Finite Group Databasebeta

← C2×#21455542 #30547412

Subgroups — C2×#21455542 #30547412

Order 15616.

2746 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840561C211yesmaximal, characteristic, complemented
2C22×#14519804C211yesmaximal, characteristic, complemented
3C2×AGL(1,ℤ/8)×D61C211yesmaximal, characteristic, complemented
4C2×#16840527C211yesmaximal, characteristic, complemented
5#21455542C2116yesmaximal, direct product factor
6C2×#16840033C211yesmaximal, characteristic, complemented
7C2×#16840032C211yesmaximal, characteristic, complemented
8C2×#16840031C211yesmaximal, characteristic, complemented
9C2×#16840030C211yesmaximal, characteristic, complemented
10C2×#16840028C211yesmaximal, characteristic, complemented
11C2×#16840027C211yesmaximal, characteristic, complemented
12C2×#16840022C211yesmaximal, characteristic, complemented
13C2×#16839809C211yesmaximal, characteristic, complemented
14C2×#16839745C211yesmaximal, characteristic, complemented
15C2×#100×D61C211yesmaximal, characteristic, complemented
16C2×C61×#471C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C2×#41×D61C2211yescharacteristic
19C22×D4×D61C2211yescharacteristic
20#16840561—24no—
21#16840561C2218yescomplemented
22C2×#14519809—21no—
23C2×#14519808C2211yescharacteristic, complemented
24C2×#14519805C2211yescharacteristic
25C2×#14519805C2211yescharacteristic, complemented
26C2×#14519804—21no—
27C2×#14519804—21no—
28C2×#14519804—21no—
29C2×#14519804—21no—
30C2×#14519804—24no—
31C2×#14519804—21no—
32C2×#14519804—21no—
33C2×#14519804C2218yescomplemented
34C2×#14519803C2211yescharacteristic
35C2×#14519802C2211yescharacteristic
36C2×#14519802C2211yescharacteristic, complemented
37C2×#14519801—21no—
38AGL(1,ℤ/8)×D61—24no—
39AGL(1,ℤ/8)×D61C2218yescomplemented
40C2×#14519800—21no—
41C2×#14519798—21no—
42C22×#11758201C2211yescharacteristic, complemented
43C2×SD16×D61—21no—
44C22×D488C2211yescharacteristic, complemented
45C22×#11758199C2211yescharacteristic, complemented
46C2×D8×D61—21no—
47#16840527—24no—
48#16840527C2218yescomplemented
49C2×#14519785—21no—
50C2×#14519785C2211yescharacteristic, complemented
51C2×#14519784C2211yescharacteristic, complemented
52C2×#14519783—21no—
53C2×#14519783C2211yescharacteristic, complemented
54C22×#11758189—21no—
55C22×#11758189C2211yescharacteristic
56C2×M16×D61—21no—
57C2×M16×D61C2211yescharacteristic
58C2×M16×D61C2211yescharacteristic
59C2×M16×D61C2211yescharacteristic
60#16840033C2218yescomplemented
61#16840032C2218yescomplemented
62#16840031C2218yescomplemented
63#16840030C2218yescomplemented
64#16840028C2218yescomplemented
65#16840027C2218yescomplemented
66#16840022C2218yescomplemented
67#16839809C2218yescomplemented
68C2×#14519713C2211yescharacteristic, complemented
69C2×#14519712C2211yescharacteristic, complemented
70C2×#14519712C2211yescharacteristic, complemented
71#16839745C2218yescomplemented
72C2×#14519696C2211yescharacteristic, complemented
73C2×#14519694C2211yescharacteristic, complemented
74C2×#14519693C2211yescharacteristic, complemented
75C2×#14519693C2211yescharacteristic, complemented
76C2×#14519693C2211yescharacteristic, complemented
77C2×#14519693C2211yescharacteristic, complemented
78#100×D61C2218yescomplemented
79C2×#137×C61C2211yescharacteristic, complemented
80C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
81C22×SD16×C61C2211yescharacteristic, complemented
82C2×#131×C61C2211yescharacteristic, complemented
83C61×#471C2218yescomplemented
84C2×#108×C61C2211yescharacteristic, complemented
85C2×#101×C61C2211yescharacteristic, complemented
86C2×#100×C61C2211yescharacteristic, complemented
87C24×D61—21no—
88C2×#11758226—22no—
89C2×#11758226—21no—
90C2×#11758226—21no—
91C2×#11758226—22no—
92C2×#11758226—21no—
93C2×#11758226—21no—
94C2×#11758226—22no—
95C2×#11758226D411yescharacteristic
96C2×#11758226C2314yes—
97C2×#11758222—21no—
98C2×#11758222C2311yescharacteristic
99C2×#11758224—21no—
100C2×#11758224D411yescharacteristic
101#41×D61—22no—
102#41×D61—22no—
103#41×D61D414yes—
104#41×D61C2314yes—
105C2×Q8×D61D411yescharacteristic
106C22×D244—21no—
107C22×D244C2311yescharacteristic
108C22×D244C2311yescharacteristic
109C22×C22⋊D61—21no—
110C2×D4×D61—21no—
111C2×D4×D61—21no—
112C2×D4×D61—22no—
113C2×D4×D61—21no—
114C2×D4×D61—21no—
115C2×D4×D61—22no—
116C2×D4×D61—21no—
117C2×D4×D61—22no—
118C2×D4×D61D411yescharacteristic
119C2×D4×D61C2314yes—
120C22×C4×D61—21no—
121C22×C4×D61—21no—
122C22×C4×D61C2311yescharacteristic
123#14519809—28no—
124#14519808—22no—
125#14519808C2314yescomplemented
126#14519805—22no—
127#14519805—22no—
128#14519805C2314yes—
129#14519805C2314yescomplemented
130#14519804—28no—
131#14519804—28no—
132#14519804—28no—
133#14519804—28no—
134#14519804—28no—
135#14519804—28no—
136#14519803—22no—
137#14519803C2314yes—
138#14519802—22no—
139#14519802—22no—
140#14519802C2314yes—
141#14519802C2314yescomplemented
142#14519801—28no—
143#14519800—28no—
144#14519798—28no—
145C2×#11758202—21no—
146C2×#11758190—21no—
147C2×#11758190—21no—
148C2×#11758200—21no—
149C2×#11758201—21no—
150C2×#11758201—21no—
151C2×#11758201—21no—
152C2×#11758201—21no—
153C2×#11758201—21no—
154C2×#11758201—22no—
155C2×#11758201C2314yescomplemented
156SD16×D61—28no—
157C2×D488—21no—
158C2×D488—21no—
159C2×D488—21no—
160C2×D488—21no—
161C2×D488—22no—
162C2×D488C2314yescomplemented
163C2×#11758199—21no—
164C2×#11758199—21no—
165C2×#11758199—21no—
166C2×#11758199—21no—
167C2×#11758199—21no—
168C2×#11758199—22no—
169C2×#11758199C2314yescomplemented
170D8×D61—28no—
171#14519785—22no—
172#14519785—28no—
173#14519785C2314yescomplemented
174#14519784—22no—
175#14519784C2314yescomplemented
176#14519783—22no—
177#14519783—28no—
178#14519783C2314yescomplemented
179C2×#11758194—21no—
180C2×#11758194C2311yescharacteristic
181C2×#11758194C2311yescharacteristic
182C2×#11758194C2311yescharacteristic
183C2×#11758189—21no—
184C2×#11758189—21no—
185C2×#11758189—21no—
186C2×#11758189—21no—
187C2×#11758189—21no—
188C2×#11758189—28no—
189C2×#11758189D411yescharacteristic
190C2×#11758189D411yescharacteristic
191C2×#11758189D411yescharacteristic
192C2×#11758189D411yescharacteristic
193C2×#11758189D414yes—
194C2×#11758189C2314yes—
195M16×D61—22no—
196M16×D61—22no—
197M16×D61—22no—
198M16×D61—28no—
199M16×D61C2314yes—
200M16×D61C2314yes—
201M16×D61C2314yes—
202C22×#92418—21no—
203C22×#92418C2311yescharacteristic
204C2×C8×D61—21no—
205C2×C8×D61—21no—
206C2×C8×D61—21no—
207C2×C8×D61—21no—
208C2×C8×D61—21no—
209#14519713C2314yescomplemented
210#14519712C2314yescomplemented
211#14519712C2314yescomplemented
212#14519696C2314yescomplemented
213#14519694C2314yescomplemented
214#14519693C2314yescomplemented
215#14519693C2314yescomplemented
216#14519693C2314yescomplemented
217#14519693C2314yescomplemented
218C2×#41×C61C2311yescharacteristic
219C22×Q8×C61C2311yescharacteristic
220C22×D4×C61C2311yescharacteristic
221#137×C61—22no—
222#137×C61C2314yescomplemented
223AGL(1,ℤ/8)×C61—22no—
224AGL(1,ℤ/8)×C61C2314yes—
225C2×Q16×C61—21no—
226C2×SD16×C61—21no—
227C2×SD16×C61—21no—
228C2×SD16×C61—21no—
229C2×SD16×C61—21no—
230C2×SD16×C61—22no—
231C2×SD16×C61C2314yescomplemented
232C2×D8×C61—21no—
233#131×C61—22no—
234#131×C61C2314yescomplemented
235C2×M16×C61—21no—
236C2×M16×C61C2311yescharacteristic
237C2×M16×C61C2311yescharacteristic
238C2×M16×C61C2311yescharacteristic
239C22×C8×C61—21no—
240C22×C8×C61C2311yescharacteristic
241#108×C61C2314yescomplemented
242#101×C61C2314yescomplemented
243#100×C61C2314yescomplemented
244C24×C61—21no—
245C23×D61—21no—
246C23×D61—21no—
247C23×D61—21no—
248C23×D61—24no—
249C23×D61—41no—
250C23×D61—41no—
251C23×D61—42no—
252C23×D61—84no—
253C23×D61#4111yescharacteristic
254#41×C61—21no—
255#41×C61—21no—
256#41×C61C2×D412yes—
257#41×C61C2412yes—
258C2×Q8×C61—21no—
259C2×Q8×C61—21no—
260C2×Q8×C61—21no—
261C2×Q8×C61—21no—
262C2×Q8×C61—21no—
263C2×Q8×C61C2×D411yescharacteristic
264C2×Q8×C61C2412yes—
265C2×D4×C61—21no—
266C2×D4×C61—21no—
267C2×D4×C61—21no—
268C2×D4×C61—21no—
269C2×D4×C61—21no—
270C2×D4×C61—21no—
271C2×D4×C61C2×D411yescharacteristic
272C2×D4×C61C2412yes—
273C22×C4×C61—21no—
274C22×C4×C61—21no—
275C22×C4×C61C2411yescharacteristic
276C2×C22⋊D61—21no—
277C2×C22⋊D61—21no—
278C2×C22⋊D61—21no—
279C2×C22⋊D61—24no—
280C2×C22⋊D61—41no—
281C2×C22⋊D61—41no—
282C2×C22⋊D61—42no—
283C22×Dic61—21no—
284C22×Dic61#4111yescharacteristic
285#11758226—22no—
286#11758226—24no—
287#11758226—24no—
288#11758226—24no—
289#11758226—24no—
290#11758226—42no—
291#11758226—42no—
292#11758226—42no—
293#11758226—42no—
294#11758226C2×D414yes—
295Q8×D61—22no—
296Q8×D61C2×D414yes—
297#11758224—24no—
298#11758224—24no—
299#11758224—22no—
300#11758224C2×D414yes—
301D4×D61—24no—
302D4×D61—24no—
303D4×D61—22no—
304D4×D61—24no—
305D4×D61—24no—
306D4×D61—24no—
307D4×D61—24no—
308D4×D61—42no—
309D4×D61—42no—
310D4×D61—42no—
311D4×D61—42no—
312D4×D61C2×D414yes—
313#11758222—21no—
314#11758222—21no—
315#11758222—24no—
316#11758222—24no—
317#11758222C2×D412yes—
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—24no—
329C2×D244—21no—
330C2×D244—21no—
331C2×D244—41no—
332C2×D244—41no—
333C2×D244—42no—
334C2×D244C2×D411yescharacteristic
335C2×D244C2412yes—
336C2×D244C2412yes—
337C2×C4×D61—21no—
338C2×C4×D61—21no—
339C2×C4×D61—21no—
340C2×C4×D61—24no—
341C2×C4×D61—24no—
342C2×C4×D61—24no—
343C2×C4×D61—41no—
344C2×C4×D61—41no—
345C2×C4×D61—42no—
346C2×C4×D61C2×D411yescharacteristic
347C2×C4×D61C2×D411yescharacteristic
348C2×C4×D61C2×D412yes—
349C2×C4×D61C2×D412yes—
350C2×C4×D61C2×D411yescharacteristic
351C2×C4×D61C2×D411yescharacteristic
352C2×C4×D61#4112yes—
353C2×C4×D61C2412yes—
354C2×Dic122—21no—
355C2×Dic122C2×D411yescharacteristic
356Q16×C61—24no—
357SD16×C61—24no—
358SD16×C61—24no—
359SD16×C61—24no—
360SD16×C61—24no—
361D8×C61—24no—
362M16×C61—21no—
363M16×C61—21no—
364M16×C61—21no—
365M16×C61—24no—
366M16×C61C2412yes—
367M16×C61C2412yes—
368M16×C61C2412yes—
369C2×C8×C61—21no—
370C2×C8×C61—21no—
371C2×C8×C61—21no—
372C2×C8×C61—24no—
373C2×C8×C61C2×D411yescharacteristic
374C2×C8×C61C2×D411yescharacteristic
375C2×C8×C61C2×D412yes—
376C2×C8×C61C2412yes—
377#11758202—24no—
378#11758201—24no—
379#11758201—24no—
380#11758201—24no—
381#11758201—24no—
382#11758201—24no—
383#11758200—24no—
384#11758199—24no—
385#11758199—24no—
386#11758199—24no—
387#11758199—24no—
388#11758199—24no—
389#11758194—21no—
390#11758194—21no—
391#11758194—21no—
392#11758194—24no—
393#11758194C2412yes—
394#11758194C2412yes—
395#11758194C2412yes—
396C2×#92418—21no—
397C2×#92418—21no—
398C2×#92418—21no—
399C2×#92418—24no—
400C2×#92418C2×D411yescharacteristic
401C2×#92418C2×D411yescharacteristic
402C2×#92418C2×D412yes—
403C2×#92418C2412yes—
404D488—24no—
405D488—24no—
406D488—24no—
407D488—24no—
408#11758190—24no—
409#11758190—24no—
410#11758189—24no—
411#11758189—24no—
412#11758189—24no—
413#11758189—24no—
414#11758189—24no—
415#11758189C2×D414yes—
416#11758189C2×D414yes—
417#11758189C2×D414yes—
418#11758189C2×D414yes—
419C8×D61—24no—
420C8×D61—24no—
421C8×D61—24no—
422C8×D61—24no—
423C8×D61—24no—
424C23×C61—21no—
425C23×C61—22no—
426C23×C61—41no—
427C23×C61—41no—
428C23×C61—82no—
429C23×C61C2×#4111yescharacteristic
430C22×D61—21no—
431C22×D61—24no—
432C22×D61—22no—
433C22×D61—22no—
434C22×D61—42no—
435C22×D61—41no—
436C22×D61—41no—
437C22×D61—41no—
438C22×D61—41no—
439C22×D61—44no—
440C22×D61—44no—
441C22×D61—82no—
442C22×D61—84no—
443C22×D61—84no—
444C22×D61—88no—
445C22×D61—88no—
446C22×D61—82no—
447C22×D61—82no—
448C22×D61#12111yescharacteristic
449C22×D61#12111yescharacteristic
450C22×D61#12112yes—
451C22×D61C2×#4112yes—
452Q8×C61—21no—
453Q8×C61—22no—
454Q8×C61—22no—
455Q8×C61—41no—
456Q8×C61—41no—
457Q8×C61C22×D412yes—
458D4×C61—22no—
459D4×C61—22no—
460D4×C61—21no—
461D4×C61—22no—
462D4×C61—22no—
463D4×C61—41no—
464D4×C61—41no—
465D4×C61C22×D412yes—
466C2×C4×C61—21no—
467C2×C4×C61—22no—
468C2×C4×C61—22no—
469C2×C4×C61—22no—
470C2×C4×C61—41no—
471C2×C4×C61—41no—
472C2×C4×C61C22×D411yescharacteristic
473C2×C4×C61C22×D411yescharacteristic
474C2×C4×C61C22×D411yescharacteristic
475C2×C4×C61C22×D411yescharacteristic
476C2×C4×C61C2×#4111yescharacteristic
477C2×C4×C61C2511yescharacteristic
478C22⋊D61—22no—
479C22⋊D61—22no—
480C22⋊D61—24no—
481C22⋊D61—24no—
482C22⋊D61—44no—
483C22⋊D61—44no—
484C2×Dic61—21no—
485C2×Dic61—24no—
486C2×Dic61#12111yescharacteristic
487C2×Dic61#12111yescharacteristic
488C2×Dic61#12112yes—
489C2×Dic61C2×#4112yes—
490D244—24no—
491D244—21no—
492D244—22no—
493D244—22no—
494D244—22no—
495D244—22no—
496D244—44no—
497D244—44no—
498D244—41no—
499D244—41no—
500D244—41no—
501D244—41no—
502D244C22×D412yes—
503C4×D61—24no—
504C4×D61—22no—
505C4×D61—22no—
506C4×D61—24no—
507C4×D61—44no—
508C4×D61—44no—
509C4×D61#12112yes—
510C4×D61#12112yes—
511C4×D61#12112yes—
512C4×D61#12112yes—
513C4×D61C22×D412yes—
514C4×D61C22×D412yes—
515C4×D61C22×D412yes—
516C4×D61C22×D412yes—
517Dic122—21no—
518Dic122—24no—
519Dic122C22×D412yes—
520C8×C61—22no—
521C8×C61—22no—
522C8×C61—22no—
523C8×C61C22×D412yes—
524C8×C61C22×D412yes—
525#92418—22no—
526#92418—22no—
527#92418—22no—
528#92418C22×D412yes—
529#92418C22×D412yes—
530C2×#3068—611nomaximal, Sylow
531C22×C61—22no—
532C22×C61—22no—
533C22×C61—42no—
534C22×C61—42no—
535C22×C61—82no—
536C22×C61—82no—
537C22×C61—82no—
538C22×C61C2×#12111yescharacteristic
539C22×C61C2×#12111yescharacteristic
540C22×C61C22×#4111yescharacteristic
541C2×D61—22no—
542C2×D61—22no—
543C2×D61—22no—
544C2×D61—42no—
545C2×D61—42no—
546C2×D61—42no—
547C2×D61—42no—
548C2×D61—42no—
549C2×D61—84no—
550C2×D61—88no—
551C2×D61—88no—
552C2×D61—82no—
553C2×D61—82no—
554C2×D61—82no—
555C2×D61—82no—
556C2×D61—82no—
557C2×D61—82no—
558C2×D61C2×#12112yes—
559C2×D61C2×#12112yes—
560C4×C61—22no—
561C4×C61—42no—
562C4×C61C2×#12111yescharacteristic
563C4×C61C2×#12111yescharacteristic
564C4×C61C23×D411yescharacteristic
565C4×C61C23×D411yescharacteristic
566Dic61—22no—
567Dic61C2×#12112yes—
568Dic61C2×#12112yes—
569C2×#575—611no—
570C22×AGL(1,ℤ/8)—611no—
571C22×AGL(1,ℤ/8)—611no—
572C2×#568—611no—
573#3068—6116no—
574C2×#472—611no—
575C2×#472—611no—
576C2×#472—611no—
577C2×#472—611no—
578C2×#471—611no—
579C2×#471—611no—
580C2×#471—611no—
581C2×#471D6111yescharacteristic, complemented
582C2×#430—611no—
583C2×#413—611no—
584C22×#100—611no—
585C2×C61—21no—
586C2×C61—21no—
587C2×C61—42no—
588C2×C61—82no—
589C2×C61#306812yescomplemented
590C2×C61C22×#12111yescharacteristic
591D61—22no—
592D61—22no—
593D61—42no—
594D61—82no—
595D61—82no—
596C22×#41—611no—
597C22×#41—611no—
598C23×D4—611no—
599#575—618no—
600#575—1224no—
601C2×#137—611no—
602C2×#137—1221no—
603C2×#137C2×D6111yescharacteristic, complemented
604C2×AGL(1,ℤ/8)—618no—
605C2×AGL(1,ℤ/8)—611no—
606C2×AGL(1,ℤ/8)—611no—
607C2×AGL(1,ℤ/8)—611no—
608C2×AGL(1,ℤ/8)—618no—
609C2×AGL(1,ℤ/8)—611no—
610C2×AGL(1,ℤ/8)—611no—
611C2×AGL(1,ℤ/8)—1221no—
612C2×AGL(1,ℤ/8)—1221no—
613C2×AGL(1,ℤ/8)—1221no—
614C2×AGL(1,ℤ/8)—1221no—
615C2×AGL(1,ℤ/8)—1224no—
616C2×AGL(1,ℤ/8)—1221no—
617C2×AGL(1,ℤ/8)—1221no—
618C2×AGL(1,ℤ/8)—1221no—
619C2×AGL(1,ℤ/8)—1224no—
620C2×AGL(1,ℤ/8)C2×D6111yescharacteristic
621C2×#135—1221no—
622C2×#135—1221no—
623C22×SD16—611no—
624C22×SD16—1221no—
625C22×SD16C2×D6111yescharacteristic, complemented
626C22×D8—611no—
627C22×D8—611no—
628C22×D8—1221no—
629#568—618no—
630#568—1224no—
631C2×#131—611no—
632C2×#131—611no—
633C2×#131—611no—
634C2×#131—1221no—
635C2×#131—1221no—
636C2×#131C2×D6111yescharacteristic, complemented
637C22×M16—611no—
638C22×M16—611no—
639C22×M16—611no—
640C22×M16—611no—
641C22×M16—1221no—
642C22×M16—1221no—
643#472—618no—
644#472—618no—
645#472—618no—
646#472—618no—
647#471—618no—
648#471—618no—
649#471—618no—
650#471C2×D6118yescomplemented
651#430—618no—
652C2×#108—611no—
653C2×#108—611no—
654C2×#108—611no—
655C2×#108C2×D6111yescharacteristic, complemented
656#413—618no—
657C2×#101—611no—
658C2×#101C2×D6111yescharacteristic, complemented
659C2×#100—611no—
660C2×#100—611no—
661C2×#100—611no—
662C2×#100—611no—
663C2×#100—611no—
664C2×#100—618no—
665C2×#100C2×D6111yescharacteristic, complemented
666C61C2×#306811yescharacteristic, complemented, Sylow
667C25—1221no—
668C2×#41—614no—
669C2×#41—614no—
670C2×#41—611no—
671C2×#41—614no—
672C2×#41—611no—
673C2×#41—611no—
674C2×#41—1221no—
675C2×#41—1221no—
676C2×#41—1222no—
677C2×#41—1222no—
678C2×#41—1222no—
679C2×#41—1221no—
680C2×#41—1221no—
681C2×#41—1221no—
682C2×#41—1222no—
683C2×#41—1221no—
684C2×#41—1222no—
685C2×#41C22×D6111yescharacteristic
686C22×Q8—611no—
687C22×Q8C22×D6111yescharacteristic
688C22×D4—611no—
689C22×D4—614no—
690C22×D4—611no—
691C22×D4—611no—
692C22×D4—1221no—
693C22×D4—1221no—
694C22×D4—1221no—
695C22×D4—1221no—
696C22×D4—1221no—
697C22×D4—1222no—
698C22×D4—1222no—
699C22×D4—1222no—
700C22×D4—1221no—
701C22×D4—1221no—
702C22×D4C22×D6111yescharacteristic
703C23×C4—611no—
704C23×C4—1221no—
705C23×C4—1221no—
706#137—22no—
707#137—614no—
708#137—1228no—
709#137—1222no—
710#137C22×D6114yescomplemented
711AGL(1,ℤ/8)—22no—
712AGL(1,ℤ/8)—614no—
713AGL(1,ℤ/8)—614no—
714AGL(1,ℤ/8)—614no—
715AGL(1,ℤ/8)—614no—
716AGL(1,ℤ/8)—614no—
717AGL(1,ℤ/8)—1222no—
718AGL(1,ℤ/8)—1222no—
719AGL(1,ℤ/8)—1228no—
720AGL(1,ℤ/8)—1228no—
721AGL(1,ℤ/8)—1228no—
722AGL(1,ℤ/8)—1228no—
723AGL(1,ℤ/8)—1228no—
724AGL(1,ℤ/8)—1228no—
725AGL(1,ℤ/8)—1228no—
726AGL(1,ℤ/8)—1222no—
727AGL(1,ℤ/8)—1222no—
728AGL(1,ℤ/8)—1222no—
729AGL(1,ℤ/8)C22×D6114yes—
730#135—1228no—
731#135—1228no—
732C2×Q16—21no—
733C2×Q16—1221no—
734C2×SD16—21no—
735C2×SD16—21no—
736C2×SD16—21no—
737C2×SD16—21no—
738C2×SD16—22no—
739C2×SD16—614no—
740C2×SD16—1221no—
741C2×SD16—1221no—
742C2×SD16—1221no—
743C2×SD16—1221no—
744C2×SD16—1222no—
745C2×SD16—1228no—
746C2×SD16—1221no—
747C2×SD16—1221no—
748C2×SD16—1221no—
749C2×SD16—1221no—
750C2×SD16C22×D6114yescomplemented
751C2×D8—21no—
752C2×D8—614no—
753C2×D8—614no—
754C2×D8—1221no—
755C2×D8—1221no—
756C2×D8—1221no—
757C2×D8—1221no—
758C2×D8—1222no—
759C2×D8—1228no—
760C2×D8—1221no—
761C2×D8—1221no—
762C2×D8—1221no—
763C2×D8—1221no—
764C2×D8—1221no—
765C2×D8—1222no—
766#131—22no—
767#131—614no—
768#131—614no—
769#131—614no—
770#131—1228no—
771#131—1222no—
772#131—1222no—
773#131—1228no—
774#131—1222no—
775#131C22×D6114yescomplemented
776C2×M16—21no—
777C2×M16—611no—
778C2×M16—611no—
779C2×M16—611no—
780C2×M16—611no—
781C2×M16—614no—
782C2×M16—614no—
783C2×M16—611no—
784C2×M16—611no—
785C2×M16—611no—
786C2×M16—614no—
787C2×M16—614no—
788C2×M16—614no—
789C2×M16—1221no—
790C2×M16—1228no—
791C2×M16—1221no—
792C2×M16—1221no—
793C2×M16—1221no—
794C2×M16—1221no—
795C2×M16—1228no—
796C2×M16—1222no—
797C2×M16—1222no—
798C2×M16—1222no—
799C2×M16—1221no—
800C2×M16C22×D6111yescharacteristic
801C2×M16C22×D6111yescharacteristic
802C2×M16C22×D6111yescharacteristic
803C22×C8—21no—
804C22×C8—611no—
805C22×C8—1221no—
806C22×C8—1221no—
807C22×C8—1221no—
808C22×C8—1221no—
809C22×C8—1221no—
810C22×C8—1221no—
811C22×C8C22×D6111yescharacteristic
812#108—614no—
813#108—614no—
814#108—614no—
815#108C22×D6114yescomplemented
816#101—614no—
817#101C22×D6114yescomplemented
818#100—614no—
819#100—614no—
820#100—614no—
821#100—614no—
822#100—614no—
823#100C22×D6114yescomplemented
824C24—21no—
825C24—611no—
826C24—1221no—
827C24—1224no—
828C24—1221no—
829C24—1221no—
830C24—4884no—
831C24—2442no—
832C24—2441no—
833C24—2441no—
834#41—21no—
835#41—21no—
836#41—614no—
837#41—614no—
838#41—612no—
839#41—612no—
840#41—1224no—
841#41—1224no—
842#41—1224no—
843#41—1224no—
844#41—1222no—
845#41—1222no—
846#41—1224no—
847#41—1224no—
848#41—1224no—
849#41—1224no—
850#41—1221no—
851#41—1221no—
852#41—2442no—
853#41—2442no—
854#41—2442no—
855#41—2442no—
856#41D4×D6112yes—
857#41C23×D6112yes—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—614no—
864C2×Q8—611no—
865C2×Q8—1221no—
866C2×Q8—1222no—
867C2×Q8D4×D6111yescharacteristic
868C2×Q8C23×D6112yes—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—614no—
876C2×D4—611no—
877C2×D4—612no—
878C2×D4—612no—
879C2×D4—1221no—
880C2×D4—1224no—
881C2×D4—1222no—
882C2×D4—1224no—
883C2×D4—1224no—
884C2×D4—1224no—
885C2×D4—1224no—
886C2×D4—1221no—
887C2×D4—1224no—
888C2×D4—1224no—
889C2×D4—1224no—
890C2×D4—1221no—
891C2×D4—1221no—
892C2×D4—1221no—
893C2×D4—1221no—
894C2×D4—1221no—
895C2×D4—1221no—
896C2×D4—1221no—
897C2×D4—1221no—
898C2×D4—1221no—
899C2×D4—1221no—
900C2×D4—1221no—
901C2×D4—1221no—
902C2×D4—2442no—
903C2×D4—2441no—
904C2×D4—2441no—
905C2×D4—2442no—
906C2×D4—2442no—
907C2×D4—2442no—
908C2×D4—2442no—
909C2×D4—2442no—
910C2×D4—2441no—
911C2×D4—2441no—
912C2×D4D4×D6111yescharacteristic
913C2×D4C23×D6112yes—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—611no—
917C22×C4—611no—
918C22×C4—611no—
919C22×C4—611no—
920C22×C4—611no—
921C22×C4—612no—
922C22×C4—612no—
923C22×C4—612no—
924C22×C4—612no—
925C22×C4—1224no—
926C22×C4—1221no—
927C22×C4—1224no—
928C22×C4—1224no—
929C22×C4—1221no—
930C22×C4—1221no—
931C22×C4—1221no—
932C22×C4—2442no—
933C22×C4—2441no—
934C22×C4—2441no—
935C22×C4C23×D6111yescharacteristic
936Q16—24no—
937Q16—1224no—
938SD16—24no—
939SD16—24no—
940SD16—24no—
941SD16—24no—
942SD16—1224no—
943SD16—1224no—
944SD16—1224no—
945SD16—1224no—
946SD16—1224no—
947SD16—1224no—
948SD16—1224no—
949SD16—1224no—
950D8—24no—
951D8—1224no—
952D8—1224no—
953D8—1224no—
954D8—1224no—
955D8—1224no—
956D8—1224no—
957D8—1224no—
958D8—1224no—
959D8—1224no—
960M16—21no—
961M16—21no—
962M16—21no—
963M16—24no—
964M16—614no—
965M16—614no—
966M16—614no—
967M16—614no—
968M16—612no—
969M16—612no—
970M16—612no—
971M16—1224no—
972M16—1224no—
973M16—1224no—
974M16—1224no—
975M16—1224no—
976M16—1221no—
977M16—1221no—
978M16—1221no—
979M16—1224no—
980M16C23×D6112yes—
981M16C23×D6112yes—
982M16C23×D6112yes—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—24no—
987C2×C8—611no—
988C2×C8—611no—
989C2×C8—612no—
990C2×C8—612no—
991C2×C8—1224no—
992C2×C8—1224no—
993C2×C8—1224no—
994C2×C8—1224no—
995C2×C8—1224no—
996C2×C8—1221no—
997C2×C8—1221no—
998C2×C8—1221no—
999C2×C8—1224no—
1000C2×C8D4×D6111yescharacteristic
1001C2×C8D4×D6111yescharacteristic
1002C2×C8D4×D6112yes—
1003C2×C8C23×D6112yes—
1004C23—21no—
1005C23—22no—
1006C23—41no—
1007C23—41no—
1008C23—82no—
1009C23—611no—
1010C23—611no—
1011C23—612no—
1012C23—612no—
1013C23—1224no—
1014C23—1221no—
1015C23—1222no—
1016C23—1222no—
1017C23—4882no—
1018C23—4882no—
1019C23—4882no—
1020C23—4884no—
1021C23—4884no—
1022C23—4888no—
1023C23—4888no—
1024C23—2442no—
1025C23—2444no—
1026C23—2444no—
1027C23—2441no—
1028C23—2441no—
1029C23—2441no—
1030C23—2441no—
1031C23#41×D6111yescharacteristic
1032Q8—21no—
1033Q8—22no—
1034Q8—22no—
1035Q8—41no—
1036Q8—41no—
1037Q8—612no—
1038Q8—1224no—
1039Q8—1221no—
1040Q8C2×D4×D6112yes—
1041D4—22no—
1042D4—22no—
1043D4—21no—
1044D4—22no—
1045D4—22no—
1046D4—41no—
1047D4—41no—
1048D4—612no—
1049D4—1224no—
1050D4—1224no—
1051D4—1224no—
1052D4—1222no—
1053D4—1222no—
1054D4—1221no—
1055D4—1222no—
1056D4—1222no—
1057D4—1222no—
1058D4—1222no—
1059D4—2444no—
1060D4—2444no—
1061D4—2444no—
1062D4—2444no—
1063D4—2441no—
1064D4—2441no—
1065D4—2441no—
1066D4—2441no—
1067D4C2×D4×D6112yes—
1068C2×C4—21no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—612no—
1075C2×C4—611no—
1076C2×C4—611no—
1077C2×C4—612no—
1078C2×C4—612no—
1079C2×C4—612no—
1080C2×C4—612no—
1081C2×C4—612no—
1082C2×C4—612no—
1083C2×C4—612no—
1084C2×C4—612no—
1085C2×C4—612no—
1086C2×C4—1224no—
1087C2×C4—1224no—
1088C2×C4—1224no—
1089C2×C4—1221no—
1090C2×C4—1222no—
1091C2×C4—1222no—
1092C2×C4—2444no—
1093C2×C4—2444no—
1094C2×C4C2×D4×D6111yescharacteristic
1095C2×C4C2×D4×D6111yescharacteristic
1096C2×C4C2×D4×D6111yescharacteristic
1097C2×C4C2×D4×D6111yescharacteristic
1098C2×C4#41×D6111yescharacteristic
1099C2×C4C24×D6111yescharacteristic
1100C8—22no—
1101C8—22no—
1102C8—22no—
1103C8—612no—
1104C8—612no—
1105C8—1222no—
1106C8—1222no—
1107C8—1222no—
1108C8C2×D4×D6112yes—
1109C8C2×D4×D6112yes—
1110C22—22no—
1111C22—22no—
1112C22—42no—
1113C22—42no—
1114C22—82no—
1115C22—82no—
1116C22—82no—
1117C22—612no—
1118C22—612no—
1119C22—1222no—
1120C22—1222no—
1121C22—1222no—
1122C22—4882no—
1123C22—4882no—
1124C22—4882no—
1125C22—4882no—
1126C22—4884no—
1127C22—4888no—
1128C22—4888no—
1129C22—4882no—
1130C22—4882no—
1131C22—2442no—
1132C22—2442no—
1133C22—2442no—
1134C22—2442no—
1135C22—2442no—
1136C22#121×D6111yescharacteristic
1137C22#121×D6111yescharacteristic
1138C22C2×#41×D6111yescharacteristic
1139C4—22no—
1140C4—42no—
1141C4—612no—
1142C4—612no—
1143C4—1222no—
1144C4#121×D6111yescharacteristic
1145C4#121×D6111yescharacteristic
1146C4C22×D4×D6111yescharacteristic
1147C4C22×D4×D6111yescharacteristic
1148C2—21no—
1149C2—21no—
1150C2—42no—
1151C2—82no—
1152C2—1222no—
1153C2—1222no—
1154C2—4882no—
1155C2—4882no—
1156C2—2442no—
1157C2#2145554212yesdirect product factor
1158C2C2×#121×D6111yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#471C2
socleC22×C61C2×#121
hypercenterC2×#471D61
hypocenterC61C2×#3068
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#471

Complements

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

NH ≅ G/Ntype
1. C2×#16840561C2semidirect
2. C22×#14519804C2semidirect
3. C2×AGL(1,ℤ/8)×D61C2semidirect
4. C2×#16840527C2semidirect
5. #21455542C2direct (N × H)
6. C2×#16840033C2semidirect
7. C2×#16840032C2semidirect
8. C2×#16840031C2semidirect
9. C2×#16840030C2semidirect
10. C2×#16840028C2semidirect
11. C2×#16840027C2semidirect
12. C2×#16840022C2semidirect
13. C2×#16839809C2semidirect
14. C2×#16839745C2semidirect
15. C2×#100×D61C2semidirect
16. C2×C61×#471C2semidirect
21. #16840561C22semidirect
23. C2×#14519808C22semidirect
25. C2×#14519805C22semidirect
33. C2×#14519804C22semidirect
36. C2×#14519802C22semidirect
39. AGL(1,ℤ/8)×D61C22semidirect
42. C22×#11758201C22semidirect
44. C22×D488C22semidirect
45. C22×#11758199C22semidirect
48. #16840527C22semidirect
50. C2×#14519785C22semidirect
51. C2×#14519784C22semidirect
53. C2×#14519783C22semidirect
60. #16840033C22semidirect
61. #16840032C22semidirect
62. #16840031C22semidirect
63. #16840030C22semidirect
64. #16840028C22semidirect
65. #16840027C22semidirect
66. #16840022C22semidirect
67. #16839809C22semidirect
68. C2×#14519713C22semidirect
69. C2×#14519712C22semidirect
70. C2×#14519712C22semidirect
71. #16839745C22semidirect
72. C2×#14519696C22semidirect
73. C2×#14519694C22semidirect
74. C2×#14519693C22semidirect
75. C2×#14519693C22semidirect
76. C2×#14519693C22semidirect
77. C2×#14519693C22semidirect
78. #100×D61C22semidirect
79. C2×#137×C61C22semidirect
81. C22×SD16×C61C22semidirect
82. C2×#131×C61C22semidirect
83. C61×#471C22semidirect
84. C2×#108×C61C22semidirect
85. C2×#101×C61C22semidirect
86. C2×#100×C61C22semidirect
125. #14519808C23semidirect
129. #14519805C23semidirect
141. #14519802C23semidirect
155. C2×#11758201C23semidirect
162. C2×D488C23semidirect
169. C2×#11758199C23semidirect
173. #14519785C23semidirect
175. #14519784C23semidirect
178. #14519783C23semidirect
209. #14519713C23semidirect
210. #14519712C23semidirect
211. #14519712C23semidirect
212. #14519696C23semidirect
213. #14519694C23semidirect
214. #14519693C23semidirect
215. #14519693C23semidirect
216. #14519693C23semidirect
217. #14519693C23semidirect
222. #137×C61C23semidirect
231. C2×SD16×C61C23semidirect
234. #131×C61C23semidirect
241. #108×C61C23semidirect
242. #101×C61C23semidirect
243. #100×C61C23semidirect
581. C2×#471D61semidirect
589. C2×C61#3068semidirect
603. C2×#137C2×D61semidirect
625. C22×SD16C2×D61semidirect
636. C2×#131C2×D61semidirect
650. #471C2×D61semidirect
655. C2×#108C2×D61semidirect
658. C2×#101C2×D61semidirect
665. C2×#100C2×D61semidirect
666. C61C2×#3068semidirect
710. #137C22×D61semidirect
750. C2×SD16C22×D61semidirect
775. #131C22×D61semidirect
815. #108C22×D61semidirect
817. #101C22×D61semidirect
823. #100C22×D61semidirect
1157. C2#21455542direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168405612
C22×#145198042
C2×AGL(1,ℤ/8)×D612
C2×#168405272
#214555422
C2×#168400332
C2×#168400322
C2×#168400312
C2×#168400302
C2×#168400282
C2×#168400272
C2×#168400222
C2×#168398092
C2×#168397452
C2×#100×D612
C2×C61×#4712
C2×#306861