Finite Group Databasebeta

← D61×#1489 #29646437

Subgroups — D61×#1489 #29646437

Order 15616.

1378 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#41×D61C211yesmaximal, characteristic
2#423×D61C211yesmaximal, characteristic, complemented
3C4×M16×D61C211yesmaximal, characteristic, complemented
4#21444259C211yesmaximal, characteristic, complemented
5#21444258C211yesmaximal, characteristic, complemented
6#21444257C212yesmaximal, complemented
7#21444256C211yesmaximal, characteristic, complemented
8#21444255C212yesmaximal, complemented
9Q8⋊C8×D61C212yesmaximal, complemented
10D4⋊C8×D61C212yesmaximal, complemented
11C61×#1489C211yesmaximal, characteristic, complemented
12C2×#41×D61C411yescharacteristic
13C2×M16×D61—21no—
14C2×M16×D61—21no—
15#41×Dic61C411yescharacteristic
16C4×#11758226C411yescharacteristic
17C4×#11758226C2211yescharacteristic
18C4×#11758222—21no—
19C4×#11758222C2211yescharacteristic
20#16840230—21no—
21#16840230C411yescharacteristic
22C4×#11758224—21no—
23C4×#11758224—21no—
24C4×#11758224C411yescharacteristic
25C4×#11758224C2211yescharacteristic
26C4×Q8×D61C411yescharacteristic
27C4×Q8×D61C2211yescharacteristic
28C4×D4×D61—21no—
29C4×D4×D61—21no—
30C4×D4×D61C411yescharacteristic
31C4×D4×D61C2211yescharacteristic
32#117×D61—21no—
33#117×D61C411yescharacteristic
34C2×C42×D61—21no—
35C2×C42×D61C2211yescharacteristic
36#16839786C2211yescharacteristic, complemented
37#16839785—21no—
38#16839784—21no—
39#16839784C2212yescomplemented
40C4⋊C8×D61—21no—
41C4⋊C8×D61C2212yes—
42C4×#11758194C2211yescharacteristic, complemented
43#16839714—21no—
44M16×Dic61—21no—
45C4×#11758189C2212yescomplemented
46#97×D61—21no—
47C4×C8×D61C2212yes—
48#16839494C2212yescomplemented
49Q8⋊#92418C2212yescomplemented
50#16839492C2212yescomplemented
51#16839491C2212yescomplemented
52D4⋊#92418C2212yescomplemented
53#16839489C2212yescomplemented
54C4×#41×C61C2211yescharacteristic
55C61×#423C2211yescharacteristic, complemented
56C4×M16×C61C2211yescharacteristic, complemented
57C61×Q8⋊C8C2212yescomplemented
58C61×D4⋊C8C2212yescomplemented
59C2×#11758226C2×C411yescharacteristic
60C2×#11758222—21no—
61C2×#11758222C2×C411yescharacteristic
62C2×#11758224—21no—
63C2×#11758224C2×C411yescharacteristic
64#41×D61—24no—
65#41×D61—24no—
66C2×Q8×D61C2×C411yescharacteristic
67C2×D4×D61—21no—
68C2×D4×D61C2×C411yescharacteristic
69C22×C4×D61—21no—
70C22×C4×D61—21no—
71C22×C4×D61—21no—
72C22×C4×D61C2×C411yescharacteristic
73C22×C4×D61D411yescharacteristic
74C22×C4×D61D411yescharacteristic
75C2×#11758194—21no—
76C2×#11758194—21no—
77C2×#11758189—22no—
78C2×#11758189—22no—
79M16×D61—28no—
80M16×D61—44no—
81C2×C8×D61—22no—
82C2×C8×D61—22no—
83Q8×Dic61C2×C411yescharacteristic
84Q8×Dic61C2×C411yescharacteristic
85C4×Dic122—21no—
86C4×Dic122—21no—
87C4×Dic122C2×C411yescharacteristic
88C4×Dic122C2311yescharacteristic
89#14519742—21no—
90#14519742—21no—
91#14519742C2×C411yescharacteristic
92#14519742C2×C411yescharacteristic
93C4×D244—21no—
94C4×D244—21no—
95C4×D244C2×C411yescharacteristic
96C4×D244C2311yescharacteristic
97D4×Dic61—21no—
98D4×Dic61—21no—
99D4×Dic61C2×C411yescharacteristic
100D4×Dic61C2×C411yescharacteristic
101#14519739—21no—
102#14519739—21no—
103#14519739C2×C411yescharacteristic
104#14519739C2×C411yescharacteristic
105C4×C22⋊D61—21no—
106C4×C22⋊D61—21no—
107C4×C22⋊D61—21no—
108C4×C22⋊D61—21no—
109C4×C22⋊D61—21no—
110C4×C22⋊D61—21no—
111#14519737—21no—
112#14519737—21no—
113#14519737—21no—
114#14519737—21no—
115#14519737—21no—
116#14519737—21no—
117#14519736—21no—
118#14519736C2×C411yescharacteristic
119#14519735—21no—
120#14519735—21no—
121#14519735C2×C411yescharacteristic
122#14519735C2×C411yescharacteristic
123#14519734—21no—
124#14519734—21no—
125#14519734—21no—
126#14519733—21no—
127#14519733—21no—
128#14519733—21no—
129C4⋊C4×D61—21no—
130C4⋊C4×D61—21no—
131C4⋊C4×D61C2×C411yescharacteristic
132C4⋊C4×D61C2×C411yescharacteristic
133C22⋊C4×D61—21no—
134C22⋊C4×D61—21no—
135C22⋊C4×D61—21no—
136C2×C4×Dic61—21no—
137C2×C4×Dic61—21no—
138C2×C4×Dic61—21no—
139C2×C4×Dic61C2×C411yescharacteristic
140C2×C4×Dic61D411yescharacteristic
141C2×C4×Dic61D411yescharacteristic
142C42×D61—21no—
143C42×D61—21no—
144C42×D61—21no—
145C42×D61—21no—
146C42×D61—21no—
147C42×D61—21no—
148C42×D61—21no—
149C42×D61C2×C411yescharacteristic
150C42×D61C2×C411yescharacteristic
151C42×D61D411yescharacteristic
152C42×D61D411yescharacteristic
153C42×D61D411yescharacteristic
154C42×D61D411yescharacteristic
155C42×D61C2311yescharacteristic
156C42×D61C2311yescharacteristic
157C4⋊#92418—21no—
158C4⋊#92418C2312yes—
159#14519706—22no—
160#14519706—22no—
161#14519688—21no—
162#14519687—22no—
163C4×#92418C2312yes—
164C8×Dic61—22no—
165C2×#41×C61C2×C411yescharacteristic
166C2×M16×C61—21no—
167C2×M16×C61—21no—
168C4×Q8×C61C2×C411yescharacteristic
169C4×Q8×C61C2311yescharacteristic
170C4×D4×C61—21no—
171C4×D4×C61—21no—
172C4×D4×C61C2×C411yescharacteristic
173C4×D4×C61C2311yescharacteristic
174#117×C61—21no—
175#117×C61C2×C411yescharacteristic
176C2×C42×C61—21no—
177C2×C42×C61C2311yescharacteristic
178C4⋊C8×C61—21no—
179C4⋊C8×C61C2312yes—
180#97×C61—21no—
181C4×C8×C61C2312yes—
182C23×D61—21no—
183C23×D61C22⋊C411yescharacteristic
184#41×C61—22no—
185#41×C61—22no—
186C2×Q8×C61C22×C411yescharacteristic
187C2×D4×C61—21no—
188C2×D4×C61C22×C411yescharacteristic
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61C22×C411yescharacteristic
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61C2×D411yescharacteristic
195C2×C22⋊D61—21no—
196C2×C22⋊D61—21no—
197C2×C22⋊D61—21no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61C22⋊C411yescharacteristic
202C22×Dic61C22⋊C411yescharacteristic
203C22×Dic61C22⋊C411yescharacteristic
204#11758226—22no—
205#11758226—22no—
206Q8×D61—22no—
207Q8×D61M1614yescomplemented
208#11758224—28no—
209#11758224—22no—
210#11758224—22no—
211D4×D61—28no—
212D4×D61—22no—
213D4×D61M1614yescomplemented
214#11758222—28no—
215#11758222—22no—
216#11758222—22no—
217C2×D244—21no—
218C2×D244C22×C411yescharacteristic
219C2×C4×D61—28no—
220C2×C4×D61—21no—
221C2×C4×D61—21no—
222C2×C4×D61—21no—
223C2×C4×D61—24no—
224C2×C4×D61—22no—
225C2×C4×D61—22no—
226C2×C4×D61—22no—
227C2×C4×D61—22no—
228C2×C4×D61—21no—
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—44no—
235C2×C4×D61—42no—
236C2×C4×D61—42no—
237C2×C4×D61C22⋊C411yescharacteristic
238C2×C4×D61C22⋊C411yescharacteristic
239C2×C4×D61C22⋊C411yescharacteristic
240C2×C4×D61C22⋊C411yescharacteristic
241C2×C4×D61C22⋊C411yescharacteristic
242C2×C4×D61C22⋊C411yescharacteristic
243C2×C4×D61C22×C411yescharacteristic
244C2×C4×D61C22×C411yescharacteristic
245C2×C4×D61C2×D411yescharacteristic
246C2×C4×D61C2×D411yescharacteristic
247C2×C4×D61C2×D411yescharacteristic
248C2×C4×D61C2×D411yescharacteristic
249C2×Dic122—21no—
250C2×Dic122C22×C411yescharacteristic
251M16×C61—24no—
252M16×C61—42no—
253C2×C8×C61—22no—
254C2×C8×C61—22no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61C22×C411yescharacteristic
258C4⋊C4×C61C22×C411yescharacteristic
259C22⋊C4×C61—21no—
260C22⋊C4×C61—21no—
261C22⋊C4×C61—21no—
262C42×C61—21no—
263C42×C61—21no—
264C42×C61—21no—
265C42×C61C22×C411yescharacteristic
266C42×C61C2×D411yescharacteristic
267C42×C61C2×D411yescharacteristic
268C42×C61C2411yescharacteristic
269C22⋊Dic61—21no—
270C22⋊Dic61—21no—
271C22⋊Dic61—21no—
272#11758198—21no—
273#11758198—21no—
274#11758198—21no—
275#11758198—21no—
276#11758198—21no—
277#11758198—21no—
278C4⋊Dic61—21no—
279C4⋊Dic61—21no—
280C4⋊Dic61C22×C411yescharacteristic
281C4⋊Dic61C22×C411yescharacteristic
282#11758196—21no—
283#11758196—21no—
284#11758196—21no—
285#11758196—21no—
286#11758196—21no—
287#11758196—21no—
288C4×Dic61—21no—
289C4×Dic61—21no—
290C4×Dic61—21no—
291C4×Dic61—21no—
292C4×Dic61—21no—
293C4×Dic61—21no—
294C4×Dic61—21no—
295C4×Dic61—21no—
296C4×Dic61—21no—
297C4×Dic61C22⋊C411yescharacteristic
298C4×Dic61C22⋊C411yescharacteristic
299C4×Dic61C22⋊C411yescharacteristic
300C4×Dic61C22⋊C411yescharacteristic
301C4×Dic61C22⋊C411yescharacteristic
302C4×Dic61C22⋊C411yescharacteristic
303C4×Dic61C22×C411yescharacteristic
304C4×Dic61C22×C411yescharacteristic
305C4×Dic61C2×D411yescharacteristic
306C4×Dic61C2×D411yescharacteristic
307C4×Dic61C2×D411yescharacteristic
308C4×Dic61C2×D411yescharacteristic
309#11758194—24no—
310#11758194—42no—
311C2×#92418—22no—
312C2×#92418—22no—
313#11758189—28no—
314#11758189—44no—
315C8×D61—28no—
316C8×D61—44no—
317C23×C61—21no—
318C23×C61C2×C22⋊C411yescharacteristic
319C22×D61—21no—
320C22×D61—22no—
321C22×D61—24no—
322C22×D61—22no—
323C22×D61—22no—
324C22×D61—42no—
325C22×D61—42no—
326C22×D61C2×C22⋊C411yescharacteristic
327C22×D61C2×C22⋊C411yescharacteristic
328Q8×C61—21no—
329Q8×C61C2×M1612yescomplemented
330D4×C61—24no—
331D4×C61—21no—
332D4×C61C2×M1612yescomplemented
333C2×C4×C61—24no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—22no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—42no—
345C2×C4×C61C2×C22⋊C411yescharacteristic
346C2×C4×C61C2×C22⋊C411yescharacteristic
347C2×C4×C61C2×C22⋊C411yescharacteristic
348C2×C4×C61C23×C411yescharacteristic
349C2×C4×C61C22×D411yescharacteristic
350C2×C4×C61C22×D411yescharacteristic
351C22⋊D61—24no—
352C22⋊D61—24no—
353C22⋊D61—24no—
354C2×Dic61—24no—
355C2×Dic61—21no—
356C2×Dic61—22no—
357C2×Dic61—22no—
358C2×Dic61—22no—
359C2×Dic61—21no—
360C2×Dic61—21no—
361C2×Dic61—42no—
362C2×Dic61—42no—
363C2×Dic61C2×C22⋊C411yescharacteristic
364C2×Dic61C2×C22⋊C411yescharacteristic
365C2×Dic61C2×C22⋊C411yescharacteristic
366C2×Dic61C2×C22⋊C411yescharacteristic
367C2×Dic61C2×C22⋊C411yescharacteristic
368C2×Dic61C2×C22⋊C411yescharacteristic
369D244—24no—
370D244—21no—
371D244C2×M1612yescomplemented
372C4×D61—24no—
373C4×D61—24no—
374C4×D61—22no—
375C4×D61—24no—
376C4×D61—22no—
377C4×D61—22no—
378C4×D61—21no—
379C4×D61—21no—
380C4×D61—21no—
381C4×D61—21no—
382C4×D61—22no—
383C4×D61—22no—
384C4×D61—22no—
385C4×D61—22no—
386C4×D61—42no—
387C4×D61—42no—
388C4×D61—41no—
389C4×D61—41no—
390C4×D61—42no—
391C4×D61—42no—
392C4×D61—42no—
393C4×D61#10414yes—
394C4×D61C2×M1612yes—
395C4×D61C2×M1612yes—
396C4×D61AGL(1,ℤ/8)12yes—
397C4×D61#13712yes—
398Dic122—21no—
399Dic122—24no—
400Dic122C2×M1612yescomplemented
401C8×C61—24no—
402C8×C61—42no—
403#92418—24no—
404#92418—42no—
405C2×#1489—611nomaximal, Sylow
406C22×C61—21no—
407C22×C61—22no—
408C22×C61—21no—
409C22×C61—21no—
410C22×C61—41no—
411C22×C61—41no—
412C22×C61C22×C22⋊C411yescharacteristic
413C2×D61—21no—
414C2×D61—22no—
415C2×D61—21no—
416C2×D61—21no—
417C2×D61—41no—
418C2×D61—41no—
419C2×D61—44no—
420C2×D61—48no—
421C2×D61#40712yes—
422C2×D61#41712yes—
423C2×D61C2×#10412yes—
424C4×C61—22no—
425C4×C61—21no—
426C4×C61—21no—
427C4×C61—21no—
428C4×C61—41no—
429C4×C61—41no—
430C4×C61C2×#10412yes—
431C4×C61C22×M1611yescharacteristic
432C4×C61C22×M1611yescharacteristic
433C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
434C4×C61C2×#13711yescharacteristic
435Dic61—22no—
436Dic61—21no—
437Dic61—21no—
438Dic61—21no—
439Dic61—41no—
440Dic61—41no—
441Dic61#40712yes—
442Dic61#41712yes—
443Dic61C2×#10412yes—
444C2×C4×#41—611no—
445C2×#423—611no—
446C2×C4×M16—611no—
447#1489—611no—
448#1489—611no—
449#1489—612no—
450#1489—612no—
451#1489—611no—
452#1489D6111yescharacteristic, direct product factor
453C2×Q8⋊C8—612no—
454C2×D4⋊C8—612no—
455C2×C61—41no—
456C2×C61—42no—
457C2×C61C2×#40711yescharacteristic
458C2×C61C2×#41711yescharacteristic
459C2×C61C22×#10411yescharacteristic
460D61—41no—
461D61—42no—
462D61#148914yesdirect product factor
463C22×#41—611no—
464C22×M16—1221no—
465C22×M16—1221no—
466C4×#41—611no—
467C4×#41—611no—
468C4×#41—611no—
469C4×#41—611no—
470C4×#41—611no—
471C4×#41—611no—
472C4×#41—611no—
473C4×#41—1221no—
474C4×#41—1221no—
475C4×#41—1221no—
476C4×#41—1221no—
477C4×#41C2×D6111yescharacteristic
478C2×C4×Q8—611no—
479C2×C4×Q8—611no—
480C2×C4×D4—611no—
481C2×C4×D4—611no—
482C2×C4×D4—1221no—
483C2×C4×D4—1221no—
484C2×#117—611no—
485C2×#117—1221no—
486C22×C42—611no—
487C22×C42—1221no—
488#423—611no—
489#423—612no—
490#423—1221no—
491#423—1221no—
492#423C2×D6111yescharacteristic, complemented
493C2×C4⋊C8—612no—
494C2×C4⋊C8—1221no—
495C4×M16—611no—
496C4×M16—612no—
497C4×M16—1221no—
498C4×M16—1221no—
499C4×M16C2×D6111yescharacteristic, complemented
500C2×#97—1221no—
501C2×C4×C8—612no—
502Q8⋊C8—612no—
503Q8⋊C8—612no—
504Q8⋊C8—612no—
505Q8⋊C8C2×D6112yescomplemented
506D4⋊C8—612no—
507D4⋊C8—612no—
508D4⋊C8—612no—
509D4⋊C8C2×D6112yescomplemented
510C61C2×#148911yescharacteristic, complemented, Sylow
511C2×#41—611no—
512C2×#41—611no—
513C2×#41—611no—
514C2×#41—1221no—
515C2×#41—1221no—
516C2×#41—1224no—
517C2×#41—1224no—
518C2×#41C4×D6111yescharacteristic
519C22×Q8—611no—
520C22×D4—611no—
521C22×D4—1221no—
522C23×C4—611no—
523C23×C4—611no—
524C23×C4—611no—
525C23×C4—1221no—
526C23×C4—1221no—
527C23×C4—1221no—
528C2×M16—21no—
529C2×M16—21no—
530C2×M16—1222no—
531C2×M16—1222no—
532C2×M16—1228no—
533C2×M16—1221no—
534C2×M16—1221no—
535C2×M16—2444no—
536C22×C8—1222no—
537C22×C8—1222no—
538C4×Q8—611no—
539C4×Q8—611no—
540C4×Q8—611no—
541C4×Q8—611no—
542C4×Q8—611no—
543C4×Q8—611no—
544C4×Q8—1221no—
545C4×Q8—1221no—
546C4×Q8—1221no—
547C4×Q8—1221no—
548C4×Q8C4×D6111yescharacteristic
549C4×Q8C22×D6111yescharacteristic
550C4×D4—21no—
551C4×D4—21no—
552C4×D4—611no—
553C4×D4—611no—
554C4×D4—611no—
555C4×D4—611no—
556C4×D4—611no—
557C4×D4—611no—
558C4×D4—1221no—
559C4×D4—1221no—
560C4×D4—1221no—
561C4×D4—1221no—
562C4×D4—1221no—
563C4×D4—1221no—
564C4×D4—1221no—
565C4×D4—1221no—
566C4×D4—1221no—
567C4×D4—1221no—
568C4×D4—1221no—
569C4×D4—1221no—
570C4×D4—1221no—
571C4×D4—1221no—
572C4×D4—1221no—
573C4×D4—1221no—
574C4×D4—1221no—
575C4×D4—1221no—
576C4×D4C4×D6111yescharacteristic
577C4×D4C22×D6111yescharacteristic
578#117—21no—
579#117—611no—
580#117—611no—
581#117—611no—
582#117—1221no—
583#117—1221no—
584#117—1221no—
585#117—1221no—
586#117—1221no—
587#117—1221no—
588#117—1221no—
589#117—1221no—
590#117—1221no—
591#117C4×D6111yescharacteristic
592C2×C4⋊C4—611no—
593C2×C4⋊C4—611no—
594C2×C4⋊C4—1221no—
595C2×C4⋊C4—1221no—
596C2×C22⋊C4—1221no—
597C2×C22⋊C4—1221no—
598C2×C22⋊C4—1221no—
599C2×C42—21no—
600C2×C42—611no—
601C2×C42—611no—
602C2×C42—611no—
603C2×C42—611no—
604C2×C42—611no—
605C2×C42—611no—
606C2×C42—611no—
607C2×C42—611no—
608C2×C42—611no—
609C2×C42—611no—
610C2×C42—611no—
611C2×C42—1221no—
612C2×C42—1221no—
613C2×C42—1221no—
614C2×C42—1221no—
615C2×C42—1221no—
616C2×C42—1221no—
617C2×C42—1221no—
618C2×C42—1221no—
619C2×C42—1221no—
620C2×C42—1221no—
621C2×C42C22×D6111yescharacteristic
622C4⋊C8—21no—
623C4⋊C8—612no—
624C4⋊C8—1222no—
625C4⋊C8—1222no—
626C4⋊C8—1221no—
627C4⋊C8C22×D6112yes—
628#97—21no—
629#97—1222no—
630#97—1221no—
631C4×C8—612no—
632C4×C8—1222no—
633C4×C8C22×D6112yes—
634C24—611no—
635C24—1221no—
636#41—22no—
637#41—22no—
638#41—1222no—
639#41—1222no—
640#41—1228no—
641#41—1222no—
642#41—1228no—
643#41—1222no—
644#41—1222no—
645#41—1222no—
646C2×Q8—614no—
647C2×Q8—611no—
648C2×Q8—1221no—
649C2×Q8—1222no—
650C2×Q8C2×C4×D6111yescharacteristic
651C2×D4—21no—
652C2×D4—614no—
653C2×D4—611no—
654C2×D4—1221no—
655C2×D4—1222no—
656C2×D4—1221no—
657C2×D4—1228no—
658C2×D4—1221no—
659C2×D4—1221no—
660C2×D4C2×C4×D6111yescharacteristic
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—611no—
665C22×C4—611no—
666C22×C4—611no—
667C22×C4—611no—
668C22×C4—611no—
669C22×C4—611no—
670C22×C4—611no—
671C22×C4—611no—
672C22×C4—611no—
673C22×C4—611no—
674C22×C4—611no—
675C22×C4—611no—
676C22×C4—611no—
677C22×C4—611no—
678C22×C4—611no—
679C22×C4—1221no—
680C22×C4—1224no—
681C22×C4—1222no—
682C22×C4—1222no—
683C22×C4—1222no—
684C22×C4—1222no—
685C22×C4—1221no—
686C22×C4—1221no—
687C22×C4—1221no—
688C22×C4—1228no—
689C22×C4—1221no—
690C22×C4—1221no—
691C22×C4—1221no—
692C22×C4—1221no—
693C22×C4—1221no—
694C22×C4—1221no—
695C22×C4—1221no—
696C22×C4—1221no—
697C22×C4—2444no—
698C22×C4—2442no—
699C22×C4—2442no—
700C22×C4C2×C4×D6111yescharacteristic
701C22×C4D4×D6111yescharacteristic
702C22×C4D4×D6111yescharacteristic
703M16—24no—
704M16—42no—
705M16—1228no—
706M16—1224no—
707M16—2444no—
708M16—2442no—
709C2×C8—22no—
710C2×C8—22no—
711C2×C8—1228no—
712C2×C8—1222no—
713C2×C8—1222no—
714C2×C8—2444no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—611no—
718C4⋊C4—611no—
719C4⋊C4—1221no—
720C4⋊C4—1221no—
721C4⋊C4—1221no—
722C4⋊C4—1221no—
723C4⋊C4—1221no—
724C4⋊C4—1221no—
725C4⋊C4—1221no—
726C4⋊C4—1221no—
727C4⋊C4C2×C4×D6111yescharacteristic
728C4⋊C4C2×C4×D6111yescharacteristic
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C22⋊C4—1221no—
733C22⋊C4—1221no—
734C22⋊C4—1221no—
735C22⋊C4—1221no—
736C22⋊C4—1221no—
737C22⋊C4—1221no—
738C22⋊C4—1221no—
739C22⋊C4—1221no—
740C22⋊C4—1221no—
741C42—21no—
742C42—21no—
743C42—21no—
744C42—611no—
745C42—611no—
746C42—611no—
747C42—611no—
748C42—611no—
749C42—611no—
750C42—611no—
751C42—611no—
752C42—611no—
753C42—611no—
754C42—611no—
755C42—611no—
756C42—1221no—
757C42—1221no—
758C42—1221no—
759C42—1221no—
760C42—1221no—
761C42—1221no—
762C42—1221no—
763C42—1221no—
764C42—1221no—
765C42C2×C4×D6111yescharacteristic
766C42D4×D6111yescharacteristic
767C42D4×D6111yescharacteristic
768C42C23×D6111yescharacteristic
769C23—21no—
770C23—611no—
771C23—611no—
772C23—1224no—
773C23—1222no—
774C23—1222no—
775C23—1222no—
776C23—1221no—
777C23—2442no—
778C23—2442no—
779C23C22⋊C4×D6111yescharacteristic
780Q8—21no—
781Q8—612no—
782Q8—1224no—
783Q8—1221no—
784Q8M16×D6112yescomplemented
785D4—24no—
786D4—21no—
787D4—612no—
788D4—1224no—
789D4—1224no—
790D4—1224no—
791D4—1224no—
792D4—1221no—
793D4M16×D6112yescomplemented
794C2×C4—24no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—611no—
807C2×C4—611no—
808C2×C4—611no—
809C2×C4—612no—
810C2×C4—612no—
811C2×C4—614no—
812C2×C4—612no—
813C2×C4—612no—
814C2×C4—611no—
815C2×C4—611no—
816C2×C4—611no—
817C2×C4—1222no—
818C2×C4—1222no—
819C2×C4—1222no—
820C2×C4—1222no—
821C2×C4—1222no—
822C2×C4—1222no—
823C2×C4—1224no—
824C2×C4—1224no—
825C2×C4—1224no—
826C2×C4—1222no—
827C2×C4—1222no—
828C2×C4—1222no—
829C2×C4—1224no—
830C2×C4—1221no—
831C2×C4—1221no—
832C2×C4—1221no—
833C2×C4—1222no—
834C2×C4—1221no—
835C2×C4—1221no—
836C2×C4—1221no—
837C2×C4—1221no—
838C2×C4—2442no—
839C2×C4—2442no—
840C2×C4—2442no—
841C2×C4—2442no—
842C2×C4—2442no—
843C2×C4—2442no—
844C2×C4—2442no—
845C2×C4—2441no—
846C2×C4—2441no—
847C2×C4C22⋊C4×D6111yescharacteristic
848C2×C4C22⋊C4×D6111yescharacteristic
849C2×C4C22⋊C4×D6111yescharacteristic
850C2×C4C22×C4×D6111yescharacteristic
851C2×C4C2×D4×D6111yescharacteristic
852C2×C4C2×D4×D6111yescharacteristic
853C8—24no—
854C8—42no—
855C8—1224no—
856C8—2442no—
857C22—21no—
858C22—21no—
859C22—22no—
860C22—21no—
861C22—41no—
862C22—41no—
863C22—612no—
864C22—612no—
865C22—612no—
866C22—1221no—
867C22—1222no—
868C22—1221no—
869C22—1221no—
870C22—2444no—
871C22—2448no—
872C22—2441no—
873C22—2441no—
874C22C2×C22⋊C4×D6111yescharacteristic
875C4—21no—
876C4—21no—
877C4—22no—
878C4—21no—
879C4—41no—
880C4—41no—
881C4—612no—
882C4—612no—
883C4—612no—
884C4—1221no—
885C4—1221no—
886C4—1222no—
887C4—1221no—
888C4—2441no—
889C4—2441no—
890C4#104×D6112yes—
891C4C2×M16×D6111yescharacteristic
892C4C2×M16×D6111yescharacteristic
893C4AGL(1,ℤ/8)×D6111yescharacteristic
894C4#137×D6111yescharacteristic
895C2—41no—
896C2—42no—
897C2—614no—
898C2—2441no—
899C2—2442no—
900C2#407×D6111yescharacteristic
901C2#417×D6111yescharacteristic
902C2C2×#104×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1489C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#41×D61C4
cosocleC42×C61C24
hypercenter#1489D61
hypocenterC61C2×#1489
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1489

Complements

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

NH ≅ G/Ntype
2. #423×D61C2semidirect
3. C4×M16×D61C2semidirect
4. #21444259C2semidirect
5. #21444258C2semidirect
6. #21444257C2semidirect
7. #21444256C2semidirect
8. #21444255C2semidirect
9. Q8⋊C8×D61C2semidirect
10. D4⋊C8×D61C2semidirect
11. C61×#1489C2semidirect
36. #16839786C22semidirect
39. #16839784C22semidirect
42. C4×#11758194C22semidirect
45. C4×#11758189C22semidirect
48. #16839494C22semidirect
49. Q8⋊#92418C22semidirect
50. #16839492C22semidirect
51. #16839491C22semidirect
52. D4⋊#92418C22semidirect
53. #16839489C22semidirect
55. C61×#423C22semidirect
56. C4×M16×C61C22semidirect
57. C61×Q8⋊C8C22semidirect
58. C61×D4⋊C8C22semidirect
207. Q8×D61M16semidirect
213. D4×D61M16semidirect
329. Q8×C61C2×M16semidirect
332. D4×C61C2×M16semidirect
371. D244C2×M16semidirect
400. Dic122C2×M16semidirect
452. #1489D61direct (N × H)
462. D61#1489direct (N × H)
492. #423C2×D61semidirect
499. C4×M16C2×D61semidirect
505. Q8⋊C8C2×D61semidirect
509. D4⋊C8C2×D61semidirect
510. C61C2×#1489semidirect
784. Q8M16×D61semidirect
793. D4M16×D61semidirect

Maximal subgroups

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

subgroupindex
C4×#41×D612
#423×D612
C4×M16×D612
#214442592
#214442582
#214442572
#214442562
#214442552
Q8⋊C8×D612
D4⋊C8×D612
C61×#14892
C2×#148961