Finite Group Databasebeta

← #29717796

Subgroups — #29717796

Order 15616.

1534 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840421C211yesmaximal, characteristic, complemented
2C2×#16839996C211yesmaximal, characteristic, complemented
3C2×#16839905C211yesmaximal, characteristic, complemented
4C2×#16839900C211yesmaximal, characteristic, complemented
5C22×#14519700C211yesmaximal, characteristic, complemented
6#21447060C211yesmaximal, characteristic, complemented
7#21447022C211yesmaximal, characteristic, complemented
8#21446895C211yesmaximal, characteristic, complemented
9#21446822C211yesmaximal, characteristic, complemented
10#21446177C211yesmaximal, characteristic, complemented
11#21446136C211yesmaximal, characteristic, complemented
12#21446112C211yesmaximal, characteristic, complemented
13#21446072C211yesmaximal, characteristic, complemented
14#21445757C211yesmaximal, characteristic, complemented
15C61×#2416C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C23×Dic122C2211yescharacteristic
18C22×#11758200C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C22×#11758199C2211yescharacteristic
21C23×#92418C2211yescharacteristic
22#16840421—24no—
23#16840421—24no—
24C2×#14519765C2211yescharacteristic
25C2×#14519763—21no—
26C2×#14519756C2211yescharacteristic
27C2×#14519755—21no—
28C2×#14519751C2211yescharacteristic
29C2×#14519749—21no—
30C2×C4×Dic122C2211yescharacteristic
31C2×#14519737—21no—
32#16839996—24no—
33#16839905—24no—
34#16839900—24no—
35C2×#14519710C2211yescharacteristic
36C2×#14519700—24no—
37C2×#14519700C2211yescharacteristic
38C2×#14519700C2211yescharacteristic
39C2×#14519700C2211yescharacteristic
40C2×#14519700C2211yescharacteristic
41C2×#14519700C2211yescharacteristic
42C2×#14519700C2211yescharacteristic
43C2×#14519698C2211yescharacteristic
44C2×#14519697C2211yescharacteristic
45C2×#14519697C2211yescharacteristic
46C2×#14519697C2211yescharacteristic
47C2×C22⋊#92418C2211yescharacteristic
48C2×C22⋊#92418C2211yescharacteristic
49C2×C22⋊#92418C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839517C2211yescharacteristic
53#16839517C2211yescharacteristic
54C2×#121×C61—21no—
55C2×#121×C61C2211yescharacteristic
56C2×#121×C61C2211yescharacteristic
57C2×C4×D4×C61C2211yescharacteristic
58C22×C4⋊C4×C61C2211yescharacteristic
59C61×#396—21no—
60C61×#394—21no—
61C61×#390C2211yescharacteristic
62C61×#389C2211yescharacteristic
63C61×#386—21no—
64C61×#380C2211yescharacteristic
65C2×#11758222—22no—
66C2×#11758222—22no—
67C2×#11758222—22no—
68C2×#11758222—22no—
69C2×#11758222—41no—
70C2×#11758222—41no—
71C22×Dic122—22no—
72C22×Dic122—22no—
73C22×Dic122—21no—
74C22×Dic122—22no—
75C22×Dic122—41no—
76C22×Dic122—41no—
77C22×Dic122D414yescomplemented
78C22×Dic122C2311yescharacteristic
79C22×Dic122C2311yescharacteristic
80C22×D244C2311yescharacteristic
81C22×C22⋊D61—21no—
82C22×C22⋊D61—21no—
83C23×Dic61—21no—
84C22×C4×D61—21no—
85C2×#11758200—22no—
86C2×#11758200—22no—
87C2×#11758200—22no—
88C2×#11758200—22no—
89C2×#11758200—41no—
90C2×#11758200—41no—
91C2×#11758199—22no—
92C2×#11758199—22no—
93C2×#11758199—41no—
94C22×#92418—22no—
95C22×#92418—22no—
96C22×#92418—41no—
97C22×#92418C2311yescharacteristic
98C22×#92418C2311yescharacteristic
99C22×#92418C2311yescharacteristic
100C22×#92418C2311yescharacteristic
101#14519765—22no—
102#14519765—22no—
103#14519763—28no—
104#14519756—22no—
105#14519756—22no—
106#14519755—28no—
107#14519751—22no—
108#14519751D414yescomplemented
109#14519749—28no—
110C4×Dic122—22no—
111C4×Dic122—22no—
112#14519737—28no—
113C2×C4⋊Dic61C2311yescharacteristic
114C2×#11758196—21no—
115C2×#11758196—21no—
116C2×C22⋊Dic61—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C2×C4×Dic61—21no—
121#14519710—22no—
122#14519700—22no—
123#14519700—22no—
124#14519700—22no—
125#14519700—22no—
126#14519700—22no—
127#14519700D414yescomplemented
128#14519698—22no—
129#14519697—22no—
130#14519697—22no—
131#14519697—41no—
132C22⋊#92418—22no—
133C22⋊#92418—22no—
134C22⋊#92418—41no—
135C22×D4×C61—21no—
136C22×D4×C61—21no—
137C22×D4×C61D411yescharacteristic
138C22×D4×C61C2311yescharacteristic
139C23×C4×C61—21no—
140C23×C4×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142#121×C61—22no—
143#121×C61—22no—
144#121×C61—22no—
145#121×C61—41no—
146#121×C61—44no—
147C4×D4×C61—22no—
148C4×D4×C61—22no—
149C2×C4⋊C4×C61—22no—
150C2×C4⋊C4×C61—21no—
151C2×C4⋊C4×C61—21no—
152C2×C4⋊C4×C61—41no—
153C2×C4⋊C4×C61D411yescharacteristic
154C2×C4⋊C4×C61C2311yescharacteristic
155C2×C4⋊C4×C61C2311yescharacteristic
156C2×C4⋊C4×C61C2311yescharacteristic
157C2×C22⋊C4×C61—21no—
158C2×C22⋊C4×C61—21no—
159C2×C22⋊C4×C61—21no—
160C2×C22⋊C4×C61—21no—
161C2×C22⋊C4×C61—21no—
162C2×C22⋊C4×C61D411yescharacteristic
163C2×C22⋊C4×C61D411yescharacteristic
164C2×C42×C61C2311yescharacteristic
165#95×C61—21no—
166#95×C61—21no—
167C24×C61—21no—
168C24×C61C2×D411yescharacteristic
169C24×C61C2×D411yescharacteristic
170C23×D61—21no—
171C2×D4×C61—22no—
172C2×D4×C61—22no—
173C2×D4×C61—22no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—42no—
181C2×D4×C61—42no—
182C2×D4×C61—42no—
183C2×D4×C61—42no—
184C2×D4×C61—42no—
185C2×D4×C61—81no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—42no—
200C22×C4×C61—42no—
201C22×C4×C61—81no—
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61C2×D412yes—
207C22×C4×C61C2×D412yes—
208C22×C4×C61C2411yescharacteristic
209C2×C22⋊D61—24no—
210C2×C22⋊D61—24no—
211C2×C22⋊D61—42no—
212C2×C22⋊D61—42no—
213C2×C22⋊D61—42no—
214C2×C22⋊D61—42no—
215C22×Dic61—21no—
216C22×Dic61—24no—
217C22×Dic61—21no—
218C22×Dic61—21no—
219C22×Dic61—42no—
220C22×Dic61—42no—
221#11758222—44no—
222#11758222—44no—
223#11758222—44no—
224#11758222—44no—
225C2×D244—21no—
226C2×D244—21no—
227C2×D244—21no—
228C2×D244—21no—
229C2×D244—21no—
230C2×D244C2×D412yes—
231C2×C4×D61—24no—
232C2×C4×D61—42no—
233C2×C4×D61—42no—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122—21no—
240C2×Dic122—21no—
241C2×Dic122—28no—
242C2×Dic122—24no—
243C2×Dic122—21no—
244C2×Dic122—44no—
245C2×Dic122—44no—
246C2×Dic122—44no—
247C2×Dic122—42no—
248C2×Dic122—42no—
249C2×Dic122C2×D412yes—
250C2×Dic122C2×D412yes—
251C2×Dic122C2×D412yes—
252C2×Dic122#4112yes—
253C4⋊C4×C61—22no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61—42no—
260C4⋊C4×C61—42no—
261C4⋊C4×C61C2×D412yes—
262C22⋊C4×C61—22no—
263C22⋊C4×C61—22no—
264C22⋊C4×C61—42no—
265C22⋊C4×C61—42no—
266C22⋊C4×C61—42no—
267C22⋊C4×C61—42no—
268C22⋊C4×C61—81no—
269C42×C61—21no—
270C42×C61—21no—
271C22⋊Dic61—24no—
272#11758200—44no—
273#11758200—44no—
274#11758199—44no—
275#11758198—24no—
276#11758198—24no—
277#11758198—24no—
278C4⋊Dic61—21no—
279C4⋊Dic61C2×D412yes—
280#11758196—24no—
281#11758196—24no—
282C4×Dic61—24no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418—21no—
286C2×#92418—21no—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418—21no—
291C2×#92418—21no—
292C2×#92418—21no—
293C2×#92418—21no—
294C2×#92418—44no—
295C2×#92418C2×D412yes—
296C23×C61—21no—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61—21no—
302C23×C61—21no—
303C23×C61—21no—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61—21no—
307C23×C61—41no—
308C23×C61—41no—
309C23×C61—41no—
310C23×C61—41no—
311C23×C61—41no—
312C23×C61—41no—
313C23×C61—41no—
314C23×C61#12012yes—
315C23×C61#13512yes—
316C23×C61AGL(1,ℤ/8)12yes—
317C23×C61C22×D411yescharacteristic
318C22×D61—22no—
319C22×D61—41no—
320C22×D61—41no—
321C22×D61—41no—
322C22×D61—41no—
323C22×D61—41no—
324C22×D61—41no—
325D4×C61—44no—
326D4×C61—41no—
327D4×C61—41no—
328D4×C61—41no—
329D4×C61—41no—
330D4×C61—84no—
331D4×C61—84no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—22no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—21no—
346C2×C4×C61—21no—
347C2×C4×C61—21no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61—41no—
353C2×C4×C61—41no—
354C2×C4×C61—41no—
355C2×C4×C61—41no—
356C2×C4×C61—41no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—84no—
361C2×C4×C61#12012yes—
362C2×C4×C61C22×D411yescharacteristic
363C2×C4×C61C22×D411yescharacteristic
364C2×C4×C61C22×D411yescharacteristic
365C2×C4×C61C2×#4111yescharacteristic
366C2×C4×C61H(5,𝔽2)11yescharacteristic
367C2×C4×C61H(5,𝔽2)11yescharacteristic
368C22⋊D61—48no—
369C22⋊D61—48no—
370C2×Dic61—22no—
371C2×Dic61—22no—
372C2×Dic61—22no—
373C2×Dic61—22no—
374C2×Dic61—22no—
375C2×Dic61—48no—
376C2×Dic61—41no—
377C2×Dic61—41no—
378C2×Dic61—41no—
379C2×Dic61—41no—
380D244—22no—
381D244—22no—
382D244—41no—
383D244—41no—
384C4×D61—48no—
385Dic122—22no—
386Dic122—22no—
387Dic122—22no—
388Dic122—22no—
389Dic122—22no—
390Dic122—48no—
391Dic122—41no—
392Dic122—41no—
393Dic122#12114yescomplemented
394#92418—22no—
395#92418—41no—
396#92418—41no—
397#92418—41no—
398#24439—611nomaximal, Sylow
399C22×C61—22no—
400C22×C61—22no—
401C22×C61—22no—
402C22×C61—22no—
403C22×C61—22no—
404C22×C61—22no—
405C22×C61—41no—
406C22×C61—41no—
407C22×C61—41no—
408C22×C61—41no—
409C22×C61—41no—
410C22×C61—41no—
411C22×C61—41no—
412C22×C61—81no—
413C22×C61—81no—
414C22×C61—81no—
415C22×C61—81no—
416C22×C61—81no—
417C22×C61—81no—
418C22×C61—81no—
419C22×C61#44914yescomplemented
420C22×C61C2×#12011yescharacteristic
421C22×C61D4211yescharacteristic
422C22×C61#54611yescharacteristic
423C22×C61C2×#13511yescharacteristic
424C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
425C22×C61#57711yescharacteristic
426C22×C61#57811yescharacteristic
427C2×D61—42no—
428C2×D61—42no—
429C2×D61—42no—
430C2×D61—81no—
431C2×D61—81no—
432C2×D61—81no—
433C2×D61—81no—
434C4×C61—22no—
435C4×C61—41no—
436C4×C61—41no—
437C4×C61—42no—
438C4×C61—41no—
439C4×C61—81no—
440C4×C61—81no—
441C4×C61C2×#12111yescharacteristic
442C4×C61#53411yescharacteristic
443C4×C61D4211yescharacteristic
444C4×C61#54611yescharacteristic
445Dic61—24no—
446Dic61—42no—
447Dic61—42no—
448C2×#548—611no—
449C2×#466—611no—
450C2×#449—611no—
451C2×#448—611no—
452C22×#103—611no—
453#2416D6111yescharacteristic, complemented
454#2042—611no—
455#2036—611no—
456#2012—611no—
457#2000—611no—
458#1880—611no—
459#1874—611no—
460#1869—611no—
461#1863—611no—
462#1788—611no—
463C2×C61—24no—
464C2×C61—81no—
465C2×C61—161no—
466C2×C61#241011yescharacteristic
467C2×C61C2×#44911yescharacteristic
468C2×C61#301311yescharacteristic
469C2×C61#326511yescharacteristic
470C2×C61#328511yescharacteristic
471C2×C61#330111yescharacteristic
472C2×C61#330811yescharacteristic
473D61—82no—
474C22×#41—611no—
475C23×Q8—611no—
476C22×SD16—611no—
477C22×SD16—611no—
478C22×D8—611no—
479C23×C8—611no—
480#548—1224no—
481#548—1224no—
482C2×#124—611no—
483C2×#124—1221no—
484C2×C22⋊Q8—611no—
485C2×C22⋊Q8—1221no—
486C2×#121—21no—
487C2×#121—611no—
488C2×#121—1221no—
489C2×#121C2×D6111yescharacteristic
490C2×#121C2×D6111yescharacteristic
491C2×C4×Q8—611no—
492C2×C4×D4—1221no—
493C2×C4×D4C2×D6111yescharacteristic
494C22×C4⋊C4C2×D6111yescharacteristic
495#466—1224no—
496#449—1224no—
497#448—1224no—
498C2×#107—611no—
499C2×#103—611no—
500C2×#103—611no—
501C2×#103—611no—
502C2×#103—611no—
503C2×#103—611no—
504C2×#103—611no—
505C2×#103—1224no—
506C2×#102—611no—
507C2×#102—611no—
508C2×#102—611no—
509C2×#102—611no—
510C2×C22⋊C8—611no—
511C2×C22⋊C8—611no—
512C2×C22⋊C8—611no—
513#396—21no—
514#394—21no—
515#390C2×D6111yescharacteristic
516#389C2×D6111yescharacteristic
517#386—21no—
518#380C2×D6111yescharacteristic
519#340—611no—
520#340—611no—
521#336—611no—
522#336—611no—
523C61#2443911yescharacteristic, complemented, Sylow
524C2×#41—1222no—
525C2×#41—1222no—
526C2×#41—1222no—
527C2×#41—1222no—
528C2×#41—2441no—
529C2×#41—2441no—
530C22×Q8—614no—
531C22×Q8—611no—
532C22×Q8—611no—
533C22×Q8—1222no—
534C22×Q8—1222no—
535C22×Q8—1222no—
536C22×Q8—1221no—
537C22×Q8—2441no—
538C22×Q8—2441no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—611no—
542C22×D4—1221no—
543C22×D4—1221no—
544C22×D4C22⋊D6111yescharacteristic
545C22×D4C22×D6111yescharacteristic
546C23×C4—21no—
547C23×C4—1221no—
548C23×C4—1221no—
549C23×C4C22×D6111yescharacteristic
550C23×C4C22×D6111yescharacteristic
551C2×SD16—1222no—
552C2×SD16—1222no—
553C2×SD16—1222no—
554C2×SD16—1222no—
555C2×SD16—2441no—
556C2×SD16—2441no—
557C2×D8—1222no—
558C2×D8—1222no—
559C2×D8—2441no—
560C22×C8—611no—
561C22×C8—611no—
562C22×C8—611no—
563C22×C8—611no—
564C22×C8—1222no—
565C22×C8—1222no—
566C22×C8—2441no—
567#124—1222no—
568#124—1222no—
569#124—1228no—
570C22⋊Q8—1228no—
571C22⋊Q8—1222no—
572C22⋊Q8—1222no—
573#121—22no—
574#121—22no—
575#121—22no—
576#121—41no—
577#121—44no—
578#121—614no—
579#121—1228no—
580#121—1222no—
581C4×Q8—1222no—
582C4×Q8—1222no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—1228no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—41no—
590C2×C4⋊C4—611no—
591C2×C4⋊C4—1221no—
592C2×C4⋊C4—1221no—
593C2×C4⋊C4C22⋊D6111yescharacteristic
594C2×C4⋊C4C22×D6111yescharacteristic
595C2×C4⋊C4C22×D6111yescharacteristic
596C2×C4⋊C4C22×D6111yescharacteristic
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—1221no—
603C2×C22⋊C4—1221no—
604C2×C22⋊C4—1221no—
605C2×C22⋊C4—1221no—
606C2×C22⋊C4C22⋊D6111yescharacteristic
607C2×C22⋊C4C22⋊D6111yescharacteristic
608C2×C42—1221no—
609C2×C42C22×D6111yescharacteristic
610#107—1222no—
611#103—614no—
612#103—1222no—
613#103—1222no—
614#103—1222no—
615#103—1222no—
616#103—1222no—
617#102—1222no—
618#102—1222no—
619#102—1222no—
620#102—2441no—
621C22⋊C8—1222no—
622C22⋊C8—1222no—
623C22⋊C8—2441no—
624#95—21no—
625#95—21no—
626C24—21no—
627C24—1221no—
628C24C2×C22⋊D6111yescharacteristic
629C24C2×C22⋊D6111yescharacteristic
630#41—2444no—
631#41—2444no—
632#41—2444no—
633#41—2444no—
634C2×Q8—612no—
635C2×Q8—612no—
636C2×Q8—612no—
637C2×Q8—612no—
638C2×Q8—1228no—
639C2×Q8—1221no—
640C2×Q8—1221no—
641C2×Q8—1221no—
642C2×Q8—1221no—
643C2×Q8—1224no—
644C2×Q8—1221no—
645C2×Q8—1221no—
646C2×Q8—1221no—
647C2×Q8—1221no—
648C2×Q8—2442no—
649C2×Q8—2442no—
650C2×Q8—2444no—
651C2×Q8—2444no—
652C2×Q8—2444no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—42no—
666C2×D4—42no—
667C2×D4—81no—
668C2×D4—612no—
669C2×D4—1224no—
670C2×D4—1224no—
671C2×D4—1221no—
672C2×D4—1221no—
673C2×D4—1221no—
674C2×D4—1221no—
675C2×D4—1221no—
676C2×D4—2442no—
677C2×D4—2442no—
678C2×D4—2442no—
679C2×D4—2442no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—42no—
694C22×C4—42no—
695C22×C4—81no—
696C22×C4—1224no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4—1221no—
700C22×C4—1224no—
701C22×C4—2442no—
702C22×C4—2442no—
703C22×C4—2442no—
704C22×C4—2442no—
705C22×C4D4×D6112yes—
706C22×C4D4×D6112yes—
707C22×C4C2×C22⋊D6111yescharacteristic
708C22×C4C2×C22⋊D6111yescharacteristic
709C22×C4C2×C22⋊D6111yescharacteristic
710C22×C4C2×C22⋊D6111yescharacteristic
711C22×C4C23×D6111yescharacteristic
712SD16—2444no—
713SD16—2444no—
714D8—2444no—
715C2×C8—612no—
716C2×C8—1221no—
717C2×C8—1221no—
718C2×C8—1221no—
719C2×C8—1221no—
720C2×C8—1221no—
721C2×C8—1221no—
722C2×C8—1221no—
723C2×C8—1221no—
724C2×C8—1221no—
725C2×C8—1221no—
726C2×C8—1221no—
727C2×C8—2444no—
728C4⋊C4—21no—
729C4⋊C4—22no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—42no—
735C4⋊C4—42no—
736C4⋊C4—612no—
737C4⋊C4—1224no—
738C4⋊C4—1224no—
739C4⋊C4—1221no—
740C4⋊C4D4×D6112yes—
741C22⋊C4—22no—
742C22⋊C4—22no—
743C22⋊C4—42no—
744C22⋊C4—42no—
745C22⋊C4—42no—
746C22⋊C4—42no—
747C22⋊C4—81no—
748C22⋊C4—1224no—
749C22⋊C4—1224no—
750C22⋊C4—1224no—
751C22⋊C4—1224no—
752C42—21no—
753C42—21no—
754C42—1224no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—1222no—
774C23—2441no—
775C23—2441no—
776C23—2441no—
777C23—2441no—
778C23—2441no—
779C23—2441no—
780C23#1451974512yes—
781C23#1451979712yes—
782C23#1451980312yes—
783C23C22×C22⋊D6111yescharacteristic
784Q8—614no—
785Q8—1222no—
786Q8—1222no—
787Q8—1222no—
788Q8—1222no—
789Q8—1222no—
790Q8—2448no—
791Q8—2441no—
792Q8—2441no—
793D4—44no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—84no—
799D4—84no—
800D4—1222no—
801D4—1222no—
802D4—2448no—
803D4—2448no—
804D4—2441no—
805D4—2441no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—22no—
821C2×C4—21no—
822C2×C4—41no—
823C2×C4—41no—
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—84no—
835C2×C4—1222no—
836C2×C4—1222no—
837C2×C4—1222no—
838C2×C4—1222no—
839C2×C4—1222no—
840C2×C4—2448no—
841C2×C4—2448no—
842C2×C4—2441no—
843C2×C4—2441no—
844C2×C4—2441no—
845C2×C4—2441no—
846C2×C4#1451974512yes—
847C2×C4C2×D4×D6111yescharacteristic
848C2×C4C2×D4×D6111yescharacteristic
849C2×C4C2×D4×D6111yescharacteristic
850C2×C4#41×D6111yescharacteristic
851C2×C4#1451982211yescharacteristic
852C2×C4#1451982311yescharacteristic
853C8—1222no—
854C8—2441no—
855C8—2441no—
856C8—2441no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—22no—
861C22—22no—
862C22—22no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22—4881no—
878C22—4881no—
879C22—4881no—
880C22—4881no—
881C22—2442no—
882C22—2442no—
883C22—2442no—
884C22#1683990514yescomplemented
885C22C2×#1451974511yescharacteristic
886C22D4×C22⋊D6111yescharacteristic
887C22#1684040011yescharacteristic
888C22C2×#1451979711yescharacteristic
889C22C2×#1451980311yescharacteristic
890C22#1684057311yescharacteristic
891C22#1684057711yescharacteristic
892C4—22no—
893C4—41no—
894C4—42no—
895C4—41no—
896C4—41no—
897C4—81no—
898C4—81no—
899C4—1224no—
900C4—2442no—
901C4—2442no—
902C4#121×D6111yescharacteristic
903C4#1684032011yescharacteristic
904C4#1684039611yescharacteristic
905C4#1684040111yescharacteristic
906C2—24no—
907C2—81no—
908C2—161no—
909C2—4882no—
910C2#2144919011yescharacteristic
911C2C2×#1683990511yescharacteristic
912C2#2145513111yescharacteristic
913C2#2145731011yescharacteristic
914C2#2145755611yescharacteristic
915C2#2145771511yescharacteristic
916C2#2145780411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2416C2
socleC23×C61C22×D4
hypercenter#2416D61
hypocenterC61#24439
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2416

Complements

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

NH ≅ G/Ntype
1. C2×#16840421C2semidirect
2. C2×#16839996C2semidirect
3. C2×#16839905C2semidirect
4. C2×#16839900C2semidirect
5. C22×#14519700C2semidirect
6. #21447060C2semidirect
7. #21447022C2semidirect
8. #21446895C2semidirect
9. #21446822C2semidirect
10. #21446177C2semidirect
11. #21446136C2semidirect
12. #21446112C2semidirect
13. #21446072C2semidirect
14. #21445757C2semidirect
15. C61×#2416C2semidirect
77. C22×Dic122D4semidirect
108. #14519751D4semidirect
127. #14519700D4semidirect
393. Dic122#121semidirect
419. C22×C61#449semidirect
453. #2416D61semidirect
523. C61#24439semidirect
884. C22#16839905semidirect

Maximal subgroups

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

subgroupindex
C2×#168404212
C2×#168399962
C2×#168399052
C2×#168399002
C22×#145197002
#214470602
#214470222
#214468952
#214468222
#214461772
#214461362
#214461122
#214460722
#214457572
C61×#24162
#2443961