Finite Group Databasebeta

← C2×#21457603 #30556221

Subgroups — C2×#21457603 #30556221

Order 15616.

2650 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840578C211yesmaximal, characteristic, complemented
2C2×#16840573C211yesmaximal, characteristic, complemented
3C2×#16840571C211yesmaximal, characteristic, complemented
4C2×#16840565C211yesmaximal, characteristic, complemented
5#21457603C2116yesmaximal, direct product factor
6C2×#16840144C211yesmaximal, characteristic, complemented
7C2×#16840035C211yesmaximal, characteristic, complemented
8C2×#16840031C211yesmaximal, characteristic, complemented
9C2×#16840027C211yesmaximal, characteristic, complemented
10C2×#16840024C211yesmaximal, characteristic, complemented
11C2×#16839936C211yesmaximal, characteristic, complemented
12C2×#16839934C211yesmaximal, characteristic, complemented
13C2×#16839941C211yesmaximal, characteristic, complemented
14C2×#16839876C211yesmaximal, characteristic, complemented
15C2×#16839876C211yesmaximal, characteristic, complemented
16C2×C61×#455C211yesmaximal, characteristic, complemented
17C2×#14519825C2211yescharacteristic, complemented
18C2×#14519824C2211yescharacteristic, complemented
19C2×#14519823C2211yescharacteristic
20#16840578—24no—
21#16840578C2218yescomplemented
22#16840573—24no—
23#16840573C2218yescomplemented
24#16840571—24no—
25#16840571C2218yescomplemented
26#16840565—24no—
27#16840565C2218yescomplemented
28C2×#14519810C2211yescharacteristic, complemented
29C2×#14519809—21no—
30C2×#14519809—21no—
31C2×#14519807—21no—
32C2×#14519807C2211yescharacteristic
33C2×#14519806—21no—
34C2×#14519805C2211yescharacteristic, complemented
35C2×#14519804—21no—
36C2×#14519803—21no—
37C2×#14519803—21no—
38C2×#14519803C2211yescharacteristic
39C2×#14519803C2211yescharacteristic, complemented
40C2×#14519802—21no—
41C2×#14519802C2211yescharacteristic
42C2×#14519800—21no—
43C2×#14519798—21no—
44C2×#14519797—21no—
45C2×#14519797—21no—
46C2×#14519797C2211yescharacteristic
47C2×#14519797C2211yescharacteristic
48C22×#11758202C2211yescharacteristic, complemented
49C2×Q16×D61—21no—
50C22×#11758200—21no—
51C22×#11758200C2211yescharacteristic, complemented
52C22×#11758201C2211yescharacteristic, complemented
53C2×SD16×D61—21no—
54C22×#11758199—21no—
55C22×#11758199C2211yescharacteristic
56C2×#14519785C2211yescharacteristic, complemented
57C2×#14519785C2211yescharacteristic, complemented
58C2×#14519784C2211yescharacteristic
59C2×#14519784C2211yescharacteristic, complemented
60C2×#14519765C2211yescharacteristic, complemented
61#16840144C2218yescomplemented
62#16840035C2218yescomplemented
63#16840031C2218yescomplemented
64#16840027C2218yescomplemented
65#16840024C2218yescomplemented
66#16839941C2218yescomplemented
67#16839936C2218yescomplemented
68#16839934C2218yescomplemented
69#16839876C2218yescomplemented
70#16839876C2218yescomplemented
71C2×#14519712C2211yescharacteristic, complemented
72C2×#14519712C2211yescharacteristic, complemented
73C2×#14519705C2211yescharacteristic, complemented
74C2×#14519705C2211yescharacteristic, complemented
75C2×#14519696C2211yescharacteristic, complemented
76C2×#14519695C2211yescharacteristic, complemented
77C2×#14519693C2211yescharacteristic, complemented
78C2×C4×#92418C2211yescharacteristic, complemented
79C2×H(5,𝔽2)×C61C2211yescharacteristic
80C2×#137×C61C2211yescharacteristic
81C2×#137×C61C2211yescharacteristic, complemented
82C2×#124×C61C2211yescharacteristic, complemented
83C61×#455C2218yescomplemented
84C2×#104×C61C2211yescharacteristic
85C2×#104×C61C2211yescharacteristic, complemented
86C2×#100×C61C2211yescharacteristic, complemented
87#14519825—22no—
88#14519825—22no—
89#14519825—41no—
90#14519825C2314yescomplemented
91#14519824—22no—
92#14519824—22no—
93#14519824—41no—
94#14519824C2314yescomplemented
95#14519823—22no—
96#14519823—22no—
97#14519823—41no—
98#14519823C2314yes—
99C2×#11758226—21no—
100C2×#11758226—21no—
101C2×#11758226—21no—
102C2×#11758222—21no—
103C2×#11758222—21no—
104C2×#11758222—41no—
105C2×#11758222C2311yescharacteristic
106C2×#11758222C2311yescharacteristic
107C2×#11758224—21no—
108C2×#11758224—41no—
109C22×Dic122—21no—
110C22×Dic122C2311yescharacteristic
111C2×Q8×D61—21no—
112C2×Q8×D61—21no—
113C2×Q8×D61—21no—
114C22×D244—21no—
115C22×D244C2311yescharacteristic
116C2×D4×D61—21no—
117C2×D4×D61—41no—
118#14519810—22no—
119#14519810C2314yescomplemented
120#14519809—28no—
121#14519809—28no—
122#14519807—22no—
123#14519807—28no—
124#14519807C2314yes—
125#14519806—28no—
126#14519805—22no—
127#14519805C2314yescomplemented
128#14519804—28no—
129#14519803—22no—
130#14519803—22no—
131#14519803—28no—
132#14519803—28no—
133#14519803C2314yes—
134#14519803C2314yescomplemented
135#14519802—22no—
136#14519802—28no—
137#14519802C2314yes—
138#14519800—28no—
139#14519798—28no—
140#14519797—28no—
141#14519797—28no—
142#14519797D414yes—
143#14519797D414yes—
144#14519797C2314yes—
145#14519797C2314yes—
146C2×Dic244—21no—
147C2×#11758202—21no—
148C2×#11758202—21no—
149C2×#11758202—21no—
150C2×#11758202—22no—
151C2×#11758202D411yescharacteristic
152C2×#11758202D411yescharacteristic
153C2×#11758202C2314yescomplemented
154Q16×D61—28no—
155C2×#11758190—21no—
156C2×#11758190—21no—
157C2×#11758200—21no—
158C2×#11758200—21no—
159C2×#11758200—21no—
160C2×#11758200—28no—
161C2×#11758200—21no—
162C2×#11758200—21no—
163C2×#11758200—22no—
164C2×#11758200D411yescharacteristic
165C2×#11758200D411yescharacteristic
166C2×#11758200C2314yescomplemented
167C2×#11758201—21no—
168C2×#11758201—21no—
169C2×#11758201—21no—
170C2×#11758201—22no—
171C2×#11758201D411yescharacteristic
172C2×#11758201D411yescharacteristic
173C2×#11758201C2314yescomplemented
174SD16×D61—28no—
175C2×D488—21no—
176C2×#11758199—21no—
177C2×#11758199—21no—
178C2×#11758199—21no—
179C2×#11758199—28no—
180C2×#11758199—21no—
181C2×#11758199—21no—
182C2×#11758199—22no—
183C2×#11758199D411yescharacteristic
184C2×#11758199D411yescharacteristic
185C2×#11758199C2314yes—
186#14519785—22no—
187#14519785—22no—
188#14519785C2314yescomplemented
189#14519785C2314yescomplemented
190#14519784—22no—
191#14519784—22no—
192#14519784C2314yes—
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#14519696C2314yescomplemented
214#14519695C2314yescomplemented
215#14519693C2314yescomplemented
216C4×#92418C2314yescomplemented
217H(5,𝔽2)×C61—22no—
218H(5,𝔽2)×C61—22no—
219H(5,𝔽2)×C61—41no—
220H(5,𝔽2)×C61C2314yes—
221C2×#41×C61—21no—
222C2×#41×C61—21no—
223C2×#41×C61C2311yescharacteristic
224C2×#41×C61C2311yescharacteristic
225C22×Q8×C61C2311yescharacteristic
226C22×D4×C61—21no—
227C22×D4×C61—21no—
228C22×D4×C61—41no—
229C22×D4×C61C2311yescharacteristic
230#137×C61—22no—
231#137×C61—22no—
232#137×C61C2314yes—
233#137×C61C2314yescomplemented
234C2×Q16×C61—21no—
235C2×Q16×C61—21no—
236C2×SD16×C61—21no—
237C2×SD16×C61—21no—
238C2×M16×C61C2311yescharacteristic
239C2×M16×C61C2311yescharacteristic
240#124×C61—41no—
241#124×C61C2314yescomplemented
242C2×C22⋊C4×C61—41no—
243C2×C42×C61C2311yescharacteristic
244#104×C61C2314yes—
245#104×C61C2314yescomplemented
246#100×C61C2314yescomplemented
247C24×C61—21no—
248C24×C61—41no—
249C23×D61—21no—
250C23×D61—41no—
251#41×C61—21no—
252#41×C61—21no—
253#41×C61—21no—
254#41×C61—21no—
255#41×C61—24no—
256#41×C61—24no—
257#41×C61—42no—
258#41×C61—42no—
259#41×C61C2×D412yes—
260#41×C61C2×D412yes—
261#41×C61C2412yes—
262#41×C61C2412yes—
263C2×Q8×C61—21no—
264C2×Q8×C61—21no—
265C2×Q8×C61—21no—
266C2×Q8×C61—21no—
267C2×Q8×C61—21no—
268C2×Q8×C61C2×D411yescharacteristic
269C2×Q8×C61C2×D411yescharacteristic
270C2×Q8×C61C2412yes—
271C2×D4×C61—21no—
272C2×D4×C61—21no—
273C2×D4×C61—24no—
274C2×D4×C61—24no—
275C2×D4×C61—21no—
276C2×D4×C61—21no—
277C2×D4×C61—21no—
278C2×D4×C61—21no—
279C2×D4×C61—21no—
280C2×D4×C61—42no—
281C2×D4×C61—42no—
282C2×D4×C61—41no—
283C2×D4×C61—41no—
284C2×D4×C61—44no—
285C2×D4×C61—44no—
286C2×D4×C61C2×D411yescharacteristic
287C2×D4×C61C2×D411yescharacteristic
288C2×D4×C61C2412yes—
289C22×C4×C61—21no—
290C22×C4×C61—21no—
291C22×C4×C61—21no—
292C22×C4×C61—21no—
293C22×C4×C61—41no—
294C22×C4×C61C2411yescharacteristic
295C2×C22⋊D61—21no—
296C2×C22⋊D61—21no—
297C2×C22⋊D61—41no—
298C2×C22⋊D61—41no—
299C22×Dic61—21no—
300C22×Dic61—41no—
301#11758226—24no—
302#11758226—24no—
303#11758226—24no—
304#11758226—42no—
305#11758226—42no—
306#11758226—42no—
307Q8×D61—24no—
308Q8×D61—24no—
309Q8×D61—24no—
310Q8×D61—42no—
311Q8×D61—42no—
312Q8×D61—42no—
313#11758224—24no—
314#11758224—42no—
315#11758224—44no—
316#11758224—44no—
317D4×D61—24no—
318D4×D61—42no—
319D4×D61—44no—
320D4×D61—44no—
321#11758222—21no—
322#11758222—21no—
323#11758222—21no—
324#11758222—21no—
325#11758222—24no—
326#11758222—24no—
327#11758222—42no—
328#11758222—42no—
329#11758222—44no—
330#11758222—44no—
331#11758222C2×D412yes—
332#11758222C2×D412yes—
333#11758222C2412yes—
334#11758222C2412yes—
335C2×D244—21no—
336C2×D244—21no—
337C2×D244—21no—
338C2×D244—21no—
339C2×D244—24no—
340C2×D244—21no—
341C2×D244—42no—
342C2×D244—41no—
343C2×D244—41no—
344C2×D244C2×D411yescharacteristic
345C2×D244C2×D411yescharacteristic
346C2×D244C2412yes—
347C2×C4×D61—21no—
348C2×C4×D61—21no—
349C2×C4×D61—41no—
350C2×C4×D61—41no—
351C2×C4×D61—41no—
352C2×C4×D61—41no—
353C2×Dic122—21no—
354C2×Dic122—21no—
355C2×Dic122—21no—
356C2×Dic122—21no—
357C2×Dic122—24no—
358C2×Dic122—21no—
359C2×Dic122—42no—
360C2×Dic122—41no—
361C2×Dic122—41no—
362C2×Dic122C2×D411yescharacteristic
363C2×Dic122C2×D411yescharacteristic
364C2×Dic122C2412yes—
365Q16×C61—24no—
366Q16×C61—24no—
367SD16×C61—24no—
368SD16×C61—24no—
369M16×C61—21no—
370M16×C61—21no—
371M16×C61C2412yes—
372M16×C61C2412yes—
373C2×C8×C61—21no—
374C2×C8×C61—21no—
375C22⋊C4×C61—44no—
376C42×C61—21no—
377C42×C61C2412yes—
378#11758202—24no—
379#11758202—24no—
380#11758202—24no—
381#11758202C2×D414yes—
382#11758202C2×D414yes—
383#11758201—24no—
384#11758201—24no—
385#11758201—24no—
386#11758201C2×D414yes—
387#11758201C2×D414yes—
388#11758200—24no—
389#11758200—24no—
390#11758200—24no—
391#11758200—24no—
392#11758200—24no—
393#11758200C2×D414yes—
394#11758200C2×D414yes—
395#11758199—24no—
396#11758199—24no—
397#11758199—24no—
398#11758199—24no—
399#11758199—24no—
400#11758199C2×D414yes—
401#11758199C2×D414yes—
402#11758198—44no—
403#11758194—21no—
404#11758194—21no—
405#11758194—24no—
406#11758194—24no—
407#11758194C2412yes—
408#11758194C2412yes—
409C2×#92418—21no—
410C2×#92418—21no—
411C2×#92418—24no—
412C2×#92418—24no—
413C2×#92418C2×D411yescharacteristic
414C2×#92418C2×D411yescharacteristic
415C2×#92418C2×D411yescharacteristic
416C2×#92418C2×D411yescharacteristic
417C2×#92418C2×D412yes—
418C2×#92418C2×D412yes—
419C2×#92418C2412yes—
420C2×#92418C2412yes—
421Dic244—24no—
422D488—24no—
423#11758190—24no—
424#11758190—24no—
425#11758189—24no—
426#11758189—24no—
427C8×D61—24no—
428C8×D61—24no—
429C23×C61—21no—
430C23×C61—21no—
431C23×C61—22no—
432C23×C61—44no—
433C23×C61—41no—
434C23×C61—41no—
435C23×C61—82no—
436C23×C61—162no—
437C23×C61H(5,𝔽2)11yescharacteristic
438C22×D61—21no—
439C22×D61—21no—
440C22×D61—22no—
441C22×D61—44no—
442C22×D61—41no—
443C22×D61—41no—
444C22×D61—82no—
445C22×D61—162no—
446Q8×C61—21no—
447Q8×C61—21no—
448Q8×C61—22no—
449Q8×C61—22no—
450Q8×C61—41no—
451Q8×C61—41no—
452Q8×C61C22×D412yes—
453Q8×C61C22×D412yes—
454D4×C61—22no—
455D4×C61—22no—
456D4×C61—22no—
457D4×C61—22no—
458D4×C61—21no—
459D4×C61—21no—
460D4×C61—22no—
461D4×C61—22no—
462D4×C61—44no—
463D4×C61—44no—
464D4×C61—41no—
465D4×C61—41no—
466D4×C61C22×D412yes—
467D4×C61C22×D412yes—
468C2×C4×C61—21no—
469C2×C4×C61—21no—
470C2×C4×C61—22no—
471C2×C4×C61—22no—
472C2×C4×C61—22no—
473C2×C4×C61—22no—
474C2×C4×C61—22no—
475C2×C4×C61—22no—
476C2×C4×C61—44no—
477C2×C4×C61—42no—
478C2×C4×C61—41no—
479C2×C4×C61—41no—
480C2×C4×C61C22×D411yescharacteristic
481C2×C4×C61C22×D411yescharacteristic
482C2×C4×C61C22×D411yescharacteristic
483C2×C4×C61C22×D411yescharacteristic
484C2×C4×C61H(5,𝔽2)11yescharacteristic
485C2×C4×C61C2511yescharacteristic
486C22⋊D61—22no—
487C22⋊D61—22no—
488C22⋊D61—22no—
489C22⋊D61—22no—
490C22⋊D61—44no—
491C22⋊D61—44no—
492C2×Dic61—21no—
493C2×Dic61—21no—
494C2×Dic61—22no—
495C2×Dic61—44no—
496C2×Dic61—41no—
497C2×Dic61—41no—
498D244—21no—
499D244—21no—
500D244—22no—
501D244—22no—
502D244—44no—
503D244—44no—
504D244—41no—
505D244—41no—
506D244C22×D412yes—
507D244C22×D412yes—
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—22no—
519Dic122—22no—
520Dic122—44no—
521Dic122—44no—
522Dic122—41no—
523Dic122—41no—
524Dic122C22×D412yes—
525Dic122C22×D412yes—
526C8×C61—22no—
527C8×C61—22no—
528#92418—22no—
529#92418—22no—
530#92418C22×D412yes—
531#92418C22×D412yes—
532#92418C22×D412yes—
533#92418C22×D412yes—
534C2×#3290—611nomaximal, Sylow
535C22×C61—22no—
536C22×C61—22no—
537C22×C61—22no—
538C22×C61—42no—
539C22×C61—42no—
540C22×C61—42no—
541C22×C61—82no—
542C22×C61—82no—
543C22×C61—161no—
544C22×C61—164no—
545C22×C61D4211yescharacteristic
546C22×C61D4211yescharacteristic
547C22×C61C2×H(5,𝔽2)11yescharacteristic
548C2×D61—22no—
549C2×D61—22no—
550C2×D61—42no—
551C2×D61—42no—
552C2×D61—42no—
553C2×D61—82no—
554C2×D61—82no—
555C2×D61—164no—
556C2×D61—161no—
557C4×C61—22no—
558C4×C61—22no—
559C4×C61—42no—
560C4×C61—42no—
561C4×C61D4211yescharacteristic
562C4×C61D4211yescharacteristic
563C4×C61C23×D411yescharacteristic
564C4×C61C23×D411yescharacteristic
565Dic61—22no—
566Dic61—22no—
567Dic61—42no—
568C2×#578—611no—
569C2×#577—611no—
570C2×#577—611no—
571C2×#576—611no—
572#3290—6116no—
573C2×#495—611no—
574C2×#473—611no—
575C2×#472—611no—
576C2×#471—611no—
577C2×#471—611no—
578C2×#454—611no—
579C2×#454—611no—
580C2×#455—611no—
581C2×#455D6111yescharacteristic, complemented
582C2×#443—611no—
583C2×#443—611no—
584C2×C61—21no—
585C2×C61—21no—
586C2×C61—42no—
587C2×C61—42no—
588C2×C61—82no—
589C2×C61#329012yescomplemented
590C2×C61C2×D4211yescharacteristic
591D61—42no—
592D61—42no—
593D61—82no—
594C2×2−1+4—611no—
595C2×2−1+4—611no—
596C2×H(5,𝔽2)—611no—
597C2×H(5,𝔽2)C2×D6111yescharacteristic
598#578—618no—
599#578—1224no—
600#577—618no—
601#577—618no—
602#577—1224no—
603#577—1224no—
604#576—618no—
605#576—1224no—
606C2×#137—611no—
607C2×#137—611no—
608C2×#137—1221no—
609C2×#137—1221no—
610C2×#137—1221no—
611C2×#137—1221no—
612C2×#137C2×D6111yescharacteristic
613C2×#137C2×D6111yescharacteristic, complemented
614C2×AGL(1,ℤ/8)—611no—
615C2×AGL(1,ℤ/8)—611no—
616C2×AGL(1,ℤ/8)—611no—
617C2×AGL(1,ℤ/8)—611no—
618C2×AGL(1,ℤ/8)—1221no—
619C2×AGL(1,ℤ/8)—1221no—
620C2×AGL(1,ℤ/8)—1221no—
621C2×AGL(1,ℤ/8)—1221no—
622C2×#135—611no—
623C2×#135—611no—
624C2×#135—1221no—
625C2×#135—1221no—
626C2×#135—1221no—
627C2×#135—1221no—
628C22×Q16—611no—
629C22×Q16—1221no—
630C22×SD16—611no—
631C22×SD16—611no—
632C22×SD16—1221no—
633C22×SD16—1221no—
634C22×D8—611no—
635C22×D8—1221no—
636C2×#131—611no—
637C2×#131—611no—
638C2×#131—611no—
639C2×#131—611no—
640C2×#124—611no—
641C2×#124C2×D6111yescharacteristic, complemented
642#495—618no—
643#473—618no—
644#472—618no—
645#471—618no—
646#471—618no—
647#455—618no—
648#455C2×D6118yescomplemented
649#454—618no—
650#454—618no—
651#443—618no—
652#443—618no—
653C2×#108—611no—
654C2×#108—611no—
655C2×#104—611no—
656C2×#104—611no—
657C2×#104C2×D6111yescharacteristic
658C2×#104C2×D6111yescharacteristic, complemented
659C2×#101—611no—
660C2×#101—611no—
661C2×#100—611no—
662C2×#100C2×D6111yescharacteristic, complemented
663C2×C4×C8—611no—
664C61C2×#329011yescharacteristic, complemented, Sylow
6652−1+4—614no—
6662−1+4—614no—
6672−1+4—1222no—
6682−1+4—1222no—
6692−1+4—1222no—
6702−1+4—1222no—
6712−1+4—2441no—
6722−1+4—2441no—
673H(5,𝔽2)—22no—
674H(5,𝔽2)—22no—
675H(5,𝔽2)—41no—
676H(5,𝔽2)—614no—
677H(5,𝔽2)—1222no—
678H(5,𝔽2)—1222no—
679H(5,𝔽2)—2441no—
680H(5,𝔽2)C22×D6114yes—
681C2×#41—21no—
682C2×#41—21no—
683C2×#41—611no—
684C2×#41—611no—
685C2×#41—1221no—
686C2×#41—1221no—
687C2×#41—1221no—
688C2×#41—1221no—
689C2×#41—1221no—
690C2×#41—1221no—
691C2×#41—2441no—
692C2×#41—2441no—
693C2×#41C22×D6111yescharacteristic
694C2×#41C22×D6111yescharacteristic
695C22×Q8—611no—
696C22×Q8—1221no—
697C22×Q8—1221no—
698C22×Q8—1221no—
699C22×Q8—1221no—
700C22×Q8C22×D6111yescharacteristic
701C22×D4—21no—
702C22×D4—21no—
703C22×D4—41no—
704C22×D4—611no—
705C22×D4—1221no—
706C22×D4—1221no—
707C22×D4—2441no—
708C22×D4C22×D6111yescharacteristic
709#137—22no—
710#137—22no—
711#137—614no—
712#137—614no—
713#137—1222no—
714#137—1228no—
715#137—1228no—
716#137—1228no—
717#137—1228no—
718#137—1222no—
719#137C22×D6114yes—
720#137C22×D6114yescomplemented
721AGL(1,ℤ/8)—614no—
722AGL(1,ℤ/8)—614no—
723AGL(1,ℤ/8)—614no—
724AGL(1,ℤ/8)—614no—
725AGL(1,ℤ/8)—1222no—
726AGL(1,ℤ/8)—1228no—
727AGL(1,ℤ/8)—1228no—
728AGL(1,ℤ/8)—1228no—
729AGL(1,ℤ/8)—1228no—
730AGL(1,ℤ/8)—1222no—
731AGL(1,ℤ/8)—1222no—
732AGL(1,ℤ/8)—1222no—
733#135—614no—
734#135—614no—
735#135—614no—
736#135—614no—
737#135—1228no—
738#135—1228no—
739#135—1228no—
740#135—1228no—
741C2×Q16—21no—
742C2×Q16—21no—
743C2×Q16—611no—
744C2×Q16—611no—
745C2×Q16—614no—
746C2×Q16—1221no—
747C2×Q16—1221no—
748C2×Q16—1221no—
749C2×Q16—1222no—
750C2×Q16—1228no—
751C2×Q16—1221no—
752C2×SD16—21no—
753C2×SD16—21no—
754C2×SD16—611no—
755C2×SD16—611no—
756C2×SD16—611no—
757C2×SD16—611no—
758C2×SD16—614no—
759C2×SD16—614no—
760C2×SD16—1221no—
761C2×SD16—1221no—
762C2×SD16—1221no—
763C2×SD16—1221no—
764C2×SD16—1222no—
765C2×SD16—1221no—
766C2×SD16—1221no—
767C2×SD16—1222no—
768C2×SD16—1228no—
769C2×SD16—1228no—
770C2×SD16—1221no—
771C2×SD16—1221no—
772C2×SD16—1221no—
773C2×SD16—1221no—
774C2×D8—611no—
775C2×D8—611no—
776C2×D8—614no—
777C2×D8—1221no—
778C2×D8—1221no—
779C2×D8—1221no—
780C2×D8—1222no—
781C2×D8—1228no—
782C2×D8—1221no—
783C2×D8—1221no—
784C2×D8—1221no—
785#131—614no—
786#131—614no—
787#131—614no—
788#131—614no—
789#131—1222no—
790#131—1222no—
791#131—1222no—
792#131—1222no—
793C2×M16—611no—
794C2×M16—611no—
795C2×M16—1221no—
796C2×M16—1221no—
797C2×M16—1221no—
798C2×M16—1221no—
799C2×M16C22×D6111yescharacteristic
800C2×M16C22×D6111yescharacteristic
801C22×C8—611no—
802C22×C8—611no—
803C22×C8—1221no—
804C22×C8—1221no—
805C22×C8—1221no—
806C22×C8—1221no—
807#124—41no—
808#124—614no—
809#124—2441no—
810#124C22×D6114yescomplemented
811C2×C22⋊C4—41no—
812C2×C22⋊C4—2441no—
813C2×C42C22×D6111yescharacteristic
814#108—614no—
815#108—614no—
816#104—614no—
817#104—614no—
818#104C22×D6114yes—
819#104C22×D6114yescomplemented
820#101—614no—
821#101—614no—
822#100—614no—
823#100C22×D6114yescomplemented
824C4×C8—614no—
825C24—21no—
826C24—41no—
827C24—1221no—
828C24—2441no—
829#41—21no—
830#41—21no—
831#41—21no—
832#41—21no—
833#41—24no—
834#41—24no—
835#41—42no—
836#41—42no—
837#41—612no—
838#41—612no—
839#41—612no—
840#41—612no—
841#41—1224no—
842#41—1224no—
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—2444no—
852#41—2442no—
853#41—2442no—
854#41—2444no—
855#41—2444no—
856#41—2442no—
857#41—2442no—
858#41—2442no—
859#41—2442no—
860#41—2444no—
861#41D4×D6112yes—
862#41D4×D6112yes—
863#41C23×D6112yes—
864#41C23×D6112yes—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—611no—
871C2×Q8—611no—
872C2×Q8—612no—
873C2×Q8—1224no—
874C2×Q8—1221no—
875C2×Q8—1224no—
876C2×Q8—1224no—
877C2×Q8—1224no—
878C2×Q8—1221no—
879C2×Q8—1221no—
880C2×Q8—1221no—
881C2×Q8—1221no—
882C2×Q8—2441no—
883C2×Q8—2442no—
884C2×Q8—2441no—
885C2×Q8—2442no—
886C2×Q8—2442no—
887C2×Q8—2442no—
888C2×Q8D4×D6111yescharacteristic
889C2×Q8D4×D6111yescharacteristic
890C2×Q8C23×D6112yes—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—24no—
894C2×D4—24no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—21no—
898C2×D4—21no—
899C2×D4—21no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—41no—
903C2×D4—41no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—611no—
907C2×D4—611no—
908C2×D4—612no—
909C2×D4—1224no—
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—2442no—
919C2×D4—2441no—
920C2×D4—2441no—
921C2×D4—2442no—
922C2×D4—2441no—
923C2×D4—2444no—
924C2×D4—2444no—
925C2×D4—2441no—
926C2×D4D4×D6111yescharacteristic
927C2×D4D4×D6111yescharacteristic
928C2×D4C23×D6112yes—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—41no—
934C22×C4—1221no—
935C22×C4—1221no—
936C22×C4—1221no—
937C22×C4—2441no—
938C22×C4—2441no—
939C22×C4—2441no—
940C22×C4—2441no—
941C22×C4—2441no—
942C22×C4C23×D6111yescharacteristic
943Q16—24no—
944Q16—24no—
945Q16—614no—
946Q16—614no—
947Q16—1224no—
948Q16—1224no—
949Q16—1224no—
950Q16—1224no—
951SD16—24no—
952SD16—24no—
953SD16—614no—
954SD16—614no—
955SD16—614no—
956SD16—614no—
957SD16—1224no—
958SD16—1224no—
959SD16—1224no—
960SD16—1224no—
961SD16—1224no—
962SD16—1224no—
963SD16—1224no—
964SD16—1224no—
965SD16—1224no—
966SD16—1224no—
967D8—614no—
968D8—614no—
969D8—1224no—
970D8—1224no—
971D8—1224no—
972D8—1224no—
973D8—1224no—
974D8—1224no—
975M16—21no—
976M16—21no—
977M16—612no—
978M16—612no—
979M16—1224no—
980M16—1224no—
981M16—1224no—
982M16—1224no—
983M16—1221no—
984M16—1221no—
985M16C23×D6112yes—
986M16C23×D6112yes—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—611no—
990C2×C8—611no—
991C2×C8—611no—
992C2×C8—611no—
993C2×C8—612no—
994C2×C8—612no—
995C2×C8—612no—
996C2×C8—612no—
997C2×C8—1224no—
998C2×C8—1224no—
999C2×C8—1224no—
1000C2×C8—1224no—
1001C2×C8—1221no—
1002C2×C8—1221no—
1003C22⋊C4—44no—
1004C22⋊C4—2444no—
1005C42—21no—
1006C42C23×D6112yes—
1007C23—21no—
1008C23—21no—
1009C23—22no—
1010C23—44no—
1011C23—41no—
1012C23—41no—
1013C23—82no—
1014C23—162no—
1015C23—1221no—
1016C23—1221no—
1017C23—1222no—
1018C23—9762no—
1019C23—4882no—
1020C23—2444no—
1021C23—2441no—
1022C23—2441no—
1023C23#1451982211yescharacteristic
1024Q8—21no—
1025Q8—21no—
1026Q8—22no—
1027Q8—22no—
1028Q8—41no—
1029Q8—41no—
1030Q8—612no—
1031Q8—612no—
1032Q8—1221no—
1033Q8—1221no—
1034Q8—1222no—
1035Q8—1222no—
1036Q8—2444no—
1037Q8—2444no—
1038Q8—2441no—
1039Q8—2441no—
1040Q8C2×D4×D6112yes—
1041Q8C2×D4×D6112yes—
1042D4—22no—
1043D4—22no—
1044D4—22no—
1045D4—22no—
1046D4—22no—
1047D4—22no—
1048D4—21no—
1049D4—21no—
1050D4—44no—
1051D4—44no—
1052D4—41no—
1053D4—41no—
1054D4—612no—
1055D4—612no—
1056D4—1222no—
1057D4—1222no—
1058D4—1222no—
1059D4—1222no—
1060D4—1222no—
1061D4—1222no—
1062D4—1221no—
1063D4—1221no—
1064D4—2444no—
1065D4—2444no—
1066D4—2444no—
1067D4—2444no—
1068D4—2441no—
1069D4—2441no—
1070D4C2×D4×D6112yes—
1071D4C2×D4×D6112yes—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—44no—
1081C2×C4—42no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—1221no—
1085C2×C4—1221no—
1086C2×C4—1222no—
1087C2×C4—1222no—
1088C2×C4—1222no—
1089C2×C4—1222no—
1090C2×C4—1222no—
1091C2×C4—2444no—
1092C2×C4—2444no—
1093C2×C4—2444no—
1094C2×C4—2444no—
1095C2×C4—2444no—
1096C2×C4—2441no—
1097C2×C4—2441no—
1098C2×C4C2×D4×D6111yescharacteristic
1099C2×C4C2×D4×D6111yescharacteristic
1100C2×C4C2×D4×D6111yescharacteristic
1101C2×C4C2×D4×D6111yescharacteristic
1102C2×C4#1451982211yescharacteristic
1103C2×C4C24×D6111yescharacteristic
1104C8—22no—
1105C8—22no—
1106C8—612no—
1107C8—612no—
1108C8—612no—
1109C8—612no—
1110C8—1222no—
1111C8—1222no—
1112C22—22no—
1113C22—22no—
1114C22—22no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—82no—
1119C22—82no—
1120C22—161no—
1121C22—164no—
1122C22—1222no—
1123C22—1222no—
1124C22—9761no—
1125C22—9764no—
1126C22—4882no—
1127C22—4882no—
1128C22—2442no—
1129C22—2442no—
1130C22—2442no—
1131C22#1684039411yescharacteristic
1132C22#1684039411yescharacteristic
1133C22C2×#1451982211yescharacteristic
1134C4—22no—
1135C4—22no—
1136C4—42no—
1137C4—42no—
1138C4—1222no—
1139C4—1222no—
1140C4—2442no—
1141C4#1684039411yescharacteristic
1142C4#1684039411yescharacteristic
1143C4C22×D4×D6111yescharacteristic
1144C4C22×D4×D6111yescharacteristic
1145C2—21no—
1146C2—21no—
1147C2—42no—
1148C2—42no—
1149C2—82no—
1150C2—4882no—
1151C2—2442no—
1152C2—2442no—
1153C2#2145760312yesdirect product factor
1154C2C2×#1684039411yescharacteristic
subgroupG/H
centerC22#16840394
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#455C2
socleC22×C61D42
hypercenterC2×#455D61
hypocenterC61C2×#3290
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#455

Complements

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

NH ≅ G/Ntype
1. C2×#16840578C2semidirect
2. C2×#16840573C2semidirect
3. C2×#16840571C2semidirect
4. C2×#16840565C2semidirect
5. #21457603C2direct (N × H)
6. C2×#16840144C2semidirect
7. C2×#16840035C2semidirect
8. C2×#16840031C2semidirect
9. C2×#16840027C2semidirect
10. C2×#16840024C2semidirect
11. C2×#16839936C2semidirect
12. C2×#16839934C2semidirect
13. C2×#16839941C2semidirect
14. C2×#16839876C2semidirect
15. C2×#16839876C2semidirect
16. C2×C61×#455C2semidirect
17. C2×#14519825C22semidirect
18. C2×#14519824C22semidirect
21. #16840578C22semidirect
23. #16840573C22semidirect
25. #16840571C22semidirect
27. #16840565C22semidirect
28. C2×#14519810C22semidirect
34. C2×#14519805C22semidirect
39. C2×#14519803C22semidirect
48. C22×#11758202C22semidirect
51. C22×#11758200C22semidirect
52. C22×#11758201C22semidirect
56. C2×#14519785C22semidirect
57. C2×#14519785C22semidirect
59. C2×#14519784C22semidirect
60. C2×#14519765C22semidirect
61. #16840144C22semidirect
62. #16840035C22semidirect
63. #16840031C22semidirect
64. #16840027C22semidirect
65. #16840024C22semidirect
66. #16839941C22semidirect
67. #16839936C22semidirect
68. #16839934C22semidirect
69. #16839876C22semidirect
70. #16839876C22semidirect
71. C2×#14519712C22semidirect
72. C2×#14519712C22semidirect
73. C2×#14519705C22semidirect
74. C2×#14519705C22semidirect
75. C2×#14519696C22semidirect
76. C2×#14519695C22semidirect
77. C2×#14519693C22semidirect
78. C2×C4×#92418C22semidirect
81. C2×#137×C61C22semidirect
82. C2×#124×C61C22semidirect
83. C61×#455C22semidirect
85. C2×#104×C61C22semidirect
86. C2×#100×C61C22semidirect
90. #14519825C23semidirect
94. #14519824C23semidirect
119. #14519810C23semidirect
127. #14519805C23semidirect
134. #14519803C23semidirect
153. C2×#11758202C23semidirect
166. C2×#11758200C23semidirect
173. C2×#11758201C23semidirect
188. #14519785C23semidirect
189. #14519785C23semidirect
193. #14519784C23semidirect
207. #14519765C23semidirect
209. #14519712C23semidirect
210. #14519712C23semidirect
211. #14519705C23semidirect
212. #14519705C23semidirect
213. #14519696C23semidirect
214. #14519695C23semidirect
215. #14519693C23semidirect
216. C4×#92418C23semidirect
233. #137×C61C23semidirect
241. #124×C61C23semidirect
245. #104×C61C23semidirect
246. #100×C61C23semidirect
581. C2×#455D61semidirect
589. C2×C61#3290semidirect
613. C2×#137C2×D61semidirect
641. C2×#124C2×D61semidirect
648. #455C2×D61semidirect
658. C2×#104C2×D61semidirect
662. C2×#100C2×D61semidirect
664. C61C2×#3290semidirect
720. #137C22×D61semidirect
810. #124C22×D61semidirect
819. #104C22×D61semidirect
823. #100C22×D61semidirect
1153. C2#21457603direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168405782
C2×#168405732
C2×#168405712
C2×#168405652
#214576032
C2×#168401442
C2×#168400352
C2×#168400312
C2×#168400272
C2×#168400242
C2×#168399362
C2×#168399342
C2×#168399412
C2×#168398762
C2×C61×#4552
C2×#329061