Finite Group Databasebeta

← D61×#1871 #29681183

Subgroups — D61×#1871 #29681183

Order 15616.

2050 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D61C211yesmaximal, characteristic, complemented
2#525×D61C211yesmaximal, characteristic
3C2×#104×D61C212yesmaximal, complemented
4C4×C22⋊C4×D61C211yesmaximal, characteristic, complemented
5#21446122C211yesmaximal, characteristic, complemented
6#21446121C211yesmaximal, characteristic, complemented
7#21446120C212yesmaximal, complemented
8#21446119C211yesmaximal, characteristic, complemented
9#21446118C212yesmaximal, complemented
10#339×D61C212yesmaximal, complemented
11C61×#1871C211yesmaximal, characteristic, complemented
12C2×#41×D61C2211yescharacteristic
13C23×C4×D61C2211yescharacteristic
14C22×#11758194C2211yescharacteristic, complemented
15C22×#11758189—21no—
16C2×M16×D61—28no—
17C2×M16×D61—21no—
18C2×M16×D61—21no—
19C2×M16×D61C2212yes—
20C2×M16×D61C2212yescomplemented
21C22×C8×D61—21no—
22#16840275C411yescharacteristic, complemented
23#16840275C411yescharacteristic, complemented
24#16840274C2211yescharacteristic
25#16840273C2211yescharacteristic
26#16840272C411yescharacteristic, complemented
27#16840272C411yescharacteristic, complemented
28#16840271—21no—
29#16840271—21no—
30#16840270—21no—
31#16840269C2211yescharacteristic
32#16840268—21no—
33#123×D61—21no—
34C22⋊Q8×D61C411yescharacteristic, complemented
35C22⋊Q8×D61C411yescharacteristic, complemented
36#121×D61C411yescharacteristic, complemented
37#121×D61C411yescharacteristic, complemented
38#120×D61—21no—
39C4×D4×D61—21no—
40C4×D4×D61—21no—
41#117×D61C2211yescharacteristic
42C2×C22⋊C4×D61—21no—
43C2×C42×D61C2212yes—
44C2×#14519705C2212yescomplemented
45C2×#14519704C2212yescomplemented
46C2×#14519703C2212yescomplemented
47#104×D61—28no—
48C22⋊C4×Dic61—21no—
49C4×#11758198C2212yescomplemented
50C4×C22⋊Dic61C2211yescharacteristic, complemented
51#16839609—21no—
52#95×D61—21no—
53#16839523C2212yescomplemented
54#16839522C2212yescomplemented
55#16839521C2212yescomplemented
56C22×M16×C61C2211yescharacteristic, complemented
57C61×#525C2211yescharacteristic
58C2×#104×C61C2212yescomplemented
59C4×C22⋊C4×C61C2211yescharacteristic, complemented
60C61×#339C2212yescomplemented
61C24×D61D411yescharacteristic
62C2×#11758226C2×C411yescharacteristic
63C2×#11758222—21no—
64C2×#11758222C2311yescharacteristic
65C2×#11758224—21no—
66C2×#11758224C2×C411yescharacteristic
67#41×D61—24no—
68#41×D61—24no—
69C2×Q8×D61C2×C411yescharacteristic
70C2×D4×D61—21no—
71C2×D4×D61—21no—
72C2×D4×D61—21no—
73C2×D4×D61C2×C411yescharacteristic
74C23×Dic61D411yescharacteristic
75C22×C4×D61—24no—
76C22×C4×D61—24no—
77C22×C4×D61—22no—
78C22×C4×D61—21no—
79C22×C4×D61C2×C411yescharacteristic
80C22×C4×D61C2×C411yescharacteristic
81C22×C4×D61C2×C411yescharacteristic
82C22×C4×D61C2×C411yescharacteristic
83C22×C4×D61D411yescharacteristic
84C22×C4×D61D411yescharacteristic
85C22×C4×D61D411yescharacteristic
86C22×C4×D61D411yescharacteristic
87C22×C4×D61D411yescharacteristic
88C22×C4×D61D411yescharacteristic
89C22×C4×D61C2311yescharacteristic
90C22×C4×D61C2311yescharacteristic
91C2×#11758194—21no—
92C2×#11758194—24no—
93C2×#11758194C2312yes—
94C2×#11758189—28no—
95C2×#11758189—22no—
96C2×#11758189—22no—
97M16×D61—28no—
98M16×D61—28no—
99M16×D61—24no—
100M16×D61—24no—
101M16×D61—24no—
102M16×D61D418yescomplemented
103C22×#92418—21no—
104C2×C8×D61—28no—
105C2×C8×D61—22no—
106C2×C8×D61—22no—
107#14519762—21no—
108#14519762—21no—
109#14519761—21no—
110#14519760—21no—
111#14519759—21no—
112#14519759—21no—
113#14519758—21no—
114#14519757C2×C411yescharacteristic, complemented
115#14519757C2×C411yescharacteristic, complemented
116#14519756C2×C411yescharacteristic, complemented
117#14519756C2×C411yescharacteristic, complemented
118#14519755—21no—
119#14519755—21no—
120#14519754—21no—
121#14519754—21no—
122#14519753C2×C411yescharacteristic, complemented
123#14519753C2×C411yescharacteristic, complemented
124#14519752C2×C411yescharacteristic, complemented
125#14519752C2×C411yescharacteristic, complemented
126#14519751C2×C411yescharacteristic, complemented
127#14519751C2×C411yescharacteristic, complemented
128#14519750—21no—
129#14519750—21no—
130#14519749—21no—
131#14519749—21no—
132#14519748C2×C411yescharacteristic, complemented
133#14519748C2×C411yescharacteristic, complemented
134#14519747—21no—
135#14519747—21no—
136#14519747—21no—
137#14519746—21no—
138#14519745—21no—
139#14519745—21no—
140#14519745—21no—
141C4×D244—21no—
142C4×D244—21no—
143D4×Dic61—21no—
144D4×Dic61—21no—
145#14519739—21no—
146#14519739—21no—
147C4×C22⋊D61—21no—
148C4×C22⋊D61—21no—
149C4×C22⋊D61—21no—
150C4×C22⋊D61—21no—
151#14519737—21no—
152#14519737—21no—
153#14519737—21no—
154#14519737—21no—
155#14519736C2311yescharacteristic
156#14519735C2×C411yescharacteristic
157#14519735C2×C411yescharacteristic
158#14519734—21no—
159#14519733—21no—
160C4⋊C4×D61—21no—
161C4⋊C4×D61—21no—
162C4⋊C4×D61C2×C411yescharacteristic
163C4⋊C4×D61C2×C411yescharacteristic
164C2×C22⋊Dic61—21no—
165C2×#11758198—22no—
166C22⋊C4×D61—28no—
167C22⋊C4×D61—21no—
168C22⋊C4×D61—21no—
169C22⋊C4×D61—21no—
170C22⋊C4×D61—21no—
171C22⋊C4×D61—21no—
172C2×C4×Dic61—22no—
173C2×C4×Dic61C2312yes—
174C42×D61—21no—
175C42×D61—24no—
176C42×D61—24no—
177#14519705—24no—
178#14519704—24no—
179#14519703—24no—
180#14519684—21no—
181#14519684—22no—
182C2×#41×C61C2311yescharacteristic
183C23×C4×C61C2311yescharacteristic
184C2×M16×C61—21no—
185C2×M16×C61—24no—
186C2×M16×C61C2312yes—
187C22×C8×C61—21no—
188#123×C61—21no—
189C22⋊Q8×C61C2×C411yescharacteristic, complemented
190C22⋊Q8×C61C2×C411yescharacteristic, complemented
191#121×C61C2×C411yescharacteristic, complemented
192#121×C61C2×C411yescharacteristic, complemented
193#120×C61—21no—
194C4×D4×C61—21no—
195C4×D4×C61—21no—
196#117×C61C2311yescharacteristic
197C2×C22⋊C4×C61—21no—
198C2×C42×C61C2312yes—
199#104×C61—24no—
200#95×C61—21no—
201C24×C61C2×D411yescharacteristic
202C23×D61—24no—
203C23×D61—24no—
204C23×D61—21no—
205C23×D61—42no—
206C23×D61C22⋊C411yescharacteristic
207C23×D61C22⋊C411yescharacteristic
208C23×D61C22⋊C411yescharacteristic
209C23×D61C22⋊C411yescharacteristic
210C23×D61C2×D411yescharacteristic
211C23×D61C2×D411yescharacteristic
212#41×C61—22no—
213#41×C61—22no—
214C2×Q8×C61C22×C411yescharacteristic
215C2×D4×C61—21no—
216C2×D4×C61—21no—
217C2×D4×C61—21no—
218C2×D4×C61C22×C411yescharacteristic
219C22×C4×C61—22no—
220C22×C4×C61—22no—
221C22×C4×C61—22no—
222C22×C4×C61—21no—
223C22×C4×C61C22×C411yescharacteristic
224C22×C4×C61C22×C411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2411yescharacteristic
229C2×C22⋊D61—21no—
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—21no—
233C2×C22⋊D61—21no—
234C2×C22⋊D61—21no—
235C2×C22⋊D61—21no—
236C22×Dic61—24no—
237C22×Dic61—22no—
238C22×Dic61—21no—
239C22×Dic61C22⋊C411yescharacteristic
240C22×Dic61C22⋊C411yescharacteristic
241C22×Dic61C22⋊C411yescharacteristic
242C22×Dic61C22⋊C411yescharacteristic
243C22×Dic61C2×D411yescharacteristic
244C22×Dic61C2×D411yescharacteristic
245#11758226—24no—
246Q8×D61—24no—
247#11758224—24no—
248#11758224—44no—
249D4×D61—24no—
250D4×D61—44no—
251D4×D61—44no—
252D4×D61—44no—
253#11758222—22no—
254#11758222—22no—
255#11758222—42no—
256#11758222—42no—
257C2×D244—21no—
258C2×D244—21no—
259C2×D244—21no—
260C2×D244C22×C411yescharacteristic
261C2×C4×D61—24no—
262C2×C4×D61—22no—
263C2×C4×D61—22no—
264C2×C4×D61—24no—
265C2×C4×D61—24no—
266C2×C4×D61—24no—
267C2×C4×D61—24no—
268C2×C4×D61—24no—
269C2×C4×D61—22no—
270C2×C4×D61—22no—
271C2×C4×D61—22no—
272C2×C4×D61—22no—
273C2×C4×D61—22no—
274C2×C4×D61—22no—
275C2×C4×D61—22no—
276C2×C4×D61—22no—
277C2×C4×D61—28no—
278C2×C4×D61—21no—
279C2×C4×D61—21no—
280C2×C4×D61—21no—
281C2×C4×D61—21no—
282C2×C4×D61—21no—
283C2×C4×D61—44no—
284C2×C4×D61—44no—
285C2×C4×D61—42no—
286C2×C4×D61—42no—
287C2×C4×D61C22⋊C411yescharacteristic
288C2×C4×D61C22⋊C411yescharacteristic
289C2×C4×D61C22⋊C411yescharacteristic
290C2×C4×D61C22⋊C411yescharacteristic
291C2×C4×D61C22⋊C411yescharacteristic
292C2×C4×D61C22⋊C411yescharacteristic
293C2×C4×D61C22⋊C411yescharacteristic
294C2×C4×D61C22⋊C411yescharacteristic
295C2×C4×D61C22×C411yescharacteristic
296C2×C4×D61C22×C411yescharacteristic
297C2×C4×D61C22×C411yescharacteristic
298C2×C4×D61C22×C411yescharacteristic
299C2×C4×D61C2×D411yescharacteristic
300C2×C4×D61C2×D411yescharacteristic
301C2×C4×D61C2×D414yes—
302C2×C4×D61C2×D411yescharacteristic
303C2×C4×D61C2×D411yescharacteristic
304C2×C4×D61#4114yes—
305C2×Dic122—21no—
306C2×Dic122C22×C411yescharacteristic
307M16×C61—24no—
308M16×C61—22no—
309M16×C61C2×D414yescomplemented
310C2×C8×C61—24no—
311C2×C8×C61—22no—
312C4⋊C4×C61—21no—
313C4⋊C4×C61—21no—
314C4⋊C4×C61C22×C411yescharacteristic
315C4⋊C4×C61C22×C411yescharacteristic
316C22⋊C4×C61—24no—
317C22⋊C4×C61—21no—
318C22⋊C4×C61—21no—
319C22⋊C4×C61—21no—
320C22⋊C4×C61—21no—
321C22⋊C4×C61—21no—
322C42×C61—21no—
323C42×C61—22no—
324C42×C61—22no—
325C22⋊Dic61—24no—
326C22⋊Dic61—21no—
327C22⋊Dic61—21no—
328C22⋊Dic61—21no—
329C22⋊Dic61—21no—
330C22⋊Dic61—21no—
331#11758198—28no—
332#11758198—21no—
333#11758198—21no—
334#11758198—21no—
335#11758198—21no—
336#11758198—21no—
337#11758198—21no—
338#11758198—21no—
339#11758198—21no—
340#11758198—21no—
341#11758198—21no—
342C4⋊Dic61—21no—
343C4⋊Dic61—21no—
344C4⋊Dic61C22×C411yescharacteristic
345C4⋊Dic61C22×C411yescharacteristic
346#11758196—21no—
347#11758196—21no—
348#11758196—21no—
349#11758196—21no—
350#11758196—21no—
351#11758196—21no—
352C4×Dic61—21no—
353C4×Dic61—21no—
354C4×Dic61—21no—
355C4×Dic61—22no—
356C4×Dic61—22no—
357C4×Dic61—44no—
358#11758194—24no—
359#11758194—22no—
360#11758194C2×D414yescomplemented
361C2×#92418—24no—
362C2×#92418—22no—
363#11758189—28no—
364#11758189—28no—
365C8×D61—28no—
366C8×D61—28no—
367C23×C61—22no—
368C23×C61—22no—
369C23×C61—21no—
370C23×C61—41no—
371C23×C61C2×C22⋊C411yescharacteristic
372C23×C61C2×C22⋊C411yescharacteristic
373C23×C61C22×D411yescharacteristic
374C22×D61—22no—
375C22×D61—22no—
376C22×D61—22no—
377C22×D61—22no—
378C22×D61—22no—
379C22×D61—22no—
380C22×D61—22no—
381C22×D61—22no—
382C22×D61—22no—
383C22×D61—22no—
384C22×D61—22no—
385C22×D61—22no—
386C22×D61—22no—
387C22×D61—21no—
388C22×D61—41no—
389C22×D61—41no—
390C22×D61—41no—
391C22×D61—416no—
392C22×D61—42no—
393C22×D61—42no—
394C22×D61—42no—
395C22×D61#10414yescomplemented
396C22×D61C2×C22⋊C411yescharacteristic
397C22×D61C2×C22⋊C411yescharacteristic
398C22×D61C2×C22⋊C411yescharacteristic
399C22×D61C2×C22⋊C411yescharacteristic
400C22×D61#12114yes—
401Q8×C61—22no—
402D4×C61—22no—
403D4×C61—42no—
404D4×C61—42no—
405D4×C61—42no—
406C2×C4×C61—22no—
407C2×C4×C61—22no—
408C2×C4×C61—22no—
409C2×C4×C61—21no—
410C2×C4×C61—21no—
411C2×C4×C61—21no—
412C2×C4×C61—21no—
413C2×C4×C61—24no—
414C2×C4×C61—21no—
415C2×C4×C61—21no—
416C2×C4×C61—21no—
417C2×C4×C61—42no—
418C2×C4×C61—42no—
419C2×C4×C61—41no—
420C2×C4×C61—41no—
421C2×C4×C61C2×C22⋊C411yescharacteristic
422C2×C4×C61C2×C22⋊C411yescharacteristic
423C2×C4×C61C23×C411yescharacteristic
424C2×C4×C61C22×D412yes—
425C2×C4×C61C22×D411yescharacteristic
426C2×C4×C61C2×#4112yes—
427C22⋊D61—42no—
428C22⋊D61—42no—
429C22⋊D61—42no—
430C22⋊D61—42no—
431C22⋊D61—42no—
432C22⋊D61—42no—
433C22⋊D61—42no—
434C2×Dic61—22no—
435C2×Dic61—22no—
436C2×Dic61—22no—
437C2×Dic61—22no—
438C2×Dic61—22no—
439C2×Dic61—24no—
440C2×Dic61—21no—
441C2×Dic61—21no—
442C2×Dic61—21no—
443C2×Dic61—42no—
444C2×Dic61—42no—
445C2×Dic61—42no—
446C2×Dic61C2×C22⋊C411yescharacteristic
447C2×Dic61C2×C22⋊C411yescharacteristic
448C2×Dic61C2×C22⋊C411yescharacteristic
449C2×Dic61C2×C22⋊C411yescharacteristic
450C2×Dic61#12114yes—
451D244—22no—
452D244—42no—
453D244—42no—
454D244—42no—
455C4×D61—22no—
456C4×D61—22no—
457C4×D61—22no—
458C4×D61—22no—
459C4×D61—22no—
460C4×D61—22no—
461C4×D61—21no—
462C4×D61—21no—
463C4×D61—21no—
464C4×D61—21no—
465C4×D61—22no—
466C4×D61—22no—
467C4×D61—22no—
468C4×D61—22no—
469C4×D61—416no—
470C4×D61—42no—
471C4×D61—42no—
472C4×D61—42no—
473C4×D61—41no—
474C4×D61—41no—
475C4×D61—42no—
476C4×D61C4×D414yes—
477C4×D61C4×D414yes—
478C4×D61#12012yes—
479C4×D61#12012yes—
480C4×D61#12312yes—
481C4×D61#12312yes—
482Dic122—22no—
483Dic122—42no—
484C8×C61—24no—
485#92418—24no—
486C2×#1871—611nomaximal, Sylow
487C22×C61—21no—
488C22×C61—21no—
489C22×C61—21no—
490C22×C61—21no—
491C22×C61—21no—
492C22×C61—21no—
493C22×C61—21no—
494C22×C61—44no—
495C22×C61—41no—
496C22×C61—41no—
497C22×C61—41no—
498C22×C61C2×#10412yescomplemented
499C22×C61C22×C22⋊C411yescharacteristic
500C22×C61C2×#12112yes—
501C2×D61—21no—
502C2×D61—21no—
503C2×D61—21no—
504C2×D61—21no—
505C2×D61—28no—
506C2×D61—28no—
507C2×D61—21no—
508C2×D61—21no—
509C2×D61—21no—
510C2×D61—44no—
511C2×D61—44no—
512C2×D61—44no—
513C2×D61—44no—
514C2×D61—41no—
515C2×D61—41no—
516C2×D61—41no—
517C2×D61—84no—
518C2×D61#38612yes—
519C2×D61#38612yes—
520C2×D61C2×#10412yes—
521C2×D61C2×#10412yescomplemented
522C2×D61#42112yes—
523C4×C61—21no—
524C4×C61—21no—
525C4×C61—44no—
526C4×C61—41no—
527C4×C61—41no—
528C4×C61—41no—
529C4×C61C2×C4×D412yes—
530C4×C61C2×#12011yescharacteristic
531C4×C61C2×#12311yescharacteristic
532Dic61—21no—
533Dic61—21no—
534Dic61—44no—
535Dic61—41no—
536Dic61—41no—
537Dic61—41no—
538Dic61#38612yes—
539Dic61#38612yes—
540C23×M16—611no—
541C2×#525—611no—
542C22×#104—612no—
543C2×C4×C22⋊C4—611no—
544#1871—612no—
545#1871—611no—
546#1871—612no—
547#1871—611no—
548#1871—611no—
549#1871D6111yescharacteristic, direct product factor
550C2×#339—612no—
551C2×C61—22no—
552C2×C61—22no—
553C2×C61—41no—
554C2×C61—81no—
555C2×C61C2×#38611yescharacteristic
556C2×C61C22×#10411yescharacteristic
557C2×C61C2×#42111yescharacteristic
558D61—22no—
559D61—22no—
560D61—41no—
561D61—81no—
562D61#187114yesdirect product factor
563C22×#41—611no—
564C24×C4—611no—
565C22×M16—612no—
566C22×M16—611no—
567C22×M16—612no—
568C22×M16—1221no—
569C22×M16—1228no—
570C22×M16—1221no—
571C22×M16—1221no—
572C22×M16C2×D6111yescharacteristic, complemented
573C23×C8—1221no—
574#525—611no—
575#525—611no—
576#525—611no—
577#525—611no—
578#525—611no—
579#525—611no—
580#525—611no—
581#525—1221no—
582#525—1221no—
583#525—1221no—
584#525—1221no—
585#525C2×D6111yescharacteristic
586C2×#123—1221no—
587C2×C22⋊Q8—611no—
588C2×C22⋊Q8—611no—
589C2×#121—611no—
590C2×#121—611no—
591C2×#120—1221no—
592C2×C4×D4—1221no—
593C2×C4×D4—1221no—
594C2×#117—611no—
595C22×C22⋊C4—1221no—
596C22×C42—612no—
597C2×#104—612no—
598C2×#104—612no—
599C2×#104—612no—
600C2×#104—1228no—
601C2×#104C2×D6112yescomplemented
602C4×C22⋊C4—611no—
603C4×C22⋊C4—612no—
604C4×C22⋊C4—1221no—
605C4×C22⋊C4—1221no—
606C4×C22⋊C4C2×D6111yescharacteristic, complemented
607C2×#95—1221no—
608#339—612no—
609#339—612no—
610#339—612no—
611#339C2×D6112yescomplemented
612C61C2×#187111yescharacteristic, complemented, Sylow
613C25—611no—
614C2×#41—611no—
615C2×#41—611no—
616C2×#41—611no—
617C2×#41—1221no—
618C2×#41—1221no—
619C2×#41—1224no—
620C2×#41—1224no—
621C2×#41C22×D6111yescharacteristic
622C22×Q8—611no—
623C22×D4—611no—
624C22×D4—1221no—
625C22×D4—1221no—
626C22×D4—1221no—
627C23×C4—611no—
628C23×C4—611no—
629C23×C4—611no—
630C23×C4—611no—
631C23×C4—611no—
632C23×C4—611no—
633C23×C4—611no—
634C23×C4—611no—
635C23×C4—611no—
636C23×C4—611no—
637C23×C4—611no—
638C23×C4—611no—
639C23×C4—611no—
640C23×C4—1224no—
641C23×C4—1224no—
642C23×C4—1221no—
643C23×C4—1222no—
644C23×C4C22×D6111yescharacteristic
645C2×M16—21no—
646C2×M16—24no—
647C2×M16—612no—
648C2×M16—618no—
649C2×M16—1222no—
650C2×M16—1222no—
651C2×M16—1228no—
652C2×M16—1224no—
653C2×M16—1224no—
654C2×M16—1228no—
655C2×M16—1228no—
656C2×M16—1224no—
657C2×M16—1221no—
658C2×M16—1224no—
659C2×M16C22×D6112yes—
660C22×C8—21no—
661C22×C8—1222no—
662C22×C8—1222no—
663C22×C8—1228no—
664C22×C8—1221no—
665#123—21no—
666#123—1221no—
667#123—1221no—
668#123—1221no—
669#123—1221no—
670#123—1221no—
671#123—1221no—
672#123—1221no—
673C22⋊Q8—611no—
674C22⋊Q8—611no—
675C22⋊Q8—611no—
676C22⋊Q8—611no—
677C22⋊Q8—611no—
678C22⋊Q8—611no—
679C22⋊Q8—1221no—
680C22⋊Q8—1221no—
681C22⋊Q8—1221no—
682C22⋊Q8—1221no—
683C22⋊Q8C4×D6111yescharacteristic, complemented
684C22⋊Q8C4×D6111yescharacteristic, complemented
685#121—611no—
686#121—611no—
687#121—611no—
688#121—611no—
689#121—611no—
690#121—611no—
691#121—1221no—
692#121—1221no—
693#121—1221no—
694#121—1221no—
695#121C4×D6111yescharacteristic, complemented
696#121C4×D6111yescharacteristic, complemented
697#120—21no—
698#120—1221no—
699#120—1221no—
700#120—1221no—
701#120—1221no—
702#120—1221no—
703#120—1221no—
704#120—1221no—
705C4×D4—21no—
706C4×D4—21no—
707C4×D4—1221no—
708C4×D4—1221no—
709C4×D4—1221no—
710C4×D4—1221no—
711C4×D4—1221no—
712C4×D4—1221no—
713C4×D4—1221no—
714C4×D4—1221no—
715C4×D4—1221no—
716C4×D4—1221no—
717C4×D4—1221no—
718C4×D4—1221no—
719C4×D4—1221no—
720C4×D4—1221no—
721#117—611no—
722#117—611no—
723#117—611no—
724#117—1221no—
725#117—1221no—
726#117C22×D6111yescharacteristic
727C2×C4⋊C4—611no—
728C2×C4⋊C4—611no—
729C2×C4⋊C4—1221no—
730C2×C4⋊C4—1221no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—1221no—
733C2×C22⋊C4—1221no—
734C2×C22⋊C4—1221no—
735C2×C22⋊C4—1221no—
736C2×C22⋊C4—1221no—
737C2×C22⋊C4—1228no—
738C2×C22⋊C4—1222no—
739C2×C22⋊C4—1221no—
740C2×C42—612no—
741C2×C42—1221no—
742C2×C42—1224no—
743C2×C42—1224no—
744C2×C42—1222no—
745C2×C42C22×D6112yes—
746#104—24no—
747#104—1224no—
748#104—1224no—
749#104—1224no—
750#95—21no—
751#95—1222no—
752#95—1221no—
753C24—611no—
754C24—611no—
755C24—611no—
756C24—611no—
757C24—611no—
758C24—611no—
759C24—1224no—
760C24—1224no—
761C24—1221no—
762C24—2442no—
763C24D4×D6111yescharacteristic
764#41—22no—
765#41—22no—
766#41—1224no—
767#41—1224no—
768#41—1222no—
769#41—1222no—
770#41—2442no—
771#41—2442no—
772#41—2444no—
773C2×Q8—611no—
774C2×Q8—1221no—
775C2×Q8—1224no—
776C2×Q8C2×C4×D6111yescharacteristic
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—611no—
781C2×D4—1221no—
782C2×D4—1221no—
783C2×D4—1221no—
784C2×D4—1224no—
785C2×D4—1221no—
786C2×D4—1221no—
787C2×D4—1221no—
788C2×D4—1221no—
789C2×D4—1221no—
790C2×D4—1221no—
791C2×D4—1221no—
792C2×D4—2444no—
793C2×D4—2444no—
794C2×D4—2444no—
795C2×D4C2×C4×D6111yescharacteristic
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—21no—
800C22×C4—611no—
801C22×C4—611no—
802C22×C4—611no—
803C22×C4—614no—
804C22×C4—611no—
805C22×C4—611no—
806C22×C4—614no—
807C22×C4—611no—
808C22×C4—611no—
809C22×C4—611no—
810C22×C4—611no—
811C22×C4—611no—
812C22×C4—611no—
813C22×C4—611no—
814C22×C4—611no—
815C22×C4—611no—
816C22×C4—611no—
817C22×C4—611no—
818C22×C4—611no—
819C22×C4—611no—
820C22×C4—611no—
821C22×C4—611no—
822C22×C4—611no—
823C22×C4—611no—
824C22×C4—1222no—
825C22×C4—1222no—
826C22×C4—1222no—
827C22×C4—1222no—
828C22×C4—1224no—
829C22×C4—1224no—
830C22×C4—1224no—
831C22×C4—1224no—
832C22×C4—1224no—
833C22×C4—1222no—
834C22×C4—1222no—
835C22×C4—1222no—
836C22×C4—1222no—
837C22×C4—1221no—
838C22×C4—1224no—
839C22×C4—1221no—
840C22×C4—1221no—
841C22×C4—1221no—
842C22×C4—1228no—
843C22×C4—1224no—
844C22×C4—1221no—
845C22×C4—1222no—
846C22×C4—1222no—
847C22×C4—1222no—
848C22×C4—1221no—
849C22×C4—2442no—
850C22×C4—2442no—
851C22×C4—2444no—
852C22×C4—2444no—
853C22×C4C2×C4×D6111yescharacteristic
854C22×C4C2×C4×D6111yescharacteristic
855C22×C4D4×D6111yescharacteristic
856C22×C4D4×D6111yescharacteristic
857C22×C4D4×D6111yescharacteristic
858C22×C4C23×D6111yescharacteristic
859M16—24no—
860M16—22no—
861M16—614no—
862M16—1228no—
863M16—1228no—
864M16—1224no—
865M16—1222no—
866M16D4×D6114yescomplemented
867C2×C8—24no—
868C2×C8—22no—
869C2×C8—1228no—
870C2×C8—1228no—
871C2×C8—1224no—
872C2×C8—1222no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—611no—
876C4⋊C4—611no—
877C4⋊C4—1221no—
878C4⋊C4—1221no—
879C4⋊C4—1221no—
880C4⋊C4—1221no—
881C4⋊C4—1221no—
882C4⋊C4—1221no—
883C4⋊C4—1221no—
884C4⋊C4—1221no—
885C4⋊C4C2×C4×D6111yescharacteristic
886C4⋊C4C2×C4×D6111yescharacteristic
887C22⋊C4—24no—
888C22⋊C4—21no—
889C22⋊C4—21no—
890C22⋊C4—21no—
891C22⋊C4—21no—
892C22⋊C4—21no—
893C22⋊C4—1221no—
894C22⋊C4—1221no—
895C22⋊C4—1221no—
896C22⋊C4—1221no—
897C22⋊C4—1221no—
898C22⋊C4—1221no—
899C22⋊C4—1221no—
900C22⋊C4—1221no—
901C22⋊C4—1228no—
902C22⋊C4—1221no—
903C22⋊C4—1221no—
904C22⋊C4—1224no—
905C22⋊C4—1221no—
906C22⋊C4—1221no—
907C22⋊C4—1221no—
908C22⋊C4—1221no—
909C22⋊C4—1221no—
910C42—21no—
911C42—22no—
912C42—22no—
913C42—1221no—
914C42—1221no—
915C42—1221no—
916C42—1222no—
917C42—1222no—
918C42—2444no—
919C23—22no—
920C23—22no—
921C23—21no—
922C23—41no—
923C23—611no—
924C23—611no—
925C23—611no—
926C23—614no—
927C23—614no—
928C23—611no—
929C23—1222no—
930C23—1222no—
931C23—1222no—
932C23—1222no—
933C23—1222no—
934C23—1222no—
935C23—1222no—
936C23—1222no—
937C23—1222no—
938C23—1222no—
939C23—1222no—
940C23—1222no—
941C23—1222no—
942C23—1221no—
943C23—2441no—
944C23—2441no—
945C23—2441no—
946C23—2442no—
947C23—2442no—
948C23—2442no—
949C23—24416no—
950C23C22⋊C4×D6111yescharacteristic
951C23C22⋊C4×D6111yescharacteristic
952C23C2×D4×D6111yescharacteristic
953Q8—22no—
954Q8—1222no—
955Q8—2442no—
956D4—22no—
957D4—42no—
958D4—42no—
959D4—42no—
960D4—1222no—
961D4—2442no—
962D4—2442no—
963D4—2442no—
964D4—2442no—
965D4—2442no—
966D4—2442no—
967D4—2442no—
968D4—2442no—
969D4—2442no—
970D4—2442no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—24no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—42no—
983C2×C4—42no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—611no—
987C2×C4—611no—
988C2×C4—614no—
989C2×C4—614no—
990C2×C4—614no—
991C2×C4—612no—
992C2×C4—612no—
993C2×C4—612no—
994C2×C4—612no—
995C2×C4—611no—
996C2×C4—611no—
997C2×C4—1222no—
998C2×C4—1222no—
999C2×C4—1222no—
1000C2×C4—1222no—
1001C2×C4—1222no—
1002C2×C4—1222no—
1003C2×C4—1222no—
1004C2×C4—1222no—
1005C2×C4—1222no—
1006C2×C4—1222no—
1007C2×C4—1222no—
1008C2×C4—1222no—
1009C2×C4—1222no—
1010C2×C4—1222no—
1011C2×C4—1222no—
1012C2×C4—1221no—
1013C2×C4—1221no—
1014C2×C4—1221no—
1015C2×C4—1221no—
1016C2×C4—1224no—
1017C2×C4—1221no—
1018C2×C4—1221no—
1019C2×C4—1221no—
1020C2×C4—2442no—
1021C2×C4—2442no—
1022C2×C4—2442no—
1023C2×C4—2442no—
1024C2×C4—24416no—
1025C2×C4—2442no—
1026C2×C4—2442no—
1027C2×C4—2442no—
1028C2×C4—2441no—
1029C2×C4—2441no—
1030C2×C4C22⋊C4×D6111yescharacteristic
1031C2×C4C22⋊C4×D6111yescharacteristic
1032C2×C4C22×C4×D6111yescharacteristic
1033C2×C4C2×D4×D6112yes—
1034C2×C4C2×D4×D6111yescharacteristic
1035C2×C4#41×D6112yes—
1036C8—24no—
1037C8—1224no—
1038C22—21no—
1039C22—21no—
1040C22—21no—
1041C22—21no—
1042C22—21no—
1043C22—21no—
1044C22—21no—
1045C22—44no—
1046C22—41no—
1047C22—41no—
1048C22—41no—
1049C22—612no—
1050C22—612no—
1051C22—612no—
1052C22—612no—
1053C22—612no—
1054C22—1228no—
1055C22—1228no—
1056C22—1221no—
1057C22—1221no—
1058C22—1221no—
1059C22—1221no—
1060C22—1221no—
1061C22—1221no—
1062C22—1221no—
1063C22—4884no—
1064C22—2444no—
1065C22—2444no—
1066C22—2444no—
1067C22—2444no—
1068C22—2441no—
1069C22—2441no—
1070C22—2441no—
1071C22#104×D6112yescomplemented
1072C22C2×C22⋊C4×D6111yescharacteristic
1073C22#121×D6112yes—
1074C4—21no—
1075C4—21no—
1076C4—44no—
1077C4—41no—
1078C4—41no—
1079C4—41no—
1080C4—612no—
1081C4—612no—
1082C4—1221no—
1083C4—1221no—
1084C4—2444no—
1085C4—2441no—
1086C4—2441no—
1087C4—2441no—
1088C4C4×D4×D6112yes—
1089C4#120×D6111yescharacteristic
1090C4#123×D6111yescharacteristic
1091C2—22no—
1092C2—22no—
1093C2—41no—
1094C2—81no—
1095C2—614no—
1096C2—1222no—
1097C2—1222no—
1098C2—4881no—
1099C2—2441no—
1100C2#386×D6111yescharacteristic
1101C2C2×#104×D6111yescharacteristic
1102C2#421×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1871C2
socleC22×C61C22×C22⋊C4
prime radical#525×D61C2
cosocleC22×C4×C61C24
hypercenter#1871D61
hypocenterC61C2×#1871
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1871

Complements

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

NH ≅ G/Ntype
1. C22×M16×D61C2semidirect
3. C2×#104×D61C2semidirect
4. C4×C22⋊C4×D61C2semidirect
5. #21446122C2semidirect
6. #21446121C2semidirect
7. #21446120C2semidirect
8. #21446119C2semidirect
9. #21446118C2semidirect
10. #339×D61C2semidirect
11. C61×#1871C2semidirect
14. C22×#11758194C22semidirect
20. C2×M16×D61C22semidirect
22. #16840275C4semidirect
23. #16840275C4semidirect
26. #16840272C4semidirect
27. #16840272C4semidirect
34. C22⋊Q8×D61C4semidirect
35. C22⋊Q8×D61C4semidirect
36. #121×D61C4semidirect
37. #121×D61C4semidirect
44. C2×#14519705C22semidirect
45. C2×#14519704C22semidirect
46. C2×#14519703C22semidirect
49. C4×#11758198C22semidirect
50. C4×C22⋊Dic61C22semidirect
53. #16839523C22semidirect
54. #16839522C22semidirect
55. #16839521C22semidirect
56. C22×M16×C61C22semidirect
58. C2×#104×C61C22semidirect
59. C4×C22⋊C4×C61C22semidirect
60. C61×#339C22semidirect
102. M16×D61D4semidirect
114. #14519757C2×C4semidirect
115. #14519757C2×C4semidirect
116. #14519756C2×C4semidirect
117. #14519756C2×C4semidirect
122. #14519753C2×C4semidirect
123. #14519753C2×C4semidirect
124. #14519752C2×C4semidirect
125. #14519752C2×C4semidirect
126. #14519751C2×C4semidirect
127. #14519751C2×C4semidirect
132. #14519748C2×C4semidirect
133. #14519748C2×C4semidirect
189. C22⋊Q8×C61C2×C4semidirect
190. C22⋊Q8×C61C2×C4semidirect
191. #121×C61C2×C4semidirect
192. #121×C61C2×C4semidirect
309. M16×C61C2×D4semidirect
360. #11758194C2×D4semidirect
395. C22×D61#104semidirect
498. C22×C61C2×#104semidirect
521. C2×D61C2×#104semidirect
549. #1871D61direct (N × H)
562. D61#1871direct (N × H)
572. C22×M16C2×D61semidirect
601. C2×#104C2×D61semidirect
606. C4×C22⋊C4C2×D61semidirect
611. #339C2×D61semidirect
612. C61C2×#1871semidirect
683. C22⋊Q8C4×D61semidirect
684. C22⋊Q8C4×D61semidirect
695. #121C4×D61semidirect
696. #121C4×D61semidirect
866. M16D4×D61semidirect
1071. C22#104×D61semidirect

Maximal subgroups

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

subgroupindex
C22×M16×D612
#525×D612
C2×#104×D612
C4×C22⋊C4×D612
#214461222
#214461212
#214461202
#214461192
#214461182
#339×D612
C61×#18712
C2×#187161