Finite Group Databasebeta

← D61⋊#1871 #30615587

Subgroups — D61⋊#1871 #30615587

Order 15616.

2050 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D61⋊M16C211yesmaximal, characteristic, complemented
2C2×D61⋊#104C212yesmaximal, complemented
3C2×C4×C22⋊#6923C211yesmaximal, characteristic, complemented
4#21461803C212yesmaximal, complemented
5#21461802C212yesmaximal, complemented
6#21461801C212yesmaximal, complemented
7#21461800C212yesmaximal, complemented
8#21461495C212yesmaximal, complemented
9#525×D61C211yesmaximal, characteristic
10C22×#11758213C2212yescomplemented
11C2×D61⋊M16—28no—
12C2×D61⋊M16—21no—
13C2×D61⋊M16—21no—
14C2×D61⋊M16C2212yes—
15C2×D61⋊M16C2212yescomplemented
16C22×#11758217—21no—
17C22×D61⋊C8—21no—
18C22×C22⋊#6923—21no—
19C22×C4×#6923C2212yes—
20C2×#14519842C2214yescomplemented
21D61⋊#104—28no—
22C2×#14519841C2214yescomplemented
23C4×C22⋊#6923—21no—
24C4×C22⋊#6923—21no—
25C4×C22⋊#6923C2212yescomplemented
26C4×C22⋊#6923C2212yescomplemented
27C2×(C2×#6923)⋊C4—21no—
28#16840632C2214yescomplemented
29#16840632C2214yescomplemented
30C2×#41×D61C2211yescharacteristic
31C23×C4×D61C2211yescharacteristic
32#16840275C2211yescharacteristic
33#16840275C2211yescharacteristic
34#16840274C411yescharacteristic, complemented
35#16840273C411yescharacteristic, complemented
36#16840272C2211yescharacteristic
37#16840272C2211yescharacteristic
38#16840271—21no—
39#16840271—21no—
40#16840270—21no—
41#16840269C411yescharacteristic, complemented
42#16840268—21no—
43#123×D61—21no—
44C22⋊Q8×D61C411yescharacteristic, complemented
45C22⋊Q8×D61C411yescharacteristic, complemented
46#121×D61C411yescharacteristic, complemented
47#121×D61C411yescharacteristic, complemented
48#120×D61—21no—
49C4×D4×D61—21no—
50C4×D4×D61—21no—
51#117×D61C2211yescharacteristic
52C61×#525C411yescharacteristic, complemented
53C23×#6923—22no—
54C2×#11758213—22no—
55C2×#11758213—28no—
56C2×#11758213C2314yes—
57D61⋊M16—28no—
58D61⋊M16—28no—
59D61⋊M16—24no—
60D61⋊M16—28no—
61D61⋊M16D418yescomplemented
62C2×#11758217—28no—
63C2×#11758217—22no—
64C2×#11758217—22no—
65C2×D61⋊C8—28no—
66C2×D61⋊C8—22no—
67C2×D61⋊C8—22no—
68C22×#92420—22no—
69C2×C22⋊#6923—28no—
70C2×C22⋊#6923—22no—
71C2×C22⋊#6923—22no—
72C2×C4×#6923—24no—
73C2×C4×#6923—24no—
74C2×C4×#6923—22no—
75C2×C4×#6923C2314yes—
76#14519842—28no—
77#14519841—28no—
78(C2×#6923)⋊C4—22no—
79(C2×#6923)⋊C4—22no—
80C24×D61D411yescharacteristic
81C2×#11758226C2311yescharacteristic
82C2×#11758222—21no—
83C2×#11758222C2×C411yescharacteristic
84C2×#11758224—21no—
85C2×#11758224C2311yescharacteristic
86#41×D61—24no—
87#41×D61—24no—
88C2×Q8×D61C2×C411yescharacteristic
89C2×D4×D61—21no—
90C2×D4×D61—21no—
91C2×D4×D61—21no—
92C2×D4×D61C2×C411yescharacteristic
93C23×Dic61D411yescharacteristic
94C22×C4×D61—24no—
95C22×C4×D61—24no—
96C22×C4×D61—21no—
97C22×C4×D61C2×C411yescharacteristic
98C22×C4×D61C2×C411yescharacteristic
99C22×C4×D61C2×C411yescharacteristic
100C22×C4×D61D411yescharacteristic
101C22×C4×D61D411yescharacteristic
102C22×C4×D61D411yescharacteristic
103C22×C4×D61D411yescharacteristic
104C22×C4×D61D411yescharacteristic
105C22×C4×D61D411yescharacteristic
106C22×C4×D61C2311yescharacteristic
107C22×C4×D61C2311yescharacteristic
108C22×C4×D61C2311yescharacteristic
109#14519762—21no—
110#14519762—21no—
111#14519761—21no—
112#14519760—21no—
113#14519759—21no—
114#14519759—21no—
115#14519758—21no—
116#14519757C2×C411yescharacteristic, complemented
117#14519757C2×C411yescharacteristic, complemented
118#14519756C2×C411yescharacteristic, complemented
119#14519756C2×C411yescharacteristic, complemented
120#14519755—21no—
121#14519755—21no—
122#14519754—21no—
123#14519754—21no—
124#14519753C2×C411yescharacteristic, complemented
125#14519753C2×C411yescharacteristic, complemented
126#14519752C2×C411yescharacteristic, complemented
127#14519752C2×C411yescharacteristic, complemented
128#14519751C2×C411yescharacteristic, complemented
129#14519751C2×C411yescharacteristic, complemented
130#14519750—21no—
131#14519750—21no—
132#14519749—21no—
133#14519749—21no—
134#14519748C2×C411yescharacteristic, complemented
135#14519748C2×C411yescharacteristic, complemented
136#14519747—21no—
137#14519747—21no—
138#14519747—21no—
139#14519746—21no—
140#14519745—21no—
141#14519745—21no—
142#14519745—21no—
143C4×D244—21no—
144C4×D244—21no—
145D4×Dic61—21no—
146D4×Dic61—21no—
147#14519739—21no—
148#14519739—21no—
149C4×C22⋊D61—21no—
150C4×C22⋊D61—21no—
151C4×C22⋊D61—21no—
152C4×C22⋊D61—21no—
153#14519737—21no—
154#14519737—21no—
155#14519737—21no—
156#14519737—21no—
157#14519736C2×C411yescharacteristic
158#14519735C2311yescharacteristic
159#14519735C2311yescharacteristic
160#14519734—21no—
161#14519733—21no—
162C4⋊C4×D61—21no—
163C4⋊C4×D61—21no—
164C4⋊C4×D61C2×C411yescharacteristic
165C4⋊C4×D61C2×C411yescharacteristic
166C22⋊C4×D61—21no—
167C22⋊C4×D61—21no—
168C22⋊C4×D61—21no—
169C22⋊C4×D61—21no—
170C22⋊C4×D61—21no—
171C42×D61—21no—
172C2×#41×C61C2×C411yescharacteristic
173C23×C4×C61C2×C411yescharacteristic
174#123×C61—21no—
175C22⋊Q8×C61C2×C411yescharacteristic, complemented
176C22⋊Q8×C61C2×C411yescharacteristic, complemented
177#121×C61C2×C411yescharacteristic, complemented
178#121×C61C2×C411yescharacteristic, complemented
179#120×C61—21no—
180C4×D4×C61—21no—
181C4×D4×C61—21no—
182#117×C61C2×C411yescharacteristic
183C24×C61C22⋊C411yescharacteristic
184C23×D61—24no—
185C23×D61—24no—
186C23×D61—21no—
187C23×D61—42no—
188C23×D61C22⋊C411yescharacteristic
189C23×D61C22⋊C411yescharacteristic
190C23×D61C22⋊C411yescharacteristic
191C23×D61C2×D411yescharacteristic
192C23×D61C2×D411yescharacteristic
193C23×D61C2×D411yescharacteristic
194C22×#6923—28no—
195C22×#6923—24no—
196C22×#6923—44no—
197C22×#6923—44no—
198#41×C61—24no—
199C2×Q8×C61C22×C411yescharacteristic
200C2×D4×C61—21no—
201C2×D4×C61—21no—
202C2×D4×C61—21no—
203C2×D4×C61C22×C411yescharacteristic
204C22×C4×C61—24no—
205C22×C4×C61—21no—
206C22×C4×C61C22⋊C411yescharacteristic
207C22×C4×C61C22⋊C411yescharacteristic
208C22×C4×C61C22⋊C411yescharacteristic
209C22×C4×C61C22×C411yescharacteristic
210C22×C4×C61C22×C411yescharacteristic
211C22×C4×C61C22×C411yescharacteristic
212C2×C22⋊D61—21no—
213C2×C22⋊D61—21no—
214C2×C22⋊D61—21no—
215C2×C22⋊D61—21no—
216C2×C22⋊D61—21no—
217C2×C22⋊D61—21no—
218C2×C22⋊D61—21no—
219C22×Dic61—22no—
220C22×Dic61—22no—
221C22×Dic61—21no—
222C22×Dic61C22⋊C411yescharacteristic
223C22×Dic61C22⋊C411yescharacteristic
224C22×Dic61C22⋊C411yescharacteristic
225C22×Dic61C2×D411yescharacteristic
226C22×Dic61C2×D411yescharacteristic
227C22×Dic61C2×D411yescharacteristic
228#11758226—22no—
229#11758226—22no—
230Q8×D61—24no—
231#11758224—22no—
232#11758224—22no—
233#11758224—42no—
234#11758224—42no—
235D4×D61—24no—
236D4×D61—44no—
237D4×D61—44no—
238D4×D61—44no—
239#11758222—24no—
240#11758222—44no—
241C2×D244—21no—
242C2×D244—21no—
243C2×D244—21no—
244C2×D244C22×C411yescharacteristic
245C2×C4×D61—24no—
246C2×C4×D61—24no—
247C2×C4×D61—22no—
248C2×C4×D61—22no—
249C2×C4×D61—24no—
250C2×C4×D61—24no—
251C2×C4×D61—22no—
252C2×C4×D61—22no—
253C2×C4×D61—24no—
254C2×C4×D61—24no—
255C2×C4×D61—22no—
256C2×C4×D61—22no—
257C2×C4×D61—22no—
258C2×C4×D61—22no—
259C2×C4×D61—22no—
260C2×C4×D61—22no—
261C2×C4×D61—21no—
262C2×C4×D61—21no—
263C2×C4×D61—21no—
264C2×C4×D61—21no—
265C2×C4×D61—21no—
266C2×C4×D61—42no—
267C2×C4×D61—42no—
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×D61C22×C411yescharacteristic
275C2×C4×D61C22×C411yescharacteristic
276C2×C4×D61C22×C411yescharacteristic
277C2×C4×D61C2×D411yescharacteristic
278C2×C4×D61C2×D411yescharacteristic
279C2×C4×D61C2×D411yescharacteristic
280C2×C4×D61C2×D411yescharacteristic
281C2×C4×D61C2×D414yes—
282C2×C4×D61C2×D411yescharacteristic
283C2×C4×D61C2×D411yescharacteristic
284C2×C4×D61#4114yes—
285C2×C4×D61C2411yescharacteristic
286C2×Dic122—21no—
287C2×Dic122C22×C411yescharacteristic
288C22⋊#6923—28no—
289C22⋊#6923—28no—
290#11758217—28no—
291#11758217—28no—
292C2×#92420—28no—
293C2×#92420—24no—
294C4×#6923—24no—
295C4×#6923—24no—
296C4×#6923—44no—
297#11758213—28no—
298#11758213—24no—
299#11758213C2×D418yescomplemented
300D61⋊C8—28no—
301D61⋊C8—28no—
302C4⋊C4×C61—21no—
303C4⋊C4×C61—21no—
304C4⋊C4×C61C22×C411yescharacteristic
305C4⋊C4×C61C22×C411yescharacteristic
306C22⋊C4×C61—21no—
307C22⋊C4×C61—21no—
308C22⋊C4×C61—21no—
309C22⋊C4×C61—21no—
310C22⋊C4×C61—21no—
311C42×C61—21no—
312C22⋊Dic61—21no—
313C22⋊Dic61—21no—
314C22⋊Dic61—21no—
315C22⋊Dic61—21no—
316C22⋊Dic61—21no—
317#11758198—21no—
318#11758198—21no—
319#11758198—21no—
320#11758198—21no—
321#11758198—21no—
322#11758198—21no—
323#11758198—21no—
324#11758198—21no—
325#11758198—21no—
326#11758198—21no—
327C4⋊Dic61—21no—
328C4⋊Dic61—21no—
329C4⋊Dic61C22×C411yescharacteristic
330C4⋊Dic61C22×C411yescharacteristic
331#11758196—21no—
332#11758196—21no—
333#11758196—21no—
334#11758196—21no—
335#11758196—21no—
336#11758196—21no—
337C4×Dic61—21no—
338C4×Dic61—21no—
339C4×Dic61—21no—
340C23×C61—22no—
341C23×C61—22no—
342C23×C61—21no—
343C23×C61—41no—
344C23×C61C2×C22⋊C411yescharacteristic
345C23×C61C2×C22⋊C411yescharacteristic
346C23×C61C2×C22⋊C411yescharacteristic
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—21no—
361C22×D61—41no—
362C22×D61—41no—
363C22×D61—41no—
364C22×D61—416no—
365C22×D61—42no—
366C22×D61—42no—
367C22×D61—42no—
368C22×D61#10414yescomplemented
369C22×D61C2×C22⋊C411yescharacteristic
370C22×D61C2×C22⋊C411yescharacteristic
371C22×D61C2×C22⋊C411yescharacteristic
372C22×D61#12114yes—
373C22×D61C22×D411yescharacteristic
374C2×#6923—28no—
375C2×#6923—44no—
376C2×#6923—416no—
377C2×#6923—44no—
378Q8×C61—22no—
379D4×C61—22no—
380D4×C61—42no—
381D4×C61—42no—
382D4×C61—42no—
383C2×C4×C61—22no—
384C2×C4×C61—22no—
385C2×C4×C61—22no—
386C2×C4×C61—22no—
387C2×C4×C61—22no—
388C2×C4×C61—21no—
389C2×C4×C61—21no—
390C2×C4×C61—21no—
391C2×C4×C61—42no—
392C2×C4×C61C2×C22⋊C411yescharacteristic
393C2×C4×C61C2×C22⋊C411yescharacteristic
394C2×C4×C61C2×C22⋊C411yescharacteristic
395C2×C4×C61C4×D414yes—
396C2×C4×C61C23×C411yescharacteristic
397C22⋊D61—42no—
398C22⋊D61—42no—
399C22⋊D61—42no—
400C22⋊D61—42no—
401C22⋊D61—42no—
402C22⋊D61—42no—
403C22⋊D61—42no—
404C2×Dic61—22no—
405C2×Dic61—21no—
406C2×Dic61—21no—
407C2×Dic61—21no—
408C2×Dic61—21no—
409C2×Dic61—22no—
410C2×Dic61—22no—
411C2×Dic61—21no—
412C2×Dic61—21no—
413C2×Dic61—21no—
414C2×Dic61—41no—
415C2×Dic61—41no—
416C2×Dic61C2×C22⋊C411yescharacteristic
417C2×Dic61C2×C22⋊C411yescharacteristic
418C2×Dic61C2×C22⋊C411yescharacteristic
419C2×Dic61#12012yes—
420C2×Dic61#12312yes—
421C2×Dic61C22×D411yescharacteristic
422D244—22no—
423D244—42no—
424D244—42no—
425D244—42no—
426C4×D61—22no—
427C4×D61—22no—
428C4×D61—22no—
429C4×D61—22no—
430C4×D61—22no—
431C4×D61—22no—
432C4×D61—22no—
433C4×D61—22no—
434C4×D61—21no—
435C4×D61—21no—
436C4×D61—21no—
437C4×D61—21no—
438C4×D61—22no—
439C4×D61—22no—
440C4×D61—42no—
441C4×D61—42no—
442C4×D61—42no—
443C4×D61—42no—
444C4×D61—41no—
445C4×D61—41no—
446C4×D61C4×D414yes—
447C4×D61#12012yes—
448C4×D61#12114yes—
449C4×D61#12312yes—
450C4×D61C22×D412yes—
451C4×D61C2×#4112yes—
452Dic122—22no—
453Dic122—42no—
454#92420—28no—
455C2×#1871—611nomaximal, Sylow
456C22×C61—21no—
457C22×C61—21no—
458C22×C61—21no—
459C22×C61—21no—
460C22×C61—21no—
461C22×C61—21no—
462C22×C61—21no—
463C22×C61—44no—
464C22×C61—41no—
465C22×C61—41no—
466C22×C61—41no—
467C22×C61#38612yes—
468C22×C61C2×#10412yescomplemented
469C22×C61C22×C22⋊C411yescharacteristic
470C2×D61—21no—
471C2×D61—21no—
472C2×D61—21no—
473C2×D61—21no—
474C2×D61—28no—
475C2×D61—28no—
476C2×D61—21no—
477C2×D61—21no—
478C2×D61—21no—
479C2×D61—44no—
480C2×D61—44no—
481C2×D61—44no—
482C2×D61—44no—
483C2×D61—41no—
484C2×D61—41no—
485C2×D61—41no—
486C2×D61—84no—
487C2×D61#38612yes—
488C2×D61C2×#10412yes—
489C2×D61C2×#10412yescomplemented
490C2×D61#42112yes—
491C2×D61C2×#12112yes—
492#6923—48no—
493C4×C61—21no—
494C4×C61—21no—
495C4×C61—41no—
496C4×C61—41no—
497C4×C61—41no—
498C4×C61#38612yes—
499C4×C61C2×C4×D412yes—
500Dic61—21no—
501Dic61—21no—
502Dic61—41no—
503Dic61—41no—
504Dic61—41no—
505Dic61#38612yes—
506Dic61C2×#12011yescharacteristic
507Dic61C2×#12311yescharacteristic
508C23×M16—611no—
509C2×#525—611no—
510C22×#104—612no—
511C2×C4×C22⋊C4—611no—
512#1871—612no—
513#1871—612no—
514#1871—612no—
515#1871—612no—
516C2×#339—612no—
517C2×C61—22no—
518C2×C61—22no—
519C2×C61—41no—
520C2×C61—81no—
521C2×C61C2×#38611yescharacteristic
522C2×C61C22×#10411yescharacteristic
523C2×C61C2×#42111yescharacteristic
524D61—22no—
525D61—22no—
526D61—41no—
527D61—81no—
528D61#187114yescomplemented
529C22×#41—611no—
530C24×C4—611no—
531C22×M16—612no—
532C22×M16—612no—
533C22×M16—612no—
534C22×M16—1228no—
535C22×M16—1221no—
536C22×M16—1221no—
537C22×M16—1221no—
538C23×C8—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#525#692311yescharacteristic, complemented
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—
560C22×C22⋊C4—1221no—
561C22×C42—612no—
562C2×#104—614no—
563C2×#104—614no—
564C2×#104—1228no—
565C4×C22⋊C4—612no—
566C4×C22⋊C4—612no—
567C4×C22⋊C4—1221no—
568C4×C22⋊C4—1221no—
569C2×#95—1221no—
570#339—614no—
571#339—614no—
572C61C2×#187111yescharacteristic, complemented, Sylow
573C25—611no—
574C2×#41—611no—
575C2×#41—611no—
576C2×#41—611no—
577C2×#41—1221no—
578C2×#41—1221no—
579C2×#41—1224no—
580C2×#41—1224no—
581C2×#41C2×#692311yescharacteristic
582C22×Q8—611no—
583C22×D4—611no—
584C22×D4—1221no—
585C22×D4—1221no—
586C22×D4—1221no—
587C23×C4—611no—
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—1224no—
601C23×C4—1224no—
602C23×C4—1221no—
603C23×C4—1222no—
604C23×C4C2×#692311yescharacteristic
605C2×M16—614no—
606C2×M16—618no—
607C2×M16—1228no—
608C2×M16—1228no—
609C2×M16—1222no—
610C2×M16—1222no—
611C2×M16—1224no—
612C2×M16—1222no—
613C2×M16—1228no—
614C2×M16—1228no—
615C2×M16—1228no—
616C22×C8—1222no—
617C22×C8—1222no—
618C22×C8—1222no—
619C22×C8—1228no—
620#123—21no—
621#123—1221no—
622#123—1221no—
623#123—1221no—
624#123—1221no—
625#123—1221no—
626#123—1221no—
627#123—1221no—
628C22⋊Q8—611no—
629C22⋊Q8—611no—
630C22⋊Q8—611no—
631C22⋊Q8—611no—
632C22⋊Q8—611no—
633C22⋊Q8—611no—
634C22⋊Q8—1221no—
635C22⋊Q8—1221no—
636C22⋊Q8—1221no—
637C22⋊Q8—1221no—
638C22⋊Q8C2×#692311yescharacteristic, complemented
639C22⋊Q8C2×#692311yescharacteristic, complemented
640#121—611no—
641#121—611no—
642#121—611no—
643#121—611no—
644#121—611no—
645#121—611no—
646#121—1221no—
647#121—1221no—
648#121—1221no—
649#121—1221no—
650#121C2×#692311yescharacteristic, complemented
651#121C2×#692311yescharacteristic, complemented
652#120—21no—
653#120—1221no—
654#120—1221no—
655#120—1221no—
656#120—1221no—
657#120—1221no—
658#120—1221no—
659#120—1221no—
660C4×D4—21no—
661C4×D4—21no—
662C4×D4—1221no—
663C4×D4—1221no—
664C4×D4—1221no—
665C4×D4—1221no—
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—
676#117—611no—
677#117—611no—
678#117—611no—
679#117—1221no—
680#117—1221no—
681#117C2×#692311yescharacteristic
682C2×C4⋊C4—611no—
683C2×C4⋊C4—611no—
684C2×C4⋊C4—1221no—
685C2×C4⋊C4—1221no—
686C2×C22⋊C4—1221no—
687C2×C22⋊C4—1221no—
688C2×C22⋊C4—1221no—
689C2×C22⋊C4—1221no—
690C2×C22⋊C4—1221no—
691C2×C22⋊C4—1222no—
692C2×C22⋊C4—1222no—
693C2×C22⋊C4—1228no—
694C2×C42—614no—
695C2×C42—1221no—
696C2×C42—1224no—
697C2×C42—1224no—
698C2×C42—1222no—
699#104—1228no—
700#104—1228no—
701#95—1222no—
702#95—1222no—
703C24—611no—
704C24—611no—
705C24—611no—
706C24—611no—
707C24—611no—
708C24—611no—
709C24—1224no—
710C24—1224no—
711C24—1221no—
712C24—2442no—
713C24C22⋊#692311yescharacteristic
714#41—24no—
715#41—1222no—
716#41—1222no—
717#41—1222no—
718#41—1222no—
719#41—1224no—
720#41—2444no—
721#41—2442no—
722#41—2442no—
723C2×Q8—611no—
724C2×Q8—1221no—
725C2×Q8—1224no—
726C2×Q8C22×#692311yescharacteristic
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—611no—
731C2×D4—1221no—
732C2×D4—1221no—
733C2×D4—1221no—
734C2×D4—1224no—
735C2×D4—1221no—
736C2×D4—1221no—
737C2×D4—1221no—
738C2×D4—1221no—
739C2×D4—1221no—
740C2×D4—1221no—
741C2×D4—1221no—
742C2×D4—2444no—
743C2×D4—2444no—
744C2×D4—2444no—
745C2×D4C22×#692311yescharacteristic
746C22×C4—24no—
747C22×C4—21no—
748C22×C4—611no—
749C22×C4—611no—
750C22×C4—611no—
751C22×C4—614no—
752C22×C4—614no—
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—611no—
767C22×C4—611no—
768C22×C4—611no—
769C22×C4—611no—
770C22×C4—611no—
771C22×C4—611no—
772C22×C4—1222no—
773C22×C4—1222no—
774C22×C4—1222no—
775C22×C4—1222no—
776C22×C4—1222no—
777C22×C4—1222no—
778C22×C4—1224no—
779C22×C4—1224no—
780C22×C4—1222no—
781C22×C4—1222no—
782C22×C4—1224no—
783C22×C4—1224no—
784C22×C4—1222no—
785C22×C4—1222no—
786C22×C4—1221no—
787C22×C4—1224no—
788C22×C4—1221no—
789C22×C4—1221no—
790C22×C4—1221no—
791C22×C4—1222no—
792C22×C4—1222no—
793C22×C4—1221no—
794C22×C4—1224no—
795C22×C4—1224no—
796C22×C4—1228no—
797C22×C4—1221no—
798C22×C4—2442no—
799C22×C4—2442no—
800C22×C4—2444no—
801C22×C4—2444no—
802C22×C4C22⋊#692311yescharacteristic
803C22×C4C22⋊#692311yescharacteristic
804C22×C4C22⋊#692311yescharacteristic
805C22×C4C22×#692311yescharacteristic
806C22×C4C22×#692311yescharacteristic
807C22×C4C22×#692311yescharacteristic
808M16—618no—
809M16—1224no—
810M16—1228no—
811M16—1228no—
812M16—1228no—
813C2×C8—1228no—
814C2×C8—1224no—
815C2×C8—1228no—
816C2×C8—1228no—
817C4⋊C4—21no—
818C4⋊C4—21no—
819C4⋊C4—611no—
820C4⋊C4—611no—
821C4⋊C4—1221no—
822C4⋊C4—1221no—
823C4⋊C4—1221no—
824C4⋊C4—1221no—
825C4⋊C4—1221no—
826C4⋊C4—1221no—
827C4⋊C4—1221no—
828C4⋊C4—1221no—
829C4⋊C4C22×#692311yescharacteristic
830C4⋊C4C22×#692311yescharacteristic
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—21no—
834C22⋊C4—21no—
835C22⋊C4—21no—
836C22⋊C4—1221no—
837C22⋊C4—1221no—
838C22⋊C4—1221no—
839C22⋊C4—1221no—
840C22⋊C4—1221no—
841C22⋊C4—1221no—
842C22⋊C4—1221no—
843C22⋊C4—1221no—
844C22⋊C4—1221no—
845C22⋊C4—1221no—
846C22⋊C4—1228no—
847C22⋊C4—1228no—
848C22⋊C4—1221no—
849C22⋊C4—1221no—
850C22⋊C4—1221no—
851C22⋊C4—1221no—
852C22⋊C4—1221no—
853C42—21no—
854C42—1221no—
855C42—1221no—
856C42—1224no—
857C42—1224no—
858C42—1221no—
859C42—2444no—
860C23—22no—
861C23—22no—
862C23—21no—
863C23—41no—
864C23—611no—
865C23—614no—
866C23—614no—
867C23—611no—
868C23—611no—
869C23—611no—
870C23—1222no—
871C23—1222no—
872C23—1222no—
873C23—1222no—
874C23—1222no—
875C23—1222no—
876C23—1222no—
877C23—1222no—
878C23—1222no—
879C23—1222no—
880C23—1222no—
881C23—1222no—
882C23—1222no—
883C23—1221no—
884C23—2441no—
885C23—2441no—
886C23—2441no—
887C23—2442no—
888C23—2442no—
889C23—2442no—
890C23—24416no—
891C23C2×C22⋊#692311yescharacteristic
892C23C2×C22⋊#692311yescharacteristic
893C23C2×C22⋊#692311yescharacteristic
894Q8—22no—
895Q8—1222no—
896Q8—2442no—
897D4—22no—
898D4—42no—
899D4—42no—
900D4—42no—
901D4—1222no—
902D4—2442no—
903D4—2442no—
904D4—2442no—
905D4—2442no—
906D4—2442no—
907D4—2442no—
908D4—2442no—
909D4—2442no—
910D4—2442no—
911D4—2442no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—42no—
921C2×C4—612no—
922C2×C4—612no—
923C2×C4—611no—
924C2×C4—611no—
925C2×C4—612no—
926C2×C4—614no—
927C2×C4—612no—
928C2×C4—614no—
929C2×C4—612no—
930C2×C4—612no—
931C2×C4—611no—
932C2×C4—611no—
933C2×C4—1221no—
934C2×C4—1221no—
935C2×C4—1221no—
936C2×C4—1221no—
937C2×C4—1222no—
938C2×C4—1222no—
939C2×C4—1222no—
940C2×C4—1222no—
941C2×C4—1222no—
942C2×C4—1222no—
943C2×C4—1221no—
944C2×C4—1221no—
945C2×C4—1221no—
946C2×C4—1221no—
947C2×C4—1222no—
948C2×C4—1222no—
949C2×C4—1222no—
950C2×C4—1222no—
951C2×C4—1222no—
952C2×C4—1222no—
953C2×C4—1222no—
954C2×C4—1228no—
955C2×C4—1221no—
956C2×C4—1221no—
957C2×C4—1221no—
958C2×C4—2441no—
959C2×C4—2441no—
960C2×C4—2442no—
961C2×C4—2442no—
962C2×C4—2442no—
963C2×C4—2441no—
964C2×C4—2441no—
965C2×C4—2444no—
966C2×C4—24416no—
967C2×C4—2444no—
968C2×C4—2442no—
969C2×C4C2×C22⋊#692311yescharacteristic
970C2×C4C2×C22⋊#692311yescharacteristic
971C2×C4C2×C22⋊#692311yescharacteristic
972C2×C4D4×#692314yes—
973C2×C4C23×#692311yescharacteristic
974C8—1228no—
975C22—21no—
976C22—21no—
977C22—21no—
978C22—21no—
979C22—21no—
980C22—21no—
981C22—21no—
982C22—44no—
983C22—41no—
984C22—41no—
985C22—41no—
986C22—612no—
987C22—612no—
988C22—612no—
989C22—612no—
990C22—612no—
991C22—1228no—
992C22—1228no—
993C22—1221no—
994C22—1221no—
995C22—1221no—
996C22—1221no—
997C22—1221no—
998C22—1221no—
999C22—1221no—
1000C22—4884no—
1001C22—2444no—
1002C22—2444no—
1003C22—2444no—
1004C22—2444no—
1005C22—2441no—
1006C22—2441no—
1007C22—2441no—
1008C22#1684071012yes—
1009C22D61⋊#10412yescomplemented
1010C22C22×C22⋊#692311yescharacteristic
1011C4—21no—
1012C4—21no—
1013C4—41no—
1014C4—41no—
1015C4—41no—
1016C4—611no—
1017C4—611no—
1018C4—612no—
1019C4—1221no—
1020C4—1221no—
1021C4—2448no—
1022C4—2441no—
1023C4—2441no—
1024C4—2441no—
1025C4#1684071012yes—
1026C4C2×D4×#692312yes—
1027C2—22no—
1028C2—22no—
1029C2—41no—
1030C2—81no—
1031C2—614no—
1032C2—1222no—
1033C2—1222no—
1034C2—4881no—
1035C2—2441no—
1036C2C2×#1684071011yescharacteristic
1037C2C2×D61⋊#10411yescharacteristic
1038C2D61⋊#42111yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#525C4
socleC22×C61C22×C22⋊C4
prime radical#525×D61C2
cosocleC2×C4×D61C24
hypercenter#525#6923
hypocenterC61C2×#1871
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C22×D61⋊M16C2semidirect
2. C2×D61⋊#104C2semidirect
3. C2×C4×C22⋊#6923C2semidirect
4. #21461803C2semidirect
5. #21461802C2semidirect
6. #21461801C2semidirect
7. #21461800C2semidirect
8. #21461495C2semidirect
10. C22×#11758213C22semidirect
15. C2×D61⋊M16C22semidirect
20. C2×#14519842C22semidirect
22. C2×#14519841C22semidirect
25. C4×C22⋊#6923C22semidirect
26. C4×C22⋊#6923C22semidirect
28. #16840632C22semidirect
29. #16840632C22semidirect
34. #16840274C4semidirect
35. #16840273C4semidirect
41. #16840269C4semidirect
44. C22⋊Q8×D61C4semidirect
45. C22⋊Q8×D61C4semidirect
46. #121×D61C4semidirect
47. #121×D61C4semidirect
52. C61×#525C4semidirect
61. D61⋊M16D4semidirect
116. #14519757C2×C4semidirect
117. #14519757C2×C4semidirect
118. #14519756C2×C4semidirect
119. #14519756C2×C4semidirect
124. #14519753C2×C4semidirect
125. #14519753C2×C4semidirect
126. #14519752C2×C4semidirect
127. #14519752C2×C4semidirect
128. #14519751C2×C4semidirect
129. #14519751C2×C4semidirect
134. #14519748C2×C4semidirect
135. #14519748C2×C4semidirect
175. C22⋊Q8×C61C2×C4semidirect
176. C22⋊Q8×C61C2×C4semidirect
177. #121×C61C2×C4semidirect
178. #121×C61C2×C4semidirect
299. #11758213C2×D4semidirect
368. C22×D61#104semidirect
468. C22×C61C2×#104semidirect
489. C2×D61C2×#104semidirect
528. D61#1871semidirect
550. #525#6923semidirect
572. C61C2×#1871semidirect
638. C22⋊Q8C2×#6923semidirect
639. C22⋊Q8C2×#6923semidirect
650. #121C2×#6923semidirect
651. #121C2×#6923semidirect
1009. C22D61⋊#104semidirect

Maximal subgroups

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

subgroupindex
C22×D61⋊M162
C2×D61⋊#1042
C2×C4×C22⋊#69232
#214618032
#214618022
#214618012
#214618002
#214614952
#525×D612
C2×#187161