×C4—128no—
639C22×C4—128no—
640C22×C4—128no—
641C22×C4—128no—
642C22×C4—128no—
643C22×C4C2×D1212yes—
644C22×C4D3×D412yes—
645C22×C4#23712yes—
646C22×C4C2×#6712yes—
647C22×C4C2×#6712yes—
648C4⋊C4—616no—
649C4⋊C4—68no—
650C22⋊C4—44no—
651C22⋊C4—44no—
652C22⋊C4—44no—
653C22⋊C4—616no—
654C22⋊C4—616no—
655C22⋊C4—616no—
656C22⋊C4—128no—
657C22⋊C4—128no—
658C22×C3—24no—
659C22×C3—24no—
660C22×C3—28no—
661C22×C3—24no—
662C22×C3—24no—
663C22×C3—28no—
664C22×C3—24no—
665C22×C3—28no—
666C22×C3—28no—
667C22×C3—24no—
668C22×C3—42no—
669C22×C3—44no—
670C22×C3—42no—
671C22×C3—44no—
672C22×C3—42no—
673C22×C3—81no—
674C22×C3—81no—
675C22×C3—81no—
676C22×C3—82no—
677C22×C3—81no—
678C22×C3—82no—
679C22×C3#39218yescomplemented
680C22×C3C2×#12012yes—
681C22×C3C2×#12011yescharacteristic
682C22×C3C2×#12112yes—
683C22×C3C2×#12111yescharacteristic
684C22×C3C2×#12111yescharacteristic
685C22×C3C2×#12112yes—
686C22×C3C2×#12711yescharacteristic
687C22×C3#53211yescharacteristic
688C22×C3#53212yes—
689C22×C3#53411yescharacteristic
690C22×C3#53412yes—
691C22×C3#53711yescharacteristic
692C22×C3#53712yes—
693C22×C3D4211yescharacteristic
694C22×C3D4212yes—
695C22×C3#54612yes—
696C22×C3#54612yes—
697C22×C3#54612yes—
698C22×C3#54712yes—
699C22×C3#54711yescharacteristic
700C22×C3#54811yescharacteristic
701C22×C3#55312yes—
702C22×C3#55311yescharacteristic
703C2×D3—44no—
704C2×D3—44no—
705C2×D3—44no—
706C2×D3—44no—
707C2×D3—44no—
708C2×D3—44no—
709C2×D3—44no—
710C2×D3—82no—
711C2×D3—82no—
712C2×D3—82no—
713C2×D3—82no—
714C2×D3—82no—
715C2×D3—82no—
716C2×D3—82no—
717C2×D3—82no—
718C3×C4—24no—
719C3×C4—42no—
720C3×C4—42no—
721C3×C4—81no—
722C3×C4—81no—
723Dic3—28no—
724Dic3—44no—
725Dic3—44no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—24no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—24no—
739C23—24no—
740C23—24no—
741C23—24no—
742C23—24no—
743C23—24no—
744C23—24no—
745C23—22no—
746C23—22no—
747C23—24no—
748C23—22no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—42no—
767C23—64no—
768C23—64no—
769C23—64no—
770C23—64no—
771C23—64no—
772C23—64no—
773C23—64no—
774C23—122no—
775C23—122no—
776C23—122no—
777C23—122no—
778C23—122no—
779C23—122no—
780C23—122no—
781C23—122no—
782C23—122no—
783C23—122no—
784C23—122no—
785C23—122no—
786C23—122no—
787C23—122no—
788C23—122no—
789C23—122no—
790C23—122no—
791C23—122no—
792C23—122no—
793C23—122no—
794C23—122no—
795C23—122no—
796C23—122no—
797C23—122no—
798C23—122no—
799C23—122no—
800C23—122no—
801C23—122no—
802C23#88218yes—
803C23#88418yes—
804C23#93014yes—
805C23#93714yes—
806C23#94014yes—
807C23C22×D1211yescharacteristic
808C23C2×#23511yescharacteristic
809C23C2×D3×D412yes—
810C23C2×D3×D412yes—
811C23C2×D3×D411yescharacteristic
812C23C2×#23711yescharacteristic
813C23#100412yes—
814C23D3×#4112yes—
815C23#100911yescharacteristic
816C23#101011yescharacteristic
817C23C22×#6711yescharacteristic
818D4—416no—
819D4—1216no—
820D4—1232no—
821D4—1232no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—38no—
832C2×C4—416no—
833C2×C4—42no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—64no—
849C2×C4—64no—
850C2×C4—64no—
851C2×C4—64no—
852C2×C4—64no—
853C2×C4—64no—
854C2×C4—64no—
855C2×C4—64no—
856C2×C4—64no—
857C2×C4—64no—
858C2×C4—64no—
859C2×C4—64no—
860C2×C4—1232no—
861C2×C4—122no—
862C2×C4—122no—
863C2×C4—122no—
864C2×C4—122no—
865C2×C4—122no—
866C2×C4—122no—
867C2×C4—122no—
868C2×C4—122no—
869C2×C4#93914yescomplemented
870C2×C3—28no—
871C2×C3—82no—
872C2×C3C2×#39211yescharacteristic
873C2×C3#241012yes—
874C2×C3#241011yescharacteristic
875C2×C3#241611yescharacteristic
876C2×C3#241612yes—
877C2×C3#243011yescharacteristic
878C2×C3#243012yes—
879C2×C3#254312yes—
880C2×C3#254311yescharacteristic
881C2×C3#265611yescharacteristic
882C2×C3#285611yescharacteristic
883D3—84no—
884C22—28no—
885C22—24no—
886C22—28no—
887C22—24no—
888C22—24no—
889C22—24no—
890C22—28no—
891C22—28no—
892C22—24no—
893C22—24no—
894C22—44no—
895C22—42no—
896C22—44no—
897C22—42no—
898C22—42no—
899C22—82no—
900C22—81no—
901C22—81no—
902C22—81no—
903C22—82no—
904C22—81no—
905C22—124no—
906C22—124no—
907C22—124no—
908C22—124no—
909C22—124no—
910C22—124no—
911C22—124no—
912C22—242no—
913C22—242no—
914C22—242no—
915C22—242no—
916C22—242no—
917C22—242no—
918C22—242no—
919C22—242no—
920C22#496018yescomplemented
921C22C2×#88212yes—
922C22C2×#88412yes—
923C22#554012yes—
924C22D4×D1211yescharacteristic
925C22#555211yescharacteristic
926C22#555412yes—
927C22#555511yescharacteristic
928C22#556511yescharacteristic
929C22#559012yes—
930C22#559112yes—
931C22#559612yes—
932C22#559712yes—
933C22D3×#12112yes—
934C22#560512yes—
935C22#565412yes—
936C22#565512yes—
937C22C2×#93011yescharacteristic
938C22C2×#93711yescharacteristic
939C22C2×#93911yescharacteristic
940C22C2×#94011yescharacteristic
941C22#580411yescharacteristic
942C22#583211yescharacteristic
943C22#583311yescharacteristic
944C4—24no—
945C4—42no—
946C4—42no—
947C4—68no—
948C4—81no—
949C4—81no—
950C4—124no—
951C4—124no—
952C3#1475711yescharacteristic, complemented, Sylow
953C2—28no—
954C2—82no—
955C2—244no—
956C2#7469212yes—
957C2#7469912yes—
958C2#7475212yes—
959C2#7488812yes—
960C2C2×#496011yescharacteristic
961C2#8235211yescharacteristic
962C2#8238011yescharacteristic
963C2#8260611yescharacteristic
964C2#8268011yescharacteristic
965C2#8270011yescharacteristic
966C2#8284811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#386C2
hypercenterC2×#386D3
hypocenterC3#14757
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#939C2semidirect
2. C22×#930C2semidirect
3. C2×C3×#386C2semidirect
4. C22×C3⋊#95C2semidirect
5. C2×#4960C2semidirect
6. C2×#4958C2semidirect
7. #71550C2semidirect
8. #71546C2semidirect
9. #69428C2semidirect
10. #69426C2semidirect
11. #69420C2semidirect
49. C2×#386D3semidirect
63. C22×C3×D4D4semidirect
68. C23×C3×C4D4semidirect
87. C22×#67D4semidirect
94. C23×Dic3D4semidirect
138. C3⋊#95D4semidirect
327. C22×D4D12semidirect
342. C23×C4#67semidirect
502. C2×C3×C4#121semidirect
526. C2×Dic3#121semidirect
679. C22×C3#392semidirect
869. C2×C4#939semidirect
920. C22#4960semidirect
952. C3#14757semidirect

Maximal subgroups

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

subgroupindex
C22×#9392
C22×#9302
C2×C3×#3862
C22×C3⋊#952
C2×#49602
C2×#49582
#715502
#715462
#694282
#694262
#694202
#147573