Finite Group Databasebeta

← C2×#471×D61 #30547382

Subgroups — C2×#471×D61 #30547382

Order 15616.

2758 conjugacy classes of subgroups.

The subgroup lattice has 1150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#137×D61C211yesmaximal, characteristic, complemented
2C2×AGL(1,ℤ/8)×D61C211yesmaximal, characteristic
3C22×SD16×D61C211yesmaximal, characteristic, complemented
4C2×#131×D61C211yesmaximal, characteristic, complemented
5C2×#16840028C211yesmaximal, characteristic, complemented
6C2×#16840027C211yesmaximal, characteristic, complemented
7C2×#16840026C211yesmaximal, characteristic, complemented
8C2×#16840025C211yesmaximal, characteristic, complemented
9C2×#16840024C211yesmaximal, characteristic, complemented
10C2×#16840023C211yesmaximal, characteristic, complemented
11C2×#16840022C211yesmaximal, characteristic, complemented
12#471×D61C2116yesmaximal, direct product factor
13C2×#108×D61C211yesmaximal, characteristic, complemented
14C2×#101×D61C211yesmaximal, characteristic, complemented
15C2×#100×D61C211yesmaximal, characteristic, complemented
16C2×C61×#471C211yesmaximal, characteristic, complemented
17C2×#41×D61C2211yescharacteristic
18C22×Q8×D61C2211yescharacteristic
19C22×D4×D61C2211yescharacteristic
20C2×#14519810C2211yescharacteristic, complemented
21C2×#14519809—21no—
22C2×#14519808C2211yescharacteristic, complemented
23C2×#14519807C2211yescharacteristic, complemented
24C2×#14519806—21no—
25#137×D61—24no—
26#137×D61C2218yescomplemented
27C2×#14519805C2211yescharacteristic
28C2×#14519804—21no—
29C2×#14519803C2211yescharacteristic
30C2×#14519802C2211yescharacteristic
31C2×#14519801—21no—
32AGL(1,ℤ/8)×D61—24no—
33AGL(1,ℤ/8)×D61C2218yes—
34C2×Q16×D61—21no—
35C22×#11758190C2211yescharacteristic, complemented
36C22×#11758200C2211yescharacteristic, complemented
37C22×#11758201C2211yescharacteristic, complemented
38C2×SD16×D61—21no—
39C2×SD16×D61—21no—
40C2×SD16×D61—24no—
41C2×SD16×D61—21no—
42C2×SD16×D61—21no—
43C2×SD16×D61—21no—
44C2×SD16×D61—21no—
45C2×SD16×D61C2218yescomplemented
46C2×D8×D61—21no—
47C2×#14519785—21no—
48C2×#14519785C2211yescharacteristic, complemented
49C2×#14519784C2211yescharacteristic, complemented
50C2×#14519783—21no—
51C2×#14519783C2211yescharacteristic, complemented
52#131×D61—24no—
53#131×D61C2218yescomplemented
54C2×M16×D61—21no—
55C2×M16×D61C2211yescharacteristic
56C2×M16×D61C2211yescharacteristic
57C2×M16×D61C2211yescharacteristic
58C22×C8×D61—21no—
59C22×C8×D61C2211yescharacteristic
60#16840028C2218yescomplemented
61#16840027C2218yescomplemented
62#16840026C2218yescomplemented
63#16840025C2218yescomplemented
64#16840024C2218yescomplemented
65#16840023C2218yescomplemented
66#16840022C2218yescomplemented
67C2×#14519713C2211yescharacteristic, complemented
68C2×#14519712C2211yescharacteristic, complemented
69C2×#14519712C2211yescharacteristic, complemented
70#108×D61C2218yescomplemented
71C2×#14519696C2211yescharacteristic, complemented
72C2×#14519695C2211yescharacteristic, complemented
73C2×#14519695C2211yescharacteristic, complemented
74#101×D61C2218yescomplemented
75C2×#14519694C2211yescharacteristic, 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×#11758226D411yescharacteristic
89C2×#11758222—21no—
90C2×#11758222C2311yescharacteristic
91C2×#11758224—21no—
92C2×#11758224D411yescharacteristic
93#41×D61—22no—
94#41×D61—22no—
95#41×D61D414yes—
96#41×D61C2314yes—
97C22×Dic122—21no—
98C22×Dic122C2311yescharacteristic
99C2×Q8×D61—22no—
100C2×Q8×D61—21no—
101C2×Q8×D61—22no—
102C2×Q8×D61—21no—
103C2×Q8×D61—21no—
104C2×Q8×D61—22no—
105C2×Q8×D61—21no—
106C2×Q8×D61D411yescharacteristic
107C2×Q8×D61C2314yes—
108C22×D244C2311yescharacteristic
109C22×C22⋊D61—21no—
110C2×D4×D61—21no—
111C2×D4×D61—21no—
112C2×D4×D61—21no—
113C2×D4×D61—22no—
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#14519810—22no—
124#14519810C2314yescomplemented
125#14519809—28no—
126#14519808—22no—
127#14519808C2314yescomplemented
128#14519807—22no—
129#14519807C2314yescomplemented
130#14519806—28no—
131#14519805—22no—
132#14519805C2314yes—
133#14519804—28no—
134#14519803—22no—
135#14519803C2314yes—
136#14519802—22no—
137#14519802C2314yes—
138#14519801—28no—
139C2×Dic244—21no—
140C2×#11758202—21no—
141C2×#11758202—21no—
142Q16×D61—28no—
143C2×#11758190—21no—
144C2×#11758190—21no—
145C2×#11758190—21no—
146C2×#11758190—21no—
147C2×#11758190—22no—
148C2×#11758190C2314yescomplemented
149C2×#11758200—21no—
150C2×#11758200—21no—
151C2×#11758200—21no—
152C2×#11758200—21no—
153C2×#11758200—22no—
154C2×#11758200C2314yescomplemented
155C2×#11758201—21no—
156C2×#11758201—21no—
157C2×#11758201—21no—
158C2×#11758201—21no—
159C2×#11758201—22no—
160C2×#11758201C2314yescomplemented
161SD16×D61—28no—
162SD16×D61—28no—
163SD16×D61—28no—
164SD16×D61—28no—
165SD16×D61—28no—
166SD16×D61—28no—
167C2×D488—21no—
168C2×#11758199—21no—
169C2×#11758199—21no—
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—
188M16×D61—22no—
189M16×D61—22no—
190M16×D61—22no—
191M16×D61—28no—
192M16×D61C2314yes—
193M16×D61C2314yes—
194M16×D61C2314yes—
195C22×#92418—21no—
196C22×#92418C2311yescharacteristic
197C2×C8×D61—21no—
198C2×C8×D61—21no—
199C2×C8×D61—21no—
200C2×C8×D61—21no—
201C2×C8×D61—21no—
202C2×C8×D61—28no—
203C2×C8×D61D411yescharacteristic
204C2×C8×D61D411yescharacteristic
205C2×C8×D61D414yes—
206C2×C8×D61D411yescharacteristic
207C2×C8×D61D411yescharacteristic
208C2×C8×D61C2314yes—
209#14519713C2314yescomplemented
210#14519712C2314yescomplemented
211#14519712C2314yescomplemented
212#14519696C2314yescomplemented
213#14519695C2314yescomplemented
214#14519695C2314yescomplemented
215#14519694C2314yescomplemented
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—24no—
248C23×D61—41no—
249C23×D61—42no—
250C23×D61—41no—
251C23×D61—84no—
252C23×D61#4111yescharacteristic
253#41×C61—21no—
254#41×C61—21no—
255#41×C61C2×D412yes—
256#41×C61C2412yes—
257C2×Q8×C61—21no—
258C2×Q8×C61—21no—
259C2×Q8×C61—21no—
260C2×Q8×C61—21no—
261C2×Q8×C61—21no—
262C2×Q8×C61C2×D411yescharacteristic
263C2×Q8×C61C2412yes—
264C2×D4×C61—21no—
265C2×D4×C61—21no—
266C2×D4×C61—21no—
267C2×D4×C61—21no—
268C2×D4×C61—21no—
269C2×D4×C61—21no—
270C2×D4×C61C2×D411yescharacteristic
271C2×D4×C61C2412yes—
272C22×C4×C61—21no—
273C22×C4×C61—21no—
274C22×C4×C61C2411yescharacteristic
275C2×C22⋊D61—21no—
276C2×C22⋊D61—21no—
277C2×C22⋊D61—21no—
278C2×C22⋊D61—24no—
279C2×C22⋊D61—41no—
280C2×C22⋊D61—41no—
281C2×C22⋊D61—42no—
282C22×Dic61—21no—
283C22×Dic61—21no—
284C22×Dic61#4111yescharacteristic
285#11758226—22no—
286#11758226C2×D414yes—
287Q8×D61—22no—
288Q8×D61—24no—
289Q8×D61—24no—
290Q8×D61—24no—
291Q8×D61—24no—
292Q8×D61—42no—
293Q8×D61—42no—
294Q8×D61—42no—
295Q8×D61—42no—
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×D244C2×D411yescharacteristic
326C2×D244C2412yes—
327C2×C4×D61—21no—
328C2×C4×D61—21no—
329C2×C4×D61—21no—
330C2×C4×D61—24no—
331C2×C4×D61—24no—
332C2×C4×D61—24no—
333C2×C4×D61—41no—
334C2×C4×D61—42no—
335C2×C4×D61—41no—
336C2×C4×D61C2×D411yescharacteristic
337C2×C4×D61C2×D411yescharacteristic
338C2×C4×D61C2×D412yes—
339C2×C4×D61C2×D412yes—
340C2×C4×D61C2×D411yescharacteristic
341C2×C4×D61C2×D411yescharacteristic
342C2×C4×D61#4112yes—
343C2×C4×D61C2412yes—
344C2×Dic122—21no—
345C2×Dic122—21no—
346C2×Dic122—21no—
347C2×Dic122—21no—
348C2×Dic122—21no—
349C2×Dic122—21no—
350C2×Dic122—24no—
351C2×Dic122—41no—
352C2×Dic122—41no—
353C2×Dic122—42no—
354C2×Dic122C2×D411yescharacteristic
355C2×Dic122C2412yes—
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#11758202—24no—
379#11758201—24no—
380#11758201—24no—
381#11758201—24no—
382#11758201—24no—
383#11758200—24no—
384#11758200—24no—
385#11758200—24no—
386#11758200—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—
404Dic244—24no—
405D488—24no—
406#11758190—24no—
407#11758190—24no—
408#11758190—24no—
409#11758190—24no—
410#11758189—24no—
411#11758189—24no—
412#11758189—24no—
413#11758189—24no—
414#11758189—24no—
415C8×D61—24no—
416C8×D61—24no—
417C8×D61—24no—
418C8×D61—24no—
419C8×D61—24no—
420C8×D61C2×D414yes—
421C8×D61C2×D414yes—
422C8×D61C2×D414yes—
423C8×D61C2×D414yes—
424C23×C61—21no—
425C23×C61—22no—
426C23×C61—41no—
427C23×C61—41no—
428C23×C61—82no—
429C23×C61C2×#4111yescharacteristic
430C22×D61—24no—
431C22×D61—21no—
432C22×D61—24no—
433C22×D61—22no—
434C22×D61—44no—
435C22×D61—41no—
436C22×D61—41no—
437C22×D61—44no—
438C22×D61—44no—
439C22×D61—84no—
440C22×D61—88no—
441C22×D61—88no—
442C22×D61—84no—
443C22×D61—82no—
444C22×D61#12111yescharacteristic
445C22×D61#12112yes—
446C22×D61#12111yescharacteristic
447C22×D61C2×#4112yes—
448Q8×C61—21no—
449Q8×C61—22no—
450Q8×C61—22no—
451Q8×C61—41no—
452Q8×C61—41no—
453Q8×C61C22×D412yes—
454D4×C61—22no—
455D4×C61—22no—
456D4×C61—21no—
457D4×C61—22no—
458D4×C61—22no—
459D4×C61—41no—
460D4×C61—41no—
461D4×C61C22×D412yes—
462C2×C4×C61—21no—
463C2×C4×C61—22no—
464C2×C4×C61—22no—
465C2×C4×C61—22no—
466C2×C4×C61—41no—
467C2×C4×C61—41no—
468C2×C4×C61C22×D411yescharacteristic
469C2×C4×C61C22×D411yescharacteristic
470C2×C4×C61C22×D411yescharacteristic
471C2×C4×C61C22×D411yescharacteristic
472C2×C4×C61C2×#4111yescharacteristic
473C2×C4×C61C2511yescharacteristic
474C22⋊D61—22no—
475C22⋊D61—22no—
476C22⋊D61—24no—
477C22⋊D61—24no—
478C22⋊D61—44no—
479C22⋊D61—44no—
480C2×Dic61—21no—
481C2×Dic61—24no—
482C2×Dic61—22no—
483C2×Dic61—41no—
484C2×Dic61—41no—
485C2×Dic61#12111yescharacteristic
486C2×Dic61#12111yescharacteristic
487C2×Dic61#12112yes—
488C2×Dic61C2×#4112yes—
489D244—24no—
490D244—21no—
491D244—22no—
492D244—22no—
493D244—41no—
494D244—41no—
495D244C22×D412yes—
496C4×D61—24no—
497C4×D61—22no—
498C4×D61—22no—
499C4×D61—24no—
500C4×D61—44no—
501C4×D61—44no—
502C4×D61#12112yes—
503C4×D61#12112yes—
504C4×D61#12112yes—
505C4×D61#12112yes—
506C4×D61C22×D412yes—
507C4×D61C22×D412yes—
508C4×D61C22×D412yes—
509C4×D61C22×D412yes—
510Dic122—21no—
511Dic122—24no—
512Dic122—22no—
513Dic122—22no—
514Dic122—41no—
515Dic122—41no—
516Dic122—44no—
517Dic122—44no—
518Dic122C22×D412yes—
519C8×C61—22no—
520C8×C61—22no—
521C8×C61—22no—
522C8×C61C22×D412yes—
523C8×C61C22×D412yes—
524#92418—22no—
525#92418—22no—
526#92418—22no—
527#92418C22×D412yes—
528#92418C22×D412yes—
529C22×#471—611nomaximal, Sylow
530C22×C61—22no—
531C22×C61—22no—
532C22×C61—42no—
533C22×C61—42no—
534C22×C61—82no—
535C22×C61—82no—
536C22×C61—82no—
537C22×C61C2×#12111yescharacteristic
538C22×C61C2×#12111yescharacteristic
539C22×C61C22×#4111yescharacteristic
540C2×D61—22no—
541C2×D61—24no—
542C2×D61—24no—
543C2×D61—22no—
544C2×D61—42no—
545C2×D61—48no—
546C2×D61—42no—
547C2×D61—88no—
548C2×D61—82no—
549C2×D61—82no—
550C2×D61—88no—
551C2×D61—82no—
552C2×D61#47114yesdirect product factor
553C2×D61C2×#12112yes—
554C2×D61C2×#12112yes—
555C4×C61—22no—
556C4×C61—42no—
557C4×C61C2×#12111yescharacteristic
558C4×C61C2×#12111yescharacteristic
559C4×C61C23×D411yescharacteristic
560C4×C61C23×D411yescharacteristic
561Dic61—22no—
562Dic61—42no—
563Dic61C2×#12112yes—
564Dic61C2×#12112yes—
565C22×#137—611no—
566C22×AGL(1,ℤ/8)—611no—
567C23×SD16—611no—
568C22×#131—611no—
569C2×#471—6116no—
570C2×#471—611no—
571C2×#471—611no—
572C2×#471—611no—
573C2×#471—611no—
574C2×#471—611no—
575C2×#471—611no—
576C2×#471—611no—
577C2×#471D6111yescharacteristic, direct product factor
578C22×#108—611no—
579C22×#101—611no—
580C22×#100—611no—
581C2×C61—21no—
582C2×C61—21no—
583C2×C61—42no—
584C2×C61—82no—
585C2×C61C2×#47112yescomplemented
586C2×C61C22×#12111yescharacteristic
587D61—22no—
588D61—42no—
589D61—82no—
590D61C2×#47114yesdirect product factor
591C22×#41—611no—
592C23×Q8—611no—
593C23×D4—611no—
594C2×#137—611no—
595C2×#137—611no—
596C2×#137—618no—
597C2×#137—611no—
598C2×#137—1221no—
599C2×#137—1221no—
600C2×#137—1224no—
601C2×#137C2×D6111yescharacteristic, complemented
602C2×AGL(1,ℤ/8)—611no—
603C2×AGL(1,ℤ/8)—611no—
604C2×AGL(1,ℤ/8)—618no—
605C2×AGL(1,ℤ/8)—611no—
606C2×AGL(1,ℤ/8)—1221no—
607C2×AGL(1,ℤ/8)—1221no—
608C2×AGL(1,ℤ/8)—1224no—
609C2×AGL(1,ℤ/8)C2×D6111yescharacteristic
610C22×Q16—1221no—
611C22×SD16—611no—
612C22×SD16—611no—
613C22×SD16—618no—
614C22×SD16—611no—
615C22×SD16—1221no—
616C22×SD16—1221no—
617C22×SD16—1221no—
618C22×SD16—1221no—
619C22×SD16—1224no—
620C22×SD16—1221no—
621C22×SD16—1221no—
622C22×SD16C2×D6111yescharacteristic, complemented
623C22×D8—1221no—
624C2×#131—611no—
625C2×#131—618no—
626C2×#131—611no—
627C2×#131—611no—
628C2×#131—1221no—
629C2×#131—1221no—
630C2×#131—1224no—
631C2×#131C2×D6111yescharacteristic, complemented
632C22×M16—611no—
633C22×M16—611no—
634C22×M16—611no—
635C22×M16—1221no—
636C23×C8—611no—
637C23×C8—1221no—
638#471—618no—
639#471—618no—
640#471—618no—
641#471—618no—
642#471—618no—
643#471—618no—
644#471—618no—
645#471C2×D6118yesdirect product factor
646C2×#108—611no—
647C2×#108—611no—
648C2×#108—611no—
649C2×#108—618no—
650C2×#108C2×D6111yescharacteristic, complemented
651C2×#101—611no—
652C2×#101—611no—
653C2×#101—611no—
654C2×#101—618no—
655C2×#101C2×D6111yescharacteristic, complemented
656C2×#100—611no—
657C2×#100—611no—
658C2×#100—611no—
659C2×#100—618no—
660C2×#100C2×D6111yescharacteristic, complemented
661C61C22×#47111yescharacteristic, complemented, Sylow
662C25—1221no—
663C2×#41—614no—
664C2×#41—614no—
665C2×#41—611no—
666C2×#41—611no—
667C2×#41—611no—
668C2×#41—1221no—
669C2×#41—1221no—
670C2×#41—1222no—
671C2×#41—1222no—
672C2×#41C22×D6111yescharacteristic
673C22×Q8—611no—
674C22×Q8—614no—
675C22×Q8—611no—
676C22×Q8—1221no—
677C22×Q8—1222no—
678C22×Q8—1221no—
679C22×Q8—1222no—
680C22×Q8—1221no—
681C22×Q8—1221no—
682C22×Q8—1221no—
683C22×Q8—1222no—
684C22×Q8C22×D6111yescharacteristic
685C22×D4—611no—
686C22×D4—614no—
687C22×D4—611no—
688C22×D4—1221no—
689C22×D4—1221no—
690C22×D4—1222no—
691C22×D4—1221no—
692C22×D4—1221no—
693C22×D4—1222no—
694C22×D4—1222no—
695C22×D4—1221no—
696C22×D4—1221no—
697C22×D4C22×D6111yescharacteristic
698C23×C4—611no—
699C23×C4—1221no—
700C23×C4—1221no—
701#137—22no—
702#137—614no—
703#137—614no—
704#137—614no—
705#137—1222no—
706#137—1228no—
707#137—1228no—
708#137—1222no—
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)—1222no—
716AGL(1,ℤ/8)—1228no—
717AGL(1,ℤ/8)—1228no—
718AGL(1,ℤ/8)—1222no—
719AGL(1,ℤ/8)—1222no—
720AGL(1,ℤ/8)C22×D6114yes—
721C2×Q16—21no—
722C2×Q16—1221no—
723C2×Q16—1228no—
724C2×Q16—1221no—
725C2×Q16—1221no—
726C2×SD16—21no—
727C2×SD16—21no—
728C2×SD16—21no—
729C2×SD16—21no—
730C2×SD16—22no—
731C2×SD16—614no—
732C2×SD16—614no—
733C2×SD16—614no—
734C2×SD16—1221no—
735C2×SD16—1221no—
736C2×SD16—1228no—
737C2×SD16—1228no—
738C2×SD16—1228no—
739C2×SD16—1228no—
740C2×SD16—1221no—
741C2×SD16—1221no—
742C2×SD16—1222no—
743C2×SD16—1221no—
744C2×SD16—1221no—
745C2×SD16—1222no—
746C2×SD16—1228no—
747C2×SD16—1228no—
748C2×SD16—1221no—
749C2×SD16—1221no—
750C2×SD16—1221no—
751C2×SD16—1221no—
752C2×SD16—1221no—
753C2×SD16—1221no—
754C2×SD16—1222no—
755C2×SD16C22×D6114yescomplemented
756C2×D8—21no—
757C2×D8—1221no—
758C2×D8—1228no—
759C2×D8—1221no—
760C2×D8—1221no—
761#131—22no—
762#131—614no—
763#131—614no—
764#131—614no—
765#131—1228no—
766#131—1222no—
767#131—1228no—
768#131—1222no—
769#131—1222no—
770#131C22×D6114yescomplemented
771C2×M16—21no—
772C2×M16—611no—
773C2×M16—611no—
774C2×M16—611no—
775C2×M16—614no—
776C2×M16—614no—
777C2×M16—614no—
778C2×M16—1221no—
779C2×M16—1221no—
780C2×M16—1221no—
781C2×M16—1221no—
782C2×M16—1228no—
783C2×M16—1221no—
784C2×M16—1222no—
785C2×M16—1222no—
786C2×M16—1222no—
787C2×M16—1221no—
788C2×M16C22×D6111yescharacteristic
789C2×M16C22×D6111yescharacteristic
790C2×M16C22×D6111yescharacteristic
791C22×C8—21no—
792C22×C8—611no—
793C22×C8—611no—
794C22×C8—611no—
795C22×C8—611no—
796C22×C8—611no—
797C22×C8—614no—
798C22×C8—614no—
799C22×C8—1221no—
800C22×C8—1228no—
801C22×C8—1221no—
802C22×C8—1221no—
803C22×C8—1221no—
804C22×C8—1221no—
805C22×C8—1221no—
806C22×C8C22×D6111yescharacteristic
807#108—614no—
808#108—614no—
809#108—614no—
810#108C22×D6114yescomplemented
811#101—614no—
812#101—614no—
813#101—614no—
814#101C22×D6114yescomplemented
815#100—614no—
816#100—614no—
817#100—614no—
818#100C22×D6114yescomplemented
819C24—21no—
820C24—611no—
821C24—1221no—
822C24—1224no—
823C24—1221no—
824C24—4884no—
825C24—2442no—
826C24—2441no—
827C24—2441no—
828#41—21no—
829#41—21no—
830#41—614no—
831#41—614no—
832#41—612no—
833#41—612no—
834#41—1224no—
835#41—1224no—
836#41—1224no—
837#41—1224no—
838#41—1222no—
839#41—1222no—
840#41—1221no—
841#41—1221no—
842#41D4×D6112yes—
843#41C23×D6112yes—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—614no—
850C2×Q8—611no—
851C2×Q8—612no—
852C2×Q8—1221no—
853C2×Q8—1224no—
854C2×Q8—1222no—
855C2×Q8—1224no—
856C2×Q8—1224no—
857C2×Q8—1224no—
858C2×Q8—1224no—
859C2×Q8—1221no—
860C2×Q8—1221no—
861C2×Q8—1221no—
862C2×Q8—1221no—
863C2×Q8—1221no—
864C2×Q8—2442no—
865C2×Q8—2441no—
866C2×Q8—2441no—
867C2×Q8—2442no—
868C2×Q8—2442no—
869C2×Q8—2442no—
870C2×Q8—2442no—
871C2×Q8D4×D6111yescharacteristic
872C2×Q8C23×D6112yes—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—614no—
880C2×D4—611no—
881C2×D4—612no—
882C2×D4—1221no—
883C2×D4—1222no—
884C2×D4—1224no—
885C2×D4—1224no—
886C2×D4—1224no—
887C2×D4—1224no—
888C2×D4—1221no—
889C2×D4—1224no—
890C2×D4—1224no—
891C2×D4—1224no—
892C2×D4—1221no—
893C2×D4—1221no—
894C2×D4—1221no—
895C2×D4—1221no—
896C2×D4—1221no—
897C2×D4—1221no—
898C2×D4—1221no—
899C2×D4—2442no—
900C2×D4—2442no—
901C2×D4—2442no—
902C2×D4—2442no—
903C2×D4—2442no—
904C2×D4—2441no—
905C2×D4—2441no—
906C2×D4D4×D6111yescharacteristic
907C2×D4C23×D6112yes—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—611no—
911C22×C4—611no—
912C22×C4—612no—
913C22×C4—611no—
914C22×C4—611no—
915C22×C4—612no—
916C22×C4—611no—
917C22×C4—612no—
918C22×C4—612no—
919C22×C4—1224no—
920C22×C4—1221no—
921C22×C4—1224no—
922C22×C4—1221no—
923C22×C4—1224no—
924C22×C4—1221no—
925C22×C4—1221no—
926C22×C4—1221no—
927C22×C4—2442no—
928C22×C4—2441no—
929C22×C4—2441no—
930C22×C4C23×D6111yescharacteristic
931Q16—24no—
932Q16—1224no—
933Q16—1224no—
934Q16—1224no—
935SD16—24no—
936SD16—24no—
937SD16—24no—
938SD16—24no—
939SD16—1224no—
940SD16—1224no—
941SD16—1224no—
942SD16—1224no—
943SD16—1224no—
944SD16—1224no—
945SD16—1224no—
946SD16—1224no—
947SD16—1224no—
948SD16—1224no—
949SD16—1224no—
950SD16—1224no—
951D8—24no—
952D8—1224no—
953D8—1224no—
954D8—1224no—
955M16—21no—
956M16—21no—
957M16—21no—
958M16—24no—
959M16—612no—
960M16—612no—
961M16—612no—
962M16—1224no—
963M16—1224no—
964M16—1224no—
965M16—1224no—
966M16—1224no—
967M16—1221no—
968M16—1221no—
969M16—1221no—
970M16—1224no—
971M16C23×D6112yes—
972M16C23×D6112yes—
973M16C23×D6112yes—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—24no—
978C2×C8—611no—
979C2×C8—611no—
980C2×C8—612no—
981C2×C8—612no—
982C2×C8—614no—
983C2×C8—614no—
984C2×C8—614no—
985C2×C8—614no—
986C2×C8—1224no—
987C2×C8—1224no—
988C2×C8—1224no—
989C2×C8—1224no—
990C2×C8—1224no—
991C2×C8—1221no—
992C2×C8—1221no—
993C2×C8—1221no—
994C2×C8—1224no—
995C2×C8D4×D6111yescharacteristic
996C2×C8D4×D6111yescharacteristic
997C2×C8D4×D6112yes—
998C2×C8C23×D6112yes—
999C23—21no—
1000C23—22no—
1001C23—41no—
1002C23—41no—
1003C23—82no—
1004C23—611no—
1005C23—612no—
1006C23—611no—
1007C23—612no—
1008C23—1224no—
1009C23—1224no—
1010C23—1221no—
1011C23—1222no—
1012C23—4882no—
1013C23—4884no—
1014C23—4888no—
1015C23—4888no—
1016C23—4884no—
1017C23—2444no—
1018C23—2444no—
1019C23—2444no—
1020C23—2441no—
1021C23—2441no—
1022C23#41×D6111yescharacteristic
1023Q8—21no—
1024Q8—22no—
1025Q8—22no—
1026Q8—41no—
1027Q8—41no—
1028Q8—612no—
1029Q8—1224no—
1030Q8—1221no—
1031Q8—1222no—
1032Q8—1222no—
1033Q8—2444no—
1034Q8—2444no—
1035Q8—2441no—
1036Q8—2441no—
1037Q8C2×D4×D6112yes—
1038D4—22no—
1039D4—22no—
1040D4—21no—
1041D4—22no—
1042D4—22no—
1043D4—41no—
1044D4—41no—
1045D4—612no—
1046D4—1224no—
1047D4—1224no—
1048D4—1224no—
1049D4—1222no—
1050D4—1222no—
1051D4—1221no—
1052D4—1222no—
1053D4—1222no—
1054D4—2444no—
1055D4—2444no—
1056D4—2441no—
1057D4—2441no—
1058D4C2×D4×D6112yes—
1059C2×C4—21no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—612no—
1066C2×C4—611no—
1067C2×C4—611no—
1068C2×C4—612no—
1069C2×C4—612no—
1070C2×C4—612no—
1071C2×C4—612no—
1072C2×C4—612no—
1073C2×C4—612no—
1074C2×C4—612no—
1075C2×C4—612no—
1076C2×C4—612no—
1077C2×C4—1224no—
1078C2×C4—1224no—
1079C2×C4—1224no—
1080C2×C4—1221no—
1081C2×C4—1222no—
1082C2×C4—1222no—
1083C2×C4—1222no—
1084C2×C4—2444no—
1085C2×C4—2444no—
1086C2×C4—2441no—
1087C2×C4—2441no—
1088C2×C4C2×D4×D6111yescharacteristic
1089C2×C4C2×D4×D6111yescharacteristic
1090C2×C4C2×D4×D6111yescharacteristic
1091C2×C4C2×D4×D6111yescharacteristic
1092C2×C4#41×D6111yescharacteristic
1093C2×C4C24×D6111yescharacteristic
1094C8—22no—
1095C8—22no—
1096C8—22no—
1097C8—612no—
1098C8—612no—
1099C8—1222no—
1100C8—1222no—
1101C8—1222no—
1102C8C2×D4×D6112yes—
1103C8C2×D4×D6112yes—
1104C22—22no—
1105C22—22no—
1106C22—42no—
1107C22—42no—
1108C22—82no—
1109C22—82no—
1110C22—82no—
1111C22—612no—
1112C22—614no—
1113C22—612no—
1114C22—1224no—
1115C22—1224no—
1116C22—1222no—
1117C22—1222no—
1118C22—4882no—
1119C22—4882no—
1120C22—4888no—
1121C22—4888no—
1122C22—4882no—
1123C22—2448no—
1124C22—2442no—
1125C22—2442no—
1126C22#121×D6111yescharacteristic
1127C22#121×D6111yescharacteristic
1128C22C2×#41×D6111yescharacteristic
1129C4—22no—
1130C4—42no—
1131C4—612no—
1132C4—612no—
1133C4—1222no—
1134C4—2442no—
1135C4#121×D6111yescharacteristic
1136C4#121×D6111yescharacteristic
1137C4C22×D4×D6111yescharacteristic
1138C4C22×D4×D6111yescharacteristic
1139C2—21no—
1140C2—21no—
1141C2—42no—
1142C2—82no—
1143C2—614no—
1144C2—1222no—
1145C2—4882no—
1146C2—2442no—
1147C2#471×D6112yesdirect product factor
1148C2C2×#121×D6111yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#471C2
socleC22×C61C2×#121
prime radicalC2×AGL(1,ℤ/8)×D61C2
hypercenterC2×#471D61
hypocenterC61C22×#471
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×#137×D61C2semidirect
3. C22×SD16×D61C2semidirect
4. C2×#131×D61C2semidirect
5. C2×#16840028C2semidirect
6. C2×#16840027C2semidirect
7. C2×#16840026C2semidirect
8. C2×#16840025C2semidirect
9. C2×#16840024C2semidirect
10. C2×#16840023C2semidirect
11. C2×#16840022C2semidirect
12. #471×D61C2direct (N × H)
13. C2×#108×D61C2semidirect
14. C2×#101×D61C2semidirect
15. C2×#100×D61C2semidirect
16. C2×C61×#471C2semidirect
20. C2×#14519810C22semidirect
22. C2×#14519808C22semidirect
23. C2×#14519807C22semidirect
26. #137×D61C22semidirect
35. C22×#11758190C22semidirect
36. C22×#11758200C22semidirect
37. C22×#11758201C22semidirect
45. C2×SD16×D61C22semidirect
48. C2×#14519785C22semidirect
49. C2×#14519784C22semidirect
51. C2×#14519783C22semidirect
53. #131×D61C22semidirect
60. #16840028C22semidirect
61. #16840027C22semidirect
62. #16840026C22semidirect
63. #16840025C22semidirect
64. #16840024C22semidirect
65. #16840023C22semidirect
66. #16840022C22semidirect
67. C2×#14519713C22semidirect
68. C2×#14519712C22semidirect
69. C2×#14519712C22semidirect
70. #108×D61C22semidirect
71. C2×#14519696C22semidirect
72. C2×#14519695C22semidirect
73. C2×#14519695C22semidirect
74. #101×D61C22semidirect
75. C2×#14519694C22semidirect
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
124. #14519810C23semidirect
127. #14519808C23semidirect
129. #14519807C23semidirect
148. C2×#11758190C23semidirect
154. C2×#11758200C23semidirect
160. C2×#11758201C23semidirect
173. #14519785C23semidirect
175. #14519784C23semidirect
178. #14519783C23semidirect
209. #14519713C23semidirect
210. #14519712C23semidirect
211. #14519712C23semidirect
212. #14519696C23semidirect
213. #14519695C23semidirect
214. #14519695C23semidirect
215. #14519694C23semidirect
216. #14519693C23semidirect
217. #14519693C23semidirect
222. #137×C61C23semidirect
231. C2×SD16×C61C23semidirect
234. #131×C61C23semidirect
241. #108×C61C23semidirect
242. #101×C61C23semidirect
243. #100×C61C23semidirect
552. C2×D61#471direct (N × H)
577. C2×#471D61direct (N × H)
585. C2×C61C2×#471semidirect
590. D61C2×#471direct (N × H)
601. C2×#137C2×D61semidirect
622. C22×SD16C2×D61semidirect
631. C2×#131C2×D61semidirect
645. #471C2×D61direct (N × H)
650. C2×#108C2×D61semidirect
655. C2×#101C2×D61semidirect
660. C2×#100C2×D61semidirect
661. C61C22×#471semidirect
710. #137C22×D61semidirect
755. C2×SD16C22×D61semidirect
770. #131C22×D61semidirect
810. #108C22×D61semidirect
814. #101C22×D61semidirect
818. #100C22×D61semidirect
1147. C2#471×D61direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#137×D612
C2×AGL(1,ℤ/8)×D612
C22×SD16×D612
C2×#131×D612
C2×#168400282
C2×#168400272
C2×#168400262
C2×#168400252
C2×#168400242
C2×#168400232
C2×#168400222
#471×D612
C2×#108×D612
C2×#101×D612
C2×#100×D612
C2×C61×#4712
C22×#47161