Finite Group Databasebeta

← D61×#1513 #29647264

Subgroups — D61×#1513 #29647264

Order 15616.

1510 conjugacy classes of subgroups.

The subgroup lattice has 1032 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
3#380×D61C211yesmaximal, characteristic, complemented
4#21444363C211yesmaximal, characteristic, complemented
5#21444362C211yesmaximal, characteristic, complemented
6#21444361C212yesmaximal, complemented
7#21444360C211yesmaximal, characteristic, complemented
8#21444359C212yesmaximal, complemented
9#328×D61C212yesmaximal, complemented
10#327×D61C212yesmaximal, complemented
11C61×#1513C211yesmaximal, characteristic, complemented
12C2×#41×D61C411yescharacteristic, complemented
13C23×C4×D61C2211yescharacteristic
14C2×M16×D61—21no—
15#16840275C411yescharacteristic, complemented
16#16840275C2211yescharacteristic
17#16840274C411yescharacteristic, complemented
18#16840273C2211yescharacteristic
19#16840272C411yescharacteristic, complemented
20#16840272C2211yescharacteristic
21#16840271—21no—
22#16840271—21no—
23#16840270—21no—
24#16840269C411yescharacteristic, complemented
25#16840268—21no—
26#123×D61—21no—
27C22⋊Q8×D61C411yescharacteristic, complemented
28C22⋊Q8×D61C2211yescharacteristic
29#121×D61C411yescharacteristic, complemented
30#121×D61C2211yescharacteristic
31#120×D61—21no—
32C4×D4×D61—21no—
33C4×D4×D61—21no—
34#117×D61C411yescharacteristic, complemented
35C2×C4⋊C4×D61—21no—
36C2×C22⋊C4×D61—21no—
37#16839726C2211yescharacteristic, complemented
38#16839725—21no—
39#16839724—21no—
40#16839724C2212yescomplemented
41C22⋊C8×D61—21no—
42C22⋊C8×D61C2212yes—
43#16839622C2211yescharacteristic, complemented
44#16839621C2212yescomplemented
45#16839620—21no—
46#16839619—21no—
47#95×D61C2212yes—
48#16839500C2212yescomplemented
49#16839499C2212yescomplemented
50#16839498C2212yescomplemented
51#16839497C2212yescomplemented
52#16839496C2212yescomplemented
53#16839495C2212yescomplemented
54C61×#525C2211yescharacteristic
55C61×#407C2211yescharacteristic, complemented
56C61×#380C2211yescharacteristic, 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
67C2×D4×D61—21no—
68C2×D4×D61—21no—
69C2×D4×D61—21no—
70C2×D4×D61C2×C411yescharacteristic
71C23×Dic61D411yescharacteristic
72C22×C4×D61—21no—
73C22×C4×D61—22no—
74C22×C4×D61—44no—
75C22×C4×D61C2×C411yescharacteristic
76C22×C4×D61C2×C411yescharacteristic
77C22×C4×D61C2×C411yescharacteristic
78C22×C4×D61C2×C411yescharacteristic
79C22×C4×D61D411yescharacteristic
80C22×C4×D61D411yescharacteristic
81C22×C4×D61D411yescharacteristic
82C22×C4×D61D411yescharacteristic
83C22×C4×D61D411yescharacteristic
84C22×C4×D61D411yescharacteristic
85C22×C4×D61C2311yescharacteristic
86C22×C4×D61C2311yescharacteristic
87C2×#11758194—21no—
88C2×#11758189—22no—
89M16×D61—44no—
90C2×C8×D61—22no—
91#14519762—21no—
92#14519762—21no—
93#14519761—21no—
94#14519760—21no—
95#14519759—21no—
96#14519759—21no—
97#14519758—21no—
98#14519757C2×C411yescharacteristic
99#14519757C2×C411yescharacteristic, complemented
100#14519756C2×C411yescharacteristic, complemented
101#14519756C2311yescharacteristic
102#14519755—21no—
103#14519755—21no—
104#14519754—21no—
105#14519754—21no—
106#14519753C2×C411yescharacteristic
107#14519753C2×C411yescharacteristic, complemented
108#14519752C2×C411yescharacteristic
109#14519752C2×C411yescharacteristic, complemented
110#14519751C2×C411yescharacteristic, complemented
111#14519751C2311yescharacteristic
112#14519750—21no—
113#14519750—21no—
114#14519749—21no—
115#14519749—21no—
116#14519748C2×C411yescharacteristic
117#14519748C2×C411yescharacteristic, complemented
118#14519747—21no—
119#14519747—21no—
120#14519747—21no—
121#14519746—21no—
122#14519745—21no—
123#14519745—21no—
124#14519745—21no—
125C4×D244—21no—
126C4×D244—21no—
127D4×Dic61—21no—
128D4×Dic61—21no—
129#14519739—21no—
130#14519739—21no—
131C4×C22⋊D61—21no—
132C4×C22⋊D61—21no—
133C4×C22⋊D61—21no—
134C4×C22⋊D61—21no—
135#14519737—21no—
136#14519737—21no—
137#14519737—21no—
138#14519737—21no—
139#14519736C2×C411yescharacteristic, complemented
140#14519735C2×C411yescharacteristic, complemented
141#14519735C2×C411yescharacteristic, complemented
142#14519734—21no—
143#14519733—21no—
144C2×C4⋊Dic61—21no—
145C2×#11758196—22no—
146C4⋊C4×D61—21no—
147C4⋊C4×D61—21no—
148C4⋊C4×D61—44no—
149C4⋊C4×D61C2×C411yescharacteristic
150C4⋊C4×D61C2×C411yescharacteristic
151C2×C22⋊Dic61—21no—
152C2×#11758198—22no—
153C22⋊C4×D61—21no—
154C22⋊C4×D61—21no—
155C22⋊C4×D61—21no—
156C22⋊C4×D61—21no—
157C22⋊C4×D61—21no—
158C22⋊C4×D61—44no—
159C42×D61—21no—
160C22⋊#92418—21no—
161C22⋊#92418C2312yes—
162#14519689—22no—
163#14519689—22no—
164#14519684—22no—
165#14519684C2312yes—
166C2×#41×C61C2×C411yescharacteristic, complemented
167C23×C4×C61C2311yescharacteristic
168C2×M16×C61—21no—
169#123×C61—21no—
170C22⋊Q8×C61C2×C411yescharacteristic, complemented
171C22⋊Q8×C61C2311yescharacteristic
172#121×C61C2×C411yescharacteristic, complemented
173#121×C61C2311yescharacteristic
174#120×C61—21no—
175C4×D4×C61—21no—
176C4×D4×C61—21no—
177#117×C61C2×C411yescharacteristic, complemented
178C2×C4⋊C4×C61—21no—
179C2×C22⋊C4×C61—21no—
180C22⋊C8×C61—21no—
181C22⋊C8×C61C2312yes—
182#95×C61C2312yes—
183C24×C61C2×D411yescharacteristic
184C23×D61—22no—
185C23×D61—22no—
186C23×D61—21no—
187C23×D61—42no—
188C23×D61—42no—
189C23×D61C22⋊C411yescharacteristic
190C23×D61C22⋊C411yescharacteristic
191C23×D61C22⋊C411yescharacteristic
192C23×D61C22⋊C411yescharacteristic
193C23×D61C2×D411yescharacteristic
194C23×D61C2×D411yescharacteristic
195#41×C61—42no—
196C2×Q8×C61C22×C411yescharacteristic
197C2×D4×C61—21no—
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61C22×C411yescharacteristic
201C22×C4×C61—21no—
202C22×C4×C61—22no—
203C22×C4×C61—42no—
204C22×C4×C61C22×C411yescharacteristic
205C22×C4×C61C22×C411yescharacteristic
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2411yescharacteristic
210C2×C22⋊D61—21no—
211C2×C22⋊D61—21no—
212C2×C22⋊D61—21no—
213C2×C22⋊D61—21no—
214C2×C22⋊D61—21no—
215C2×C22⋊D61—21no—
216C2×C22⋊D61—21no—
217C22×Dic61—21no—
218C22×Dic61—22no—
219C22×Dic61—42no—
220C22×Dic61C22⋊C411yescharacteristic
221C22×Dic61C22⋊C411yescharacteristic
222C22×Dic61C22⋊C411yescharacteristic
223C22×Dic61C22⋊C411yescharacteristic
224C22×Dic61C2×D411yescharacteristic
225C22×Dic61C2×D411yescharacteristic
226#11758226—42no—
227Q8×D61—42no—
228#11758224—42no—
229#11758224—44no—
230D4×D61—42no—
231D4×D61—44no—
232D4×D61—44no—
233D4×D61—42no—
234D4×D61—42no—
235#11758222—44no—
236#11758222—42no—
237C2×D244—21no—
238C2×D244—21no—
239C2×D244—21no—
240C2×D244C22×C411yescharacteristic
241C2×C4×D61—24no—
242C2×C4×D61—24no—
243C2×C4×D61—24no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—42no—
250C2×C4×D61—42no—
251C2×C4×D61—42no—
252C2×C4×D61—42no—
253C2×C4×D61—42no—
254C2×C4×D61—42no—
255C2×C4×D61—42no—
256C2×C4×D61—42no—
257C2×C4×D61—42no—
258C2×C4×D61—44no—
259C2×C4×D61—44no—
260C2×C4×D61—44no—
261C2×C4×D61—44no—
262C2×C4×D61C22⋊C411yescharacteristic
263C2×C4×D61C22⋊C411yescharacteristic
264C2×C4×D61C22⋊C411yescharacteristic
265C2×C4×D61C22⋊C411yescharacteristic
266C2×C4×D61C22⋊C411yescharacteristic
267C2×C4×D61C22⋊C411yescharacteristic
268C2×C4×D61C22⋊C411yescharacteristic
269C2×C4×D61C22⋊C411yescharacteristic
270C2×C4×D61C22×C411yescharacteristic
271C2×C4×D61C22×C411yescharacteristic
272C2×C4×D61C22×C411yescharacteristic
273C2×C4×D61C22×C411yescharacteristic
274C2×C4×D61C2×D411yescharacteristic
275C2×C4×D61C2×D411yescharacteristic
276C2×C4×D61C2×D411yescharacteristic
277C2×C4×D61C2×D411yescharacteristic
278C2×Dic122—21no—
279C2×Dic122C22×C411yescharacteristic
280M16×C61—42no—
281C2×C8×C61—22no—
282C4⋊C4×C61—21no—
283C4⋊C4×C61—21no—
284C4⋊C4×C61—42no—
285C4⋊C4×C61C22×C411yescharacteristic
286C4⋊C4×C61C22×C411yescharacteristic
287C22⋊C4×C61—21no—
288C22⋊C4×C61—21no—
289C22⋊C4×C61—21no—
290C22⋊C4×C61—21no—
291C22⋊C4×C61—21no—
292C22⋊C4×C61—42no—
293C42×C61—21no—
294C22⋊Dic61—21no—
295C22⋊Dic61—21no—
296C22⋊Dic61—21no—
297C22⋊Dic61—21no—
298C22⋊Dic61—21no—
299C22⋊Dic61—42no—
300#11758198—21no—
301#11758198—21no—
302#11758198—21no—
303#11758198—21no—
304#11758198—21no—
305#11758198—21no—
306#11758198—21no—
307#11758198—21no—
308#11758198—21no—
309#11758198—21no—
310#11758198—44no—
311C4⋊Dic61—21no—
312C4⋊Dic61—21no—
313C4⋊Dic61—42no—
314C4⋊Dic61C22×C411yescharacteristic
315C4⋊Dic61C22×C411yescharacteristic
316#11758196—21no—
317#11758196—21no—
318#11758196—21no—
319#11758196—21no—
320#11758196—21no—
321#11758196—21no—
322#11758196—44no—
323C4×Dic61—21no—
324C4×Dic61—21no—
325C4×Dic61—21no—
326#11758194—42no—
327C2×#92418—22no—
328#11758189—44no—
329C8×D61—44no—
330C23×C61—21no—
331C23×C61—21no—
332C23×C61—21no—
333C23×C61—41no—
334C23×C61—41no—
335C23×C61C2×C22⋊C411yescharacteristic
336C23×C61C2×C22⋊C411yescharacteristic
337C23×C61C22×D411yescharacteristic
338C22×D61—22no—
339C22×D61—22no—
340C22×D61—21no—
341C22×D61—21no—
342C22×D61—22no—
343C22×D61—22no—
344C22×D61—22no—
345C22×D61—22no—
346C22×D61—22no—
347C22×D61—22no—
348C22×D61—22no—
349C22×D61—22no—
350C22×D61—21no—
351C22×D61—41no—
352C22×D61—41no—
353C22×D61—41no—
354C22×D61—41no—
355C22×D61—41no—
356C22×D61—41no—
357C22×D61—48no—
358C22×D61—48no—
359C22×D61—42no—
360C22×D61—42no—
361C22×D61—42no—
362C22×D61C2×C22⋊C411yescharacteristic
363C22×D61C2×C22⋊C411yescharacteristic
364C22×D61C2×C22⋊C411yescharacteristic
365C22×D61C2×C22⋊C411yescharacteristic
366C22×D61AGL(1,ℤ/8)12yes—
367C22×D61#13712yes—
368Q8×C61—41no—
369D4×C61—41no—
370D4×C61—42no—
371D4×C61—42no—
372D4×C61—41no—
373D4×C61—41no—
374C2×C4×C61—22no—
375C2×C4×C61—22no—
376C2×C4×C61—22no—
377C2×C4×C61—21no—
378C2×C4×C61—21no—
379C2×C4×C61—21no—
380C2×C4×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61—42no—
384C2×C4×C61—42no—
385C2×C4×C61—42no—
386C2×C4×C61—42no—
387C2×C4×C61C2×C22⋊C411yescharacteristic
388C2×C4×C61C2×C22⋊C411yescharacteristic
389C2×C4×C61C23×C411yescharacteristic
390C2×C4×C61C22×D411yescharacteristic
391C22⋊D61—42no—
392C22⋊D61—42no—
393C22⋊D61—42no—
394C22⋊D61—42no—
395C22⋊D61—42no—
396C22⋊D61—41no—
397C22⋊D61—41no—
398C22⋊D61—42no—
399C2×Dic61—22no—
400C2×Dic61—22no—
401C2×Dic61—22no—
402C2×Dic61—21no—
403C2×Dic61—21no—
404C2×Dic61—21no—
405C2×Dic61—41no—
406C2×Dic61—41no—
407C2×Dic61—41no—
408C2×Dic61—42no—
409C2×Dic61—42no—
410C2×Dic61—42no—
411C2×Dic61—42no—
412C2×Dic61C2×C22⋊C411yescharacteristic
413C2×Dic61C2×C22⋊C411yescharacteristic
414C2×Dic61C2×C22⋊C411yescharacteristic
415C2×Dic61C2×C22⋊C411yescharacteristic
416D244—41no—
417D244—42no—
418D244—42no—
419D244—42no—
420C4×D61—22no—
421C4×D61—22no—
422C4×D61—22no—
423C4×D61—22no—
424C4×D61—22no—
425C4×D61—22no—
426C4×D61—22no—
427C4×D61—22no—
428C4×D61—22no—
429C4×D61—41no—
430C4×D61—41no—
431C4×D61—41no—
432C4×D61—41no—
433C4×D61—41no—
434C4×D61—41no—
435C4×D61—42no—
436C4×D61—42no—
437C4×D61—42no—
438C4×D61—42no—
439C4×D61—42no—
440C4×D61—88no—
441C4×D61#9914yes—
442Dic122—42no—
443Dic122—41no—
444C8×C61—42no—
445#92418—42no—
446C2×#1513—611nomaximal, Sylow
447C22×C61—21no—
448C22×C61—21no—
449C22×C61—21no—
450C22×C61—21no—
451C22×C61—21no—
452C22×C61—21no—
453C22×C61—21no—
454C22×C61—21no—
455C22×C61—42no—
456C22×C61—42no—
457C22×C61—41no—
458C22×C61—41no—
459C22×C61—41no—
460C22×C61C22×C22⋊C411yescharacteristic
461C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
462C22×C61C2×#13711yescharacteristic
463C2×D61—21no—
464C2×D61—21no—
465C2×D61—24no—
466C2×D61—24no—
467C2×D61—21no—
468C2×D61—21no—
469C2×D61—21no—
470C2×D61—21no—
471C2×D61—21no—
472C2×D61—21no—
473C2×D61—44no—
474C2×D61—44no—
475C2×D61—42no—
476C2×D61—42no—
477C2×D61—44no—
478C2×D61—44no—
479C2×D61—41no—
480C2×D61—41no—
481C2×D61—41no—
482C2×D61—84no—
483C2×D61C2×#9912yes—
484C2×D61#41712yes—
485C2×D61#41712yes—
486C2×D61#42112yes—
487C4×C61—21no—
488C4×C61—21no—
489C4×C61—21no—
490C4×C61—41no—
491C4×C61—41no—
492C4×C61—41no—
493C4×C61—82no—
494C4×C61C2×#9912yes—
495Dic61—21no—
496Dic61—21no—
497Dic61—21no—
498Dic61—41no—
499Dic61—41no—
500Dic61—41no—
501Dic61—82no—
502Dic61C2×#9912yes—
503C2×#525—611no—
504C2×#407—611no—
505C2×#380—611no—
506#1513—611no—
507#1513—611no—
508#1513—612no—
509#1513—612no—
510#1513—611no—
511#1513D6111yescharacteristic, direct product factor
512C2×#328—612no—
513C2×#327—612no—
514C2×C61—21no—
515C2×C61—21no—
516C2×C61—41no—
517C2×C61—41no—
518C2×C61—81no—
519C2×C61C22×#9911yescharacteristic
520C2×C61C2×#41711yescharacteristic
521C2×C61C2×#42111yescharacteristic
522D61—22no—
523D61—41no—
524D61—41no—
525D61—81no—
526D61#151314yesdirect product factor
527C22×#41—611no—
528C24×C4—611no—
529C22×M16—1221no—
530#525—611no—
531#525—611no—
532#525—611no—
533#525—611no—
534#525—611no—
535#525—611no—
536#525—611no—
537#525—1221no—
538#525—1221no—
539#525—1221no—
540#525—1221no—
541#525C2×D6111yescharacteristic
542C2×#123—1221no—
543C2×C22⋊Q8—611no—
544C2×C22⋊Q8—611no—
545C2×#121—611no—
546C2×#121—611no—
547C2×#120—1221no—
548C2×C4×D4—1221no—
549C2×C4×D4—1221no—
550C2×#117—611no—
551C22×C4⋊C4—1221no—
552C22×C22⋊C4—1221no—
553#407—611no—
554#407—612no—
555#407—1221no—
556#407—1221no—
557#407C2×D6111yescharacteristic, complemented
558C2×C22⋊C8—612no—
559C2×C22⋊C8—1221no—
560#380—611no—
561#380—612no—
562#380—1221no—
563#380—1221no—
564#380C2×D6111yescharacteristic, complemented
565C2×#95—612no—
566#328—612no—
567#328—612no—
568#328—612no—
569#328C2×D6112yescomplemented
570#327—612no—
571#327—612no—
572#327—612no—
573#327C2×D6112yescomplemented
574C61C2×#151311yescharacteristic, complemented, Sylow
575C25—611no—
576C2×#41—611no—
577C2×#41—611no—
578C2×#41—611no—
579C2×#41—1221no—
580C2×#41—1221no—
581C2×#41—2444no—
582C2×#41C4×D6111yescharacteristic, complemented
583C22×Q8—611no—
584C22×D4—611no—
585C22×D4—1221no—
586C22×D4—1221no—
587C22×D4—1221no—
588C23×C4—611no—
589C23×C4—611no—
590C23×C4—611no—
591C23×C4—611no—
592C23×C4—611no—
593C23×C4—611no—
594C23×C4—611no—
595C23×C4—611no—
596C23×C4—611no—
597C23×C4—611no—
598C23×C4—611no—
599C23×C4—611no—
600C23×C4—611no—
601C23×C4—1221no—
602C23×C4—1222no—
603C23×C4—2444no—
604C23×C4C22×D6111yescharacteristic
605C2×M16—21no—
606C2×M16—1222no—
607C2×M16—1221no—
608C2×M16—2444no—
609C22×C8—1222no—
610#123—21no—
611#123—1221no—
612#123—1221no—
613#123—1221no—
614#123—1221no—
615#123—1221no—
616#123—1221no—
617#123—1221no—
618C22⋊Q8—611no—
619C22⋊Q8—611no—
620C22⋊Q8—611no—
621C22⋊Q8—611no—
622C22⋊Q8—611no—
623C22⋊Q8—611no—
624C22⋊Q8—1221no—
625C22⋊Q8—1221no—
626C22⋊Q8—1221no—
627C22⋊Q8—1221no—
628C22⋊Q8C4×D6111yescharacteristic, complemented
629C22⋊Q8C22×D6111yescharacteristic
630#121—611no—
631#121—611no—
632#121—611no—
633#121—611no—
634#121—611no—
635#121—611no—
636#121—1221no—
637#121—1221no—
638#121—1221no—
639#121—1221no—
640#121C4×D6111yescharacteristic, complemented
641#121C22×D6111yescharacteristic
642#120—21no—
643#120—1221no—
644#120—1221no—
645#120—1221no—
646#120—1221no—
647#120—1221no—
648#120—1221no—
649#120—1221no—
650C4×D4—21no—
651C4×D4—21no—
652C4×D4—1221no—
653C4×D4—1221no—
654C4×D4—1221no—
655C4×D4—1221no—
656C4×D4—1221no—
657C4×D4—1221no—
658C4×D4—1221no—
659C4×D4—1221no—
660C4×D4—1221no—
661C4×D4—1221no—
662C4×D4—1221no—
663C4×D4—1221no—
664C4×D4—1221no—
665C4×D4—1221no—
666#117—611no—
667#117—611no—
668#117—611no—
669#117—1221no—
670#117—1221no—
671#117C4×D6111yescharacteristic, complemented
672C2×C4⋊C4—21no—
673C2×C4⋊C4—611no—
674C2×C4⋊C4—611no—
675C2×C4⋊C4—1221no—
676C2×C4⋊C4—1221no—
677C2×C4⋊C4—1222no—
678C2×C4⋊C4—1221no—
679C2×C4⋊C4—2444no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—1221no—
682C2×C22⋊C4—1221no—
683C2×C22⋊C4—1221no—
684C2×C22⋊C4—1221no—
685C2×C22⋊C4—1221no—
686C2×C22⋊C4—1222no—
687C2×C22⋊C4—1221no—
688C2×C22⋊C4—2444no—
689C2×C42—1221no—
690C22⋊C8—21no—
691C22⋊C8—612no—
692C22⋊C8—1222no—
693C22⋊C8—1222no—
694C22⋊C8—1221no—
695C22⋊C8C22×D6112yes—
696#95—612no—
697#95—1222no—
698#95C22×D6112yes—
699C24—611no—
700C24—611no—
701C24—611no—
702C24—611no—
703C24—611no—
704C24—611no—
705C24—1222no—
706C24—1222no—
707C24—1221no—
708C24—2442no—
709C24—2442no—
710C24D4×D6111yescharacteristic
711#41—42no—
712#41—2442no—
713#41—2444no—
714#41—2444no—
715#41—2442no—
716#41—2442no—
717C2×Q8—611no—
718C2×Q8—1221no—
719C2×Q8—2442no—
720C2×Q8C2×C4×D6111yescharacteristic
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—611no—
725C2×D4—1221no—
726C2×D4—1221no—
727C2×D4—1221no—
728C2×D4—1221no—
729C2×D4—1221no—
730C2×D4—1221no—
731C2×D4—1221no—
732C2×D4—1221no—
733C2×D4—1221no—
734C2×D4—1221no—
735C2×D4—2442no—
736C2×D4—2442no—
737C2×D4—2442no—
738C2×D4—2444no—
739C2×D4—2444no—
740C2×D4C2×C4×D6111yescharacteristic
741C22×C4—21no—
742C22×C4—22no—
743C22×C4—42no—
744C22×C4—611no—
745C22×C4—611no—
746C22×C4—611no—
747C22×C4—611no—
748C22×C4—611no—
749C22×C4—611no—
750C22×C4—611no—
751C22×C4—611no—
752C22×C4—611no—
753C22×C4—611no—
754C22×C4—611no—
755C22×C4—611no—
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—1224no—
767C22×C4—1224no—
768C22×C4—1224no—
769C22×C4—1221no—
770C22×C4—1221no—
771C22×C4—1221no—
772C22×C4—1221no—
773C22×C4—1221no—
774C22×C4—1221no—
775C22×C4—1222no—
776C22×C4—2442no—
777C22×C4—2442no—
778C22×C4—2442no—
779C22×C4—2444no—
780C22×C4—2442no—
781C22×C4—2442no—
782C22×C4—2442no—
783C22×C4—2442no—
784C22×C4—2442no—
785C22×C4—2442no—
786C22×C4—2444no—
787C22×C4—2444no—
788C22×C4—2444no—
789C22×C4—2442no—
790C22×C4C2×C4×D6111yescharacteristic
791C22×C4C2×C4×D6111yescharacteristic
792C22×C4D4×D6111yescharacteristic
793C22×C4D4×D6111yescharacteristic
794C22×C4D4×D6111yescharacteristic
795C22×C4C23×D6111yescharacteristic
796M16—42no—
797M16—2444no—
798M16—2442no—
799C2×C8—22no—
800C2×C8—1222no—
801C2×C8—2444no—
802C4⋊C4—21no—
803C4⋊C4—21no—
804C4⋊C4—42no—
805C4⋊C4—611no—
806C4⋊C4—611no—
807C4⋊C4—1221no—
808C4⋊C4—1221no—
809C4⋊C4—1221no—
810C4⋊C4—1221no—
811C4⋊C4—1221no—
812C4⋊C4—1221no—
813C4⋊C4—1221no—
814C4⋊C4—1221no—
815C4⋊C4—2442no—
816C4⋊C4—2444no—
817C4⋊C4C2×C4×D6111yescharacteristic
818C4⋊C4C2×C4×D6111yescharacteristic
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—42no—
825C22⋊C4—1221no—
826C22⋊C4—1221no—
827C22⋊C4—1221no—
828C22⋊C4—1221no—
829C22⋊C4—1221no—
830C22⋊C4—1221no—
831C22⋊C4—1221no—
832C22⋊C4—1221no—
833C22⋊C4—1221no—
834C22⋊C4—1221no—
835C22⋊C4—1221no—
836C22⋊C4—1221no—
837C22⋊C4—1221no—
838C22⋊C4—1221no—
839C22⋊C4—1221no—
840C22⋊C4—2444no—
841C22⋊C4—2442no—
842C42—21no—
843C42—1221no—
844C42—1221no—
845C42—1221no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—41no—
850C23—41no—
851C23—611no—
852C23—611no—
853C23—612no—
854C23—612no—
855C23—611no—
856C23—611no—
857C23—1222no—
858C23—1222no—
859C23—1222no—
860C23—1222no—
861C23—1222no—
862C23—1222no—
863C23—1222no—
864C23—1222no—
865C23—1222no—
866C23—1222no—
867C23—1221no—
868C23—1221no—
869C23—1221no—
870C23—2441no—
871C23—2441no—
872C23—2441no—
873C23—2441no—
874C23—2441no—
875C23—2441no—
876C23—2442no—
877C23—2442no—
878C23—2442no—
879C23—2448no—
880C23—2448no—
881C23C22⋊C4×D6111yescharacteristic
882C23C22⋊C4×D6111yescharacteristic
883C23C2×D4×D6111yescharacteristic
884Q8—41no—
885Q8—2441no—
886Q8—2442no—
887D4—41no—
888D4—42no—
889D4—42no—
890D4—41no—
891D4—41no—
892D4—2441no—
893D4—2442no—
894D4—2442no—
895D4—2442no—
896D4—2442no—
897D4—2442no—
898D4—2442no—
899D4—2442no—
900D4—2442no—
901D4—2442no—
902D4—2441no—
903D4—2441no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—611no—
918C2×C4—614no—
919C2×C4—611no—
920C2×C4—611no—
921C2×C4—611no—
922C2×C4—1222no—
923C2×C4—1222no—
924C2×C4—1222no—
925C2×C4—1222no—
926C2×C4—1222no—
927C2×C4—1222no—
928C2×C4—1222no—
929C2×C4—1222no—
930C2×C4—1222no—
931C2×C4—1222no—
932C2×C4—1222no—
933C2×C4—1222no—
934C2×C4—1221no—
935C2×C4—1221no—
936C2×C4—1221no—
937C2×C4—4888no—
938C2×C4—2441no—
939C2×C4—2441no—
940C2×C4—2441no—
941C2×C4—2441no—
942C2×C4—2441no—
943C2×C4—2441no—
944C2×C4—2442no—
945C2×C4—2442no—
946C2×C4—2442no—
947C2×C4—2442no—
948C2×C4—2442no—
949C2×C4—2441no—
950C2×C4—2441no—
951C2×C4—2441no—
952C2×C4—2442no—
953C2×C4—2442no—
954C2×C4—2442no—
955C2×C4—2442no—
956C2×C4C22⋊C4×D6111yescharacteristic
957C2×C4C22⋊C4×D6111yescharacteristic
958C2×C4C22×C4×D6111yescharacteristic
959C2×C4C2×D4×D6111yescharacteristic
960C8—42no—
961C8—2442no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—21no—
968C22—21no—
969C22—21no—
970C22—42no—
971C22—42no—
972C22—41no—
973C22—41no—
974C22—41no—
975C22—612no—
976C22—612no—
977C22—612no—
978C22—612no—
979C22—1224no—
980C22—1224no—
981C22—1221no—
982C22—1221no—
983C22—1221no—
984C22—1221no—
985C22—1221no—
986C22—1221no—
987C22—1221no—
988C22—1221no—
989C22—4884no—
990C22—2442no—
991C22—2442no—
992C22—2444no—
993C22—2444no—
994C22—2444no—
995C22—2444no—
996C22—2441no—
997C22—2441no—
998C22—2441no—
999C22C2×C22⋊C4×D6111yescharacteristic
1000C22AGL(1,ℤ/8)×D6111yescharacteristic
1001C22#137×D6111yescharacteristic
1002C4—21no—
1003C4—21no—
1004C4—21no—
1005C4—41no—
1006C4—41no—
1007C4—41no—
1008C4—82no—
1009C4—612no—
1010C4—1221no—
1011C4—1221no—
1012C4—1221no—
1013C4—4882no—
1014C4—2441no—
1015C4—2441no—
1016C4—2441no—
1017C4#99×D6112yes—
1018C2—21no—
1019C2—21no—
1020C2—41no—
1021C2—41no—
1022C2—81no—
1023C2—614no—
1024C2—1222no—
1025C2—4881no—
1026C2—2441no—
1027C2—2441no—
1028C2C2×#99×D6111yescharacteristic
1029C2#417×D6111yescharacteristic
1030C2#421×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1513C2
socleC22×C61C22×C22⋊C4
prime radical#525×D61C2
cosocleC22×C4×C61C24
hypercenter#1513D61
hypocenterC61C2×#1513
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1513

Complements

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

NH ≅ G/Ntype
2. #407×D61C2semidirect
3. #380×D61C2semidirect
4. #21444363C2semidirect
5. #21444362C2semidirect
6. #21444361C2semidirect
7. #21444360C2semidirect
8. #21444359C2semidirect
9. #328×D61C2semidirect
10. #327×D61C2semidirect
11. C61×#1513C2semidirect
12. C2×#41×D61C4semidirect
15. #16840275C4semidirect
17. #16840274C4semidirect
19. #16840272C4semidirect
24. #16840269C4semidirect
27. C22⋊Q8×D61C4semidirect
29. #121×D61C4semidirect
34. #117×D61C4semidirect
37. #16839726C22semidirect
40. #16839724C22semidirect
43. #16839622C22semidirect
44. #16839621C22semidirect
48. #16839500C22semidirect
49. #16839499C22semidirect
50. #16839498C22semidirect
51. #16839497C22semidirect
52. #16839496C22semidirect
53. #16839495C22semidirect
55. C61×#407C22semidirect
56. C61×#380C22semidirect
57. C61×#328C22semidirect
58. C61×#327C22semidirect
60. C2×#11758226C2×C4semidirect
62. C2×#11758222C2×C4semidirect
64. C2×#11758224C2×C4semidirect
99. #14519757C2×C4semidirect
100. #14519756C2×C4semidirect
107. #14519753C2×C4semidirect
109. #14519752C2×C4semidirect
110. #14519751C2×C4semidirect
117. #14519748C2×C4semidirect
139. #14519736C2×C4semidirect
140. #14519735C2×C4semidirect
141. #14519735C2×C4semidirect
166. C2×#41×C61C2×C4semidirect
170. C22⋊Q8×C61C2×C4semidirect
172. #121×C61C2×C4semidirect
177. #117×C61C2×C4semidirect
511. #1513D61direct (N × H)
526. D61#1513direct (N × H)
557. #407C2×D61semidirect
564. #380C2×D61semidirect
569. #328C2×D61semidirect
573. #327C2×D61semidirect
574. C61C2×#1513semidirect
582. C2×#41C4×D61semidirect
628. C22⋊Q8C4×D61semidirect
640. #121C4×D61semidirect
671. #117C4×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
#380×D612
#214443632
#214443622
#214443612
#214443602
#214443592
#328×D612
#327×D612
C61×#15132
C2×#151361