Finite Group Databasebeta

← #29691185

Subgroups — #29691185

Order 15616.

1224 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839914C211yesmaximal, characteristic
2C4×#14519757C211yesmaximal, characteristic, complemented
3#390×D61C211yesmaximal, characteristic
4#21446674C211yesmaximal, characteristic, complemented
5#21446671C211yesmaximal, characteristic, complemented
6#21446504C211yesmaximal, characteristic, complemented
7#21446503C211yesmaximal, characteristic, complemented
8#21446446C211yesmaximal, characteristic, complemented
9#21446177C211yesmaximal, characteristic, complemented
10#21446173C211yesmaximal, characteristic, complemented
11#21446125C211yesmaximal, characteristic, complemented
12#21446010C211yesmaximal, characteristic, complemented
13#21445748C211yesmaximal, characteristic
14#21445576C211yesmaximal, characteristic, complemented
15C61×#1926C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×#11758190C2211yescharacteristic
18C22×#11758200C2211yescharacteristic
19C2×#14519757C2211yescharacteristic
20C2×C4×Dic122C2211yescharacteristic, complemented
21C2×C4⋊C4×D61C2211yescharacteristic
22C2×C22⋊C4×D61—21no—
23C2×C22⋊C4×D61—21no—
24C2×C42×D61C2211yescharacteristic
25#16839914C418yescomplemented
26C2×#14519708C2211yescharacteristic, complemented
27C2×#14519702C2211yescharacteristic, complemented
28C2×#14519700C2211yescharacteristic, complemented
29C2×#14519699C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519697C2211yescharacteristic
32C2×#14519697C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34C2×#14519689C2211yescharacteristic
35C2×C8×Dic61C2211yescharacteristic, complemented
36C2×C8×Dic61C2211yescharacteristic, complemented
37#16839667C2211yescharacteristic, complemented
38#16839665C2211yescharacteristic
39#16839664C2211yescharacteristic
40#16839663C2211yescharacteristic
41#16839662—21no—
42#16839662—21no—
43#16839661C2211yescharacteristic, complemented
44#16839647—21no—
45#16839636—21no—
46#16839619C2211yescharacteristic
47C4×C4⋊Dic61—21no—
48C4×#11758198—21no—
49#16839525C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839517C2211yescharacteristic, complemented
53C2×#106×C61C2211yescharacteristic, complemented
54C2×#102×C61C2211yescharacteristic
55C2×#102×C61C2211yescharacteristic
56C61×#390C2211yescharacteristic
57C4×C4⋊C4×C61C2211yescharacteristic, complemented
58C61×#340C2211yescharacteristic, complemented
59C61×#336C2211yescharacteristic, complemented
60C24×D61—21no—
61C22×Dic122C2311yescharacteristic
62C22×D244C2311yescharacteristic
63C22×C22⋊D61—21no—
64C2×D4×D61—22no—
65C2×D4×D61—41no—
66C2×D4×D61—41no—
67C2×D4×D61—41no—
68C2×D4×D61—41no—
69C2×D4×D61C2×C414yes—
70C22×C4×D61—21no—
71C22×C4×D61D411yescharacteristic
72C22×C4×D61D411yescharacteristic
73C22×C4×D61C2311yescharacteristic
74C2×#11758190—41no—
75C2×#11758190—41no—
76C2×#11758190C2×C414yescomplemented
77C2×#11758200—41no—
78C2×#11758200—41no—
79C2×#11758200C2×C414yescomplemented
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82#14519757—22no—
83#14519757C2×C414yes—
84C4×Dic122—41no—
85C4×Dic122—41no—
86C2×C4⋊Dic61—21no—
87C2×C4⋊Dic61—21no—
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×#11758196—21no—
91C2×#11758196—21no—
92C4⋊C4×D61—41no—
93C4⋊C4×D61—41no—
94C2×C22⋊Dic61—21no—
95C2×C22⋊Dic61—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C22⋊C4×D61—44no—
103C22⋊C4×D61—44no—
104C2×C4×Dic61—21no—
105C2×C4×Dic61D411yescharacteristic
106C2×C4×Dic61D411yescharacteristic
107C2×C4×Dic61C2311yescharacteristic
108C42×D61—41no—
109C42×D61—41no—
110#14519708—41no—
111#14519702—41no—
112#14519700—41no—
113#14519699—41no—
114#14519698—41no—
115#14519697—41no—
116#14519697C2×C414yescomplemented
117#14519689—22no—
118#14519689C2×C414yes—
119C8×Dic61—41no—
120C8×Dic61—41no—
121#14519684—21no—
122#14519684—21no—
123#14519684—21no—
124#14519684—21no—
125C22×D4×C61C2311yescharacteristic
126C22×C8×C61C2311yescharacteristic
127C22×C8×C61C2311yescharacteristic
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C4⋊C4×C61C2311yescharacteristic
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—21no—
133C2×C42×C61—21no—
134C2×C42×C61C2311yescharacteristic
135#106×C61—41no—
136#102×C61—41no—
137#102×C61C2×C414yescomplemented
138#95×C61—21no—
139C24×C61—21no—
140C23×D61—21no—
141C23×D61—24no—
142C23×D61—42no—
143C23×D61—42no—
144C23×D61—42no—
145C23×D61—42no—
146C23×D61—42no—
147C23×D61—42no—
148C23×D61C2×D411yescharacteristic
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61C22×C412yes—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2411yescharacteristic
161C2×C22⋊D61—24no—
162C2×C22⋊D61—42no—
163C2×C22⋊D61—42no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61C2×D411yescharacteristic
168C22×Dic61C2×D411yescharacteristic
169C22×Dic61C2×D411yescharacteristic
170D4×D61—44no—
171D4×D61—44no—
172D4×D61—44no—
173D4×D61—44no—
174C2×D244—21no—
175C2×D244—21no—
176C2×D244—21no—
177C2×D244—21no—
178C2×D244—21no—
179C2×D244C22×C412yes—
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—22no—
185C2×C4×D61—22no—
186C2×C4×D61—41no—
187C2×C4×D61—41no—
188C2×C4×D61—41no—
189C2×C4×D61—42no—
190C2×C4×D61—42no—
191C2×C4×D61—42no—
192C2×C4×D61SD1614yescomplemented
193C2×C4×D61C22×C412yes—
194C2×C4×D61#4112yes—
195C2×Dic122—21no—
196C2×Dic122—21no—
197C2×Dic122—21no—
198C2×Dic122—21no—
199C2×Dic122—21no—
200C2×Dic122C22×C412yes—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61C22×C412yes—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61C22×C412yes—
213C22⋊C4×C61—42no—
214C22⋊C4×C61—42no—
215C42×C61—21no—
216C42×C61—21no—
217C42×C61—42no—
218C22⋊Dic61—42no—
219C22⋊Dic61—42no—
220#11758200—44no—
221#11758198—24no—
222#11758198—42no—
223#11758198—42no—
224#11758198—42no—
225#11758198—42no—
226#11758198—42no—
227C4⋊Dic61—24no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—42no—
233#11758196—42no—
234#11758196—42no—
235C4×Dic61—21no—
236C4×Dic61—21no—
237C4×Dic61—41no—
238C4×Dic61—41no—
239C4×Dic61—42no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418C22×C412yes—
246#11758190—44no—
247C23×C61—22no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61C22×D411yescharacteristic
255C22×D61—21no—
256C22×D61—21no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—22no—
260C22×D61—48no—
261C22×D61—48no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61—48no—
269C22×D61—84no—
270C22×D61—84no—
271C22×D61—84no—
272C22×D61—84no—
273C22×D61C4×D412yes—
274C22×D61C2×SD1612yes—
275C22×D61#13512yes—
276D4×C61—22no—
277D4×C61—22no—
278D4×C61—41no—
279D4×C61—41no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—22no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61C2×SD1612yes—
295C2×C4×C61C23×C411yescharacteristic
296C2×C4×C61C2×#4111yescharacteristic
297C2×C4×C61H(5,𝔽2)11yescharacteristic
298C2×C4×C61H(5,𝔽2)11yescharacteristic
299C2×C4×C61H(5,𝔽2)11yescharacteristic
300C2×C4×C61H(5,𝔽2)11yescharacteristic
301C22⋊D61—48no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—22no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61C4×D412yes—
318C2×Dic61C2×SD1612yes—
319C2×Dic61AGL(1,ℤ/8)12yes—
320D244—22no—
321D244—22no—
322D244—41no—
323D244—41no—
324C4×D61—22no—
325C4×D61—22no—
326C4×D61—22no—
327C4×D61—22no—
328C4×D61—44no—
329C4×D61—44no—
330C4×D61—84no—
331Dic122—22no—
332Dic122—22no—
333Dic122—41no—
334Dic122—41no—
335C8×C61—22no—
336C8×C61—41no—
337#92418—22no—
338#92418—41no—
339#22043—611nomaximal, Sylow
340C22×C61—42no—
341C22×C61—42no—
342C22×C61—42no—
343C22×C61—81no—
344C22×C61—81no—
345C22×C61—81no—
346C22×C61—81no—
347C22×C61C2×C4×D411yescharacteristic
348C22×C61#53411yescharacteristic
349C22×C61#53511yescharacteristic
350C22×C61C22×SD1611yescharacteristic
351C22×C61C2×#13511yescharacteristic
352C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
353C22×C61#57511yescharacteristic
354C2×D61—22no—
355C2×D61—22no—
356C2×D61—22no—
357C2×D61—22no—
358C2×D61—22no—
359C2×D61—22no—
360C2×D61—42no—
361C2×D61—42no—
362C2×D61—42no—
363C2×D61—816no—
364C2×D61—81no—
365C2×D61—81no—
366C2×D61—81no—
367C2×D61—81no—
368C2×D61C4×SD1614yes—
369C4×C61—22no—
370C4×C61—41no—
371C4×C61—42no—
372C4×C61—81no—
373C4×C61—81no—
374C4×C61#51811yescharacteristic
375C4×C61#51811yescharacteristic
376C4×C61#53811yescharacteristic
377C4×C61#53811yescharacteristic
378Dic61—22no—
379Dic61—22no—
380Dic61—22no—
381Dic61—42no—
382Dic61—81no—
383Dic61—81no—
384C2×#450—611no—
385C4×C22⋊Q8—611no—
386C2×#390—611no—
387#1968—611no—
388#1968—611no—
389#1934—611no—
390#1934—611no—
391#1926—611no—
392#1926D6111yescharacteristic, complemented
393#1880—611no—
394#1880—611no—
395#1872—611no—
396#1853—611no—
397#1786—611no—
398C4×C22⋊C8—611no—
399C2×C61—82no—
400C2×C61#232111yescharacteristic
401C2×C61C2×C4×SD1611yescharacteristic
402C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
403C2×C61#318711yescharacteristic
404C2×C61#318811yescharacteristic
405C2×C61#320811yescharacteristic
406C2×C61#321111yescharacteristic
407D61—24no—
408D61—82no—
409C23×D4—611no—
410C22×SD16—611no—
411C22×SD16—611no—
412C2×C22⋊Q8—611no—
413C2×C4×Q8—611no—
414C22×C4⋊C4—611no—
415C22×C22⋊C4—1221no—
416C22×C22⋊C4—1221no—
417C22×C42—611no—
418#450—618no—
419C2×#106—611no—
420C2×#106C2×D6111yescharacteristic, complemented
421C2×#103—611no—
422C2×#103—611no—
423C2×#102—611no—
424C2×#102—611no—
425C2×#102—611no—
426C2×#102—611no—
427C2×#102C2×D6111yescharacteristic
428C2×#102C2×D6111yescharacteristic
429C2×C22⋊C8—611no—
430C2×C22⋊C8—611no—
431C2×C4×C8—611no—
432C2×C4×C8—611no—
433#391—611no—
434#390—611no—
435#390—611no—
436#390—611no—
437#390—1221no—
438#390—1221no—
439#390C2×D6111yescharacteristic
440#389—611no—
441#387—1221no—
442#385—1221no—
443#380—611no—
444C4×C4⋊C4—1221no—
445C4×C4⋊C4C2×D6111yescharacteristic, complemented
446C4×C22⋊C4—1221no—
447#340—611no—
448#340—611no—
449#340—611no—
450#340C2×D6111yescharacteristic, complemented
451#336—611no—
452#336C2×D6111yescharacteristic, complemented
453C61#2204311yescharacteristic, complemented, Sylow
454C25—1221no—
455C22×Q8—611no—
456C22×D4—614no—
457C22×D4—611no—
458C22×D4—1222no—
459C22×D4—1221no—
460C22×D4—2441no—
461C22×D4—2441no—
462C22×D4—2441no—
463C22×D4—2441no—
464C22×D4C22×D6111yescharacteristic
465C23×C4—611no—
466C23×C4—611no—
467C23×C4—611no—
468C23×C4—1221no—
469C2×SD16—614no—
470C2×SD16—614no—
471C2×SD16—2441no—
472C2×SD16—2441no—
473C2×SD16—2441no—
474C2×SD16—2441no—
475C22×C8—611no—
476C22×C8—611no—
477C22×C8C22×D6111yescharacteristic
478C22×C8C22×D6111yescharacteristic
479C22⋊Q8—614no—
480C22⋊Q8—1222no—
481C4×Q8—2441no—
482C4×Q8—2441no—
483C2×C4⋊C4—611no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—1221no—
486C2×C4⋊C4—1221no—
487C2×C4⋊C4—1221no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4—2441no—
490C2×C4⋊C4—2441no—
491C2×C4⋊C4C22×D6111yescharacteristic
492C2×C4⋊C4C22×D6111yescharacteristic
493C2×C4⋊C4C22×D6111yescharacteristic
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—1221no—
497C2×C22⋊C4—1221no—
498C2×C22⋊C4—1221no—
499C2×C22⋊C4—1221no—
500C2×C22⋊C4—1221no—
501C2×C22⋊C4—1221no—
502C2×C22⋊C4—1221no—
503C2×C22⋊C4—1221no—
504C2×C22⋊C4—2444no—
505C2×C22⋊C4—2444no—
506C2×C42—21no—
507C2×C42—611no—
508C2×C42—611no—
509C2×C42—611no—
510C2×C42—1221no—
511C2×C42—2441no—
512C2×C42—2441no—
513C2×C42C22×D6111yescharacteristic
514#106—41no—
515#106—2441no—
516#103—2441no—
517#103—2441no—
518#102—41no—
519#102—614no—
520#102—2441no—
521#102—2441no—
522#102—2441no—
523#102C4×D6114yescomplemented
524C22⋊C8—614no—
525C22⋊C8—1222no—
526C4×C8—2441no—
527C4×C8—2441no—
528#95—21no—
529#95—1221no—
530#95—1221no—
531#95—1221no—
532#95—1221no—
533C24—21no—
534C24—611no—
535C24—1224no—
536C24—1221no—
537C24—2442no—
538C24—2442no—
539C24—2442no—
540C24—2442no—
541C24—2442no—
542C24—2442no—
543C2×Q8—612no—
544C2×Q8—1221no—
545C2×Q8—1221no—
546C2×Q8—1221no—
547C2×Q8—1221no—
548C2×Q8—1221no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—612no—
555C2×D4—1224no—
556C2×D4—1221no—
557C2×D4—1221no—
558C2×D4—1221no—
559C2×D4—1221no—
560C2×D4—1221no—
561C2×D4—2444no—
562C2×D4—2444no—
563C2×D4—2444no—
564C2×D4—2444no—
565C2×D4—2442no—
566C2×D4—2442no—
567C2×D4C2×C4×D6112yes—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—611no—
572C22×C4—611no—
573C22×C4—611no—
574C22×C4—612no—
575C22×C4—612no—
576C22×C4—614no—
577C22×C4—1222no—
578C22×C4—1222no—
579C22×C4—1221no—
580C22×C4—1221no—
581C22×C4—1221no—
582C22×C4—1221no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—2441no—
587C22×C4—2441no—
588C22×C4—2441no—
589C22×C4—2442no—
590C22×C4—2442no—
591C22×C4—2442no—
592C22×C4D4×D6111yescharacteristic
593C22×C4D4×D6111yescharacteristic
594C22×C4C23×D6111yescharacteristic
595SD16—2444no—
596SD16—2444no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—612no—
603C2×C8—1221no—
604C2×C8—1221no—
605C2×C8—1221no—
606C2×C8—1221no—
607C2×C8—1221no—
608C2×C8C2×C4×D6112yes—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—1224no—
615C4⋊C4—1221no—
616C4⋊C4—1221no—
617C4⋊C4—1221no—
618C4⋊C4—1221no—
619C4⋊C4—2442no—
620C4⋊C4—2442no—
621C4⋊C4—2442no—
622C4⋊C4C2×C4×D6112yes—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—1224no—
626C22⋊C4—2442no—
627C22⋊C4—2442no—
628C22⋊C4—2442no—
629C22⋊C4—2442no—
630C22⋊C4—2442no—
631C22⋊C4—2442no—
632C22⋊C4—2442no—
633C42—21no—
634C42—21no—
635C42—42no—
636C42—1221no—
637C42—1221no—
638C42—2441no—
639C42—2441no—
640C42—2442no—
641C23—22no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—612no—
649C23—612no—
650C23—612no—
651C23—1221no—
652C23—1221no—
653C23—1221no—
654C23—1221no—
655C23—1222no—
656C23—4884no—
657C23—4884no—
658C23—4884no—
659C23—4884no—
660C23—2448no—
661C23—2448no—
662C23—2448no—
663C23—2441no—
664C23—2441no—
665C23—2441no—
666C23—2441no—
667C23—2441no—
668C23—2441no—
669C23C2×D4×D6111yescharacteristic
670Q8—1222no—
671Q8—1222no—
672Q8—2441no—
673Q8—2441no—
674D4—22no—
675D4—22no—
676D4—41no—
677D4—41no—
678D4—1222no—
679D4—1222no—
680D4—2448no—
681D4—2441no—
682D4—2441no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—612no—
698C2×C4—612no—
699C2×C4—612no—
700C2×C4—1221no—
701C2×C4—1221no—
702C2×C4—1221no—
703C2×C4—1221no—
704C2×C4—1221no—
705C2×C4—1221no—
706C2×C4—1222no—
707C2×C4—1222no—
708C2×C4—1222no—
709C2×C4—1222no—
710C2×C4—1222no—
711C2×C4—4884no—
712C2×C4—2444no—
713C2×C4—2444no—
714C2×C4—2441no—
715C2×C4—2441no—
716C2×C4—2441no—
717C2×C4—2441no—
718C2×C4—2441no—
719C2×C4—2441no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4SD16×D6112yes—
723C2×C4C22×C4×D6111yescharacteristic
724C2×C4#41×D6111yescharacteristic
725C2×C4#1451982211yescharacteristic
726C2×C4#1451982311yescharacteristic
727C2×C4#1451982311yescharacteristic
728C2×C4#1451982311yescharacteristic
729C8—22no—
730C8—41no—
731C8—1222no—
732C8—2441no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—81no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—614no—
741C22—1222no—
742C22—1222no—
743C22—1222no—
744C22—1222no—
745C22—1222no—
746C22—1222no—
747C22—48816no—
748C22—4881no—
749C22—4881no—
750C22—4881no—
751C22—4881no—
752C22—2442no—
753C22—2442no—
754C22—2442no—
755C22C4×D4×D6111yescharacteristic
756C22#1684032311yescharacteristic
757C22#1684032811yescharacteristic
758C22C2×SD16×D6111yescharacteristic
759C22#135×D6111yescharacteristic
760C22AGL(1,ℤ/8)×D6111yescharacteristic
761C22#1684055811yescharacteristic
762C4—22no—
763C4—42no—
764C4—41no—
765C4—81no—
766C4—81no—
767C4—1222no—
768C4—1222no—
769C4—1222no—
770C4—4881no—
771C4—4881no—
772C4—2442no—
773C4#1684023411yescharacteristic
774C4#1684023611yescharacteristic
775C4#1684034611yescharacteristic
776C4#1684035111yescharacteristic
777C2—82no—
778C2—1224no—
779C2—4882no—
780C2#2144848111yescharacteristic
781C2C4×SD16×D6111yescharacteristic
782C2#2145463011yescharacteristic
783C2#2145657811yescharacteristic
784C2#2145658811yescharacteristic
785C2#2145675911yescharacteristic
786C2#2145678211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1926C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
cosocleC22×C4×C61C24
hypercenter#1926D61
hypocenterC61#22043
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1926

Complements

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

NH ≅ G/Ntype
2. C4×#14519757C2semidirect
4. #21446674C2semidirect
5. #21446671C2semidirect
6. #21446504C2semidirect
7. #21446503C2semidirect
8. #21446446C2semidirect
9. #21446177C2semidirect
10. #21446173C2semidirect
11. #21446125C2semidirect
12. #21446010C2semidirect
14. #21445576C2semidirect
15. C61×#1926C2semidirect
20. C2×C4×Dic122C22semidirect
25. #16839914C4semidirect
26. C2×#14519708C22semidirect
27. C2×#14519702C22semidirect
28. C2×#14519700C22semidirect
35. C2×C8×Dic61C22semidirect
36. C2×C8×Dic61C22semidirect
37. #16839667C22semidirect
43. #16839661C22semidirect
49. #16839525C22semidirect
50. #16839524C22semidirect
51. #16839524C22semidirect
52. #16839517C22semidirect
53. C2×#106×C61C22semidirect
57. C4×C4⋊C4×C61C22semidirect
58. C61×#340C22semidirect
59. C61×#336C22semidirect
76. C2×#11758190C2×C4semidirect
79. C2×#11758200C2×C4semidirect
116. #14519697C2×C4semidirect
137. #102×C61C2×C4semidirect
192. C2×C4×D61SD16semidirect
392. #1926D61semidirect
420. C2×#106C2×D61semidirect
445. C4×C4⋊C4C2×D61semidirect
450. #340C2×D61semidirect
452. #336C2×D61semidirect
453. C61#22043semidirect
523. #102C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399142
C4×#145197572
#390×D612
#214466742
#214466712
#214465042
#214465032
#214464462
#214461772
#214461732
#214461252
#214460102
#214457482
#214455762
C61×#19262
#2204361