Finite Group Databasebeta

← #10732228

Subgroups — #10732228

Order 768.

2314 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×#67C211yesmaximal, characteristic
2C2×C3×#380C211yesmaximal, characteristic, complemented
3C2×#5212C211yesmaximal, characteristic, complemented
4C2×#4987C211yesmaximal, characteristic, complemented
5C2×#4987C211yesmaximal, characteristic, complemented
6C2×#4984C211yesmaximal, characteristic, complemented
7#71563C211yesmaximal, characteristic, complemented
8#71550C212yesmaximal
9#71546C212yesmaximal, complemented
10#69427C212yesmaximal, complemented
11#69413C212yesmaximal, complemented
12#15181—31nomaximal, Sylow
13C24×C3×C4C2211yescharacteristic
14C23×#67C2211yescharacteristic
15C23×C4×D3C2211yescharacteristic
16C22×C3×C4⋊C4C2211yescharacteristic
17C22×C3×C4⋊C4C2211yescharacteristic
18C22×C3×C22⋊C4C2212yes—
19C22×#217C2211yescharacteristic
20C22×#217C2212yes—
21C2×C4×#67—24no—
22C2×C4×#67—24no—
23C2×C4×#67—24no—
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2212yes—
26C22×(C2×D3)⋊C4C2212yes—
27C22×C4⋊Dic3C2211yescharacteristic
28C22×C4⋊Dic3C2211yescharacteristic
29C22×C4⋊Dic3C2212yes—
30C22×Dic3⋊C4C2211yescharacteristic
31C22×C4×Dic3C2211yescharacteristic
32C3×#380—24no—
33C2×C3×#95C2212yes—
34#5212—24no—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2212yes—
41#4987—24no—
42#4987—24no—
43#4984—24no—
44C22×C4×D4—31no—
45C2×#389—31no—
46C2×#380—31no—
47C2×#380—31no—
48C2×#380—31no—
49C2×#380D311yescharacteristic, complemented
50#1442—32no—
51#1439—32no—
52#1439—32no—
53#1438—32no—
54C4⋊#95—31no—
55C25×C3C2311yescharacteristic
56C24×D3C2311yescharacteristic
57C23×C3×C4—22no—
58C23×C3×C4—22no—
59C23×C3×C4—22no—
60C23×C3×C4—22no—
61C23×C3×C4—22no—
62C23×C3×C4—22no—
63C23×C3×C4D414yes—
64C23×C3×C4C2312yes—
65C23×C3×C4C2311yescharacteristic
66C23×C3×C4C2312yes—
67C23×C3×C4C2311yescharacteristic
68C22×#67—22no—
69C22×#67—22no—
70C22×#67—22no—
71C22×#67—22no—
72C22×#67—22no—
73C22×#67—22no—
74C22×#67Q814yes—
75C23×Dic3C2312yes—
76C23×Dic3C2312yes—
77C23×Dic3C2311yescharacteristic
78C23×Dic3C2311yescharacteristic
79C23×Dic3C2311yescharacteristic
80C22×C4×D3—22no—
81C22×C4×D3—22no—
82C22×C4×D3—22no—
83C22×C4×D3—22no—
84C22×C4×D3—22no—
85C22×C4×D3—22no—
86C22×C4×D3D414yes—
87C2×C3×C4⋊C4—22no—
88C2×C3×C4⋊C4—22no—
89C2×C3×C4⋊C4—22no—
90C2×C3×C4⋊C4—22no—
91C2×C3×C4⋊C4—22no—
92C2×C3×C4⋊C4D414yescomplemented
93C2×C3×C22⋊C4—24no—
94C2×C3×C22⋊C4—24no—
95C2×C3×C22⋊C4—42no—
96C2×#217—22no—
97C2×#217—22no—
98C2×#217—22no—
99C2×#217—24no—
100C2×#217—42no—
101C2×#217—42no—
102C4×#67—232no—
103C2×(C2×D3)⋊C4—22no—
104C2×(C2×D3)⋊C4—22no—
105C2×(C2×D3)⋊C4—22no—
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)⋊C4—42no—
112C2×C4⋊Dic3—22no—
113C2×C4⋊Dic3—22no—
114C2×C4⋊Dic3—22no—
115C2×C4⋊Dic3—22no—
116C2×C4⋊Dic3—22no—
117C2×C4⋊Dic3—22no—
118C2×C4⋊Dic3—24no—
119C2×C4⋊Dic3—42no—
120C2×C4⋊Dic3—42no—
121C2×Dic3⋊C4—22no—
122C2×Dic3⋊C4—22no—
123C2×Dic3⋊C4—22no—
124C2×C4×Dic3—22no—
125C2×C4×Dic3—22no—
126C2×C4×Dic3D414yes—
127C3×#95—24no—
128C3⋊#95—24no—
129C3⋊#95—24no—
130C3⋊#95—24no—
131C3⋊#95—24no—
132C3⋊#95—24no—
133C3⋊#95—42no—
134C23×D4—31no—
135C24×C4—31no—
136C24×C4C2×D311yescharacteristic
137C2×C4×D4—64no—
138C2×C4×D4—64no—
139C2×C4×D4—64no—
140C22×C4⋊C4—31no—
141C22×C4⋊C4—31no—
142C22×C4⋊C4—31no—
143C22×C4⋊C4—32no—
144C22×C4⋊C4C2×D311yescharacteristic
145C22×C4⋊C4C2×D311yescharacteristic
146C22×C22⋊C4—31no—
147C22×C22⋊C4—31no—
148C22×C22⋊C4—32no—
149C22×C22⋊C4—32no—
150C22×C22⋊C4—32no—
151C22×C22⋊C4C2×D312yes—
152C22×C42—31no—
153#389—64no—
154#380—24no—
155#380—64no—
156#380—64no—
157#380—64no—
158C2×#95—32no—
159C2×#95—32no—
160C2×#95—32no—
161C2×#95—32no—
162C2×#95—32no—
163C2×#95—32no—
164C2×#95C2×D312yes—
165C24×C3—21no—
166C24×C3—21no—
167C24×C3—21no—
168C24×C3—21no—
169C24×C3—21no—
170C24×C3—21no—
171C24×C3—21no—
172C24×C3—21no—
173C24×C3—21no—
174C24×C3—21no—
175C24×C3—21no—
176C24×C3—21no—
177C24×C3C2×D412yes—
178C24×C3C2×Q812yes—
179C24×C3#4112yes—
180C24×C3C2411yescharacteristic
181C23×D3—21no—
182C23×D3—21no—
183C23×D3—21no—
184C23×D3—21no—
185C23×D3—21no—
186C23×D3—21no—
187C23×D3—21no—
188C23×D3—21no—
189C23×D3—21no—
190C23×D3—21no—
191C23×D3—21no—
192C23×D3—21no—
193C23×D3C2×D412yes—
194C23×D3C2×Q812yes—
195C23×D3#4112yes—
196C22×C3×C4—22no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—22no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4—28no—
209C22×C3×C4—28no—
210C22×C3×C4—28no—
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—22no—
214C22×C3×C4—22no—
215C22×C3×C4—22no—
216C22×C3×C4—22no—
217C22×C3×C4—22no—
218C22×C3×C4—44no—
219C22×C3×C4—44no—
220C22×C3×C4—44no—
221C22×C3×C4—44no—
222C22×C3×C4C2×D412yes—
223C22×C3×C4C2×D412yes—
224C22×C3×C4C2×D412yes—
225C22×C3×C4C2×D412yes—
226C22×C3×C4C2×D414yes—
227C22×C3×C4C2×D412yes—
228C22×C3×C4#4112yes—
229C22×C3×C4#4112yes—
230C22×C3×C4#4112yes—
231C2×#67—28no—
232C2×#67—28no—
233C2×#67—28no—
234C2×#67—28no—
235C2×#67—28no—
236C2×#67—28no—
237C2×#67—28no—
238C22×Dic3—21no—
239C22×Dic3—21no—
240C22×Dic3—21no—
241C22×Dic3—21no—
242C22×Dic3—21no—
243C22×Dic3—21no—
244C22×Dic3—21no—
245C22×Dic3—21no—
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3—21no—
249C22×Dic3—21no—
250C22×Dic3—21no—
251C22×Dic3—21no—
252C22×Dic3—21no—
253C22×Dic3—21no—
254C22×Dic3—22no—
255C22×Dic3—22no—
256C22×Dic3—22no—
257C22×Dic3—22no—
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×Dic3C2×D412yes—
269C22×Dic3C2×D412yes—
270C22×Dic3C2×D412yes—
271C22×Dic3C2×Q812yes—
272C22×Dic3#4112yes—
273C2×C4×D3—28no—
274C2×C4×D3—28no—
275C2×C4×D3—28no—
276C2×C4×D3—44no—
277C2×C4×D3—44no—
278C2×C4×D3—44no—
279C2×C4×D3—44no—
280C3×C4⋊C4—28no—
281C3×C4⋊C4—44no—
282C3×C22⋊C4—48no—
283#217—28no—
284#217—48no—
285(C2×D3)⋊C4—28no—
286(C2×D3)⋊C4—48no—
287(C2×D3)⋊C4—48no—
288C4⋊Dic3—48no—
289C4⋊Dic3—44no—
290C4⋊Dic3—44no—
291Dic3⋊C4—28no—
292C4×Dic3—28no—
293C25—31no—
294C25C22×D311yescharacteristic
295C22×D4—34no—
296C22×D4—62no—
297C22×D4—62no—
298C22×D4—62no—
299C22×D4—62no—
300C22×D4—62no—
301C22×D4—62no—
302C23×C4—22no—
303C23×C4—22no—
304C23×C4—22no—
305C23×C4—22no—
306C23×C4—22no—
307C23×C4—22no—
308C23×C4—31no—
309C23×C4—31no—
310C23×C4—31no—
311C23×C4—34no—
312C23×C4—32no—
313C23×C4—32no—
314C23×C4—62no—
315C23×C4—62no—
316C23×C4—62no—
317C23×C4—62no—
318C23×C4—62no—
319C23×C4—62no—
320C23×C4D1214yes—
321C23×C4C22×D312yes—
322C23×C4C22×D311yescharacteristic
323C23×C4C22×D312yes—
324C23×C4C22×D311yescharacteristic
325C4×D4—632no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—62no—
332C2×C4⋊C4—62no—
333C2×C4⋊C4—62no—
334C2×C4⋊C4—64no—
335C2×C4⋊C4—62no—
336C2×C4⋊C4—62no—
337C2×C4⋊C4—62no—
338C2×C4⋊C4—62no—
339C2×C4⋊C4—62no—
340C2×C4⋊C4—62no—
341C2×C4⋊C4—122no—
342C2×C4⋊C4—122no—
343C2×C4⋊C4#6714yescomplemented
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—62no—
348C2×C22⋊C4—62no—
349C2×C22⋊C4—62no—
350C2×C22⋊C4—62no—
351C2×C22⋊C4—62no—
352C2×C22⋊C4—62no—
353C2×C22⋊C4—64no—
354C2×C22⋊C4—64no—
355C2×C22⋊C4—64no—
356C2×C22⋊C4—64no—
357C2×C22⋊C4—122no—
358C2×C22⋊C4—122no—
359C2×C22⋊C4—122no—
360C2×C22⋊C4—122no—
361C2×C22⋊C4—122no—
362C2×C42—34no—
363C2×C42—62no—
364C2×C42—62no—
365#95—24no—
366#95—64no—
367#95—64no—
368#95—64no—
369#95—64no—
370#95—64no—
371#95—122no—
372C23×C3—22no—
373C23×C3—22no—
374C23×C3—22no—
375C23×C3—22no—
376C23×C3—22no—
377C23×C3—22no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—22no—
381C23×C3—22no—
382C23×C3—22no—
383C23×C3—22no—
384C23×C3—22no—
385C23×C3—22no—
386C23×C3—22no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—22no—
390C23×C3—41no—
391C23×C3—41no—
392C23×C3—41no—
393C23×C3—41no—
394C23×C3—41no—
395C23×C3—41no—
396C23×C3—41no—
397C23×C3—41no—
398C23×C3—41no—
399C23×C3—41no—
400C23×C3—41no—
401C23×C3—41no—
402C23×C3—41no—
403C23×C3—41no—
404C23×C3—41no—
405C23×C3—41no—
406C23×C3C22⋊Q814yes—
407C23×C3C22×D411yescharacteristic
408C23×C3C22×D411yescharacteristic
409C23×C3C22×D411yescharacteristic
410C23×C3C22×D411yescharacteristic
411C23×C3C22×Q811yescharacteristic
412C23×C3C2×#4111yescharacteristic
413C23×C3C2×#4111yescharacteristic
414C23×C3C2×#4111yescharacteristic
415C23×C3C2×#4111yescharacteristic
416C23×C3C2×#4111yescharacteristic
417C23×C3C2×#4111yescharacteristic
418C23×C3H(5,𝔽2)11yescharacteristic
419C23×C3H(5,𝔽2)11yescharacteristic
420C23×C3H(5,𝔽2)11yescharacteristic
421C23×C32−1+411yescharacteristic
422C22×D3—22no—
423C22×D3—22no—
424C22×D3—22no—
425C22×D3—22no—
426C22×D3—22no—
427C22×D3—22no—
428C22×D3—22no—
429C22×D3—22no—
430C22×D3—22no—
431C22×D3—22no—
432C22×D3—22no—
433C22×D3—22no—
434C22×D3—22no—
435C22×D3—22no—
436C22×D3—22no—
437C22×D3—22no—
438C22×D3—22no—
439C22×D3—22no—
440C22×D3—41no—
441C22×D3—41no—
442C22×D3—41no—
443C22×D3—41no—
444C22×D3—41no—
445C22×D3—41no—
446C22×D3—41no—
447C22×D3—41no—
448C22×D3—41no—
449C22×D3—41no—
450C22×D3—41no—
451C22×D3—41no—
452C22×D3—41no—
453C22×D3—41no—
454C22×D3—41no—
455C22×D3—41no—
456C22×D3C22⋊Q814yes—
457C2×C3×C4—22no—
458C2×C3×C4—24no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—24no—
462C2×C3×C4—24no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—42no—
467C2×C3×C4—41no—
468C2×C3×C4—42no—
469C2×C3×C4—42no—
470C2×C3×C4—42no—
471C2×C3×C4—416no—
472C2×C3×C4—42no—
473C2×C3×C4—42no—
474C2×C3×C4—42no—
475C2×C3×C4—42no—
476C2×C3×C4—42no—
477C2×C3×C4—42no—
478C2×C3×C4—42no—
479C2×C3×C4#12014yes—
480C2×C3×C4#12114yes—
481C2×C3×C4#12114yes—
482C2×C3×C4#12114yes—
483C2×C3×C4#12314yes—
484C2×C3×C4#12314yes—
485C2×C3×C4#12414yes—
486#67—232no—
487C2×Dic3—22no—
488C2×Dic3—22no—
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—22no—
498C2×Dic3—22no—
499C2×Dic3—41no—
500C2×Dic3—41no—
501C2×Dic3—41no—
502C2×Dic3—41no—
503C2×Dic3—41no—
504C2×Dic3—41no—
505C2×Dic3—41no—
506C2×Dic3—41no—
507C2×Dic3—42no—
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×Dic3C22⋊Q814yes—
522C4×D3—416no—
523C24—21no—
524C24—21no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—21no—
530C24—21no—
531C24—21no—
532C24—21no—
533C24—21no—
534C24—21no—
535C24—32no—
536C24—32no—
537C24—32no—
538C24—61no—
539C24—61no—
540C24—61no—
541C24—61no—
542C24—61no—
543C24—61no—
544C24—61no—
545C24—61no—
546C24—61no—
547C24—61no—
548C24—61no—
549C24—61no—
550C24C2×D1212yes—
551C24#23712yes—
552C24D3×Q812yes—
553C24C23×D311yescharacteristic
554C2×D4—68no—
555C2×D4—68no—
556C2×D4—68no—
557C2×D4—68no—
558C2×D4—68no—
559C2×D4—68no—
560C2×D4—68no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—28no—
574C22×C4—28no—
575C22×C4—28no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—32no—
584C22×C4—32no—
585C22×C4—32no—
586C22×C4—32no—
587C22×C4—32no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—61no—
593C22×C4—61no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4—61no—
597C22×C4—61no—
598C22×C4—61no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4—61no—
602C22×C4—61no—
603C22×C4—61no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—68no—
609C22×C4—68no—
610C22×C4—68no—
611C22×C4—62no—
612C22×C4—62no—
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—124no—
626C22×C4—124no—
627C22×C4—124no—
628C22×C4—124no—
629C22×C4C2×D1212yes—
630C22×C4C2×D1212yes—
631C22×C4#23512yes—
632C22×C4D3×D412yes—
633C22×C4D3×D412yes—
634C22×C4#23712yes—
635C22×C4#23712yes—
636C22×C4C2×#6714yes—
637C22×C4C2×#6712yes—
638C4⋊C4—28no—
639C4⋊C4—44no—
640C4⋊C4—68no—
641C4⋊C4—128no—
642C4⋊C4—124no—
643C4⋊C4—124no—
644C22⋊C4—48no—
645C22⋊C4—68no—
646C22⋊C4—68no—
647C22⋊C4—128no—
648C22⋊C4—128no—
649C22⋊C4—128no—
650C42—68no—
651C22×C3—24no—
652C22×C3—24no—
653C22×C3—24no—
654C22×C3—42no—
655C22×C3—42no—
656C22×C3—42no—
657C22×C3—42no—
658C22×C3—42no—
659C22×C3—42no—
660C22×C3—42no—
661C22×C3—42no—
662C22×C3—42no—
663C22×C3—42no—
664C22×C3—42no—
665C22×C3—42no—
666C22×C3C2×#12011yescharacteristic
667C22×C3C2×#12111yescharacteristic
668C22×C3C2×#12111yescharacteristic
669C22×C3C2×#12111yescharacteristic
670C22×C3C2×C22⋊Q811yescharacteristic
671C22×C3C2×C22⋊Q811yescharacteristic
672C22×C3C2×C22⋊Q811yescharacteristic
673C22×C3C2×#12311yescharacteristic
674C22×C3C2×#12311yescharacteristic
675C22×C3#52511yescharacteristic
676C22×C3#52511yescharacteristic
677C22×C3#52511yescharacteristic
678C22×C3C2×#12411yescharacteristic
679C22×C3#53511yescharacteristic
680C22×C3#53511yescharacteristic
681C22×C3#53511yescharacteristic
682C22×C3#53711yescharacteristic
683C22×C3#53711yescharacteristic
684C22×C3#53711yescharacteristic
685C22×C3#54611yescharacteristic
686C22×C3#54611yescharacteristic
687C22×C3D4×Q811yescharacteristic
688C22×C3#55011yescharacteristic
689C22×C3#55211yescharacteristic
690C22×C3#55211yescharacteristic
691C22×C3#55311yescharacteristic
692C22×C3#55311yescharacteristic
693C22×C3#55311yescharacteristic
694C22×C3#55311yescharacteristic
695C22×C3#55411yescharacteristic
696C22×C3#55411yescharacteristic
697C22×C3#55411yescharacteristic
698C22×C3#55511yescharacteristic
699C22×C3#55511yescharacteristic
700C22×C3#55611yescharacteristic
701C2×D3—24no—
702C2×D3—24no—
703C2×D3—24no—
704C2×D3—42no—
705C2×D3—42no—
706C2×D3—42no—
707C2×D3—42no—
708C2×D3—42no—
709C2×D3—42no—
710C2×D3—42no—
711C2×D3—42no—
712C2×D3—42no—
713C2×D3—42no—
714C2×D3—42no—
715C2×D3—42no—
716C3×C4—42no—
717C3×C4—44no—
718C3×C4—82no—
719C3×C4#39418yes—
720Dic3—24no—
721Dic3—42no—
722Dic3—42no—
723Dic3—82no—
724Dic3—82no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—34no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—62no—
761C23—62no—
762C23—62no—
763C23—62no—
764C23—62no—
765C23—62no—
766C23—62no—
767C23—62no—
768C23—62no—
769C23—62no—
770C23—62no—
771C23—62no—
772C23—62no—
773C23—62no—
774C23—62no—
775C23—62no—
776C23—62no—
777C23—62no—
778C23—121no—
779C23—121no—
780C23—121no—
781C23—121no—
782C23—121no—
783C23—121no—
784C23—121no—
785C23—121no—
786C23—121no—
787C23—121no—
788C23—121no—
789C23—121no—
790C23—121no—
791C23—121no—
792C23—121no—
793C23—121no—
794C23#89714yes—
795C23C22×D1211yescharacteristic
796C23C2×#23511yescharacteristic
797C23C2×D3×D411yescharacteristic
798C23C2×D3×D411yescharacteristic
799C23C2×#23711yescharacteristic
800C23C2×#23711yescharacteristic
801C23C2×#23711yescharacteristic
802C23#100411yescharacteristic
803C23C2×D3×Q811yescharacteristic
804C23#100711yescharacteristic
805C23D3×#4111yescharacteristic
806C23D3×#4111yescharacteristic
807C23#100911yescharacteristic
808C23#100911yescharacteristic
809C23C22×#6711yescharacteristic
810D4—632no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—34no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—416no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—62no—
835C2×C4—62no—
836C2×C4—62no—
837C2×C4—62no—
838C2×C4—62no—
839C2×C4—62no—
840C2×C4—62no—
841C2×C4—62no—
842C2×C4—62no—
843C2×C4—62no—
844C2×C4—62no—
845C2×C4—62no—
846C2×C4—121no—
847C2×C4—121no—
848C2×C4—121no—
849C2×C4—121no—
850C2×C4—121no—
851C2×C4—121no—
852C2×C4—121no—
853C2×C4—121no—
854C2×C4—1216no—
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—122no—
864C2×C4—122no—
865C2×C4—122no—
866C2×C4—122no—
867C2×C4—122no—
868C2×C4—122no—
869C2×C4#88214yes—
870C2×C4#88314yes—
871C2×C4#88514yes—
872C2×C4#88614yes—
873C2×C4#93014yes—
874C2×C4#93814yes—
875C2×C4#93914yes—
876C2×C3—44no—
877C2×C3C2×#39411yescharacteristic
878C2×C3#241411yescharacteristic
879C2×C3#241411yescharacteristic
880C2×C3#241711yescharacteristic
881C2×C3#241711yescharacteristic
882C2×C3#248511yescharacteristic
883C2×C3#248511yescharacteristic
884C2×C3#248711yescharacteristic
885C2×C3#248711yescharacteristic
886C2×C3#253511yescharacteristic
887C2×C3#253811yescharacteristic
888C2×C3#256211yescharacteristic
889C2×C3#256311yescharacteristic
890C2×C3#261511yescharacteristic
891C2×C3#284811yescharacteristic
892D3—44no—
893C22—24no—
894C22—24no—
895C22—24no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—64no—
909C22—64no—
910C22—64no—
911C22—122no—
912C22—122no—
913C22—122no—
914C22—122no—
915C22—122no—
916C22—122no—
917C22—122no—
918C22—122no—
919C22—122no—
920C22—122no—
921C22—122no—
922C22—122no—
923C22C2×#88211yescharacteristic
924C22C2×#88311yescharacteristic
925C22C2×#88511yescharacteristic
926C22C2×#88611yescharacteristic
927C22C2×#89711yescharacteristic
928C22#551011yescharacteristic
929C22#551111yescharacteristic
930C22#551311yescharacteristic
931C22#552411yescharacteristic
932C22#552511yescharacteristic
933C22#553011yescharacteristic
934C22#553211yescharacteristic
935C22#560611yescharacteristic
936C22#560611yescharacteristic
937C22#560711yescharacteristic
938C22#560711yescharacteristic
939C22#561411yescharacteristic
940C22#561611yescharacteristic
941C22#561811yescharacteristic
942C22#561811yescharacteristic
943C22D3×C22⋊Q811yescharacteristic
944C22D3×C22⋊Q811yescharacteristic
945C22#562911yescharacteristic
946C22#562911yescharacteristic
947C22#563511yescharacteristic
948C22#563511yescharacteristic
949C22#563911yescharacteristic
950C22#564111yescharacteristic
951C22C2×#93011yescharacteristic
952C22C2×#93811yescharacteristic
953C22C2×#93911yescharacteristic
954C22#580611yescharacteristic
955C22Q8×#6711yescharacteristic
956C22#582911yescharacteristic
957C22#583411yescharacteristic
958C4—42no—
959C4—44no—
960C4—64no—
961C4—82no—
962C4—122no—
963C4—122no—
964C4—242no—
965C4—242no—
966C4#496118yes—
967C3#1518111yescharacteristic, complemented, Sylow
968C2—44no—
969C2—124no—
970C2#7391211yescharacteristic
971C2#7394011yescharacteristic
972C2#7394211yescharacteristic
973C2#7402411yescharacteristic
974C2#7402611yescharacteristic
975C2#7402811yescharacteristic
976C2#7403011yescharacteristic
977C2#7404911yescharacteristic
978C2C2×#496111yescharacteristic
979C2#8219411yescharacteristic
980C2#8227611yescharacteristic
981C2#8266611yescharacteristic
982C2#8270311yescharacteristic
983C2#8275211yescharacteristic
984C2#8277811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#380C2
prime radicalC23×#67C22
hypercenterC2×#380D3
hypocenterC3#15181
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×C3×#380C2semidirect
3. C2×#5212C2semidirect
4. C2×#4987C2semidirect
5. C2×#4987C2semidirect
6. C2×#4984C2semidirect
7. #71563C2semidirect
9. #71546C2semidirect
10. #69427C2semidirect
11. #69413C2semidirect
49. C2×#380D3semidirect
92. C2×C3×C4⋊C4D4semidirect
343. C2×C4⋊C4#67semidirect
967. C3#15181semidirect

Maximal subgroups

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

subgroupindex
C22×C4×#672
C2×C3×#3802
C2×#52122
C2×#49872
C2×#49842
#715632
#715502
#715462
#694272
#694132
#151813