Finite Group Databasebeta

← #10729247

Subgroups — #10729247

Order 768.

1614 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#898C211yesmaximal, characteristic
2C2×#4972C211yesmaximal, characteristic, complemented
3C2×#4669C211yesmaximal, characteristic
4C2×#4654C211yesmaximal, characteristic, complemented
5C3×#1441C211yesmaximal, characteristic, complemented
6#71570C211yesmaximal, characteristic
7#71567C211yesmaximal, characteristic, complemented
8#69429C211yesmaximal, characteristic
9#69427C211yesmaximal, characteristic
10#69427C211yesmaximal, characteristic
11#69419C211yesmaximal, characteristic, complemented
12#69415C211yesmaximal, characteristic, complemented
13#69408C211yesmaximal, characteristic
14#69406C211yesmaximal, characteristic, complemented
15Dic3×#95C211yesmaximal, characteristic, complemented
16#14931—31nomaximal, Sylow
17C22×C3×C4⋊C4C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×(C2×D3)⋊C4C2211yescharacteristic
20C22×(C2×D3)⋊C4C2211yescharacteristic
21C22×(C2×D3)⋊C4C2211yescharacteristic
22C22×(C2×D3)⋊C4C2211yescharacteristic
23C22×(C2×D3)⋊C4C2211yescharacteristic
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×C4⋊Dic3C2211yescharacteristic
27C22×C4⋊Dic3C2211yescharacteristic
28C22×C4⋊Dic3C2211yescharacteristic
29C22×Dic3⋊C4C2211yescharacteristic
30C22×Dic3⋊C4C2211yescharacteristic
31C22×C4×Dic3C2211yescharacteristic
32C22×C4×Dic3C2211yescharacteristic
33C22×C4×Dic3C2211yescharacteristic
34C2×#898—24no—
35C2×#898—24no—
36C2×#898—24no—
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
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55#4972—24no—
56#4669—24no—
57#4654—24no—
58C22×#126—31no—
59C2×#389—31no—
60C2×#388—31no—
61C2×#387—31no—
62#1444—31no—
63#1442—31no—
64#1442—31no—
65#1441D311yescharacteristic, complemented
66#1440—31no—
67#1439—31no—
68#1439—31no—
69#1439—31no—
70#1437—31no—
71#1436—31no—
72C4×#95—31no—
73C24×D3C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×Dic3C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C2×C3×C4⋊C4—22no—
89C2×C3×C4⋊C4—22no—
90C2×C3×C4⋊C4—22no—
91C2×C3×C4⋊C4—22no—
92C2×C3×C4⋊C4—22no—
93C2×C3×C4⋊C4—41no—
94C2×(C2×D3)⋊C4—22no—
95C2×(C2×D3)⋊C4—22no—
96C2×(C2×D3)⋊C4—22no—
97C2×(C2×D3)⋊C4—22no—
98C2×(C2×D3)⋊C4—22no—
99C2×(C2×D3)⋊C4—22no—
100C2×(C2×D3)⋊C4—22no—
101C2×(C2×D3)⋊C4—22no—
102C2×(C2×D3)⋊C4—22no—
103C2×(C2×D3)⋊C4—22no—
104C2×(C2×D3)⋊C4—22no—
105C2×(C2×D3)⋊C4—22no—
106C2×(C2×D3)⋊C4—22no—
107C2×(C2×D3)⋊C4—22no—
108C2×(C2×D3)⋊C4—22no—
109C2×(C2×D3)⋊C4—22no—
110C2×(C2×D3)⋊C4—22no—
111C2×(C2×D3)⋊C4—22no—
112C2×(C2×D3)⋊C4—41no—
113C2×(C2×D3)⋊C4—41no—
114C2×(C2×D3)⋊C4D414yes—
115C2×C4⋊Dic3—22no—
116C2×C4⋊Dic3—22no—
117C2×C4⋊Dic3—22no—
118C2×C4⋊Dic3—22no—
119C2×C4⋊Dic3—22no—
120C2×C4⋊Dic3—22no—
121C2×C4⋊Dic3—22no—
122C2×C4⋊Dic3—22no—
123C2×C4⋊Dic3—22no—
124C2×Dic3⋊C4—22no—
125C2×Dic3⋊C4—22no—
126C2×Dic3⋊C4—22no—
127C2×Dic3⋊C4—22no—
128C2×Dic3⋊C4—22no—
129C2×Dic3⋊C4D414yes—
130C2×C4×Dic3—22no—
131C2×C4×Dic3—22no—
132C2×C4×Dic3—22no—
133C2×C4×Dic3—22no—
134C2×C4×Dic3—22no—
135C2×C4×Dic3—22no—
136C2×C4×Dic3—41no—
137C2×C4×Dic3—41no—
138C2×C4×Dic3D414yes—
139#898—232no—
140C3×#95—22no—
141C3×#95—22no—
142C3×#95—22no—
143C3×#95—22no—
144C3×#95—41no—
145C3⋊#95—22no—
146C3⋊#95—22no—
147C3⋊#95—22no—
148C3⋊#95—22no—
149C3⋊#95—22no—
150C3⋊#95—22no—
151C3⋊#95—22no—
152C3⋊#95—22no—
153C3⋊#95—22no—
154C3⋊#95—22no—
155C3⋊#95—22no—
156C3⋊#95—22no—
157C3⋊#95—22no—
158C2×#126—64no—
159C2×#126—64no—
160C2×#126—64no—
161C22×C4⋊C4—31no—
162C22×C4⋊C4—31no—
163C22×C4⋊C4—31no—
164C22×C4⋊C4—31no—
165C22×C4⋊C4—31no—
166C22×C4⋊C4C2×D311yescharacteristic
167C22×C4⋊C4C2×D311yescharacteristic
168C22×C22⋊C4—31no—
169C22×C22⋊C4—31no—
170C22×C22⋊C4—31no—
171C22×C22⋊C4—31no—
172C22×C22⋊C4—31no—
173C22×C22⋊C4—31no—
174C22×C22⋊C4—31no—
175C22×C42—31no—
176C22×C42—31no—
177C22×C42—31no—
178#389—64no—
179#388—64no—
180#387—64no—
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×#95—31no—
192C2×#95—31no—
193C2×#95—31no—
194C2×#95C2×D311yescharacteristic
195C2×#95C2×D311yescharacteristic
196C2×#95C2×D311yescharacteristic
197C2×#95C2×D311yescharacteristic
198C2×#95C2×D311yescharacteristic
199C24×C3C2411yescharacteristic
200C23×D3—21no—
201C23×D3—21no—
202C23×D3—21no—
203C23×D3—21no—
204C23×D3—21no—
205C23×D3—21no—
206C23×D3—21no—
207C23×D3—21no—
208C23×D3—21no—
209C23×D3—21no—
210C23×D3—21no—
211C23×D3—21no—
212C23×D3—21no—
213C23×D3—21no—
214C23×D3C2×D412yes—
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×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4C2×D412yes—
257C22×C3×C4C2×D412yes—
258C22×C3×C4C2×D412yes—
259C22×C3×C4#4112yes—
260C22×C3×C4#4112yes—
261C22×C3×C4#4112yes—
262C22×C3×C4#4112yes—
263C22×C3×C4#4112yes—
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—21no—
302C22×Dic3—21no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3C2×D412yes—
306C22×Dic3C2×D412yes—
307C22×Dic3C2×D412yes—
308C22×Dic3C2×D412yes—
309C22×Dic3C2×D412yes—
310C22×Dic3#4112yes—
311C22×Dic3#4112yes—
312C22×Dic3#4112yes—
313C3×C4⋊C4—28no—
314C3×C4⋊C4—44no—
315(C2×D3)⋊C4—28no—
316(C2×D3)⋊C4—28no—
317(C2×D3)⋊C4—28no—
318(C2×D3)⋊C4—28no—
319(C2×D3)⋊C4—44no—
320(C2×D3)⋊C4—44no—
321(C2×D3)⋊C4—44no—
322C4⋊Dic3—28no—
323C4⋊Dic3—28no—
324C4⋊Dic3—28no—
325Dic3⋊C4—28no—
326Dic3⋊C4—44no—
327C4×Dic3—28no—
328C4×Dic3—44no—
329C4×Dic3—44no—
330C25—31no—
331C23×C4—31no—
332C23×C4—31no—
333C23×C4—31no—
334C23×C4—31no—
335C23×C4—31no—
336C23×C4—31no—
337C23×C4—31no—
338C23×C4C22×D311yescharacteristic
339C23×C4C22×D311yescharacteristic
340C23×C4C22×D311yescharacteristic
341C23×C4C22×D311yescharacteristic
342C23×C4C22×D311yescharacteristic
343C23×C4C22×D311yescharacteristic
344C23×C4C22×D311yescharacteristic
345#126—632no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—34no—
352C2×C4⋊C4—41no—
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—62no—
366C2×C4⋊C4—62no—
367C2×C22⋊C4—34no—
368C2×C22⋊C4—62no—
369C2×C22⋊C4—62no—
370C2×C22⋊C4—62no—
371C2×C22⋊C4—62no—
372C2×C22⋊C4—62no—
373C2×C22⋊C4—62no—
374C2×C22⋊C4—62no—
375C2×C22⋊C4—62no—
376C2×C22⋊C4—62no—
377C2×C22⋊C4—62no—
378C2×C22⋊C4—62no—
379C2×C22⋊C4—62no—
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—121no—
387C2×C22⋊C4—121no—
388C2×C42—34no—
389C2×C42—62no—
390C2×C42—62no—
391C2×C42—62no—
392C2×C42—62no—
393C2×C42—62no—
394C2×C42—62no—
395C2×C42—121no—
396C2×C42—121no—
397#95—22no—
398#95—22no—
399#95—22no—
400#95—22no—
401#95—41no—
402#95—62no—
403#95—62no—
404#95—62no—
405#95—62no—
406#95—62no—
407#95—62no—
408#95—62no—
409#95—62no—
410#95—62no—
411#95—62no—
412#95—62no—
413#95—62no—
414#95—62no—
415C23×C3C22×D411yescharacteristic
416C23×C3C22×D411yescharacteristic
417C23×C3C22×D411yescharacteristic
418C23×C3C2×#4111yescharacteristic
419C23×C3C2×#4111yescharacteristic
420C23×C3C2×#4111yescharacteristic
421C23×C3C2×#4111yescharacteristic
422C23×C3C2×#4111yescharacteristic
423C23×C3C2×#4111yescharacteristic
424C23×C3C2×#4111yescharacteristic
425C23×C3C2×#4111yescharacteristic
426C23×C3H(5,𝔽2)11yescharacteristic
427C23×C32−1+411yescharacteristic
428C23×C32−1+411yescharacteristic
429C23×C32−1+411yescharacteristic
430C22×D3—22no—
431C22×D3—22no—
432C22×D3—22no—
433C22×D3—22no—
434C22×D3—22no—
435C22×D3—22no—
436C22×D3—22no—
437C22×D3—41no—
438C22×D3—41no—
439C22×D3—41no—
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×D3—41no—
457C22×D3—41no—
458C22×D3—41no—
459C22×D3—41no—
460C22×D3—41no—
461C22×D3—41no—
462C22×D3—41no—
463C22×D3—41no—
464C22×D3—41no—
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—22no—
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—22no—
485C2×C3×C4—22no—
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×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4#12614yescomplemented
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—22no—
527C2×Dic3—22no—
528C2×Dic3—22no—
529C2×Dic3—22no—
530C2×Dic3—22no—
531C2×Dic3—22no—
532C2×Dic3—22no—
533C2×Dic3—22no—
534C2×Dic3—22no—
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—41no—
562C2×Dic3#12014yes—
563C24—32no—
564C24—61no—
565C24—61no—
566C24—61no—
567C24—61no—
568C24—61no—
569C24—61no—
570C24—61no—
571C24—61no—
572C24—61no—
573C24—61no—
574C24—61no—
575C24—61no—
576C24—61no—
577C24—61no—
578C24C23×D311yescharacteristic
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—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—32no—
621C22×C4—32no—
622C22×C4—32no—
623C22×C4—32no—
624C22×C4—32no—
625C22×C4—32no—
626C22×C4—32no—
627C22×C4—32no—
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—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#23512yes—
670C22×C4D3×D412yes—
671C22×C4D3×D412yes—
672C22×C4D3×D412yes—
673C22×C4#23712yes—
674C22×C4#23912yes—
675C22×C4#23912yes—
676C22×C4#23912yes—
677C4⋊C4—28no—
678C4⋊C4—44no—
679C4⋊C4—68no—
680C4⋊C4—68no—
681C4⋊C4—68no—
682C4⋊C4—68no—
683C4⋊C4—124no—
684C22⋊C4—68no—
685C22⋊C4—68no—
686C22⋊C4—68no—
687C22⋊C4—68no—
688C22⋊C4—124no—
689C22⋊C4—124no—
690C22⋊C4—124no—
691C42—68no—
692C42—124no—
693C42—124no—
694C22×C3C2×#12011yescharacteristic
695C22×C3#52511yescharacteristic
696C22×C3#52511yescharacteristic
697C22×C3#52511yescharacteristic
698C22×C3C2×#12611yescharacteristic
699C22×C3#52911yescharacteristic
700C22×C3#52911yescharacteristic
701C22×C3#52911yescharacteristic
702C22×C3#53211yescharacteristic
703C22×C3#53211yescharacteristic
704C22×C3#53211yescharacteristic
705C22×C3#53211yescharacteristic
706C22×C3#53211yescharacteristic
707C22×C3#53611yescharacteristic
708C22×C3#53711yescharacteristic
709C22×C3#53911yescharacteristic
710C22×C3#53911yescharacteristic
711C22×C3#54111yescharacteristic
712C22×C3#54111yescharacteristic
713C22×C3#54611yescharacteristic
714C22×C3#54611yescharacteristic
715C22×C3#54711yescharacteristic
716C22×C3#54711yescharacteristic
717C22×C3#54711yescharacteristic
718C22×C3#54711yescharacteristic
719C22×C3#54811yescharacteristic
720C22×C3#54811yescharacteristic
721C22×C3#55111yescharacteristic
722C22×C3#55211yescharacteristic
723C22×C3#55211yescharacteristic
724C22×C3#55211yescharacteristic
725C22×C3#55311yescharacteristic
726C22×C3#55611yescharacteristic
727C22×C3#55611yescharacteristic
728C22×C3#55611yescharacteristic
729C2×D3—42no—
730C2×D3—42no—
731C2×D3—42no—
732C2×D3—42no—
733C2×D3—42no—
734C2×D3—42no—
735C2×D3—42no—
736C2×D3—81no—
737C2×D3—81no—
738C2×D3—81no—
739C2×D3—81no—
740C2×D3—81no—
741C2×D3—81no—
742C2×D3—81no—
743C2×D3—81no—
744C3×C4—24no—
745C3×C4—42no—
746C3×C4—42no—
747C3×C4—42no—
748C3×C4—42no—
749C3×C4—42no—
750C3×C4—81no—
751Dic3—24no—
752Dic3—42no—
753Dic3—42no—
754Dic3—42no—
755Dic3—42no—
756Dic3—42no—
757Dic3—81no—
758C23—62no—
759C23—62no—
760C23—62no—
761C23—62no—
762C23—62no—
763C23—62no—
764C23—62no—
765C23—121no—
766C23—121no—
767C23—121no—
768C23—121no—
769C23—121no—
770C23—121no—
771C23—121no—
772C23—121no—
773C23—121no—
774C23—121no—
775C23—121no—
776C23—121no—
777C23—121no—
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—
793C23C2×#23511yescharacteristic
794C23C2×D3×D411yescharacteristic
795C23C2×D3×D411yescharacteristic
796C23C2×D3×D411yescharacteristic
797C23C2×#23711yescharacteristic
798C23#100411yescharacteristic
799C23C2×#23911yescharacteristic
800C23C2×#23911yescharacteristic
801C23C2×#23911yescharacteristic
802C23D3×#4111yescharacteristic
803C23D3×#4111yescharacteristic
804C23D3×#4111yescharacteristic
805C23#101011yescharacteristic
806C23#101011yescharacteristic
807C23#101011yescharacteristic
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
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—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—34no—
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—41no—
855C2×C4—41no—
856C2×C4—41no—
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—62no—
876C2×C4—62no—
877C2×C4—62no—
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#89814yescomplemented
906C2×C3#238811yescharacteristic
907C2×C3#243011yescharacteristic
908C2×C3#243211yescharacteristic
909C2×C3#246611yescharacteristic
910C2×C3#246911yescharacteristic
911C2×C3#247811yescharacteristic
912C2×C3#248111yescharacteristic
913C2×C3#249611yescharacteristic
914C2×C3#251911yescharacteristic
915C2×C3#255311yescharacteristic
916C2×C3#256011yescharacteristic
917C2×C3#260111yescharacteristic
918C2×C3#260411yescharacteristic
919C2×C3#266411yescharacteristic
920C2×C3#286011yescharacteristic
921D3—82no—
922C22—122no—
923C22—122no—
924C22—122no—
925C22—122no—
926C22—122no—
927C22—122no—
928C22—122no—
929C22—241no—
930C22—241no—
931C22—241no—
932C22—241no—
933C22—241no—
934C22—241no—
935C22—241no—
936C22—241no—
937C22#549011yescharacteristic
938C22C2×#89811yescharacteristic
939C22#553111yescharacteristic
940C22#554811yescharacteristic
941C22#555111yescharacteristic
942C22#558011yescharacteristic
943C22#558411yescharacteristic
944C22D3×#12011yescharacteristic
945C22#559611yescharacteristic
946C22#559811yescharacteristic
947C22#560111yescharacteristic
948C22#560811yescharacteristic
949C22#561111yescharacteristic
950C22#561211yescharacteristic
951C22#562411yescharacteristic
952C22#562711yescharacteristic
953C22#562711yescharacteristic
954C22#562711yescharacteristic
955C22#563711yescharacteristic
956C22#564211yescharacteristic
957C22#564511yescharacteristic
958C22#564511yescharacteristic
959C22#564811yescharacteristic
960C22#565511yescharacteristic
961C22#565511yescharacteristic
962C22#567711yescharacteristic
963C22#569111yescharacteristic
964C22#569411yescharacteristic
965C22#569811yescharacteristic
966C22#569811yescharacteristic
967C22#570211yescharacteristic
968C22#570211yescharacteristic
969C22#572511yescharacteristic
970C22#572511yescharacteristic
971C22#572511yescharacteristic
972C4—24no—
973C4—42no—
974C4—42no—
975C4—42no—
976C4—42no—
977C4—42no—
978C4—64no—
979C4—81no—
980C4—122no—
981C4—122no—
982C4—122no—
983C4—122no—
984C4—122no—
985C4—241no—
986C3#1493111yescharacteristic, complemented, Sylow
987C2—242no—
988C2#7391011yescharacteristic
989C2#7489611yescharacteristic
990C2#7501711yescharacteristic
991C2#7512611yescharacteristic
992C2#7619111yescharacteristic
993C2#7623811yescharacteristic
994C2#7654011yescharacteristic
995C2#7690411yescharacteristic
996C2#7716911yescharacteristic
997C2#7729711yescharacteristic
998C2#7732711yescharacteristic
999C2#7777211yescharacteristic
1000C2#7778811yescharacteristic
1001C2#7784011yescharacteristic
1002C2#7813911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1441C2
prime radicalC24×D3C23
hypercenter#1441D3
hypocenterC3#14931
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
2. C2×#4972C2semidirect
4. C2×#4654C2semidirect
5. C3×#1441C2semidirect
7. #71567C2semidirect
11. #69419C2semidirect
12. #69415C2semidirect
14. #69406C2semidirect
15. Dic3×#95C2semidirect
65. #1441D3semidirect
513. C2×C3×C4#126semidirect
905. C2×C4#898semidirect
986. C3#14931semidirect

Maximal subgroups

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

subgroupindex
C22×#8982
C2×#49722
C2×#46692
C2×#46542
C3×#14412
#715702
#715672
#694292
#694272
#694192
#694152
#694082
#694062
Dic3×#952
#149313