Finite Group Databasebeta

← #30609909

Subgroups — #30609909

Order 15616.

1314 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#431C212yesmaximal, complemented
2#21461061C212yesmaximal, complemented
3#21461058C212yesmaximal, complemented
4#21461056C212yesmaximal, complemented
5#21461054C212yesmaximal, complemented
6#21461052C212yesmaximal, complemented
7#21461050C212yesmaximal, complemented
8C2×C4×#11758222C211yesmaximal, characteristic
9#16840781—22no—
10#16840780—22no—
11#16840779C2214yes—
12#16840778C2214yes—
13D61⋊(C4⋊C8)—22no—
14D61⋊(C22⋊C8)C2214yes—
15C4×D61⋊C8—22no—
16#16840608C2214yes—
17#16840607C2214yes—
18#16840606C2214yes—
19#16840605C2214yes—
20C22×#11758222C411yescharacteristic
21C4×#11758222—22no—
22C4×#11758222—22no—
23C4×#11758222—22no—
24C4×#11758222—22no—
25C2×C4×Dic122C411yescharacteristic
26C2×C4×Dic122C2211yescharacteristic
27C2×C4×D244C411yescharacteristic
28C2×C4×D244C2211yescharacteristic
29C2×C4×C22⋊D61C411yescharacteristic
30C2×C4×C22⋊D61C411yescharacteristic
31C2×C4×C22⋊D61C2211yescharacteristic
32C2×C4×C22⋊D61C2211yescharacteristic
33C2×#14519736C2211yescharacteristic
34C2×#14519734C411yescharacteristic
35C2×#14519734C2211yescharacteristic
36C2×C42×D61C411yescharacteristic
37C2×C42×D61C2211yescharacteristic
38C22×C42×C61C411yescharacteristic
39C2×D61⋊C8—24no—
40#14519844—24no—
41C4⋊#92420—24no—
42#14519834—24no—
43C22⋊#92420C2318yes—
44C4×#92420—24no—
45C4×#92420—24no—
46C2×#11758222—22no—
47C2×#11758222—22no—
48C2×#11758222—24no—
49C2×#11758222C818yescomplemented
50C22×Dic122C2×C411yescharacteristic
51C22×D244C2×C411yescharacteristic
52C22×C22⋊D61C2×C411yescharacteristic
53C22×C22⋊D61C2×C411yescharacteristic
54C22×C4×D61C2×C411yescharacteristic
55C22×C4×D61C2×C411yescharacteristic
56C22×C4×D61C2×C411yescharacteristic
57C22×C4×D61C2×C411yescharacteristic
58C22×C4×D61C2×C411yescharacteristic
59C22×C4×D61C2311yescharacteristic
60C4×Dic122—22no—
61C4×Dic122—22no—
62C4×Dic122—22no—
63C4×Dic122—22no—
64C4×D244—22no—
65C4×D244—22no—
66C4×D244—22no—
67C4×D244—22no—
68C4×C22⋊D61—22no—
69C4×C22⋊D61—22no—
70C4×C22⋊D61—22no—
71C4×C22⋊D61—22no—
72C4×C22⋊D61—22no—
73C4×C22⋊D61—22no—
74C4×C22⋊D61—22no—
75C4×C22⋊D61—22no—
76#14519736—22no—
77#14519736—22no—
78#14519734—22no—
79#14519734—22no—
80#14519734—22no—
81#14519734—22no—
82C2×C4⋊Dic61C2×C411yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×#11758196C2×C411yescharacteristic
85C2×#11758196C2×C411yescharacteristic
86C2×#11758196C2×C411yescharacteristic
87C2×#11758196C2311yescharacteristic
88C2×C22⋊Dic61C2×C411yescharacteristic
89C2×C22⋊Dic61C2311yescharacteristic
90C2×#11758198C2×C411yescharacteristic
91C2×#11758198C2×C411yescharacteristic
92C2×#11758198C2×C411yescharacteristic
93C2×#11758198C2311yescharacteristic
94C2×C4×Dic61C2×C411yescharacteristic
95C2×C4×Dic61C2×C411yescharacteristic
96C2×C4×Dic61C2×C411yescharacteristic
97C2×C4×Dic61C2×C411yescharacteristic
98C2×C4×Dic61C2311yescharacteristic
99C2×C4×Dic61C2311yescharacteristic
100C42×D61—21no—
101C42×D61—21no—
102C42×D61—21no—
103C42×D61—21no—
104C42×D61D412yes—
105C42×D61D412yes—
106C42×D61D412yes—
107C42×D61D412yes—
108C23×C4×C61C2×C411yescharacteristic
109C23×C4×C61C2×C411yescharacteristic
110C23×C4×C61C2×C411yescharacteristic
111C2×C42×C61—21no—
112C2×C42×C61—21no—
113C2×C42×C61—21no—
114C2×C42×C61—21no—
115C2×C42×C61C2×C411yescharacteristic
116C2×C42×C61C2×C411yescharacteristic
117C2×C42×C61C2×C411yescharacteristic
118C2×C42×C61C2×C411yescharacteristic
119C24×C61C22×C411yescharacteristic
120C23×D61C22×C411yescharacteristic
121C23×D61C22×C411yescharacteristic
122C22×C4×C61—21no—
123C22×C4×C61—21no—
124C22×C4×C61—22no—
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—42no—
130C22×C4×C61—42no—
131C22×C4×C61C2×C814yescomplemented
132C22×C4×C61C22×C411yescharacteristic
133C22×C4×C61C22×C411yescharacteristic
134C22×C4×C61C22×C411yescharacteristic
135C22×C4×C61C22×C411yescharacteristic
136C22×C4×C61C22×C411yescharacteristic
137C22×C4×C61C22×C411yescharacteristic
138C2×C22⋊D61—22no—
139C2×C22⋊D61—22no—
140C2×C22⋊D61—22no—
141C2×C22⋊D61—22no—
142C2×C22⋊D61C2×C814yes—
143C2×C22⋊D61C2×C814yescomplemented
144C22×Dic61C22×C411yescharacteristic
145C22×Dic61C22×C411yescharacteristic
146C22×Dic61C22×C411yescharacteristic
147C22×Dic61C22×C411yescharacteristic
148C22×Dic61C22×C411yescharacteristic
149C22×Dic61C2411yescharacteristic
150#11758222—216no—
151#11758222—216no—
152C2×D244—22no—
153C2×D244—22no—
154C2×D244C2×C814yes—
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×C4×D61—22no—
158C2×C4×D61—21no—
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×C4×D61—42no—
163C2×C4×D61—42no—
164C2×C4×D61—42no—
165C2×C4×D61—42no—
166C2×C4×D61C22⋊C412yes—
167C2×C4×D61C22⋊C412yes—
168C2×C4×D61C22⋊C412yes—
169C2×C4×D61C22⋊C412yes—
170C2×C4×D61C2×C814yes—
171C2×C4×D61C2×C814yescomplemented
172C2×C4×D61M1614yes—
173C2×C4×D61C2×D412yes—
174C2×C4×D61C2×D412yes—
175C2×Dic122—22no—
176C2×Dic122—22no—
177C2×Dic122C2×C814yescomplemented
178C2×#92420—28no—
179D61⋊C8—48no—
180C42×C61—21no—
181C42×C61—21no—
182C42×C61—21no—
183C42×C61—21no—
184C42×C61—21no—
185C42×C61—21no—
186C42×C61C22⋊C411yescharacteristic
187C42×C61C22⋊C411yescharacteristic
188C42×C61C22⋊C411yescharacteristic
189C42×C61C22⋊C411yescharacteristic
190C22⋊Dic61—22no—
191C22⋊Dic61—22no—
192#11758198—22no—
193#11758198—22no—
194#11758198—22no—
195#11758198—22no—
196C4⋊Dic61—22no—
197C4⋊Dic61—22no—
198#11758196—22no—
199#11758196—22no—
200#11758196—22no—
201#11758196—22no—
202C4×Dic61—21no—
203C4×Dic61—21no—
204C4×Dic61—21no—
205C4×Dic61—21no—
206C4×Dic61—21no—
207C4×Dic61—21no—
208C4×Dic61C22⋊C412yes—
209C4×Dic61C22⋊C412yes—
210C4×Dic61C2×D412yes—
211C4×Dic61C2×D412yes—
212C4×Dic61C2×D412yes—
213C4×Dic61C2×D412yes—
214C23×C61—21no—
215C23×C61—21no—
216C23×C61—41no—
217C23×C61—41no—
218C23×C61C22×C812yes—
219C23×C61C23×C411yescharacteristic
220C22×D61—21no—
221C22×D61—21no—
222C22×D61—41no—
223C22×D61—41no—
224C22×D61—41no—
225C22×D61—41no—
226C22×D61C2×C22⋊C412yes—
227C22×D61C22×C812yes—
228C22×D61C22×C812yes—
229C22×D61C2×M1612yes—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—24no—
233C2×C4×C61—24no—
234C2×C4×C61—22no—
235C2×C4×C61—22no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—42no—
239C2×C4×C61—42no—
240C2×C4×C61—42no—
241C2×C4×C61—42no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61C2×C22⋊C411yescharacteristic
245C2×C4×C61C2×C22⋊C411yescharacteristic
246C2×C4×C61C2×C22⋊C411yescharacteristic
247C2×C4×C61C2×C22⋊C411yescharacteristic
248C2×C4×C61C2×C22⋊C411yescharacteristic
249C2×C4×C61C2×C22⋊C411yescharacteristic
250C2×C4×C61C22×C812yes—
251C2×C4×C61C22×C812yes—
252C2×C4×C61C2×M1612yes—
253C22⋊D61—28no—
254C22⋊D61—28no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61C2×C22⋊C412yes—
264C2×Dic61C2×C22⋊C412yes—
265C2×Dic61C22×C812yes—
266C2×Dic61C22×C812yes—
267C2×Dic61C2×M1612yes—
268C2×Dic61C22×D412yes—
269D244—28no—
270C4×D61—24no—
271C4×D61—24no—
272C4×D61—24no—
273C4×D61—24no—
274C4×D61—42no—
275C4×D61—42no—
276C4×D61—42no—
277C4×D61—42no—
278C4×D61—42no—
279C4×D61—42no—
280C4×D61C22⋊C818yes—
281C4×D61C22⋊C818yes—
282Dic122—28no—
283#92420—48no—
284#17349—611nomaximal, Sylow
285C22×C61—21no—
286C22×C61—21no—
287C22×C61—22no—
288C22×C61—42no—
289C22×C61—42no—
290C22×C61—41no—
291C22×C61—41no—
292C22×C61C22×C22⋊C411yescharacteristic
293C22×C61C23×C811yescharacteristic
294C22×C61C22×M1611yescharacteristic
295C2×D61—22no—
296C2×D61—22no—
297C2×D61—22no—
298C2×D61—42no—
299C2×D61—42no—
300C2×D61—42no—
301C2×D61—41no—
302C2×D61—41no—
303C2×D61—42no—
304C2×D61C2×C22⋊C814yes—
305C4×C61—22no—
306C4×C61—21no—
307C4×C61—21no—
308C4×C61—41no—
309C4×C61—41no—
310C4×C61C2×C22⋊C812yes—
311C4×C61C2×C22⋊C812yes—
312C4×C61#41012yes—
313C4×C61#41312yes—
314Dic61—22no—
315Dic61—22no—
316Dic61—22no—
317Dic61—41no—
318Dic61—41no—
319Dic61C2×C22⋊C814yes—
320C2×C4×#41—611no—
321C2×#431—612no—
322#1461—612no—
323#1460—612no—
324#1459—612no—
325#1459—612no—
326#1458—612no—
327#1458—612no—
328C2×C61—21no—
329C2×C61—21no—
330C2×C61—42no—
331C2×C61C22×C22⋊C811yescharacteristic
332C2×C61C2×#41011yescharacteristic
333C2×C61C2×#41311yescharacteristic
334D61—24no—
335D61—42no—
336C22×#41—611no—
337C4×#41—1222no—
338C4×#41—1222no—
339C4×#41—1222no—
340C4×#41—1222no—
341C2×C4×Q8—611no—
342C2×C4×Q8—611no—
343C2×C4×D4—611no—
344C2×C4×D4—611no—
345C2×C4×D4—611no—
346C2×C4×D4—611no—
347C2×C4×D4—611no—
348C2×C4×D4—611no—
349C2×#117—611no—
350C2×#117—611no—
351C2×#117—611no—
352C22×C42—611no—
353C22×C42—611no—
354C22×C42#692311yescharacteristic
355#431—614no—
356#431—614no—
357#431—1222no—
358#431—1222no—
359C2×C4⋊C8—1222no—
360C2×C22⋊C8—614no—
361C2×C4×C8—1222no—
362#324—614no—
363#324—614no—
364#323—614no—
365#323—614no—
366C61#1734911yescharacteristic, complemented, Sylow
367C2×#41—618no—
368C2×#41—1222no—
369C2×#41—1222no—
370C2×#41—1224no—
371C22×Q8—611no—
372C22×D4—611no—
373C22×D4—611no—
374C22×D4—611no—
375C23×C4—611no—
376C23×C4—611no—
377C23×C4—611no—
378C23×C4—611no—
379C23×C4—611no—
380C23×C4—611no—
381C23×C4C2×#692311yescharacteristic
382C23×C4C2×#692311yescharacteristic
383C23×C4C2×#692311yescharacteristic
384C22×C8—1224no—
385C4×Q8—1222no—
386C4×Q8—1222no—
387C4×Q8—1222no—
388C4×Q8—1222no—
389C4×D4—1222no—
390C4×D4—1222no—
391C4×D4—1222no—
392C4×D4—1222no—
393C4×D4—1222no—
394C4×D4—1222no—
395C4×D4—1222no—
396C4×D4—1222no—
397C4×D4—1222no—
398C4×D4—1222no—
399C4×D4—1222no—
400C4×D4—1222no—
401#117—1222no—
402#117—1222no—
403#117—1222no—
404#117—1222no—
405#117—1222no—
406#117—1222no—
407C2×C4⋊C4—611no—
408C2×C4⋊C4—611no—
409C2×C4⋊C4—611no—
410C2×C4⋊C4—611no—
411C2×C4⋊C4—611no—
412C2×C4⋊C4—611no—
413C2×C22⋊C4—611no—
414C2×C22⋊C4—611no—
415C2×C22⋊C4—611no—
416C2×C22⋊C4—611no—
417C2×C22⋊C4—611no—
418C2×C22⋊C4—611no—
419C2×C42—21no—
420C2×C42—21no—
421C2×C42—21no—
422C2×C42—21no—
423C2×C42—611no—
424C2×C42—611no—
425C2×C42—611no—
426C2×C42—612no—
427C2×C42—612no—
428C2×C42—612no—
429C2×C42—612no—
430C2×C42—611no—
431C2×C42—611no—
432C2×C42—611no—
433C2×C42—1221no—
434C2×C42—1221no—
435C2×C42—1221no—
436C2×C42—1221no—
437C2×C42C2×#692311yescharacteristic
438C2×C42C2×#692311yescharacteristic
439C2×C42C2×#692311yescharacteristic
440C2×C42C2×#692311yescharacteristic
441C4⋊C8—1224no—
442C4⋊C8—1224no—
443C22⋊C8—618no—
444C22⋊C8—1224no—
445C4×C8—1224no—
446C4×C8—1224no—
447C24—611no—
448C24—611no—
449C24C22×#692311yescharacteristic
450#41—12216no—
451#41—12216no—
452C2×Q8—614no—
453C2×Q8—1222no—
454C2×Q8—1222no—
455C2×D4—614no—
456C2×D4—614no—
457C2×D4—614no—
458C2×D4—1222no—
459C2×D4—1222no—
460C2×D4—1222no—
461C2×D4—1222no—
462C2×D4—1222no—
463C2×D4—1222no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—611no—
474C22×C4—612no—
475C22×C4—612no—
476C22×C4—614no—
477C22×C4—614no—
478C22×C4—611no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—612no—
482C22×C4—612no—
483C22×C4—614no—
484C22×C4—612no—
485C22×C4—612no—
486C22×C4—611no—
487C22×C4—611no—
488C22×C4—1221no—
489C22×C4—1221no—
490C22×C4—1222no—
491C22×C4—1221no—
492C22×C4—1221no—
493C22×C4—1221no—
494C22×C4—1221no—
495C22×C4—2442no—
496C22×C4—2442no—
497C22×C4—2442no—
498C22×C4—2442no—
499C22×C4D61⋊C814yescomplemented
500C22×C4C22×#692311yescharacteristic
501C22×C4C22×#692311yescharacteristic
502C22×C4C22×#692311yescharacteristic
503C22×C4C22×#692311yescharacteristic
504C22×C4C22×#692311yescharacteristic
505C22×C4C22×#692311yescharacteristic
506C2×C8—1228no—
507C2×C8—2448no—
508C4⋊C4—1222no—
509C4⋊C4—1222no—
510C4⋊C4—1222no—
511C4⋊C4—1222no—
512C4⋊C4—1222no—
513C4⋊C4—1222no—
514C22⋊C4—1222no—
515C22⋊C4—1222no—
516C22⋊C4—1222no—
517C22⋊C4—1222no—
518C22⋊C4—1222no—
519C22⋊C4—1222no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42—612no—
527C42—612no—
528C42—612no—
529C42—612no—
530C42—612no—
531C42—612no—
532C42—1221no—
533C42—1221no—
534C42—1221no—
535C42—1221no—
536C42—1221no—
537C42—1221no—
538C42C22⋊#692311yescharacteristic
539C42C22⋊#692311yescharacteristic
540C42C22⋊#692311yescharacteristic
541C42C22⋊#692311yescharacteristic
542C23—21no—
543C23—21no—
544C23—41no—
545C23—41no—
546C23—612no—
547C23—612no—
548C23—612no—
549C23—612no—
550C23—1221no—
551C23—1221no—
552C23—2441no—
553C23—2441no—
554C23—2441no—
555C23—2441no—
556C23C2×D61⋊C812yes—
557C23C23×#692311yescharacteristic
558Q8—1228no—
559D4—1228no—
560D4—1228no—
561D4—1228no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—612no—
577C2×C4—612no—
578C2×C4—612no—
579C2×C4—618no—
580C2×C4—618no—
581C2×C4—612no—
582C2×C4—612no—
583C2×C4—612no—
584C2×C4—1221no—
585C2×C4—1221no—
586C2×C4—1224no—
587C2×C4—1224no—
588C2×C4—1224no—
589C2×C4—1224no—
590C2×C4—1221no—
591C2×C4—1221no—
592C2×C4—2442no—
593C2×C4—2442no—
594C2×C4—2442no—
595C2×C4—2442no—
596C2×C4—2441no—
597C2×C4—2441no—
598C2×C4—2442no—
599C2×C4—2442no—
600C2×C4—2441no—
601C2×C4—2441no—
602C2×C4C2×C22⋊#692311yescharacteristic
603C2×C4C2×C22⋊#692311yescharacteristic
604C2×C4C2×C22⋊#692311yescharacteristic
605C2×C4C2×C22⋊#692311yescharacteristic
606C2×C4C2×C22⋊#692311yescharacteristic
607C2×C4C2×C22⋊#692311yescharacteristic
608C2×C4C2×D61⋊C812yes—
609C2×C4C2×D61⋊C812yes—
610C2×C4D61⋊M1612yes—
611C8—2448no—
612C22—21no—
613C22—21no—
614C22—22no—
615C22—42no—
616C22—42no—
617C22—41no—
618C22—41no—
619C22—614no—
620C22—1222no—
621C22—1222no—
622C22—1222no—
623C22—2442no—
624C22—2442no—
625C22—2442no—
626C22—2442no—
627C22—2441no—
628C22—2441no—
629C22C22×C22⋊#692311yescharacteristic
630C22C22×D61⋊C811yescharacteristic
631C22C2×D61⋊M1611yescharacteristic
632C4—22no—
633C4—21no—
634C4—21no—
635C4—41no—
636C4—41no—
637C4—614no—
638C4—1222no—
639C4—1222no—
640C4—1222no—
641C4—2441no—
642C4—2441no—
643C4D61⋊(C22⋊C8)12yes—
644C4D61⋊(C22⋊C8)12yes—
645C4#1684074112yes—
646C4#1684074812yes—
647C2—21no—
648C2—21no—
649C2—42no—
650C2—1224no—
651C2—2442no—
652C2C2×D61⋊(C22⋊C8)11yescharacteristic
653C2C2×#1684074111yescharacteristic
654C2C2×#1684074811yescharacteristic
subgroupG/H
centerC42C22⋊#6923
commutatorC22×C61C23×C8
FrattiniC23C23×#6923
FittingC22×C42×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC22×#11758222C4
cosocleC22×Dic61C24
hypercenterC22×C42#6923
hypocenterC61#17349
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C42 ◁ C2×C42 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
1. D61⋊#431C2semidirect
2. #21461061C2semidirect
3. #21461058C2semidirect
4. #21461056C2semidirect
5. #21461054C2semidirect
6. #21461052C2semidirect
7. #21461050C2semidirect
49. C2×#11758222C8semidirect
131. C22×C4×C61C2×C8semidirect
143. C2×C22⋊D61C2×C8semidirect
171. C2×C4×D61C2×C8semidirect
177. C2×Dic122C2×C8semidirect
366. C61#17349semidirect
499. C22×C4D61⋊C8semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4312
#214610612
#214610582
#214610562
#214610542
#214610522
#214610502
C2×C4×#117582222
#1734961