Finite Group Databasebeta

← #10728679

Subgroups — #10728679

Order 768.

1634 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic6C211yesmaximal, characteristic
2C2×#4979C211yesmaximal, characteristic
3C2×#4657C211yesmaximal, characteristic
4C2×#4654C211yesmaximal, characteristic
5C3×#1436C211yesmaximal, characteristic
6#71565C211yesmaximal, characteristic
7#71536C211yesmaximal, characteristic
8#69424C211yesmaximal, characteristic
9#69421C211yesmaximal, characteristic
10#69420C211yesmaximal, characteristic
11#69419C211yesmaximal, characteristic
12#69409C211yesmaximal, characteristic
13#69407C211yesmaximal, characteristic
14#69406C211yesmaximal, characteristic
15#69401C211yesmaximal, characteristic
16#14879—31nomaximal, Sylow
17C23×Dic6C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C42C2211yescharacteristic
20C22×C4⋊Dic3C2211yescharacteristic
21C22×C4⋊Dic3C2211yescharacteristic
22C22×C4⋊Dic3C2211yescharacteristic
23C22×Dic3⋊C4C2211yescharacteristic
24C22×Dic3⋊C4C2211yescharacteristic
25C22×Dic3⋊C4C2211yescharacteristic
26C22×Dic3⋊C4C2211yescharacteristic
27C22×Dic3⋊C4C2211yescharacteristic
28C22×C4×Dic3C2211yescharacteristic
29C22×C4×Dic3C2211yescharacteristic
30C2×C4×Dic6—24no—
31C2×C4×Dic6—24no—
32C2×C4×Dic6—24no—
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
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55#4979—24no—
56#4657—24no—
57#4654—24no—
58C22×C4×Q8—31no—
59C2×#398—31no—
60C2×#395—31no—
61C2×#387—31no—
62#1446—31no—
63#1445—31no—
64#1444—31no—
65#1444—31no—
66#1441—31no—
67#1441—31no—
68#1436—31no—
69#1436—31no—
70#1436—31no—
71#1436D311yescharacteristic
72#1434—31no—
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×Dic3C2311yescharacteristic
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×C3×C42—22no—
99C2×C3×C42—22no—
100C2×C3×C42—22no—
101C2×C4⋊Dic3—22no—
102C2×C4⋊Dic3—22no—
103C2×C4⋊Dic3—22no—
104C2×C4⋊Dic3—22no—
105C2×C4⋊Dic3—22no—
106C2×C4⋊Dic3—22no—
107C2×C4⋊Dic3—22no—
108C2×C4⋊Dic3—22no—
109C2×C4⋊Dic3—41no—
110C2×Dic3⋊C4—22no—
111C2×Dic3⋊C4—22no—
112C2×Dic3⋊C4—22no—
113C2×Dic3⋊C4—22no—
114C2×Dic3⋊C4—22no—
115C2×Dic3⋊C4—22no—
116C2×Dic3⋊C4—22no—
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—41no—
124C2×Dic3⋊C4D414yes—
125C2×C4×Dic3—22no—
126C2×C4×Dic3—22no—
127C2×C4×Dic3—22no—
128C2×C4×Dic3—22no—
129C2×C4×Dic3—22no—
130C2×C4×Dic3D414yes—
131C4×Dic6—232no—
132C3×#95—22no—
133C3×#95—22no—
134C3×#95—22no—
135C3×#95—22no—
136C3×#95Q814yescomplemented
137C3⋊#95—22no—
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⋊#95Q814yescomplemented
154C23×Q8—31no—
155C2×C4×Q8—64no—
156C2×C4×Q8—64no—
157C2×C4×Q8—64no—
158C22×C4⋊C4—31no—
159C22×C4⋊C4—31no—
160C22×C4⋊C4—31no—
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×C42—31no—
168C22×C42—31no—
169C22×C42C2×D311yescharacteristic
170#398—64no—
171#395—64no—
172#387—64no—
173C2×#95—31no—
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×#95C2×D311yescharacteristic
191C2×#95C2×D311yescharacteristic
192C2×#95C2×D311yescharacteristic
193C2×#95C2×D311yescharacteristic
194C2×#95C2×D311yescharacteristic
195C24×C3C2411yescharacteristic
196C22×C3×C4—21no—
197C22×C3×C4—21no—
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×C4C2×D412yes—
236C22×C3×C4C2×D412yes—
237C22×C3×C4C2×D412yes—
238C22×C3×C4C2×Q812yes—
239C22×C3×C4C2×Q812yes—
240C22×C3×C4C2×Q812yes—
241C22×C3×C4C2×Q812yes—
242C22×C3×C4#4112yes—
243C22×C3×C4#4112yes—
244C22×C3×C4#4112yes—
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×Dic3C2×D412yes—
291C22×Dic3C2×D412yes—
292C22×Dic3C2×D412yes—
293C22×Dic3C2×D412yes—
294C22×Dic3C2×D412yes—
295C22×Dic3C2×D412yes—
296C22×Dic3C2×Q812yes—
297C22×Dic3C2×Q812yes—
298C22×Dic3#4112yes—
299C22×Dic3#4112yes—
300C22×Dic3#4112yes—
301C2×Dic6—28no—
302C2×Dic6—28no—
303C2×Dic6—28no—
304C2×Dic6—28no—
305C2×Dic6—28no—
306C2×Dic6—28no—
307C2×Dic6—28no—
308C3×C4⋊C4—44no—
309C3×C42—28no—
310C4⋊Dic3—28no—
311C4⋊Dic3—28no—
312C4⋊Dic3—44no—
313Dic3⋊C4—28no—
314Dic3⋊C4—28no—
315Dic3⋊C4—44no—
316Dic3⋊C4—44no—
317Dic3⋊C4—44no—
318C4×Dic3—28no—
319C4×Dic3—28no—
320C22×Q8—34no—
321C22×Q8—62no—
322C22×Q8—62no—
323C22×Q8—62no—
324C22×Q8—62no—
325C22×Q8—62no—
326C22×Q8—62no—
327C23×C4—31no—
328C23×C4—31no—
329C23×C4—31no—
330C23×C4—31no—
331C23×C4—31no—
332C23×C4—31no—
333C23×C4—31no—
334C23×C4—31no—
335C23×C4C22×D311yescharacteristic
336C23×C4C22×D311yescharacteristic
337C23×C4C22×D311yescharacteristic
338C23×C4C22×D311yescharacteristic
339C23×C4C22×D311yescharacteristic
340C23×C4C22×D311yescharacteristic
341C23×C4C22×D311yescharacteristic
342C4×Q8—632no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—34no—
347C2×C4⋊C4—62no—
348C2×C4⋊C4—62no—
349C2×C4⋊C4—62no—
350C2×C4⋊C4—62no—
351C2×C4⋊C4—62no—
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—62no—
366C2×C4⋊C4—62no—
367C2×C4⋊C4—62no—
368C2×C4⋊C4—121no—
369C2×C4⋊C4—121no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—34no—
374C2×C42—62no—
375C2×C42—62no—
376C2×C42—62no—
377C2×C42—62no—
378C2×C42—62no—
379#95—22no—
380#95—22no—
381#95—22no—
382#95—22no—
383#95—34no—
384#95—62no—
385#95—62no—
386#95—62no—
387#95—62no—
388#95—62no—
389#95—62no—
390#95—62no—
391#95—62no—
392#95—62no—
393#95—62no—
394#95—62no—
395#95—62no—
396#95—121no—
397#95—121no—
398#95—121no—
399#95—121no—
400#95Dic614yescomplemented
401C23×C3C22×D411yescharacteristic
402C23×C3C22×D411yescharacteristic
403C23×C3C22×D411yescharacteristic
404C23×C3C22×Q811yescharacteristic
405C23×C3C22×Q811yescharacteristic
406C23×C3C2×#4111yescharacteristic
407C23×C3C2×#4111yescharacteristic
408C23×C3C2×#4111yescharacteristic
409C23×C3C2×#4111yescharacteristic
410C23×C3C2×#4111yescharacteristic
411C23×C3C2×#4111yescharacteristic
412C23×C3H(5,𝔽2)11yescharacteristic
413C23×C32−1+411yescharacteristic
414C23×C32−1+411yescharacteristic
415C23×C32−1+411yescharacteristic
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
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#12314yes—
464C2×C3×C4C4⋊Q814yes—
465C2×Dic3—22no—
466C2×Dic3—22no—
467C2×Dic3—22no—
468C2×Dic3—22no—
469C2×Dic3—22no—
470C2×Dic3—22no—
471C2×Dic3—22no—
472C2×Dic3—22no—
473C2×Dic3—22no—
474C2×Dic3—22no—
475C2×Dic3—22no—
476C2×Dic3—22no—
477C2×Dic3—22no—
478C2×Dic3—22no—
479C2×Dic3—22no—
480C2×Dic3—22no—
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—41no—
493C2×Dic3—41no—
494C2×Dic3—41no—
495C2×Dic3—41no—
496C2×Dic3—41no—
497C2×Dic3—41no—
498C2×Dic3—41no—
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—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#12014yes—
520C2×Dic3#12314yes—
521Dic6—232no—
522C24C23×D311yescharacteristic
523C2×Q8—68no—
524C2×Q8—68no—
525C2×Q8—68no—
526C2×Q8—68no—
527C2×Q8—68no—
528C2×Q8—68no—
529C2×Q8—68no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
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—32no—
570C22×C4—32no—
571C22×C4—32no—
572C22×C4—32no—
573C22×C4—32no—
574C22×C4—32no—
575C22×C4—32no—
576C22×C4—32no—
577C22×C4—32no—
578C22×C4—32no—
579C22×C4—32no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—61no—
584C22×C4—61no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4—61no—
588C22×C4—61no—
589C22×C4—61no—
590C22×C4—61no—
591C22×C4—61no—
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—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×C4C2×Dic612yes—
626C22×C4C2×Dic612yes—
627C22×C4C2×Dic612yes—
628C22×C4#23512yes—
629C22×C4#23512yes—
630C22×C4D3×D412yes—
631C22×C4D3×D412yes—
632C22×C4D3×D412yes—
633C22×C4#23712yes—
634C22×C4D3×Q812yes—
635C4⋊C4—44no—
636C4⋊C4—68no—
637C4⋊C4—68no—
638C4⋊C4—68no—
639C4⋊C4—68no—
640C4⋊C4—124no—
641C4⋊C4—124no—
642C4⋊C4—124no—
643C4⋊C4—124no—
644C42—28no—
645C42—68no—
646C42—68no—
647C22×C3C2×#12011yescharacteristic
648C22×C3C2×#12311yescharacteristic
649C22×C3C2×#12311yescharacteristic
650C22×C3#52511yescharacteristic
651C22×C3#52511yescharacteristic
652C22×C3#52511yescharacteristic
653C22×C3#52511yescharacteristic
654C22×C3#52511yescharacteristic
655C22×C3C2×C4⋊Q811yescharacteristic
656C22×C3#53311yescharacteristic
657C22×C3#53311yescharacteristic
658C22×C3#53311yescharacteristic
659C22×C3#53311yescharacteristic
660C22×C3#53611yescharacteristic
661C22×C3#53711yescharacteristic
662C22×C3#54111yescharacteristic
663C22×C3#54111yescharacteristic
664C22×C3#54211yescharacteristic
665C22×C3#54211yescharacteristic
666C22×C3#54611yescharacteristic
667C22×C3#54711yescharacteristic
668C22×C3#54811yescharacteristic
669C22×C3D4×Q811yescharacteristic
670C22×C3D4×Q811yescharacteristic
671C22×C3D4×Q811yescharacteristic
672C22×C3D4×Q811yescharacteristic
673C22×C3#55011yescharacteristic
674C22×C3#55211yescharacteristic
675C22×C3#55211yescharacteristic
676C22×C3#55411yescharacteristic
677C22×C3#55411yescharacteristic
678C22×C3#55611yescharacteristic
679C22×C3#55611yescharacteristic
680C22×C3#55711yescharacteristic
681C22×C3#55711yescharacteristic
682C3×C4—24no—
683C3×C4—24no—
684C3×C4—42no—
685C3×C4—42no—
686C3×C4—42no—
687C3×C4—42no—
688C3×C4—81no—
689Dic3—24no—
690Dic3—24no—
691Dic3—42no—
692Dic3—42no—
693Dic3—42no—
694Dic3—42no—
695Dic3—42no—
696Dic3—81no—
697C23C22×Dic611yescharacteristic
698C23C2×#23511yescharacteristic
699C23C2×#23511yescharacteristic
700C23C2×D3×D411yescharacteristic
701C23C2×D3×D411yescharacteristic
702C23C2×D3×D411yescharacteristic
703C23C2×#23711yescharacteristic
704C23C2×D3×Q811yescharacteristic
705C23#100711yescharacteristic
706C23D3×#4111yescharacteristic
707C23D3×#4111yescharacteristic
708C23D3×#4111yescharacteristic
709C23#100911yescharacteristic
710C23#101011yescharacteristic
711C23#101011yescharacteristic
712Q8—632no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—34no—
738C2×C4—34no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—62no—
763C2×C4—62no—
764C2×C4—62no—
765C2×C4—62no—
766C2×C4—62no—
767C2×C4—62no—
768C2×C4—62no—
769C2×C4—62no—
770C2×C4—62no—
771C2×C4—62no—
772C2×C4—62no—
773C2×C4—62no—
774C2×C4—62no—
775C2×C4—62no—
776C2×C4—62no—
777C2×C4—62no—
778C2×C4—62no—
779C2×C4—62no—
780C2×C4—62no—
781C2×C4—62no—
782C2×C4—62no—
783C2×C4—62no—
784C2×C4—62no—
785C2×C4—62no—
786C2×C4—62no—
787C2×C4—62no—
788C2×C4—62no—
789C2×C4—121no—
790C2×C4—121no—
791C2×C4—121no—
792C2×C4—121no—
793C2×C4—121no—
794C2×C4—121no—
795C2×C4—121no—
796C2×C4—121no—
797C2×C4—121no—
798C2×C4—121no—
799C2×C4—121no—
800C2×C4—121no—
801C2×C4—121no—
802C2×C4—121no—
803C2×C4—121no—
804C2×C4—121no—
805C2×C4—121no—
806C2×C4—121no—
807C2×C4—121no—
808C2×C4—121no—
809C2×C4—121no—
810C2×C4—121no—
811C2×C4—121no—
812C2×C4—121no—
813C2×C4—121no—
814C2×C4—121no—
815C2×C4—121no—
816C2×C4#88314yes—
817C2×C4#88814yes—
818C2×C3#239911yescharacteristic
819C2×C3#240711yescharacteristic
820C2×C3#242311yescharacteristic
821C2×C3#242311yescharacteristic
822C2×C3#243411yescharacteristic
823C2×C3#244611yescharacteristic
824C2×C3#244611yescharacteristic
825C2×C3#246211yescharacteristic
826C2×C3#246211yescharacteristic
827C2×C3#246511yescharacteristic
828C2×C3#246511yescharacteristic
829C2×C3#258411yescharacteristic
830C2×C3#259911yescharacteristic
831C2×C3#263711yescharacteristic
832C2×C3#284911yescharacteristic
833C22#547011yescharacteristic
834C22C2×#88311yescharacteristic
835C22C2×#88811yescharacteristic
836C22#550711yescharacteristic
837C22#551711yescharacteristic
838C22#553111yescharacteristic
839C22#553411yescharacteristic
840C22D4×Dic611yescharacteristic
841C22D4×Dic611yescharacteristic
842C22#554111yescharacteristic
843C22#554311yescharacteristic
844C22#554711yescharacteristic
845C22#554711yescharacteristic
846C22#554711yescharacteristic
847C22#555311yescharacteristic
848C22#556911yescharacteristic
849C22#557811yescharacteristic
850C22#557811yescharacteristic
851C22#558311yescharacteristic
852C22D3×#12011yescharacteristic
853C22#560611yescharacteristic
854C22#560611yescharacteristic
855C22#562911yescharacteristic
856C22#563211yescharacteristic
857C22#563211yescharacteristic
858C22#563311yescharacteristic
859C22#564811yescharacteristic
860C22D3×#12311yescharacteristic
861C22#565411yescharacteristic
862C22#567111yescharacteristic
863C22#569011yescharacteristic
864C22#569611yescharacteristic
865C22#570211yescharacteristic
866C22#571011yescharacteristic
867C22#572111yescharacteristic
868C4—24no—
869C4—24no—
870C4—42no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—64no—
875C4—64no—
876C4—81no—
877C4—122no—
878C4—122no—
879C4—122no—
880C4—122no—
881C4—122no—
882C4—241no—
883C3#1487911yescharacteristic, complemented, Sylow
884C2#7348411yescharacteristic
885C2#7366911yescharacteristic
886C2#7367811yescharacteristic
887C2#7440411yescharacteristic
888C2#7441211yescharacteristic
889C2#7493611yescharacteristic
890C2#7498211yescharacteristic
891C2#7498611yescharacteristic
892C2#7532811yescharacteristic
893C2#7537811yescharacteristic
894C2#7551511yescharacteristic
895C2#7564211yescharacteristic
896C2#7601811yescharacteristic
897C2#7607811yescharacteristic
898C2#7650211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, prime radical, cosocleC24×C3C24
FittingC3×#1436C2
hypercenter#1436D3
hypocenterC3#14879
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
136. C3×#95Q8semidirect
153. C3⋊#95Q8semidirect
400. #95Dic6semidirect
883. C3#14879semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic62
C2×#49792
C2×#46572
C2×#46542
C3×#14362
#715652
#715362
#694242
#694212
#694202
#694192
#694092
#694072
#694062
#694012
#148793