Finite Group Databasebeta

← #10746856

Subgroups — #10746856

Order 768.

2894 conjugacy classes of subgroups.

The subgroup lattice has 962 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#123C211yesmaximal, characteristic, complemented
2C22×#930C211yesmaximal, characteristic, complemented
3C2×#5223C212yesmaximal, complemented
4C2×#4991C211yesmaximal, characteristic, complemented
5C2×#4960C211yesmaximal, characteristic, complemented
6#72127C211yesmaximal, characteristic, complemented
7#71570C212yesmaximal, complemented
8#71565C211yesmaximal, characteristic, complemented
9#71550C212yesmaximal, complemented
10#71550C212yesmaximal, complemented
11#71546C211yesmaximal, characteristic, complemented
12#16250—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C23×#67C2212yes—
16C23×#67C2212yes—
17C23×D12C2211yescharacteristic
18C2×C3×#123—24no—
19C2×C3×#123—24no—
20C2×C3×#123—24no—
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×#217C2212yes—
27C22×#217C2212yes—
28C2×#930—24no—
29C2×#930—28no—
30C22×(C2×D3)⋊C4C2212yes—
31C22×(C2×D3)⋊C4C2212yes—
32C22×(C2×D3)⋊C4C2212yes—
33C22×(C2×D3)⋊C4C2212yes—
34C22×C4⋊Dic3C2211yescharacteristic
35#5223—28no—
36C2×C3⋊#95C2211yescharacteristic
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2211yescharacteristic
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2212yes—
41C2×C3⋊#95C2212yes—
42#4991—24no—
43#4960—24no—
44C22×#123D311yescharacteristic, complemented
45C22×#121—31no—
46C2×#394—31no—
47C2×#392—32no—
48C2×#392—31no—
49#1441—31no—
50#1439—32no—
51#1439—31no—
52#1438—32no—
53#1438—32no—
54C22⋊#95—31no—
55C25×C3C2311yescharacteristic
56C25×C3C2311yescharacteristic
57C24×D3C2312yes—
58C22×C3×D4—22no—
59C22×C3×D4—22no—
60C22×C3×D4—24no—
61C22×C3×D4—22no—
62C22×C3×D4—42no—
63C23×C3×C4—24no—
64C23×C3×C4—22no—
65C23×C3×C4—22no—
66C23×C3×C4—42no—
67C23×C3×C4D414yescomplemented
68C23×C3×C4C2311yescharacteristic
69C23×C3×C4C2311yescharacteristic
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C22×#67—24no—
74C22×#67—24no—
75C22×#67—24no—
76C22×#67—24no—
77C22×#67—24no—
78C22×#67—42no—
79C22×#67—42no—
80C22×#67—42no—
81C22×#67—42no—
82C22×#67—42no—
83C22×#67—42no—
84C22×#67—42no—
85C22×#67—42no—
86C22×#67D418yescomplemented
87C23×Dic3C2312yes—
88C23×Dic3C2312yes—
89C23×Dic3C2312yes—
90C22×D12—24no—
91C22×D12—22no—
92C22×D12—22no—
93C22×D12—22no—
94C22×D12—42no—
95C3×#123—232no—
96C2×C3×C4⋊C4—22no—
97C2×C3×C4⋊C4—22no—
98C2×C3×C4⋊C4—22no—
99C2×C3×C4⋊C4—22no—
100C2×C3×C4⋊C4—22no—
101C2×C3×C4⋊C4D414yescomplemented
102C2×C3×C22⋊C4—22no—
103C2×C3×C22⋊C4—22no—
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—22no—
110C2×C3×C22⋊C4D414yescomplemented
111C2×#217—24no—
112C2×#217—24no—
113C2×#217—24no—
114C2×#217—42no—
115C2×#217—42no—
116C2×#217—42no—
117#930—232no—
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—24no—
126C2×(C2×D3)⋊C4—42no—
127C2×(C2×D3)⋊C4—42no—
128C2×(C2×D3)⋊C4—42no—
129C2×(C2×D3)⋊C4—42no—
130C2×C4⋊Dic3—22no—
131C2×C4⋊Dic3—24no—
132C3⋊#95—22no—
133C3⋊#95—22no—
134C3⋊#95—24no—
135C3⋊#95—42no—
136C3⋊#95—42no—
137C3⋊#95—42no—
138C23×D4—32no—
139C23×D4—32no—
140C23×D4—31no—
141C23×D4C2×D311yescharacteristic
142C24×C4C2×D311yescharacteristic
143C2×#123—24no—
144C2×#123—24no—
145C2×#123—24no—
146C2×#121—68no—
147C2×#121—64no—
148C22×C4⋊C4—31no—
149C22×C4⋊C4C2×D311yescharacteristic
150C22×C4⋊C4C2×D311yescharacteristic
151C22×C22⋊C4—32no—
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#394—64no—
161#392—68no—
162#392—64no—
163C2×#95—31no—
164C2×#95—32no—
165C2×#95—31no—
166C2×#95—32no—
167C2×#95—32no—
168C2×#95—32no—
169C24×C3—21no—
170C24×C3—21no—
171C24×C3—22no—
172C24×C3—21no—
173C24×C3—21no—
174C24×C3—21no—
175C24×C3—22no—
176C24×C3—22no—
177C24×C3—21no—
178C24×C3—22no—
179C24×C3—21no—
180C24×C3—21no—
181C24×C3—22no—
182C24×C3—21no—
183C24×C3—22no—
184C24×C3—21no—
185C24×C3—21no—
186C24×C3—22no—
187C24×C3—21no—
188C24×C3C2×D414yes—
189C24×C3C2×D412yes—
190C24×C3C2×D412yes—
191C24×C3C2411yescharacteristic
192C23×D3—22no—
193C23×D3—22no—
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×D3C2×D414yes—
207C2×C3×D4—28no—
208C2×C3×D4—48no—
209C2×C3×D4—48no—
210C2×C3×D4—44no—
211C2×C3×D4—44no—
212C22×C3×C4—22no—
213C22×C3×C4—22no—
214C22×C3×C4—28no—
215C22×C3×C4—22no—
216C22×C3×C4—22no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—22no—
226C22×C3×C4—21no—
227C22×C3×C4—22no—
228C22×C3×C4—22no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—22no—
232C22×C3×C4—21no—
233C22×C3×C4—28no—
234C22×C3×C4—44no—
235C22×C3×C4—48no—
236C22×C3×C4—48no—
237C22×C3×C4C2×D412yes—
238C22×C3×C4C2×D412yes—
239C22×C3×C4C2×D412yes—
240C22×C3×C4C2×D412yes—
241C22×C3×C4C2×D412yes—
242C22×C3×C4C2×D412yes—
243C22×C3×C4C2×D412yes—
244C2×#67—216no—
245C2×#67—48no—
246C2×#67—48no—
247C2×#67—48no—
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—22no—
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—22no—
276C22×Dic3—22no—
277C22×Dic3C2×D414yes—
278C22×Dic3#4114yes—
279C2×D12—28no—
280C2×D12—48no—
281C2×D12—48no—
282C2×D12—44no—
283C2×D12—44no—
284C3×C4⋊C4—28no—
285C3×C4⋊C4—28no—
286C3×C22⋊C4—28no—
287C3×C22⋊C4—28no—
288C3×C22⋊C4—28no—
289#217—48no—
290#217—48no—
291(C2×D3)⋊C4—216no—
292(C2×D3)⋊C4—48no—
293(C2×D3)⋊C4—48no—
294(C2×D3)⋊C4—48no—
295C4⋊Dic3—28no—
296C25—32no—
297C25C22×D311yescharacteristic
298C25C22×D311yescharacteristic
299C22×D4—22no—
300C22×D4—22no—
301C22×D4—24no—
302C22×D4—22no—
303C22×D4—38no—
304C22×D4—42no—
305C22×D4—64no—
306C22×D4—64no—
307C22×D4—64no—
308C22×D4—64no—
309C22×D4—64no—
310C22×D4—64no—
311C22×D4—62no—
312C22×D4—62no—
313C22×D4—62no—
314C22×D4—122no—
315C22×D4—122no—
316C22×D4—122no—
317C22×D4—122no—
318C22×D4—122no—
319C22×D4—122no—
320C22×D4—122no—
321C22×D4—122no—
322C22×D4—122no—
323C23×C4—24no—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—32no—
327C23×C4—32no—
328C23×C4—32no—
329C23×C4—42no—
330C23×C4#6714yescomplemented
331C23×C4C22×D311yescharacteristic
332C23×C4C22×D311yescharacteristic
333C23×C4C22×D311yescharacteristic
334C23×C4C22×D311yescharacteristic
335C23×C4C22×D311yescharacteristic
336#123—232no—
337#121—632no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—64no—
344C2×C4⋊C4—62no—
345C2×C4⋊C4#6714yescomplemented
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—64no—
355C2×C22⋊C4—64no—
356C2×C22⋊C4—64no—
357C2×C22⋊C4—64no—
358C2×C22⋊C4—64no—
359C2×C22⋊C4—64no—
360C2×C22⋊C4—64no—
361C2×C22⋊C4—64no—
362C2×C22⋊C4—64no—
363C2×C22⋊C4—64no—
364C2×C22⋊C4—64no—
365C2×C22⋊C4—122no—
366C2×C22⋊C4—122no—
367C2×C22⋊C4—122no—
368C2×C22⋊C4—122no—
369C2×C22⋊C4—122no—
370C2×C22⋊C4—122no—
371C2×C22⋊C4—122no—
372C2×C22⋊C4#6714yescomplemented
373#95—64no—
374#95—62no—
375#95—62no—
376#95—122no—
377#95—122no—
378#95—122no—
379C23×C3—22no—
380C23×C3—22no—
381C23×C3—24no—
382C23×C3—24no—
383C23×C3—22no—
384C23×C3—22no—
385C23×C3—22no—
386C23×C3—22no—
387C23×C3—24no—
388C23×C3—24no—
389C23×C3—24no—
390C23×C3—24no—
391C23×C3—22no—
392C23×C3—22no—
393C23×C3—22no—
394C23×C3—24no—
395C23×C3—24no—
396C23×C3—41no—
397C23×C3—41no—
398C23×C3—41no—
399C23×C3—41no—
400C23×C3—42no—
401C23×C3—42no—
402C23×C3—42no—
403C23×C3—42no—
404C23×C3—42no—
405C23×C3—42no—
406C23×C3—41no—
407C23×C3—41no—
408C23×C3—42no—
409C23×C3—42no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
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#12014yes—
425C23×C3C22×D412yes—
426C23×C3C22×D411yescharacteristic
427C23×C3C22×D411yescharacteristic
428C23×C3C22×D411yescharacteristic
429C23×C3C2×#4112yes—
430C23×C3H(5,𝔽2)12yes—
431C23×C3H(5,𝔽2)11yescharacteristic
432C23×C3H(5,𝔽2)11yescharacteristic
433C23×C3H(5,𝔽2)12yes—
434C23×C3H(5,𝔽2)11yescharacteristic
435C23×C32−1+411yescharacteristic
436C22×D3—24no—
437C22×D3—24no—
438C22×D3—24no—
439C22×D3—24no—
440C22×D3—24no—
441C22×D3—24no—
442C22×D3—24no—
443C22×D3—42no—
444C22×D3—42no—
445C22×D3—42no—
446C22×D3—42no—
447C22×D3—42no—
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—
471C3×D4—416no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—24no—
475C2×C3×C4—24no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—24no—
485C2×C3×C4—24no—
486C2×C3×C4—416no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—42no—
496C2×C3×C4—42no—
497C2×C3×C4—42no—
498C2×C3×C4—42no—
499C2×C3×C4#12014yes—
500#67—432no—
501#67—432no—
502C2×Dic3—24no—
503C2×Dic3—24no—
504C2×Dic3—24no—
505C2×Dic3—24no—
506C2×Dic3—24no—
507C2×Dic3—24no—
508C2×Dic3—42no—
509C2×Dic3—42no—
510C2×Dic3—42no—
511C2×Dic3—42no—
512C2×Dic3—42no—
513C2×Dic3—42no—
514C2×Dic3—42no—
515C2×Dic3—42no—
516C2×Dic3—42no—
517C2×Dic3—42no—
518C2×Dic3—42no—
519C2×Dic3—42no—
520C2×Dic3—42no—
521C2×Dic3—42no—
522C2×Dic3—42no—
523D12—416no—
524C24—22no—
525C24—22no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—22no—
530C24—21no—
531C24—21no—
532C24—21no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—21no—
537C24—22no—
538C24—21no—
539C24—21no—
540C24—21no—
541C24—21no—
542C24—21no—
543C24—34no—
544C24—62no—
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—
558C24D3×D414yes—
559C24C2×#6712yes—
560C24C2×#6712yes—
561C24C23×D311yescharacteristic
562C2×D4—28no—
563C2×D4—48no—
564C2×D4—48no—
565C2×D4—44no—
566C2×D4—44no—
567C2×D4—68no—
568C2×D4—616no—
569C2×D4—128no—
570C2×D4—128no—
571C2×D4—124no—
572C2×D4—128no—
573C2×D4—128no—
574C2×D4—128no—
575C2×D4—128no—
576C2×D4—128no—
577C2×D4—128no—
578C2×D4—128no—
579C2×D4—128no—
580C2×D4—128no—
581C2×D4—128no—
582C2×D4—128no—
583C2×D4—128no—
584C2×D4—128no—
585C2×D4—124no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—28no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—28no—
608C22×C4—34no—
609C22×C4—34no—
610C22×C4—44no—
611C22×C4—48no—
612C22×C4—48no—
613C22×C4—62no—
614C22×C4—62no—
615C22×C4—62no—
616C22×C4—62no—
617C22×C4—62no—
618C22×C4—62no—
619C22×C4—62no—
620C22×C4—62no—
621C22×C4—62no—
622C22×C4—62no—
623C22×C4—62no—
624C22×C4—62no—
625C22×C4—62no—
626C22×C4—62no—
627C22×C4—62no—
628C22×C4—62no—
629C22×C4—62no—
630C22×C4—62no—
631C22×C4—62no—
632C22×C4C2×#6712yes—
633C22×C4C2×#6712yes—
634C22×C4C2×#6712yes—
635C22×C4C2×#6712yes—
636C22×C4C2×#6712yes—
637C22×C4C2×#6712yes—
638C22×C4C2×#6712yes—
639C4⋊C4—28no—
640C4⋊C4—28no—
641C4⋊C4—68no—
642C22⋊C4—28no—
643C22⋊C4—28no—
644C22⋊C4—28no—
645C22⋊C4—616no—
646C22⋊C4—128no—
647C22⋊C4—128no—
648C22⋊C4—128no—
649C22⋊C4—128no—
650C22⋊C4—128no—
651C22×C3—24no—
652C22×C3—24no—
653C22×C3—24no—
654C22×C3—42no—
655C22×C3—42no—
656C22×C3—44no—
657C22×C3—44no—
658C22×C3—44no—
659C22×C3—44no—
660C22×C3—42no—
661C22×C3—42no—
662C22×C3—42no—
663C22×C3—42no—
664C22×C3—44no—
665C22×C3—44no—
666C22×C3—42no—
667C22×C3—81no—
668C22×C3—81no—
669C22×C3—82no—
670C22×C3—82no—
671C22×C3—81no—
672C22×C3—81no—
673C22×C3C2×#12011yescharacteristic
674C22×C3C2×#12011yescharacteristic
675C22×C3#53211yescharacteristic
676C22×C3#53412yes—
677C22×C3#53412yes—
678C22×C3#53411yescharacteristic
679C22×C3#53511yescharacteristic
680C22×C3#53511yescharacteristic
681C22×C3#53511yescharacteristic
682C22×C3#53511yescharacteristic
683C22×C3#53711yescharacteristic
684C22×C3#53711yescharacteristic
685C22×C3#53711yescharacteristic
686C22×C3#53812yes—
687C22×C3#54012yes—
688C22×C3D4212yes—
689C22×C3D4212yes—
690C22×C3#54612yes—
691C22×C3#54612yes—
692C22×C3#54712yes—
693C22×C3#55012yes—
694C22×C3#56012yes—
695C22×C3#56212yes—
696C2×D3—44no—
697C2×D3—44no—
698C2×D3—44no—
699C2×D3—44no—
700C2×D3—44no—
701C2×D3—44no—
702C2×D3—44no—
703C2×D3—82no—
704C2×D3—82no—
705C2×D3—82no—
706C2×D3—82no—
707C2×D3—82no—
708C2×D3—82no—
709C2×D3—82no—
710C2×D3—82no—
711C3×C4—24no—
712C3×C4—42no—
713C3×C4—42no—
714C3×C4—42no—
715C3×C4—42no—
716Dic3—44no—
717Dic3—44no—
718Dic3—82no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—24no—
732C23—24no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—41no—
755C23—42no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—42no—
764C23—64no—
765C23—64no—
766C23—64no—
767C23—64no—
768C23—64no—
769C23—64no—
770C23—64no—
771C23—122no—
772C23—122no—
773C23—122no—
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#93714yes—
800C23C2×D3×D412yes—
801C23#100412yes—
802C23D3×#4112yes—
803C23#100911yescharacteristic
804C23#100911yescharacteristic
805C23#100912yes—
806C23#100911yescharacteristic
807C23#101011yescharacteristic
808C23C22×#6711yescharacteristic
809C23C22×#6711yescharacteristic
810C23C22×#6711yescharacteristic
811D4—416no—
812D4—1216no—
813D4—1232no—
814D4—1232no—
815C2×C4—22no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—24no—
821C2×C4—22no—
822C2×C4—24no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—416no—
830C2×C4—41no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—42no—
842C2×C4—64no—
843C2×C4—64no—
844C2×C4—64no—
845C2×C4—64no—
846C2×C4—64no—
847C2×C4—64no—
848C2×C4—122no—
849C2×C4—122no—
850C2×C4—122no—
851C2×C4—122no—
852C2×C4—122no—
853C2×C4—122no—
854C2×C4—122no—
855C2×C4—122no—
856C2×C4—122no—
857C2×C4—122no—
858C2×C4—122no—
859C2×C4—122no—
860C2×C4—122no—
861C2×C4—122no—
862C2×C4—122no—
863C2×C4#95314yes—
864C2×C3—44no—
865C2×C3—82no—
866C2×C3#240311yescharacteristic
867C2×C3#243011yescharacteristic
868C2×C3#243111yescharacteristic
869C2×C3#261311yescharacteristic
870C2×C3#261511yescharacteristic
871C2×C3#266111yescharacteristic
872C2×C3#267112yes—
873C2×C3#267312yes—
874C2×C3#267812yes—
875C2×C3#268212yes—
876C2×C3#281311yescharacteristic
877D3—84no—
878C22—24no—
879C22—24no—
880C22—24no—
881C22—42no—
882C22—42no—
883C22—42no—
884C22—44no—
885C22—44no—
886C22—44no—
887C22—44no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—44no—
893C22—44no—
894C22—81no—
895C22—81no—
896C22—82no—
897C22—81no—
898C22—82no—
899C22—81no—
900C22—124no—
901C22—124no—
902C22—124no—
903C22—124no—
904C22—124no—
905C22—124no—
906C22—124no—
907C22—242no—
908C22—242no—
909C22—242no—
910C22—242no—
911C22—242no—
912C22—242no—
913C22—242no—
914C22—242no—
915C22#565312yes—
916C22#565312yes—
917C22#565412yes—
918C22#565512yes—
919C22#565712yes—
920C22#566312yes—
921C22#566612yes—
922C22#566712yes—
923C22C2×#93711yescharacteristic
924C22D4×#6712yes—
925C22D4×#6712yes—
926C22#580411yescharacteristic
927C22#582912yes—
928C22#583011yescharacteristic
929C22#583011yescharacteristic
930C22#583011yescharacteristic
931C22#583011yescharacteristic
932C22#583211yescharacteristic
933C22#583311yescharacteristic
934C22#583311yescharacteristic
935C22#583311yescharacteristic
936C22#583412yes—
937C22C2×#95311yescharacteristic
938C4—24no—
939C4—42no—
940C4—42no—
941C4—42no—
942C4—42no—
943C4—124no—
944C4—124no—
945C4—242no—
946C3#1625011yescharacteristic, complemented, Sylow
947C2—44no—
948C2—82no—
949C2—244no—
950C2#8284811yescharacteristic
951C2#8286711yescharacteristic
952C2#8287312yes—
953C2#8290311yescharacteristic
954C2#8290512yes—
955C2#8290612yes—
956C2#8290712yes—
957C2#8291111yescharacteristic
958C2#8405211yescharacteristic
959C2#8409211yescharacteristic
960C2#8409811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC22×C3×#123C2
hypercenterC22×#123D3
hypocenterC3#16250
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×C3×#123C2semidirect
2. C22×#930C2semidirect
3. C2×#5223C2semidirect
4. C2×#4991C2semidirect
5. C2×#4960C2semidirect
6. #72127C2semidirect
7. #71570C2semidirect
8. #71565C2semidirect
9. #71550C2semidirect
10. #71550C2semidirect
11. #71546C2semidirect
44. C22×#123D3semidirect
67. C23×C3×C4D4semidirect
86. C22×#67D4semidirect
101. C2×C3×C4⋊C4D4semidirect
110. C2×C3×C22⋊C4D4semidirect
330. C23×C4#67semidirect
345. C2×C4⋊C4#67semidirect
372. C2×C22⋊C4#67semidirect
946. C3#16250semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#1232
C22×#9302
C2×#52232
C2×#49912
C2×#49602
#721272
#715702
#715652
#715502
#715462
#162503