Finite Group Databasebeta

← C2×#21457586 #30556195

Subgroups — C2×#21457586 #30556195

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×#16840569C211yesmaximal, characteristic, complemented
3C2×#16840567C211yesmaximal, characteristic, complemented
4C2×#16840564C211yesmaximal, characteristic, complemented
5#21457586C2116yesmaximal, direct product factor
6C2×#16840151C211yesmaximal, characteristic, complemented
7C2×#16840033C211yesmaximal, characteristic, complemented
8C2×#16840032C211yesmaximal, characteristic, complemented
9C2×#16840026C211yesmaximal, characteristic, complemented
10C2×#16840025C211yesmaximal, characteristic, complemented
11C2×#16839936C211yesmaximal, characteristic, complemented
12C2×#16839941C211yesmaximal, characteristic, complemented
13C2×#16839931C211yesmaximal, characteristic, complemented
14C2×#16839931C211yesmaximal, characteristic, complemented
15C2×#16839885C211yesmaximal, characteristic, complemented
16C2×C61×#444C211yesmaximal, characteristic, complemented
17C2×#14519824C2211yescharacteristic, complemented
18C2×#14519823C2211yescharacteristic
19C2×#14519823C2211yescharacteristic, complemented
20C2×#14519823C2211yescharacteristic, complemented
21#16840574—24no—
22#16840574C2218yescomplemented
23#16840569—24no—
24#16840569C2218yescomplemented
25#16840567—24no—
26#16840567C2218yescomplemented
27#16840564—24no—
28#16840564C2218yescomplemented
29C2×#14519810—21no—
30C2×#14519810C2211yescharacteristic, complemented
31C2×#14519809—21no—
32C2×#14519807C2211yescharacteristic, complemented
33C2×#14519805—21no—
34C2×#14519805—21no—
35C2×#14519805—21no—
36C2×#14519805C2211yescharacteristic
37C2×#14519805C2211yescharacteristic, complemented
38C2×#14519805C2211yescharacteristic, complemented
39C2×#14519804—21no—
40C2×#14519804—21no—
41C2×#14519802C2211yescharacteristic
42C2×#14519802C2211yescharacteristic, complemented
43C2×#14519802C2211yescharacteristic, complemented
44C2×#14519801—21no—
45C2×#14519800—21no—
46C2×#14519799—21no—
47C2×#14519799—21no—
48C2×#14519799C2211yescharacteristic
49C2×#14519798—21no—
50C22×#11758190—21no—
51C22×#11758190C2211yescharacteristic, complemented
52C22×#11758190C2211yescharacteristic, complemented
53C2×SD16×D61—21no—
54C22×D488—21no—
55C22×D488C2211yescharacteristic, complemented
56C22×D488C2211yescharacteristic, complemented
57C2×D8×D61—21no—
58C2×#14519783C2211yescharacteristic, complemented
59C2×#14519783C2211yescharacteristic, complemented
60C2×#14519774C2211yescharacteristic, complemented
61C2×#14519765C2211yescharacteristic, complemented
62#16840151C2218yescomplemented
63#16840033C2218yescomplemented
64#16840032C2218yescomplemented
65#16840026C2218yescomplemented
66#16840025C2218yescomplemented
67#16839941C2218yescomplemented
68#16839936C2218yescomplemented
69#16839931C2218yescomplemented
70#16839931C2218yescomplemented
71#16839885C2218yescomplemented
72C2×#14519713C2211yescharacteristic, complemented
73C2×#14519705C2211yescharacteristic, complemented
74C2×#14519705C2211yescharacteristic, complemented
75C2×#14519695C2211yescharacteristic, complemented
76C2×#14519693C2211yescharacteristic, complemented
77C2×#14519693C2211yescharacteristic, complemented
78C2×#14519693C2211yescharacteristic, complemented
79C2×#135×C61C2211yescharacteristic
80C2×#131×C61C2211yescharacteristic, complemented
81C2×#131×C61C2211yescharacteristic, complemented
82C61×#444C2218yescomplemented
83C2×#108×C61C2211yescharacteristic, complemented
84C2×#104×C61C2211yescharacteristic, complemented
85C2×#104×C61C2211yescharacteristic, complemented
86C2×#97×C61C2211yescharacteristic, complemented
87#14519824—22no—
88#14519824—22no—
89#14519824—41no—
90#14519824C2314yescomplemented
91#14519823—22no—
92#14519823—22no—
93#14519823—22no—
94#14519823—22no—
95#14519823—22no—
96#14519823—22no—
97#14519823—41no—
98#14519823—41no—
99#14519823—41no—
100#14519823C2314yes—
101#14519823C2314yescomplemented
102#14519823C2314yescomplemented
103C2×#11758226—21no—
104C2×#11758226—21no—
105C2×#11758226—21no—
106C2×#11758222—21no—
107C2×#11758222—21no—
108C2×#11758222—21no—
109C2×#11758222—21no—
110C2×#11758222C2311yescharacteristic
111C2×#11758222C2311yescharacteristic
112C2×#11758224—21no—
113C2×#11758224—41no—
114C22×Dic122—21no—
115C22×Dic122C2311yescharacteristic
116C2×Q8×D61—21no—
117C22×D244—21no—
118C22×D244—21no—
119C22×D244—21no—
120C22×D244—41no—
121C22×D244C2311yescharacteristic
122C22×D244C2311yescharacteristic
123C22×D244C2311yescharacteristic
124C2×D4×D61—21no—
125C2×D4×D61—21no—
126C2×D4×D61—21no—
127C2×D4×D61—41no—
128C2×D4×D61—41no—
129C2×D4×D61—41no—
130#14519810—22no—
131#14519810—28no—
132#14519810C2314yescomplemented
133#14519809—28no—
134#14519807—22no—
135#14519807C2314yescomplemented
136#14519805—22no—
137#14519805—22no—
138#14519805—22no—
139#14519805—28no—
140#14519805—28no—
141#14519805—28no—
142#14519805C2314yes—
143#14519805C2314yescomplemented
144#14519805C2314yescomplemented
145#14519804—28no—
146#14519804—28no—
147#14519802—22no—
148#14519802—22no—
149#14519802—22no—
150#14519802C2314yes—
151#14519802C2314yescomplemented
152#14519802C2314yescomplemented
153#14519801—28no—
154#14519800—28no—
155#14519799—28no—
156#14519799—28no—
157#14519799D414yescomplemented
158#14519799C2314yes—
159#14519798—28no—
160C2×Dic244—21no—
161C2×Dic244D411yescharacteristic, complemented
162C2×#11758202—21no—
163C2×#11758190—21no—
164C2×#11758190—21no—
165C2×#11758190—21no—
166C2×#11758190—21no—
167C2×#11758190—21no—
168C2×#11758190—21no—
169C2×#11758190—21no—
170C2×#11758190—21no—
171C2×#11758190—22no—
172C2×#11758190—22no—
173C2×#11758190—28no—
174C2×#11758190D411yescharacteristic, complemented
175C2×#11758190D411yescharacteristic, complemented
176C2×#11758190C2314yescomplemented
177C2×#11758190C2314yescomplemented
178C2×#11758200—21no—
179C2×#11758201—21no—
180C2×#11758201—21no—
181C2×#11758201—21no—
182SD16×D61—28no—
183C2×D488—21no—
184C2×D488—21no—
185C2×D488—21no—
186C2×D488—21no—
187C2×D488—21no—
188C2×D488—21no—
189C2×D488—21no—
190C2×D488—22no—
191C2×D488—22no—
192C2×D488—28no—
193C2×D488D411yescharacteristic, complemented
194C2×D488C2314yescomplemented
195C2×D488C2314yescomplemented
196C2×#11758199—21no—
197C2×#11758199—21no—
198C2×#11758199—21no—
199D8×D61—28no—
200#14519783—22no—
201#14519783—22no—
202#14519783C2314yescomplemented
203#14519783C2314yescomplemented
204C2×#11758194C2311yescharacteristic
205C2×#11758194C2311yescharacteristic
206C2×#11758189—21no—
207C2×#11758189—21no—
208C2×C8×D61—21no—
209C2×C8×D61—21no—
210#14519774—41no—
211#14519774C2314yescomplemented
212#14519765—41no—
213#14519765C2314yescomplemented
214C2×#11758198—41no—
215#14519713C2314yescomplemented
216#14519705C2314yescomplemented
217#14519705C2314yescomplemented
218#14519695C2314yescomplemented
219#14519693C2314yescomplemented
220#14519693C2314yescomplemented
221#14519693C2314yescomplemented
222C2×#41×C61C2311yescharacteristic
223C2×#41×C61C2311yescharacteristic
224#135×C61D414yescomplemented
225#135×C61C2314yes—
226C2×Q16×C61D411yescharacteristic, complemented
227C2×SD16×C61D411yescharacteristic, complemented
228C2×SD16×C61D411yescharacteristic, complemented
229C2×D8×C61D411yescharacteristic, complemented
230#131×C61—22no—
231#131×C61—22no—
232#131×C61C2314yescomplemented
233#131×C61C2314yescomplemented
234C2×M16×C61—21no—
235C2×M16×C61—21no—
236C2×M16×C61C2311yescharacteristic
237C2×M16×C61C2311yescharacteristic
238C22×C8×C61—21no—
239C22×C8×C61—21no—
240C22×C8×C61C2311yescharacteristic
241C22×C8×C61C2311yescharacteristic
242C2×C42×C61C2311yescharacteristic
243#108×C61C2314yescomplemented
244#104×C61C2314yescomplemented
245#104×C61C2314yescomplemented
246#97×C61C2314yescomplemented
247C23×D61—21no—
248C23×D61—21no—
249C23×D61—21no—
250C23×D61—41no—
251C23×D61—41no—
252C23×D61—41no—
253#41×C61—21no—
254#41×C61—21no—
255#41×C61—21no—
256#41×C61—21no—
257#41×C61C2×D412yes—
258#41×C61C2×D412yes—
259#41×C61C2412yes—
260#41×C61C2412yes—
261C2×Q8×C61C2×D411yescharacteristic
262C2×Q8×C61C2×D411yescharacteristic
263C2×D4×C61—21no—
264C2×D4×C61—21no—
265C2×D4×C61C2×D411yescharacteristic
266C2×D4×C61C2×D411yescharacteristic
267C22×C4×C61—21no—
268C22×C4×C61—21no—
269C22×C4×C61—21no—
270C22×C4×C61C2411yescharacteristic
271C2×C22⋊D61—21no—
272C2×C22⋊D61—21no—
273C2×C22⋊D61—41no—
274C2×C22⋊D61—41no—
275C2×C22⋊D61—41no—
276C2×C22⋊D61—41no—
277C22×Dic61—21no—
278C22×Dic61—41no—
279#11758226—24no—
280#11758226—24no—
281#11758226—24no—
282#11758226—42no—
283#11758226—42no—
284#11758226—42no—
285Q8×D61—24no—
286Q8×D61—42no—
287#11758224—24no—
288#11758224—42no—
289#11758224—44no—
290#11758224—44no—
291D4×D61—24no—
292D4×D61—24no—
293D4×D61—24no—
294D4×D61—42no—
295D4×D61—42no—
296D4×D61—42no—
297D4×D61—44no—
298D4×D61—44no—
299D4×D61—44no—
300D4×D61—44no—
301D4×D61—44no—
302D4×D61—44no—
303#11758222—21no—
304#11758222—21no—
305#11758222—21no—
306#11758222—21no—
307#11758222—24no—
308#11758222—24no—
309#11758222—24no—
310#11758222—24no—
311#11758222—42no—
312#11758222—42no—
313#11758222—42no—
314#11758222—42no—
315#11758222C2×D412yes—
316#11758222C2×D412yes—
317#11758222C2412yes—
318#11758222C2412yes—
319C2×D244—21no—
320C2×D244—21no—
321C2×D244—21no—
322C2×D244—21no—
323C2×D244—21no—
324C2×D244—21no—
325C2×D244—21no—
326C2×D244—21no—
327C2×D244—21no—
328C2×D244—21no—
329C2×D244—21no—
330C2×D244—21no—
331C2×D244—24no—
332C2×D244—24no—
333C2×D244—24no—
334C2×D244—21no—
335C2×D244—21no—
336C2×D244—21no—
337C2×D244—42no—
338C2×D244—42no—
339C2×D244—42no—
340C2×D244—41no—
341C2×D244—41no—
342C2×D244—41no—
343C2×D244—44no—
344C2×D244—84no—
345C2×D244C2×D411yescharacteristic
346C2×D244C2×D411yescharacteristic
347C2×D244C2412yes—
348C2×D244C2412yes—
349C2×D244C2412yes—
350C2×C4×D61—21no—
351C2×C4×D61—21no—
352C2×C4×D61—41no—
353C2×C4×D61—41no—
354C2×C4×D61—41no—
355C2×C4×D61—41no—
356C2×Dic122—21no—
357C2×Dic122—21no—
358C2×Dic122—21no—
359C2×Dic122—21no—
360C2×Dic122—24no—
361C2×Dic122—21no—
362C2×Dic122—42no—
363C2×Dic122—41no—
364C2×Dic122C2×D411yescharacteristic
365C2×Dic122C2×D411yescharacteristic
366C2×Dic122C2412yes—
367Q16×C61C2×D414yescomplemented
368SD16×C61C2×D414yescomplemented
369SD16×C61C2×D414yescomplemented
370D8×C61C2×D414yescomplemented
371M16×C61—21no—
372M16×C61—21no—
373M16×C61—24no—
374M16×C61—24no—
375M16×C61C2412yes—
376M16×C61C2412yes—
377C2×C8×C61—21no—
378C2×C8×C61—21no—
379C2×C8×C61—24no—
380C2×C8×C61—24no—
381C2×C8×C61C2×D411yescharacteristic
382C2×C8×C61C2×D411yescharacteristic
383C2×C8×C61C2×D412yes—
384C2×C8×C61C2×D411yescharacteristic
385C2×C8×C61C2×D411yescharacteristic
386C2×C8×C61C2×D412yes—
387C2×C8×C61C2412yes—
388C2×C8×C61C2412yes—
389C42×C61—21no—
390C42×C61C2412yes—
391#11758202—24no—
392#11758201—24no—
393#11758201—24no—
394#11758201—24no—
395#11758200—24no—
396#11758199—24no—
397#11758199—24no—
398#11758199—24no—
399#11758198—44no—
400#11758194—21no—
401#11758194—21no—
402#11758194C2412yes—
403#11758194C2412yes—
404C2×#92418—21no—
405C2×#92418—21no—
406Dic244—24no—
407Dic244C2×D414yescomplemented
408D488—24no—
409D488—24no—
410D488—24no—
411D488—24no—
412D488—24no—
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#11758190—24no—
423#11758190—24no—
424#11758190C2×D414yescomplemented
425#11758190C2×D414yescomplemented
426#11758189—24no—
427#11758189—24no—
428C8×D61—24no—
429C8×D61—24no—
430C23×C61—21no—
431C23×C61—21no—
432C23×C61H(5,𝔽2)11yescharacteristic
433C22×D61—21no—
434C22×D61—21no—
435C22×D61—22no—
436C22×D61—22no—
437C22×D61—22no—
438C22×D61—44no—
439C22×D61—44no—
440C22×D61—44no—
441C22×D61—41no—
442C22×D61—41no—
443C22×D61—41no—
444C22×D61—41no—
445C22×D61—41no—
446C22×D61—41no—
447C22×D61—82no—
448C22×D61—82no—
449C22×D61—82no—
450C22×D61—162no—
451C22×D61—162no—
452C22×D61—162no—
453Q8×C61—21no—
454Q8×C61—21no—
455Q8×C61C22×D412yes—
456Q8×C61C22×D412yes—
457D4×C61—22no—
458D4×C61—22no—
459D4×C61—22no—
460D4×C61—22no—
461D4×C61—21no—
462D4×C61—21no—
463D4×C61C22×D412yes—
464D4×C61C22×D412yes—
465C2×C4×C61—21no—
466C2×C4×C61—21no—
467C2×C4×C61—22no—
468C2×C4×C61—22no—
469C2×C4×C61—22no—
470C2×C4×C61—22no—
471C2×C4×C61—22no—
472C2×C4×C61—42no—
473C2×C4×C61C22×D411yescharacteristic
474C2×C4×C61C22×D411yescharacteristic
475C2×C4×C61C22×D411yescharacteristic
476C2×C4×C61C22×D411yescharacteristic
477C2×C4×C61H(5,𝔽2)11yescharacteristic
478C2×C4×C61C2511yescharacteristic
479C22⋊D61—22no—
480C22⋊D61—22no—
481C22⋊D61—22no—
482C22⋊D61—22no—
483C22⋊D61—44no—
484C22⋊D61—44no—
485C22⋊D61—44no—
486C22⋊D61—44no—
487C2×Dic61—21no—
488C2×Dic61—21no—
489C2×Dic61—22no—
490C2×Dic61—44no—
491C2×Dic61—41no—
492C2×Dic61—41no—
493D244—21no—
494D244—21no—
495D244—22no—
496D244—22no—
497D244—22no—
498D244—22no—
499D244—22no—
500D244—22no—
501D244—44no—
502D244—44no—
503D244—44no—
504D244—41no—
505D244—41no—
506D244—41no—
507D244—41no—
508D244—41no—
509D244—41no—
510D244—88no—
511D244C22×D412yes—
512D244C22×D412yes—
513C4×D61—22no—
514C4×D61—22no—
515C4×D61—22no—
516C4×D61—22no—
517C4×D61—44no—
518C4×D61—44no—
519C4×D61—44no—
520C4×D61—44no—
521Dic122—21no—
522Dic122—21no—
523Dic122—22no—
524Dic122—22no—
525Dic122—44no—
526Dic122—41no—
527Dic122—41no—
528Dic122C22×D412yes—
529Dic122C22×D412yes—
530C8×C61—22no—
531C8×C61—22no—
532C8×C61C22×D412yes—
533C8×C61C22×D412yes—
534C8×C61C22×D412yes—
535C8×C61C22×D412yes—
536#92418—22no—
537#92418—22no—
538C2×#3288—611nomaximal, Sylow
539C22×C61—22no—
540C22×C61—22no—
541C22×C61—22no—
542C22×C61—42no—
543C22×C61—42no—
544C22×C61D4211yescharacteristic
545C22×C61D4211yescharacteristic
546C22×C61C2×H(5,𝔽2)11yescharacteristic
547C2×D61—22no—
548C2×D61—22no—
549C2×D61—42no—
550C2×D61—42no—
551C2×D61—42no—
552C2×D61—42no—
553C2×D61—42no—
554C2×D61—82no—
555C2×D61—82no—
556C2×D61—82no—
557C2×D61—82no—
558C2×D61—82no—
559C2×D61—82no—
560C2×D61—164no—
561C2×D61—164no—
562C2×D61—164no—
563C2×D61—161no—
564C2×D61—161no—
565C2×D61—161no—
566C4×C61—22no—
567C4×C61—22no—
568C4×C61—42no—
569C4×C61D4211yescharacteristic
570C4×C61D4211yescharacteristic
571C4×C61C23×D411yescharacteristic
572C4×C61C23×D411yescharacteristic
573Dic61—22no—
574Dic61—22no—
575Dic61—42no—
576C2×#577—611no—
577C2×#577—611no—
578C2×#576—611no—
579C2×#576—611no—
580#3288—6116no—
581C2×#496—611no—
582C2×#472—611no—
583C2×#472—611no—
584C2×#471—611no—
585C2×#471—611no—
586C2×#454—611no—
587C2×#455—611no—
588C2×#453—611no—
589C2×#453—611no—
590C2×#444—611no—
591C2×#444D6111yescharacteristic, complemented
592C2×C61—21no—
593C2×C61—21no—
594C2×C61—42no—
595C2×C61—42no—
596C2×C61#328812yescomplemented
597C2×C61C2×D4211yescharacteristic
598D61—42no—
599D61—42no—
600D61—82no—
601D61—82no—
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)—611no—
624C2×AGL(1,ℤ/8)—611no—
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)—1221no—
630C2×AGL(1,ℤ/8)—1221no—
631C2×#135—611no—
632C2×#135—1221no—
633C2×#135—1221no—
634C2×#135—1221no—
635C2×#135—1221no—
636C2×#135C2×D6111yescharacteristic
637C22×SD16—611no—
638C22×SD16—611no—
639C22×SD16—1221no—
640C22×SD16—1221no—
641C22×D8—611no—
642C22×D8—611no—
643C22×D8—1221no—
644C22×D8—1221no—
645C2×#131—611no—
646C2×#131—611no—
647C2×#131C2×D6111yescharacteristic, complemented
648C2×#131C2×D6111yescharacteristic, complemented
649C2×#127—611no—
650C2×#124—611no—
651#496—618no—
652#472—618no—
653#472—618no—
654#471—618no—
655#471—618no—
656#455—618no—
657#454—618no—
658#453—618no—
659#453—618no—
660#444—618no—
661#444C2×D6118yescomplemented
662C2×#108—611no—
663C2×#108C2×D6111yescharacteristic, complemented
664C2×#104—611no—
665C2×#104—611no—
666C2×#104C2×D6111yescharacteristic, complemented
667C2×#104C2×D6111yescharacteristic, complemented
668C2×#101—611no—
669C2×#100—611no—
670C2×#100—611no—
671C2×#100—611no—
672C2×#97C2×D6111yescharacteristic, complemented
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—1221no—
693C2×#41—1221no—
694C2×#41—1221no—
695C2×#41—1221no—
696C2×#41—1221no—
697C2×#41—1221no—
698C2×#41—1221no—
699C2×#41—1221no—
700C2×#41—2441no—
701C2×#41C22×D6111yescharacteristic
702C2×#41C22×D6111yescharacteristic
703C22×Q8—611no—
704C22×Q8—1221no—
705C22×Q8—1221no—
706C22×D4—611no—
707C22×D4—611no—
708C22×D4—611no—
709C22×D4—1221no—
710C22×D4—1221no—
711C22×D4—1221no—
712C22×D4—1221no—
713C22×D4—1221no—
714C22×D4—1221no—
715C22×D4—2441no—
716C22×D4—2441no—
717C22×D4—2441no—
718C22×D4—2441no—
719#137—614no—
720#137—614no—
721#137—1228no—
722#137—1222no—
723#137—1222no—
724#137—1228no—
725AGL(1,ℤ/8)—614no—
726AGL(1,ℤ/8)—614no—
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)—1228no—
733AGL(1,ℤ/8)—1228no—
734AGL(1,ℤ/8)—1222no—
735AGL(1,ℤ/8)—1222no—
736AGL(1,ℤ/8)—1222no—
737AGL(1,ℤ/8)—1222no—
738AGL(1,ℤ/8)—1222no—
739AGL(1,ℤ/8)—1222no—
740AGL(1,ℤ/8)—1228no—
741AGL(1,ℤ/8)—1228no—
742AGL(1,ℤ/8)—1228no—
743#135—614no—
744#135—614no—
745#135—1228no—
746#135—1228no—
747#135—1228no—
748#135—1228no—
749#135D24414yescomplemented
750#135C22×D6114yes—
751C2×Q16—611no—
752C2×Q16—1221no—
753C2×Q16—1221no—
754C2×Q16D24411yescharacteristic, complemented
755C2×SD16—611no—
756C2×SD16—611no—
757C2×SD16—614no—
758C2×SD16—614no—
759C2×SD16—1228no—
760C2×SD16—1221no—
761C2×SD16—1221no—
762C2×SD16—1221no—
763C2×SD16—1221no—
764C2×SD16—1221no—
765C2×SD16—1221no—
766C2×SD16—1221no—
767C2×SD16—1221no—
768C2×SD16—1228no—
769C2×SD16—1221no—
770C2×SD16—1221no—
771C2×SD16—1222no—
772C2×SD16—1221no—
773C2×SD16—1221no—
774C2×SD16—1222no—
775C2×SD16D24411yescharacteristic, complemented
776C2×SD16D24411yescharacteristic, complemented
777C2×D8—611no—
778C2×D8—614no—
779C2×D8—614no—
780C2×D8—1228no—
781C2×D8—1221no—
782C2×D8—1221no—
783C2×D8—1221no—
784C2×D8—1221no—
785C2×D8—1221no—
786C2×D8—1221no—
787C2×D8—1228no—
788C2×D8—1221no—
789C2×D8—1221no—
790C2×D8—1222no—
791C2×D8—1221no—
792C2×D8—1221no—
793C2×D8—1222no—
794C2×D8D24411yescharacteristic, complemented
795#131—22no—
796#131—22no—
797#131—614no—
798#131—614no—
799#131—1222no—
800#131—1222no—
801#131C22×D6114yescomplemented
802#131C22×D6114yescomplemented
803C2×M16—21no—
804C2×M16—21no—
805C2×M16—611no—
806C2×M16—611no—
807C2×M16—1221no—
808C2×M16—1221no—
809C2×M16C22×D6111yescharacteristic
810C2×M16C22×D6111yescharacteristic
811C22×C8—21no—
812C22×C8—21no—
813C22×C8—1221no—
814C22×C8—1221no—
815C22×C8C22×D6111yescharacteristic
816C22×C8C22×D6111yescharacteristic
817#127—614no—
818#127—2441no—
819#124—614no—
820#124—2441no—
821C2×C22⋊C4—2441no—
822C2×C42C22×D6111yescharacteristic
823#108—614no—
824#108C22×D6114yescomplemented
825#104—614no—
826#104—614no—
827#104C22×D6114yescomplemented
828#104C22×D6114yescomplemented
829#101—614no—
830#100—614no—
831#100—614no—
832#100—614no—
833#97C22×D6114yescomplemented
834C24—1221no—
835C24—1221no—
836C24—1221no—
837C24—2441no—
838C24—2441no—
839C24—2441no—
840#41—21no—
841#41—21no—
842#41—21no—
843#41—21no—
844#41—612no—
845#41—612no—
846#41—612no—
847#41—612no—
848#41—1224no—
849#41—1224no—
850#41—1224no—
851#41—1224no—
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—2442no—
861#41—2442no—
862#41—2442no—
863#41—2442no—
864#41—2444no—
865#41—2442no—
866#41—2442no—
867#41—2442no—
868#41—2442no—
869#41—2444no—
870#41C2×D24412yes—
871#41C2×D24412yes—
872#41C23×D6112yes—
873#41C23×D6112yes—
874C2×Q8—611no—
875C2×Q8—611no—
876C2×Q8—612no—
877C2×Q8—1224no—
878C2×Q8—1221no—
879C2×Q8—1224no—
880C2×Q8—1221no—
881C2×Q8—1221no—
882C2×Q8—1221no—
883C2×Q8—1221no—
884C2×Q8—2441no—
885C2×Q8—2442no—
886C2×Q8—2442no—
887C2×Q8C2×D24411yescharacteristic
888C2×Q8C2×D24411yescharacteristic
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—611no—
892C2×D4—611no—
893C2×D4—612no—
894C2×D4—612no—
895C2×D4—612no—
896C2×D4—1224no—
897C2×D4—1224no—
898C2×D4—1224no—
899C2×D4—1221no—
900C2×D4—1221no—
901C2×D4—1224no—
902C2×D4—1224no—
903C2×D4—1224no—
904C2×D4—1221no—
905C2×D4—1221no—
906C2×D4—1221no—
907C2×D4—1221no—
908C2×D4—1221no—
909C2×D4—1221no—
910C2×D4—1221no—
911C2×D4—1221no—
912C2×D4—1221no—
913C2×D4—1221no—
914C2×D4—1221no—
915C2×D4—1221no—
916C2×D4—1221no—
917C2×D4—1221no—
918C2×D4—1221no—
919C2×D4—4884no—
920C2×D4—2442no—
921C2×D4—2442no—
922C2×D4—2442no—
923C2×D4—2444no—
924C2×D4—2441no—
925C2×D4—2441no—
926C2×D4—2441no—
927C2×D4—2442no—
928C2×D4—2442no—
929C2×D4—2442no—
930C2×D4—2441no—
931C2×D4—2441no—
932C2×D4—2441no—
933C2×D4—2444no—
934C2×D4—2444no—
935C2×D4—2444no—
936C2×D4—2444no—
937C2×D4—2444no—
938C2×D4—2444no—
939C2×D4—2441no—
940C2×D4C2×D24411yescharacteristic
941C2×D4C2×D24411yescharacteristic
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
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—1224no—
956Q16—1224no—
957Q16C2×D24414yescomplemented
958SD16—614no—
959SD16—614no—
960SD16—1224no—
961SD16—1224no—
962SD16—1224no—
963SD16—1224no—
964SD16—1224no—
965SD16—1224no—
966SD16—1224no—
967SD16—1224no—
968SD16—1224no—
969SD16—1224no—
970SD16—1224no—
971SD16—1224no—
972SD16C2×D24414yescomplemented
973SD16C2×D24414yescomplemented
974D8—614no—
975D8—1224no—
976D8—1224no—
977D8—1224no—
978D8—1224no—
979D8—1224no—
980D8—1224no—
981D8—1224no—
982D8—1224no—
983D8—1224no—
984D8—1224no—
985D8C2×D24414yescomplemented
986M16—21no—
987M16—21no—
988M16—24no—
989M16—24no—
990M16—612no—
991M16—612no—
992M16—1221no—
993M16—1221no—
994M16—1224no—
995M16—1224no—
996M16C23×D6112yes—
997M16C23×D6112yes—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—24no—
1001C2×C8—24no—
1002C2×C8—1221no—
1003C2×C8—1221no—
1004C2×C8—1224no—
1005C2×C8—1224no—
1006C2×C8C2×D24411yescharacteristic
1007C2×C8C2×D24411yescharacteristic
1008C2×C8C2×D24412yes—
1009C2×C8D4×D6111yescharacteristic
1010C2×C8D4×D6111yescharacteristic
1011C2×C8D4×D6112yes—
1012C2×C8C23×D6112yes—
1013C2×C8C23×D6112yes—
1014C22⋊C4—2444no—
1015C42—21no—
1016C42C23×D6112yes—
1017C23—21no—
1018C23—21no—
1019C23—1221no—
1020C23—1221no—
1021C23—1222no—
1022C23—1222no—
1023C23—1222no—
1024C23—9762no—
1025C23—9762no—
1026C23—9762no—
1027C23—4882no—
1028C23—4882no—
1029C23—4882no—
1030C23—2444no—
1031C23—2444no—
1032C23—2444no—
1033C23—2441no—
1034C23—2441no—
1035C23—2441no—
1036C23—2441no—
1037C23—2441no—
1038C23—2441no—
1039C23#1451982311yescharacteristic
1040Q8—21no—
1041Q8—21no—
1042Q8—612no—
1043Q8—612no—
1044Q8—1221no—
1045Q8—1221no—
1046Q8—1222no—
1047Q8—1222no—
1048Q8—2444no—
1049Q8—2441no—
1050Q8—2441no—
1051Q8C22×D24412yes—
1052Q8C22×D24412yes—
1053D4—22no—
1054D4—22no—
1055D4—22no—
1056D4—22no—
1057D4—21no—
1058D4—21no—
1059D4—612no—
1060D4—612no—
1061D4—1222no—
1062D4—1222no—
1063D4—1222no—
1064D4—1222no—
1065D4—1222no—
1066D4—1222no—
1067D4—1222no—
1068D4—1222no—
1069D4—1222no—
1070D4—1222no—
1071D4—1221no—
1072D4—1221no—
1073D4—4888no—
1074D4—2444no—
1075D4—2444no—
1076D4—2444no—
1077D4—2444no—
1078D4—2444no—
1079D4—2444no—
1080D4—2444no—
1081D4—2441no—
1082D4—2441no—
1083D4—2441no—
1084D4—2441no—
1085D4—2441no—
1086D4—2441no—
1087D4C22×D24412yes—
1088D4C22×D24412yes—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—42no—
1097C2×C4—1221no—
1098C2×C4—1221no—
1099C2×C4—1222no—
1100C2×C4—1222no—
1101C2×C4—1222no—
1102C2×C4—1222no—
1103C2×C4—1222no—
1104C2×C4—2444no—
1105C2×C4—2444no—
1106C2×C4—2444no—
1107C2×C4—2444no—
1108C2×C4—2444no—
1109C2×C4—2441no—
1110C2×C4—2441no—
1111C2×C4C2×D4×D6111yescharacteristic
1112C2×C4C2×D4×D6111yescharacteristic
1113C2×C4C22×D24411yescharacteristic
1114C2×C4C22×D24411yescharacteristic
1115C2×C4#1451982311yescharacteristic
1116C2×C4C24×D6111yescharacteristic
1117C8—22no—
1118C8—22no—
1119C8—1222no—
1120C8—1222no—
1121C8C2×D4×D6112yes—
1122C8C2×D4×D6112yes—
1123C8C22×D24412yes—
1124C8C22×D24412yes—
1125C22—22no—
1126C22—22no—
1127C22—22no—
1128C22—42no—
1129C22—42no—
1130C22—1222no—
1131C22—1222no—
1132C22—9761no—
1133C22—9761no—
1134C22—9761no—
1135C22—9764no—
1136C22—9764no—
1137C22—9764no—
1138C22—4882no—
1139C22—4882no—
1140C22—4882no—
1141C22—4882no—
1142C22—4882no—
1143C22—4882no—
1144C22—2442no—
1145C22—2442no—
1146C22—2442no—
1147C22—2442no—
1148C22—2442no—
1149C22D4×D24411yescharacteristic
1150C22D4×D24411yescharacteristic
1151C22C2×#1451982311yescharacteristic
1152C4—22no—
1153C4—22no—
1154C4—42no—
1155C4—1222no—
1156C4—1222no—
1157C4—2442no—
1158C4D4×D24411yescharacteristic
1159C4D4×D24411yescharacteristic
1160C4C22×D4×D6111yescharacteristic
1161C4C23×D24411yescharacteristic
1162C2—21no—
1163C2—21no—
1164C2—42no—
1165C2—42no—
1166C2—4882no—
1167C2—4882no—
1168C2—4882no—
1169C2—2442no—
1170C2—2442no—
1171C2#2145758612yesdirect product factor
1172C2C2×D4×D24411yescharacteristic
subgroupG/H
centerC22D4×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#444C2
socleC22×C61D42
hypercenterC2×#444D61
hypocenterC61C2×#3288
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#444

Complements

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

NH ≅ G/Ntype
1. C2×#16840574C2semidirect
2. C2×#16840569C2semidirect
3. C2×#16840567C2semidirect
4. C2×#16840564C2semidirect
5. #21457586C2direct (N × H)
6. C2×#16840151C2semidirect
7. C2×#16840033C2semidirect
8. C2×#16840032C2semidirect
9. C2×#16840026C2semidirect
10. C2×#16840025C2semidirect
11. C2×#16839936C2semidirect
12. C2×#16839941C2semidirect
13. C2×#16839931C2semidirect
14. C2×#16839931C2semidirect
15. C2×#16839885C2semidirect
16. C2×C61×#444C2semidirect
17. C2×#14519824C22semidirect
19. C2×#14519823C22semidirect
20. C2×#14519823C22semidirect
22. #16840574C22semidirect
24. #16840569C22semidirect
26. #16840567C22semidirect
28. #16840564C22semidirect
30. C2×#14519810C22semidirect
32. C2×#14519807C22semidirect
37. C2×#14519805C22semidirect
38. C2×#14519805C22semidirect
42. C2×#14519802C22semidirect
43. C2×#14519802C22semidirect
51. C22×#11758190C22semidirect
52. C22×#11758190C22semidirect
55. C22×D488C22semidirect
56. C22×D488C22semidirect
58. C2×#14519783C22semidirect
59. C2×#14519783C22semidirect
60. C2×#14519774C22semidirect
61. C2×#14519765C22semidirect
62. #16840151C22semidirect
63. #16840033C22semidirect
64. #16840032C22semidirect
65. #16840026C22semidirect
66. #16840025C22semidirect
67. #16839941C22semidirect
68. #16839936C22semidirect
69. #16839931C22semidirect
70. #16839931C22semidirect
71. #16839885C22semidirect
72. C2×#14519713C22semidirect
73. C2×#14519705C22semidirect
74. C2×#14519705C22semidirect
75. C2×#14519695C22semidirect
76. C2×#14519693C22semidirect
77. C2×#14519693C22semidirect
78. C2×#14519693C22semidirect
80. C2×#131×C61C22semidirect
81. C2×#131×C61C22semidirect
82. C61×#444C22semidirect
83. C2×#108×C61C22semidirect
84. C2×#104×C61C22semidirect
85. C2×#104×C61C22semidirect
86. C2×#97×C61C22semidirect
90. #14519824C23semidirect
101. #14519823C23semidirect
102. #14519823C23semidirect
132. #14519810C23semidirect
135. #14519807C23semidirect
143. #14519805C23semidirect
144. #14519805C23semidirect
151. #14519802C23semidirect
152. #14519802C23semidirect
157. #14519799D4semidirect
161. C2×Dic244D4semidirect
174. C2×#11758190D4semidirect
175. C2×#11758190D4semidirect
176. C2×#11758190C23semidirect
177. C2×#11758190C23semidirect
193. C2×D488D4semidirect
194. C2×D488C23semidirect
195. C2×D488C23semidirect
202. #14519783C23semidirect
203. #14519783C23semidirect
211. #14519774C23semidirect
213. #14519765C23semidirect
215. #14519713C23semidirect
216. #14519705C23semidirect
217. #14519705C23semidirect
218. #14519695C23semidirect
219. #14519693C23semidirect
220. #14519693C23semidirect
221. #14519693C23semidirect
224. #135×C61D4semidirect
226. C2×Q16×C61D4semidirect
227. C2×SD16×C61D4semidirect
228. C2×SD16×C61D4semidirect
229. C2×D8×C61D4semidirect
232. #131×C61C23semidirect
233. #131×C61C23semidirect
243. #108×C61C23semidirect
244. #104×C61C23semidirect
245. #104×C61C23semidirect
246. #97×C61C23semidirect
367. Q16×C61C2×D4semidirect
368. SD16×C61C2×D4semidirect
369. SD16×C61C2×D4semidirect
370. D8×C61C2×D4semidirect
407. Dic244C2×D4semidirect
415. D488C2×D4semidirect
424. #11758190C2×D4semidirect
425. #11758190C2×D4semidirect
591. C2×#444D61semidirect
596. C2×C61#3288semidirect
647. C2×#131C2×D61semidirect
648. C2×#131C2×D61semidirect
661. #444C2×D61semidirect
663. C2×#108C2×D61semidirect
666. C2×#104C2×D61semidirect
667. C2×#104C2×D61semidirect
672. C2×#97C2×D61semidirect
673. C61C2×#3288semidirect
749. #135D244semidirect
754. C2×Q16D244semidirect
775. C2×SD16D244semidirect
776. C2×SD16D244semidirect
794. C2×D8D244semidirect
801. #131C22×D61semidirect
802. #131C22×D61semidirect
824. #108C22×D61semidirect
827. #104C22×D61semidirect
828. #104C22×D61semidirect
833. #97C22×D61semidirect
957. Q16C2×D244semidirect
972. SD16C2×D244semidirect
973. SD16C2×D244semidirect
985. D8C2×D244semidirect
1171. C2#21457586direct (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×#168405692
C2×#168405672
C2×#168405642
#214575862
C2×#168401512
C2×#168400332
C2×#168400322
C2×#168400262
C2×#168400252
C2×#168399362
C2×#168399412
C2×#168399312
C2×#168398852
C2×C61×#4442
C2×#328861