Finite Group Databasebeta

← C2×#21457591 #30556201

Subgroups — C2×#21457591 #30556201

Order 15616.

2620 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840579C211yesmaximal, characteristic, complemented
2C2×#16840578C211yesmaximal, characteristic, complemented
3C2×#16840572C211yesmaximal, characteristic, complemented
4C2×#16840568C211yesmaximal, characteristic, complemented
5#21457591C2116yesmaximal, direct product factor
6C2×#16840153C211yesmaximal, characteristic, complemented
7C2×#16840038C211yesmaximal, characteristic, complemented
8C2×#16840036C211yesmaximal, characteristic, complemented
9C2×#16840024C211yesmaximal, characteristic, complemented
10C2×#16839947C211yesmaximal, characteristic, complemented
11C2×#16839943C211yesmaximal, characteristic, complemented
12C2×#16839933C211yesmaximal, characteristic, complemented
13C2×#16839942C211yesmaximal, characteristic, complemented
14C2×#16839883C211yesmaximal, characteristic, complemented
15C2×#16839882C211yesmaximal, characteristic, complemented
16C2×C61×#471C211yesmaximal, characteristic, complemented
17C2×#14519825C2211yescharacteristic
18C2×#14519824C2211yescharacteristic
19C2×#14519824C2211yescharacteristic, complemented
20C2×#14519822C2211yescharacteristic
21#16840579—24no—
22#16840579C2218yescomplemented
23#16840578—24no—
24#16840578C2218yescomplemented
25#16840572—24no—
26#16840572C2218yescomplemented
27#16840568—24no—
28#16840568C2218yescomplemented
29C2×#14519810—21no—
30C2×#14519810—21no—
31C2×#14519810C2211yescharacteristic
32C2×#14519810C2211yescharacteristic
33C2×#14519810C2211yescharacteristic
34C2×#14519810C2211yescharacteristic, complemented
35C2×#14519809—21no—
36C2×#14519808C2211yescharacteristic
37C2×#14519806—21no—
38C2×#14519806—21no—
39C2×#14519806—21no—
40C2×#14519804—21no—
41C2×#14519803C2211yescharacteristic
42C2×#14519801—21no—
43C2×#14519799—21no—
44C2×#14519799C2211yescharacteristic
45C2×#14519798—21no—
46C2×#14519798—21no—
47C2×#14519797C2211yescharacteristic
48C2×#14519796—21no—
49C22×Dic244—21no—
50C22×Dic244C2211yescharacteristic, complemented
51C22×#11758202C2211yescharacteristic, complemented
52C2×Q16×D61—21no—
53C22×#11758200C2211yescharacteristic
54C2×SD16×D61—21no—
55C2×SD16×D61—21no—
56C2×#14519785C2211yescharacteristic
57C2×#14519785C2211yescharacteristic, complemented
58C2×#14519783C2211yescharacteristic
59C2×#14519775C2211yescharacteristic, complemented
60C2×#14519764C2211yescharacteristic
61#16840153C2218yescomplemented
62#16840038C2218yescomplemented
63#16840036C2218yescomplemented
64#16840024C2218yescomplemented
65#16839947C2218yescomplemented
66#16839943C2218yescomplemented
67#16839942C2218yescomplemented
68#16839933C2218yescomplemented
69#16839883C2218yescomplemented
70#16839882C2218yescomplemented
71C2×#14519712C2211yescharacteristic, complemented
72C2×#14519704C2211yescharacteristic, complemented
73C2×#14519703C2211yescharacteristic
74C2×#14519703C2211yescharacteristic
75C2×#14519703C2211yescharacteristic, complemented
76C2×#14519695C2211yescharacteristic, complemented
77C2×#14519695C2211yescharacteristic, complemented
78C2×#14519687C2211yescharacteristic, complemented
79C2×#137×C61C2211yescharacteristic, complemented
80C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
81C22×SD16×C61C2211yescharacteristic
82C2×#131×C61C2211yescharacteristic, complemented
83C61×#471C2218yescomplemented
84C2×#108×C61C2211yescharacteristic, complemented
85C2×#101×C61C2211yescharacteristic, complemented
86C2×#100×C61C2211yescharacteristic
87#14519825—22no—
88#14519825—22no—
89#14519825—41no—
90#14519825C2314yes—
91#14519824—22no—
92#14519824—22no—
93#14519824—22no—
94#14519824—22no—
95#14519824—41no—
96#14519824—41no—
97#14519824C2314yes—
98#14519824C2314yescomplemented
99#14519822—22no—
100#14519822—22no—
101#14519822—41no—
102#14519822C2314yes—
103C2×#11758226—21no—
104C2×#11758226—21no—
105C2×#11758222—21no—
106C2×#11758222—21no—
107C2×#11758222—41no—
108C2×#11758222C2311yescharacteristic
109C2×#11758222C2311yescharacteristic
110C2×#11758222C2311yescharacteristic
111C2×#11758224—21no—
112C2×#11758224—21no—
113C2×#11758224—21no—
114C2×#11758224—21no—
115C2×#11758224—41no—
116C2×#11758224—41no—
117C22×Dic122—21no—
118C22×Dic122—21no—
119C22×Dic122C2311yescharacteristic
120C22×Dic122C2311yescharacteristic
121C2×Q8×D61—21no—
122C2×Q8×D61—21no—
123C2×Q8×D61—21no—
124C2×Q8×D61—21no—
125C22×C22⋊D61—41no—
126C2×D4×D61—21no—
127C2×D4×D61—21no—
128#14519810—22no—
129#14519810—22no—
130#14519810—22no—
131#14519810—22no—
132#14519810—28no—
133#14519810—28no—
134#14519810C2314yes—
135#14519810C2314yes—
136#14519810C2314yes—
137#14519810C2314yescomplemented
138#14519809—28no—
139#14519808—22no—
140#14519808C2314yes—
141#14519806—28no—
142#14519806—28no—
143#14519806—28no—
144#14519804—28no—
145#14519803—22no—
146#14519803C2314yes—
147#14519801—28no—
148#14519799—28no—
149#14519799D414yes—
150#14519799C2314yes—
151#14519798—28no—
152#14519798—28no—
153#14519797D414yes—
154#14519797C2314yes—
155#14519796—28no—
156C2×Dic244—21no—
157C2×Dic244—21no—
158C2×Dic244—21no—
159C2×Dic244—21no—
160C2×Dic244—21no—
161C2×Dic244—21no—
162C2×Dic244—22no—
163C2×Dic244—28no—
164C2×Dic244D411yescharacteristic
165C2×Dic244C2314yescomplemented
166C2×#11758202—21no—
167C2×#11758202—21no—
168C2×#11758202—21no—
169C2×#11758202—22no—
170C2×#11758202D411yescharacteristic
171C2×#11758202C2314yescomplemented
172Q16×D61—28no—
173C2×#11758190—21no—
174C2×#11758190—21no—
175C2×#11758190—21no—
176C2×#11758190—21no—
177C2×#11758190D411yescharacteristic
178C2×#11758190D411yescharacteristic
179C2×#11758200—21no—
180C2×#11758200—21no—
181C2×#11758200—21no—
182C2×#11758200—22no—
183C2×#11758200D411yescharacteristic
184C2×#11758200C2314yes—
185C2×#11758201—21no—
186C2×#11758201D411yescharacteristic
187SD16×D61—28no—
188SD16×D61—28no—
189C2×D488D411yescharacteristic
190C2×#11758199—21no—
191C2×#11758199D411yescharacteristic
192#14519785—22no—
193#14519785—22no—
194#14519785C2314yes—
195#14519785C2314yescomplemented
196#14519783—22no—
197#14519783C2314yes—
198C2×#11758194C2311yescharacteristic
199C2×#11758189—21no—
200C2×#11758189—21no—
201C2×#11758189—21no—
202C22×#92418C2311yescharacteristic
203C2×C8×D61—21no—
204C2×C8×D61—21no—
205C2×C8×D61—21no—
206#14519775—41no—
207#14519775C2314yescomplemented
208#14519764—41no—
209#14519764C2314yes—
210C2×#11758196—41no—
211C2×C22⋊Dic61—41no—
212C2×C4×Dic61C2311yescharacteristic
213#14519712C2314yescomplemented
214#14519704C2314yescomplemented
215#14519703C2314yes—
216#14519703C2314yes—
217#14519703C2314yescomplemented
218#14519695C2314yescomplemented
219#14519695C2314yescomplemented
220#14519687C2314yescomplemented
221C2×#41×C61C2311yescharacteristic
222C22×Q8×C61C2311yescharacteristic
223C22×D4×C61C2311yescharacteristic
224#137×C61—22no—
225#137×C61C2314yescomplemented
226AGL(1,ℤ/8)×C61—22no—
227AGL(1,ℤ/8)×C61C2314yes—
228C2×Q16×C61—21no—
229C2×SD16×C61—21no—
230C2×SD16×C61—21no—
231C2×SD16×C61—21no—
232C2×SD16×C61—21no—
233C2×SD16×C61—22no—
234C2×SD16×C61C2314yes—
235C2×D8×C61—21no—
236#131×C61—22no—
237#131×C61C2314yescomplemented
238C2×M16×C61—21no—
239C2×M16×C61C2311yescharacteristic
240C2×M16×C61C2311yescharacteristic
241C2×M16×C61C2311yescharacteristic
242C22×C8×C61—21no—
243C22×C8×C61C2311yescharacteristic
244#108×C61C2314yescomplemented
245#101×C61C2314yescomplemented
246#100×C61C2314yes—
247C24×C61—21no—
248C23×D61—41no—
249#41×C61—21no—
250#41×C61—21no—
251#41×C61C2×D412yes—
252#41×C61C2412yes—
253C2×Q8×C61—21no—
254C2×Q8×C61—21no—
255C2×Q8×C61—21no—
256C2×Q8×C61—21no—
257C2×Q8×C61—21no—
258C2×Q8×C61C2×D411yescharacteristic
259C2×Q8×C61C2412yes—
260C2×D4×C61—21no—
261C2×D4×C61—21no—
262C2×D4×C61—21no—
263C2×D4×C61—21no—
264C2×D4×C61—21no—
265C2×D4×C61—21no—
266C2×D4×C61C2×D411yescharacteristic
267C2×D4×C61C2412yes—
268C22×C4×C61—21no—
269C22×C4×C61—21no—
270C22×C4×C61C2411yescharacteristic
271C2×C22⋊D61—21no—
272C2×C22⋊D61—21no—
273C2×C22⋊D61—21no—
274C2×C22⋊D61—41no—
275C2×C22⋊D61—41no—
276C2×C22⋊D61—44no—
277C2×C22⋊D61—44no—
278C2×C22⋊D61—41no—
279C2×C22⋊D61—41no—
280C22×Dic61—21no—
281C22×Dic61—21no—
282C22×Dic61—21no—
283C22×Dic61—41no—
284C22×Dic61—41no—
285C22×Dic61—41no—
286#11758226—24no—
287#11758226—24no—
288#11758226—42no—
289#11758226—42no—
290Q8×D61—24no—
291Q8×D61—24no—
292Q8×D61—24no—
293Q8×D61—24no—
294Q8×D61—42no—
295Q8×D61—42no—
296Q8×D61—42no—
297Q8×D61—42no—
298#11758224—24no—
299#11758224—24no—
300#11758224—24no—
301#11758224—24no—
302#11758224—42no—
303#11758224—42no—
304#11758224—42no—
305#11758224—42no—
306#11758224—44no—
307#11758224—44no—
308#11758224—44no—
309#11758224—44no—
310D4×D61—24no—
311D4×D61—24no—
312D4×D61—42no—
313D4×D61—42no—
314#11758222—21no—
315#11758222—21no—
316#11758222—21no—
317#11758222—21no—
318#11758222—21no—
319#11758222—21no—
320#11758222—24no—
321#11758222—24no—
322#11758222—42no—
323#11758222—42no—
324#11758222—44no—
325#11758222—44no—
326#11758222C2×D412yes—
327#11758222C2×D412yes—
328#11758222C2×D412yes—
329#11758222C2412yes—
330#11758222C2412yes—
331#11758222C2412yes—
332C2×D244—41no—
333C2×D244C2×D411yescharacteristic
334C2×D244C2×D411yescharacteristic
335C2×D244C2×D411yescharacteristic
336C2×C4×D61—21no—
337C2×C4×D61—21no—
338C2×C4×D61—21no—
339C2×C4×D61—41no—
340C2×C4×D61—41no—
341C2×C4×D61—41no—
342C2×C4×D61—41no—
343C2×Dic122—21no—
344C2×Dic122—21no—
345C2×Dic122—21no—
346C2×Dic122—21no—
347C2×Dic122—21no—
348C2×Dic122—21no—
349C2×Dic122—21no—
350C2×Dic122—21no—
351C2×Dic122—24no—
352C2×Dic122—24no—
353C2×Dic122—21no—
354C2×Dic122—21no—
355C2×Dic122—42no—
356C2×Dic122—42no—
357C2×Dic122—41no—
358C2×Dic122—41no—
359C2×Dic122—41no—
360C2×Dic122C2×D411yescharacteristic
361C2×Dic122C2×D411yescharacteristic
362C2×Dic122C2×D411yescharacteristic
363C2×Dic122C2412yes—
364C2×Dic122C2412yes—
365Q16×C61—24no—
366SD16×C61—24no—
367SD16×C61—24no—
368SD16×C61—24no—
369SD16×C61—24no—
370D8×C61—24no—
371M16×C61—21no—
372M16×C61—21no—
373M16×C61—21no—
374M16×C61—24no—
375M16×C61C2412yes—
376M16×C61C2412yes—
377M16×C61C2412yes—
378C2×C8×C61—21no—
379C2×C8×C61—21no—
380C2×C8×C61—21no—
381C2×C8×C61—24no—
382C2×C8×C61C2×D411yescharacteristic
383C2×C8×C61C2×D411yescharacteristic
384C2×C8×C61C2×D412yes—
385C2×C8×C61C2412yes—
386C22⋊Dic61—44no—
387#11758202—24no—
388#11758202—24no—
389#11758202—24no—
390#11758202C2×D414yes—
391#11758201—24no—
392#11758201C2×D414yes—
393#11758200—24no—
394#11758200—24no—
395#11758200—24no—
396#11758200C2×D414yes—
397#11758199—24no—
398#11758199C2×D414yes—
399#11758196—44no—
400C4×Dic61—21no—
401C4×Dic61C2412yes—
402#11758194—21no—
403#11758194C2412yes—
404C2×#92418—21no—
405C2×#92418C2×D411yescharacteristic
406C2×#92418C2×D411yescharacteristic
407C2×#92418C2×D412yes—
408C2×#92418C2412yes—
409Dic244—24no—
410Dic244—24no—
411Dic244—24no—
412Dic244—24no—
413Dic244—24no—
414Dic244—24no—
415Dic244C2×D414yes—
416D488C2×D414yes—
417#11758190—24no—
418#11758190—24no—
419#11758190—24no—
420#11758190—24no—
421#11758190C2×D414yes—
422#11758190C2×D414yes—
423#11758189—24no—
424#11758189—24no—
425#11758189—24no—
426C8×D61—24no—
427C8×D61—24no—
428C8×D61—24no—
429C23×C61—21no—
430C23×C61—22no—
431C23×C61—41no—
432C23×C61—41no—
433C23×C61—82no—
434C23×C61H(5,𝔽2)11yescharacteristic
435C22×D61—21no—
436C22×D61—21no—
437C22×D61—21no—
438C22×D61—44no—
439C22×D61—162no—
440Q8×C61—21no—
441Q8×C61—22no—
442Q8×C61—22no—
443Q8×C61—41no—
444Q8×C61—41no—
445Q8×C61C22×D412yes—
446D4×C61—22no—
447D4×C61—22no—
448D4×C61—21no—
449D4×C61—22no—
450D4×C61—22no—
451D4×C61—41no—
452D4×C61—41no—
453D4×C61C22×D412yes—
454C2×C4×C61—21no—
455C2×C4×C61—22no—
456C2×C4×C61—22no—
457C2×C4×C61—22no—
458C2×C4×C61—41no—
459C2×C4×C61—41no—
460C2×C4×C61C22×D411yescharacteristic
461C2×C4×C61C22×D411yescharacteristic
462C2×C4×C61C22×D411yescharacteristic
463C2×C4×C61C22×D411yescharacteristic
464C2×C4×C61H(5,𝔽2)11yescharacteristic
465C2×C4×C61C2511yescharacteristic
466C22⋊D61—22no—
467C22⋊D61—22no—
468C22⋊D61—22no—
469C22⋊D61—22no—
470C22⋊D61—22no—
471C22⋊D61—22no—
472C22⋊D61—44no—
473C22⋊D61—44no—
474C22⋊D61—44no—
475C22⋊D61—44no—
476C2×Dic61—21no—
477C2×Dic61—21no—
478C2×Dic61—21no—
479C2×Dic61—22no—
480C2×Dic61—22no—
481C2×Dic61—22no—
482C2×Dic61—44no—
483C2×Dic61—44no—
484C2×Dic61—44no—
485C2×Dic61—42no—
486C2×Dic61—41no—
487C2×Dic61—41no—
488C2×Dic61—41no—
489C2×Dic61—41no—
490D244—21no—
491D244—21no—
492D244—21no—
493D244—44no—
494D244C22×D412yes—
495D244C22×D412yes—
496D244C22×D412yes—
497C4×D61—22no—
498C4×D61—22no—
499C4×D61—22no—
500C4×D61—22no—
501C4×D61—22no—
502C4×D61—22no—
503C4×D61—44no—
504C4×D61—44no—
505C4×D61—44no—
506C4×D61—44no—
507Dic122—21no—
508Dic122—21no—
509Dic122—21no—
510Dic122—22no—
511Dic122—22no—
512Dic122—22no—
513Dic122—22no—
514Dic122—44no—
515Dic122—44no—
516Dic122—44no—
517Dic122—41no—
518Dic122—41no—
519Dic122—41no—
520Dic122—41no—
521Dic122C22×D412yes—
522Dic122C22×D412yes—
523Dic122C22×D412yes—
524C8×C61—22no—
525C8×C61—22no—
526C8×C61—22no—
527C8×C61C22×D412yes—
528C8×C61C22×D412yes—
529#92418—22no—
530#92418C22×D412yes—
531#92418C22×D412yes—
532C2×#3289—611nomaximal, Sylow
533C22×C61—22no—
534C22×C61—22no—
535C22×C61—42no—
536C22×C61—42no—
537C22×C61—82no—
538C22×C61—82no—
539C22×C61—161no—
540C22×C61D4211yescharacteristic
541C22×C61D4211yescharacteristic
542C22×C61C2×H(5,𝔽2)11yescharacteristic
543C2×D61—22no—
544C2×D61—22no—
545C2×D61—22no—
546C2×D61—42no—
547C2×D61—42no—
548C2×D61—42no—
549C2×D61—164no—
550C4×C61—22no—
551C4×C61—42no—
552C4×C61D4211yescharacteristic
553C4×C61D4211yescharacteristic
554C4×C61C23×D411yescharacteristic
555C4×C61C23×D411yescharacteristic
556Dic61—22no—
557Dic61—22no—
558Dic61—22no—
559Dic61—42no—
560Dic61—42no—
561Dic61—42no—
562C2×#578—611no—
563C2×#578—611no—
564C2×#577—611no—
565C2×#577—611no—
566#3289—6116no—
567C2×#497—611no—
568C2×#473—611no—
569C2×#473—611no—
570C2×#471—611no—
571C2×#471D6111yescharacteristic, complemented
572C2×#456—611no—
573C2×#456—611no—
574C2×#454—611no—
575C2×#455—611no—
576C2×#444—611no—
577C2×#444—611no—
578C2×C61—21no—
579C2×C61—21no—
580C2×C61—42no—
581C2×C61—82no—
582C2×C61#328912yescomplemented
583C2×C61C2×D4211yescharacteristic
584D61—42no—
585D61—42no—
586D61—42no—
587C2×2−1+4—611no—
588C2×2−1+4—611no—
589C2×2−1+4—611no—
590C2×H(5,𝔽2)—611no—
591#578—618no—
592#578—618no—
593#578—1224no—
594#578—1224no—
595#577—618no—
596#577—618no—
597#577—1224no—
598#577—1224no—
599C2×#137—611no—
600C2×#137—611no—
601C2×#137—611no—
602C2×#137—611no—
603C2×#137—611no—
604C2×#137—1221no—
605C2×#137—1221no—
606C2×#137—1221no—
607C2×#137—1221no—
608C2×#137—1221no—
609C2×#137—1221no—
610C2×#137C2×D6111yescharacteristic, complemented
611C2×AGL(1,ℤ/8)—611no—
612C2×AGL(1,ℤ/8)—1221no—
613C2×AGL(1,ℤ/8)—1221no—
614C2×AGL(1,ℤ/8)C2×D6111yescharacteristic
615C2×#135—611no—
616C2×#135—611no—
617C2×#135—1221no—
618C2×#135—1221no—
619C2×#135—1221no—
620C2×#135—1221no—
621C22×Q16—611no—
622C22×Q16—611no—
623C22×Q16—1221no—
624C22×Q16—1221no—
625C22×SD16—611no—
626C22×SD16—1221no—
627C22×SD16—1221no—
628C22×SD16C2×D6111yescharacteristic
629C2×#131—611no—
630C2×#131—611no—
631C2×#131—611no—
632C2×#131C2×D6111yescharacteristic, complemented
633C2×C4⋊Q8—611no—
634C2×#124—611no—
635#497—618no—
636#473—618no—
637#473—618no—
638#471—618no—
639#471C2×D6118yescomplemented
640#456—618no—
641#456—618no—
642#455—618no—
643#454—618no—
644#444—618no—
645#444—618no—
646C2×#108—611no—
647C2×#108C2×D6111yescharacteristic, complemented
648C2×#104—611no—
649C2×#104—611no—
650C2×#104—611no—
651C2×#104—611no—
652C2×#101—611no—
653C2×#101—611no—
654C2×#101C2×D6111yescharacteristic, complemented
655C2×#100C2×D6111yescharacteristic
656C2×#97—611no—
657C61C2×#328911yescharacteristic, complemented, Sylow
6582−1+4—614no—
6592−1+4—614no—
6602−1+4—614no—
6612−1+4—1222no—
6622−1+4—1222no—
6632−1+4—1222no—
6642−1+4—1222no—
6652−1+4—1222no—
6662−1+4—1222no—
6672−1+4—2441no—
6682−1+4—2441no—
6692−1+4—2441no—
670H(5,𝔽2)—614no—
671H(5,𝔽2)—1222no—
672H(5,𝔽2)—1222no—
673H(5,𝔽2)—2441no—
674C2×#41—611no—
675C2×#41—611no—
676C2×#41—611no—
677C2×#41—1221no—
678C2×#41—1221no—
679C2×#41—1221no—
680C2×#41—1221no—
681C2×#41—1221no—
682C2×#41—1221no—
683C2×#41—1221no—
684C2×#41—1221no—
685C2×#41—2441no—
686C2×#41—2441no—
687C2×#41—2441no—
688C2×#41C22×D6111yescharacteristic
689C22×Q8—611no—
690C22×Q8—611no—
691C22×Q8—1221no—
692C22×Q8—1221no—
693C22×Q8—1221no—
694C22×Q8—1221no—
695C22×Q8—1221no—
696C22×Q8—1221no—
697C22×Q8C22×D6111yescharacteristic
698C22×D4—1221no—
699C22×D4—1221no—
700C22×D4—2441no—
701C22×D4C22×D6111yescharacteristic
702#137—22no—
703#137—614no—
704#137—614no—
705#137—614no—
706#137—614no—
707#137—614no—
708#137—1228no—
709#137—1228no—
710#137—1222no—
711#137—1222no—
712#137—1222no—
713#137—1222no—
714#137—1228no—
715#137—1228no—
716#137—1228no—
717#137—1228no—
718#137—1222no—
719#137C22×D6114yescomplemented
720AGL(1,ℤ/8)—22no—
721AGL(1,ℤ/8)—614no—
722AGL(1,ℤ/8)—1228no—
723AGL(1,ℤ/8)—1228no—
724AGL(1,ℤ/8)—1222no—
725AGL(1,ℤ/8)C22×D6114yes—
726#135—614no—
727#135—614no—
728#135—614no—
729#135—614no—
730#135—1228no—
731#135—1228no—
732#135—1228no—
733#135—1228no—
734C2×Q16—21no—
735C2×Q16—611no—
736C2×Q16—614no—
737C2×Q16—611no—
738C2×Q16—614no—
739C2×Q16—1228no—
740C2×Q16—1221no—
741C2×Q16—1221no—
742C2×Q16—1221no—
743C2×Q16—1221no—
744C2×Q16—1221no—
745C2×Q16—1221no—
746C2×Q16—1222no—
747C2×Q16—1228no—
748C2×Q16—1221no—
749C2×Q16—1221no—
750C2×Q16—1221no—
751C2×Q16—1222no—
752C2×SD16—21no—
753C2×SD16—21no—
754C2×SD16—21no—
755C2×SD16—21no—
756C2×SD16—22no—
757C2×SD16—611no—
758C2×SD16—611no—
759C2×SD16—614no—
760C2×SD16—611no—
761C2×SD16—611no—
762C2×SD16—1221no—
763C2×SD16—1221no—
764C2×SD16—1221no—
765C2×SD16—1221no—
766C2×SD16—1221no—
767C2×SD16—1221no—
768C2×SD16—1222no—
769C2×SD16—1228no—
770C2×SD16—1228no—
771C2×SD16—1221no—
772C2×SD16—1221no—
773C2×SD16C22×D6114yes—
774C2×D8—21no—
775C2×D8—611no—
776C2×D8—611no—
777C2×D8—1221no—
778#131—22no—
779#131—614no—
780#131—614no—
781#131—614no—
782#131—1222no—
783#131—1222no—
784#131—1222no—
785#131C22×D6114yescomplemented
786C2×M16—21no—
787C2×M16—611no—
788C2×M16—1221no—
789C2×M16—1221no—
790C2×M16—1221no—
791C2×M16C22×D6111yescharacteristic
792C2×M16C22×D6111yescharacteristic
793C2×M16C22×D6111yescharacteristic
794C22×C8—21no—
795C22×C8—611no—
796C22×C8—1221no—
797C22×C8—1221no—
798C22×C8—1221no—
799C22×C8C22×D6111yescharacteristic
800C4⋊Q8—614no—
801C4⋊Q8—2441no—
802#124—614no—
803#124—2441no—
804C2×C4⋊C4—2441no—
805C2×C22⋊C4—2441no—
806C2×C42—611no—
807#108—614no—
808#108C22×D6114yescomplemented
809#104—614no—
810#104—614no—
811#104—614no—
812#104—614no—
813#101—614no—
814#101—614no—
815#101C22×D6114yescomplemented
816#100C22×D6114yes—
817#97—614no—
818C24—21no—
819C24—2441no—
820#41—21no—
821#41—21no—
822#41—612no—
823#41—612no—
824#41—612no—
825#41—612no—
826#41—612no—
827#41—612no—
828#41—1224no—
829#41—1224no—
830#41—1221no—
831#41—1221no—
832#41—1221no—
833#41—1221no—
834#41—1221no—
835#41—1221no—
836#41—1224no—
837#41—1224no—
838#41—1224no—
839#41—1224no—
840#41—1224no—
841#41—1224no—
842#41—2444no—
843#41—2442no—
844#41—2442no—
845#41—2444no—
846#41—2444no—
847#41—2444no—
848#41—2442no—
849#41—2442no—
850#41—2442no—
851#41—2442no—
852#41—2442no—
853#41—2442no—
854#41—2444no—
855#41—2444no—
856#41D4×D6112yes—
857#41C23×D6112yes—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—611no—
864C2×Q8—611no—
865C2×Q8—611no—
866C2×Q8—612no—
867C2×Q8—612no—
868C2×Q8—1224no—
869C2×Q8—1224no—
870C2×Q8—1221no—
871C2×Q8—1221no—
872C2×Q8—1224no—
873C2×Q8—1224no—
874C2×Q8—1224no—
875C2×Q8—1224no—
876C2×Q8—1221no—
877C2×Q8—1221no—
878C2×Q8—1221no—
879C2×Q8—1221no—
880C2×Q8—1221no—
881C2×Q8—1221no—
882C2×Q8—1221no—
883C2×Q8—1221no—
884C2×Q8—2441no—
885C2×Q8—2441no—
886C2×Q8—2442no—
887C2×Q8—2442no—
888C2×Q8—2441no—
889C2×Q8—2442no—
890C2×Q8—2442no—
891C2×Q8—2442no—
892C2×Q8—2442no—
893C2×Q8D4×D6111yescharacteristic
894C2×Q8C23×D6112yes—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—21no—
898C2×D4—21no—
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—611no—
902C2×D4—611no—
903C2×D4—611no—
904C2×D4—1224no—
905C2×D4—1224no—
906C2×D4—1221no—
907C2×D4—1221no—
908C2×D4—1221no—
909C2×D4—2441no—
910C2×D4—2442no—
911C2×D4—2442no—
912C2×D4—2441no—
913C2×D4—2441no—
914C2×D4—2444no—
915C2×D4—2444no—
916C2×D4—2441no—
917C2×D4—2441no—
918C2×D4D4×D6111yescharacteristic
919C2×D4C23×D6112yes—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—1221no—
923C22×C4—1221no—
924C22×C4—1221no—
925C22×C4—1221no—
926C22×C4—1221no—
927C22×C4—1221no—
928C22×C4—2441no—
929C22×C4—2441no—
930C22×C4—2441no—
931C22×C4—2441no—
932C22×C4—2441no—
933C22×C4—2441no—
934C22×C4—2441no—
935C22×C4C23×D6111yescharacteristic
936Q16—24no—
937Q16—614no—
938Q16—614no—
939Q16—1224no—
940Q16—1224no—
941Q16—1224no—
942Q16—1224no—
943Q16—1224no—
944Q16—1224no—
945Q16—1224no—
946Q16—1224no—
947Q16—1224no—
948SD16—24no—
949SD16—24no—
950SD16—24no—
951SD16—24no—
952SD16—614no—
953SD16—614no—
954SD16—614no—
955SD16—614no—
956SD16—1224no—
957SD16—1224no—
958SD16—1224no—
959SD16—1224no—
960SD16—1224no—
961SD16—1224no—
962SD16—1224no—
963SD16—1224no—
964D8—24no—
965D8—614no—
966D8—614no—
967D8—1224no—
968M16—21no—
969M16—21no—
970M16—21no—
971M16—24no—
972M16—612no—
973M16—1224no—
974M16—1224no—
975M16—1221no—
976M16—1224no—
977M16C23×D6112yes—
978M16C23×D6112yes—
979M16C23×D6112yes—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—24no—
984C2×C8—611no—
985C2×C8—611no—
986C2×C8—612no—
987C2×C8—612no—
988C2×C8—1224no—
989C2×C8—1224no—
990C2×C8—1221no—
991C2×C8—1224no—
992C2×C8D4×D6111yescharacteristic
993C2×C8D4×D6111yescharacteristic
994C2×C8D4×D6112yes—
995C2×C8C23×D6112yes—
996C4⋊C4—2444no—
997C22⋊C4—2444no—
998C42—612no—
999C42—1221no—
1000C23—21no—
1001C23—22no—
1002C23—41no—
1003C23—41no—
1004C23—82no—
1005C23—1221no—
1006C23—1221no—
1007C23—1221no—
1008C23—9762no—
1009C23—2444no—
1010C23#1451982311yescharacteristic
1011Q8—21no—
1012Q8—22no—
1013Q8—22no—
1014Q8—41no—
1015Q8—41no—
1016Q8—612no—
1017Q8—612no—
1018Q8—612no—
1019Q8—1221no—
1020Q8—1221no—
1021Q8—1221no—
1022Q8—1222no—
1023Q8—1222no—
1024Q8—1222no—
1025Q8—1222no—
1026Q8—2444no—
1027Q8—2444no—
1028Q8—2444no—
1029Q8—2441no—
1030Q8—2441no—
1031Q8—2441no—
1032Q8—2441no—
1033Q8C2×D4×D6112yes—
1034D4—22no—
1035D4—22no—
1036D4—22no—
1037D4—22no—
1038D4—21no—
1039D4—41no—
1040D4—41no—
1041D4—612no—
1042D4—612no—
1043D4—612no—
1044D4—1222no—
1045D4—1222no—
1046D4—1222no—
1047D4—1222no—
1048D4—1222no—
1049D4—1222no—
1050D4—1221no—
1051D4—1221no—
1052D4—1221no—
1053D4—2444no—
1054D4—2444no—
1055D4—2444no—
1056D4—2444no—
1057D4—2444no—
1058D4C2×D4×D6112yes—
1059C2×C4—21no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—1221no—
1066C2×C4—1221no—
1067C2×C4—1221no—
1068C2×C4—1222no—
1069C2×C4—1222no—
1070C2×C4—1222no—
1071C2×C4—1222no—
1072C2×C4—1222no—
1073C2×C4—1222no—
1074C2×C4—1222no—
1075C2×C4—1222no—
1076C2×C4—1222no—
1077C2×C4—2444no—
1078C2×C4—2444no—
1079C2×C4—2444no—
1080C2×C4—2444no—
1081C2×C4—2444no—
1082C2×C4—2444no—
1083C2×C4—2444no—
1084C2×C4—2442no—
1085C2×C4—2441no—
1086C2×C4—2441no—
1087C2×C4—2441no—
1088C2×C4—2441no—
1089C2×C4C2×D4×D6111yescharacteristic
1090C2×C4C2×D4×D6111yescharacteristic
1091C2×C4C2×D4×D6111yescharacteristic
1092C2×C4C2×D4×D6111yescharacteristic
1093C2×C4#1451982311yescharacteristic
1094C2×C4C24×D6111yescharacteristic
1095C8—22no—
1096C8—22no—
1097C8—22no—
1098C8—612no—
1099C8—612no—
1100C8—1222no—
1101C8C2×D4×D6112yes—
1102C8C2×D4×D6112yes—
1103C22—22no—
1104C22—22no—
1105C22—42no—
1106C22—42no—
1107C22—82no—
1108C22—82no—
1109C22—161no—
1110C22—1222no—
1111C22—1222no—
1112C22—1222no—
1113C22—9764no—
1114C22—2442no—
1115C22—2442no—
1116C22—2442no—
1117C22#1684039611yescharacteristic
1118C22#1684039611yescharacteristic
1119C22C2×#1451982311yescharacteristic
1120C4—22no—
1121C4—42no—
1122C4—1222no—
1123C4—1222no—
1124C4—1222no—
1125C4—2442no—
1126C4—2442no—
1127C4—2442no—
1128C4#1684039611yescharacteristic
1129C4#1684039611yescharacteristic
1130C4C22×D4×D6111yescharacteristic
1131C4C22×D4×D6111yescharacteristic
1132C2—21no—
1133C2—21no—
1134C2—42no—
1135C2—82no—
1136C2—2442no—
1137C2—2442no—
1138C2—2442no—
1139C2#2145759112yesdirect product factor
1140C2C2×#1684039611yescharacteristic
subgroupG/H
centerC22#16840396
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#471C2
socleC22×C61D42
hypercenterC2×#471D61
hypocenterC61C2×#3289
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#471

Complements

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

NH ≅ G/Ntype
1. C2×#16840579C2semidirect
2. C2×#16840578C2semidirect
3. C2×#16840572C2semidirect
4. C2×#16840568C2semidirect
5. #21457591C2direct (N × H)
6. C2×#16840153C2semidirect
7. C2×#16840038C2semidirect
8. C2×#16840036C2semidirect
9. C2×#16840024C2semidirect
10. C2×#16839947C2semidirect
11. C2×#16839943C2semidirect
12. C2×#16839933C2semidirect
13. C2×#16839942C2semidirect
14. C2×#16839883C2semidirect
15. C2×#16839882C2semidirect
16. C2×C61×#471C2semidirect
19. C2×#14519824C22semidirect
22. #16840579C22semidirect
24. #16840578C22semidirect
26. #16840572C22semidirect
28. #16840568C22semidirect
34. C2×#14519810C22semidirect
50. C22×Dic244C22semidirect
51. C22×#11758202C22semidirect
57. C2×#14519785C22semidirect
59. C2×#14519775C22semidirect
61. #16840153C22semidirect
62. #16840038C22semidirect
63. #16840036C22semidirect
64. #16840024C22semidirect
65. #16839947C22semidirect
66. #16839943C22semidirect
67. #16839942C22semidirect
68. #16839933C22semidirect
69. #16839883C22semidirect
70. #16839882C22semidirect
71. C2×#14519712C22semidirect
72. C2×#14519704C22semidirect
75. C2×#14519703C22semidirect
76. C2×#14519695C22semidirect
77. C2×#14519695C22semidirect
78. C2×#14519687C22semidirect
79. C2×#137×C61C22semidirect
82. C2×#131×C61C22semidirect
83. C61×#471C22semidirect
84. C2×#108×C61C22semidirect
85. C2×#101×C61C22semidirect
98. #14519824C23semidirect
137. #14519810C23semidirect
165. C2×Dic244C23semidirect
171. C2×#11758202C23semidirect
195. #14519785C23semidirect
207. #14519775C23semidirect
213. #14519712C23semidirect
214. #14519704C23semidirect
217. #14519703C23semidirect
218. #14519695C23semidirect
219. #14519695C23semidirect
220. #14519687C23semidirect
225. #137×C61C23semidirect
237. #131×C61C23semidirect
244. #108×C61C23semidirect
245. #101×C61C23semidirect
571. C2×#471D61semidirect
582. C2×C61#3289semidirect
610. C2×#137C2×D61semidirect
632. C2×#131C2×D61semidirect
639. #471C2×D61semidirect
647. C2×#108C2×D61semidirect
654. C2×#101C2×D61semidirect
657. C61C2×#3289semidirect
719. #137C22×D61semidirect
785. #131C22×D61semidirect
808. #108C22×D61semidirect
815. #101C22×D61semidirect
1139. C2#21457591direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168405792
C2×#168405782
C2×#168405722
C2×#168405682
#214575912
C2×#168401532
C2×#168400382
C2×#168400362
C2×#168400242
C2×#168399472
C2×#168399432
C2×#168399332
C2×#168399422
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