Finite Group Databasebeta

← #30617017

Subgroups — #30617017

Order 15616.

1124 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840803C211yesmaximal, characteristic
2C2×#16840801C211yesmaximal, characteristic, complemented
3#124×#6923C211yesmaximal, characteristic, complemented
4C4×D4×#6923C211yesmaximal, characteristic, complemented
5#21461987C211yesmaximal, characteristic, complemented
6#21461932C211yesmaximal, characteristic, complemented
7#21461898C211yesmaximal, characteristic, complemented
8#21461896C211yesmaximal, characteristic, complemented
9#21461814C211yesmaximal, characteristic
10#21461812C211yesmaximal, characteristic, complemented
11#21461689C211yesmaximal, characteristic, complemented
12#21461606C211yesmaximal, characteristic, complemented
13#21461592C211yesmaximal, characteristic, complemented
14#21461590C211yesmaximal, characteristic, complemented
15#463×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×D4×#6923C2211yescharacteristic
18C2×D4×#6923C2211yescharacteristic
19C2×D4×#6923C2211yescharacteristic
20C22×C4×#6923—21no—
21#16840803—24no—
22#16840801—24no—
23C2×#14519846C2211yescharacteristic
24C2×#14519845C2211yescharacteristic
25D61⋊(C4⋊C8)C2211yescharacteristic
26C2×#14519840C2211yescharacteristic
27C2×#14519840C2211yescharacteristic
28C2×#14519839C2211yescharacteristic
29C2×#14519839C2211yescharacteristic
30C2×#14519839C2211yescharacteristic
31C2×#14519839C2211yescharacteristic
32C2×#14519831C2211yescharacteristic
33C2×#14519831C2211yescharacteristic
34(C2×#6923)⋊Q8C2211yescharacteristic
35#16840714C2211yescharacteristic
36#16840712—21no—
37#16840712—21no—
38#16840706C2211yescharacteristic
39C4⋊C4×#6923C2211yescharacteristic
40C4⋊C4×#6923C2211yescharacteristic
41C4×C4⋊#6923C2211yescharacteristic
42C22⋊C4×#6923—21no—
43C22⋊C4×#6923—21no—
44C22⋊C4×#6923—21no—
45C22⋊C4×#6923—21no—
46C4×C22⋊#6923—21no—
47C42×#6923C2211yescharacteristic
48#16840636C2211yescharacteristic
49#16840636C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52(C2×#6923)⋊C8C2211yescharacteristic
53(C2×#6923)⋊C8C2211yescharacteristic
54C2×SD16×D61C2211yescharacteristic
55C2×D8×D61C2211yescharacteristic
56#124×D61C2211yescharacteristic
57C4×D4×D61C2211yescharacteristic
58#16839980C411yescharacteristic, complemented
59#16839979C411yescharacteristic, complemented
60#16839978C411yescharacteristic, complemented
61#16839977C411yescharacteristic, complemented
62#16839976C411yescharacteristic, complemented
63#16839975C411yescharacteristic, complemented
64#16839974C411yescharacteristic, complemented
65C4⋊C8×D61C2211yescharacteristic
66#103×D61C2211yescharacteristic
67#102×D61C2211yescharacteristic
68C61×#463C411yescharacteristic, complemented
69C23×#6923—21no—
70C23×#6923—21no—
71C23×#6923—21no—
72C2×D61⋊C8C2311yescharacteristic
73C2×D61⋊C8C2311yescharacteristic
74Q8×#6923—22no—
75Q8×#6923—22no—
76D4×#6923—22no—
77D4×#6923—22no—
78D4×#6923—22no—
79D4×#6923—22no—
80D4×#6923—22no—
81D4×#6923D414yes—
82C2×C4⋊#6923—21no—
83C2×C4⋊#6923C2311yescharacteristic
84C2×C4⋊#6923C2311yescharacteristic
85C2×C4⋊#6923C2311yescharacteristic
86C2×C4⋊#6923C2311yescharacteristic
87C2×C22⋊#6923—21no—
88C2×C22⋊#6923—21no—
89C2×C22⋊#6923—21no—
90C2×C22⋊#6923—21no—
91C2×C22⋊#6923—21no—
92C2×C4×#6923—21no—
93C2×C4×#6923—21no—
94C2×C4×#6923—21no—
95C2×C4×#6923—21no—
96C2×C4×#6923—44no—
97C2×C4×#6923D411yescharacteristic
98C2×C4×#6923D411yescharacteristic
99C2×C4×#6923D411yescharacteristic
100C2×C4×#6923D411yescharacteristic
101C2×C4×#6923C2311yescharacteristic
102C2×C4×#6923C2311yescharacteristic
103#14519846—22no—
104#14519845—22no—
105#14519844—21no—
106C4⋊#92420—21no—
107#14519840—22no—
108#14519840—22no—
109#14519839—22no—
110#14519839—22no—
111#14519839—22no—
112#14519839—22no—
113#14519831—22no—
114#14519831—22no—
115(C2×#6923)⋊C4—21no—
116(C2×#6923)⋊C4—21no—
117(C2×#6923)⋊C4—21no—
118(C2×#6923)⋊C4—21no—
119(C2×#6923)⋊C4—21no—
120(C2×#6923)⋊C4—21no—
121(C2×#6923)⋊C4—21no—
122C2×Q8×D61C2311yescharacteristic
123C2×D4×D61C2311yescharacteristic
124C2×D4×D61C2311yescharacteristic
125C22×C4×D61—21no—
126C2×#11758190C2×C411yescharacteristic, complemented
127C2×#11758200C2×C411yescharacteristic, complemented
128C2×#11758201C2×C411yescharacteristic, complemented
129SD16×D61—22no—
130SD16×D61—22no—
131C2×D488C2×C411yescharacteristic
132C2×#11758199C2×C411yescharacteristic
133C2×#11758199C2×C411yescharacteristic
134D8×D61—22no—
135D8×D61—22no—
136C2×C8×D61C2311yescharacteristic
137C2×C8×D61C2311yescharacteristic
138#14519766C2×C411yescharacteristic, complemented
139#14519765C2×C411yescharacteristic, complemented
140#14519764C2×C411yescharacteristic, complemented
141#14519763—21no—
142#14519763—21no—
143C4×D244C2×C411yescharacteristic, complemented
144D4×Dic61C2×C411yescharacteristic, complemented
145#14519739C2×C411yescharacteristic, complemented
146C4×C22⋊D61—21no—
147#14519737—21no—
148C4⋊C4×D61C2311yescharacteristic
149C22⋊C4×D61—21no—
150C22⋊C4×D61—21no—
151C22⋊C4×D61—21no—
152C42×D61C2311yescharacteristic
153C4⋊#92418C2×C411yescharacteristic, complemented
154#14519706C2×C411yescharacteristic, complemented
155#14519706C2×C411yescharacteristic, complemented
156#14519702C2×C411yescharacteristic, complemented
157#14519701C2×C411yescharacteristic, complemented
158#14519700C2×C411yescharacteristic, complemented
159#14519699C2×C411yescharacteristic, complemented
160#14519698C2×C411yescharacteristic, complemented
161#14519697C2×C411yescharacteristic, complemented
162C2×SD16×C61C2×C411yescharacteristic, complemented
163C2×D8×C61C2×C411yescharacteristic
164#124×C61C2×C411yescharacteristic, complemented
165C4×D4×C61C2×C411yescharacteristic, complemented
166C4⋊C8×C61C2×C411yescharacteristic, complemented
167#103×C61C2×C411yescharacteristic, complemented
168#102×C61C2×C411yescharacteristic, complemented
169C23×D61—21no—
170C23×D61—21no—
171C22×#6923—24no—
172C22×#6923—21no—
173C22×#6923—21no—
174C22×#6923—24no—
175C22×#6923—21no—
176C22×#6923—21no—
177C22×#6923—42no—
178C22×#6923—42no—
179C22×#6923—42no—
180C22×#6923—42no—
181C22×#6923—42no—
182C22×#6923—42no—
183C22×#6923—42no—
184C22×#6923C2×D411yescharacteristic
185C22×#6923C2×D411yescharacteristic
186C22×#6923C2×D411yescharacteristic
187C22×#6923C2×D411yescharacteristic
188C2×Q8×C61C22×C411yescharacteristic
189C2×D4×C61C22×C411yescharacteristic
190C2×D4×C61C22×C411yescharacteristic
191C22×C4×C61—21no—
192C2×C22⋊D61—21no—
193C2×C22⋊D61—21no—
194C22×Dic61—21no—
195Q8×D61—21no—
196Q8×D61—21no—
197Q8×D61—21no—
198Q8×D61—21no—
199D4×D61—21no—
200D4×D61—21no—
201D4×D61—21no—
202D4×D61—21no—
203D4×D61—21no—
204D4×D61—21no—
205D4×D61C2×D412yes—
206D4×D61#4112yes—
207C2×D244C22×C411yescharacteristic
208C2×D244C22×C411yescharacteristic
209C2×C4×D61—21no—
210C2×C4×D61—21no—
211C2×C4×D61—21no—
212C2×C4×D61—21no—
213C2×C4×D61—42no—
214C2×C4×D61—42no—
215C2×C4×D61C2×D411yescharacteristic
216C2×C4×D61C2×D411yescharacteristic
217C2×C4×D61C2411yescharacteristic
218C2×Dic122—21no—
219C2×Dic122C22×C411yescharacteristic
220C22⋊#6923—24no—
221C22⋊#6923—24no—
222C22⋊#6923—42no—
223C22⋊#6923—42no—
224C22⋊#6923—42no—
225C2×#92420—21no—
226C2×#92420—21no—
227C4⋊#6923—21no—
228C4⋊#6923—21no—
229C4⋊#6923—21no—
230C4⋊#6923—21no—
231C4⋊#6923—21no—
232C4⋊#6923—21no—
233C4⋊#6923—42no—
234C4⋊#6923C2×D412yes—
235C4⋊#6923#4112yes—
236C4×#6923—22no—
237C4×#6923—21no—
238C4×#6923—21no—
239C4×#6923—41no—
240C4×#6923—41no—
241C4×#6923—41no—
242C4×#6923—42no—
243C4×#6923—42no—
244C4×#6923—42no—
245C4×#6923—42no—
246C4×#6923C2×D412yes—
247C4×#6923#4112yes—
248D61⋊C8—21no—
249D61⋊C8—21no—
250D61⋊C8—21no—
251D61⋊C8—21no—
252SD16×C61—22no—
253D8×C61—22no—
254C2×C8×C61C22×C411yescharacteristic
255C2×C8×C61C22×C411yescharacteristic
256C4⋊C4×C61C22×C411yescharacteristic
257C22⋊C4×C61—21no—
258C22⋊C4×C61—21no—
259C22⋊C4×C61—21no—
260C42×C61C22×C411yescharacteristic
261C22⋊Dic61—21no—
262C22⋊Dic61—21no—
263C22⋊Dic61—21no—
264#11758201—22no—
265#11758200—22no—
266#11758199—22no—
267#11758199—22no—
268#11758198—21no—
269#11758198—21no—
270#11758198—21no—
271#11758198—21no—
272#11758198—21no—
273#11758198—21no—
274C4⋊Dic61C22×C411yescharacteristic
275#11758196—21no—
276C4×Dic61C22×C411yescharacteristic
277C4×Dic61#4111yescharacteristic
278C4×Dic61#4111yescharacteristic
279C2×#92418C22×C411yescharacteristic
280C2×#92418C22×C411yescharacteristic
281D488—22no—
282#11758190—22no—
283C8×D61—21no—
284C8×D61—21no—
285C8×D61—21no—
286C8×D61—21no—
287C23×C61—21no—
288C23×C61—21no—
289C22×D61—21no—
290C22×D61—22no—
291C22×D61—22no—
292C22×D61—21no—
293C22×D61—41no—
294C22×D61—41no—
295C22×D61—41no—
296C22×D61—41no—
297C22×D61—41no—
298C22×D61—41no—
299C22×D61—41no—
300C22×D61—41no—
301C22×D61—41no—
302C22×D61—41no—
303C22×D61C22×D411yescharacteristic
304C2×#6923—21no—
305C2×#6923—21no—
306C2×#6923—21no—
307C2×#6923—21no—
308C2×#6923—21no—
309C2×#6923—21no—
310C2×#6923—22no—
311C2×#6923—21no—
312C2×#6923—22no—
313C2×#6923—21no—
314C2×#6923—21no—
315C2×#6923—48no—
316C2×#6923—48no—
317C2×#6923—41no—
318C2×#6923—41no—
319C2×#6923—41no—
320C2×#6923—41no—
321C2×#6923—41no—
322C2×#6923—41no—
323C2×#6923—41no—
324C2×#6923—41no—
325C2×#6923—41no—
326C2×#6923—41no—
327C2×#6923—84no—
328C2×#6923#12112yes—
329C2×#6923#12112yes—
330C2×#6923AGL(1,ℤ/8)12yes—
331Q8×C61—21no—
332Q8×C61—21no—
333D4×C61—21no—
334D4×C61—21no—
335D4×C61—21no—
336D4×C61C4×D412yes—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—42no—
340C2×C4×C61C4×D411yescharacteristic
341C2×C4×C61C4×D411yescharacteristic
342C2×C4×C61C23×C411yescharacteristic
343C22⋊D61—22no—
344C22⋊D61—22no—
345C22⋊D61—41no—
346C22⋊D61—41no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—42no—
350C2×Dic61C4×D411yescharacteristic
351C2×Dic61C4×D411yescharacteristic
352C2×Dic61C2×#4111yescharacteristic
353D244—21no—
354D244—21no—
355D244—21no—
356D244C4×D412yes—
357C4×D61—21no—
358C4×D61—21no—
359C4×D61—21no—
360C4×D61—21no—
361C4×D61—42no—
362C4×D61—42no—
363C4×D61—41no—
364C4×D61—41no—
365C4×D61—41no—
366C4×D61—41no—
367C4×D61C22×D411yescharacteristic
368C4×D61C2×#4111yescharacteristic
369C4×D61C2×#4111yescharacteristic
370C4×D61C2×#4111yescharacteristic
371Dic122—21no—
372Dic122—21no—
373Dic122—41no—
374Dic122—41no—
375#92420—41no—
376#92420—41no—
377C8×C61—21no—
378C8×C61—21no—
379#92418—21no—
380#92418—21no—
381#21507—611nomaximal, Sylow
382C22×C61—22no—
383C22×C61—41no—
384C22×C61—41no—
385C22×C61—41no—
386C22×C61—41no—
387C22×C61—41no—
388C22×C61C2×C4×D411yescharacteristic
389C2×D61—22no—
390C2×D61—41no—
391C2×D61—41no—
392C2×D61—42no—
393C2×D61—42no—
394C2×D61—42no—
395C2×D61—42no—
396C2×D61—41no—
397C2×D61—41no—
398C2×D61—41no—
399C2×D61—81no—
400C2×D61—81no—
401C2×D61—81no—
402C2×D61—81no—
403C2×D61C2×#12111yescharacteristic
404C2×D61#52511yescharacteristic
405C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
406C2×D61#57511yescharacteristic
407C2×D61#57511yescharacteristic
408C2×D61#57511yescharacteristic
409#6923—22no—
410#6923—22no—
411#6923—22no—
412#6923—41no—
413#6923—42no—
414#6923—42no—
415#6923—81no—
416#6923—81no—
417C4×C61—21no—
418C4×C61—21no—
419C4×C61—41no—
420C4×C61—41no—
421C4×C61C2×C4×D411yescharacteristic
422C4×C61C4×#4111yescharacteristic
423Dic61—21no—
424Dic61—21no—
425Dic61—41no—
426Dic61—41no—
427Dic61#52911yescharacteristic
428Dic61#53211yescharacteristic
429C2×#463—611no—
430C2×#442—611no—
431C2×#440—611no—
432C4×#124—611no—
433C42×D4—611no—
434#1983—611no—
435#1949—611no—
436#1927—611no—
437#1925—611no—
438#1879—611no—
439#1877—611no—
440#1804—611no—
441#1767—611no—
442#1763—611no—
443#1762—611no—
444C2×C61—42no—
445C2×C61—81no—
446C2×C61C4×#12111yescharacteristic
447C2×C61#294311yescharacteristic
448C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
449D61—42no—
450D61—81no—
451D61#303611yescharacteristic
452D61#304011yescharacteristic
453D61#311111yescharacteristic
454D61#311411yescharacteristic
455C22×SD16—611no—
456C22×D8—611no—
457C2×#124—611no—
458C2×C4×Q8—611no—
459C2×C4×D4—611no—
460C2×C4×D4—611no—
461C2×C4×D4—611no—
462C2×C4×D4—611no—
463C22×C42—1221no—
464#463—611no—
465#463—611no—
466#463—611no—
467#463—611no—
468#463—611no—
469#463—611no—
470#463—611no—
471#463#692311yescharacteristic, complemented
472#442—1224no—
473#440—1224no—
474C2×#107—611no—
475C2×#106—611no—
476C2×C4⋊C8—611no—
477C2×C4⋊C8—611no—
478C2×#103—611no—
479C2×#103—611no—
480C2×#103—611no—
481C2×#102—611no—
482C2×#102—611no—
483C2×#102—611no—
484C2×#102—611no—
485C2×#102—611no—
486C2×#97—611no—
487C2×#97—611no—
488#391—611no—
489#390—611no—
490#388—1221no—
491#388—1221no—
492#382—611no—
493C4×C4⋊C4—611no—
494C4×C4⋊C4—611no—
495C4×C4⋊C4—611no—
496C4×C22⋊C4—1221no—
497C4×C22⋊C4—1221no—
498C4×C22⋊C4—1221no—
499C4×C22⋊C4—1221no—
500C4×C22⋊C4—1221no—
501C43—611no—
502#340—611no—
503#340—611no—
504#340—611no—
505#340—611no—
506#336—611no—
507#336—611no—
508C61#2150711yescharacteristic, complemented, Sylow
509C22×Q8—611no—
510C22×D4—611no—
511C22×D4—611no—
512C23×C4—1221no—
513C23×C4—1221no—
514C23×C4—1221no—
515C23×C4—1221no—
516C2×SD16—611no—
517C2×SD16—611no—
518C2×SD16—611no—
519C2×SD16—1222no—
520C2×SD16—1222no—
521C2×SD16C2×#692311yescharacteristic, complemented
522C2×D8—611no—
523C2×D8—611no—
524C2×D8—611no—
525C2×D8—1222no—
526C2×D8—1222no—
527C2×D8C2×#692311yescharacteristic
528C22×C8—611no—
529C22×C8—611no—
530C22×C8—611no—
531C22×C8—611no—
532#124—611no—
533#124—611no—
534#124—611no—
535#124—1221no—
536#124—1221no—
537#124C2×#692311yescharacteristic, complemented
538C4×Q8—1222no—
539C4×Q8—1222no—
540C4×D4—614no—
541C4×D4—611no—
542C4×D4—611no—
543C4×D4—611no—
544C4×D4—1221no—
545C4×D4—1221no—
546C4×D4—1222no—
547C4×D4—1222no—
548C4×D4—1222no—
549C4×D4—1222no—
550C4×D4—1222no—
551C4×D4C2×#692311yescharacteristic, complemented
552C2×C4⋊C4—611no—
553C2×C4⋊C4—611no—
554C2×C4⋊C4—611no—
555C2×C4⋊C4—611no—
556C2×C4⋊C4—611no—
557C2×C4⋊C4—1221no—
558C2×C22⋊C4—1221no—
559C2×C22⋊C4—1221no—
560C2×C22⋊C4—1221no—
561C2×C22⋊C4—1221no—
562C2×C22⋊C4—1221no—
563C2×C22⋊C4—1221no—
564C2×C22⋊C4—1221no—
565C2×C22⋊C4—1221no—
566C2×C42—611no—
567C2×C42—611no—
568C2×C42—611no—
569C2×C42—611no—
570C2×C42—611no—
571C2×C42—611no—
572C2×C42—611no—
573C2×C42—1221no—
574C2×C42—1221no—
575C2×C42—1221no—
576C2×C42—1221no—
577C2×C42—2444no—
578#107—1222no—
579#106—1222no—
580C4⋊C8—611no—
581C4⋊C8—611no—
582C4⋊C8—611no—
583C4⋊C8—1221no—
584C4⋊C8—1221no—
585C4⋊C8C2×#692311yescharacteristic, complemented
586#103—611no—
587#103—611no—
588#103—611no—
589#103—1222no—
590#103—1222no—
591#103C2×#692311yescharacteristic, complemented
592#102—611no—
593#102—611no—
594#102—611no—
595#102—1222no—
596#102—1222no—
597#102—1222no—
598#102—1222no—
599#102C2×#692311yescharacteristic, complemented
600#97—1222no—
601#97—1222no—
602#95—1221no—
603#95—1221no—
604#95—1221no—
605#95—1221no—
606#95—1221no—
607#95—1221no—
608#95—1221no—
609C24—1221no—
610C24—1221no—
611C2×Q8—611no—
612C2×Q8—1221no—
613C2×Q8—1221no—
614C2×Q8—1221no—
615C2×Q8—1221no—
616C2×Q8—1221no—
617C2×Q8C22×#692311yescharacteristic
618C2×D4—612no—
619C2×D4—612no—
620C2×D4—611no—
621C2×D4—611no—
622C2×D4—1221no—
623C2×D4—1221no—
624C2×D4—1221no—
625C2×D4—1221no—
626C2×D4—1221no—
627C2×D4—1221no—
628C2×D4—1221no—
629C2×D4—1221no—
630C2×D4C22×#692311yescharacteristic
631C2×D4C22×#692311yescharacteristic
632C22×C4—21no—
633C22×C4—611no—
634C22×C4—611no—
635C22×C4—611no—
636C22×C4—611no—
637C22×C4—611no—
638C22×C4—611no—
639C22×C4—611no—
640C22×C4—1221no—
641C22×C4—1221no—
642C22×C4—1221no—
643C22×C4—1221no—
644C22×C4—1224no—
645C22×C4—1221no—
646C22×C4—1221no—
647C22×C4—1224no—
648C22×C4—1221no—
649C22×C4—1221no—
650C22×C4—1221no—
651C22×C4—2442no—
652C22×C4—2442no—
653C22×C4—2442no—
654C22×C4—2442no—
655C22×C4—2442no—
656C22×C4—2442no—
657C22×C4—2442no—
658C22×C4—2442no—
659C22×C4—2442no—
660SD16—22no—
661SD16—1222no—
662SD16—1222no—
663SD16—1222no—
664D8—22no—
665D8—1222no—
666D8—1222no—
667D8—1222no—
668C2×C8—611no—
669C2×C8—611no—
670C2×C8—1221no—
671C2×C8—1221no—
672C2×C8—1221no—
673C2×C8—1221no—
674C2×C8—1221no—
675C2×C8—1221no—
676C2×C8—1221no—
677C2×C8—1221no—
678C2×C8—1221no—
679C2×C8—1221no—
680C2×C8C22×#692311yescharacteristic
681C2×C8C22×#692311yescharacteristic
682C4⋊C4—612no—
683C4⋊C4—612no—
684C4⋊C4—611no—
685C4⋊C4—1221no—
686C4⋊C4—1221no—
687C4⋊C4—1221no—
688C4⋊C4—1221no—
689C4⋊C4—1221no—
690C4⋊C4—1221no—
691C4⋊C4—1221no—
692C4⋊C4—2442no—
693C4⋊C4C22×#692311yescharacteristic
694C22⋊C4—21no—
695C22⋊C4—21no—
696C22⋊C4—21no—
697C22⋊C4—1221no—
698C22⋊C4—1221no—
699C22⋊C4—1221no—
700C22⋊C4—1221no—
701C22⋊C4—1221no—
702C22⋊C4—1221no—
703C22⋊C4—1224no—
704C22⋊C4—1224no—
705C22⋊C4—1221no—
706C22⋊C4—1221no—
707C22⋊C4—1221no—
708C22⋊C4—2442no—
709C22⋊C4—2442no—
710C22⋊C4—2442no—
711C42—612no—
712C42—612no—
713C42—611no—
714C42—611no—
715C42—611no—
716C42—1222no—
717C42—1221no—
718C42—1221no—
719C42—2442no—
720C42—2442no—
721C42—2441no—
722C42—2441no—
723C42—2441no—
724C42—2442no—
725C42—2442no—
726C42C22×#692311yescharacteristic
727C23—21no—
728C23—21no—
729C23—611no—
730C23—1222no—
731C23—1222no—
732C23—1221no—
733C23—1221no—
734C23—2441no—
735C23—2441no—
736C23—2441no—
737C23—2441no—
738C23—2441no—
739C23—2441no—
740C23—2441no—
741C23—2441no—
742C23—2441no—
743C23—2441no—
744Q8—21no—
745Q8—21no—
746Q8—1221no—
747Q8—1221no—
748Q8—2441no—
749Q8—2441no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—612no—
754D4—1222no—
755D4—1222no—
756D4—1221no—
757D4—1221no—
758D4—1221no—
759D4—2441no—
760D4—2441no—
761D4D4×#692312yes—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—42no—
765C2×C4—611no—
766C2×C4—611no—
767C2×C4—611no—
768C2×C4—611no—
769C2×C4—611no—
770C2×C4—612no—
771C2×C4—612no—
772C2×C4—612no—
773C2×C4—611no—
774C2×C4—611no—
775C2×C4—1221no—
776C2×C4—1221no—
777C2×C4—1221no—
778C2×C4—1221no—
779C2×C4—1221no—
780C2×C4—1221no—
781C2×C4—1221no—
782C2×C4—1221no—
783C2×C4—1221no—
784C2×C4—1221no—
785C2×C4—1221no—
786C2×C4—1221no—
787C2×C4—1221no—
788C2×C4—1222no—
789C2×C4—1222no—
790C2×C4—1221no—
791C2×C4—1221no—
792C2×C4—4884no—
793C2×C4—2442no—
794C2×C4—2442no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4—2441no—
798C2×C4—2441no—
799C2×C4—2442no—
800C2×C4—2448no—
801C2×C4—2448no—
802C2×C4—2441no—
803C2×C4—2441no—
804C2×C4—2441no—
805C2×C4—2441no—
806C2×C4—2441no—
807C2×C4—2441no—
808C2×C4—2441no—
809C2×C4—2441no—
810C2×C4—2441no—
811C2×C4—2441no—
812C2×C4D4×#692311yescharacteristic
813C2×C4D4×#692311yescharacteristic
814C2×C4C23×#692311yescharacteristic
815C8—21no—
816C8—21no—
817C8—1221no—
818C8—1221no—
819C8—2441no—
820C8—2441no—
821C22—22no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—611no—
828C22—611no—
829C22—611no—
830C22—611no—
831C22—611no—
832C22—611no—
833C22—1222no—
834C22—4881no—
835C22—4881no—
836C22—4881no—
837C22—4881no—
838C22—2442no—
839C22—2442no—
840C22—2442no—
841C22—2442no—
842C22—2441no—
843C22—2441no—
844C22—2441no—
845C22—2441no—
846C22—2441no—
847C22C2×D4×#692311yescharacteristic
848C4—21no—
849C4—21no—
850C4—41no—
851C4—41no—
852C4—611no—
853C4—611no—
854C4—1222no—
855C4—1222no—
856C4—1222no—
857C4—1221no—
858C4—1221no—
859C4—4881no—
860C4—4881no—
861C4—2441no—
862C4—2442no—
863C4—2442no—
864C4—2441no—
865C4—2441no—
866C4C2×D4×#692311yescharacteristic
867C4#41×#692311yescharacteristic
868C2—42no—
869C2—81no—
870C2—611no—
871C2—611no—
872C2—611no—
873C2—611no—
874C2—4881no—
875C2—2442no—
876C2#121×#692311yescharacteristic
877C2#2146257311yescharacteristic
878C2AGL(1,ℤ/8)×#692311yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#463C4
socleC22×C61C2×C4×D4
prime radicalC2×D8×D61C22
cosocleC2×C4×D61C24
hypercenter#463#6923
hypocenterC61#21507
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
2. C2×#16840801C2semidirect
3. #124×#6923C2semidirect
4. C4×D4×#6923C2semidirect
5. #21461987C2semidirect
6. #21461932C2semidirect
7. #21461898C2semidirect
8. #21461896C2semidirect
10. #21461812C2semidirect
11. #21461689C2semidirect
12. #21461606C2semidirect
13. #21461592C2semidirect
14. #21461590C2semidirect
58. #16839980C4semidirect
59. #16839979C4semidirect
60. #16839978C4semidirect
61. #16839977C4semidirect
62. #16839976C4semidirect
63. #16839975C4semidirect
64. #16839974C4semidirect
68. C61×#463C4semidirect
126. C2×#11758190C2×C4semidirect
127. C2×#11758200C2×C4semidirect
128. C2×#11758201C2×C4semidirect
138. #14519766C2×C4semidirect
139. #14519765C2×C4semidirect
140. #14519764C2×C4semidirect
143. C4×D244C2×C4semidirect
144. D4×Dic61C2×C4semidirect
145. #14519739C2×C4semidirect
153. C4⋊#92418C2×C4semidirect
154. #14519706C2×C4semidirect
155. #14519706C2×C4semidirect
156. #14519702C2×C4semidirect
157. #14519701C2×C4semidirect
158. #14519700C2×C4semidirect
159. #14519699C2×C4semidirect
160. #14519698C2×C4semidirect
161. #14519697C2×C4semidirect
162. C2×SD16×C61C2×C4semidirect
164. #124×C61C2×C4semidirect
165. C4×D4×C61C2×C4semidirect
166. C4⋊C8×C61C2×C4semidirect
167. #103×C61C2×C4semidirect
168. #102×C61C2×C4semidirect
471. #463#6923semidirect
508. C61#21507semidirect
521. C2×SD16C2×#6923semidirect
537. #124C2×#6923semidirect
551. C4×D4C2×#6923semidirect
585. C4⋊C8C2×#6923semidirect
591. #103C2×#6923semidirect
599. #102C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168408032
C2×#168408012
#124×#69232
C4×D4×#69232
#214619872
#214619322
#214618982
#214618962
#214618142
#214618122
#214616892
#214616062
#214615922
#214615902
#463×D612
#2150761