Finite Group Databasebeta

← #10740401

Subgroups — #10740401

Order 768.

1530 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4946C211yesmaximal, characteristic
2C2×#4942C211yesmaximal, characteristic
3C2×#4933C211yesmaximal, characteristic, complemented
4C2×#4657C211yesmaximal, characteristic, complemented
5C3×#1437C211yesmaximal, characteristic
6#71547C211yesmaximal, characteristic
7#71547C211yesmaximal, characteristic
8#71546C211yesmaximal, characteristic
9#71544C211yesmaximal, characteristic
10#71536C211yesmaximal, characteristic, complemented
11#69421C211yesmaximal, characteristic, complemented
12#69414C211yesmaximal, characteristic, complemented
13#69414C211yesmaximal, characteristic, complemented
14#69411C211yesmaximal, characteristic, complemented
15#69409C211yesmaximal, characteristic, complemented
16#15786—31nomaximal, Sylow
17C24×Dic3C2211yescharacteristic
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C42C2211yescharacteristic
22C22×#217C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×C4⋊Dic3C2211yescharacteristic
26C22×Dic3⋊C4C2211yescharacteristic
27C22×Dic3⋊C4C2211yescharacteristic
28C22×Dic3⋊C4C2211yescharacteristic
29C22×Dic3⋊C4C2211yescharacteristic
30C22×Dic3⋊C4C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
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#4946—24no—
53#4942—24no—
54#4933—24no—
55#4657—24no—
56C2×#398—31no—
57C2×#387—31no—
58C2×#385—31no—
59C2×#380—31no—
60#1445—31no—
61#1442—31no—
62#1442—31no—
63#1441—31no—
64#1441—31no—
65#1439—31no—
66#1439—31no—
67#1439—31no—
68#1437D311yescharacteristic
69#1436—31no—
70C22⋊#95—31no—
71C25×C3C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×Dic3—22no—
79C23×Dic3—22no—
80C23×Dic3—22no—
81C23×Dic3—22no—
82C23×Dic3—22no—
83C23×Dic3—41no—
84C23×Dic3—41no—
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C23×Dic3C2311yescharacteristic
93C2×C3×C22⋊C4—22no—
94C2×C3×C22⋊C4—22no—
95C2×C3×C22⋊C4—22no—
96C2×C3×C22⋊C4—22no—
97C2×C3×C22⋊C4—41no—
98C2×C3×C22⋊C4—41no—
99C2×C3×C22⋊C4—41no—
100C2×C3×C22⋊C4—41no—
101C2×C3×C22⋊C4Q814yes—
102C2×C3×C42—22no—
103C2×C3×C42—41no—
104C2×C3×C42—41no—
105C2×#217—22no—
106C2×#217—22no—
107C2×#217—22no—
108C2×#217—22no—
109C2×#217—22no—
110C2×#217—22no—
111C2×#217—22no—
112C2×#217—41no—
113C2×#217—41no—
114C2×C4⋊Dic3—22no—
115C2×C4⋊Dic3—22no—
116C2×C4⋊Dic3—41no—
117C2×Dic3⋊C4—22no—
118C2×Dic3⋊C4—22no—
119C2×Dic3⋊C4—22no—
120C2×Dic3⋊C4—22no—
121C2×Dic3⋊C4—22no—
122C2×Dic3⋊C4—22no—
123C2×Dic3⋊C4—22no—
124C2×Dic3⋊C4—22no—
125C2×Dic3⋊C4—22no—
126C2×Dic3⋊C4—22no—
127C2×Dic3⋊C4—22no—
128C2×Dic3⋊C4—41no—
129C2×Dic3⋊C4—41no—
130C2×Dic3⋊C4—41no—
131C2×Dic3⋊C4—41no—
132C2×Dic3⋊C4—41no—
133C2×Dic3⋊C4—41no—
134C2×Dic3⋊C4D414yes—
135C3×#95—22no—
136C3×#95—41no—
137C3×#95—41no—
138C3⋊#95—22no—
139C3⋊#95—22no—
140C3⋊#95—22no—
141C3⋊#95—22no—
142C3⋊#95—22no—
143C3⋊#95—22no—
144C3⋊#95—22no—
145C3⋊#95—22no—
146C3⋊#95—22no—
147C3⋊#95—22no—
148C3⋊#95—22no—
149C3⋊#95—41no—
150C3⋊#95—41no—
151C3⋊#95—41no—
152C3⋊#95—41no—
153C3⋊#95—41no—
154C3⋊#95D414yes—
155C24×C4—31no—
156C22×C4⋊C4—31no—
157C22×C4⋊C4—31no—
158C22×C4⋊C4—31no—
159C22×C4⋊C4—31no—
160C22×C4⋊C4—31no—
161C22×C4⋊C4—31no—
162C22×C4⋊C4—31no—
163C22×C22⋊C4—31no—
164C22×C22⋊C4—31no—
165C22×C22⋊C4—31no—
166C22×C22⋊C4C2×D311yescharacteristic
167C22×C22⋊C4C2×D311yescharacteristic
168C22×C22⋊C4C2×D311yescharacteristic
169C22×C42C2×D311yescharacteristic
170#398—64no—
171#387—64no—
172#385—64no—
173#380—64no—
174C2×#95—31no—
175C2×#95—31no—
176C2×#95—31no—
177C2×#95—31no—
178C2×#95—31no—
179C2×#95—31no—
180C2×#95—31no—
181C2×#95—31no—
182C2×#95—31no—
183C2×#95—31no—
184C2×#95—31no—
185C2×#95—31no—
186C2×#95—31no—
187C2×#95—31no—
188C2×#95—31no—
189C2×#95—31no—
190C2×#95—31no—
191C2×#95C2×D311yescharacteristic
192C2×#95C2×D311yescharacteristic
193C2×#95C2×D311yescharacteristic
194C24×C3—21no—
195C24×C3—21no—
196C24×C3—21no—
197C24×C3—21no—
198C24×C3—21no—
199C24×C3—21no—
200C24×C3—21no—
201C24×C3—21no—
202C24×C3—21no—
203C24×C3—21no—
204C24×C3—21no—
205C24×C3—21no—
206C24×C3C2×Q812yes—
207C24×C3#4112yes—
208C24×C3#4112yes—
209C24×C3C2411yescharacteristic
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×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4C2×D412yes—
249C22×C3×C4C2×D412yes—
250C22×C3×C4C2×Q812yes—
251C22×C3×C4C2×Q812yes—
252C22×Dic3—21no—
253C22×Dic3—21no—
254C22×Dic3—21no—
255C22×Dic3—21no—
256C22×Dic3—28no—
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—21no—
291C22×Dic3—21no—
292C22×Dic3—21no—
293C22×Dic3—21no—
294C22×Dic3—21no—
295C22×Dic3—21no—
296C22×Dic3—21no—
297C22×Dic3—21no—
298C22×Dic3—21no—
299C22×Dic3—21no—
300C22×Dic3—21no—
301C22×Dic3—44no—
302C22×Dic3—44no—
303C22×Dic3—44no—
304C22×Dic3—44no—
305C22×Dic3—44no—
306C22×Dic3—44no—
307C22×Dic3C2×D412yes—
308C22×Dic3C2×D412yes—
309C22×Dic3C2×D412yes—
310C22×Dic3C2×D412yes—
311C22×Dic3#4112yes—
312C22×Dic3#4112yes—
313C22×Dic3#4112yes—
314C22×Dic3#4112yes—
315C3×C22⋊C4—44no—
316C3×C22⋊C4—44no—
317C3×C22⋊C4—44no—
318C3×C42—44no—
319#217—28no—
320#217—44no—
321#217—44no—
322C4⋊Dic3—44no—
323Dic3⋊C4—28no—
324Dic3⋊C4—44no—
325Dic3⋊C4—44no—
326Dic3⋊C4—44no—
327Dic3⋊C4—44no—
328Dic3⋊C4—44no—
329C25C22×D311yescharacteristic
330C23×C4—31no—
331C23×C4—31no—
332C23×C4—31no—
333C23×C4—31no—
334C23×C4—31no—
335C23×C4—31no—
336C23×C4—31no—
337C23×C4—31no—
338C23×C4—62no—
339C23×C4—62no—
340C23×C4—62no—
341C23×C4—62no—
342C23×C4—62no—
343C23×C4—121no—
344C23×C4—121no—
345C23×C4C22×D311yescharacteristic
346C23×C4C22×D311yescharacteristic
347C23×C4C22×D311yescharacteristic
348C23×C4C22×D311yescharacteristic
349C23×C4C22×D311yescharacteristic
350C23×C4C22×D311yescharacteristic
351C2×C4⋊C4—34no—
352C2×C4⋊C4—62no—
353C2×C4⋊C4—62no—
354C2×C4⋊C4—62no—
355C2×C4⋊C4—62no—
356C2×C4⋊C4—62no—
357C2×C4⋊C4—62no—
358C2×C4⋊C4—62no—
359C2×C4⋊C4—62no—
360C2×C4⋊C4—62no—
361C2×C4⋊C4—62no—
362C2×C4⋊C4—62no—
363C2×C4⋊C4—62no—
364C2×C4⋊C4—62no—
365C2×C4⋊C4—121no—
366C2×C4⋊C4—121no—
367C2×C4⋊C4—121no—
368C2×C4⋊C4—121no—
369C2×C4⋊C4—121no—
370C2×C4⋊C4—121no—
371C2×C4⋊C4—121no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—41no—
377C2×C22⋊C4—41no—
378C2×C22⋊C4—41no—
379C2×C22⋊C4—41no—
380C2×C22⋊C4—62no—
381C2×C22⋊C4—62no—
382C2×C22⋊C4—62no—
383C2×C22⋊C4—62no—
384C2×C22⋊C4—62no—
385C2×C22⋊C4—62no—
386C2×C22⋊C4—62no—
387C2×C22⋊C4—121no—
388C2×C22⋊C4—121no—
389C2×C22⋊C4Dic614yes—
390C2×C42—22no—
391C2×C42—41no—
392C2×C42—41no—
393#95—22no—
394#95—34no—
395#95—41no—
396#95—41no—
397#95—62no—
398#95—62no—
399#95—62no—
400#95—62no—
401#95—62no—
402#95—62no—
403#95—62no—
404#95—62no—
405#95—62no—
406#95—62no—
407#95—62no—
408#95—121no—
409#95—121no—
410#95—121no—
411#95—121no—
412#95—121no—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—22no—
416C23×C3—22no—
417C23×C3—22no—
418C23×C3—22no—
419C23×C3—22no—
420C23×C3—22no—
421C23×C3—22no—
422C23×C3—22no—
423C23×C3—22no—
424C23×C3—22no—
425C23×C3—22no—
426C23×C3—22no—
427C23×C3—22no—
428C23×C3—22no—
429C23×C3—22no—
430C23×C3—22no—
431C23×C3—41no—
432C23×C3—41no—
433C23×C3—41no—
434C23×C3—41no—
435C23×C3—41no—
436C23×C3—41no—
437C23×C3—41no—
438C23×C3—41no—
439C23×C3—41no—
440C23×C3—41no—
441C23×C3—41no—
442C23×C3—41no—
443C23×C3—41no—
444C23×C3—41no—
445C23×C3—41no—
446C23×C3—41no—
447C23×C3#12514yes—
448C23×C3C22×D411yescharacteristic
449C23×C3C22×D411yescharacteristic
450C23×C3C22×Q811yescharacteristic
451C23×C3C2×#4111yescharacteristic
452C23×C3C2×#4111yescharacteristic
453C23×C3C2×#4111yescharacteristic
454C23×C3C2×#4111yescharacteristic
455C23×C3C2×#4111yescharacteristic
456C23×C3C2×#4111yescharacteristic
457C23×C3H(5,𝔽2)11yescharacteristic
458C23×C3H(5,𝔽2)11yescharacteristic
459C23×C3H(5,𝔽2)11yescharacteristic
460C23×C3H(5,𝔽2)11yescharacteristic
461C23×C32−1+411yescharacteristic
462C23×C32−1+411yescharacteristic
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
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×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
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—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—22no—
509C2×Dic3—22no—
510C2×Dic3—22no—
511C2×Dic3—22no—
512C2×Dic3—22no—
513C2×Dic3—22no—
514C2×Dic3—22no—
515C2×Dic3—22no—
516C2×Dic3—22no—
517C2×Dic3—22no—
518C2×Dic3—22no—
519C2×Dic3—22no—
520C2×Dic3—22no—
521C2×Dic3—22no—
522C2×Dic3—22no—
523C2×Dic3—22no—
524C2×Dic3—22no—
525C2×Dic3—22no—
526C2×Dic3—416no—
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—41no—
538C2×Dic3—41no—
539C2×Dic3—41no—
540C2×Dic3—41no—
541C2×Dic3—41no—
542C2×Dic3—41no—
543C2×Dic3—41no—
544C2×Dic3—41no—
545C2×Dic3—41no—
546C2×Dic3—41no—
547C2×Dic3—41no—
548C2×Dic3—41no—
549C2×Dic3—41no—
550C2×Dic3—41no—
551C2×Dic3—41no—
552C2×Dic3—41no—
553C2×Dic3—41no—
554C2×Dic3—41no—
555C2×Dic3—41no—
556C2×Dic3—41no—
557C2×Dic3—41no—
558C2×Dic3—41no—
559C2×Dic3—41no—
560C2×Dic3—41no—
561C2×Dic3#12114yes—
562C24—21no—
563C24—21no—
564C24—21no—
565C24—21no—
566C24—21no—
567C24—21no—
568C24—21no—
569C24—21no—
570C24—21no—
571C24—21no—
572C24—21no—
573C24—21no—
574C24C2×Dic612yes—
575C24#23512yes—
576C24#23512yes—
577C24C23×D311yescharacteristic
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—21no—
594C22×C4—21no—
595C22×C4—21no—
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—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—32no—
617C22×C4—32no—
618C22×C4—32no—
619C22×C4—32no—
620C22×C4—32no—
621C22×C4—32no—
622C22×C4—32no—
623C22×C4—32no—
624C22×C4—61no—
625C22×C4—61no—
626C22×C4—61no—
627C22×C4—61no—
628C22×C4—68no—
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—61no—
651C22×C4—61no—
652C22×C4—61no—
653C22×C4—61no—
654C22×C4—61no—
655C22×C4—61no—
656C22×C4—61no—
657C22×C4—61no—
658C22×C4—61no—
659C22×C4—61no—
660C22×C4—61no—
661C22×C4—61no—
662C22×C4—61no—
663C22×C4—61no—
664C22×C4—61no—
665C22×C4—61no—
666C22×C4—61no—
667C22×C4—61no—
668C22×C4—61no—
669C22×C4—61no—
670C22×C4—61no—
671C22×C4—61no—
672C22×C4—61no—
673C22×C4—124no—
674C22×C4—124no—
675C22×C4—124no—
676C22×C4—124no—
677C22×C4—124no—
678C22×C4—124no—
679C22×C4C2×Dic612yes—
680C22×C4C2×Dic612yes—
681C22×C4D3×D412yes—
682C22×C4D3×D412yes—
683C4⋊C4—68no—
684C4⋊C4—124no—
685C4⋊C4—124no—
686C4⋊C4—124no—
687C4⋊C4—124no—
688C4⋊C4—124no—
689C4⋊C4—124no—
690C22⋊C4—44no—
691C22⋊C4—44no—
692C22⋊C4—44no—
693C22⋊C4—68no—
694C22⋊C4—124no—
695C22⋊C4—124no—
696C42—44no—
697C22×C3—24no—
698C22×C3—24no—
699C22×C3—24no—
700C22×C3—42no—
701C22×C3—42no—
702C22×C3—42no—
703C22×C3—42no—
704C22×C3—42no—
705C22×C3—42no—
706C22×C3—42no—
707C22×C3—42no—
708C22×C3—42no—
709C22×C3—42no—
710C22×C3—42no—
711C22×C3—42no—
712C22×C3C2×#12111yescharacteristic
713C22×C3#52511yescharacteristic
714C22×C3#52511yescharacteristic
715C22×C3C2×#12511yescharacteristic
716C22×C3#52911yescharacteristic
717C22×C3#53311yescharacteristic
718C22×C3#53511yescharacteristic
719C22×C3#53511yescharacteristic
720C22×C3#53911yescharacteristic
721C22×C3#53911yescharacteristic
722C22×C3#54011yescharacteristic
723C22×C3#54111yescharacteristic
724C22×C3#54211yescharacteristic
725C22×C3#54211yescharacteristic
726C22×C3#54311yescharacteristic
727C22×C3#54611yescharacteristic
728C22×C3#54611yescharacteristic
729C22×C3#54611yescharacteristic
730C22×C3#54611yescharacteristic
731C22×C3#54711yescharacteristic
732C22×C3#54811yescharacteristic
733C22×C3D4×Q811yescharacteristic
734C22×C3D4×Q811yescharacteristic
735C22×C3#55111yescharacteristic
736C22×C3#55111yescharacteristic
737C22×C3#55111yescharacteristic
738C22×C3#55211yescharacteristic
739C22×C3#55211yescharacteristic
740C22×C3#55311yescharacteristic
741C22×C3#55311yescharacteristic
742C22×C3#55311yescharacteristic
743C22×C3#55411yescharacteristic
744C22×C3#55411yescharacteristic
745C22×C3#56211yescharacteristic
746C22×C3#56211yescharacteristic
747C3×C4—42no—
748C3×C4—42no—
749C3×C4—42no—
750C3×C4—42no—
751C3×C4—81no—
752C3×C4—81no—
753Dic3—24no—
754Dic3—42no—
755Dic3—42no—
756Dic3—42no—
757Dic3—42no—
758Dic3—42no—
759Dic3—81no—
760Dic3—81no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23#87014yes—
796C23C22×Dic611yescharacteristic
797C23C2×#23511yescharacteristic
798C23C2×#23511yescharacteristic
799C23C2×D3×D411yescharacteristic
800C23C2×D3×D411yescharacteristic
801C23#100411yescharacteristic
802C23#100411yescharacteristic
803C23#100411yescharacteristic
804C23#100411yescharacteristic
805C23D3×#4111yescharacteristic
806C23D3×#4111yescharacteristic
807C23D3×#4111yescharacteristic
808C23D3×#4111yescharacteristic
809C23#101011yescharacteristic
810C23#101011yescharacteristic
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—34no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—62no—
855C2×C4—62no—
856C2×C4—62no—
857C2×C4—62no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—62no—
861C2×C4—62no—
862C2×C4—62no—
863C2×C4—62no—
864C2×C4—62no—
865C2×C4—62no—
866C2×C4—62no—
867C2×C4—62no—
868C2×C4—62no—
869C2×C4—62no—
870C2×C4—62no—
871C2×C4—62no—
872C2×C4—62no—
873C2×C4—62no—
874C2×C4—62no—
875C2×C4—1216no—
876C2×C4—121no—
877C2×C4—121no—
878C2×C4—121no—
879C2×C4—121no—
880C2×C4—121no—
881C2×C4—121no—
882C2×C4—121no—
883C2×C4—121no—
884C2×C4—121no—
885C2×C4—121no—
886C2×C4—121no—
887C2×C4—121no—
888C2×C4—121no—
889C2×C4—121no—
890C2×C4—121no—
891C2×C4—121no—
892C2×C4—121no—
893C2×C4—121no—
894C2×C4—121no—
895C2×C4—121no—
896C2×C4—121no—
897C2×C4—121no—
898C2×C4—121no—
899C2×C4—121no—
900C2×C4—121no—
901C2×C4—121no—
902C2×C4—121no—
903C2×C4—121no—
904C2×C4—121no—
905C2×C4—121no—
906C2×C4—121no—
907C2×C4—121no—
908C2×C4—121no—
909C2×C4—121no—
910C2×C3—44no—
911C2×C3#241111yescharacteristic
912C2×C3#242911yescharacteristic
913C2×C3#246811yescharacteristic
914C2×C3#247311yescharacteristic
915C2×C3#247311yescharacteristic
916C2×C3#247711yescharacteristic
917C2×C3#252211yescharacteristic
918C2×C3#253511yescharacteristic
919C2×C3#256911yescharacteristic
920C2×C3#269211yescharacteristic
921C2×C3#269211yescharacteristic
922C2×C3#270611yescharacteristic
923C2×C3#271111yescharacteristic
924C2×C3#273911yescharacteristic
925C2×C3#274711yescharacteristic
926C22—24no—
927C22—24no—
928C22—24no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22C2×#87011yescharacteristic
942C22#548311yescharacteristic
943C22#549011yescharacteristic
944C22#549011yescharacteristic
945C22#551711yescharacteristic
946C22#553111yescharacteristic
947C22#553111yescharacteristic
948C22D4×Dic611yescharacteristic
949C22D4×Dic611yescharacteristic
950C22#553911yescharacteristic
951C22#553911yescharacteristic
952C22#554011yescharacteristic
953C22#554011yescharacteristic
954C22#554711yescharacteristic
955C22#554711yescharacteristic
956C22#555611yescharacteristic
957C22#555611yescharacteristic
958C22#556411yescharacteristic
959C22#556411yescharacteristic
960C22#559211yescharacteristic
961C22D3×#12111yescharacteristic
962C22#561011yescharacteristic
963C22#561211yescharacteristic
964C22#561511yescharacteristic
965C22#562111yescharacteristic
966C22#562111yescharacteristic
967C22#565511yescharacteristic
968C22#566111yescharacteristic
969C22#566211yescharacteristic
970C22#566911yescharacteristic
971C22#567711yescharacteristic
972C22#567911yescharacteristic
973C22#570111yescharacteristic
974C22#570611yescharacteristic
975C22#571511yescharacteristic
976C4—42no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—64no—
981C4—81no—
982C4—81no—
983C4—122no—
984C4—122no—
985C4—122no—
986C4—122no—
987C4—122no—
988C4—241no—
989C4—241no—
990C3#1578611yescharacteristic, complemented, Sylow
991C2—44no—
992C2#7350111yescharacteristic
993C2#7350111yescharacteristic
994C2#7353911yescharacteristic
995C2#7475111yescharacteristic
996C2#7480311yescharacteristic
997C2#7481811yescharacteristic
998C2#7550011yescharacteristic
999C2#7551811yescharacteristic
1000C2#7556811yescharacteristic
1001C2#7571711yescharacteristic
1002C2#7572911yescharacteristic
1003C2#7586511yescharacteristic
1004C2#7638211yescharacteristic
1005C2#7639311yescharacteristic
1006C2#7643711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1437C2
prime radicalC25×C3C23
hypercenter#1437D3
hypocenterC3#15786
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
3. C2×#4933C2semidirect
4. C2×#4657C2semidirect
10. #71536C2semidirect
11. #69421C2semidirect
12. #69414C2semidirect
13. #69414C2semidirect
14. #69411C2semidirect
15. #69409C2semidirect
990. C3#15786semidirect

Maximal subgroups

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

subgroupindex
C2×#49462
C2×#49422
C2×#49332
C2×#46572
C3×#14372
#715472
#715462
#715442
#715362
#694212
#694142
#694112
#694092
#157863