Finite Group Databasebeta

← C2×#21457582 #30556191

Subgroups — C2×#21457582 #30556191

Order 15616.

2704 conjugacy classes of subgroups.

The subgroup lattice has 1174 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×#16840566C211yesmaximal, characteristic, complemented
4C2×#16840563C211yesmaximal, characteristic, complemented
5#21457582C2116yesmaximal, direct product factor
6C2×#16840150C211yesmaximal, characteristic, complemented
7C2×#16840031C211yesmaximal, characteristic, complemented
8C2×#16840026C211yesmaximal, characteristic, complemented
9C2×#16840024C211yesmaximal, characteristic, complemented
10C2×#16839933C211yesmaximal, characteristic, complemented
11C2×#16839942C211yesmaximal, characteristic, complemented
12C2×#16839932C211yesmaximal, characteristic, complemented
13C2×#16839928C211yesmaximal, characteristic, complemented
14C2×#16839883C211yesmaximal, characteristic, complemented
15C2×#16839882C211yesmaximal, characteristic, complemented
16C2×C61×#472C211yesmaximal, characteristic, complemented
17C2×#14519824C2211yescharacteristic, complemented
18C2×#14519823C2211yescharacteristic, complemented
19C2×#14519822C2211yescharacteristic
20C2×#14519822C2211yescharacteristic, complemented
21#16840574—24no—
22#16840574C2218yescomplemented
23#16840572—24no—
24#16840572C2218yescomplemented
25#16840566—24no—
26#16840566C2218yescomplemented
27#16840563—24no—
28#16840563C2218yescomplemented
29C2×#14519810—21no—
30C2×#14519810C2211yescharacteristic, complemented
31C2×#14519810C2211yescharacteristic, complemented
32C2×#14519806—21no—
33C2×#14519805—21no—
34C2×#14519805C2211yescharacteristic
35C2×#14519805C2211yescharacteristic, complemented
36C2×#14519804—21no—
37C2×#14519803C2211yescharacteristic
38C2×#14519803C2211yescharacteristic, complemented
39C2×#14519801—21no—
40C2×#14519801—21no—
41C2×#14519801—21no—
42C2×#14519801—21no—
43C2×#14519799—21no—
44C2×#14519799C2211yescharacteristic
45C2×#14519798—21no—
46C2×#14519797C2211yescharacteristic
47C2×#14519796—21no—
48C2×#14519796—21no—
49C22×#11758190—21no—
50C22×#11758190C2211yescharacteristic, complemented
51C22×#11758200C2211yescharacteristic, complemented
52C2×SD16×D61—21no—
53C22×#11758199C2211yescharacteristic, complemented
54C2×D8×D61—21no—
55C2×D8×D61—21no—
56C2×#14519785C2211yescharacteristic, complemented
57C2×#14519785C2211yescharacteristic, complemented
58C2×#14519783C2211yescharacteristic, complemented
59C2×#14519773C2211yescharacteristic, complemented
60C2×#14519764C2211yescharacteristic, complemented
61#16840150C2218yescomplemented
62#16840031C2218yescomplemented
63#16840026C2218yescomplemented
64#16840024C2218yescomplemented
65#16839942C2218yescomplemented
66#16839933C2218yescomplemented
67#16839932C2218yescomplemented
68#16839928C2218yescomplemented
69#16839883C2218yescomplemented
70#16839882C2218yescomplemented
71C2×#14519712C2211yescharacteristic, complemented
72C2×#14519704C2211yescharacteristic, complemented
73C2×#14519703C2211yescharacteristic, complemented
74C2×#14519703C2211yescharacteristic, complemented
75C2×#14519703C2211yescharacteristic, complemented
76C2×#14519695C2211yescharacteristic, complemented
77C2×#14519693C2211yescharacteristic, complemented
78C2×#14519687C2211yescharacteristic, complemented
79C2×AGL(1,ℤ/8)×C61C2211yescharacteristic, complemented
80C2×AGL(1,ℤ/8)×C61C2211yescharacteristic, complemented
81C22×D8×C61C2211yescharacteristic, complemented
82C2×#131×C61C2211yescharacteristic, complemented
83C61×#472C2218yescomplemented
84C2×#108×C61C2211yescharacteristic, complemented
85C2×#100×C61C2211yescharacteristic, complemented
86C2×#100×C61C2211yescharacteristic, complemented
87#14519824—22no—
88#14519824—22no—
89#14519824—41no—
90#14519824C2314yescomplemented
91#14519823—22no—
92#14519823—22no—
93#14519823—41no—
94#14519823C2314yescomplemented
95#14519822—22no—
96#14519822—22no—
97#14519822—22no—
98#14519822—22no—
99#14519822—41no—
100#14519822—41no—
101#14519822C2314yes—
102#14519822C2314yescomplemented
103C2×#11758226—21no—
104C2×#11758222—21no—
105C2×#11758222—21no—
106C2×#11758222C2311yescharacteristic
107C2×#11758222C2311yescharacteristic
108C2×#11758222C2311yescharacteristic
109C2×#11758224—21no—
110C2×#11758224—21no—
111C2×#11758224—21no—
112C2×#11758224—21no—
113C2×#11758224—21no—
114C2×#11758224—41no—
115C22×Dic122—21no—
116C22×Dic122C2311yescharacteristic
117C2×Q8×D61—21no—
118C22×D244—21no—
119C22×D244C2311yescharacteristic
120C22×C22⋊D61—41no—
121C22×C22⋊D61—41no—
122C22×C22⋊D61—41no—
123C2×D4×D61—21no—
124C2×D4×D61—21no—
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#14519806—28no—
135#14519805—22no—
136#14519805—22no—
137#14519805—28no—
138#14519805C2314yes—
139#14519805C2314yescomplemented
140#14519804—28no—
141#14519803—22no—
142#14519803—22no—
143#14519803C2314yes—
144#14519803C2314yescomplemented
145#14519801—28no—
146#14519801—28no—
147#14519801—28no—
148#14519801—28no—
149#14519799—28no—
150#14519799D414yescomplemented
151#14519799C2314yes—
152#14519798—28no—
153#14519797D414yescomplemented
154#14519797C2314yes—
155#14519796—28no—
156#14519796—28no—
157C2×Dic244—21no—
158C2×Dic244—21no—
159C2×Dic244D411yescharacteristic, complemented
160C2×#11758202D411yescharacteristic, complemented
161C2×#11758190—21no—
162C2×#11758190—21no—
163C2×#11758190—21no—
164C2×#11758190—21no—
165C2×#11758190—21no—
166C2×#11758190—21no—
167C2×#11758190—22no—
168C2×#11758190—28no—
169C2×#11758190D411yescharacteristic, complemented
170C2×#11758190D411yescharacteristic, complemented
171C2×#11758190C2314yescomplemented
172C2×#11758200—21no—
173C2×#11758200—21no—
174C2×#11758200—21no—
175C2×#11758200—21no—
176C2×#11758200—22no—
177C2×#11758200D411yescharacteristic, complemented
178C2×#11758200C2314yescomplemented
179C2×#11758201D411yescharacteristic, complemented
180SD16×D61—28no—
181C2×D488—21no—
182C2×D488—21no—
183C2×D488D411yescharacteristic, complemented
184C2×#11758199—21no—
185C2×#11758199—21no—
186C2×#11758199—21no—
187C2×#11758199—21no—
188C2×#11758199—22no—
189C2×#11758199D411yescharacteristic, complemented
190C2×#11758199C2314yescomplemented
191D8×D61—28no—
192D8×D61—28no—
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#14519773—41no—
208#14519773C2314yescomplemented
209#14519764—41no—
210#14519764C2314yescomplemented
211C2×C22⋊Dic61—41no—
212C2×C4×Dic61C2311yescharacteristic
213#14519712C2314yescomplemented
214#14519704C2314yescomplemented
215#14519703C2314yescomplemented
216#14519703C2314yescomplemented
217#14519703C2314yescomplemented
218#14519695C2314yescomplemented
219#14519693C2314yescomplemented
220#14519687C2314yescomplemented
221C2×#41×C61C2311yescharacteristic
222C22×D4×C61C2311yescharacteristic
223C22×D4×C61C2311yescharacteristic
224AGL(1,ℤ/8)×C61—22no—
225AGL(1,ℤ/8)×C61—22no—
226AGL(1,ℤ/8)×C61C2314yescomplemented
227AGL(1,ℤ/8)×C61C2314yescomplemented
228C2×SD16×C61—21no—
229C2×SD16×C61—21no—
230C2×D8×C61—21no—
231C2×D8×C61—21no—
232C2×D8×C61—21no—
233C2×D8×C61—21no—
234C2×D8×C61—22no—
235C2×D8×C61C2314yescomplemented
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#100×C61C2314yescomplemented
246#100×C61C2314yescomplemented
247C24×C61—21no—
248C24×C61—21no—
249C23×D61—21no—
250C23×D61—41no—
251C23×D61—41no—
252C23×D61—41no—
253#41×C61—21no—
254#41×C61—21no—
255#41×C61C2×D412yes—
256#41×C61C2412yes—
257C2×Q8×C61C2×D411yescharacteristic
258C2×D4×C61—21no—
259C2×D4×C61—21no—
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×C61—21no—
267C2×D4×C61—21no—
268C2×D4×C61—21no—
269C2×D4×C61C2×D411yescharacteristic
270C2×D4×C61C2412yes—
271C2×D4×C61C2412yes—
272C22×C4×C61—21no—
273C22×C4×C61C2411yescharacteristic
274C2×C22⋊D61—21no—
275C2×C22⋊D61—21no—
276C2×C22⋊D61—21no—
277C2×C22⋊D61—41no—
278C2×C22⋊D61—41no—
279C2×C22⋊D61—41no—
280C2×C22⋊D61—41no—
281C2×C22⋊D61—41no—
282C2×C22⋊D61—44no—
283C2×C22⋊D61—44no—
284C2×C22⋊D61—44no—
285C2×C22⋊D61—44no—
286C2×C22⋊D61—44no—
287C2×C22⋊D61—41no—
288C2×C22⋊D61—84no—
289C22×Dic61—21no—
290C22×Dic61—21no—
291C22×Dic61—41no—
292C22×Dic61—41no—
293C22×Dic61—41no—
294#11758226—24no—
295#11758226—42no—
296Q8×D61—24no—
297Q8×D61—42no—
298#11758224—24no—
299#11758224—24no—
300#11758224—24no—
301#11758224—24no—
302#11758224—24no—
303#11758224—42no—
304#11758224—42no—
305#11758224—42no—
306#11758224—42no—
307#11758224—42no—
308#11758224—44no—
309#11758224—44no—
310D4×D61—24no—
311D4×D61—24no—
312D4×D61—24no—
313D4×D61—24no—
314D4×D61—24no—
315D4×D61—42no—
316D4×D61—42no—
317D4×D61—42no—
318D4×D61—42no—
319D4×D61—42no—
320D4×D61—44no—
321D4×D61—44no—
322#11758222—21no—
323#11758222—21no—
324#11758222—21no—
325#11758222—21no—
326#11758222—21no—
327#11758222—21no—
328#11758222—24no—
329#11758222—24no—
330#11758222—42no—
331#11758222—42no—
332#11758222C2×D412yes—
333#11758222C2×D412yes—
334#11758222C2×D412yes—
335#11758222C2412yes—
336#11758222C2412yes—
337#11758222C2412yes—
338C2×D244—21no—
339C2×D244—21no—
340C2×D244—21no—
341C2×D244—21no—
342C2×D244—24no—
343C2×D244—21no—
344C2×D244—42no—
345C2×D244—41no—
346C2×D244C2×D411yescharacteristic
347C2×D244C2×D411yescharacteristic
348C2×D244C2×D411yescharacteristic
349C2×D244C2412yes—
350C2×C4×D61—21no—
351C2×C4×D61—21no—
352C2×C4×D61—21no—
353C2×C4×D61—41no—
354C2×C4×D61—41no—
355C2×Dic122—21no—
356C2×Dic122—21no—
357C2×Dic122—21no—
358C2×Dic122—21no—
359C2×Dic122—24no—
360C2×Dic122—21no—
361C2×Dic122—42no—
362C2×Dic122—41no—
363C2×Dic122C2×D411yescharacteristic
364C2×Dic122C2×D411yescharacteristic
365C2×Dic122C2×D411yescharacteristic
366C2×Dic122C2412yes—
367SD16×C61—24no—
368SD16×C61—24no—
369D8×C61—24no—
370D8×C61—24no—
371D8×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—
388C22⋊Dic61—44no—
389#11758202C2×D414yescomplemented
390#11758201C2×D414yescomplemented
391#11758200—24no—
392#11758200—24no—
393#11758200—24no—
394#11758200—24no—
395#11758200C2×D414yescomplemented
396#11758199—24no—
397#11758199—24no—
398#11758199—24no—
399#11758199—24no—
400#11758199C2×D414yescomplemented
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—22no—
433C23×C61—41no—
434C23×C61—41no—
435C23×C61—41no—
436C23×C61—41no—
437C23×C61—82no—
438C23×C61—82no—
439C23×C61H(5,𝔽2)11yescharacteristic
440C22×D61—21no—
441C22×D61—21no—
442C22×D61—21no—
443C22×D61—22no—
444C22×D61—44no—
445C22×D61—44no—
446C22×D61—44no—
447C22×D61—41no—
448C22×D61—41no—
449C22×D61—82no—
450C22×D61—162no—
451C22×D61—162no—
452C22×D61—162no—
453Q8×C61—21no—
454Q8×C61C22×D412yes—
455D4×C61—22no—
456D4×C61—22no—
457D4×C61—21no—
458D4×C61—22no—
459D4×C61—22no—
460D4×C61—22no—
461D4×C61—22no—
462D4×C61—41no—
463D4×C61—41no—
464D4×C61—41no—
465D4×C61—41no—
466D4×C61C22×D412yes—
467C2×C4×C61—21no—
468C2×C4×C61—22no—
469C2×C4×C61—22no—
470C2×C4×C61C22×D411yescharacteristic
471C2×C4×C61C22×D411yescharacteristic
472C2×C4×C61C22×D411yescharacteristic
473C2×C4×C61C22×D411yescharacteristic
474C2×C4×C61H(5,𝔽2)11yescharacteristic
475C2×C4×C61C2511yescharacteristic
476C22⋊D61—22no—
477C22⋊D61—22no—
478C22⋊D61—22no—
479C22⋊D61—22no—
480C22⋊D61—22no—
481C22⋊D61—22no—
482C22⋊D61—44no—
483C22⋊D61—44no—
484C22⋊D61—44no—
485C22⋊D61—44no—
486C22⋊D61—44no—
487C22⋊D61—44no—
488C22⋊D61—88no—
489C2×Dic61—21no—
490C2×Dic61—21no—
491C2×Dic61—21no—
492C2×Dic61—22no—
493C2×Dic61—22no—
494C2×Dic61—44no—
495C2×Dic61—44no—
496C2×Dic61—44no—
497C2×Dic61—42no—
498C2×Dic61—41no—
499C2×Dic61—41no—
500D244—21no—
501D244—21no—
502D244—21no—
503D244—22no—
504D244—22no—
505D244—44no—
506D244—41no—
507D244—41no—
508D244C22×D412yes—
509D244C22×D412yes—
510D244C22×D412yes—
511C4×D61—22no—
512C4×D61—22no—
513C4×D61—22no—
514C4×D61—22no—
515C4×D61—22no—
516C4×D61—22no—
517C4×D61—44no—
518C4×D61—44no—
519Dic122—21no—
520Dic122—21no—
521Dic122—21no—
522Dic122—22no—
523Dic122—22no—
524Dic122—44no—
525Dic122—41no—
526Dic122—41no—
527Dic122C22×D412yes—
528Dic122C22×D412yes—
529Dic122C22×D412yes—
530C8×C61—22no—
531C8×C61—22no—
532C8×C61—22no—
533C8×C61C22×D412yes—
534C8×C61C22×D412yes—
535#92418—22no—
536#92418C22×D412yes—
537#92418C22×D412yes—
538C2×#3288—611nomaximal, Sylow
539C22×C61—22no—
540C22×C61—22no—
541C22×C61—42no—
542C22×C61—42no—
543C22×C61—42no—
544C22×C61—82no—
545C22×C61—82no—
546C22×C61—82no—
547C22×C61—82no—
548C22×C61—161no—
549C22×C61—161no—
550C22×C61D4211yescharacteristic
551C22×C61D4211yescharacteristic
552C22×C61C2×H(5,𝔽2)11yescharacteristic
553C2×D61—22no—
554C2×D61—22no—
555C2×D61—22no—
556C2×D61—42no—
557C2×D61—42no—
558C2×D61—42no—
559C2×D61—42no—
560C2×D61—82no—
561C2×D61—82no—
562C2×D61—164no—
563C2×D61—164no—
564C2×D61—164no—
565C2×D61—161no—
566C4×C61—22no—
567C4×C61D4211yescharacteristic
568C4×C61D4211yescharacteristic
569C4×C61C23×D411yescharacteristic
570C4×C61C23×D411yescharacteristic
571Dic61—22no—
572Dic61—22no—
573Dic61—22no—
574Dic61—42no—
575Dic61—42no—
576C2×#577—611no—
577C2×#577—611no—
578C2×#576—611no—
579C2×#576—611no—
580#3288—6116no—
581C2×#496—611no—
582C2×#472—611no—
583C2×#472D6111yescharacteristic, complemented
584C2×#471—611no—
585C2×#471—611no—
586C2×#454—611no—
587C2×#455—611no—
588C2×#453—611no—
589C2×#453—611no—
590C2×#444—611no—
591C2×#444—611no—
592C2×C61—21no—
593C2×C61—21no—
594C2×C61—42no—
595C2×C61—82no—
596C2×C61—82no—
597C2×C61#328812yescomplemented
598C2×C61C2×D4211yescharacteristic
599D61—42no—
600D61—42no—
601D61—42no—
602D61—82no—
603C2×2−1+4—611no—
604C2×H(5,𝔽2)—611no—
605C2×H(5,𝔽2)—611no—
606C2×H(5,𝔽2)—611no—
607#577—618no—
608#577—618no—
609#577—1224no—
610#577—1224no—
611#576—618no—
612#576—618no—
613#576—1224no—
614#576—1224no—
615C2×#137—611no—
616C2×#137—611no—
617C2×#137—1221no—
618C2×#137—1221no—
619C2×AGL(1,ℤ/8)—611no—
620C2×AGL(1,ℤ/8)—611no—
621C2×AGL(1,ℤ/8)—611no—
622C2×AGL(1,ℤ/8)—611no—
623C2×AGL(1,ℤ/8)—1221no—
624C2×AGL(1,ℤ/8)—1221no—
625C2×AGL(1,ℤ/8)—1221no—
626C2×AGL(1,ℤ/8)—1221no—
627C2×AGL(1,ℤ/8)—1221no—
628C2×AGL(1,ℤ/8)—1221no—
629C2×AGL(1,ℤ/8)C2×D6111yescharacteristic, complemented
630C2×AGL(1,ℤ/8)C2×D6111yescharacteristic, complemented
631C2×#135—611no—
632C2×#135—611no—
633C2×#135—1221no—
634C2×#135—1221no—
635C2×#135—1221no—
636C2×#135—1221no—
637C22×SD16—611no—
638C22×SD16—611no—
639C22×SD16—1221no—
640C22×SD16—1221no—
641C22×D8—611no—
642C22×D8—1221no—
643C22×D8—1221no—
644C22×D8C2×D6111yescharacteristic, complemented
645C2×#131—611no—
646C2×#131—611no—
647C2×#131—611no—
648C2×#131C2×D6111yescharacteristic, complemented
649C2×#127—611no—
650C2×#124—611no—
651#496—618no—
652#472—618no—
653#472C2×D6118yescomplemented
654#471—618no—
655#471—618no—
656#455—618no—
657#454—618no—
658#453—618no—
659#453—618no—
660#444—618no—
661#444—618no—
662C2×#108—611no—
663C2×#108C2×D6111yescharacteristic, complemented
664C2×#104—611no—
665C2×#104—611no—
666C2×#104—611no—
667C2×#104—611no—
668C2×#101—611no—
669C2×#100—611no—
670C2×#100C2×D6111yescharacteristic, complemented
671C2×#100C2×D6111yescharacteristic, complemented
672C2×#97—611no—
673C61C2×#328811yescharacteristic, complemented, Sylow
6742−1+4—614no—
6752−1+4—1222no—
6762−1+4—1222no—
6772−1+4—2441no—
678H(5,𝔽2)—614no—
679H(5,𝔽2)—614no—
680H(5,𝔽2)—614no—
681H(5,𝔽2)—1222no—
682H(5,𝔽2)—1222no—
683H(5,𝔽2)—1222no—
684H(5,𝔽2)—1222no—
685H(5,𝔽2)—1222no—
686H(5,𝔽2)—1222no—
687H(5,𝔽2)—2441no—
688H(5,𝔽2)—2441no—
689H(5,𝔽2)—2441no—
690C2×#41—611no—
691C2×#41—611no—
692C2×#41—611no—
693C2×#41—1221no—
694C2×#41—1221no—
695C2×#41—1221no—
696C2×#41—1221no—
697C2×#41—1221no—
698C2×#41—1221no—
699C2×#41—1221no—
700C2×#41—1221no—
701C2×#41—2441no—
702C2×#41C22×D6111yescharacteristic
703C22×Q8—611no—
704C22×Q8—1221no—
705C22×Q8—1221no—
706C22×D4—611no—
707C22×D4—1221no—
708C22×D4—1221no—
709C22×D4—1221no—
710C22×D4—1221no—
711C22×D4—1221no—
712C22×D4—1221no—
713C22×D4—2441no—
714C22×D4—2441no—
715C22×D4—2441no—
716C22×D4—2441no—
717C22×D4C22×D6111yescharacteristic
718C22×D4C22×D6111yescharacteristic
719#137—614no—
720#137—614no—
721#137—1228no—
722#137—1222no—
723#137—1222no—
724#137—1228no—
725AGL(1,ℤ/8)—22no—
726AGL(1,ℤ/8)—22no—
727AGL(1,ℤ/8)—614no—
728AGL(1,ℤ/8)—614no—
729AGL(1,ℤ/8)—614no—
730AGL(1,ℤ/8)—614no—
731AGL(1,ℤ/8)—1228no—
732AGL(1,ℤ/8)—1222no—
733AGL(1,ℤ/8)—1222no—
734AGL(1,ℤ/8)—1228no—
735AGL(1,ℤ/8)—1228no—
736AGL(1,ℤ/8)—1228no—
737AGL(1,ℤ/8)—1228no—
738AGL(1,ℤ/8)—1228no—
739AGL(1,ℤ/8)—1222no—
740AGL(1,ℤ/8)—1222no—
741AGL(1,ℤ/8)C22×D6114yescomplemented
742AGL(1,ℤ/8)C22×D6114yescomplemented
743#135—614no—
744#135—614no—
745#135—614no—
746#135—614no—
747#135—1228no—
748#135—1228no—
749#135—1228no—
750#135—1228no—
751C2×Q16—611no—
752C2×Q16—611no—
753C2×Q16—1221no—
754C2×Q16—1221no—
755C2×SD16—21no—
756C2×SD16—21no—
757C2×SD16—611no—
758C2×SD16—611no—
759C2×SD16—614no—
760C2×SD16—611no—
761C2×SD16—611no—
762C2×SD16—614no—
763C2×SD16—1228no—
764C2×SD16—1221no—
765C2×SD16—1221no—
766C2×SD16—1221no—
767C2×SD16—1221no—
768C2×SD16—1221no—
769C2×SD16—1221no—
770C2×SD16—1222no—
771C2×SD16—1228no—
772C2×SD16—1221no—
773C2×SD16—1221no—
774C2×SD16—1221no—
775C2×SD16—1221no—
776C2×SD16—1222no—
777C2×D8—21no—
778C2×D8—21no—
779C2×D8—21no—
780C2×D8—21no—
781C2×D8—22no—
782C2×D8—611no—
783C2×D8—614no—
784C2×D8—611no—
785C2×D8—1221no—
786C2×D8—1221no—
787C2×D8—1221no—
788C2×D8—1221no—
789C2×D8—1222no—
790C2×D8—1228no—
791C2×D8—1228no—
792C2×D8—1221no—
793C2×D8—1221no—
794C2×D8C22×D6114yescomplemented
795#131—22no—
796#131—614no—
797#131—614no—
798#131—614no—
799#131—1222no—
800#131—1222no—
801#131—1222no—
802#131C22×D6114yescomplemented
803C2×M16—21no—
804C2×M16—611no—
805C2×M16—1221no—
806C2×M16—1221no—
807C2×M16—1221no—
808C2×M16C22×D6111yescharacteristic
809C2×M16C22×D6111yescharacteristic
810C2×M16C22×D6111yescharacteristic
811C22×C8—21no—
812C22×C8—611no—
813C22×C8—1221no—
814C22×C8—1221no—
815C22×C8—1221no—
816C22×C8C22×D6111yescharacteristic
817#127—614no—
818#127—2441no—
819#124—614no—
820#124—2441no—
821C2×C22⋊C4—2441no—
822C2×C42—611no—
823#108—614no—
824#108C22×D6114yescomplemented
825#104—614no—
826#104—614no—
827#104—614no—
828#104—614no—
829#101—614no—
830#100—614no—
831#100C22×D6114yescomplemented
832#100C22×D6114yescomplemented
833#97—614no—
834C24—21no—
835C24—21no—
836C24—1221no—
837C24—2441no—
838C24—2441no—
839C24—2441no—
840#41—21no—
841#41—21no—
842#41—612no—
843#41—612no—
844#41—612no—
845#41—612no—
846#41—612no—
847#41—612no—
848#41—1224no—
849#41—1224no—
850#41—1221no—
851#41—1221no—
852#41—1221no—
853#41—1221no—
854#41—1221no—
855#41—1221no—
856#41—1224no—
857#41—1224no—
858#41—1224no—
859#41—1224no—
860#41—1224no—
861#41—1224no—
862#41—2442no—
863#41—2442no—
864#41—2444no—
865#41—2442no—
866#41—2442no—
867#41—2442no—
868#41—2442no—
869#41—2442no—
870#41—2442no—
871#41—2444no—
872#41D4×D6112yes—
873#41C23×D6112yes—
874C2×Q8—611no—
875C2×Q8—611no—
876C2×Q8—611no—
877C2×Q8—612no—
878C2×Q8—1224no—
879C2×Q8—1221no—
880C2×Q8—1224no—
881C2×Q8—1221no—
882C2×Q8—1221no—
883C2×Q8—1221no—
884C2×Q8—1221no—
885C2×Q8—2441no—
886C2×Q8—2442no—
887C2×Q8—2442no—
888C2×Q8D4×D6111yescharacteristic
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—21no—
898C2×D4—21no—
899C2×D4—21no—
900C2×D4—611no—
901C2×D4—611no—
902C2×D4—611no—
903C2×D4—612no—
904C2×D4—1224no—
905C2×D4—1224no—
906C2×D4—1224no—
907C2×D4—1224no—
908C2×D4—1224no—
909C2×D4—1221no—
910C2×D4—1221no—
911C2×D4—1221no—
912C2×D4—1224no—
913C2×D4—1221no—
914C2×D4—1221no—
915C2×D4—1221no—
916C2×D4—1221no—
917C2×D4—1221no—
918C2×D4—4884no—
919C2×D4—2442no—
920C2×D4—2441no—
921C2×D4—2442no—
922C2×D4—2442no—
923C2×D4—2442no—
924C2×D4—2442no—
925C2×D4—2442no—
926C2×D4—2444no—
927C2×D4—2441no—
928C2×D4—2441no—
929C2×D4—2441no—
930C2×D4—2441no—
931C2×D4—2441no—
932C2×D4—2444no—
933C2×D4—2444no—
934C2×D4—2444no—
935C2×D4—2444no—
936C2×D4—2444no—
937C2×D4—2444no—
938C2×D4—2441no—
939C2×D4D4×D6111yescharacteristic
940C2×D4C23×D6112yes—
941C2×D4C23×D6112yes—
942C22×C4—21no—
943C22×C4—1221no—
944C22×C4—1221no—
945C22×C4—1221no—
946C22×C4—1221no—
947C22×C4—1221no—
948C22×C4—2441no—
949C22×C4—2441no—
950C22×C4—2441no—
951C22×C4—2441no—
952C22×C4—2441no—
953C22×C4C23×D6111yescharacteristic
954Q16—614no—
955Q16—614no—
956Q16—1224no—
957Q16—1224no—
958SD16—24no—
959SD16—24no—
960SD16—614no—
961SD16—614no—
962SD16—614no—
963SD16—614no—
964SD16—1224no—
965SD16—1224no—
966SD16—1224no—
967SD16—1224no—
968SD16—1224no—
969SD16—1224no—
970SD16—1224no—
971SD16—1224no—
972SD16—1224no—
973SD16—1224no—
974D8—24no—
975D8—24no—
976D8—24no—
977D8—24no—
978D8—614no—
979D8—614no—
980D8—1224no—
981D8—1224no—
982D8—1224no—
983D8—1224no—
984D8—1224no—
985D8—1224no—
986M16—21no—
987M16—21no—
988M16—21no—
989M16—24no—
990M16—612no—
991M16—1224no—
992M16—1224no—
993M16—1221no—
994M16—1224no—
995M16C23×D6112yes—
996M16C23×D6112yes—
997M16C23×D6112yes—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—24no—
1002C2×C8—611no—
1003C2×C8—611no—
1004C2×C8—612no—
1005C2×C8—612no—
1006C2×C8—1224no—
1007C2×C8—1224no—
1008C2×C8—1221no—
1009C2×C8—1224no—
1010C2×C8D4×D6111yescharacteristic
1011C2×C8D4×D6111yescharacteristic
1012C2×C8D4×D6112yes—
1013C2×C8C23×D6112yes—
1014C22⋊C4—2444no—
1015C42—612no—
1016C42—1221no—
1017C23—21no—
1018C23—22no—
1019C23—22no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—82no—
1025C23—82no—
1026C23—1221no—
1027C23—1221no—
1028C23—1221no—
1029C23—1222no—
1030C23—9762no—
1031C23—9762no—
1032C23—9762no—
1033C23—4882no—
1034C23—2444no—
1035C23—2444no—
1036C23—2444no—
1037C23—2441no—
1038C23—2441no—
1039C23#1451982311yescharacteristic
1040Q8—21no—
1041Q8—612no—
1042Q8—612no—
1043Q8—612no—
1044Q8—1221no—
1045Q8—1221no—
1046Q8—1221no—
1047Q8—1222no—
1048Q8—1222no—
1049Q8—2444no—
1050Q8—2441no—
1051Q8—2441no—
1052Q8C2×D4×D6112yes—
1053D4—22no—
1054D4—22no—
1055D4—22no—
1056D4—22no—
1057D4—22no—
1058D4—22no—
1059D4—21no—
1060D4—41no—
1061D4—41no—
1062D4—41no—
1063D4—41no—
1064D4—612no—
1065D4—612no—
1066D4—612no—
1067D4—1222no—
1068D4—1222no—
1069D4—1222no—
1070D4—1222no—
1071D4—1222no—
1072D4—1222no—
1073D4—1222no—
1074D4—1222no—
1075D4—1221no—
1076D4—1221no—
1077D4—1221no—
1078D4—4888no—
1079D4—2444no—
1080D4—2444no—
1081D4—2444no—
1082D4—2444no—
1083D4—2444no—
1084D4—2444no—
1085D4—2444no—
1086D4—2441no—
1087D4—2441no—
1088D4C2×D4×D6112yes—
1089C2×C4—21no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—1221no—
1093C2×C4—1221no—
1094C2×C4—1221no—
1095C2×C4—1222no—
1096C2×C4—1222no—
1097C2×C4—1222no—
1098C2×C4—1222no—
1099C2×C4—1222no—
1100C2×C4—1222no—
1101C2×C4—1222no—
1102C2×C4—1222no—
1103C2×C4—2444no—
1104C2×C4—2444no—
1105C2×C4—2444no—
1106C2×C4—2444no—
1107C2×C4—2444no—
1108C2×C4—2442no—
1109C2×C4—2441no—
1110C2×C4—2441no—
1111C2×C4C2×D4×D6111yescharacteristic
1112C2×C4C2×D4×D6111yescharacteristic
1113C2×C4C2×D4×D6111yescharacteristic
1114C2×C4C2×D4×D6111yescharacteristic
1115C2×C4#1451982311yescharacteristic
1116C2×C4C24×D6111yescharacteristic
1117C8—22no—
1118C8—22no—
1119C8—22no—
1120C8—612no—
1121C8—612no—
1122C8—1222no—
1123C8C2×D4×D6112yes—
1124C8C2×D4×D6112yes—
1125C22—22no—
1126C22—22no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—82no—
1131C22—82no—
1132C22—82no—
1133C22—82no—
1134C22—161no—
1135C22—161no—
1136C22—1222no—
1137C22—1222no—
1138C22—1222no—
1139C22—9761no—
1140C22—9764no—
1141C22—9764no—
1142C22—9764no—
1143C22—4882no—
1144C22—4882no—
1145C22—2442no—
1146C22—2442no—
1147C22—2442no—
1148C22—2442no—
1149C22#1684039611yescharacteristic
1150C22#1684039611yescharacteristic
1151C22C2×#1451982311yescharacteristic
1152C4—22no—
1153C4—1222no—
1154C4—1222no—
1155C4—1222no—
1156C4—2442no—
1157C4—2442no—
1158C4#1684039611yescharacteristic
1159C4#1684039611yescharacteristic
1160C4C22×D4×D6111yescharacteristic
1161C4C22×D4×D6111yescharacteristic
1162C2—21no—
1163C2—21no—
1164C2—42no—
1165C2—82no—
1166C2—82no—
1167C2—4882no—
1168C2—2442no—
1169C2—2442no—
1170C2—2442no—
1171C2#2145758212yesdirect product factor
1172C2C2×#1684039611yescharacteristic
subgroupG/H
centerC22#16840396
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#472C2
socleC22×C61D42
hypercenterC2×#472D61
hypocenterC61C2×#3288
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#472

Complements

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

NH ≅ G/Ntype
1. C2×#16840574C2semidirect
2. C2×#16840572C2semidirect
3. C2×#16840566C2semidirect
4. C2×#16840563C2semidirect
5. #21457582C2direct (N × H)
6. C2×#16840150C2semidirect
7. C2×#16840031C2semidirect
8. C2×#16840026C2semidirect
9. C2×#16840024C2semidirect
10. C2×#16839933C2semidirect
11. C2×#16839942C2semidirect
12. C2×#16839932C2semidirect
13. C2×#16839928C2semidirect
14. C2×#16839883C2semidirect
15. C2×#16839882C2semidirect
16. C2×C61×#472C2semidirect
17. C2×#14519824C22semidirect
18. C2×#14519823C22semidirect
20. C2×#14519822C22semidirect
22. #16840574C22semidirect
24. #16840572C22semidirect
26. #16840566C22semidirect
28. #16840563C22semidirect
30. C2×#14519810C22semidirect
31. C2×#14519810C22semidirect
35. C2×#14519805C22semidirect
38. C2×#14519803C22semidirect
50. C22×#11758190C22semidirect
51. C22×#11758200C22semidirect
53. C22×#11758199C22semidirect
56. C2×#14519785C22semidirect
57. C2×#14519785C22semidirect
58. C2×#14519783C22semidirect
59. C2×#14519773C22semidirect
60. C2×#14519764C22semidirect
61. #16840150C22semidirect
62. #16840031C22semidirect
63. #16840026C22semidirect
64. #16840024C22semidirect
65. #16839942C22semidirect
66. #16839933C22semidirect
67. #16839932C22semidirect
68. #16839928C22semidirect
69. #16839883C22semidirect
70. #16839882C22semidirect
71. C2×#14519712C22semidirect
72. C2×#14519704C22semidirect
73. C2×#14519703C22semidirect
74. C2×#14519703C22semidirect
75. C2×#14519703C22semidirect
76. C2×#14519695C22semidirect
77. C2×#14519693C22semidirect
78. C2×#14519687C22semidirect
79. C2×AGL(1,ℤ/8)×C61C22semidirect
80. C2×AGL(1,ℤ/8)×C61C22semidirect
81. C22×D8×C61C22semidirect
82. C2×#131×C61C22semidirect
83. C61×#472C22semidirect
84. C2×#108×C61C22semidirect
85. C2×#100×C61C22semidirect
86. C2×#100×C61C22semidirect
90. #14519824C23semidirect
94. #14519823C23semidirect
102. #14519822C23semidirect
132. #14519810C23semidirect
133. #14519810C23semidirect
139. #14519805C23semidirect
144. #14519803C23semidirect
150. #14519799D4semidirect
153. #14519797D4semidirect
159. C2×Dic244D4semidirect
160. C2×#11758202D4semidirect
169. C2×#11758190D4semidirect
170. C2×#11758190D4semidirect
171. C2×#11758190C23semidirect
177. C2×#11758200D4semidirect
178. C2×#11758200C23semidirect
179. C2×#11758201D4semidirect
183. C2×D488D4semidirect
189. C2×#11758199D4semidirect
190. C2×#11758199C23semidirect
195. #14519785C23semidirect
196. #14519785C23semidirect
198. #14519783C23semidirect
208. #14519773C23semidirect
210. #14519764C23semidirect
213. #14519712C23semidirect
214. #14519704C23semidirect
215. #14519703C23semidirect
216. #14519703C23semidirect
217. #14519703C23semidirect
218. #14519695C23semidirect
219. #14519693C23semidirect
220. #14519687C23semidirect
226. AGL(1,ℤ/8)×C61C23semidirect
227. AGL(1,ℤ/8)×C61C23semidirect
235. C2×D8×C61C23semidirect
237. #131×C61C23semidirect
244. #108×C61C23semidirect
245. #100×C61C23semidirect
246. #100×C61C23semidirect
389. #11758202C2×D4semidirect
390. #11758201C2×D4semidirect
395. #11758200C2×D4semidirect
400. #11758199C2×D4semidirect
412. Dic244C2×D4semidirect
415. D488C2×D4semidirect
422. #11758190C2×D4semidirect
423. #11758190C2×D4semidirect
583. C2×#472D61semidirect
597. C2×C61#3288semidirect
629. C2×AGL(1,ℤ/8)C2×D61semidirect
630. C2×AGL(1,ℤ/8)C2×D61semidirect
644. C22×D8C2×D61semidirect
648. C2×#131C2×D61semidirect
653. #472C2×D61semidirect
663. C2×#108C2×D61semidirect
670. C2×#100C2×D61semidirect
671. C2×#100C2×D61semidirect
673. C61C2×#3288semidirect
741. AGL(1,ℤ/8)C22×D61semidirect
742. AGL(1,ℤ/8)C22×D61semidirect
794. C2×D8C22×D61semidirect
802. #131C22×D61semidirect
824. #108C22×D61semidirect
831. #100C22×D61semidirect
832. #100C22×D61semidirect
1171. C2#21457582direct (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×#168405662
C2×#168405632
#214575822
C2×#168401502
C2×#168400312
C2×#168400262
C2×#168400242
C2×#168399332
C2×#168399422
C2×#168399322
C2×#168399282
C2×#168398832
C2×#168398822
C2×C61×#4722
C2×#328861