Finite Group Databasebeta

← C2×#21457611 #30556230

Subgroups — C2×#21457611 #30556230

Order 15616.

2682 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840574C211yesmaximal, characteristic, complemented
2C2×#16840572C211yesmaximal, characteristic, complemented
3C2×#16840571C211yesmaximal, characteristic, complemented
4C2×#16840568C211yesmaximal, characteristic, complemented
5#21457611C2116yesmaximal, direct product factor
6C2×#16840133C211yesmaximal, characteristic, complemented
7C2×#16840028C211yesmaximal, characteristic, complemented
8C2×#16840026C211yesmaximal, characteristic, complemented
9C2×#16840024C211yesmaximal, characteristic, complemented
10C2×#16839947C211yesmaximal, characteristic, complemented
11C2×#16839943C211yesmaximal, characteristic, complemented
12C2×#16839932C211yesmaximal, characteristic, complemented
13C2×#16839928C211yesmaximal, characteristic, complemented
14C2×#16839878C211yesmaximal, characteristic, complemented
15C2×#16839877C211yesmaximal, characteristic, complemented
16C2×C61×#471C211yesmaximal, characteristic, complemented
17C2×#14519825C2211yescharacteristic
18C2×#14519824C2211yescharacteristic
19C2×#14519823C2211yescharacteristic, complemented
20C2×#14519822C2211yescharacteristic, complemented
21#16840574—24no—
22#16840574C2218yescomplemented
23#16840572—24no—
24#16840572C2218yescomplemented
25#16840571—24no—
26#16840571C2218yescomplemented
27#16840568—24no—
28#16840568C2218yescomplemented
29C2×#14519810—21no—
30C2×#14519810C2211yescharacteristic, complemented
31C2×#14519810C2211yescharacteristic, complemented
32C2×#14519809—21no—
33C2×#14519808C2211yescharacteristic, complemented
34C2×#14519806—21no—
35C2×#14519806—21no—
36C2×#14519805—21no—
37C2×#14519805C2211yescharacteristic
38C2×#14519805C2211yescharacteristic
39C2×#14519804—21no—
40C2×#14519804—21no—
41C2×#14519803C2211yescharacteristic
42C2×#14519801—21no—
43C2×#14519800—21no—
44C2×#14519799—21no—
45C2×#14519799C2211yescharacteristic
46C2×#14519798—21no—
47C2×#14519797C2211yescharacteristic
48C2×#14519796—21no—
49C22×#11758190—21no—
50C22×#11758190C2211yescharacteristic, complemented
51C22×#11758200C2211yescharacteristic, complemented
52C22×#11758201C2211yescharacteristic, complemented
53C2×SD16×D61—21no—
54C2×SD16×D61—21no—
55C2×SD16×D61—21no—
56C2×#14519785C2211yescharacteristic, complemented
57C2×#14519785C2211yescharacteristic, complemented
58C2×#14519783C2211yescharacteristic, complemented
59C2×#14519775C2211yescharacteristic, complemented
60C2×#14519773C2211yescharacteristic
61#16840133C2218yescomplemented
62#16840028C2218yescomplemented
63#16840026C2218yescomplemented
64#16840024C2218yescomplemented
65#16839947C2218yescomplemented
66#16839943C2218yescomplemented
67#16839932C2218yescomplemented
68#16839928C2218yescomplemented
69#16839878C2218yescomplemented
70#16839877C2218yescomplemented
71C2×#14519712C2211yescharacteristic, complemented
72C2×#14519704C2211yescharacteristic, complemented
73C2×#14519703C2211yescharacteristic, complemented
74C2×#14519703C2211yescharacteristic, complemented
75C2×#14519703C2211yescharacteristic, complemented
76C2×#14519695C2211yescharacteristic, complemented
77C2×#14519693C2211yescharacteristic, complemented
78C2×C8×Dic61C2211yescharacteristic, complemented
79C2×#137×C61C2211yescharacteristic, complemented
80C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
81C22×SD16×C61C2211yescharacteristic, complemented
82C2×#131×C61C2211yescharacteristic, complemented
83C61×#471C2218yescomplemented
84C2×#108×C61C2211yescharacteristic, complemented
85C2×#101×C61C2211yescharacteristic, complemented
86C2×#100×C61C2211yescharacteristic, complemented
87#14519825—22no—
88#14519825—22no—
89#14519825—41no—
90#14519825C2314yes—
91#14519824—22no—
92#14519824—22no—
93#14519824—41no—
94#14519824C2314yes—
95#14519823—22no—
96#14519823—22no—
97#14519823—41no—
98#14519823C2314yescomplemented
99#14519822—22no—
100#14519822—22no—
101#14519822—41no—
102#14519822C2314yescomplemented
103C2×#11758226—21no—
104C2×#11758226—21no—
105C2×#11758226—21no—
106C2×#11758222—21no—
107C2×#11758222—21no—
108C2×#11758222—41no—
109C2×#11758222C2311yescharacteristic
110C2×#11758222C2311yescharacteristic
111C2×#11758222C2311yescharacteristic
112C2×#11758224—21no—
113C2×#11758224—21no—
114C2×#11758224—21no—
115C2×#11758224—41no—
116C22×Dic122—21no—
117C22×Dic122C2311yescharacteristic
118C2×Q8×D61—21no—
119C2×Q8×D61—21no—
120C2×Q8×D61—21no—
121C22×D244—21no—
122C22×D244C2311yescharacteristic
123C22×C22⋊D61—41no—
124C22×C22⋊D61—41no—
125C2×D4×D61—21no—
126C2×D4×D61—21no—
127C2×D4×D61—21no—
128C2×D4×D61—41no—
129#14519810—22no—
130#14519810—22no—
131#14519810—28no—
132#14519810C2314yescomplemented
133#14519810C2314yescomplemented
134#14519809—28no—
135#14519808—22no—
136#14519808C2314yescomplemented
137#14519806—28no—
138#14519806—28no—
139#14519805—22no—
140#14519805—22no—
141#14519805—28no—
142#14519805C2314yes—
143#14519805C2314yes—
144#14519804—28no—
145#14519804—28no—
146#14519803—22no—
147#14519803C2314yes—
148#14519801—28no—
149#14519800—28no—
150#14519799—28no—
151#14519799D414yescomplemented
152#14519799C2314yes—
153#14519798—28no—
154#14519797D414yescomplemented
155#14519797C2314yes—
156#14519796—28no—
157C2×Dic244—21no—
158C2×Dic244—21no—
159C2×Dic244D411yescharacteristic, complemented
160C2×#11758202—21no—
161C2×#11758202D411yescharacteristic, complemented
162C2×#11758190—21no—
163C2×#11758190—21no—
164C2×#11758190—21no—
165C2×#11758190—21no—
166C2×#11758190—21no—
167C2×#11758190—21no—
168C2×#11758190—22no—
169C2×#11758190—28no—
170C2×#11758190D411yescharacteristic, complemented
171C2×#11758190D411yescharacteristic, complemented
172C2×#11758190C2314yescomplemented
173C2×#11758200—21no—
174C2×#11758200—21no—
175C2×#11758200—21no—
176C2×#11758200—22no—
177C2×#11758200D411yescharacteristic, complemented
178C2×#11758200C2314yescomplemented
179C2×#11758201—21no—
180C2×#11758201—21no—
181C2×#11758201—21no—
182C2×#11758201—22no—
183C2×#11758201D411yescharacteristic, complemented
184C2×#11758201C2314yescomplemented
185SD16×D61—28no—
186SD16×D61—28no—
187SD16×D61—28no—
188C2×D488—21no—
189C2×D488—21no—
190C2×D488D411yescharacteristic, complemented
191C2×#11758199—21no—
192C2×#11758199D411yescharacteristic, complemented
193#14519785—22no—
194#14519785—22no—
195#14519785C2314yescomplemented
196#14519785C2314yescomplemented
197#14519783—22no—
198#14519783C2314yescomplemented
199C2×#11758194C2311yescharacteristic
200C2×#11758189—21no—
201C2×#11758189—21no—
202C2×#11758189—21no—
203C22×#92418C2311yescharacteristic
204C2×C8×D61—21no—
205C2×C8×D61—21no—
206C2×C8×D61—21no—
207#14519775—41no—
208#14519775C2314yescomplemented
209#14519773—41no—
210#14519773C2314yes—
211C2×#11758196—41no—
212C2×C4×Dic61C2311yescharacteristic
213#14519712C2314yescomplemented
214#14519704C2314yescomplemented
215#14519703C2314yescomplemented
216#14519703C2314yescomplemented
217#14519703C2314yescomplemented
218#14519695C2314yescomplemented
219#14519693C2314yescomplemented
220C8×Dic61C2314yescomplemented
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×C61C2314yescomplemented
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×C61C2314yescomplemented
247C24×C61—21no—
248C23×D61—21no—
249C23×D61—41no—
250C23×D61—41no—
251#41×C61—21no—
252#41×C61—21no—
253#41×C61C2×D412yes—
254#41×C61C2412yes—
255C2×Q8×C61—21no—
256C2×Q8×C61—21no—
257C2×Q8×C61—21no—
258C2×Q8×C61—21no—
259C2×Q8×C61—21no—
260C2×Q8×C61C2×D411yescharacteristic
261C2×Q8×C61C2412yes—
262C2×D4×C61—21no—
263C2×D4×C61—21no—
264C2×D4×C61—21no—
265C2×D4×C61—21no—
266C2×D4×C61—21no—
267C2×D4×C61—21no—
268C2×D4×C61C2×D411yescharacteristic
269C2×D4×C61C2412yes—
270C22×C4×C61—21no—
271C22×C4×C61—21no—
272C22×C4×C61C2411yescharacteristic
273C2×C22⋊D61—21no—
274C2×C22⋊D61—21no—
275C2×C22⋊D61—21no—
276C2×C22⋊D61—41no—
277C2×C22⋊D61—41no—
278C2×C22⋊D61—41no—
279C2×C22⋊D61—44no—
280C2×C22⋊D61—44no—
281C2×C22⋊D61—44no—
282C2×C22⋊D61—41no—
283C2×C22⋊D61—84no—
284C22×Dic61—21no—
285C22×Dic61—21no—
286C22×Dic61—41no—
287C22×Dic61—41no—
288#11758226—24no—
289#11758226—24no—
290#11758226—24no—
291#11758226—42no—
292#11758226—42no—
293#11758226—42no—
294Q8×D61—24no—
295Q8×D61—24no—
296Q8×D61—24no—
297Q8×D61—42no—
298Q8×D61—42no—
299Q8×D61—42no—
300#11758224—24no—
301#11758224—24no—
302#11758224—24no—
303#11758224—42no—
304#11758224—42no—
305#11758224—42no—
306#11758224—44no—
307#11758224—44no—
308D4×D61—24no—
309D4×D61—24no—
310D4×D61—24no—
311D4×D61—42no—
312D4×D61—42no—
313D4×D61—42no—
314D4×D61—44no—
315D4×D61—44no—
316#11758222—21no—
317#11758222—21no—
318#11758222—21no—
319#11758222—21no—
320#11758222—21no—
321#11758222—21no—
322#11758222—24no—
323#11758222—24no—
324#11758222—42no—
325#11758222—42no—
326#11758222—44no—
327#11758222—44no—
328#11758222C2×D412yes—
329#11758222C2×D412yes—
330#11758222C2×D412yes—
331#11758222C2412yes—
332#11758222C2412yes—
333#11758222C2412yes—
334C2×D244—21no—
335C2×D244—21no—
336C2×D244—21no—
337C2×D244—21no—
338C2×D244—24no—
339C2×D244—21no—
340C2×D244—42no—
341C2×D244—41no—
342C2×D244—41no—
343C2×D244C2×D411yescharacteristic
344C2×D244C2×D411yescharacteristic
345C2×D244C2×D411yescharacteristic
346C2×D244C2412yes—
347C2×C4×D61—21no—
348C2×C4×D61—21no—
349C2×C4×D61—21no—
350C2×C4×D61—41no—
351C2×C4×D61—41no—
352C2×C4×D61—41no—
353C2×C4×D61—41no—
354C2×Dic122—21no—
355C2×Dic122—21no—
356C2×Dic122—21no—
357C2×Dic122—21no—
358C2×Dic122—24no—
359C2×Dic122—21no—
360C2×Dic122—42no—
361C2×Dic122—41no—
362C2×Dic122—41no—
363C2×Dic122C2×D411yescharacteristic
364C2×Dic122C2×D411yescharacteristic
365C2×Dic122C2×D411yescharacteristic
366C2×Dic122C2412yes—
367Q16×C61—24no—
368SD16×C61—24no—
369SD16×C61—24no—
370SD16×C61—24no—
371SD16×C61—24no—
372D8×C61—24no—
373M16×C61—21no—
374M16×C61—21no—
375M16×C61—21no—
376M16×C61—24no—
377M16×C61C2412yes—
378M16×C61C2412yes—
379M16×C61C2412yes—
380C2×C8×C61—21no—
381C2×C8×C61—21no—
382C2×C8×C61—21no—
383C2×C8×C61—24no—
384C2×C8×C61C2×D411yescharacteristic
385C2×C8×C61C2×D411yescharacteristic
386C2×C8×C61C2×D412yes—
387C2×C8×C61C2412yes—
388#11758202—24no—
389#11758202C2×D414yescomplemented
390#11758201—24no—
391#11758201—24no—
392#11758201—24no—
393#11758201C2×D414yescomplemented
394#11758200—24no—
395#11758200—24no—
396#11758200—24no—
397#11758200C2×D414yescomplemented
398#11758199—24no—
399#11758199C2×D414yescomplemented
400#11758196—44no—
401C4×Dic61—21no—
402C4×Dic61C2412yes—
403#11758194—21no—
404#11758194C2412yes—
405C2×#92418—21no—
406C2×#92418C2×D411yescharacteristic
407C2×#92418C2×D411yescharacteristic
408C2×#92418C2×D412yes—
409C2×#92418C2412yes—
410Dic244—24no—
411Dic244—24no—
412Dic244C2×D414yescomplemented
413D488—24no—
414D488—24no—
415D488C2×D414yescomplemented
416#11758190—24no—
417#11758190—24no—
418#11758190—24no—
419#11758190—24no—
420#11758190—24no—
421#11758190—24no—
422#11758190C2×D414yescomplemented
423#11758190C2×D414yescomplemented
424#11758189—24no—
425#11758189—24no—
426#11758189—24no—
427C8×D61—24no—
428C8×D61—24no—
429C8×D61—24no—
430C23×C61—21no—
431C23×C61—22no—
432C23×C61—41no—
433C23×C61—41no—
434C23×C61—82no—
435C23×C61H(5,𝔽2)11yescharacteristic
436C22×D61—21no—
437C22×D61—21no—
438C22×D61—21no—
439C22×D61—22no—
440C22×D61—44no—
441C22×D61—44no—
442C22×D61—41no—
443C22×D61—41no—
444C22×D61—82no—
445C22×D61—162no—
446C22×D61—162no—
447Q8×C61—21no—
448Q8×C61—22no—
449Q8×C61—22no—
450Q8×C61—41no—
451Q8×C61—41no—
452Q8×C61C22×D412yes—
453D4×C61—22no—
454D4×C61—22no—
455D4×C61—21no—
456D4×C61—22no—
457D4×C61—22no—
458D4×C61—41no—
459D4×C61—41no—
460D4×C61C22×D412yes—
461C2×C4×C61—21no—
462C2×C4×C61—22no—
463C2×C4×C61—22no—
464C2×C4×C61—22no—
465C2×C4×C61—41no—
466C2×C4×C61—41no—
467C2×C4×C61C22×D411yescharacteristic
468C2×C4×C61C22×D411yescharacteristic
469C2×C4×C61C22×D411yescharacteristic
470C2×C4×C61C22×D411yescharacteristic
471C2×C4×C61H(5,𝔽2)11yescharacteristic
472C2×C4×C61C2511yescharacteristic
473C22⋊D61—22no—
474C22⋊D61—22no—
475C22⋊D61—22no—
476C22⋊D61—22no—
477C22⋊D61—22no—
478C22⋊D61—22no—
479C22⋊D61—44no—
480C22⋊D61—44no—
481C22⋊D61—44no—
482C22⋊D61—44no—
483C22⋊D61—88no—
484C2×Dic61—24no—
485C2×Dic61—21no—
486C2×Dic61—21no—
487C2×Dic61—21no—
488C2×Dic61—22no—
489C2×Dic61—22no—
490C2×Dic61—44no—
491C2×Dic61—44no—
492C2×Dic61—41no—
493C2×Dic61—41no—
494D244—21no—
495D244—21no—
496D244—21no—
497D244—22no—
498D244—22no—
499D244—44no—
500D244—44no—
501D244—41no—
502D244—41no—
503D244C22×D412yes—
504D244C22×D412yes—
505D244C22×D412yes—
506C4×D61—22no—
507C4×D61—22no—
508C4×D61—22no—
509C4×D61—22no—
510C4×D61—22no—
511C4×D61—22no—
512C4×D61—44no—
513C4×D61—44no—
514C4×D61—44no—
515C4×D61—44no—
516Dic122—21no—
517Dic122—21no—
518Dic122—21no—
519Dic122—22no—
520Dic122—22no—
521Dic122—44no—
522Dic122—44no—
523Dic122—41no—
524Dic122—41no—
525Dic122C22×D412yes—
526Dic122C22×D412yes—
527Dic122C22×D412yes—
528C8×C61—22no—
529C8×C61—22no—
530C8×C61—22no—
531C8×C61C22×D412yes—
532C8×C61C22×D412yes—
533#92418—22no—
534#92418C22×D412yes—
535#92418C22×D412yes—
536C2×#3291—611nomaximal, Sylow
537C22×C61—22no—
538C22×C61—22no—
539C22×C61—42no—
540C22×C61—42no—
541C22×C61—82no—
542C22×C61—82no—
543C22×C61—161no—
544C22×C61D4211yescharacteristic
545C22×C61D4211yescharacteristic
546C22×C61C2×H(5,𝔽2)11yescharacteristic
547C2×D61—22no—
548C2×D61—22no—
549C2×D61—22no—
550C2×D61—42no—
551C2×D61—42no—
552C2×D61—42no—
553C2×D61—42no—
554C2×D61—82no—
555C2×D61—82no—
556C2×D61—164no—
557C2×D61—164no—
558C2×D61—161no—
559C4×C61—22no—
560C4×C61—42no—
561C4×C61D4211yescharacteristic
562C4×C61D4211yescharacteristic
563C4×C61C23×D411yescharacteristic
564C4×C61C23×D411yescharacteristic
565Dic61—24no—
566Dic61—22no—
567Dic61—22no—
568Dic61—22no—
569Dic61—42no—
570C2×#577—611no—
571C2×#577—611no—
572C2×#577—611no—
573C2×#577—611no—
574#3291—6116no—
575C2×#492—611no—
576C2×#471—611no—
577C2×#471—611no—
578C2×#471—611no—
579C2×#471D6111yescharacteristic, complemented
580C2×#456—611no—
581C2×#456—611no—
582C2×#453—611no—
583C2×#453—611no—
584C2×#443—611no—
585C2×#443—611no—
586C2×C61—21no—
587C2×C61—21no—
588C2×C61—42no—
589C2×C61—82no—
590C2×C61#329112yescomplemented
591C2×C61C2×D4211yescharacteristic
592D61—42no—
593D61—42no—
594D61—42no—
595D61—82no—
596C2×2−1+4—611no—
597C2×2−1+4—611no—
598C2×H(5,𝔽2)—611no—
599C2×H(5,𝔽2)—611no—
600#577—618no—
601#577—618no—
602#577—618no—
603#577—618no—
604#577—1224no—
605#577—1224no—
606#577—1224no—
607#577—1224no—
608C2×#137—611no—
609C2×#137—611no—
610C2×#137—611no—
611C2×#137—1221no—
612C2×#137—1221no—
613C2×#137—1221no—
614C2×#137—1221no—
615C2×#137C2×D6111yescharacteristic, complemented
616C2×AGL(1,ℤ/8)—611no—
617C2×AGL(1,ℤ/8)—611no—
618C2×AGL(1,ℤ/8)—611no—
619C2×AGL(1,ℤ/8)—1221no—
620C2×AGL(1,ℤ/8)—1221no—
621C2×AGL(1,ℤ/8)—1221no—
622C2×AGL(1,ℤ/8)—1221no—
623C2×AGL(1,ℤ/8)C2×D6111yescharacteristic
624C2×#135—611no—
625C2×#135—611no—
626C2×#135—1221no—
627C2×#135—1221no—
628C2×#135—1221no—
629C2×#135—1221no—
630C22×SD16—611no—
631C22×SD16—611no—
632C22×SD16—611no—
633C22×SD16—1221no—
634C22×SD16—1221no—
635C22×SD16—1221no—
636C22×SD16—1221no—
637C22×SD16C2×D6111yescharacteristic, complemented
638C2×#131—611no—
639C2×#131—611no—
640C2×#131—611no—
641C2×#131C2×D6111yescharacteristic, complemented
642C2×C4⋊Q8—611no—
643C2×#127—611no—
644#492—618no—
645#471—618no—
646#471—618no—
647#471—618no—
648#471C2×D6118yescomplemented
649#456—618no—
650#456—618no—
651#453—618no—
652#453—618no—
653#443—618no—
654#443—618no—
655C2×#108—611no—
656C2×#108C2×D6111yescharacteristic, complemented
657C2×#104—611no—
658C2×#104—611no—
659C2×#104—611no—
660C2×#104—611no—
661C2×#101—611no—
662C2×#101C2×D6111yescharacteristic, complemented
663C2×#100—611no—
664C2×#100C2×D6111yescharacteristic, complemented
665C2×C4×C8—611no—
666C61C2×#329111yescharacteristic, complemented, Sylow
6672−1+4—614no—
6682−1+4—614no—
6692−1+4—1222no—
6702−1+4—1222no—
6712−1+4—1222no—
6722−1+4—1222no—
6732−1+4—2441no—
6742−1+4—2441no—
675H(5,𝔽2)—614no—
676H(5,𝔽2)—614no—
677H(5,𝔽2)—1222no—
678H(5,𝔽2)—1222no—
679H(5,𝔽2)—1222no—
680H(5,𝔽2)—1222no—
681H(5,𝔽2)—2441no—
682H(5,𝔽2)—2441no—
683C2×#41—611no—
684C2×#41—611no—
685C2×#41—611no—
686C2×#41—1221no—
687C2×#41—1221no—
688C2×#41—1221no—
689C2×#41—1221no—
690C2×#41—1221no—
691C2×#41—1221no—
692C2×#41—1221no—
693C2×#41—1221no—
694C2×#41—2441no—
695C2×#41—2441no—
696C2×#41C22×D6111yescharacteristic
697C22×Q8—611no—
698C22×Q8—1221no—
699C22×Q8—1221no—
700C22×Q8—1221no—
701C22×Q8—1221no—
702C22×Q8C22×D6111yescharacteristic
703C22×D4—611no—
704C22×D4—1221no—
705C22×D4—1221no—
706C22×D4—1221no—
707C22×D4—1221no—
708C22×D4—2441no—
709C22×D4—2441no—
710C22×D4—2441no—
711C22×D4C22×D6111yescharacteristic
712#137—22no—
713#137—614no—
714#137—614no—
715#137—614no—
716#137—1228no—
717#137—1222no—
718#137—1222no—
719#137—1228no—
720#137—1228no—
721#137—1228no—
722#137—1222no—
723#137C22×D6114yescomplemented
724AGL(1,ℤ/8)—22no—
725AGL(1,ℤ/8)—614no—
726AGL(1,ℤ/8)—614no—
727AGL(1,ℤ/8)—614no—
728AGL(1,ℤ/8)—1228no—
729AGL(1,ℤ/8)—1222no—
730AGL(1,ℤ/8)—1222no—
731AGL(1,ℤ/8)—1228no—
732AGL(1,ℤ/8)—1228no—
733AGL(1,ℤ/8)—1228no—
734AGL(1,ℤ/8)—1222no—
735AGL(1,ℤ/8)C22×D6114yes—
736#135—614no—
737#135—614no—
738#135—614no—
739#135—614no—
740#135—1228no—
741#135—1228no—
742#135—1228no—
743#135—1228no—
744C2×Q16—21no—
745C2×Q16—611no—
746C2×Q16—611no—
747C2×Q16—1221no—
748C2×Q16—1221no—
749C2×Q16—1221no—
750C2×SD16—21no—
751C2×SD16—21no—
752C2×SD16—21no—
753C2×SD16—21no—
754C2×SD16—22no—
755C2×SD16—611no—
756C2×SD16—611no—
757C2×SD16—614no—
758C2×SD16—614no—
759C2×SD16—611no—
760C2×SD16—611no—
761C2×SD16—614no—
762C2×SD16—1228no—
763C2×SD16—1221no—
764C2×SD16—1221no—
765C2×SD16—1221no—
766C2×SD16—1221no—
767C2×SD16—1221no—
768C2×SD16—1221no—
769C2×SD16—1222no—
770C2×SD16—1221no—
771C2×SD16—1221no—
772C2×SD16—1222no—
773C2×SD16—1228no—
774C2×SD16—1228no—
775C2×SD16—1228no—
776C2×SD16—1221no—
777C2×SD16—1221no—
778C2×SD16—1221no—
779C2×SD16—1221no—
780C2×SD16—1222no—
781C2×SD16C22×D6114yescomplemented
782C2×D8—21no—
783C2×D8—611no—
784C2×D8—611no—
785C2×D8—1221no—
786C2×D8—1221no—
787C2×D8—1221no—
788#131—22no—
789#131—614no—
790#131—614no—
791#131—614no—
792#131—1222no—
793#131—1222no—
794#131—1222no—
795#131C22×D6114yescomplemented
796C2×M16—21no—
797C2×M16—611no—
798C2×M16—1221no—
799C2×M16—1221no—
800C2×M16—1221no—
801C2×M16C22×D6111yescharacteristic
802C2×M16C22×D6111yescharacteristic
803C2×M16C22×D6111yescharacteristic
804C22×C8—21no—
805C22×C8—611no—
806C22×C8—1221no—
807C22×C8—1221no—
808C22×C8—1221no—
809C22×C8C22×D6111yescharacteristic
810C4⋊Q8—614no—
811C4⋊Q8—2441no—
812#127—614no—
813#127—2441no—
814C2×C4⋊C4—2441no—
815C2×C42—611no—
816#108—614no—
817#108C22×D6114yescomplemented
818#104—614no—
819#104—614no—
820#104—614no—
821#104—614no—
822#101—614no—
823#101C22×D6114yescomplemented
824#100—614no—
825#100C22×D6114yescomplemented
826C4×C8—614no—
827C24—21no—
828C24—1221no—
829C24—2441no—
830C24—2441no—
831#41—21no—
832#41—21no—
833#41—612no—
834#41—612no—
835#41—612no—
836#41—612no—
837#41—612no—
838#41—612no—
839#41—1224no—
840#41—1224no—
841#41—1221no—
842#41—1221no—
843#41—1221no—
844#41—1221no—
845#41—1221no—
846#41—1221no—
847#41—1224no—
848#41—1224no—
849#41—1224no—
850#41—1224no—
851#41—1224no—
852#41—1224no—
853#41—2444no—
854#41—2442no—
855#41—2442no—
856#41—2444no—
857#41—2444no—
858#41—2442no—
859#41—2442no—
860#41—2442no—
861#41—2442no—
862#41—2442no—
863#41—2442no—
864#41—2444no—
865#41D4×D6112yes—
866#41C23×D6112yes—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—611no—
873C2×Q8—611no—
874C2×Q8—611no—
875C2×Q8—612no—
876C2×Q8—1224no—
877C2×Q8—1221no—
878C2×Q8—1224no—
879C2×Q8—1224no—
880C2×Q8—1224no—
881C2×Q8—1221no—
882C2×Q8—1221no—
883C2×Q8—1221no—
884C2×Q8—1221no—
885C2×Q8—2441no—
886C2×Q8—2442no—
887C2×Q8—2441no—
888C2×Q8—2442no—
889C2×Q8—2442no—
890C2×Q8—2442no—
891C2×Q8D4×D6111yescharacteristic
892C2×Q8C23×D6112yes—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—21no—
898C2×D4—21no—
899C2×D4—611no—
900C2×D4—611no—
901C2×D4—611no—
902C2×D4—612no—
903C2×D4—1224no—
904C2×D4—1224no—
905C2×D4—1224no—
906C2×D4—1221no—
907C2×D4—1221no—
908C2×D4—1221no—
909C2×D4—1224no—
910C2×D4—1221no—
911C2×D4—1221no—
912C2×D4—1221no—
913C2×D4—1221no—
914C2×D4—1221no—
915C2×D4—4884no—
916C2×D4—2442no—
917C2×D4—2441no—
918C2×D4—2441no—
919C2×D4—2442no—
920C2×D4—2442no—
921C2×D4—2442no—
922C2×D4—2444no—
923C2×D4—2441no—
924C2×D4—2441no—
925C2×D4—2441no—
926C2×D4—2444no—
927C2×D4—2444no—
928C2×D4—2444no—
929C2×D4—2444no—
930C2×D4—2441no—
931C2×D4D4×D6111yescharacteristic
932C2×D4C23×D6112yes—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—1221no—
936C22×C4—1221no—
937C22×C4—1221no—
938C22×C4—1221no—
939C22×C4—1221no—
940C22×C4—2441no—
941C22×C4—2441no—
942C22×C4—2441no—
943C22×C4—2441no—
944C22×C4—2441no—
945C22×C4—2441no—
946C22×C4C23×D6111yescharacteristic
947Q16—24no—
948Q16—614no—
949Q16—614no—
950Q16—1224no—
951Q16—1224no—
952Q16—1224no—
953SD16—24no—
954SD16—24no—
955SD16—24no—
956SD16—24no—
957SD16—614no—
958SD16—614no—
959SD16—614no—
960SD16—614no—
961SD16—1224no—
962SD16—1224no—
963SD16—1224no—
964SD16—1224no—
965SD16—1224no—
966SD16—1224no—
967SD16—1224no—
968SD16—1224no—
969SD16—1224no—
970SD16—1224no—
971SD16—1224no—
972SD16—1224no—
973D8—24no—
974D8—614no—
975D8—614no—
976D8—1224no—
977D8—1224no—
978D8—1224no—
979M16—21no—
980M16—21no—
981M16—21no—
982M16—24no—
983M16—612no—
984M16—1224no—
985M16—1224no—
986M16—1221no—
987M16—1224no—
988M16C23×D6112yes—
989M16C23×D6112yes—
990M16C23×D6112yes—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—24no—
995C2×C8—611no—
996C2×C8—611no—
997C2×C8—612no—
998C2×C8—612no—
999C2×C8—1224no—
1000C2×C8—1224no—
1001C2×C8—1221no—
1002C2×C8—1224no—
1003C2×C8D4×D6111yescharacteristic
1004C2×C8D4×D6111yescharacteristic
1005C2×C8D4×D6112yes—
1006C2×C8C23×D6112yes—
1007C4⋊C4—2444no—
1008C42—612no—
1009C42—1221no—
1010C23—21no—
1011C23—22no—
1012C23—41no—
1013C23—41no—
1014C23—82no—
1015C23—1221no—
1016C23—1221no—
1017C23—1221no—
1018C23—1222no—
1019C23—9762no—
1020C23—9762no—
1021C23—4882no—
1022C23—2444no—
1023C23—2444no—
1024C23—2441no—
1025C23—2441no—
1026C23#1451982311yescharacteristic
1027Q8—21no—
1028Q8—22no—
1029Q8—22no—
1030Q8—41no—
1031Q8—41no—
1032Q8—612no—
1033Q8—612no—
1034Q8—612no—
1035Q8—1221no—
1036Q8—1221no—
1037Q8—1221no—
1038Q8—1222no—
1039Q8—1222no—
1040Q8—2444no—
1041Q8—2444no—
1042Q8—2441no—
1043Q8—2441no—
1044Q8C2×D4×D6112yes—
1045D4—22no—
1046D4—22no—
1047D4—22no—
1048D4—22no—
1049D4—21no—
1050D4—41no—
1051D4—41no—
1052D4—612no—
1053D4—612no—
1054D4—612no—
1055D4—1222no—
1056D4—1222no—
1057D4—1222no—
1058D4—1222no—
1059D4—1222no—
1060D4—1222no—
1061D4—1222no—
1062D4—1222no—
1063D4—1221no—
1064D4—1221no—
1065D4—1221no—
1066D4—4888no—
1067D4—2444no—
1068D4—2444no—
1069D4—2444no—
1070D4—2444no—
1071D4—2444no—
1072D4—2444no—
1073D4—2441no—
1074D4—2441no—
1075D4C2×D4×D6112yes—
1076C2×C4—21no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—1224no—
1083C2×C4—1222no—
1084C2×C4—1221no—
1085C2×C4—1221no—
1086C2×C4—1221no—
1087C2×C4—1222no—
1088C2×C4—1222no—
1089C2×C4—1222no—
1090C2×C4—1222no—
1091C2×C4—1222no—
1092C2×C4—1222no—
1093C2×C4—1222no—
1094C2×C4—2444no—
1095C2×C4—2444no—
1096C2×C4—2444no—
1097C2×C4—2444no—
1098C2×C4—2444no—
1099C2×C4—2444no—
1100C2×C4—2441no—
1101C2×C4—2441no—
1102C2×C4C2×D4×D6111yescharacteristic
1103C2×C4C2×D4×D6111yescharacteristic
1104C2×C4C2×D4×D6111yescharacteristic
1105C2×C4C2×D4×D6111yescharacteristic
1106C2×C4#1451982311yescharacteristic
1107C2×C4C24×D6111yescharacteristic
1108C8—22no—
1109C8—22no—
1110C8—22no—
1111C8—612no—
1112C8—612no—
1113C8—1222no—
1114C8C2×D4×D6112yes—
1115C8C2×D4×D6112yes—
1116C22—22no—
1117C22—22no—
1118C22—42no—
1119C22—42no—
1120C22—82no—
1121C22—82no—
1122C22—161no—
1123C22—1222no—
1124C22—1222no—
1125C22—1222no—
1126C22—9761no—
1127C22—9764no—
1128C22—9764no—
1129C22—4882no—
1130C22—4882no—
1131C22—2442no—
1132C22—2442no—
1133C22—2442no—
1134C22—2442no—
1135C22#1684039611yescharacteristic
1136C22#1684039611yescharacteristic
1137C22C2×#1451982311yescharacteristic
1138C4—22no—
1139C4—42no—
1140C4—1224no—
1141C4—1222no—
1142C4—1222no—
1143C4—1222no—
1144C4—2442no—
1145C4#1684039611yescharacteristic
1146C4#1684039611yescharacteristic
1147C4C22×D4×D6111yescharacteristic
1148C4C22×D4×D6111yescharacteristic
1149C2—21no—
1150C2—21no—
1151C2—42no—
1152C2—82no—
1153C2—4882no—
1154C2—2442no—
1155C2—2442no—
1156C2—2442no—
1157C2#2145761112yesdirect product factor
1158C2C2×#1684039611yescharacteristic
subgroupG/H
centerC22#16840396
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#471C2
socleC22×C61D42
hypercenterC2×#471D61
hypocenterC61C2×#3291
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×#16840574C2semidirect
2. C2×#16840572C2semidirect
3. C2×#16840571C2semidirect
4. C2×#16840568C2semidirect
5. #21457611C2direct (N × H)
6. C2×#16840133C2semidirect
7. C2×#16840028C2semidirect
8. C2×#16840026C2semidirect
9. C2×#16840024C2semidirect
10. C2×#16839947C2semidirect
11. C2×#16839943C2semidirect
12. C2×#16839932C2semidirect
13. C2×#16839928C2semidirect
14. C2×#16839878C2semidirect
15. C2×#16839877C2semidirect
16. C2×C61×#471C2semidirect
19. C2×#14519823C22semidirect
20. C2×#14519822C22semidirect
22. #16840574C22semidirect
24. #16840572C22semidirect
26. #16840571C22semidirect
28. #16840568C22semidirect
30. C2×#14519810C22semidirect
31. C2×#14519810C22semidirect
33. C2×#14519808C22semidirect
50. C22×#11758190C22semidirect
51. C22×#11758200C22semidirect
52. C22×#11758201C22semidirect
56. C2×#14519785C22semidirect
57. C2×#14519785C22semidirect
58. C2×#14519783C22semidirect
59. C2×#14519775C22semidirect
61. #16840133C22semidirect
62. #16840028C22semidirect
63. #16840026C22semidirect
64. #16840024C22semidirect
65. #16839947C22semidirect
66. #16839943C22semidirect
67. #16839932C22semidirect
68. #16839928C22semidirect
69. #16839878C22semidirect
70. #16839877C22semidirect
71. C2×#14519712C22semidirect
72. C2×#14519704C22semidirect
73. C2×#14519703C22semidirect
74. C2×#14519703C22semidirect
75. C2×#14519703C22semidirect
76. C2×#14519695C22semidirect
77. C2×#14519693C22semidirect
78. C2×C8×Dic61C22semidirect
79. C2×#137×C61C22semidirect
81. C22×SD16×C61C22semidirect
82. C2×#131×C61C22semidirect
83. C61×#471C22semidirect
84. C2×#108×C61C22semidirect
85. C2×#101×C61C22semidirect
86. C2×#100×C61C22semidirect
98. #14519823C23semidirect
102. #14519822C23semidirect
132. #14519810C23semidirect
133. #14519810C23semidirect
136. #14519808C23semidirect
151. #14519799D4semidirect
154. #14519797D4semidirect
159. C2×Dic244D4semidirect
161. C2×#11758202D4semidirect
170. C2×#11758190D4semidirect
171. C2×#11758190D4semidirect
172. C2×#11758190C23semidirect
177. C2×#11758200D4semidirect
178. C2×#11758200C23semidirect
183. C2×#11758201D4semidirect
184. C2×#11758201C23semidirect
190. C2×D488D4semidirect
192. C2×#11758199D4semidirect
195. #14519785C23semidirect
196. #14519785C23semidirect
198. #14519783C23semidirect
208. #14519775C23semidirect
213. #14519712C23semidirect
214. #14519704C23semidirect
215. #14519703C23semidirect
216. #14519703C23semidirect
217. #14519703C23semidirect
218. #14519695C23semidirect
219. #14519693C23semidirect
220. C8×Dic61C23semidirect
225. #137×C61C23semidirect
234. C2×SD16×C61C23semidirect
237. #131×C61C23semidirect
244. #108×C61C23semidirect
245. #101×C61C23semidirect
246. #100×C61C23semidirect
389. #11758202C2×D4semidirect
393. #11758201C2×D4semidirect
397. #11758200C2×D4semidirect
399. #11758199C2×D4semidirect
412. Dic244C2×D4semidirect
415. D488C2×D4semidirect
422. #11758190C2×D4semidirect
423. #11758190C2×D4semidirect
579. C2×#471D61semidirect
590. C2×C61#3291semidirect
615. C2×#137C2×D61semidirect
637. C22×SD16C2×D61semidirect
641. C2×#131C2×D61semidirect
648. #471C2×D61semidirect
656. C2×#108C2×D61semidirect
662. C2×#101C2×D61semidirect
664. C2×#100C2×D61semidirect
666. C61C2×#3291semidirect
723. #137C22×D61semidirect
781. C2×SD16C22×D61semidirect
795. #131C22×D61semidirect
817. #108C22×D61semidirect
823. #101C22×D61semidirect
825. #100C22×D61semidirect
1157. C2#21457611direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168405742
C2×#168405722
C2×#168405712
C2×#168405682
#214576112
C2×#168401332
C2×#168400282
C2×#168400262
C2×#168400242
C2×#168399472
C2×#168399432
C2×#168399322
C2×#168399282
C2×#168398782
C2×#168398772
C2×C61×#4712
C2×#329161