Finite Group Databasebeta

← D61×#1504 #29647149

Subgroups — D61×#1504 #29647149

Order 15616.

1834 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#525×D61C211yesmaximal, characteristic
2#407×D61C211yesmaximal, characteristic, complemented
3C2×#95×D61C211yesmaximal, characteristic, complemented
4#21444324C211yesmaximal, characteristic, complemented
5#21444323C211yesmaximal, characteristic, complemented
6#21444322C212yesmaximal, complemented
7#21444321C211yesmaximal, characteristic, complemented
8#21444320C212yesmaximal, complemented
9#328×D61C212yesmaximal, complemented
10#327×D61C212yesmaximal, complemented
11C61×#1504C211yesmaximal, characteristic, complemented
12C2×#41×D61C411yescharacteristic, complemented
13C23×C4×D61—21no—
14C23×C4×D61C2211yescharacteristic
15C2×M16×D61—21no—
16#16840275C411yescharacteristic, complemented
17#16840275C2211yescharacteristic
18#16840274C411yescharacteristic, complemented
19#16840273C2211yescharacteristic
20#16840272C411yescharacteristic, complemented
21#16840272C2211yescharacteristic
22#16840271—21no—
23#16840271—21no—
24#16840270—21no—
25#16840269C411yescharacteristic, complemented
26#16840268—21no—
27#123×D61—21no—
28C22⋊Q8×D61C411yescharacteristic, complemented
29C22⋊Q8×D61C2211yescharacteristic
30#121×D61C411yescharacteristic, complemented
31#121×D61C2211yescharacteristic
32#120×D61—21no—
33C4×D4×D61—21no—
34C4×D4×D61—21no—
35#117×D61C411yescharacteristic, complemented
36#16839726C2211yescharacteristic, complemented
37#16839725—21no—
38#16839724—21no—
39#16839724C2212yescomplemented
40C22⋊C8×D61—21no—
41C22⋊C8×D61C2212yes—
42C2×#14519684—21no—
43C2×#14519684C2211yescharacteristic, complemented
44#95×D61—21no—
45#95×D61—21no—
46#95×D61C2212yes—
47#95×D61C2212yescomplemented
48#16839500C2212yescomplemented
49#16839499C2212yescomplemented
50#16839498C2212yescomplemented
51#16839497C2212yescomplemented
52#16839496C2212yescomplemented
53#16839495C2212yescomplemented
54C61×#525C2211yescharacteristic
55C61×#407C2211yescharacteristic, complemented
56C2×#95×C61C2211yescharacteristic, complemented
57C61×#328C2212yescomplemented
58C61×#327C2212yescomplemented
59C24×D61D411yescharacteristic
60C2×#11758226C2×C411yescharacteristic, complemented
61C2×#11758222—21no—
62C2×#11758222C2×C411yescharacteristic, complemented
63C2×#11758224—21no—
64C2×#11758224C2×C411yescharacteristic, complemented
65#41×D61—44no—
66C2×Q8×D61C2×C411yescharacteristic, complemented
67C2×D4×D61—21no—
68C2×D4×D61—21no—
69C2×D4×D61—21no—
70C2×D4×D61C2×C411yescharacteristic, complemented
71C23×Dic61—21no—
72C23×Dic61D411yescharacteristic
73C22×C4×D61—28no—
74C22×C4×D61—22no—
75C22×C4×D61—22no—
76C22×C4×D61—21no—
77C22×C4×D61—44no—
78C22×C4×D61—44no—
79C22×C4×D61—44no—
80C22×C4×D61C2×C411yescharacteristic
81C22×C4×D61C2×C411yescharacteristic
82C22×C4×D61C2×C411yescharacteristic
83C22×C4×D61C2×C411yescharacteristic
84C22×C4×D61D411yescharacteristic
85C22×C4×D61D411yescharacteristic
86C22×C4×D61D411yescharacteristic
87C22×C4×D61D411yescharacteristic
88C22×C4×D61D411yescharacteristic
89C22×C4×D61D411yescharacteristic
90C22×C4×D61C2311yescharacteristic
91C22×C4×D61C2311yescharacteristic
92C2×#11758194—21no—
93C2×#11758189—22no—
94M16×D61—44no—
95C2×C8×D61—22no—
96#14519762—21no—
97#14519762—21no—
98#14519761—21no—
99#14519760—21no—
100#14519759—21no—
101#14519759—21no—
102#14519758—21no—
103#14519757C2×C411yescharacteristic, complemented
104#14519757C2×C411yescharacteristic, complemented
105#14519756C2×C411yescharacteristic, complemented
106#14519756C2311yescharacteristic
107#14519755—21no—
108#14519755—21no—
109#14519754—21no—
110#14519754—21no—
111#14519753C2×C411yescharacteristic, complemented
112#14519753C2×C411yescharacteristic, complemented
113#14519752C2×C411yescharacteristic, complemented
114#14519752C2×C411yescharacteristic, complemented
115#14519751C2×C411yescharacteristic, complemented
116#14519751C2311yescharacteristic
117#14519750—21no—
118#14519750—21no—
119#14519749—21no—
120#14519749—21no—
121#14519748C2×C411yescharacteristic, complemented
122#14519748C2×C411yescharacteristic, complemented
123#14519747—21no—
124#14519747—21no—
125#14519747—21no—
126#14519746—21no—
127#14519745—21no—
128#14519745—21no—
129#14519745—21no—
130C4×D244—21no—
131C4×D244—21no—
132D4×Dic61—21no—
133D4×Dic61—21no—
134#14519739—21no—
135#14519739—21no—
136C4×C22⋊D61—21no—
137C4×C22⋊D61—21no—
138C4×C22⋊D61—21no—
139C4×C22⋊D61—21no—
140#14519737—21no—
141#14519737—21no—
142#14519737—21no—
143#14519737—21no—
144#14519736C2×C411yescharacteristic, complemented
145#14519735C2×C411yescharacteristic, complemented
146#14519735C2×C411yescharacteristic, complemented
147#14519734—21no—
148#14519733—21no—
149C4⋊C4×D61—21no—
150C4⋊C4×D61—21no—
151C4⋊C4×D61C2×C411yescharacteristic, complemented
152C4⋊C4×D61C2×C411yescharacteristic, complemented
153C22⋊C4×D61—21no—
154C22⋊C4×D61—21no—
155C22⋊C4×D61—21no—
156C22⋊C4×D61—21no—
157C22⋊C4×D61—21no—
158C42×D61—21no—
159C22⋊#92418—21no—
160C22⋊#92418C2312yes—
161#14519689—22no—
162#14519689—22no—
163#14519684—21no—
164#14519684—22no—
165#14519684—22no—
166#14519684C2312yes—
167C2×#41×C61C2×C411yescharacteristic, complemented
168C23×C4×C61—21no—
169C23×C4×C61C2311yescharacteristic
170C2×M16×C61—21no—
171#123×C61—21no—
172C22⋊Q8×C61C2×C411yescharacteristic, complemented
173C22⋊Q8×C61C2311yescharacteristic
174#121×C61C2×C411yescharacteristic, complemented
175#121×C61C2311yescharacteristic
176#120×C61—21no—
177C4×D4×C61—21no—
178C4×D4×C61—21no—
179#117×C61C2×C411yescharacteristic, complemented
180C22⋊C8×C61—21no—
181C22⋊C8×C61C2312yes—
182#95×C61—21no—
183#95×C61C2312yes—
184C24×C61C2×D411yescharacteristic
185C23×D61—24no—
186C23×D61—24no—
187C23×D61—22no—
188C23×D61—22no—
189C23×D61—21no—
190C23×D61C22⋊C411yescharacteristic
191C23×D61C22⋊C411yescharacteristic
192C23×D61C22⋊C411yescharacteristic
193C23×D61C22⋊C411yescharacteristic
194C23×D61C2×D411yescharacteristic
195C23×D61C2×D411yescharacteristic
196#41×C61—42no—
197C2×Q8×C61C22×C411yescharacteristic, complemented
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61C22×C411yescharacteristic, complemented
202C22×C4×C61—24no—
203C22×C4×C61—22no—
204C22×C4×C61—21no—
205C22×C4×C61—42no—
206C22×C4×C61—42no—
207C22×C4×C61—42no—
208C22×C4×C61C22×C411yescharacteristic
209C22×C4×C61C22×C411yescharacteristic
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D411yescharacteristic
212C22×C4×C61C2×D411yescharacteristic
213C22×C4×C61C2411yescharacteristic
214C2×C22⋊D61—21no—
215C2×C22⋊D61—21no—
216C2×C22⋊D61—21no—
217C2×C22⋊D61—21no—
218C2×C22⋊D61—21no—
219C2×C22⋊D61—21no—
220C2×C22⋊D61—21no—
221C22×Dic61—24no—
222C22×Dic61—22no—
223C22×Dic61—21no—
224C22×Dic61—42no—
225C22×Dic61—42no—
226C22×Dic61—42no—
227C22×Dic61C22⋊C411yescharacteristic
228C22×Dic61C22⋊C411yescharacteristic
229C22×Dic61C22⋊C411yescharacteristic
230C22×Dic61C22⋊C411yescharacteristic
231C22×Dic61C2×D411yescharacteristic
232C22×Dic61C2×D411yescharacteristic
233#11758226—42no—
234Q8×D61—42no—
235#11758224—42no—
236#11758224—44no—
237D4×D61—42no—
238D4×D61—44no—
239D4×D61—44no—
240D4×D61—42no—
241D4×D61—42no—
242#11758222—44no—
243#11758222—42no—
244C2×D244—21no—
245C2×D244—21no—
246C2×D244—21no—
247C2×D244C22×C411yescharacteristic, complemented
248C2×C4×D61—24no—
249C2×C4×D61—24no—
250C2×C4×D61—28no—
251C2×C4×D61—28no—
252C2×C4×D61—21no—
253C2×C4×D61—21no—
254C2×C4×D61—21no—
255C2×C4×D61—21no—
256C2×C4×D61—21no—
257C2×C4×D61—42no—
258C2×C4×D61—42no—
259C2×C4×D61—42no—
260C2×C4×D61—42no—
261C2×C4×D61—42no—
262C2×C4×D61—42no—
263C2×C4×D61—42no—
264C2×C4×D61—42no—
265C2×C4×D61—44no—
266C2×C4×D61—42no—
267C2×C4×D61—42no—
268C2×C4×D61—432no—
269C2×C4×D61—44no—
270C2×C4×D61—44no—
271C2×C4×D61—44no—
272C2×C4×D61—44no—
273C2×C4×D61C22⋊C411yescharacteristic
274C2×C4×D61C22⋊C411yescharacteristic
275C2×C4×D61C22⋊C411yescharacteristic
276C2×C4×D61C22⋊C411yescharacteristic
277C2×C4×D61C22⋊C411yescharacteristic
278C2×C4×D61C22⋊C411yescharacteristic
279C2×C4×D61C22⋊C411yescharacteristic
280C2×C4×D61C22⋊C411yescharacteristic
281C2×C4×D61C22×C411yescharacteristic
282C2×C4×D61C22×C411yescharacteristic
283C2×C4×D61C22×C411yescharacteristic
284C2×C4×D61C22×C411yescharacteristic
285C2×C4×D61C2×D411yescharacteristic
286C2×C4×D61C2×D411yescharacteristic
287C2×C4×D61C2×D411yescharacteristic
288C2×C4×D61C2×D411yescharacteristic
289C2×Dic122—21no—
290C2×Dic122C22×C411yescharacteristic, complemented
291M16×C61—42no—
292C2×C8×C61—22no—
293C4⋊C4×C61—21no—
294C4⋊C4×C61—21no—
295C4⋊C4×C61C22×C411yescharacteristic, complemented
296C4⋊C4×C61C22×C411yescharacteristic, complemented
297C22⋊C4×C61—21no—
298C22⋊C4×C61—21no—
299C22⋊C4×C61—21no—
300C22⋊C4×C61—21no—
301C22⋊C4×C61—21no—
302C42×C61—21no—
303C22⋊Dic61—21no—
304C22⋊Dic61—21no—
305C22⋊Dic61—21no—
306C22⋊Dic61—21no—
307C22⋊Dic61—21no—
308#11758198—21no—
309#11758198—21no—
310#11758198—21no—
311#11758198—21no—
312#11758198—21no—
313#11758198—21no—
314#11758198—21no—
315#11758198—21no—
316#11758198—21no—
317#11758198—21no—
318C4⋊Dic61—21no—
319C4⋊Dic61—21no—
320C4⋊Dic61C22×C411yescharacteristic, complemented
321C4⋊Dic61C22×C411yescharacteristic, complemented
322#11758196—21no—
323#11758196—21no—
324#11758196—21no—
325#11758196—21no—
326#11758196—21no—
327#11758196—21no—
328C4×Dic61—21no—
329C4×Dic61—21no—
330C4×Dic61—21no—
331#11758194—42no—
332C2×#92418—22no—
333#11758189—44no—
334C8×D61—44no—
335C23×C61—21no—
336C23×C61—21no—
337C23×C61—22no—
338C23×C61—22no—
339C23×C61—21no—
340C23×C61C2×C22⋊C411yescharacteristic
341C23×C61C2×C22⋊C411yescharacteristic
342C23×C61C22×D411yescharacteristic
343C22×D61—216no—
344C22×D61—216no—
345C22×D61—21no—
346C22×D61—21no—
347C22×D61—22no—
348C22×D61—22no—
349C22×D61—22no—
350C22×D61—22no—
351C22×D61—22no—
352C22×D61—22no—
353C22×D61—22no—
354C22×D61—22no—
355C22×D61—22no—
356C22×D61—22no—
357C22×D61—22no—
358C22×D61—22no—
359C22×D61—22no—
360C22×D61—22no—
361C22×D61—21no—
362C22×D61—42no—
363C22×D61—42no—
364C22×D61—42no—
365C22×D61#9914yes—
366C22×D61#10414yes—
367C22×D61C2×C22⋊C411yescharacteristic
368C22×D61C2×C22⋊C411yescharacteristic
369C22×D61C2×C22⋊C411yescharacteristic
370C22×D61C2×C22⋊C411yescharacteristic
371C22×D61AGL(1,ℤ/8)12yes—
372C22×D61#13712yes—
373Q8×C61—41no—
374D4×C61—41no—
375D4×C61—41no—
376D4×C61—41no—
377D4×C61—42no—
378D4×C61—42no—
379C2×C4×C61—22no—
380C2×C4×C61—22no—
381C2×C4×C61—24no—
382C2×C4×C61—21no—
383C2×C4×C61—21no—
384C2×C4×C61—21no—
385C2×C4×C61—41no—
386C2×C4×C61—41no—
387C2×C4×C61—41no—
388C2×C4×C61—41no—
389C2×C4×C61—42no—
390C2×C4×C61—48no—
391C2×C4×C61—42no—
392C2×C4×C61—42no—
393C2×C4×C61C2×C22⋊C411yescharacteristic
394C2×C4×C61C2×C22⋊C411yescharacteristic
395C2×C4×C61C23×C411yescharacteristic
396C2×C4×C61C22×D411yescharacteristic
397C22⋊D61—42no—
398C22⋊D61—41no—
399C22⋊D61—41no—
400C22⋊D61—42no—
401C22⋊D61—42no—
402C22⋊D61—42no—
403C22⋊D61—42no—
404C22⋊D61—42no—
405C2×Dic61—22no—
406C2×Dic61—22no—
407C2×Dic61—24no—
408C2×Dic61—21no—
409C2×Dic61—21no—
410C2×Dic61—21no—
411C2×Dic61—41no—
412C2×Dic61—41no—
413C2×Dic61—41no—
414C2×Dic61—41no—
415C2×Dic61—42no—
416C2×Dic61—48no—
417C2×Dic61—42no—
418C2×Dic61—42no—
419C2×Dic61C2×C22⋊C411yescharacteristic
420C2×Dic61C2×C22⋊C411yescharacteristic
421C2×Dic61C2×C22⋊C411yescharacteristic
422C2×Dic61C2×C22⋊C411yescharacteristic
423D244—41no—
424D244—42no—
425D244—42no—
426D244—42no—
427C4×D61—22no—
428C4×D61—22no—
429C4×D61—22no—
430C4×D61—22no—
431C4×D61—22no—
432C4×D61—22no—
433C4×D61—22no—
434C4×D61—22no—
435C4×D61—41no—
436C4×D61—41no—
437C4×D61—41no—
438C4×D61—41no—
439C4×D61—41no—
440C4×D61—41no—
441C4×D61—41no—
442C4×D61—41no—
443C4×D61—42no—
444C4×D61—42no—
445C4×D61—416no—
446C4×D61—416no—
447C4×D61—42no—
448C4×D61—42no—
449C4×D61—42no—
450Dic122—42no—
451Dic122—41no—
452C8×C61—42no—
453#92418—42no—
454C2×#1504—611nomaximal, Sylow
455C22×C61—24no—
456C22×C61—24no—
457C22×C61—21no—
458C22×C61—21no—
459C22×C61—21no—
460C22×C61—21no—
461C22×C61—21no—
462C22×C61—21no—
463C22×C61—41no—
464C22×C61—41no—
465C22×C61—41no—
466C22×C61C2×#9912yes—
467C22×C61C2×#10412yes—
468C22×C61C22×C22⋊C411yescharacteristic
469C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
470C22×C61C2×#13711yescharacteristic
471C2×D61—24no—
472C2×D61—28no—
473C2×D61—24no—
474C2×D61—28no—
475C2×D61—21no—
476C2×D61—21no—
477C2×D61—21no—
478C2×D61—21no—
479C2×D61—21no—
480C2×D61—21no—
481C2×D61—24no—
482C2×D61—28no—
483C2×D61—28no—
484C2×D61—24no—
485C2×D61—41no—
486C2×D61—41no—
487C2×D61—41no—
488C2×D61—84no—
489C2×D61C2×#9912yes—
490C2×D61C2×#9912yes—
491C2×D61#41712yes—
492C2×D61#41712yes—
493C2×D61C2×#10412yes—
494C2×D61C2×#10412yes—
495C4×C61—21no—
496C4×C61—21no—
497C4×C61—21no—
498C4×C61—21no—
499C4×C61—44no—
500C4×C61—41no—
501C4×C61—41no—
502C4×C61—41no—
503Dic61—21no—
504Dic61—21no—
505Dic61—21no—
506Dic61—21no—
507Dic61—44no—
508Dic61—41no—
509Dic61—41no—
510Dic61—41no—
511C2×#525—611no—
512C2×#407—611no—
513C22×#95—611no—
514#1504—611no—
515#1504—611no—
516#1504—612no—
517#1504—612no—
518#1504—611no—
519#1504D6111yescharacteristic, direct product factor
520C2×#328—612no—
521C2×#327—612no—
522C2×C61—21no—
523C2×C61—21no—
524C2×C61—22no—
525C2×C61—22no—
526C2×C61—81no—
527C2×C61C22×#9911yescharacteristic
528C2×C61C2×#41711yescharacteristic
529C2×C61C22×#10411yescharacteristic
530D61—22no—
531D61—22no—
532D61—22no—
533D61—81no—
534D61#150414yesdirect product factor
535C22×#41—611no—
536C24×C4—611no—
537C24×C4—1221no—
538C22×M16—1221no—
539#525—611no—
540#525—611no—
541#525—611no—
542#525—611no—
543#525—611no—
544#525—611no—
545#525—611no—
546#525—1221no—
547#525—1221no—
548#525—1221no—
549#525—1221no—
550#525C2×D6111yescharacteristic
551C2×#123—1221no—
552C2×C22⋊Q8—611no—
553C2×C22⋊Q8—611no—
554C2×#121—611no—
555C2×#121—611no—
556C2×#120—1221no—
557C2×C4×D4—1221no—
558C2×C4×D4—1221no—
559C2×#117—611no—
560#407—611no—
561#407—612no—
562#407—1221no—
563#407—1221no—
564#407C2×D6111yescharacteristic, complemented
565C2×C22⋊C8—612no—
566C2×C22⋊C8—1221no—
567C2×#95—611no—
568C2×#95—612no—
569C2×#95—612no—
570C2×#95—1221no—
571C2×#95—1221no—
572C2×#95—1221no—
573C2×#95C2×D6111yescharacteristic, complemented
574#328—612no—
575#328—612no—
576#328—612no—
577#328C2×D6112yescomplemented
578#327—612no—
579#327—612no—
580#327—612no—
581#327C2×D6112yescomplemented
582C61C2×#150411yescharacteristic, complemented, Sylow
583C25—611no—
584C2×#41—611no—
585C2×#41—611no—
586C2×#41—611no—
587C2×#41—1221no—
588C2×#41—1221no—
589C2×#41—2444no—
590C2×#41C4×D6111yescharacteristic, complemented
591C22×Q8—611no—
592C22×D4—611no—
593C22×D4—1221no—
594C22×D4—1221no—
595C22×D4—1221no—
596C23×C4—21no—
597C23×C4—611no—
598C23×C4—611no—
599C23×C4—611no—
600C23×C4—611no—
601C23×C4—611no—
602C23×C4—611no—
603C23×C4—611no—
604C23×C4—611no—
605C23×C4—611no—
606C23×C4—611no—
607C23×C4—611no—
608C23×C4—611no—
609C23×C4—611no—
610C23×C4—1221no—
611C23×C4—1222no—
612C23×C4—1222no—
613C23×C4—1228no—
614C23×C4—1221no—
615C23×C4—2444no—
616C23×C4—2444no—
617C23×C4—2444no—
618C23×C4C22×D6111yescharacteristic
619C2×M16—21no—
620C2×M16—1222no—
621C2×M16—1221no—
622C2×M16—2444no—
623C22×C8—1222no—
624#123—21no—
625#123—1221no—
626#123—1221no—
627#123—1221no—
628#123—1221no—
629#123—1221no—
630#123—1221no—
631#123—1221no—
632C22⋊Q8—611no—
633C22⋊Q8—611no—
634C22⋊Q8—611no—
635C22⋊Q8—611no—
636C22⋊Q8—611no—
637C22⋊Q8—611no—
638C22⋊Q8—1221no—
639C22⋊Q8—1221no—
640C22⋊Q8—1221no—
641C22⋊Q8—1221no—
642C22⋊Q8C4×D6111yescharacteristic, complemented
643C22⋊Q8C22×D6111yescharacteristic
644#121—611no—
645#121—611no—
646#121—611no—
647#121—611no—
648#121—611no—
649#121—611no—
650#121—1221no—
651#121—1221no—
652#121—1221no—
653#121—1221no—
654#121C4×D6111yescharacteristic, complemented
655#121C22×D6111yescharacteristic
656#120—21no—
657#120—1221no—
658#120—1221no—
659#120—1221no—
660#120—1221no—
661#120—1221no—
662#120—1221no—
663#120—1221no—
664C4×D4—21no—
665C4×D4—21no—
666C4×D4—1221no—
667C4×D4—1221no—
668C4×D4—1221no—
669C4×D4—1221no—
670C4×D4—1221no—
671C4×D4—1221no—
672C4×D4—1221no—
673C4×D4—1221no—
674C4×D4—1221no—
675C4×D4—1221no—
676C4×D4—1221no—
677C4×D4—1221no—
678C4×D4—1221no—
679C4×D4—1221no—
680#117—611no—
681#117—611no—
682#117—611no—
683#117—1221no—
684#117—1221no—
685#117C4×D6111yescharacteristic, complemented
686C2×C4⋊C4—611no—
687C2×C4⋊C4—611no—
688C2×C4⋊C4—1221no—
689C2×C4⋊C4—1221no—
690C2×C22⋊C4—1221no—
691C2×C22⋊C4—1221no—
692C2×C22⋊C4—1221no—
693C2×C22⋊C4—1221no—
694C2×C22⋊C4—1221no—
695C2×C42—1221no—
696C22⋊C8—21no—
697C22⋊C8—612no—
698C22⋊C8—1222no—
699C22⋊C8—1222no—
700C22⋊C8—1221no—
701C22⋊C8C22×D6112yes—
702#95—21no—
703#95—612no—
704#95—1222no—
705#95—1222no—
706#95—1221no—
707#95C22×D6112yes—
708C24—611no—
709C24—611no—
710C24—611no—
711C24—611no—
712C24—611no—
713C24—611no—
714C24—1224no—
715C24—1224no—
716C24—1222no—
717C24—1222no—
718C24—1221no—
719C24D4×D6111yescharacteristic
720#41—42no—
721#41—2442no—
722#41—2444no—
723#41—2444no—
724#41—2442no—
725#41—2442no—
726C2×Q8—611no—
727C2×Q8—1221no—
728C2×Q8—2442no—
729C2×Q8C2×C4×D6111yescharacteristic, complemented
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—611no—
734C2×D4—1221no—
735C2×D4—1221no—
736C2×D4—1221no—
737C2×D4—1221no—
738C2×D4—1221no—
739C2×D4—1221no—
740C2×D4—1221no—
741C2×D4—1221no—
742C2×D4—1221no—
743C2×D4—1221no—
744C2×D4—2442no—
745C2×D4—2444no—
746C2×D4—2444no—
747C2×D4—2442no—
748C2×D4—2442no—
749C2×D4C2×C4×D6111yescharacteristic, complemented
750C22×C4—24no—
751C22×C4—22no—
752C22×C4—21no—
753C22×C4—42no—
754C22×C4—42no—
755C22×C4—42no—
756C22×C4—611no—
757C22×C4—611no—
758C22×C4—611no—
759C22×C4—611no—
760C22×C4—611no—
761C22×C4—611no—
762C22×C4—611no—
763C22×C4—611no—
764C22×C4—611no—
765C22×C4—611no—
766C22×C4—611no—
767C22×C4—611no—
768C22×C4—611no—
769C22×C4—611no—
770C22×C4—611no—
771C22×C4—611no—
772C22×C4—611no—
773C22×C4—611no—
774C22×C4—611no—
775C22×C4—611no—
776C22×C4—611no—
777C22×C4—611no—
778C22×C4—1221no—
779C22×C4—1224no—
780C22×C4—1224no—
781C22×C4—1221no—
782C22×C4—1221no—
783C22×C4—1221no—
784C22×C4—1228no—
785C22×C4—1228no—
786C22×C4—1221no—
787C22×C4—1224no—
788C22×C4—1222no—
789C22×C4—1221no—
790C22×C4—2442no—
791C22×C4—2442no—
792C22×C4—2442no—
793C22×C4—2442no—
794C22×C4—2442no—
795C22×C4—2442no—
796C22×C4—2442no—
797C22×C4—2442no—
798C22×C4—2442no—
799C22×C4—2442no—
800C22×C4—2444no—
801C22×C4—2444no—
802C22×C4—2444no—
803C22×C4—2444no—
804C22×C4—24432no—
805C22×C4—2444no—
806C22×C4—2442no—
807C22×C4—2442no—
808C22×C4—2442no—
809C22×C4C2×C4×D6111yescharacteristic
810C22×C4C2×C4×D6111yescharacteristic
811C22×C4D4×D6111yescharacteristic
812C22×C4D4×D6111yescharacteristic
813C22×C4D4×D6111yescharacteristic
814C22×C4C23×D6111yescharacteristic
815M16—42no—
816M16—2444no—
817M16—2442no—
818C2×C8—22no—
819C2×C8—1222no—
820C2×C8—2444no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—611no—
824C4⋊C4—611no—
825C4⋊C4—1221no—
826C4⋊C4—1221no—
827C4⋊C4—1221no—
828C4⋊C4—1221no—
829C4⋊C4—1221no—
830C4⋊C4—1221no—
831C4⋊C4—1221no—
832C4⋊C4—1221no—
833C4⋊C4C2×C4×D6111yescharacteristic, complemented
834C4⋊C4C2×C4×D6111yescharacteristic, complemented
835C22⋊C4—21no—
836C22⋊C4—21no—
837C22⋊C4—21no—
838C22⋊C4—21no—
839C22⋊C4—21no—
840C22⋊C4—1221no—
841C22⋊C4—1221no—
842C22⋊C4—1221no—
843C22⋊C4—1221no—
844C22⋊C4—1221no—
845C22⋊C4—1221no—
846C22⋊C4—1221no—
847C22⋊C4—1221no—
848C22⋊C4—1221no—
849C22⋊C4—1221no—
850C22⋊C4—1221no—
851C22⋊C4—1221no—
852C22⋊C4—1221no—
853C22⋊C4—1221no—
854C22⋊C4—1221no—
855C42—21no—
856C42—1221no—
857C42—1221no—
858C42—1221no—
859C23—22no—
860C23—22no—
861C23—21no—
862C23—21no—
863C23—21no—
864C23—611no—
865C23—611no—
866C23—611no—
867C23—611no—
868C23—614no—
869C23—614no—
870C23—612no—
871C23—612no—
872C23—1222no—
873C23—1222no—
874C23—1222no—
875C23—1222no—
876C23—1222no—
877C23—1222no—
878C23—1222no—
879C23—1222no—
880C23—1222no—
881C23—1222no—
882C23—1222no—
883C23—1222no—
884C23—12216no—
885C23—12216no—
886C23—1222no—
887C23—1222no—
888C23—1221no—
889C23—1221no—
890C23—1221no—
891C23—2442no—
892C23—2442no—
893C23—2442no—
894C23C22⋊C4×D6111yescharacteristic
895C23C22⋊C4×D6111yescharacteristic
896C23C2×D4×D6111yescharacteristic
897Q8—41no—
898Q8—2441no—
899Q8—2442no—
900D4—41no—
901D4—42no—
902D4—42no—
903D4—41no—
904D4—41no—
905D4—2441no—
906D4—2442no—
907D4—2442no—
908D4—2442no—
909D4—2442no—
910D4—2442no—
911D4—2442no—
912D4—2442no—
913D4—2442no—
914D4—2442no—
915D4—2441no—
916D4—2441no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—24no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—42no—
928C2×C4—48no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—611no—
932C2×C4—611no—
933C2×C4—611no—
934C2×C4—611no—
935C2×C4—1222no—
936C2×C4—1222no—
937C2×C4—1222no—
938C2×C4—1222no—
939C2×C4—1222no—
940C2×C4—1222no—
941C2×C4—1222no—
942C2×C4—1222no—
943C2×C4—1222no—
944C2×C4—1222no—
945C2×C4—1224no—
946C2×C4—1221no—
947C2×C4—1221no—
948C2×C4—1221no—
949C2×C4—2441no—
950C2×C4—2441no—
951C2×C4—2441no—
952C2×C4—2441no—
953C2×C4—2441no—
954C2×C4—2441no—
955C2×C4—2441no—
956C2×C4—2441no—
957C2×C4—2442no—
958C2×C4—2442no—
959C2×C4—2442no—
960C2×C4—2442no—
961C2×C4—2442no—
962C2×C4—24416no—
963C2×C4—24416no—
964C2×C4—2441no—
965C2×C4—2441no—
966C2×C4—2441no—
967C2×C4—2441no—
968C2×C4—2442no—
969C2×C4—2448no—
970C2×C4—2442no—
971C2×C4—2442no—
972C2×C4C22⋊C4×D6111yescharacteristic
973C2×C4C22⋊C4×D6111yescharacteristic
974C2×C4C22×C4×D6111yescharacteristic
975C2×C4C2×D4×D6111yescharacteristic
976C8—42no—
977C8—2442no—
978C22—24no—
979C22—24no—
980C22—21no—
981C22—21no—
982C22—21no—
983C22—21no—
984C22—21no—
985C22—21no—
986C22—41no—
987C22—41no—
988C22—41no—
989C22—612no—
990C22—612no—
991C22—612no—
992C22—612no—
993C22—612no—
994C22—612no—
995C22—1224no—
996C22—1228no—
997C22—1228no—
998C22—1224no—
999C22—1224no—
1000C22—1228no—
1001C22—1228no—
1002C22—1224no—
1003C22—1221no—
1004C22—1221no—
1005C22—1221no—
1006C22—1221no—
1007C22—1221no—
1008C22—1221no—
1009C22—4884no—
1010C22—2441no—
1011C22—2441no—
1012C22—2441no—
1013C22#99×D6112yes—
1014C22#104×D6112yes—
1015C22C2×C22⋊C4×D6111yescharacteristic
1016C22AGL(1,ℤ/8)×D6111yescharacteristic
1017C22#137×D6111yescharacteristic
1018C4—21no—
1019C4—21no—
1020C4—21no—
1021C4—21no—
1022C4—44no—
1023C4—41no—
1024C4—41no—
1025C4—41no—
1026C4—1221no—
1027C4—1221no—
1028C4—1221no—
1029C4—1221no—
1030C4—2444no—
1031C4—2441no—
1032C4—2441no—
1033C4—2441no—
1034C2—21no—
1035C2—22no—
1036C2—22no—
1037C2—21no—
1038C2—81no—
1039C2—614no—
1040C2—1222no—
1041C2—1222no—
1042C2—1222no—
1043C2—4881no—
1044C2C2×#99×D6111yescharacteristic
1045C2#417×D6111yescharacteristic
1046C2C2×#104×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1504C2
socleC22×C61C22×C22⋊C4
prime radical#525×D61C2
cosocleC22×C4×C61C24
hypercenter#1504D61
hypocenterC61C2×#1504
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1504

Complements

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

NH ≅ G/Ntype
2. #407×D61C2semidirect
3. C2×#95×D61C2semidirect
4. #21444324C2semidirect
5. #21444323C2semidirect
6. #21444322C2semidirect
7. #21444321C2semidirect
8. #21444320C2semidirect
9. #328×D61C2semidirect
10. #327×D61C2semidirect
11. C61×#1504C2semidirect
12. C2×#41×D61C4semidirect
16. #16840275C4semidirect
18. #16840274C4semidirect
20. #16840272C4semidirect
25. #16840269C4semidirect
28. C22⋊Q8×D61C4semidirect
30. #121×D61C4semidirect
35. #117×D61C4semidirect
36. #16839726C22semidirect
39. #16839724C22semidirect
43. C2×#14519684C22semidirect
47. #95×D61C22semidirect
48. #16839500C22semidirect
49. #16839499C22semidirect
50. #16839498C22semidirect
51. #16839497C22semidirect
52. #16839496C22semidirect
53. #16839495C22semidirect
55. C61×#407C22semidirect
56. C2×#95×C61C22semidirect
57. C61×#328C22semidirect
58. C61×#327C22semidirect
60. C2×#11758226C2×C4semidirect
62. C2×#11758222C2×C4semidirect
64. C2×#11758224C2×C4semidirect
66. C2×Q8×D61C2×C4semidirect
70. C2×D4×D61C2×C4semidirect
103. #14519757C2×C4semidirect
104. #14519757C2×C4semidirect
105. #14519756C2×C4semidirect
111. #14519753C2×C4semidirect
112. #14519753C2×C4semidirect
113. #14519752C2×C4semidirect
114. #14519752C2×C4semidirect
115. #14519751C2×C4semidirect
121. #14519748C2×C4semidirect
122. #14519748C2×C4semidirect
144. #14519736C2×C4semidirect
145. #14519735C2×C4semidirect
146. #14519735C2×C4semidirect
151. C4⋊C4×D61C2×C4semidirect
152. C4⋊C4×D61C2×C4semidirect
167. C2×#41×C61C2×C4semidirect
172. C22⋊Q8×C61C2×C4semidirect
174. #121×C61C2×C4semidirect
179. #117×C61C2×C4semidirect
197. C2×Q8×C61C22×C4semidirect
201. C2×D4×C61C22×C4semidirect
247. C2×D244C22×C4semidirect
290. C2×Dic122C22×C4semidirect
295. C4⋊C4×C61C22×C4semidirect
296. C4⋊C4×C61C22×C4semidirect
320. C4⋊Dic61C22×C4semidirect
321. C4⋊Dic61C22×C4semidirect
519. #1504D61direct (N × H)
534. D61#1504direct (N × H)
564. #407C2×D61semidirect
573. C2×#95C2×D61semidirect
577. #328C2×D61semidirect
581. #327C2×D61semidirect
582. C61C2×#1504semidirect
590. C2×#41C4×D61semidirect
642. C22⋊Q8C4×D61semidirect
654. #121C4×D61semidirect
685. #117C4×D61semidirect
729. C2×Q8C2×C4×D61semidirect
749. C2×D4C2×C4×D61semidirect
833. C4⋊C4C2×C4×D61semidirect
834. C4⋊C4C2×C4×D61semidirect

Maximal subgroups

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

subgroupindex
#525×D612
#407×D612
C2×#95×D612
#214443242
#214443232
#214443222
#214443212
#214443202
#328×D612
#327×D612
C61×#15042
C2×#150461