Finite Group Databasebeta

← C2×#21460594 #30593849

Subgroups — C2×#21460594 #30593849

Order 15616.

11138 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840597C211yesmaximal, characteristic, complemented
2C2×H(5,𝔽2)×D61C211yesmaximal, characteristic, complemented
3#21460594C2132yesmaximal, direct product factor
4C2×#16840574C211yesmaximal, characteristic, complemented
5C2×#16840573C211yesmaximal, characteristic, complemented
6C2×#16840572C213yesmaximal, complemented
7C2×#16840569C213yesmaximal, complemented
8C2×#16840566C213yesmaximal, complemented
9C2×#16840565C211yesmaximal, characteristic, complemented
10C2×#16840563C213yesmaximal, complemented
11C2×#16840559C213yesmaximal, complemented
12C2×#16840558C213yesmaximal, complemented
13C22×#14519801C213yesmaximal, complemented
14C2×AGL(1,ℤ/8)×D61C213yesmaximal, complemented
15C2×#16840527C211yesmaximal, characteristic, complemented
16C2×C61×#576C211yesmaximal, characteristic, complemented
17#16840597—28no—
18#16840597C22116yescomplemented
19C2×#14519824—21no—
20C2×#14519824C2211yescharacteristic, complemented
21C2×#14519824C2213yescomplemented
22C2×#14519823—21no—
23C2×#14519823C2211yescharacteristic, complemented
24C2×#14519823C2213yescomplemented
25C2×#14519822—23no—
26C2×#14519822—23no—
27C2×#14519822C2213yescomplemented
28C2×#14519822C2213yescomplemented
29H(5,𝔽2)×D61—28no—
30H(5,𝔽2)×D61C22116yescomplemented
31C22×#11758224—23no—
32C22×#11758224C2213yescomplemented
33C2×#41×D61—21no—
34C2×#41×D61—21no—
35C2×#41×D61C2211yescharacteristic
36C2×#41×D61C2213yescomplemented
37C2×#41×D61C2213yescomplemented
38C22×D4×D61—23no—
39C22×D4×D61C2213yescomplemented
40#16840574C22116yescomplemented
41#16840573C22116yescomplemented
42#16840572C22148yescomplemented
43#16840569C22148yescomplemented
44#16840566C22148yescomplemented
45#16840565C22116yescomplemented
46#16840563C22148yescomplemented
47#16840559C22148yescomplemented
48#16840558C22148yescomplemented
49C2×#14519810C2213yescomplemented
50C2×#14519809C2211yescharacteristic, complemented
51C2×#14519809C2213yescomplemented
52C2×#14519807C2213yescomplemented
53C2×#14519806C2213yescomplemented
54C2×#14519806C2213yescomplemented
55C2×#14519805C2213yescomplemented
56C2×#14519804C2213yescomplemented
57C2×#14519804C2213yescomplemented
58C2×#14519803C2213yescomplemented
59C2×#14519803C2213yescomplemented
60C2×#14519802C2213yescomplemented
61C2×#14519801C2216yescomplemented
62C2×#14519801C2213yescomplemented
63C2×#14519801C2216yescomplemented
64C2×#14519801C2216yescomplemented
65C2×#14519801C2213yescomplemented
66C2×#14519801C22148yescomplemented
67AGL(1,ℤ/8)×D61C22148yescomplemented
68C2×#14519799C2213yescomplemented
69C2×#14519798C2216yescomplemented
70C2×#14519797C2213yescomplemented
71C2×#14519797C2213yescomplemented
72C2×#14519796C2216yescomplemented
73C22×#11758190C2213yescomplemented
74C22×#11758200C2213yescomplemented
75C2×SD16×D61C2216yescomplemented
76C22×#11758199C2213yescomplemented
77C2×D8×D61C2216yescomplemented
78#16840527C22116yescomplemented
79C2×#14519785C2213yescomplemented
80C2×#14519784C2211yescharacteristic, complemented
81C2×#14519783C2213yescomplemented
82C22×#11758189C2213yescomplemented
83C2×M16×D61C2213yescomplemented
84C2×H(5,𝔽2)×C61C2211yescharacteristic, complemented
85C2×H(5,𝔽2)×C61C2211yescharacteristic, complemented
86C61×#576C22116yescomplemented
87C2×AGL(1,ℤ/8)×C61C2213yescomplemented
88C2×AGL(1,ℤ/8)×C61C2213yescomplemented
89C2×#135×C61C2213yescomplemented
90C22×D8×C61C2213yescomplemented
91C2×#131×C61C2211yescharacteristic, complemented
92C24×D61—23no—
93#14519824—24no—
94#14519824—216no—
95#14519824—212no—
96#14519824C23124yescomplemented
97#14519824C2318yescomplemented
98#14519823—24no—
99#14519823—216no—
100#14519823—212no—
101#14519823C23124yescomplemented
102#14519823C2318yescomplemented
103#14519822—248no—
104#14519822—248no—
105#14519822—212no—
106#14519822—212no—
107#14519822C23124yescomplemented
108#14519822C23124yescomplemented
109C2×#11758226—21no—
110C2×#11758226D411yescharacteristic
111C2×#11758226C2313yes—
112C2×#11758226C2311yescharacteristic
113C2×#11758222—23no—
114C2×#11758222—23no—
115C2×#11758222—23no—
116C2×#11758222—23no—
117C2×#11758222C2313yes—
118C2×#11758222C2313yes—
119C2×#11758222C2313yescomplemented
120C2×#11758224—23no—
121C2×#11758224—26no—
122C2×#11758224—23no—
123C2×#11758224—23no—
124C2×#11758224—248no—
125C2×#11758224—23no—
126C2×#11758224—23no—
127C2×#11758224—212no—
128C2×#11758224—23no—
129C2×#11758224—23no—
130C2×#11758224D413yes—
131C2×#11758224C2313yes—
132C2×#11758224C2313yes—
133C2×#11758224C2316yescomplemented
134C2×#11758224C23124yescomplemented
135#41×D61—216no—
136#41×D61—216no—
137#41×D61—212no—
138#41×D61—212no—
139#41×D61D418yes—
140#41×D61C2318yes—
141#41×D61C23124yescomplemented
142#41×D61C23124yescomplemented
143C22×Dic122—23no—
144C22×Dic122C2313yescomplemented
145C2×Q8×D61—21no—
146C2×Q8×D61D411yescharacteristic
147C2×Q8×D61C2311yescharacteristic
148C2×Q8×D61C2313yescomplemented
149C22×D244—23no—
150C22×D244C2313yes—
151C22×C22⋊D61—23no—
152C22×C22⋊D61—26no—
153C22×C22⋊D61—26no—
154C22×C22⋊D61—23no—
155C2×D4×D61—23no—
156C2×D4×D61—23no—
157C2×D4×D61—23no—
158C2×D4×D61—26no—
159C2×D4×D61—248no—
160C2×D4×D61—23no—
161C2×D4×D61—23no—
162C2×D4×D61—23no—
163C2×D4×D61—212no—
164C2×D4×D61—23no—
165C2×D4×D61D413yes—
166C2×D4×D61C2316yes—
167C2×D4×D61C2313yes—
168C2×D4×D61C23124yescomplemented
169C2×D4×D61C2313yescomplemented
170C23×Dic61—23no—
171C22×C4×D61—23no—
172C22×C4×D61—23no—
173C22×C4×D61C2313yes—
174#14519810C23124yescomplemented
175#14519809C2318yescomplemented
176#14519809C23124yescomplemented
177#14519807C23124yescomplemented
178#14519806C23124yescomplemented
179#14519806C23124yescomplemented
180#14519805C23124yescomplemented
181#14519804C23124yescomplemented
182#14519804C23124yescomplemented
183#14519803C23124yescomplemented
184#14519803C23124yescomplemented
185#14519802C23124yescomplemented
186#14519801C23148yescomplemented
187#14519801C23124yescomplemented
188#14519801C23148yescomplemented
189#14519801C23148yescomplemented
190#14519801C23124yescomplemented
191#14519799C23124yescomplemented
192#14519798C23148yescomplemented
193#14519797C23124yescomplemented
194#14519797C23124yescomplemented
195#14519796C23148yescomplemented
196C2×Dic244C2313yescomplemented
197C2×#11758202C2311yescharacteristic, complemented
198C2×#11758202C2313yescomplemented
199C2×#11758190C2316yescomplemented
200C2×#11758190C2313yescomplemented
201C2×#11758190C2311yescharacteristic, complemented
202C2×#11758190C23124yescomplemented
203C2×#11758200C2316yescomplemented
204C2×#11758200C2313yescomplemented
205C2×#11758200C2313yescomplemented
206C2×#11758200C23124yescomplemented
207C2×#11758201C2313yescomplemented
208C2×#11758201C2311yescharacteristic, complemented
209SD16×D61C23148yescomplemented
210C2×D488C2313yescomplemented
211C2×#11758199C2313yescomplemented
212C2×#11758199C2316yescomplemented
213C2×#11758199C2313yescomplemented
214C2×#11758199C23124yescomplemented
215D8×D61C23148yescomplemented
216#14519785C23124yescomplemented
217#14519784C2318yescomplemented
218#14519783C23124yescomplemented
219C2×#11758194C2313yescomplemented
220C2×#11758189C2313yes—
221C2×#11758189C2311yescharacteristic
222C2×#11758189C23124yescomplemented
223C2×#11758189C2313yescomplemented
224C2×#11758189C2313yescomplemented
225M16×D61C23124yescomplemented
226C22×#92418C2313yescomplemented
227C2×C8×D61C2316yescomplemented
228H(5,𝔽2)×C61—24no—
229H(5,𝔽2)×C61—24no—
230H(5,𝔽2)×C61C2318yescomplemented
231H(5,𝔽2)×C61C2318yescomplemented
232C2×#41×C61—21no—
233C2×#41×C61—21no—
234C2×#41×C61C2313yes—
235C2×#41×C61C2311yescharacteristic
236C2×#41×C61C2313yescomplemented
237C22×D4×C61—23no—
238C22×D4×C61—23no—
239C22×D4×C61C2313yes—
240C22×D4×C61C2313yescomplemented
241AGL(1,ℤ/8)×C61C23124yescomplemented
242AGL(1,ℤ/8)×C61C23124yescomplemented
243#135×C61C23124yescomplemented
244C2×Q16×C61C2311yescharacteristic, complemented
245C2×SD16×C61C2313yescomplemented
246C2×SD16×C61C2313yescomplemented
247C2×D8×C61C2313yescomplemented
248C2×D8×C61C2316yescomplemented
249C2×D8×C61C23124yescomplemented
250#131×C61C2318yescomplemented
251C2×M16×C61C2313yescomplemented
252C22×C8×C61C2313yescomplemented
253C24×C61—23no—
254C24×C61—23no—
255C23×D61—23no—
256C23×D61—23no—
257C23×D61—23no—
258C23×D61—224no—
259C23×D61—26no—
260C23×D61—812no—
261C23×D61C2×D413yes—
262#41×C61—28no—
263#41×C61—28no—
264#41×C61—26no—
265#41×C61—26no—
266#41×C61C2×D414yes—
267#41×C61C24112yes—
268#41×C61C2414yes—
269#41×C61C24112yescomplemented
270C2×Q8×C61C2×D411yescharacteristic
271C2×Q8×C61C2411yescharacteristic
272C2×Q8×C61C2411yescharacteristic
273C2×D4×C61—23no—
274C2×D4×C61—23no—
275C2×D4×C61—224no—
276C2×D4×C61—224no—
277C2×D4×C61—23no—
278C2×D4×C61—26no—
279C2×D4×C61—23no—
280C2×D4×C61—26no—
281C2×D4×C61C2×D413yes—
282C2×D4×C61C2413yes—
283C2×D4×C61C24112yes—
284C2×D4×C61C2413yes—
285C2×D4×C61C24112yescomplemented
286C22×C4×C61—23no—
287C22×C4×C61—23no—
288C22×C4×C61C2413yes—
289C2×C22⋊D61—23no—
290C2×C22⋊D61—23no—
291C2×C22⋊D61—23no—
292C2×C22⋊D61—23no—
293C2×C22⋊D61—26no—
294C2×C22⋊D61—224no—
295C2×C22⋊D61—248no—
296C2×C22⋊D61—248no—
297C2×C22⋊D61—26no—
298C2×C22⋊D61—23no—
299C2×C22⋊D61—224no—
300C2×C22⋊D61—23no—
301C2×C22⋊D61C2×D416yes—
302C22×Dic61—23no—
303C22×Dic61—23no—
304C22×Dic61—23no—
305C22×Dic61—26no—
306C22×Dic61—224no—
307C22×Dic61C2×D413yes—
308#11758226—28no—
309#11758226—22no—
310#11758226—26no—
311#11758226C2×D418yes—
312#11758226C2414yes—
313#11758226C24112yes—
314Q8×D61—28no—
315Q8×D61—22no—
316Q8×D61—26no—
317Q8×D61C2×D418yes—
318Q8×D61C2414yes—
319Q8×D61C24112yescomplemented
320#11758224—224no—
321#11758224—248no—
322#11758224—224no—
323#11758224—224no—
324#11758224—26no—
325#11758224—224no—
326#11758224—26no—
327#11758224—212no—
328#11758224—224no—
329#11758224—224no—
330#11758224—224no—
331#11758224C2×D4124yes—
332#11758224C24112yes—
333#11758224C24112yes—
334#11758224C24124yescomplemented
335D4×D61—224no—
336D4×D61—224no—
337D4×D61—224no—
338D4×D61—248no—
339D4×D61—224no—
340D4×D61—224no—
341D4×D61—26no—
342D4×D61—224no—
343D4×D61—212no—
344D4×D61—224no—
345D4×D61—26no—
346D4×D61C2×D4124yes—
347D4×D61C24112yes—
348D4×D61C24124yes—
349D4×D61C24112yescomplemented
350#11758222—26no—
351#11758222—26no—
352#11758222—224no—
353#11758222—224no—
354#11758222—224no—
355#11758222—224no—
356#11758222C2×D4112yes—
357#11758222C24112yes—
358#11758222C24112yes—
359#11758222C24112yescomplemented
360C2×D244—23no—
361C2×D244—21no—
362C2×D244—23no—
363C2×D244—26no—
364C2×D244—224no—
365C2×D244C2×D413yes—
366C2×D244C2413yes—
367C2×D244C2411yescharacteristic
368C2×D244C24112yes—
369C2×C4×D61—21no—
370C2×C4×D61—23no—
371C2×C4×D61—23no—
372C2×C4×D61—23no—
373C2×C4×D61—21no—
374C2×C4×D61—23no—
375C2×C4×D61—224no—
376C2×C4×D61—224no—
377C2×C4×D61C2×D413yes—
378C2×C4×D61C2×D413yes—
379C2×C4×D61C2×D4112yes—
380C2×C4×D61C2411yescharacteristic
381C2×C4×D61C2413yes—
382C2×C4×D61C24112yes—
383C2×Dic122—23no—
384C2×Dic122—26no—
385C2×Dic122—21no—
386C2×Dic122—23no—
387C2×Dic122—224no—
388C2×Dic122C2×D413yes—
389C2×Dic122C2411yescharacteristic
390C2×Dic122C2413yes—
391C2×Dic122C24112yescomplemented
392Q16×C61C2414yescomplemented
393SD16×C61C24112yescomplemented
394SD16×C61C24112yescomplemented
395D8×C61C24112yescomplemented
396D8×C61C24124yescomplemented
397M16×C61C24112yescomplemented
398C2×C8×C61C2411yescharacteristic
399C2×C8×C61C2413yes—
400C2×C8×C61C24112yescomplemented
401#11758202C2414yescomplemented
402#11758202C24112yescomplemented
403#11758201C24112yescomplemented
404#11758201C2414yescomplemented
405#11758200C24124yescomplemented
406#11758200C24112yescomplemented
407#11758200C24112yescomplemented
408#11758199C24112yescomplemented
409#11758199C24124yescomplemented
410#11758199C24112yescomplemented
411#11758194C24112yescomplemented
412C2×#92418C2413yes—
413C2×#92418C2411yescharacteristic
414C2×#92418C24112yescomplemented
415Dic244C24112yescomplemented
416D488C24112yescomplemented
417#11758190C24112yescomplemented
418#11758190C2414yescomplemented
419#11758190C24124yescomplemented
420#11758189C2414yes—
421#11758189C24112yes—
422#11758189C24112yescomplemented
423#11758189C24112yescomplemented
424C8×D61C24124yescomplemented
425C23×C61—23no—
426C23×C61—23no—
427C23×C61—212no—
428C23×C61—212no—
429C23×C61—86no—
430C23×C61—86no—
431C23×C61C22×D413yes—
432C22×D61—21no—
433C22×D61—23no—
434C22×D61—212no—
435C22×D61—212no—
436C22×D61—212no—
437C22×D61—224no—
438C22×D61—46no—
439C22×D61—412no—
440C22×D61—86no—
441C22×D61—812no—
442C22×D61—848no—
443C22×D61—86no—
444C22×D61C22×D411yescharacteristic
445C22×D61C22×D413yes—
446C22×D61C22×D4112yes—
447Q8×C61—21no—
448Q8×C61—21no—
449Q8×C61C22×D414yes—
450Q8×C61C2512yes—
451Q8×C61C2512yes—
452D4×C61—212no—
453D4×C61—212no—
454D4×C61—23no—
455D4×C61—212no—
456D4×C61—23no—
457D4×C61—212no—
458D4×C61C22×D4112yes—
459D4×C61C2516yes—
460D4×C61C2516yes—
461C2×C4×C61—21no—
462C2×C4×C61—21no—
463C2×C4×C61—212no—
464C2×C4×C61—212no—
465C2×C4×C61C22×D413yes—
466C2×C4×C61C22×D416yes—
467C2×C4×C61C2511yescharacteristic
468C2×C4×C61C2516yes—
469C22⋊D61—212no—
470C22⋊D61—212no—
471C22⋊D61—212no—
472C22⋊D61—212no—
473C22⋊D61—224no—
474C22⋊D61—224no—
475C22⋊D61—212no—
476C22⋊D61—212no—
477C22⋊D61C22×D4124yes—
478C2×Dic61—23no—
479C2×Dic61—21no—
480C2×Dic61—212no—
481C2×Dic61—224no—
482C2×Dic61—212no—
483C2×Dic61—212no—
484C2×Dic61C22×D413yes—
485C2×Dic61C22×D411yescharacteristic
486C2×Dic61C22×D4112yes—
487D244—212no—
488D244—24no—
489D244—23no—
490D244—212no—
491D244—21no—
492D244C22×D4112yes—
493D244C2516yes—
494D244C2512yes—
495C4×D61—24no—
496C4×D61—212no—
497C4×D61—212no—
498C4×D61—212no—
499C4×D61—24no—
500C4×D61—212no—
501C4×D61C22×D4112yes—
502C4×D61C22×D4112yes—
503C4×D61C22×D412yes—
504C4×D61C22×D416yes—
505C4×D61C2516yes—
506C4×D61C2512yes—
507Dic122—23no—
508Dic122—212no—
509Dic122—21no—
510Dic122—212no—
511Dic122—24no—
512Dic122C22×D4112yes—
513Dic122C2516yes—
514Dic122C2512yes—
515C8×C61C2516yes—
516C8×C61C2512yes—
517#92418C2516yes—
518#92418C2512yes—
519C2×#3585—611nomaximal, Sylow
520C22×C61—26no—
521C22×C61—26no—
522C22×C61—26no—
523C22×C61—46no—
524C22×C61—46no—
525C22×C61—812no—
526C22×C61—812no—
527C22×C61C23×D416yes—
528C22×C61C23×D411yescharacteristic
529C2×D61—22no—
530C2×D61—26no—
531C2×D61—22no—
532C2×D61—26no—
533C2×D61—412no—
534C2×D61—424no—
535C2×D61—46no—
536C2×D61—42no—
537C2×D61—812no—
538C2×D61—824no—
539C2×D61—812no—
540C2×D61C23×D412yes—
541C2×D61C23×D416yes—
542C4×C61—22no—
543C4×C61—22no—
544C4×C61C23×D411yescharacteristic
545C4×C61C23×D416yes—
546C4×C61C2611yescharacteristic
547Dic61—26no—
548Dic61—22no—
549Dic61C23×D416yes—
550Dic61C23×D412yes—
551C2×#585—611no—
552C22×H(5,𝔽2)—611no—
553#3585—6132no—
554C2×#577—611no—
555C2×#577—613no—
556C2×#577—613no—
557C2×#577—611no—
558C2×#576—611no—
559C2×#576—613no—
560C2×#576—613no—
561C2×#576D6111yescharacteristic, complemented
562C2×#575—613no—
563C2×#575—613no—
564C22×AGL(1,ℤ/8)—613no—
565C22×AGL(1,ℤ/8)—613no—
566C2×#568—611no—
567C2×C61—26no—
568C2×C61—46no—
569C2×C61—46no—
570C2×C61#358512yescomplemented
571C2×C61C24×D411yescharacteristic
572D61—22no—
573D61—26no—
574D61—46no—
575D61—42no—
576#585—6116no—
577#585—1228no—
578C2×2−1+4—611no—
579C2×2−1+4—613no—
580C2×2−1+4—1221no—
581C2×H(5,𝔽2)—6116no—
582C2×H(5,𝔽2)—613no—
583C2×H(5,𝔽2)—611no—
584C2×H(5,𝔽2)—613no—
585C2×H(5,𝔽2)—613no—
586C2×H(5,𝔽2)—1223no—
587C2×H(5,𝔽2)—1223no—
588C2×H(5,𝔽2)—1221no—
589C2×H(5,𝔽2)—1228no—
590C2×H(5,𝔽2)C2×D6111yescharacteristic, complemented
591C2×H(5,𝔽2)C2×D6111yescharacteristic, complemented
592C22×#41—611no—
593C22×#41—613no—
594C22×#41—613no—
595C22×#41—613no—
596C22×#41—1223no—
597C22×#41—1221no—
598C22×#41—1221no—
599C23×D4—613no—
600C23×D4—1223no—
601#577—6116no—
602#577—6148no—
603#577—6148no—
604#577—6116no—
605#576—6116no—
606#576—6148no—
607#576—6148no—
608#576C2×D61116yescomplemented
609#575—6148no—
610#575—6148no—
611C2×#137—613no—
612C2×#137—611no—
613C2×#137—613no—
614C2×#137—613no—
615C2×#137—613no—
616C2×#137—613no—
617C2×AGL(1,ℤ/8)—613no—
618C2×AGL(1,ℤ/8)—613no—
619C2×AGL(1,ℤ/8)—613no—
620C2×AGL(1,ℤ/8)—6148no—
621C2×AGL(1,ℤ/8)—613no—
622C2×AGL(1,ℤ/8)—613no—
623C2×AGL(1,ℤ/8)—6148no—
624C2×AGL(1,ℤ/8)—616no—
625C2×AGL(1,ℤ/8)—613no—
626C2×AGL(1,ℤ/8)—616no—
627C2×AGL(1,ℤ/8)—616no—
628C2×AGL(1,ℤ/8)—613no—
629C2×AGL(1,ℤ/8)—613no—
630C2×AGL(1,ℤ/8)C2×D6113yescomplemented
631C2×AGL(1,ℤ/8)C2×D6113yescomplemented
632C2×#135—613no—
633C2×#135—613no—
634C2×#135—616no—
635C2×#135—616no—
636C2×#135—613no—
637C2×#135C2×D6113yescomplemented
638C22×SD16—613no—
639C22×SD16—616no—
640C22×SD16—613no—
641C22×D8—613no—
642C22×D8—616no—
643C22×D8C2×D6113yescomplemented
644#568—6116no—
645C2×#131—611no—
646C2×#131—613no—
647C2×#131—613no—
648C2×#131C2×D6111yescharacteristic, complemented
649C22×M16—613no—
650C22×M16—613no—
651C61C2×#358511yescharacteristic, complemented, Sylow
652C25—1223no—
6532−1+4—618no—
6542−1+4—6124no—
6552−1+4—12216no—
6562−1+4—12212no—
6572−1+4—1224no—
658H(5,𝔽2)—24no—
659H(5,𝔽2)—24no—
660H(5,𝔽2)—6124no—
661H(5,𝔽2)—618no—
662H(5,𝔽2)—6124no—
663H(5,𝔽2)—6124no—
664H(5,𝔽2)—12248no—
665H(5,𝔽2)—12248no—
666H(5,𝔽2)—12212no—
667H(5,𝔽2)—12212no—
668H(5,𝔽2)—12216no—
669H(5,𝔽2)—12212no—
670H(5,𝔽2)—1224no—
671H(5,𝔽2)C22×D6118yescomplemented
672H(5,𝔽2)C22×D6118yescomplemented
673C2×#41—21no—
674C2×#41—21no—
675C2×#41—618no—
676C2×#41—618no—
677C2×#41—611no—
678C2×#41—613no—
679C2×#41—613no—
680C2×#41—6124no—
681C2×#41—6124no—
682C2×#41—613no—
683C2×#41—611no—
684C2×#41—613no—
685C2×#41—613no—
686C2×#41—616no—
687C2×#41—6124no—
688C2×#41—613no—
689C2×#41—613no—
690C2×#41—1223no—
691C2×#41—1223no—
692C2×#41—1223no—
693C2×#41—1223no—
694C2×#41—1223no—
695C2×#41—1223no—
696C2×#41—1223no—
697C2×#41—1223no—
698C2×#41—12212no—
699C2×#41—12212no—
700C2×#41—12212no—
701C2×#41—1226no—
702C2×#41—1223no—
703C2×#41—1223no—
704C2×#41—12248no—
705C2×#41—12216no—
706C2×#41—12216no—
707C2×#41—1221no—
708C2×#41—1223no—
709C2×#41C22×D6113yes—
710C2×#41C22×D6111yescharacteristic
711C2×#41C22×D6113yescomplemented
712C22×Q8—611no—
713C22×Q8—611no—
714C22×Q8—613no—
715C22×Q8—613no—
716C22×Q8—1223no—
717C22×Q8—1221no—
718C22×D4—23no—
719C22×D4—23no—
720C22×D4—613no—
721C22×D4—616no—
722C22×D4—613no—
723C22×D4—613no—
724C22×D4—6124no—
725C22×D4—613no—
726C22×D4—1223no—
727C22×D4—1223no—
728C22×D4—1223no—
729C22×D4—12212no—
730C22×D4—1223no—
731C22×D4—1226no—
732C22×D4—12248no—
733C22×D4—1223no—
734C22×D4—1223no—
735C22×D4—1223no—
736C22×D4—1223no—
737C22×D4—1226no—
738C22×D4—1226no—
739C22×D4—1223no—
740C22×D4—1223no—
741C22×D4C22×D6113yes—
742C22×D4C22×D6113yescomplemented
743C23×C4—613no—
744C23×C4—1223no—
745C23×C4—1223no—
746C23×C4—1223no—
747#137—6124no—
748#137—618no—
749#137—6124no—
750#137—6124no—
751#137—6124no—
752#137—6124no—
753AGL(1,ℤ/8)—6124no—
754AGL(1,ℤ/8)—6124no—
755AGL(1,ℤ/8)—6124no—
756AGL(1,ℤ/8)—6124no—
757AGL(1,ℤ/8)—6124no—
758AGL(1,ℤ/8)—6148no—
759AGL(1,ℤ/8)—6124no—
760AGL(1,ℤ/8)—6148no—
761AGL(1,ℤ/8)—6148no—
762AGL(1,ℤ/8)—6124no—
763AGL(1,ℤ/8)—6124no—
764AGL(1,ℤ/8)C22×D61124yescomplemented
765AGL(1,ℤ/8)C22×D61124yescomplemented
766#135—6124no—
767#135—6124no—
768#135—6148no—
769#135—6148no—
770#135—6124no—
771#135C22×D61124yescomplemented
772C2×Q16—613no—
773C2×Q16—611no—
774C2×Q16—613no—
775C2×Q16C22×D6111yescharacteristic, complemented
776C2×SD16—613no—
777C2×SD16—611no—
778C2×SD16—613no—
779C2×SD16—616no—
780C2×SD16—6124no—
781C2×SD16—613no—
782C2×SD16—6148no—
783C2×SD16—616no—
784C2×SD16—613no—
785C2×SD16—611no—
786C2×SD16—6124no—
787C2×SD16C22×D6113yescomplemented
788C2×SD16C22×D6113yescomplemented
789C2×D8—613no—
790C2×D8—613no—
791C2×D8—616no—
792C2×D8—6124no—
793C2×D8—6148no—
794C2×D8—613no—
795C2×D8C22×D6116yescomplemented
796C2×D8C22×D6113yescomplemented
797C2×D8C22×D61124yescomplemented
798#131—618no—
799#131—6124no—
800#131—6124no—
801#131C22×D6118yescomplemented
802C2×M16—613no—
803C2×M16—6124no—
804C2×M16—613no—
805C2×M16—611no—
806C2×M16—613no—
807C2×M16—613no—
808C2×M16—6124no—
809C2×M16C22×D6113yescomplemented
810C22×C8—613no—
811C22×C8—616no—
812C22×C8C22×D6113yescomplemented
813C24—23no—
814C24—23no—
815C24—613no—
816C24—1223no—
817C24—1226no—
818C24—12224no—
819C24—1223no—
820C24—1223no—
821C24—48812no—
822#41—28no—
823#41—28no—
824#41—26no—
825#41—26no—
826#41—618no—
827#41—6124no—
828#41—6112no—
829#41—6112no—
830#41—6112no—
831#41—614no—
832#41—6124no—
833#41—6112no—
834#41—6112no—
835#41—6112no—
836#41—6112no—
837#41—12224no—
838#41—12224no—
839#41—12224no—
840#41—12224no—
841#41—12224no—
842#41—1226no—
843#41—12224no—
844#41—12224no—
845#41—1226no—
846#41—12224no—
847#41—12212no—
848#41—1222no—
849#41—1226no—
850#41—12248no—
851#41—12224no—
852#41—12224no—
853#41—1228no—
854#41—12224no—
855#41—1226no—
856#41—1226no—
857#41D4×D6114yes—
858#41C23×D61112yes—
859#41C23×D6114yes—
860#41C23×D61112yescomplemented
861C2×Q8—618no—
862C2×Q8—613no—
863C2×Q8—6112no—
864C2×Q8—614no—
865C2×Q8—613no—
866C2×Q8—611no—
867C2×Q8—6112no—
868C2×Q8—1223no—
869C2×Q8—1221no—
870C2×Q8—12224no—
871C2×Q8—1222no—
872C2×Q8—1226no—
873C2×Q8—1228no—
874C2×Q8—1223no—
875C2×Q8—1226no—
876C2×Q8D4×D6111yescharacteristic
877C2×Q8C23×D6111yescharacteristic
878C2×Q8C23×D6111yescharacteristic
879C2×D4—23no—
880C2×D4—23no—
881C2×D4—224no—
882C2×D4—224no—
883C2×D4—23no—
884C2×D4—23no—
885C2×D4—26no—
886C2×D4—26no—
887C2×D4—616no—
888C2×D4—6124no—
889C2×D4—6112no—
890C2×D4—6124no—
891C2×D4—6112no—
892C2×D4—613no—
893C2×D4—611no—
894C2×D4—613no—
895C2×D4—6112no—
896C2×D4—12224no—
897C2×D4—1223no—
898C2×D4—1221no—
899C2×D4—1226no—
900C2×D4—12224no—
901C2×D4—12224no—
902C2×D4—12212no—
903C2×D4—1226no—
904C2×D4—1223no—
905C2×D4—1226no—
906C2×D4—1223no—
907C2×D4—12224no—
908C2×D4—12248no—
909C2×D4—12224no—
910C2×D4—12224no—
911C2×D4—12224no—
912C2×D4—12224no—
913C2×D4—12248no—
914C2×D4—12248no—
915C2×D4—1223no—
916C2×D4—1223no—
917C2×D4—1226no—
918C2×D4—12224no—
919C2×D4—1223no—
920C2×D4—1223no—
921C2×D4—12224no—
922C2×D4—1223no—
923C2×D4—1226no—
924C2×D4D4×D6113yes—
925C2×D4C23×D6113yes—
926C2×D4C23×D6113yes—
927C2×D4C23×D61112yes—
928C2×D4C23×D61112yescomplemented
929C22×C4—23no—
930C22×C4—23no—
931C22×C4—613no—
932C22×C4—613no—
933C22×C4—613no—
934C22×C4—6112no—
935C22×C4—613no—
936C22×C4—611no—
937C22×C4—6112no—
938C22×C4—1221no—
939C22×C4—1223no—
940C22×C4—12224no—
941C22×C4—12224no—
942C22×C4—1221no—
943C22×C4—1223no—
944C22×C4—1223no—
945C22×C4—1223no—
946C22×C4—1226no—
947C22×C4—12224no—
948C22×C4—1223no—
949C22×C4—1223no—
950C22×C4—1223no—
951C22×C4C23×D6113yes—
952Q16—6112no—
953Q16—614no—
954Q16—6112no—
955Q16C23×D6114yescomplemented
956SD16—6112no—
957SD16—614no—
958SD16—6124no—
959SD16—6112no—
960SD16—6112no—
961SD16—6124no—
962SD16—6112no—
963SD16—614no—
964SD16C23×D61112yescomplemented
965SD16C23×D61112yescomplemented
966D8—6112no—
967D8—6124no—
968D8—6112no—
969D8—6112no—
970D8C23×D61124yescomplemented
971D8C23×D61112yescomplemented
972M16—6112no—
973M16—6112no—
974M16—614no—
975M16—6112no—
976M16—6112no—
977M16C23×D61112yescomplemented
978C2×C8—613no—
979C2×C8—611no—
980C2×C8—6112no—
981C2×C8—6124no—
982C2×C8C23×D6113yes—
983C2×C8C23×D6111yescharacteristic
984C2×C8C23×D61112yescomplemented
985C23—23no—
986C23—23no—
987C23—212no—
988C23—212no—
989C23—86no—
990C23—86no—
991C23—611no—
992C23—613no—
993C23—6112no—
994C23—12212no—
995C23—12224no—
996C23—12212no—
997C23—12212no—
998C23—1221no—
999C23—1223no—
1000C23—4886no—
1001C23—4886no—
1002C23—48812no—
1003C23—48848no—
1004C23—2446no—
1005C23—24412no—
1006C23C2×D4×D6113yes—
1007Q8—21no—
1008Q8—21no—
1009Q8—6112no—
1010Q8—616no—
1011Q8—612no—
1012Q8—12212no—
1013Q8—1224no—
1014Q8—12212no—
1015Q8—1223no—
1016Q8—1221no—
1017Q8C2×D4×D6114yes—
1018Q8C24×D6112yes—
1019Q8C24×D6112yes—
1020D4—212no—
1021D4—212no—
1022D4—212no—
1023D4—23no—
1024D4—23no—
1025D4—212no—
1026D4—6124no—
1027D4—6112no—
1028D4—612no—
1029D4—616no—
1030D4—12212no—
1031D4—1224no—
1032D4—12212no—
1033D4—12224no—
1034D4—12212no—
1035D4—12212no—
1036D4—12212no—
1037D4—12224no—
1038D4—12212no—
1039D4—12212no—
1040D4—12212no—
1041D4—1223no—
1042D4—1221no—
1043D4C2×D4×D61112yes—
1044D4C24×D6116yes—
1045D4C24×D6116yes—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—212no—
1049C2×C4—212no—
1050C2×C4—6112no—
1051C2×C4—611no—
1052C2×C4—613no—
1053C2×C4—612no—
1054C2×C4—6112no—
1055C2×C4—6112no—
1056C2×C4—616no—
1057C2×C4—616no—
1058C2×C4—612no—
1059C2×C4—1224no—
1060C2×C4—12212no—
1061C2×C4—1224no—
1062C2×C4—12212no—
1063C2×C4—12212no—
1064C2×C4—12212no—
1065C2×C4—12224no—
1066C2×C4—12212no—
1067C2×C4—1221no—
1068C2×C4—1223no—
1069C2×C4—12212no—
1070C2×C4—12212no—
1071C2×C4C2×D4×D6116yes—
1072C2×C4C2×D4×D6113yes—
1073C2×C4C24×D6116yes—
1074C2×C4C24×D6111yescharacteristic
1075C8—616no—
1076C8—612no—
1077C8C24×D6116yes—
1078C8C24×D6112yes—
1079C22—26no—
1080C22—26no—
1081C22—26no—
1082C22—46no—
1083C22—46no—
1084C22—812no—
1085C22—812no—
1086C22—612no—
1087C22—616no—
1088C22—1226no—
1089C22—1222no—
1090C22—1222no—
1091C22—1226no—
1092C22—48812no—
1093C22—48812no—
1094C22—48824no—
1095C22—24412no—
1096C22—24424no—
1097C22—2442no—
1098C22—2446no—
1099C22C22×D4×D6116yes—
1100C22C22×D4×D6111yescharacteristic
1101C4—22no—
1102C4—22no—
1103C4—612no—
1104C4—616no—
1105C4—1222no—
1106C4—1226no—
1107C4C22×D4×D6116yes—
1108C4C22×D4×D6111yescharacteristic
1109C4C25×D6111yescharacteristic
1110C2—26no—
1111C2—46no—
1112C2—46no—
1113C2—1226no—
1114C2—1222no—
1115C2—2446no—
1116C2—2442no—
1117C2#2146059412yesdirect product factor
1118C2C23×D4×D6111yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC4×C61C26
FrattiniC4C25×D61
FittingC2×C61×#576C2
socleC22×C61C23×D4
hypercenterC2×#576D61
hypocenterC61C2×#3585
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#576

Complements

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

NH ≅ G/Ntype
1. C2×#16840597C2semidirect
2. C2×H(5,𝔽2)×D61C2semidirect
3. #21460594C2direct (N × H)
4. C2×#16840574C2semidirect
5. C2×#16840573C2semidirect
6. C2×#16840572C2semidirect
7. C2×#16840569C2semidirect
8. C2×#16840566C2semidirect
9. C2×#16840565C2semidirect
10. C2×#16840563C2semidirect
11. C2×#16840559C2semidirect
12. C2×#16840558C2semidirect
13. C22×#14519801C2semidirect
14. C2×AGL(1,ℤ/8)×D61C2semidirect
15. C2×#16840527C2semidirect
16. C2×C61×#576C2semidirect
18. #16840597C22semidirect
20. C2×#14519824C22semidirect
21. C2×#14519824C22semidirect
23. C2×#14519823C22semidirect
24. C2×#14519823C22semidirect
27. C2×#14519822C22semidirect
28. C2×#14519822C22semidirect
30. H(5,𝔽2)×D61C22semidirect
32. C22×#11758224C22semidirect
36. C2×#41×D61C22semidirect
37. C2×#41×D61C22semidirect
39. C22×D4×D61C22semidirect
40. #16840574C22semidirect
41. #16840573C22semidirect
42. #16840572C22semidirect
43. #16840569C22semidirect
44. #16840566C22semidirect
45. #16840565C22semidirect
46. #16840563C22semidirect
47. #16840559C22semidirect
48. #16840558C22semidirect
49. C2×#14519810C22semidirect
50. C2×#14519809C22semidirect
51. C2×#14519809C22semidirect
52. C2×#14519807C22semidirect
53. C2×#14519806C22semidirect
54. C2×#14519806C22semidirect
55. C2×#14519805C22semidirect
56. C2×#14519804C22semidirect
57. C2×#14519804C22semidirect
58. C2×#14519803C22semidirect
59. C2×#14519803C22semidirect
60. C2×#14519802C22semidirect
61. C2×#14519801C22semidirect
62. C2×#14519801C22semidirect
63. C2×#14519801C22semidirect
64. C2×#14519801C22semidirect
65. C2×#14519801C22semidirect
66. C2×#14519801C22semidirect
67. AGL(1,ℤ/8)×D61C22semidirect
68. C2×#14519799C22semidirect
69. C2×#14519798C22semidirect
70. C2×#14519797C22semidirect
71. C2×#14519797C22semidirect
72. C2×#14519796C22semidirect
73. C22×#11758190C22semidirect
74. C22×#11758200C22semidirect
75. C2×SD16×D61C22semidirect
76. C22×#11758199C22semidirect
77. C2×D8×D61C22semidirect
78. #16840527C22semidirect
79. C2×#14519785C22semidirect
80. C2×#14519784C22semidirect
81. C2×#14519783C22semidirect
82. C22×#11758189C22semidirect
83. C2×M16×D61C22semidirect
84. C2×H(5,𝔽2)×C61C22semidirect
85. C2×H(5,𝔽2)×C61C22semidirect
86. C61×#576C22semidirect
87. C2×AGL(1,ℤ/8)×C61C22semidirect
88. C2×AGL(1,ℤ/8)×C61C22semidirect
89. C2×#135×C61C22semidirect
90. C22×D8×C61C22semidirect
91. C2×#131×C61C22semidirect
96. #14519824C23semidirect
97. #14519824C23semidirect
101. #14519823C23semidirect
102. #14519823C23semidirect
107. #14519822C23semidirect
108. #14519822C23semidirect
119. C2×#11758222C23semidirect
133. C2×#11758224C23semidirect
134. C2×#11758224C23semidirect
141. #41×D61C23semidirect
142. #41×D61C23semidirect
144. C22×Dic122C23semidirect
148. C2×Q8×D61C23semidirect
168. C2×D4×D61C23semidirect
169. C2×D4×D61C23semidirect
174. #14519810C23semidirect
175. #14519809C23semidirect
176. #14519809C23semidirect
177. #14519807C23semidirect
178. #14519806C23semidirect
179. #14519806C23semidirect
180. #14519805C23semidirect
181. #14519804C23semidirect
182. #14519804C23semidirect
183. #14519803C23semidirect
184. #14519803C23semidirect
185. #14519802C23semidirect
186. #14519801C23semidirect
187. #14519801C23semidirect
188. #14519801C23semidirect
189. #14519801C23semidirect
190. #14519801C23semidirect
191. #14519799C23semidirect
192. #14519798C23semidirect
193. #14519797C23semidirect
194. #14519797C23semidirect
195. #14519796C23semidirect
196. C2×Dic244C23semidirect
197. C2×#11758202C23semidirect
198. C2×#11758202C23semidirect
199. C2×#11758190C23semidirect
200. C2×#11758190C23semidirect
201. C2×#11758190C23semidirect
202. C2×#11758190C23semidirect
203. C2×#11758200C23semidirect
204. C2×#11758200C23semidirect
205. C2×#11758200C23semidirect
206. C2×#11758200C23semidirect
207. C2×#11758201C23semidirect
208. C2×#11758201C23semidirect
209. SD16×D61C23semidirect
210. C2×D488C23semidirect
211. C2×#11758199C23semidirect
212. C2×#11758199C23semidirect
213. C2×#11758199C23semidirect
214. C2×#11758199C23semidirect
215. D8×D61C23semidirect
216. #14519785C23semidirect
217. #14519784C23semidirect
218. #14519783C23semidirect
219. C2×#11758194C23semidirect
222. C2×#11758189C23semidirect
223. C2×#11758189C23semidirect
224. C2×#11758189C23semidirect
225. M16×D61C23semidirect
226. C22×#92418C23semidirect
227. C2×C8×D61C23semidirect
230. H(5,𝔽2)×C61C23semidirect
231. H(5,𝔽2)×C61C23semidirect
236. C2×#41×C61C23semidirect
240. C22×D4×C61C23semidirect
241. AGL(1,ℤ/8)×C61C23semidirect
242. AGL(1,ℤ/8)×C61C23semidirect
243. #135×C61C23semidirect
244. C2×Q16×C61C23semidirect
245. C2×SD16×C61C23semidirect
246. C2×SD16×C61C23semidirect
247. C2×D8×C61C23semidirect
248. C2×D8×C61C23semidirect
249. C2×D8×C61C23semidirect
250. #131×C61C23semidirect
251. C2×M16×C61C23semidirect
252. C22×C8×C61C23semidirect
269. #41×C61C24semidirect
285. C2×D4×C61C24semidirect
319. Q8×D61C24semidirect
334. #11758224C24semidirect
349. D4×D61C24semidirect
359. #11758222C24semidirect
391. C2×Dic122C24semidirect
392. Q16×C61C24semidirect
393. SD16×C61C24semidirect
394. SD16×C61C24semidirect
395. D8×C61C24semidirect
396. D8×C61C24semidirect
397. M16×C61C24semidirect
400. C2×C8×C61C24semidirect
401. #11758202C24semidirect
402. #11758202C24semidirect
403. #11758201C24semidirect
404. #11758201C24semidirect
405. #11758200C24semidirect
406. #11758200C24semidirect
407. #11758200C24semidirect
408. #11758199C24semidirect
409. #11758199C24semidirect
410. #11758199C24semidirect
411. #11758194C24semidirect
414. C2×#92418C24semidirect
415. Dic244C24semidirect
416. D488C24semidirect
417. #11758190C24semidirect
418. #11758190C24semidirect
419. #11758190C24semidirect
422. #11758189C24semidirect
423. #11758189C24semidirect
424. C8×D61C24semidirect
561. C2×#576D61semidirect
570. C2×C61#3585semidirect
590. C2×H(5,𝔽2)C2×D61semidirect
591. C2×H(5,𝔽2)C2×D61semidirect
608. #576C2×D61semidirect
630. C2×AGL(1,ℤ/8)C2×D61semidirect
631. C2×AGL(1,ℤ/8)C2×D61semidirect
637. C2×#135C2×D61semidirect
643. C22×D8C2×D61semidirect
648. C2×#131C2×D61semidirect
651. C61C2×#3585semidirect
671. H(5,𝔽2)C22×D61semidirect
672. H(5,𝔽2)C22×D61semidirect
711. C2×#41C22×D61semidirect
742. C22×D4C22×D61semidirect
764. AGL(1,ℤ/8)C22×D61semidirect
765. AGL(1,ℤ/8)C22×D61semidirect
771. #135C22×D61semidirect
775. C2×Q16C22×D61semidirect
787. C2×SD16C22×D61semidirect
788. C2×SD16C22×D61semidirect
795. C2×D8C22×D61semidirect
796. C2×D8C22×D61semidirect
797. C2×D8C22×D61semidirect
801. #131C22×D61semidirect
809. C2×M16C22×D61semidirect
812. C22×C8C22×D61semidirect
860. #41C23×D61semidirect
928. C2×D4C23×D61semidirect
955. Q16C23×D61semidirect
964. SD16C23×D61semidirect
965. SD16C23×D61semidirect
970. D8C23×D61semidirect
971. D8C23×D61semidirect
977. M16C23×D61semidirect
984. C2×C8C23×D61semidirect
1117. C2#21460594direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168405972
C2×H(5,𝔽2)×D612
#214605942
C2×#168405742
C2×#168405732
C2×#168405722
C2×#168405692
C2×#168405662
C2×#168405652
C2×#168405632
C2×#168405592
C2×#168405582
C22×#145198012
C2×AGL(1,ℤ/8)×D612
C2×#168405272
C2×C61×#5762
C2×#358561