Finite Group Databasebeta

← C2×#21457580 #30556189

Subgroups — C2×#21457580 #30556189

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×#16840573C211yesmaximal, characteristic, complemented
2C2×#16840572C211yesmaximal, characteristic, complemented
3C2×#16840566C211yesmaximal, characteristic, complemented
4C2×#16840565C211yesmaximal, characteristic, complemented
5#21457580C2116yesmaximal, direct product factor
6C2×#16840149C211yesmaximal, characteristic, complemented
7C2×#16840031C211yesmaximal, characteristic, complemented
8C2×#16840030C211yesmaximal, characteristic, complemented
9C2×#16840024C211yesmaximal, characteristic, complemented
10C2×#16840023C211yesmaximal, characteristic, complemented
11C2×#16839936C211yesmaximal, characteristic, complemented
12C2×#16839941C211yesmaximal, characteristic, complemented
13C2×#16839929C211yesmaximal, characteristic, complemented
14C2×#16839881C211yesmaximal, characteristic, complemented
15C2×#16839881C211yesmaximal, characteristic, complemented
16C2×C61×#453C211yesmaximal, characteristic, complemented
17C2×#14519824C2211yescharacteristic, complemented
18C2×#14519823C2211yescharacteristic
19C2×#14519822C2211yescharacteristic, complemented
20#16840573—24no—
21#16840573C2218yescomplemented
22#16840572—24no—
23#16840572C2218yescomplemented
24#16840566—24no—
25#16840566C2218yescomplemented
26#16840565—24no—
27#16840565C2218yescomplemented
28C2×#14519810C2211yescharacteristic, complemented
29C2×#14519807—21no—
30C2×#14519807C2211yescharacteristic, complemented
31C2×#14519806—21no—
32C2×#14519805C2211yescharacteristic, complemented
33C2×#14519804—21no—
34C2×#14519803—21no—
35C2×#14519803—21no—
36C2×#14519803C2211yescharacteristic
37C2×#14519803C2211yescharacteristic, complemented
38C2×#14519802—21no—
39C2×#14519802C2211yescharacteristic, complemented
40C2×#14519801—21no—
41C2×#14519801—21no—
42C2×#14519798—21no—
43C2×#14519797—21no—
44C2×#14519797—21no—
45C2×#14519797C2211yescharacteristic
46C2×#14519797C2211yescharacteristic
47C2×#14519796—21no—
48C22×#11758200—21no—
49C22×#11758200C2211yescharacteristic, complemented
50C22×#11758200C2211yescharacteristic, complemented
51C2×SD16×D61—21no—
52C22×#11758199—21no—
53C22×#11758199C2211yescharacteristic, complemented
54C22×#11758199C2211yescharacteristic, complemented
55C2×D8×D61—21no—
56C2×#14519785C2211yescharacteristic, complemented
57C2×#14519785C2211yescharacteristic, complemented
58C2×#14519784C2211yescharacteristic, complemented
59C2×#14519784C2211yescharacteristic, complemented
60C2×#14519765C2211yescharacteristic, complemented
61#16840149C2218yescomplemented
62#16840031C2218yescomplemented
63#16840030C2218yescomplemented
64#16840024C2218yescomplemented
65#16840023C2218yescomplemented
66#16839941C2218yescomplemented
67#16839936C2218yescomplemented
68#16839929C2218yescomplemented
69#16839881C2218yescomplemented
70#16839881C2218yescomplemented
71C2×#14519712C2211yescharacteristic, complemented
72C2×#14519712C2211yescharacteristic, complemented
73C2×#14519705C2211yescharacteristic, complemented
74C2×#14519705C2211yescharacteristic, complemented
75C2×#14519695C2211yescharacteristic, complemented
76C2×#14519694C2211yescharacteristic, complemented
77C2×#14519693C2211yescharacteristic, complemented
78C2×#14519688C2211yescharacteristic, complemented
79C2×H(5,𝔽2)×C61C2211yescharacteristic, complemented
80C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
81C2×AGL(1,ℤ/8)×C61C2211yescharacteristic, complemented
82C2×#127×C61C2211yescharacteristic, complemented
83C61×#453C2218yescomplemented
84C2×#104×C61C2211yescharacteristic, complemented
85C2×#104×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#14519823C2314yes—
95#14519822—22no—
96#14519822—22no—
97#14519822—41no—
98#14519822C2314yescomplemented
99C2×#11758226—21no—
100C2×#11758222—21no—
101C2×#11758222—21no—
102C2×#11758222C2311yescharacteristic
103C2×#11758222C2311yescharacteristic
104C2×#11758224—21no—
105C2×#11758224—21no—
106C2×#11758224—21no—
107C2×#11758224—41no—
108C22×Dic122—21no—
109C22×Dic122C2311yescharacteristic
110C2×Q8×D61—21no—
111C22×D244—21no—
112C22×D244C2311yescharacteristic
113C22×C22⋊D61—41no—
114C2×D4×D61—21no—
115C2×D4×D61—21no—
116C2×D4×D61—21no—
117C2×D4×D61—41no—
118#14519810—22no—
119#14519810C2314yescomplemented
120#14519807—22no—
121#14519807—28no—
122#14519807C2314yescomplemented
123#14519806—28no—
124#14519805—22no—
125#14519805C2314yescomplemented
126#14519804—28no—
127#14519803—22no—
128#14519803—22no—
129#14519803—28no—
130#14519803—28no—
131#14519803C2314yes—
132#14519803C2314yescomplemented
133#14519802—22no—
134#14519802—28no—
135#14519802C2314yescomplemented
136#14519801—28no—
137#14519801—28no—
138#14519798—28no—
139#14519797—28no—
140#14519797—28no—
141#14519797D414yescomplemented
142#14519797D414yescomplemented
143#14519797C2314yes—
144#14519797C2314yes—
145#14519796—28no—
146C2×Dic244—21no—
147C2×#11758202—21no—
148C2×#11758202D411yescharacteristic, complemented
149C2×#11758202D411yescharacteristic, complemented
150C2×#11758190—21no—
151C2×#11758190—21no—
152C2×#11758200—21no—
153C2×#11758200—21no—
154C2×#11758200—21no—
155C2×#11758200—28no—
156C2×#11758200—21no—
157C2×#11758200—21no—
158C2×#11758200—21no—
159C2×#11758200—21no—
160C2×#11758200—22no—
161C2×#11758200—22no—
162C2×#11758200D411yescharacteristic, complemented
163C2×#11758200D411yescharacteristic, complemented
164C2×#11758200C2314yescomplemented
165C2×#11758200C2314yescomplemented
166C2×#11758201—21no—
167C2×#11758201D411yescharacteristic, complemented
168C2×#11758201D411yescharacteristic, complemented
169SD16×D61—28no—
170C2×D488—21no—
171C2×#11758199—21no—
172C2×#11758199—21no—
173C2×#11758199—21no—
174C2×#11758199—28no—
175C2×#11758199—21no—
176C2×#11758199—21no—
177C2×#11758199—21no—
178C2×#11758199—21no—
179C2×#11758199—22no—
180C2×#11758199—22no—
181C2×#11758199D411yescharacteristic, complemented
182C2×#11758199D411yescharacteristic, complemented
183C2×#11758199C2314yescomplemented
184C2×#11758199C2314yescomplemented
185D8×D61—28no—
186#14519785—22no—
187#14519785—22no—
188#14519785C2314yescomplemented
189#14519785C2314yescomplemented
190#14519784—22no—
191#14519784—22no—
192#14519784C2314yescomplemented
193#14519784C2314yescomplemented
194C2×#11758194—21no—
195C2×#11758194—21no—
196C2×#11758194C2311yescharacteristic
197C2×#11758194C2311yescharacteristic
198C2×#11758189—21no—
199C2×#11758189—21no—
200C22×#92418—21no—
201C22×#92418—21no—
202C22×#92418C2311yescharacteristic
203C22×#92418C2311yescharacteristic
204C2×C8×D61—21no—
205C2×C8×D61—21no—
206#14519765—41no—
207#14519765C2314yescomplemented
208C2×#11758198—41no—
209#14519712C2314yescomplemented
210#14519712C2314yescomplemented
211#14519705C2314yescomplemented
212#14519705C2314yescomplemented
213#14519695C2314yescomplemented
214#14519694C2314yescomplemented
215#14519693C2314yescomplemented
216#14519688C2314yescomplemented
217H(5,𝔽2)×C61—22no—
218H(5,𝔽2)×C61—22no—
219H(5,𝔽2)×C61—41no—
220H(5,𝔽2)×C61C2314yescomplemented
221C2×#41×C61—21no—
222C2×#41×C61—21no—
223C2×#41×C61C2311yescharacteristic
224C2×#41×C61C2311yescharacteristic
225C22×D4×C61—21no—
226C22×D4×C61—21no—
227C22×D4×C61—41no—
228C22×D4×C61—41no—
229C22×D4×C61C2311yescharacteristic
230C22×D4×C61C2311yescharacteristic
231AGL(1,ℤ/8)×C61—22no—
232AGL(1,ℤ/8)×C61—22no—
233AGL(1,ℤ/8)×C61C2314yes—
234AGL(1,ℤ/8)×C61C2314yescomplemented
235C2×SD16×C61—21no—
236C2×SD16×C61—21no—
237C2×D8×C61—21no—
238C2×D8×C61—21no—
239C2×M16×C61C2311yescharacteristic
240C2×M16×C61C2311yescharacteristic
241#127×C61—41no—
242#127×C61C2314yescomplemented
243C2×C42×C61C2311yescharacteristic
244#104×C61C2314yescomplemented
245#104×C61C2314yescomplemented
246#100×C61C2314yescomplemented
247C24×C61—21no—
248C24×C61—21no—
249C24×C61—41no—
250C23×D61—21no—
251C23×D61—41no—
252C23×D61—41no—
253#41×C61—21no—
254#41×C61—21no—
255#41×C61—21no—
256#41×C61—21no—
257#41×C61—24no—
258#41×C61—24no—
259#41×C61—42no—
260#41×C61—42no—
261#41×C61C2×D412yes—
262#41×C61C2×D412yes—
263#41×C61C2412yes—
264#41×C61C2412yes—
265C2×Q8×C61C2×D411yescharacteristic
266C2×Q8×C61C2×D411yescharacteristic
267C2×D4×C61—21no—
268C2×D4×C61—21no—
269C2×D4×C61—24no—
270C2×D4×C61—24no—
271C2×D4×C61—21no—
272C2×D4×C61—21no—
273C2×D4×C61—21no—
274C2×D4×C61—21no—
275C2×D4×C61—21no—
276C2×D4×C61—21no—
277C2×D4×C61—21no—
278C2×D4×C61—21no—
279C2×D4×C61—21no—
280C2×D4×C61—21no—
281C2×D4×C61—42no—
282C2×D4×C61—42no—
283C2×D4×C61—41no—
284C2×D4×C61—41no—
285C2×D4×C61—44no—
286C2×D4×C61—44no—
287C2×D4×C61—44no—
288C2×D4×C61—84no—
289C2×D4×C61C2×D411yescharacteristic
290C2×D4×C61C2×D411yescharacteristic
291C2×D4×C61C2412yes—
292C2×D4×C61C2412yes—
293C22×C4×C61—21no—
294C22×C4×C61—21no—
295C22×C4×C61—21no—
296C22×C4×C61—41no—
297C22×C4×C61C2411yescharacteristic
298C2×C22⋊D61—21no—
299C2×C22⋊D61—21no—
300C2×C22⋊D61—41no—
301C2×C22⋊D61—41no—
302C2×C22⋊D61—41no—
303C2×C22⋊D61—44no—
304C2×C22⋊D61—44no—
305C2×C22⋊D61—41no—
306C22×Dic61—21no—
307C22×Dic61—41no—
308C22×Dic61—41no—
309#11758226—24no—
310#11758226—42no—
311Q8×D61—24no—
312Q8×D61—42no—
313#11758224—24no—
314#11758224—24no—
315#11758224—24no—
316#11758224—42no—
317#11758224—42no—
318#11758224—42no—
319#11758224—44no—
320#11758224—44no—
321D4×D61—24no—
322D4×D61—24no—
323D4×D61—24no—
324D4×D61—42no—
325D4×D61—42no—
326D4×D61—42no—
327D4×D61—44no—
328D4×D61—44no—
329#11758222—21no—
330#11758222—21no—
331#11758222—21no—
332#11758222—21no—
333#11758222—24no—
334#11758222—24no—
335#11758222—42no—
336#11758222—42no—
337#11758222C2×D412yes—
338#11758222C2×D412yes—
339#11758222C2412yes—
340#11758222C2412yes—
341C2×D244—21no—
342C2×D244—21no—
343C2×D244—21no—
344C2×D244—21no—
345C2×D244—24no—
346C2×D244—21no—
347C2×D244—42no—
348C2×D244—41no—
349C2×D244C2×D411yescharacteristic
350C2×D244C2×D411yescharacteristic
351C2×D244C2412yes—
352C2×C4×D61—21no—
353C2×C4×D61—21no—
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—
367SD16×C61—24no—
368SD16×C61—24no—
369D8×C61—24no—
370D8×C61—24no—
371M16×C61—21no—
372M16×C61—21no—
373M16×C61C2412yes—
374M16×C61C2412yes—
375C2×C8×C61—21no—
376C2×C8×C61—21no—
377C42×C61—21no—
378C42×C61C2412yes—
379#11758202—24no—
380#11758202C2×D414yescomplemented
381#11758202C2×D414yescomplemented
382#11758201—24no—
383#11758201C2×D414yescomplemented
384#11758201C2×D414yescomplemented
385#11758200—24no—
386#11758200—24no—
387#11758200—24no—
388#11758200—24no—
389#11758200—24no—
390#11758200—24no—
391#11758200—24no—
392#11758200C2×D414yescomplemented
393#11758200C2×D414yescomplemented
394#11758199—24no—
395#11758199—24no—
396#11758199—24no—
397#11758199—24no—
398#11758199—24no—
399#11758199—24no—
400#11758199—24no—
401#11758199C2×D414yescomplemented
402#11758199C2×D414yescomplemented
403#11758198—44no—
404#11758194—21no—
405#11758194—21no—
406#11758194—24no—
407#11758194—24no—
408#11758194C2412yes—
409#11758194C2412yes—
410C2×#92418—21no—
411C2×#92418—21no—
412C2×#92418—24no—
413C2×#92418—24no—
414C2×#92418C2×D411yescharacteristic
415C2×#92418C2×D411yescharacteristic
416C2×#92418C2×D411yescharacteristic
417C2×#92418C2×D411yescharacteristic
418C2×#92418C2×D412yes—
419C2×#92418C2×D412yes—
420C2×#92418C2412yes—
421C2×#92418C2412yes—
422Dic244—24no—
423D488—24no—
424#11758190—24no—
425#11758190—24no—
426#11758189—24no—
427#11758189—24no—
428C8×D61—24no—
429C8×D61—24no—
430C23×C61—21no—
431C23×C61—21no—
432C23×C61—22no—
433C23×C61—22no—
434C23×C61—44no—
435C23×C61—41no—
436C23×C61—41no—
437C23×C61—41no—
438C23×C61—41no—
439C23×C61—82no—
440C23×C61—82no—
441C23×C61—162no—
442C23×C61H(5,𝔽2)11yescharacteristic
443C22×D61—21no—
444C22×D61—21no—
445C22×D61—22no—
446C22×D61—44no—
447C22×D61—44no—
448C22×D61—41no—
449C22×D61—41no—
450C22×D61—82no—
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×C61—22no—
464D4×C61—22no—
465D4×C61—22no—
466D4×C61—22no—
467D4×C61—44no—
468D4×C61—44no—
469D4×C61—41no—
470D4×C61—41no—
471D4×C61—41no—
472D4×C61—41no—
473D4×C61—88no—
474D4×C61C22×D412yes—
475D4×C61C22×D412yes—
476C2×C4×C61—21no—
477C2×C4×C61—21no—
478C2×C4×C61—22no—
479C2×C4×C61—22no—
480C2×C4×C61—22no—
481C2×C4×C61—22no—
482C2×C4×C61—22no—
483C2×C4×C61—44no—
484C2×C4×C61—42no—
485C2×C4×C61C22×D411yescharacteristic
486C2×C4×C61C22×D411yescharacteristic
487C2×C4×C61C22×D411yescharacteristic
488C2×C4×C61C22×D411yescharacteristic
489C2×C4×C61H(5,𝔽2)11yescharacteristic
490C2×C4×C61C2511yescharacteristic
491C22⋊D61—22no—
492C22⋊D61—22no—
493C22⋊D61—22no—
494C22⋊D61—22no—
495C22⋊D61—44no—
496C22⋊D61—44no—
497C22⋊D61—44no—
498C22⋊D61—44no—
499C2×Dic61—21no—
500C2×Dic61—21no—
501C2×Dic61—22no—
502C2×Dic61—44no—
503C2×Dic61—44no—
504C2×Dic61—41no—
505C2×Dic61—41no—
506D244—21no—
507D244—21no—
508D244—22no—
509D244—22no—
510D244—44no—
511D244—41no—
512D244—41no—
513D244C22×D412yes—
514D244C22×D412yes—
515C4×D61—22no—
516C4×D61—22no—
517C4×D61—22no—
518C4×D61—22no—
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—
532#92418—22no—
533#92418—22no—
534#92418C22×D412yes—
535#92418C22×D412yes—
536#92418C22×D412yes—
537#92418C22×D412yes—
538C2×#3288—611nomaximal, Sylow
539C22×C61—22no—
540C22×C61—22no—
541C22×C61—22no—
542C22×C61—42no—
543C22×C61—42no—
544C22×C61—42no—
545C22×C61—42no—
546C22×C61—82no—
547C22×C61—82no—
548C22×C61—82no—
549C22×C61—82no—
550C22×C61—161no—
551C22×C61—161no—
552C22×C61—164no—
553C22×C61D4211yescharacteristic
554C22×C61D4211yescharacteristic
555C22×C61C2×H(5,𝔽2)11yescharacteristic
556C2×D61—22no—
557C2×D61—22no—
558C2×D61—42no—
559C2×D61—42no—
560C2×D61—42no—
561C2×D61—82no—
562C2×D61—82no—
563C2×D61—164no—
564C2×D61—164no—
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×#453D6111yescharacteristic, complemented
590C2×#444—611no—
591C2×#444—611no—
592C2×C61—21no—
593C2×C61—21no—
594C2×C61—42no—
595C2×C61—42no—
596C2×C61—82no—
597C2×C61—82no—
598C2×C61#328812yescomplemented
599C2×C61C2×D4211yescharacteristic
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)C2×D6111yescharacteristic, complemented
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
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—611no—
643C22×D8—1221no—
644C22×D8—1221no—
645C2×#131—611no—
646C2×#131—611no—
647C2×#131—611no—
648C2×#131—611no—
649C2×#127C2×D6111yescharacteristic, complemented
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#453C2×D6118yescomplemented
660#444—618no—
661#444—618no—
662C2×#108—611no—
663C2×#108—611no—
664C2×#104—611no—
665C2×#104—611no—
666C2×#104C2×D6111yescharacteristic, complemented
667C2×#104C2×D6111yescharacteristic, complemented
668C2×#101—611no—
669C2×#100—611no—
670C2×#100—611no—
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)—22no—
679H(5,𝔽2)—22no—
680H(5,𝔽2)—41no—
681H(5,𝔽2)—614no—
682H(5,𝔽2)—614no—
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)C22×D6114yescomplemented
690C2×#41—21no—
691C2×#41—21no—
692C2×#41—611no—
693C2×#41—611no—
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—21no—
707C22×D4—21no—
708C22×D4—41no—
709C22×D4—41no—
710C22×D4—611no—
711C22×D4—1221no—
712C22×D4—1221no—
713C22×D4—1221no—
714C22×D4—1221no—
715C22×D4—2441no—
716C22×D4—2441no—
717C22×D4C22×D6111yescharacteristic
718C22×D4C22×D6111yescharacteristic
719#137—614no—
720#137—614no—
721#137—1222no—
722#137—1228no—
723#137—1228no—
724#137—1222no—
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)—1222no—
732AGL(1,ℤ/8)—1228no—
733AGL(1,ℤ/8)—1228no—
734AGL(1,ℤ/8)—1228no—
735AGL(1,ℤ/8)—1228no—
736AGL(1,ℤ/8)—1228no—
737AGL(1,ℤ/8)—1228no—
738AGL(1,ℤ/8)—1222no—
739AGL(1,ℤ/8)—1222no—
740AGL(1,ℤ/8)—1222no—
741AGL(1,ℤ/8)C22×D6114yes—
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—611no—
760C2×SD16—611no—
761C2×SD16—614no—
762C2×SD16—614no—
763C2×SD16—1221no—
764C2×SD16—1221no—
765C2×SD16—1221no—
766C2×SD16—1221no—
767C2×SD16—1221no—
768C2×SD16—1221no—
769C2×SD16—1222no—
770C2×SD16—1222no—
771C2×SD16—1228no—
772C2×SD16—1228no—
773C2×SD16—1221no—
774C2×SD16—1221no—
775C2×SD16—1221no—
776C2×SD16—1221no—
777C2×D8—21no—
778C2×D8—21no—
779C2×D8—611no—
780C2×D8—611no—
781C2×D8—614no—
782C2×D8—614no—
783C2×D8—1221no—
784C2×D8—1221no—
785C2×D8—1221no—
786C2×D8—1221no—
787C2×D8—1221no—
788C2×D8—1222no—
789C2×D8—1222no—
790C2×D8—1228no—
791C2×D8—1228no—
792C2×D8—1221no—
793C2×D8—1221no—
794C2×D8—1221no—
795#131—614no—
796#131—614no—
797#131—614no—
798#131—614no—
799#131—1222no—
800#131—1222no—
801#131—1222no—
802#131—1222no—
803C2×M16—611no—
804C2×M16—611no—
805C2×M16—1221no—
806C2×M16—1221no—
807C2×M16—1221no—
808C2×M16—1221no—
809C2×M16C22×D6111yescharacteristic
810C2×M16C22×D6111yescharacteristic
811C22×C8—611no—
812C22×C8—611no—
813C22×C8—1221no—
814C22×C8—1221no—
815C22×C8—1221no—
816C22×C8—1221no—
817#127—41no—
818#127C22×D6114yescomplemented
819#124—614no—
820#124—2441no—
821C2×C22⋊C4—2441no—
822C2×C42C22×D6111yescharacteristic
823#108—614no—
824#108—614no—
825#104—614no—
826#104—614no—
827#104C22×D6114yescomplemented
828#104C22×D6114yescomplemented
829#101—614no—
830#100—614no—
831#100—614no—
832#100C22×D6114yescomplemented
833#97—614no—
834C24—21no—
835C24—21no—
836C24—41no—
837C24—1221no—
838C24—2441no—
839C24—2441no—
840#41—21no—
841#41—21no—
842#41—21no—
843#41—21no—
844#41—24no—
845#41—24no—
846#41—42no—
847#41—42no—
848#41—612no—
849#41—612no—
850#41—612no—
851#41—612no—
852#41—1224no—
853#41—1224no—
854#41—1221no—
855#41—1221no—
856#41—1221no—
857#41—1221no—
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—2444no—
870#41D4×D6112yes—
871#41D4×D6112yes—
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×Q8D4×D6111yescharacteristic
888C2×Q8D4×D6111yescharacteristic
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—24no—
892C2×D4—24no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—21no—
898C2×D4—21no—
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—41no—
906C2×D4—41no—
907C2×D4—44no—
908C2×D4—44no—
909C2×D4—44no—
910C2×D4—84no—
911C2×D4—611no—
912C2×D4—611no—
913C2×D4—612no—
914C2×D4—1224no—
915C2×D4—1224no—
916C2×D4—1224no—
917C2×D4—1221no—
918C2×D4—1221no—
919C2×D4—1224no—
920C2×D4—1221no—
921C2×D4—1221no—
922C2×D4—1221no—
923C2×D4—1221no—
924C2×D4—1221no—
925C2×D4—2442no—
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—2441no—
938C2×D4D4×D6111yescharacteristic
939C2×D4D4×D6111yescharacteristic
940C2×D4C23×D6112yes—
941C2×D4C23×D6112yes—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—41no—
946C22×C4—1221no—
947C22×C4—1221no—
948C22×C4—1221no—
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—614no—
977D8—614no—
978D8—1224no—
979D8—1224no—
980D8—1224no—
981D8—1224no—
982D8—1224no—
983D8—1224no—
984D8—1224no—
985D8—1224no—
986M16—21no—
987M16—21no—
988M16—612no—
989M16—612no—
990M16—1224no—
991M16—1224no—
992M16—1224no—
993M16—1224no—
994M16—1221no—
995M16—1221no—
996M16C23×D6112yes—
997M16C23×D6112yes—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—611no—
1001C2×C8—611no—
1002C2×C8—611no—
1003C2×C8—611no—
1004C2×C8—612no—
1005C2×C8—612no—
1006C2×C8—612no—
1007C2×C8—612no—
1008C2×C8—1224no—
1009C2×C8—1224no—
1010C2×C8—1224no—
1011C2×C8—1224no—
1012C2×C8—1221no—
1013C2×C8—1221no—
1014C22⋊C4—2444no—
1015C42—21no—
1016C42C23×D6112yes—
1017C23—21no—
1018C23—21no—
1019C23—22no—
1020C23—22no—
1021C23—44no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—82no—
1027C23—82no—
1028C23—162no—
1029C23—1221no—
1030C23—1221no—
1031C23—1222no—
1032C23—9762no—
1033C23—9762no—
1034C23—4882no—
1035C23—2444no—
1036C23—2444no—
1037C23—2441no—
1038C23—2441no—
1039C23#1451982211yescharacteristic
1040Q8—21no—
1041Q8—21no—
1042Q8—612no—
1043Q8—612no—
1044Q8—1221no—
1045Q8—1221no—
1046Q8—1222no—
1047Q8—1222no—
1048Q8—2444no—
1049Q8—2441no—
1050Q8—2441no—
1051Q8C2×D4×D6112yes—
1052Q8C2×D4×D6112yes—
1053D4—22no—
1054D4—22no—
1055D4—22no—
1056D4—22no—
1057D4—22no—
1058D4—22no—
1059D4—22no—
1060D4—22no—
1061D4—21no—
1062D4—21no—
1063D4—44no—
1064D4—44no—
1065D4—41no—
1066D4—41no—
1067D4—41no—
1068D4—41no—
1069D4—88no—
1070D4—612no—
1071D4—612no—
1072D4—1222no—
1073D4—1222no—
1074D4—1222no—
1075D4—1222no—
1076D4—1222no—
1077D4—1222no—
1078D4—1221no—
1079D4—1221no—
1080D4—2444no—
1081D4—2444no—
1082D4—2444no—
1083D4—2444no—
1084D4—2444no—
1085D4—2441no—
1086D4—2441no—
1087D4C2×D4×D6112yes—
1088D4C2×D4×D6112yes—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—44no—
1097C2×C4—42no—
1098C2×C4—1221no—
1099C2×C4—1221no—
1100C2×C4—1222no—
1101C2×C4—1222no—
1102C2×C4—1222no—
1103C2×C4—1222no—
1104C2×C4—1222no—
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×C4C2×D4×D6111yescharacteristic
1114C2×C4C2×D4×D6111yescharacteristic
1115C2×C4#1451982211yescharacteristic
1116C2×C4C24×D6111yescharacteristic
1117C8—22no—
1118C8—22no—
1119C8—612no—
1120C8—612no—
1121C8—612no—
1122C8—612no—
1123C8—1222no—
1124C8—1222no—
1125C22—22no—
1126C22—22no—
1127C22—22no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—82no—
1133C22—82no—
1134C22—82no—
1135C22—82no—
1136C22—161no—
1137C22—161no—
1138C22—164no—
1139C22—1222no—
1140C22—1222no—
1141C22—9761no—
1142C22—9764no—
1143C22—9764no—
1144C22—4882no—
1145C22—4882no—
1146C22—2442no—
1147C22—2442no—
1148C22—2442no—
1149C22#1684039411yescharacteristic
1150C22#1684039411yescharacteristic
1151C22C2×#1451982211yescharacteristic
1152C4—22no—
1153C4—22no—
1154C4—42no—
1155C4—1222no—
1156C4—1222no—
1157C4—2442no—
1158C4#1684039411yescharacteristic
1159C4#1684039411yescharacteristic
1160C4C22×D4×D6111yescharacteristic
1161C4C22×D4×D6111yescharacteristic
1162C2—21no—
1163C2—21no—
1164C2—42no—
1165C2—42no—
1166C2—82no—
1167C2—82no—
1168C2—4882no—
1169C2—2442no—
1170C2—2442no—
1171C2#2145758012yesdirect product factor
1172C2C2×#1684039411yescharacteristic
subgroupG/H
centerC22#16840394
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#453C2
socleC22×C61D42
hypercenterC2×#453D61
hypocenterC61C2×#3288
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#453

Complements

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

NH ≅ G/Ntype
1. C2×#16840573C2semidirect
2. C2×#16840572C2semidirect
3. C2×#16840566C2semidirect
4. C2×#16840565C2semidirect
5. #21457580C2direct (N × H)
6. C2×#16840149C2semidirect
7. C2×#16840031C2semidirect
8. C2×#16840030C2semidirect
9. C2×#16840024C2semidirect
10. C2×#16840023C2semidirect
11. C2×#16839936C2semidirect
12. C2×#16839941C2semidirect
13. C2×#16839929C2semidirect
14. C2×#16839881C2semidirect
15. C2×#16839881C2semidirect
16. C2×C61×#453C2semidirect
17. C2×#14519824C22semidirect
19. C2×#14519822C22semidirect
21. #16840573C22semidirect
23. #16840572C22semidirect
25. #16840566C22semidirect
27. #16840565C22semidirect
28. C2×#14519810C22semidirect
30. C2×#14519807C22semidirect
32. C2×#14519805C22semidirect
37. C2×#14519803C22semidirect
39. C2×#14519802C22semidirect
49. C22×#11758200C22semidirect
50. C22×#11758200C22semidirect
53. C22×#11758199C22semidirect
54. C22×#11758199C22semidirect
56. C2×#14519785C22semidirect
57. C2×#14519785C22semidirect
58. C2×#14519784C22semidirect
59. C2×#14519784C22semidirect
60. C2×#14519765C22semidirect
61. #16840149C22semidirect
62. #16840031C22semidirect
63. #16840030C22semidirect
64. #16840024C22semidirect
65. #16840023C22semidirect
66. #16839941C22semidirect
67. #16839936C22semidirect
68. #16839929C22semidirect
69. #16839881C22semidirect
70. #16839881C22semidirect
71. C2×#14519712C22semidirect
72. C2×#14519712C22semidirect
73. C2×#14519705C22semidirect
74. C2×#14519705C22semidirect
75. C2×#14519695C22semidirect
76. C2×#14519694C22semidirect
77. C2×#14519693C22semidirect
78. C2×#14519688C22semidirect
79. C2×H(5,𝔽2)×C61C22semidirect
81. C2×AGL(1,ℤ/8)×C61C22semidirect
82. C2×#127×C61C22semidirect
83. C61×#453C22semidirect
84. C2×#104×C61C22semidirect
85. C2×#104×C61C22semidirect
86. C2×#100×C61C22semidirect
90. #14519824C23semidirect
98. #14519822C23semidirect
119. #14519810C23semidirect
122. #14519807C23semidirect
125. #14519805C23semidirect
132. #14519803C23semidirect
135. #14519802C23semidirect
141. #14519797D4semidirect
142. #14519797D4semidirect
148. C2×#11758202D4semidirect
149. C2×#11758202D4semidirect
162. C2×#11758200D4semidirect
163. C2×#11758200D4semidirect
164. C2×#11758200C23semidirect
165. C2×#11758200C23semidirect
167. C2×#11758201D4semidirect
168. C2×#11758201D4semidirect
181. C2×#11758199D4semidirect
182. C2×#11758199D4semidirect
183. C2×#11758199C23semidirect
184. C2×#11758199C23semidirect
188. #14519785C23semidirect
189. #14519785C23semidirect
192. #14519784C23semidirect
193. #14519784C23semidirect
207. #14519765C23semidirect
209. #14519712C23semidirect
210. #14519712C23semidirect
211. #14519705C23semidirect
212. #14519705C23semidirect
213. #14519695C23semidirect
214. #14519694C23semidirect
215. #14519693C23semidirect
216. #14519688C23semidirect
220. H(5,𝔽2)×C61C23semidirect
234. AGL(1,ℤ/8)×C61C23semidirect
242. #127×C61C23semidirect
244. #104×C61C23semidirect
245. #104×C61C23semidirect
246. #100×C61C23semidirect
380. #11758202C2×D4semidirect
381. #11758202C2×D4semidirect
383. #11758201C2×D4semidirect
384. #11758201C2×D4semidirect
392. #11758200C2×D4semidirect
393. #11758200C2×D4semidirect
401. #11758199C2×D4semidirect
402. #11758199C2×D4semidirect
589. C2×#453D61semidirect
598. C2×C61#3288semidirect
606. C2×H(5,𝔽2)C2×D61semidirect
630. C2×AGL(1,ℤ/8)C2×D61semidirect
649. C2×#127C2×D61semidirect
659. #453C2×D61semidirect
666. C2×#104C2×D61semidirect
667. C2×#104C2×D61semidirect
671. C2×#100C2×D61semidirect
673. C61C2×#3288semidirect
689. H(5,𝔽2)C22×D61semidirect
742. AGL(1,ℤ/8)C22×D61semidirect
818. #127C22×D61semidirect
827. #104C22×D61semidirect
828. #104C22×D61semidirect
832. #100C22×D61semidirect
1171. C2#21457580direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168405732
C2×#168405722
C2×#168405662
C2×#168405652
#214575802
C2×#168401492
C2×#168400312
C2×#168400302
C2×#168400242
C2×#168400232
C2×#168399362
C2×#168399412
C2×#168399292
C2×#168398812
C2×C61×#4532
C2×#328861