Finite Group Databasebeta

← #10728709

Subgroups — #10728709

Order 768.

1742 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#887C211yesmaximal, characteristic, complemented
2C2×#4675C211yesmaximal, characteristic
3C2×#4673C211yesmaximal, characteristic
4C2×#4669C211yesmaximal, characteristic
5C3×#1442C211yesmaximal, characteristic, complemented
6#71570C211yesmaximal, characteristic
7#69428C211yesmaximal, characteristic
8#69424C211yesmaximal, characteristic, complemented
9#69421C211yesmaximal, characteristic, complemented
10#69414C211yesmaximal, characteristic, complemented
11#69408C211yesmaximal, characteristic
12#69408C211yesmaximal, characteristic
13#69406C211yesmaximal, characteristic, complemented
14#69406C211yesmaximal, characteristic, complemented
15#69403C211yesmaximal, characteristic, complemented
16#14882—31nomaximal, Sylow
17C23×Dic6C2211yescharacteristic
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×Dic3⋊C4C2211yescharacteristic
27C22×Dic3⋊C4C2211yescharacteristic
28C22×Dic3⋊C4C2211yescharacteristic
29C22×C4×Dic3C2211yescharacteristic
30C22×C4×Dic3C2211yescharacteristic
31C22×C4×Dic3C2211yescharacteristic
32C2×#887—24no—
33C2×#887—24no—
34C2×#887—24no—
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
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55#4675—24no—
56#4673—24no—
57#4669—24no—
58C22×C4×Q8—31no—
59C2×#397—31no—
60C2×#393—31no—
61C2×#388—31no—
62#1446—31no—
63#1445—31no—
64#1442—31no—
65#1442D311yescharacteristic, complemented
66#1439—31no—
67#1439—31no—
68#1437—31no—
69#1437—31no—
70#1436—31no—
71#1436—31no—
72#1434—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
88C22×Dic6—22no—
89C22×Dic6—22no—
90C22×Dic6—22no—
91C22×Dic6—22no—
92C22×Dic6—22no—
93C22×Dic6—22no—
94C22×Dic6D414yes—
95C2×C3×C4⋊C4—22no—
96C2×C3×C4⋊C4—22no—
97C2×C3×C4⋊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—22no—
113C2×(C2×D3)⋊C4—22no—
114C2×(C2×D3)⋊C4—22no—
115C2×(C2×D3)⋊C4—22no—
116C2×(C2×D3)⋊C4—22no—
117C2×(C2×D3)⋊C4—41no—
118C2×(C2×D3)⋊C4—41no—
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⋊C4D414yes—
128C2×C4×Dic3—22no—
129C2×C4×Dic3—22no—
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×Dic3D414yes—
137#887—232no—
138C3×#95—22no—
139C3×#95—22no—
140C3×#95—22no—
141C3×#95—22no—
142C3×#95—41no—
143C3×#95—41no—
144C3⋊#95—22no—
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—41no—
157C3⋊#95—41no—
158C23×Q8—31no—
159C2×C4×Q8—64no—
160C2×C4×Q8—64no—
161C2×C4×Q8—64no—
162C22×C4⋊C4—31no—
163C22×C4⋊C4—31no—
164C22×C4⋊C4—31no—
165C22×C4⋊C4C2×D311yescharacteristic
166C22×C22⋊C4—31no—
167C22×C22⋊C4—31no—
168C22×C22⋊C4—31no—
169C22×C22⋊C4—31no—
170C22×C22⋊C4—31no—
171C22×C22⋊C4—31no—
172C22×C22⋊C4—31no—
173C22×C42—31no—
174C22×C42—31no—
175C22×C42—31no—
176#397—64no—
177#393—64no—
178#388—64no—
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×#95—31no—
192C2×#95—31no—
193C2×#95C2×D311yescharacteristic
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×D3#4112yes—
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×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4C2×D412yes—
260C22×C3×C4C2×D412yes—
261C22×C3×C4C2×D412yes—
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×Dic3C2×D412yes—
303C22×Dic3C2×D412yes—
304C22×Dic3C2×D412yes—
305C22×Dic3C2×D412yes—
306C22×Dic3C2×D412yes—
307C22×Dic3C2×D412yes—
308C22×Dic3#4112yes—
309C22×Dic3#4112yes—
310C22×Dic3#4112yes—
311C22×Dic3#4112yes—
312C22×Dic3#4112yes—
313C2×Dic6—28no—
314C2×Dic6—28no—
315C2×Dic6—28no—
316C2×Dic6—28no—
317C2×Dic6—28no—
318C2×Dic6—28no—
319C2×Dic6—28no—
320C3×C4⋊C4—28no—
321(C2×D3)⋊C4—28no—
322(C2×D3)⋊C4—44no—
323(C2×D3)⋊C4—44no—
324(C2×D3)⋊C4—44no—
325(C2×D3)⋊C4—44no—
326(C2×D3)⋊C4—44no—
327(C2×D3)⋊C4—44no—
328Dic3⋊C4—28no—
329Dic3⋊C4—28no—
330Dic3⋊C4—44no—
331C4×Dic3—28no—
332C4×Dic3—28no—
333C4×Dic3—28no—
334C25—31no—
335C22×Q8—34no—
336C22×Q8—62no—
337C22×Q8—62no—
338C22×Q8—62no—
339C22×Q8—62no—
340C22×Q8—62no—
341C22×Q8—62no—
342C23×C4—31no—
343C23×C4—31no—
344C23×C4—31no—
345C23×C4—31no—
346C23×C4—31no—
347C23×C4—31no—
348C23×C4—31no—
349C23×C4C22×D311yescharacteristic
350C23×C4C22×D311yescharacteristic
351C23×C4C22×D311yescharacteristic
352C23×C4C22×D311yescharacteristic
353C23×C4C22×D311yescharacteristic
354C23×C4C22×D311yescharacteristic
355C23×C4C22×D311yescharacteristic
356C4×Q8—632no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—34no—
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×C4⋊C4—62no—
368C2×C4⋊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—62no—
387C2×C22⋊C4—62no—
388C2×C22⋊C4—121no—
389C2×C22⋊C4—121no—
390C2×C42—34no—
391C2×C42—62no—
392C2×C42—62no—
393C2×C42—62no—
394C2×C42—62no—
395C2×C42—62no—
396C2×C42—62no—
397C2×C42—62no—
398C2×C42—62no—
399#95—22no—
400#95—22no—
401#95—22no—
402#95—22no—
403#95—41no—
404#95—41no—
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—
415#95—62no—
416#95—62no—
417#95—121no—
418#95—121no—
419C23×C3C22×D411yescharacteristic
420C23×C3C22×D411yescharacteristic
421C23×C3C22×D411yescharacteristic
422C23×C3C2×#4111yescharacteristic
423C23×C3C2×#4111yescharacteristic
424C23×C3C2×#4111yescharacteristic
425C23×C3C2×#4111yescharacteristic
426C23×C3C2×#4111yescharacteristic
427C23×C3C2×#4111yescharacteristic
428C23×C3C2×#4111yescharacteristic
429C23×C3C2×#4111yescharacteristic
430C23×C3H(5,𝔽2)11yescharacteristic
431C23×C32−1+411yescharacteristic
432C23×C32−1+411yescharacteristic
433C23×C32−1+411yescharacteristic
434C22×D3—22no—
435C22×D3—22no—
436C22×D3—22no—
437C22×D3—22no—
438C22×D3—22no—
439C22×D3—22no—
440C22×D3—22no—
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—
465C22×D3—41no—
466C22×D3—41no—
467C22×D3—41no—
468C22×D3—41no—
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—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×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—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4#12314yes—
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—22no—
536C2×Dic3—22no—
537C2×Dic3—22no—
538C2×Dic3—22no—
539C2×Dic3—22no—
540C2×Dic3—22no—
541C2×Dic3—22no—
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—41no—
563C2×Dic3—41no—
564C2×Dic3#12014yes—
565C2×Dic3#12314yes—
566C2×Dic3#12414yes—
567Dic6—232no—
568C24—32no—
569C24—61no—
570C24—61no—
571C24—61no—
572C24—61no—
573C24—61no—
574C24—61no—
575C24—61no—
576C24—61no—
577C24—61no—
578C24—61no—
579C24—61no—
580C24—61no—
581C24—61no—
582C24—61no—
583C24C23×D311yescharacteristic
584C2×Q8—68no—
585C2×Q8—68no—
586C2×Q8—68no—
587C2×Q8—68no—
588C2×Q8—68no—
589C2×Q8—68no—
590C2×Q8—68no—
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—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—32no—
636C22×C4—32no—
637C22×C4—32no—
638C22×C4—32no—
639C22×C4—32no—
640C22×C4—32no—
641C22×C4—32no—
642C22×C4—32no—
643C22×C4—32no—
644C22×C4—32no—
645C22×C4—32no—
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—61no—
674C22×C4—61no—
675C22×C4—61no—
676C22×C4—61no—
677C22×C4—61no—
678C22×C4—61no—
679C22×C4—61no—
680C22×C4—61no—
681C22×C4—61no—
682C22×C4—61no—
683C22×C4—61no—
684C22×C4#23512yes—
685C22×C4D3×D412yes—
686C22×C4D3×D412yes—
687C22×C4D3×D412yes—
688C22×C4#23912yes—
689C4⋊C4—28no—
690C4⋊C4—68no—
691C4⋊C4—68no—
692C4⋊C4—124no—
693C22⋊C4—68no—
694C22⋊C4—124no—
695C22⋊C4—124no—
696C22⋊C4—124no—
697C22⋊C4—124no—
698C22⋊C4—124no—
699C22⋊C4—124no—
700C42—68no—
701C42—68no—
702C42—68no—
703C22×C3C2×#12011yescharacteristic
704C22×C3C2×#12311yescharacteristic
705C22×C3C2×#12311yescharacteristic
706C22×C3#52511yescharacteristic
707C22×C3#52511yescharacteristic
708C22×C3#52511yescharacteristic
709C22×C3#52511yescharacteristic
710C22×C3#52511yescharacteristic
711C22×C3C2×#12411yescharacteristic
712C22×C3#52911yescharacteristic
713C22×C3#52911yescharacteristic
714C22×C3#52911yescharacteristic
715C22×C3#52911yescharacteristic
716C22×C3#53611yescharacteristic
717C22×C3#53711yescharacteristic
718C22×C3#54111yescharacteristic
719C22×C3#54111yescharacteristic
720C22×C3#54211yescharacteristic
721C22×C3#54211yescharacteristic
722C22×C3#54611yescharacteristic
723C22×C3#54711yescharacteristic
724C22×C3#54811yescharacteristic
725C22×C3#54811yescharacteristic
726C22×C3#54811yescharacteristic
727C22×C3#54811yescharacteristic
728C22×C3#54811yescharacteristic
729C22×C3#55011yescharacteristic
730C22×C3#55211yescharacteristic
731C22×C3#55211yescharacteristic
732C22×C3#55611yescharacteristic
733C22×C3#55611yescharacteristic
734C22×C3#55611yescharacteristic
735C22×C3#55611yescharacteristic
736C22×C3#55911yescharacteristic
737C22×C3#55911yescharacteristic
738C2×D3—42no—
739C2×D3—42no—
740C2×D3—42no—
741C2×D3—42no—
742C2×D3—42no—
743C2×D3—42no—
744C2×D3—42no—
745C2×D3—81no—
746C2×D3—81no—
747C2×D3—81no—
748C2×D3—81no—
749C2×D3—81no—
750C2×D3—81no—
751C2×D3—81no—
752C2×D3—81no—
753C3×C4—24no—
754C3×C4—42no—
755C3×C4—42no—
756C3×C4—81no—
757C3×C4—81no—
758C3×C4—81no—
759C3×C4—81no—
760Dic3—24no—
761Dic3—24no—
762Dic3—24no—
763Dic3—42no—
764Dic3—42no—
765Dic3—81no—
766Dic3—81no—
767C23—62no—
768C23—62no—
769C23—62no—
770C23—62no—
771C23—62no—
772C23—62no—
773C23—62no—
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—
793C23—121no—
794C23—121no—
795C23—121no—
796C23—121no—
797C23—121no—
798C23—121no—
799C23—121no—
800C23—121no—
801C23—121no—
802C23C2×#23511yescharacteristic
803C23C2×D3×D411yescharacteristic
804C23C2×D3×D411yescharacteristic
805C23C2×D3×D411yescharacteristic
806C23#100411yescharacteristic
807C23C2×#23911yescharacteristic
808C23#100711yescharacteristic
809C23D3×#4111yescharacteristic
810C23D3×#4111yescharacteristic
811C23D3×#4111yescharacteristic
812C23D3×#4111yescharacteristic
813C23D3×#4111yescharacteristic
814C23D3×#4111yescharacteristic
815C23#101011yescharacteristic
816C23#101011yescharacteristic
817Q8—632no—
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—22no—
830C2×C4—34no—
831C2×C4—34no—
832C2×C4—34no—
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—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
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—62no—
879C2×C4—62no—
880C2×C4—62no—
881C2×C4—62no—
882C2×C4—62no—
883C2×C4—62no—
884C2×C4—62no—
885C2×C4—62no—
886C2×C4—62no—
887C2×C4—62no—
888C2×C4—62no—
889C2×C4—62no—
890C2×C4—62no—
891C2×C4—62no—
892C2×C4—62no—
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×C4—121no—
911C2×C4—121no—
912C2×C4—121no—
913C2×C4—121no—
914C2×C4—121no—
915C2×C4#89414yes—
916C2×C3#239811yescharacteristic
917C2×C3#240711yescharacteristic
918C2×C3#242111yescharacteristic
919C2×C3#242111yescharacteristic
920C2×C3#243611yescharacteristic
921C2×C3#244811yescharacteristic
922C2×C3#244811yescharacteristic
923C2×C3#245811yescharacteristic
924C2×C3#245811yescharacteristic
925C2×C3#246911yescharacteristic
926C2×C3#246911yescharacteristic
927C2×C3#259211yescharacteristic
928C2×C3#259911yescharacteristic
929C2×C3#263711yescharacteristic
930C2×C3#284911yescharacteristic
931D3—82no—
932C22—122no—
933C22—122no—
934C22—122no—
935C22—122no—
936C22—122no—
937C22—122no—
938C22—122no—
939C22—241no—
940C22—241no—
941C22—241no—
942C22—241no—
943C22—241no—
944C22—241no—
945C22—241no—
946C22—241no—
947C22C2×#89411yescharacteristic
948C22#552911yescharacteristic
949C22#553311yescharacteristic
950C22#554711yescharacteristic
951C22#554711yescharacteristic
952C22#555911yescharacteristic
953C22#556811yescharacteristic
954C22D3×#12011yescharacteristic
955C22#559711yescharacteristic
956C22#559911yescharacteristic
957C22#561011yescharacteristic
958C22#562711yescharacteristic
959C22#562711yescharacteristic
960C22#562811yescharacteristic
961C22#563311yescharacteristic
962C22#563311yescharacteristic
963C22D3×#12311yescharacteristic
964C22#565511yescharacteristic
965C22#565611yescharacteristic
966C22#566211yescharacteristic
967C22#566411yescharacteristic
968C22D3×#12411yescharacteristic
969C22#567711yescharacteristic
970C22#567711yescharacteristic
971C22#567711yescharacteristic
972C22#569111yescharacteristic
973C22#569111yescharacteristic
974C22#569311yescharacteristic
975C22#569611yescharacteristic
976C22#569811yescharacteristic
977C22#570211yescharacteristic
978C22#570211yescharacteristic
979C22#570611yescharacteristic
980C22#570611yescharacteristic
981C22#573311yescharacteristic
982C4—24no—
983C4—42no—
984C4—42no—
985C4—64no—
986C4—64no—
987C4—64no—
988C4—81no—
989C4—81no—
990C4—81no—
991C4—81no—
992C4—122no—
993C4—122no—
994C4—241no—
995C4—241no—
996C3#1488211yescharacteristic, complemented, Sylow
997C2—242no—
998C2#7423211yescharacteristic
999C2#7465611yescharacteristic
1000C2#7500411yescharacteristic
1001C2#7537111yescharacteristic
1002C2#7561911yescharacteristic
1003C2#7585411yescharacteristic
1004C2#7600711yescharacteristic
1005C2#7678111yescharacteristic
1006C2#7689411yescharacteristic
1007C2#7746911yescharacteristic
1008C2#7775011yescharacteristic
1009C2#7782411yescharacteristic
1010C2#7813111yescharacteristic
1011C2#7813411yescharacteristic
1012C2#7813911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1442C2
prime radicalC24×D3C23
hypercenter#1442D3
hypocenterC3#14882
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
1. C22×#887C2semidirect
5. C3×#1442C2semidirect
8. #69424C2semidirect
9. #69421C2semidirect
10. #69414C2semidirect
13. #69406C2semidirect
14. #69406C2semidirect
15. #69403C2semidirect
65. #1442D3semidirect
996. C3#14882semidirect

Maximal subgroups

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

subgroupindex
C22×#8872
C2×#46752
C2×#46732
C2×#46692
C3×#14422
#715702
#694282
#694242
#694212
#694142
#694082
#694062
#694032
#148823