Finite Group Databasebeta

← #10728019

Subgroups — #10728019

Order 768.

1434 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4952C211yesmaximal, characteristic
2C2×Dic3×C22⋊C4C211yesmaximal, characteristic
3C3×#1440C211yesmaximal, characteristic
4#71549C211yesmaximal, characteristic
5#71546C211yesmaximal, characteristic
6#71544C211yesmaximal, characteristic
7#71544C211yesmaximal, characteristic
8#69418C211yesmaximal, characteristic, complemented
9#69418C211yesmaximal, characteristic, complemented
10#69418C211yesmaximal, characteristic, complemented
11#69411C211yesmaximal, characteristic, complemented
12#69407C211yesmaximal, characteristic, complemented
13#69405C211yesmaximal, characteristic, complemented
14#69402C211yesmaximal, characteristic, complemented
15#69402C211yesmaximal, characteristic, complemented
16#14828—31nomaximal, Sylow
17C24×Dic3C2211yescharacteristic
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×#217C2211yescharacteristic
22C22×#217C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×C4⋊Dic3C2211yescharacteristic
25C22×Dic3⋊C4C2211yescharacteristic
26C22×C4×Dic3C2211yescharacteristic
27C22×C4×Dic3C2211yescharacteristic
28C2×C3×#95C2211yescharacteristic
29C2×C3×#95C2211yescharacteristic
30C2×C3×#95C2211yescharacteristic
31C2×C3×#95C2211yescharacteristic
32C2×C3⋊#95C2211yescharacteristic
33C2×C3⋊#95C2211yescharacteristic
34C2×C3⋊#95C2211yescharacteristic
35C2×C3⋊#95C2211yescharacteristic
36C2×C3⋊#95C2211yescharacteristic
37C2×C3⋊#95C2211yescharacteristic
38C2×C3⋊#95C2211yescharacteristic
39C2×C3⋊#95C2211yescharacteristic
40C2×C3⋊#95C2211yescharacteristic
41C2×C3⋊#95C2211yescharacteristic
42C2×C3⋊#95C2211yescharacteristic
43C2×C3⋊#95C2211yescharacteristic
44C2×C3⋊#95C2211yescharacteristic
45C2×C3⋊#95C2211yescharacteristic
46C2×C3⋊#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52#4952—24no—
53Dic3×C22⋊C4—24no—
54C2×#397—31no—
55C2×C4×C22⋊C4—31no—
56#1443—31no—
57#1443—31no—
58#1443—31no—
59#1441—31no—
60#1440—31no—
61#1440D311yescharacteristic
62#1439—31no—
63#1436—31no—
64#1436—31no—
65#1434—31no—
66#1434—31no—
67C22⋊#95—31no—
68C22⋊#95—31no—
69C25×C3C2311yescharacteristic
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×Dic3—22no—
77C23×Dic3—22no—
78C23×Dic3—22no—
79C23×Dic3—22no—
80C23×Dic3—22no—
81C23×Dic3—41no—
82C23×Dic3—41no—
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C2×C3×C22⋊C4—22no—
92C2×C3×C22⋊C4—22no—
93C2×C3×C22⋊C4—22no—
94C2×C3×C22⋊C4—22no—
95C2×C3×C22⋊C4—22no—
96C2×C3×C22⋊C4—41no—
97C2×C3×C22⋊C4—41no—
98C2×C3×C22⋊C4—41no—
99C2×C3×C22⋊C4D414yes—
100C2×#217—22no—
101C2×#217—22no—
102C2×#217—22no—
103C2×#217—22no—
104C2×#217—22no—
105C2×#217—22no—
106C2×#217—22no—
107C2×#217—22no—
108C2×#217—41no—
109C2×C4⋊Dic3—22no—
110C2×C4⋊Dic3—22no—
111C2×C4⋊Dic3—41no—
112C2×Dic3⋊C4—22no—
113C2×Dic3⋊C4—22no—
114C2×Dic3⋊C4—41no—
115C2×C4×Dic3—22no—
116C2×C4×Dic3—22no—
117C2×C4×Dic3—22no—
118C2×C4×Dic3—22no—
119C2×C4×Dic3—41no—
120C2×C4×Dic3—41no—
121C3×#95—22no—
122C3×#95—41no—
123C3×#95—41no—
124C3×#95—41no—
125C3⋊#95—22no—
126C3⋊#95—22no—
127C3⋊#95—22no—
128C3⋊#95—22no—
129C3⋊#95—22no—
130C3⋊#95—22no—
131C3⋊#95—22no—
132C3⋊#95—22no—
133C3⋊#95—22no—
134C3⋊#95—22no—
135C3⋊#95—22no—
136C3⋊#95—22no—
137C3⋊#95—22no—
138C3⋊#95—22no—
139C3⋊#95—22no—
140C3⋊#95—41no—
141C3⋊#95—41no—
142C3⋊#95—41no—
143C3⋊#95—41no—
144C3⋊#95—41no—
145C24×C4—31no—
146C22×C4⋊C4—31no—
147C22×C4⋊C4—31no—
148C22×C22⋊C4—31no—
149C22×C22⋊C4—31no—
150C22×C22⋊C4—31no—
151C22×C22⋊C4C2×D311yescharacteristic
152C22×C22⋊C4C2×D311yescharacteristic
153C22×C22⋊C4C2×D311yescharacteristic
154C22×C42—31no—
155C22×C42—31no—
156#397—64no—
157C4×C22⋊C4—64no—
158C2×#95—31no—
159C2×#95—31no—
160C2×#95—31no—
161C2×#95—31no—
162C2×#95—31no—
163C2×#95—31no—
164C2×#95—31no—
165C2×#95—31no—
166C2×#95—31no—
167C2×#95—31no—
168C2×#95—31no—
169C2×#95—31no—
170C2×#95—31no—
171C2×#95—31no—
172C2×#95—31no—
173C2×#95—31no—
174C2×#95—31no—
175C2×#95—31no—
176C2×#95—31no—
177C2×#95—31no—
178C2×#95C2×D311yescharacteristic
179C2×#95C2×D311yescharacteristic
180C2×#95C2×D311yescharacteristic
181C2×#95C2×D311yescharacteristic
182C24×C3—21no—
183C24×C3—21no—
184C24×C3—21no—
185C24×C3—21no—
186C24×C3—21no—
187C24×C3—21no—
188C24×C3—21no—
189C24×C3—21no—
190C24×C3—21no—
191C24×C3—21no—
192C24×C3—21no—
193C24×C3—21no—
194C24×C3C2×D412yes—
195C24×C3#4112yes—
196C24×C3#4112yes—
197C24×C3C2411yescharacteristic
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
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—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4C2×D412yes—
238C22×C3×C4C2×D412yes—
239C22×C3×C4#4112yes—
240C22×Dic3—21no—
241C22×Dic3—21no—
242C22×Dic3—21no—
243C22×Dic3—21no—
244C22×Dic3—28no—
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—21no—
255C22×Dic3—21no—
256C22×Dic3—21no—
257C22×Dic3—21no—
258C22×Dic3—21no—
259C22×Dic3—21no—
260C22×Dic3—21no—
261C22×Dic3—21no—
262C22×Dic3—21no—
263C22×Dic3—21no—
264C22×Dic3—21no—
265C22×Dic3—21no—
266C22×Dic3—21no—
267C22×Dic3—21no—
268C22×Dic3—21no—
269C22×Dic3—21no—
270C22×Dic3—21no—
271C22×Dic3—21no—
272C22×Dic3—21no—
273C22×Dic3—21no—
274C22×Dic3—21no—
275C22×Dic3—21no—
276C22×Dic3—21no—
277C22×Dic3—21no—
278C22×Dic3—21no—
279C22×Dic3—21no—
280C22×Dic3—21no—
281C22×Dic3—21no—
282C22×Dic3—21no—
283C22×Dic3—21no—
284C22×Dic3—21no—
285C22×Dic3—21no—
286C22×Dic3—21no—
287C22×Dic3—21no—
288C22×Dic3—21no—
289C22×Dic3—21no—
290C22×Dic3—44no—
291C22×Dic3—44no—
292C22×Dic3—44no—
293C22×Dic3—44no—
294C22×Dic3—44no—
295C22×Dic3—44no—
296C22×Dic3#4112yes—
297C22×Dic3#4112yes—
298C22×Dic3#4112yes—
299C22×Dic3#4112yes—
300C22×Dic3#4112yes—
301C22×Dic3#4112yes—
302C22×Dic3#4112yes—
303C3×C22⋊C4—28no—
304C3×C22⋊C4—44no—
305C3×C22⋊C4—44no—
306#217—28no—
307#217—44no—
308#217—44no—
309C4⋊Dic3—44no—
310Dic3⋊C4—44no—
311C4×Dic3—44no—
312C4×Dic3—44no—
313C25C22×D311yescharacteristic
314C23×C4—31no—
315C23×C4—31no—
316C23×C4—31no—
317C23×C4—31no—
318C23×C4—31no—
319C23×C4—31no—
320C23×C4—31no—
321C23×C4—31no—
322C23×C4—62no—
323C23×C4—62no—
324C23×C4—62no—
325C23×C4—62no—
326C23×C4—62no—
327C23×C4—121no—
328C23×C4—121no—
329C23×C4C22×D311yescharacteristic
330C23×C4C22×D311yescharacteristic
331C23×C4C22×D311yescharacteristic
332C23×C4C22×D311yescharacteristic
333C23×C4C22×D311yescharacteristic
334C23×C4C22×D311yescharacteristic
335C2×C4⋊C4—62no—
336C2×C4⋊C4—62no—
337C2×C4⋊C4—62no—
338C2×C4⋊C4—62no—
339C2×C4⋊C4—121no—
340C2×C4⋊C4—121no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—41no—
347C2×C22⋊C4—41no—
348C2×C22⋊C4—41no—
349C2×C22⋊C4—62no—
350C2×C22⋊C4—62no—
351C2×C22⋊C4—62no—
352C2×C22⋊C4—62no—
353C2×C22⋊C4—62no—
354C2×C22⋊C4—62no—
355C2×C22⋊C4—62no—
356C2×C22⋊C4—62no—
357C2×C22⋊C4—121no—
358C2×C22⋊C4D1214yes—
359C2×C42—62no—
360C2×C42—62no—
361C2×C42—62no—
362C2×C42—62no—
363C2×C42—121no—
364C2×C42—121no—
365#95—22no—
366#95—41no—
367#95—41no—
368#95—41no—
369#95—62no—
370#95—62no—
371#95—62no—
372#95—62no—
373#95—62no—
374#95—62no—
375#95—62no—
376#95—62no—
377#95—62no—
378#95—62no—
379#95—62no—
380#95—62no—
381#95—62no—
382#95—62no—
383#95—62no—
384#95—121no—
385#95—121no—
386#95—121no—
387#95—121no—
388#95—121no—
389C23×C3—22no—
390C23×C3—22no—
391C23×C3—22no—
392C23×C3—22no—
393C23×C3—22no—
394C23×C3—22no—
395C23×C3—22no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3—22no—
400C23×C3—22no—
401C23×C3—22no—
402C23×C3—22no—
403C23×C3—22no—
404C23×C3—22no—
405C23×C3—22no—
406C23×C3—22no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3#12314yes—
424C23×C3C22×D411yescharacteristic
425C23×C3C2×#4111yescharacteristic
426C23×C3C2×#4111yescharacteristic
427C23×C3C2×#4111yescharacteristic
428C23×C3C2×#4111yescharacteristic
429C23×C3C2×#4111yescharacteristic
430C23×C3C2×#4111yescharacteristic
431C23×C3C2×#4111yescharacteristic
432C23×C3C2×#4111yescharacteristic
433C23×C3C2×#4111yescharacteristic
434C23×C3C2×#4111yescharacteristic
435C23×C3H(5,𝔽2)11yescharacteristic
436C23×C3H(5,𝔽2)11yescharacteristic
437C23×C3H(5,𝔽2)11yescharacteristic
438C23×C32−1+411yescharacteristic
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×Dic3—22no—
482C2×Dic3—22no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—22no—
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—416no—
500C2×Dic3—41no—
501C2×Dic3—41no—
502C2×Dic3—41no—
503C2×Dic3—41no—
504C2×Dic3—41no—
505C2×Dic3—41no—
506C2×Dic3—41no—
507C2×Dic3—41no—
508C2×Dic3—41no—
509C2×Dic3—41no—
510C2×Dic3—41no—
511C2×Dic3—41no—
512C2×Dic3—41no—
513C2×Dic3—41no—
514C2×Dic3—41no—
515C2×Dic3—41no—
516C2×Dic3—41no—
517C2×Dic3—41no—
518C2×Dic3—41no—
519C2×Dic3—41no—
520C2×Dic3—41no—
521C2×Dic3—41no—
522C2×Dic3—41no—
523C2×Dic3—41no—
524C2×Dic3—41no—
525C2×Dic3—41no—
526C2×Dic3—41no—
527C2×Dic3—41no—
528C2×Dic3—41no—
529C2×Dic3—41no—
530C2×Dic3—41no—
531C2×Dic3—41no—
532C2×Dic3—41no—
533C2×Dic3—41no—
534C2×Dic3—41no—
535C2×Dic3—41no—
536C2×Dic3—41no—
537C2×Dic3#12614yes—
538C24—21no—
539C24—21no—
540C24—21no—
541C24—21no—
542C24—21no—
543C24—21no—
544C24—21no—
545C24—21no—
546C24—21no—
547C24—21no—
548C24—21no—
549C24—21no—
550C24C2×D1212yes—
551C24#23712yes—
552C24#23712yes—
553C24C23×D311yescharacteristic
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—32no—
594C22×C4—32no—
595C22×C4—32no—
596C22×C4—32no—
597C22×C4—32no—
598C22×C4—32no—
599C22×C4—32no—
600C22×C4—61no—
601C22×C4—61no—
602C22×C4—61no—
603C22×C4—61no—
604C22×C4—68no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4—61no—
618C22×C4—61no—
619C22×C4—61no—
620C22×C4—61no—
621C22×C4—61no—
622C22×C4—61no—
623C22×C4—61no—
624C22×C4—61no—
625C22×C4—61no—
626C22×C4—61no—
627C22×C4—61no—
628C22×C4—61no—
629C22×C4—61no—
630C22×C4—61no—
631C22×C4—61no—
632C22×C4—61no—
633C22×C4—61no—
634C22×C4—61no—
635C22×C4—61no—
636C22×C4—61no—
637C22×C4—61no—
638C22×C4—61no—
639C22×C4—61no—
640C22×C4—61no—
641C22×C4—61no—
642C22×C4—61no—
643C22×C4—61no—
644C22×C4—61no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4—61no—
649C22×C4—61no—
650C22×C4—124no—
651C22×C4—124no—
652C22×C4—124no—
653C22×C4—124no—
654C22×C4—124no—
655C22×C4—124no—
656C22×C4C2×D1212yes—
657C22×C4C2×D1212yes—
658C22×C4#23712yes—
659C4⋊C4—124no—
660C4⋊C4—124no—
661C22⋊C4—28no—
662C22⋊C4—44no—
663C22⋊C4—44no—
664C22⋊C4—68no—
665C22⋊C4—124no—
666C22⋊C4—124no—
667C42—124no—
668C42—124no—
669C22×C3—24no—
670C22×C3—24no—
671C22×C3—24no—
672C22×C3—42no—
673C22×C3—42no—
674C22×C3—42no—
675C22×C3—42no—
676C22×C3—42no—
677C22×C3—42no—
678C22×C3—42no—
679C22×C3—42no—
680C22×C3—42no—
681C22×C3—42no—
682C22×C3—42no—
683C22×C3—42no—
684C22×C3C2×#12311yescharacteristic
685C22×C3#52511yescharacteristic
686C22×C3#52511yescharacteristic
687C22×C3C2×#12611yescharacteristic
688C22×C3#52911yescharacteristic
689C22×C3#52911yescharacteristic
690C22×C3#52911yescharacteristic
691C22×C3#52911yescharacteristic
692C22×C3#52911yescharacteristic
693C22×C3#52911yescharacteristic
694C22×C3#52911yescharacteristic
695C22×C3#52911yescharacteristic
696C22×C3#52911yescharacteristic
697C22×C3#53811yescharacteristic
698C22×C3#53811yescharacteristic
699C22×C3#53911yescharacteristic
700C22×C3#53911yescharacteristic
701C22×C3#54011yescharacteristic
702C22×C3#54211yescharacteristic
703C22×C3#54611yescharacteristic
704C22×C3#54611yescharacteristic
705C22×C3#54611yescharacteristic
706C22×C3#54711yescharacteristic
707C22×C3#55111yescharacteristic
708C22×C3#55111yescharacteristic
709C22×C3#55111yescharacteristic
710C22×C3#55111yescharacteristic
711C22×C3#55211yescharacteristic
712C22×C3#55311yescharacteristic
713C22×C3#55311yescharacteristic
714C22×C3#55311yescharacteristic
715C22×C3#55311yescharacteristic
716C22×C3#55511yescharacteristic
717C22×C3#55611yescharacteristic
718C22×C3#55611yescharacteristic
719C3×C4—42no—
720C3×C4—42no—
721C3×C4—42no—
722C3×C4—81no—
723C3×C4—81no—
724C3×C4—81no—
725Dic3—24no—
726Dic3—42no—
727Dic3—42no—
728Dic3—42no—
729Dic3—42no—
730Dic3—81no—
731Dic3—81no—
732Dic3—81no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23#88614yes—
768C23C22×D1211yescharacteristic
769C23C2×#23711yescharacteristic
770C23C2×#23711yescharacteristic
771C23C2×#23711yescharacteristic
772C23#100411yescharacteristic
773C23#100411yescharacteristic
774C23#100411yescharacteristic
775C23D3×#4111yescharacteristic
776C23D3×#4111yescharacteristic
777C23D3×#4111yescharacteristic
778C23D3×#4111yescharacteristic
779C23D3×#4111yescharacteristic
780C23D3×#4111yescharacteristic
781C23D3×#4111yescharacteristic
782C23#101011yescharacteristic
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—34no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—62no—
827C2×C4—62no—
828C2×C4—62no—
829C2×C4—62no—
830C2×C4—62no—
831C2×C4—62no—
832C2×C4—62no—
833C2×C4—62no—
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—1216no—
845C2×C4—121no—
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—121no—
855C2×C4—121no—
856C2×C4—121no—
857C2×C4—121no—
858C2×C4—121no—
859C2×C4—121no—
860C2×C4—121no—
861C2×C4—121no—
862C2×C4—121no—
863C2×C4—121no—
864C2×C4—121no—
865C2×C4—121no—
866C2×C4—121no—
867C2×C4—121no—
868C2×C4—121no—
869C2×C4—121no—
870C2×C4—121no—
871C2×C4—121no—
872C2×C4—121no—
873C2×C4—121no—
874C2×C4—121no—
875C2×C4—121no—
876C2×C4—121no—
877C2×C4—121no—
878C2×C4—121no—
879C2×C4—121no—
880C2×C4—121no—
881C2×C4—121no—
882C2×C3—44no—
883C2×C3#240111yescharacteristic
884C2×C3#241911yescharacteristic
885C2×C3#244411yescharacteristic
886C2×C3#245711yescharacteristic
887C2×C3#246611yescharacteristic
888C2×C3#247411yescharacteristic
889C2×C3#248011yescharacteristic
890C2×C3#249411yescharacteristic
891C2×C3#251811yescharacteristic
892C2×C3#252311yescharacteristic
893C2×C3#253111yescharacteristic
894C2×C3#257711yescharacteristic
895C2×C3#257811yescharacteristic
896C2×C3#264911yescharacteristic
897C2×C3#285311yescharacteristic
898C22—24no—
899C22—24no—
900C22—24no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22C2×#88611yescharacteristic
914C22#552411yescharacteristic
915C22#552411yescharacteristic
916C22#555411yescharacteristic
917C22#555411yescharacteristic
918C22#555411yescharacteristic
919C22#555511yescharacteristic
920C22#558711yescharacteristic
921C22#559311yescharacteristic
922C22#560011yescharacteristic
923C22#560111yescharacteristic
924C22#560111yescharacteristic
925C22#560111yescharacteristic
926C22#560211yescharacteristic
927C22#561311yescharacteristic
928C22#561511yescharacteristic
929C22#561611yescharacteristic
930C22#564911yescharacteristic
931C22#564911yescharacteristic
932C22#564911yescharacteristic
933C22#564911yescharacteristic
934C22#564911yescharacteristic
935C22#564911yescharacteristic
936C22#565011yescharacteristic
937C22#565911yescharacteristic
938C22#566011yescharacteristic
939C22#566111yescharacteristic
940C22#566911yescharacteristic
941C22#567911yescharacteristic
942C22#567911yescharacteristic
943C22#568011yescharacteristic
944C22#570211yescharacteristic
945C22#570211yescharacteristic
946C22D3×#12611yescharacteristic
947C22#570611yescharacteristic
948C4—42no—
949C4—42no—
950C4—42no—
951C4—64no—
952C4—81no—
953C4—81no—
954C4—81no—
955C4—122no—
956C4—122no—
957C4—122no—
958C4—122no—
959C4—241no—
960C4—241no—
961C4—241no—
962C3#1482811yescharacteristic, complemented, Sylow
963C2—44no—
964C2#7411611yescharacteristic
965C2#7469411yescharacteristic
966C2#7470611yescharacteristic
967C2#7551611yescharacteristic
968C2#7552911yescharacteristic
969C2#7554011yescharacteristic
970C2#7585111yescharacteristic
971C2#7693811yescharacteristic
972C2#7694211yescharacteristic
973C2#7695811yescharacteristic
974C2#7698811yescharacteristic
975C2#7746111yescharacteristic
976C2#7748811yescharacteristic
977C2#7750211yescharacteristic
978C2#7752211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1440C2
prime radicalC25×C3C23
hypercenter#1440D3
hypocenterC3#14828
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
8. #69418C2semidirect
9. #69418C2semidirect
10. #69418C2semidirect
11. #69411C2semidirect
12. #69407C2semidirect
13. #69405C2semidirect
14. #69402C2semidirect
15. #69402C2semidirect
962. C3#14828semidirect

Maximal subgroups

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

subgroupindex
C2×#49522
C2×Dic3×C22⋊C42
C3×#14402
#715492
#715462
#715442
#694182
#694112
#694072
#694052
#694022
#148283