Finite Group Databasebeta

← C2×#21460604 #30593860

Subgroups — C2×#21460604 #30593860

Order 15616.

10794 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840599C211yesmaximal, characteristic, complemented
2C2×2−1+4×D61C211yesmaximal, characteristic, complemented
3#21460604C2132yesmaximal, direct product factor
4C2×#16840578C213yesmaximal, complemented
5C2×#16840577C211yesmaximal, characteristic, complemented
6C2×#16840575C213yesmaximal, complemented
7C2×#16840574C211yesmaximal, characteristic, complemented
8C2×#16840571C213yesmaximal, complemented
9C2×#16840570C211yesmaximal, characteristic, complemented
10C2×#16840569C213yesmaximal, complemented
11C2×#16840561C213yesmaximal, complemented
12C2×#16840559C213yesmaximal, complemented
13C22×#14519809C213yesmaximal, complemented
14C2×#137×D61C213yesmaximal, complemented
15C2×#16840527C211yesmaximal, characteristic, complemented
16C2×C61×#578C211yesmaximal, characteristic, complemented
17#16840599—28no—
18#16840599C22116yescomplemented
19C2×#14519825—21no—
20C2×#14519825—21no—
21C2×#14519825C2213yescomplemented
22C2×#14519825C2213yescomplemented
23C2×#14519824—23no—
24C2×#14519824C2211yescharacteristic, complemented
25C2×#14519824C2213yescomplemented
262−1+4×D61—28no—
272−1+4×D61C22116yescomplemented
28C2×#14519823—23no—
29C2×#14519823C2211yescharacteristic, complemented
30C2×#14519823C2213yescomplemented
31C22×#11758226—21no—
32C22×#11758226C2213yes—
33C2×#41×D61—23no—
34C2×#41×D61—23no—
35C2×#41×D61C2213yes—
36C2×#41×D61C2211yescharacteristic
37C2×#41×D61C2213yescomplemented
38C22×Q8×D61—21no—
39C22×Q8×D61C2213yescomplemented
40#16840578C22148yescomplemented
41#16840577C22116yescomplemented
42#16840575C22148yescomplemented
43#16840574C22116yescomplemented
44#16840571C22148yescomplemented
45#16840570C22116yescomplemented
46#16840569C22148yescomplemented
47#16840561C22148yescomplemented
48#16840559C22148yescomplemented
49C2×#14519810C2213yescomplemented
50C2×#14519809C2216yescomplemented
51C2×#14519809C2213yescomplemented
52C2×#14519809C2216yescomplemented
53C2×#14519809C2216yescomplemented
54C2×#14519809C2213yescomplemented
55C2×#14519809C22148yescomplemented
56C2×#14519808C2213yescomplemented
57C2×#14519808C2213yescomplemented
58C2×#14519807C2213yescomplemented
59C2×#14519806C2213yescomplemented
60C2×#14519806C2213yescomplemented
61#137×D61C22148yescomplemented
62C2×#14519805C2213yescomplemented
63C2×#14519804C2213yescomplemented
64C2×#14519804C2213yescomplemented
65C2×#14519802C2213yescomplemented
66C2×#14519801C2211yescharacteristic, complemented
67C2×#14519801C2213yescomplemented
68C2×#14519800C2216yescomplemented
69C2×#14519799C2213yescomplemented
70C2×#14519798C2216yescomplemented
71C2×#14519797C2213yescomplemented
72C2×#14519797C2213yescomplemented
73C22×#11758202C2213yescomplemented
74C2×Q16×D61C2216yescomplemented
75C22×#11758190C2213yescomplemented
76C22×#11758201C2213yescomplemented
77C2×SD16×D61C2216yescomplemented
78#16840527C22116yescomplemented
79C2×#14519785C2213yescomplemented
80C2×#14519784C2211yescharacteristic, complemented
81C2×#14519783C2213yescomplemented
82C22×#11758189C2213yescomplemented
83C2×M16×D61C2213yescomplemented
84C2×2−1+4×C61C2211yescharacteristic, complemented
85C2×2−1+4×C61C2211yescharacteristic, complemented
86C61×#578C22116yescomplemented
87C2×#137×C61C2213yescomplemented
88C2×#137×C61C2213yescomplemented
89C2×#135×C61C2213yescomplemented
90C22×Q16×C61C2213yescomplemented
91C2×#131×C61C2211yescharacteristic, complemented
92#14519825—216no—
93#14519825—216no—
94#14519825—212no—
95#14519825—212no—
96#14519825C23124yescomplemented
97#14519825C23124yescomplemented
98#14519824—24no—
99#14519824—248no—
100#14519824—212no—
101#14519824C23124yescomplemented
102#14519824C2318yescomplemented
103#14519823—24no—
104#14519823—248no—
105#14519823—212no—
106#14519823C23124yescomplemented
107#14519823C2318yescomplemented
108C2×#11758226—21no—
109C2×#11758226—216no—
110C2×#11758226—23no—
111C2×#11758226—23no—
112C2×#11758226—23no—
113C2×#11758226—23no—
114C2×#11758226—212no—
115C2×#11758226D411yescharacteristic
116C2×#11758226C2316yes—
117C2×#11758226C2313yes—
118C2×#11758226C2313yes—
119C2×#11758226C23124yes—
120C2×#11758222—26no—
121C2×#11758222—26no—
122C2×#11758222—23no—
123C2×#11758222—23no—
124C2×#11758222—23no—
125C2×#11758222—23no—
126C2×#11758222C2313yes—
127C2×#11758222C2313yes—
128C2×#11758222C2313yes—
129C2×#11758224—23no—
130C2×#11758224—26no—
131C2×#11758224—23no—
132C2×#11758224—23no—
133C2×#11758224D413yes—
134C2×#11758224C2313yes—
135C2×#11758224C2311yescharacteristic
136#41×D61—248no—
137#41×D61—248no—
138#41×D61—212no—
139#41×D61—212no—
140#41×D61D418yes—
141#41×D61C23124yes—
142#41×D61C2318yes—
143#41×D61C23124yescomplemented
144C22×Dic122—23no—
145C22×Dic122—23no—
146C22×Dic122C2313yes—
147C2×Q8×D61—21no—
148C2×Q8×D61—216no—
149C2×Q8×D61—23no—
150C2×Q8×D61—212no—
151C2×Q8×D61—23no—
152C2×Q8×D61—23no—
153C2×Q8×D61—23no—
154C2×Q8×D61D411yescharacteristic
155C2×Q8×D61C2316yes—
156C2×Q8×D61C2313yes—
157C2×Q8×D61C2313yes—
158C2×Q8×D61C23124yescomplemented
159C22×D244—23no—
160C22×D244—23no—
161C22×D244C2313yes—
162C2×D4×D61—23no—
163C2×D4×D61—23no—
164C2×D4×D61—23no—
165C2×D4×D61—26no—
166C2×D4×D61D413yes—
167C2×D4×D61C2313yes—
168C2×D4×D61C2311yescharacteristic
169C22×C4×D61—23no—
170C22×C4×D61—23no—
171C22×C4×D61—23no—
172C22×C4×D61—23no—
173C22×C4×D61C2313yes—
174#14519810C23124yescomplemented
175#14519809C23148yescomplemented
176#14519809C23124yescomplemented
177#14519809C23148yescomplemented
178#14519809C23148yescomplemented
179#14519809C23124yescomplemented
180#14519808C23124yescomplemented
181#14519808C23124yescomplemented
182#14519807C23124yescomplemented
183#14519806C23124yescomplemented
184#14519806C23124yescomplemented
185#14519805C23124yescomplemented
186#14519804C23124yescomplemented
187#14519804C23124yescomplemented
188#14519802C23124yescomplemented
189#14519801C2318yescomplemented
190#14519801C23124yescomplemented
191#14519800C23148yescomplemented
192#14519799C23124yescomplemented
193#14519798C23148yescomplemented
194#14519797C23124yescomplemented
195#14519797C23124yescomplemented
196C2×Dic244C2313yes—
197C2×#11758202C2313yes—
198C2×#11758202C2316yes—
199C2×#11758202C2313yes—
200C2×#11758202C23124yescomplemented
201Q16×D61C23148yescomplemented
202C2×#11758190C2316yes—
203C2×#11758190C2313yes—
204C2×#11758190C2311yescharacteristic
205C2×#11758190C23124yescomplemented
206C2×#11758200C2313yes—
207C2×#11758200C2311yescharacteristic
208C2×#11758201C2316yes—
209C2×#11758201C2313yes—
210C2×#11758201C2313yes—
211C2×#11758201C23124yescomplemented
212SD16×D61C23148yescomplemented
213C2×D488C2313yes—
214C2×#11758199C2311yescharacteristic
215C2×#11758199C2313yes—
216#14519785C23124yescomplemented
217#14519784C2318yescomplemented
218#14519783C23124yescomplemented
219C2×#11758194C2313yes—
220C2×#11758189C2313yes—
221C2×#11758189C2311yescharacteristic
222C2×#11758189C2313yes—
223C2×#11758189C2313yes—
224C2×#11758189C23124yescomplemented
225M16×D61C23124yescomplemented
226C22×#92418C2313yes—
227C2×C8×D61C2316yes—
2282−1+4×C61—24no—
2292−1+4×C61—24no—
2302−1+4×C61C2318yescomplemented
2312−1+4×C61C2318yescomplemented
232C2×#41×C61—23no—
233C2×#41×C61—23no—
234C2×#41×C61C2313yes—
235C2×#41×C61C2313yes—
236C2×#41×C61C2311yescharacteristic
237C22×Q8×C61—21no—
238C22×Q8×C61—21no—
239C22×Q8×C61C2313yes—
240C22×Q8×C61C2313yes—
241#137×C61C23124yescomplemented
242#137×C61C23124yescomplemented
243#135×C61C23124yescomplemented
244C2×Q16×C61C2313yes—
245C2×Q16×C61C2316yes—
246C2×Q16×C61C23124yescomplemented
247C2×SD16×C61C2313yes—
248C2×SD16×C61C2313yes—
249C2×D8×C61C2311yescharacteristic
250#131×C61C2318yescomplemented
251C2×M16×C61C2313yes—
252C22×C8×C61C2313yes—
253C23×D61—23no—
254C23×D61—21no—
255C23×D61—23no—
256C23×D61C2×D413yes—
257#41×C61—224no—
258#41×C61—224no—
259#41×C61—26no—
260#41×C61—26no—
261#41×C61C2×D414yes—
262#41×C61C24112yes—
263#41×C61C24112yes—
264#41×C61C2414yes—
265C2×Q8×C61—28no—
266C2×Q8×C61—28no—
267C2×Q8×C61—23no—
268C2×Q8×C61—26no—
269C2×Q8×C61—23no—
270C2×Q8×C61—26no—
271C2×Q8×C61C2×D411yescharacteristic
272C2×Q8×C61C24112yes—
273C2×Q8×C61C24112yes—
274C2×Q8×C61C2413yes—
275C2×Q8×C61C2413yes—
276C2×D4×C61—23no—
277C2×D4×C61—23no—
278C2×D4×C61C2×D413yes—
279C2×D4×C61C2411yescharacteristic
280C2×D4×C61C2411yescharacteristic
281C22×C4×C61—23no—
282C22×C4×C61—23no—
283C22×C4×C61—23no—
284C22×C4×C61—23no—
285C22×C4×C61C2413yes—
286C2×C22⋊D61—23no—
287C2×C22⋊D61—23no—
288C2×C22⋊D61—21no—
289C2×C22⋊D61—23no—
290C2×C22⋊D61—23no—
291C2×C22⋊D61—21no—
292C2×C22⋊D61C2×D416yes—
293C22×Dic61—23no—
294C22×Dic61—21no—
295C22×Dic61—23no—
296C22×Dic61C2×D413yes—
297#11758226—28no—
298#11758226—224no—
299#11758226—224no—
300#11758226—224no—
301#11758226—26no—
302#11758226—26no—
303#11758226—224no—
304#11758226—212no—
305#11758226C2×D418yes—
306#11758226C24112yes—
307#11758226C24124yes—
308#11758226C24112yes—
309Q8×D61—28no—
310Q8×D61—26no—
311Q8×D61—224no—
312Q8×D61—212no—
313Q8×D61—224no—
314Q8×D61—26no—
315Q8×D61—224no—
316Q8×D61—224no—
317Q8×D61C2×D418yes—
318Q8×D61C24112yes—
319Q8×D61C24124yes—
320Q8×D61C24112yes—
321#11758224—224no—
322#11758224—248no—
323#11758224—224no—
324#11758224—224no—
325#11758224—22no—
326#11758224—26no—
327#11758224C2×D4124yes—
328#11758224C2414yes—
329#11758224C24112yes—
330D4×D61—224no—
331D4×D61—224no—
332D4×D61—224no—
333D4×D61—248no—
334D4×D61—22no—
335D4×D61—26no—
336D4×D61C2×D4124yes—
337D4×D61C24112yes—
338D4×D61C2414yes—
339#11758222—26no—
340#11758222—26no—
341#11758222—248no—
342#11758222—248no—
343#11758222—224no—
344#11758222—224no—
345#11758222—224no—
346#11758222—224no—
347#11758222C2×D4112yes—
348#11758222C24112yes—
349#11758222C24112yes—
350#11758222C24112yes—
351C2×D244—23no—
352C2×D244—26no—
353C2×D244—23no—
354C2×D244—224no—
355C2×D244—23no—
356C2×D244—26no—
357C2×D244—224no—
358C2×D244C2×D413yes—
359C2×D244C2413yes—
360C2×D244C2411yescharacteristic
361C2×D244C24112yes—
362C2×C4×D61—23no—
363C2×C4×D61—23no—
364C2×C4×D61—26no—
365C2×C4×D61—224no—
366C2×C4×D61—23no—
367C2×C4×D61—23no—
368C2×C4×D61—23no—
369C2×C4×D61—26no—
370C2×C4×D61—23no—
371C2×C4×D61—224no—
372C2×C4×D61—224no—
373C2×C4×D61—224no—
374C2×C4×D61C2×D413yes—
375C2×C4×D61C2×D413yes—
376C2×C4×D61C2×D4112yes—
377C2×C4×D61C2411yescharacteristic
378C2×C4×D61C2413yes—
379C2×C4×D61C24112yes—
380C2×Dic122—23no—
381C2×Dic122—26no—
382C2×Dic122—26no—
383C2×Dic122—23no—
384C2×Dic122—23no—
385C2×Dic122—224no—
386C2×Dic122—224no—
387C2×Dic122C2×D413yes—
388C2×Dic122C24112yes—
389C2×Dic122C2413yes—
390C2×Dic122C2411yescharacteristic
391Q16×C61C24112yes—
392Q16×C61C24124yes—
393SD16×C61C24112yes—
394SD16×C61C24112yes—
395D8×C61C2414yes—
396M16×C61C24112yes—
397C2×C8×C61C2411yescharacteristic
398C2×C8×C61C2413yes—
399C2×C8×C61C24112yes—
400#11758202C24112yes—
401#11758202C24124yes—
402#11758202C24112yes—
403#11758201C24112yes—
404#11758201C24124yes—
405#11758201C24112yes—
406#11758200C24112yes—
407#11758200C2414yes—
408#11758199C2414yes—
409#11758199C24112yes—
410#11758194C24112yes—
411C2×#92418C2413yes—
412C2×#92418C2411yescharacteristic
413C2×#92418C24112yes—
414Dic244C24112yes—
415D488C24112yes—
416#11758190C24112yes—
417#11758190C2414yes—
418#11758190C24124yes—
419#11758189C2414yes—
420#11758189C24112yes—
421#11758189C24112yes—
422#11758189C24112yes—
423C8×D61C24124yes—
424C23×C61—21no—
425C23×C61—21no—
426C23×C61C22×D413yes—
427C22×D61—21no—
428C22×D61—23no—
429C22×D61—212no—
430C22×D61—24no—
431C22×D61—212no—
432C22×D61—46no—
433C22×D61—44no—
434C22×D61—86no—
435C22×D61—86no—
436C22×D61C22×D411yescharacteristic
437C22×D61C22×D413yes—
438C22×D61C22×D4112yes—
439Q8×C61—23no—
440Q8×C61—212no—
441Q8×C61—23no—
442Q8×C61—212no—
443Q8×C61C22×D414yes—
444Q8×C61C2516yes—
445Q8×C61C2516yes—
446D4×C61—212no—
447D4×C61—212no—
448D4×C61—21no—
449D4×C61—21no—
450D4×C61C22×D4112yes—
451D4×C61C2512yes—
452D4×C61C2512yes—
453C2×C4×C61—23no—
454C2×C4×C61—212no—
455C2×C4×C61—23no—
456C2×C4×C61—212no—
457C2×C4×C61—212no—
458C2×C4×C61—212no—
459C2×C4×C61C22×D413yes—
460C2×C4×C61C22×D416yes—
461C2×C4×C61C2511yescharacteristic
462C2×C4×C61C2516yes—
463C22⋊D61—212no—
464C22⋊D61—212no—
465C22⋊D61—24no—
466C22⋊D61—212no—
467C22⋊D61—212no—
468C22⋊D61—24no—
469C22⋊D61C22×D4124yes—
470C2×Dic61—23no—
471C2×Dic61—21no—
472C2×Dic61—212no—
473C2×Dic61—212no—
474C2×Dic61—24no—
475C2×Dic61C22×D413yes—
476C2×Dic61C22×D411yescharacteristic
477C2×Dic61C22×D4112yes—
478D244—212no—
479D244—224no—
480D244—212no—
481D244—23no—
482D244—212no—
483D244—21no—
484D244C22×D4112yes—
485D244C2516yes—
486D244C2512yes—
487C4×D61—212no—
488C4×D61—212no—
489C4×D61—224no—
490C4×D61—212no—
491C4×D61—212no—
492C4×D61—212no—
493C4×D61—224no—
494C4×D61—212no—
495C4×D61C22×D4112yes—
496C4×D61C22×D4112yes—
497C4×D61C22×D412yes—
498C4×D61C22×D416yes—
499C4×D61C2516yes—
500C4×D61C2512yes—
501Dic122—23no—
502Dic122—212no—
503Dic122—21no—
504Dic122—224no—
505Dic122—212no—
506Dic122—212no—
507Dic122C22×D4112yes—
508Dic122C2516yes—
509Dic122C2512yes—
510C8×C61C2516yes—
511C8×C61C2512yes—
512#92418C2516yes—
513#92418C2512yes—
514C2×#3586—611nomaximal, Sylow
515C22×C61—26no—
516C22×C61—22no—
517C22×C61—22no—
518C22×C61—42no—
519C22×C61—42no—
520C22×C61C23×D416yes—
521C22×C61C23×D411yescharacteristic
522C2×D61—22no—
523C2×D61—26no—
524C2×D61—22no—
525C2×D61—26no—
526C2×D61—412no—
527C2×D61—48no—
528C2×D61—42no—
529C2×D61—46no—
530C2×D61—812no—
531C2×D61—812no—
532C2×D61C23×D412yes—
533C2×D61C23×D416yes—
534C4×C61—26no—
535C4×C61—26no—
536C4×C61C23×D411yescharacteristic
537C4×C61C23×D416yes—
538C4×C61C2611yescharacteristic
539Dic61—26no—
540Dic61—22no—
541Dic61C23×D416yes—
542Dic61C23×D412yes—
543C2×#585—611no—
544C22×2−1+4—611no—
545#3586—6132no—
546C2×#578—611no—
547C2×#578—613no—
548C2×#578—613no—
549C2×#578D6111yescharacteristic, complemented
550C2×#577—611no—
551C2×#577—613no—
552C2×#577—613no—
553C2×#577—611no—
554C2×#575—613no—
555C2×#575—613no—
556C22×#137—613no—
557C22×#137—613no—
558C2×#568—611no—
559C2×C61—26no—
560C2×C61—42no—
561C2×C61—42no—
562C2×C61#358612yescomplemented
563C2×C61C24×D411yescharacteristic
564D61—22no—
565D61—26no—
566D61—42no—
567D61—46no—
568#585—6116no—
569#585—1228no—
570C2×2−1+4—6116no—
571C2×2−1+4—613no—
572C2×2−1+4—611no—
573C2×2−1+4—613no—
574C2×2−1+4—613no—
575C2×2−1+4—1221no—
576C2×2−1+4—1221no—
577C2×2−1+4—1223no—
578C2×2−1+4—1228no—
579C2×2−1+4C2×D6111yescharacteristic, complemented
580C2×2−1+4C2×D6111yescharacteristic, complemented
581C2×H(5,𝔽2)—613no—
582C2×H(5,𝔽2)—611no—
583C2×H(5,𝔽2)—1223no—
584C22×#41—611no—
585C22×#41—613no—
586C22×#41—613no—
587C22×#41—613no—
588C22×#41—1223no—
589C22×#41—1221no—
590C22×#41—1223no—
591C23×Q8—613no—
592C23×Q8—1221no—
593#578—6116no—
594#578—6148no—
595#578—6148no—
596#578C2×D61116yescomplemented
597#577—6116no—
598#577—6148no—
599#577—6148no—
600#577—6116no—
601#575—6148no—
602#575—6148no—
603C2×#137—613no—
604C2×#137—613no—
605C2×#137—613no—
606C2×#137—6148no—
607C2×#137—616no—
608C2×#137—613no—
609C2×#137—616no—
610C2×#137—616no—
611C2×#137—613no—
612C2×#137—6148no—
613C2×#137—613no—
614C2×#137—613no—
615C2×#137—613no—
616C2×#137C2×D6113yescomplemented
617C2×#137C2×D6113yescomplemented
618C2×AGL(1,ℤ/8)—613no—
619C2×AGL(1,ℤ/8)—613no—
620C2×AGL(1,ℤ/8)—613no—
621C2×AGL(1,ℤ/8)—611no—
622C2×AGL(1,ℤ/8)—613no—
623C2×AGL(1,ℤ/8)—613no—
624C2×#135—613no—
625C2×#135—613no—
626C2×#135—616no—
627C2×#135—616no—
628C2×#135—613no—
629C2×#135C2×D6113yescomplemented
630C22×Q16—613no—
631C22×Q16—616no—
632C22×Q16C2×D6113yescomplemented
633C22×SD16—613no—
634C22×SD16—616no—
635C22×SD16—613no—
636#568—6116no—
637C2×#131—611no—
638C2×#131—613no—
639C2×#131—613no—
640C2×#131C2×D6111yescharacteristic, complemented
641C22×M16—613no—
642C22×M16—613no—
643C61C2×#358611yescharacteristic, complemented, Sylow
6442−1+4—24no—
6452−1+4—24no—
6462−1+4—6124no—
6472−1+4—618no—
6482−1+4—6124no—
6492−1+4—6124no—
6502−1+4—12216no—
6512−1+4—12216no—
6522−1+4—12212no—
6532−1+4—12212no—
6542−1+4—12248no—
6552−1+4—12212no—
6562−1+4—1224no—
6572−1+4C22×D6118yescomplemented
6582−1+4C22×D6118yescomplemented
659H(5,𝔽2)—6124no—
660H(5,𝔽2)—618no—
661H(5,𝔽2)—12248no—
662H(5,𝔽2)—12212no—
663H(5,𝔽2)—1224no—
664C2×#41—23no—
665C2×#41—23no—
666C2×#41—618no—
667C2×#41—618no—
668C2×#41—611no—
669C2×#41—613no—
670C2×#41—613no—
671C2×#41—6124no—
672C2×#41—6124no—
673C2×#41—613no—
674C2×#41—616no—
675C2×#41—613no—
676C2×#41—6124no—
677C2×#41—613no—
678C2×#41—611no—
679C2×#41—613no—
680C2×#41—613no—
681C2×#41—1223no—
682C2×#41—1223no—
683C2×#41—1226no—
684C2×#41—1226no—
685C2×#41—1223no—
686C2×#41—1223no—
687C2×#41—1223no—
688C2×#41—1223no—
689C2×#41—1223no—
690C2×#41—1223no—
691C2×#41—12212no—
692C2×#41—12212no—
693C2×#41—12212no—
694C2×#41—1226no—
695C2×#41—1223no—
696C2×#41—1223no—
697C2×#41—12248no—
698C2×#41—12216no—
699C2×#41—12248no—
700C2×#41—1221no—
701C2×#41—1223no—
702C2×#41C22×D6113yes—
703C2×#41C22×D6113yes—
704C2×#41C22×D6111yescharacteristic
705C22×Q8—21no—
706C22×Q8—21no—
707C22×Q8—611no—
708C22×Q8—616no—
709C22×Q8—613no—
710C22×Q8—613no—
711C22×Q8—6124no—
712C22×Q8—613no—
713C22×Q8—1223no—
714C22×Q8—1223no—
715C22×Q8—1223no—
716C22×Q8—1223no—
717C22×Q8—12212no—
718C22×Q8—12216no—
719C22×Q8—1223no—
720C22×Q8—1223no—
721C22×Q8—1221no—
722C22×Q8C22×D6113yes—
723C22×Q8C22×D6113yes—
724C22×D4—613no—
725C22×D4—613no—
726C22×D4—611no—
727C22×D4—613no—
728C22×D4—1223no—
729C22×D4—1223no—
730C22×D4—1226no—
731C22×D4—1223no—
732C22×D4—1223no—
733C22×D4—1223no—
734C23×C4—613no—
735C23×C4—1223no—
736C23×C4—1223no—
737C23×C4—1223no—
738C23×C4—1223no—
739#137—6124no—
740#137—6124no—
741#137—6124no—
742#137—6148no—
743#137—6124no—
744#137—6148no—
745#137—6148no—
746#137—6124no—
747#137—6124no—
748#137—6124no—
749#137—6124no—
750#137C22×D61124yescomplemented
751#137C22×D61124yescomplemented
752AGL(1,ℤ/8)—6124no—
753AGL(1,ℤ/8)—6124no—
754AGL(1,ℤ/8)—6124no—
755AGL(1,ℤ/8)—618no—
756AGL(1,ℤ/8)—6124no—
757AGL(1,ℤ/8)—6124no—
758#135—6124no—
759#135—6124no—
760#135—6148no—
761#135—6148no—
762#135—6124no—
763#135C22×D61124yescomplemented
764C2×Q16—613no—
765C2×Q16—616no—
766C2×Q16—613no—
767C2×Q16—6124no—
768C2×Q16—6148no—
769C2×Q16—613no—
770C2×Q16C22×D6116yes—
771C2×Q16C22×D6113yes—
772C2×Q16C22×D61124yescomplemented
773C2×SD16—613no—
774C2×SD16—616no—
775C2×SD16—6124no—
776C2×SD16—613no—
777C2×SD16—613no—
778C2×SD16—611no—
779C2×SD16—6148no—
780C2×SD16—616no—
781C2×SD16—613no—
782C2×SD16—6124no—
783C2×SD16—611no—
784C2×SD16C22×D6113yes—
785C2×SD16C22×D6113yes—
786C2×D8—611no—
787C2×D8—613no—
788C2×D8—613no—
789C2×D8C22×D6111yescharacteristic
790#131—618no—
791#131—6124no—
792#131—6124no—
793#131C22×D6118yescomplemented
794C2×M16—613no—
795C2×M16—6124no—
796C2×M16—613no—
797C2×M16—611no—
798C2×M16—613no—
799C2×M16—613no—
800C2×M16—6124no—
801C2×M16C22×D6113yes—
802C22×C8—613no—
803C22×C8—616no—
804C22×C8C22×D6113yes—
805C24—613no—
806C24—1223no—
807C24—1221no—
808C24—1223no—
809#41—224no—
810#41—224no—
811#41—26no—
812#41—26no—
813#41—618no—
814#41—6124no—
815#41—6112no—
816#41—6112no—
817#41—6112no—
818#41—6124no—
819#41—6112no—
820#41—6112no—
821#41—614no—
822#41—6112no—
823#41—6112no—
824#41—12224no—
825#41—12224no—
826#41—12248no—
827#41—12248no—
828#41—12224no—
829#41—12224no—
830#41—12224no—
831#41—1222no—
832#41—12224no—
833#41—1226no—
834#41—1226no—
835#41—12224no—
836#41—12224no—
837#41—12212no—
838#41—1226no—
839#41—12248no—
840#41—12224no—
841#41—12224no—
842#41—1228no—
843#41—12224no—
844#41—1226no—
845#41—1226no—
846#41D4×D6114yes—
847#41C23×D61112yes—
848#41C23×D61112yes—
849#41C23×D6114yes—
850C2×Q8—28no—
851C2×Q8—28no—
852C2×Q8—23no—
853C2×Q8—23no—
854C2×Q8—26no—
855C2×Q8—26no—
856C2×Q8—618no—
857C2×Q8—613no—
858C2×Q8—6124no—
859C2×Q8—6112no—
860C2×Q8—6112no—
861C2×Q8—613no—
862C2×Q8—611no—
863C2×Q8—6112no—
864C2×Q8—1223no—
865C2×Q8—1226no—
866C2×Q8—1223no—
867C2×Q8—12224no—
868C2×Q8—12224no—
869C2×Q8—1226no—
870C2×Q8—12224no—
871C2×Q8—12224no—
872C2×Q8—12212no—
873C2×Q8—1226no—
874C2×Q8—12224no—
875C2×Q8—12224no—
876C2×Q8—1228no—
877C2×Q8—1223no—
878C2×Q8—1226no—
879C2×Q8D4×D6111yescharacteristic
880C2×Q8C23×D6113yes—
881C2×Q8C23×D61112yes—
882C2×Q8C23×D6113yes—
883C2×Q8C23×D61112yes—
884C2×D4—23no—
885C2×D4—23no—
886C2×D4—616no—
887C2×D4—6124no—
888C2×D4—6112no—
889C2×D4—614no—
890C2×D4—613no—
891C2×D4—611no—
892C2×D4—613no—
893C2×D4—6112no—
894C2×D4—12224no—
895C2×D4—1223no—
896C2×D4—1226no—
897C2×D4—1223no—
898C2×D4—12224no—
899C2×D4—1222no—
900C2×D4—1226no—
901C2×D4—1223no—
902C2×D4—1221no—
903C2×D4—12248no—
904C2×D4—12224no—
905C2×D4—12224no—
906C2×D4—1221no—
907C2×D4—1223no—
908C2×D4—1223no—
909C2×D4—1223no—
910C2×D4—12224no—
911C2×D4—1223no—
912C2×D4—1226no—
913C2×D4D4×D6113yes—
914C2×D4C23×D6111yescharacteristic
915C2×D4C23×D6111yescharacteristic
916C22×C4—23no—
917C22×C4—23no—
918C22×C4—23no—
919C22×C4—23no—
920C22×C4—613no—
921C22×C4—613no—
922C22×C4—613no—
923C22×C4—6112no—
924C22×C4—613no—
925C22×C4—611no—
926C22×C4—6112no—
927C22×C4—1223no—
928C22×C4—1226no—
929C22×C4—1223no—
930C22×C4—12224no—
931C22×C4—12224no—
932C22×C4—12224no—
933C22×C4—1223no—
934C22×C4—1223no—
935C22×C4—12224no—
936C22×C4—1226no—
937C22×C4—1221no—
938C22×C4—1223no—
939C22×C4—1223no—
940C22×C4—1223no—
941C22×C4—1223no—
942C22×C4C23×D6113yes—
943Q16—6124no—
944Q16—6112no—
945Q16—6112no—
946Q16—6112no—
947Q16C23×D61124yes—
948Q16C23×D61112yes—
949SD16—6124no—
950SD16—6112no—
951SD16—6112no—
952SD16—6112no—
953SD16—614no—
954SD16—6124no—
955SD16—6112no—
956SD16—614no—
957SD16C23×D61112yes—
958SD16C23×D61112yes—
959D8—614no—
960D8—6112no—
961D8—6112no—
962D8C23×D6114yes—
963M16—6112no—
964M16—6112no—
965M16—614no—
966M16—6112no—
967M16—6112no—
968M16C23×D61112yes—
969C2×C8—613no—
970C2×C8—611no—
971C2×C8—6112no—
972C2×C8—6124no—
973C2×C8C23×D6113yes—
974C2×C8C23×D6111yescharacteristic
975C2×C8C23×D61112yes—
976C23—21no—
977C23—21no—
978C23—611no—
979C23—613no—
980C23—6112no—
981C23—12212no—
982C23—1224no—
983C23—12212no—
984C23—1221no—
985C23—1223no—
986C23—4886no—
987C23—4886no—
988C23—2446no—
989C23—2444no—
990C23C2×D4×D6113yes—
991Q8—212no—
992Q8—23no—
993Q8—212no—
994Q8—23no—
995Q8—6112no—
996Q8—616no—
997Q8—612no—
998Q8—12212no—
999Q8—12224no—
1000Q8—12212no—
1001Q8—12212no—
1002Q8—1223no—
1003Q8—1221no—
1004Q8C2×D4×D6114yes—
1005Q8C24×D6116yes—
1006Q8C24×D6116yes—
1007D4—212no—
1008D4—212no—
1009D4—21no—
1010D4—21no—
1011D4—6124no—
1012D4—6112no—
1013D4—612no—
1014D4—616no—
1015D4—12212no—
1016D4—12224no—
1017D4—12212no—
1018D4—12212no—
1019D4—1224no—
1020D4—1224no—
1021D4—12212no—
1022D4—12212no—
1023D4—12212no—
1024D4—12212no—
1025D4—1223no—
1026D4—1221no—
1027D4C2×D4×D61112yes—
1028D4C24×D6112yes—
1029D4C24×D6112yes—
1030C2×C4—212no—
1031C2×C4—212no—
1032C2×C4—23no—
1033C2×C4—23no—
1034C2×C4—212no—
1035C2×C4—212no—
1036C2×C4—6112no—
1037C2×C4—611no—
1038C2×C4—613no—
1039C2×C4—612no—
1040C2×C4—6112no—
1041C2×C4—6112no—
1042C2×C4—616no—
1043C2×C4—616no—
1044C2×C4—612no—
1045C2×C4—12212no—
1046C2×C4—12224no—
1047C2×C4—12212no—
1048C2×C4—12212no—
1049C2×C4—12212no—
1050C2×C4—12224no—
1051C2×C4—1224no—
1052C2×C4—12212no—
1053C2×C4—12212no—
1054C2×C4—1221no—
1055C2×C4—1223no—
1056C2×C4—12212no—
1057C2×C4—12212no—
1058C2×C4C2×D4×D6116yes—
1059C2×C4C2×D4×D6113yes—
1060C2×C4C24×D6116yes—
1061C2×C4C24×D6111yescharacteristic
1062C8—616no—
1063C8—612no—
1064C8C24×D6116yes—
1065C8C24×D6112yes—
1066C22—26no—
1067C22—22no—
1068C22—22no—
1069C22—42no—
1070C22—42no—
1071C22—612no—
1072C22—616no—
1073C22—1226no—
1074C22—1222no—
1075C22—1222no—
1076C22—1226no—
1077C22—48812no—
1078C22—48812no—
1079C22—24412no—
1080C22—2448no—
1081C22—2446no—
1082C22—2442no—
1083C22C22×D4×D6116yes—
1084C22C22×D4×D6111yescharacteristic
1085C4—26no—
1086C4—26no—
1087C4—612no—
1088C4—616no—
1089C4—1222no—
1090C4—1226no—
1091C4C22×D4×D6116yes—
1092C4C22×D4×D6111yescharacteristic
1093C4C25×D6111yescharacteristic
1094C2—26no—
1095C2—42no—
1096C2—42no—
1097C2—1226no—
1098C2—1222no—
1099C2—2446no—
1100C2—2442no—
1101C2#2146060412yesdirect product factor
1102C2C23×D4×D6111yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC4×C61C26
FrattiniC4C25×D61
FittingC2×C61×#578C2
socleC22×C61C23×D4
hypercenterC2×#578D61
hypocenterC61C2×#3586
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#578

Complements

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

NH ≅ G/Ntype
1. C2×#16840599C2semidirect
2. C2×2−1+4×D61C2semidirect
3. #21460604C2direct (N × H)
4. C2×#16840578C2semidirect
5. C2×#16840577C2semidirect
6. C2×#16840575C2semidirect
7. C2×#16840574C2semidirect
8. C2×#16840571C2semidirect
9. C2×#16840570C2semidirect
10. C2×#16840569C2semidirect
11. C2×#16840561C2semidirect
12. C2×#16840559C2semidirect
13. C22×#14519809C2semidirect
14. C2×#137×D61C2semidirect
15. C2×#16840527C2semidirect
16. C2×C61×#578C2semidirect
18. #16840599C22semidirect
21. C2×#14519825C22semidirect
22. C2×#14519825C22semidirect
24. C2×#14519824C22semidirect
25. C2×#14519824C22semidirect
27. 2−1+4×D61C22semidirect
29. C2×#14519823C22semidirect
30. C2×#14519823C22semidirect
37. C2×#41×D61C22semidirect
39. C22×Q8×D61C22semidirect
40. #16840578C22semidirect
41. #16840577C22semidirect
42. #16840575C22semidirect
43. #16840574C22semidirect
44. #16840571C22semidirect
45. #16840570C22semidirect
46. #16840569C22semidirect
47. #16840561C22semidirect
48. #16840559C22semidirect
49. C2×#14519810C22semidirect
50. C2×#14519809C22semidirect
51. C2×#14519809C22semidirect
52. C2×#14519809C22semidirect
53. C2×#14519809C22semidirect
54. C2×#14519809C22semidirect
55. C2×#14519809C22semidirect
56. C2×#14519808C22semidirect
57. C2×#14519808C22semidirect
58. C2×#14519807C22semidirect
59. C2×#14519806C22semidirect
60. C2×#14519806C22semidirect
61. #137×D61C22semidirect
62. C2×#14519805C22semidirect
63. C2×#14519804C22semidirect
64. C2×#14519804C22semidirect
65. C2×#14519802C22semidirect
66. C2×#14519801C22semidirect
67. C2×#14519801C22semidirect
68. C2×#14519800C22semidirect
69. C2×#14519799C22semidirect
70. C2×#14519798C22semidirect
71. C2×#14519797C22semidirect
72. C2×#14519797C22semidirect
73. C22×#11758202C22semidirect
74. C2×Q16×D61C22semidirect
75. C22×#11758190C22semidirect
76. C22×#11758201C22semidirect
77. C2×SD16×D61C22semidirect
78. #16840527C22semidirect
79. C2×#14519785C22semidirect
80. C2×#14519784C22semidirect
81. C2×#14519783C22semidirect
82. C22×#11758189C22semidirect
83. C2×M16×D61C22semidirect
84. C2×2−1+4×C61C22semidirect
85. C2×2−1+4×C61C22semidirect
86. C61×#578C22semidirect
87. C2×#137×C61C22semidirect
88. C2×#137×C61C22semidirect
89. C2×#135×C61C22semidirect
90. C22×Q16×C61C22semidirect
91. C2×#131×C61C22semidirect
96. #14519825C23semidirect
97. #14519825C23semidirect
101. #14519824C23semidirect
102. #14519824C23semidirect
106. #14519823C23semidirect
107. #14519823C23semidirect
143. #41×D61C23semidirect
158. C2×Q8×D61C23semidirect
174. #14519810C23semidirect
175. #14519809C23semidirect
176. #14519809C23semidirect
177. #14519809C23semidirect
178. #14519809C23semidirect
179. #14519809C23semidirect
180. #14519808C23semidirect
181. #14519808C23semidirect
182. #14519807C23semidirect
183. #14519806C23semidirect
184. #14519806C23semidirect
185. #14519805C23semidirect
186. #14519804C23semidirect
187. #14519804C23semidirect
188. #14519802C23semidirect
189. #14519801C23semidirect
190. #14519801C23semidirect
191. #14519800C23semidirect
192. #14519799C23semidirect
193. #14519798C23semidirect
194. #14519797C23semidirect
195. #14519797C23semidirect
200. C2×#11758202C23semidirect
201. Q16×D61C23semidirect
205. C2×#11758190C23semidirect
211. C2×#11758201C23semidirect
212. SD16×D61C23semidirect
216. #14519785C23semidirect
217. #14519784C23semidirect
218. #14519783C23semidirect
224. C2×#11758189C23semidirect
225. M16×D61C23semidirect
230. 2−1+4×C61C23semidirect
231. 2−1+4×C61C23semidirect
241. #137×C61C23semidirect
242. #137×C61C23semidirect
243. #135×C61C23semidirect
246. C2×Q16×C61C23semidirect
250. #131×C61C23semidirect
549. C2×#578D61semidirect
562. C2×C61#3586semidirect
579. C2×2−1+4C2×D61semidirect
580. C2×2−1+4C2×D61semidirect
596. #578C2×D61semidirect
616. C2×#137C2×D61semidirect
617. C2×#137C2×D61semidirect
629. C2×#135C2×D61semidirect
632. C22×Q16C2×D61semidirect
640. C2×#131C2×D61semidirect
643. C61C2×#3586semidirect
657. 2−1+4C22×D61semidirect
658. 2−1+4C22×D61semidirect
750. #137C22×D61semidirect
751. #137C22×D61semidirect
763. #135C22×D61semidirect
772. C2×Q16C22×D61semidirect
793. #131C22×D61semidirect
1101. C2#21460604direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168405992
C2×2−1+4×D612
#214606042
C2×#168405782
C2×#168405772
C2×#168405752
C2×#168405742
C2×#168405712
C2×#168405702
C2×#168405692
C2×#168405612
C2×#168405592
C22×#145198092
C2×#137×D612
C2×#168405272
C2×C61×#5782
C2×#358661