Finite Group Databasebeta

← #29645836

Subgroups — #29645836

Order 15616.

1278 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840241C211yesmaximal, characteristic
2#21454841C212yesmaximal, complemented
3#21444141C212yesmaximal, complemented
4#21444137C211yesmaximal, characteristic, complemented
5#21444134C212yesmaximal, complemented
6#21444130C212yesmaximal, complemented
7C2×#16839487C212yesmaximal, complemented
8#324×D61C212yesmaximal, complemented
9C61×#1459C211yesmaximal, characteristic, complemented
10C22×#11758224C411yescharacteristic
11#16840241—24no—
12#16840241—24no—
13C2×C4×Dic122C411yescharacteristic
14C2×#14519742C2211yescharacteristic
15C2×D4×Dic61C411yescharacteristic
16C2×C4×C22⋊D61C411yescharacteristic
17C2×C4×C22⋊D61C2211yescharacteristic
18C2×#14519737C411yescharacteristic
19C2×#14519737C2211yescharacteristic
20C2×#14519734C411yescharacteristic
21C2×#14519733C411yescharacteristic
22C2×#14519733C2211yescharacteristic
23C22×#11758196C411yescharacteristic
24C22×#11758196C2211yescharacteristic
25C2×C4⋊C4×D61C2211yescharacteristic
26C8×C22⋊D61—24no—
27#16839825—24no—
28#16839812C2214yes—
29C2×C22⋊#92418C2212yes—
30C22⋊C8×D61C2214yes—
31#16839488C2212yes—
32#16839487C2214yes—
33#16839487C2214yes—
34#16839486C2212yes—
35C2×C4×D4×C61C2211yescharacteristic
36C2×C22⋊C8×C61C2212yes—
37C61×#324C2212yes—
38C61×#323C2212yes—
39C2×#11758224—24no—
40C2×#11758224—24no—
41C2×#11758224C818yescomplemented
42C22×Dic122C2×C411yescharacteristic
43C22×C22⋊D61C2×C411yescharacteristic
44C22×C22⋊D61C2×C411yescharacteristic
45C23×Dic61C2×C411yescharacteristic
46C23×Dic61C2×C411yescharacteristic
47C23×Dic61C2×C411yescharacteristic
48C23×Dic61C2×C411yescharacteristic
49C22×C4×D61C2×C411yescharacteristic
50C22×C4×D61C2×C411yescharacteristic
51C22×C4×D61C2311yescharacteristic
52C22×#92418—22no—
53C2×C8×D61—24no—
54C4×Dic122—22no—
55C4×Dic122—22no—
56#14519742—24no—
57D4×Dic61—24no—
58C4×C22⋊D61—22no—
59C4×C22⋊D61—22no—
60C4×C22⋊D61D414yes—
61C4×C22⋊D61D414yes—
62#14519737—24no—
63#14519737—24no—
64#14519734—22no—
65#14519734—22no—
66#14519733—24no—
67#14519733—24no—
68C2×C4⋊Dic61C2×C411yescharacteristic
69C2×#11758196—22no—
70C2×#11758196—22no—
71C2×#11758196—22no—
72C2×#11758196—22no—
73C2×#11758196C2×C411yescharacteristic
74C2×#11758196C2×C411yescharacteristic
75C2×#11758196C2×C411yescharacteristic
76C2×#11758196C2×C411yescharacteristic
77C2×#11758196C2×C411yescharacteristic
78C2×#11758196C2×C411yescharacteristic
79C2×#11758196C2311yescharacteristic
80C2×#11758196C2311yescharacteristic
81C4⋊C4×D61—24no—
82C2×C22⋊Dic61C2×C411yescharacteristic
83C2×C22⋊Dic61C2×C411yescharacteristic
84C2×#11758198C2×C411yescharacteristic
85C2×#11758198C2×C411yescharacteristic
86C2×C4×Dic61C2×C411yescharacteristic
87C2×C4×Dic61C2×C411yescharacteristic
88C2×C4×Dic61C2×C411yescharacteristic
89C2×C4×Dic61C2×C411yescharacteristic
90C2×C4×Dic61C2311yescharacteristic
91#14519706—24no—
92C22⋊#92418—22no—
93C22⋊#92418C2314yes—
94#14519689—24no—
95C8×Dic61—24no—
96C22×D4×C61C2×C411yescharacteristic
97C23×C4×C61C2×C411yescharacteristic
98C23×C4×C61C2311yescharacteristic
99C22×C8×C61—22no—
100C4×D4×C61—22no—
101C4×D4×C61—22no—
102C2×C4⋊C4×C61C2311yescharacteristic
103C2×C22⋊C4×C61C2×C411yescharacteristic
104C2×C22⋊C4×C61C2311yescharacteristic
105C2×C42×C61C2×C411yescharacteristic
106C22⋊C8×C61—22no—
107C22⋊C8×C61C2314yes—
108C24×C61C22×C411yescharacteristic
109C24×C61C22×C411yescharacteristic
110C23×D61C22×C411yescharacteristic
111C2×D4×C61—22no—
112C2×D4×C61—22no—
113C2×D4×C61C2×C814yescomplemented
114C22×C4×C61—21no—
115C22×C4×C61—21no—
116C22×C4×C61—81no—
117C22×C4×C61—81no—
118C22×C4×C61C22×C411yescharacteristic
119C22×C4×C61C22×C411yescharacteristic
120C22×C4×C61C22×C411yescharacteristic
121C22×C4×C61C22×C411yescharacteristic
122C22×C4×C61C2×D412yes—
123C22×C4×C61C2×D412yes—
124C22×C4×C61C2411yescharacteristic
125C2×C22⋊D61—22no—
126C2×C22⋊D61—22no—
127C2×C22⋊D61C22⋊C414yes—
128C2×C22⋊D61C2×C814yes—
129C2×C22⋊D61C2×C814yescomplemented
130C2×C22⋊D61M1614yes—
131C22×Dic61—22no—
132C22×Dic61—22no—
133C22×Dic61—22no—
134C22×Dic61—22no—
135C22×Dic61—22no—
136C22×Dic61—22no—
137C22×Dic61—81no—
138C22×Dic61—81no—
139C22×Dic61C2×C814yescomplemented
140C22×Dic61C2×C814yescomplemented
141C22×Dic61C22×C411yescharacteristic
142C22×Dic61C22×C411yescharacteristic
143C22×Dic61C22×C411yescharacteristic
144C22×Dic61C22×C411yescharacteristic
145C22×Dic61C22×C411yescharacteristic
146C22×Dic61C22×C411yescharacteristic
147C22×Dic61C22×C411yescharacteristic
148#11758224—232no—
149C2×C4×D61—22no—
150C2×C4×D61—22no—
151C2×C4×D61—22no—
152C2×C4×D61—81no—
153C2×C4×D61—81no—
154C2×C4×D61C2×C814yescomplemented
155C2×C4×D61C2×D414yes—
156C2×Dic122—22no—
157C2×Dic122—22no—
158C2×Dic122C2×C814yescomplemented
159C2×C8×C61—24no—
160C2×C8×C61—82no—
161C4⋊C4×C61—22no—
162C22⋊C4×C61—22no—
163C22⋊C4×C61—22no—
164C42×C61—21no—
165C42×C61—21no—
166C22⋊Dic61—22no—
167C22⋊Dic61C22⋊C414yes—
168#11758198—22no—
169#11758198C22⋊C412yes—
170#11758198C22⋊C412yes—
171C4⋊Dic61—22no—
172#11758196—21no—
173#11758196—21no—
174#11758196—21no—
175#11758196—21no—
176#11758196—22no—
177#11758196—22no—
178#11758196—22no—
179#11758196—22no—
180#11758196—22no—
181#11758196C22⋊C412yes—
182#11758196C22⋊C412yes—
183C4×Dic61—22no—
184C4×Dic61—22no—
185C4×Dic61—22no—
186C4×Dic61—22no—
187C4×Dic61C2×D414yes—
188C2×#92418—24no—
189C2×#92418—82no—
190C8×D61—84no—
191C23×C61—21no—
192C23×C61—21no—
193C23×C61—41no—
194C23×C61—41no—
195C23×C61—41no—
196C23×C61—41no—
197C23×C61C2×C22⋊C412yes—
198C23×C61C22×C812yes—
199C23×C61C22×C812yes—
200C23×C61C2×M1612yes—
201C23×C61C23×C411yescharacteristic
202C22×D61—41no—
203C22×D61—41no—
204C22×D61C2×C22⋊C412yes—
205C22×D61C22×C812yes—
206C22×D61C2×M1612yes—
207D4×C61—28no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—42no—
213C2×C4×C61—42no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—81no—
219C2×C4×C61—81no—
220C2×C4×C61C2×C22⋊C411yescharacteristic
221C2×C4×C61C2×C22⋊C411yescharacteristic
222C2×C4×C61C22×C812yes—
223C2×C4×C61C22×D412yes—
224C22⋊D61—28no—
225C22⋊D61C22⋊C8116yes—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—28no—
231C2×Dic61—28no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—41no—
235C2×Dic61—41no—
236C2×Dic61—41no—
237C2×Dic61—41no—
238C2×Dic61—82no—
239C2×Dic61—82no—
240C2×Dic61C2×C22⋊C412yes—
241C2×Dic61C2×C22⋊C412yes—
242C2×Dic61C2×C22⋊C412yes—
243C2×Dic61C22×C812yes—
244C2×Dic61C22×C812yes—
245C2×Dic61C22×C812yes—
246C2×Dic61C2×M1612yes—
247C4×D61—28no—
248C4×D61—44no—
249C4×D61—82no—
250Dic122—28no—
251C8×C61—44no—
252#92418—44no—
253#17351—611nomaximal, Sylow
254C22×C61—21no—
255C22×C61—22no—
256C22×C61—21no—
257C22×C61—22no—
258C22×C61—22no—
259C22×C61—42no—
260C22×C61—42no—
261C22×C61—42no—
262C22×C61—42no—
263C22×C61—41no—
264C22×C61—41no—
265C22×C61C2×C22⋊C814yes—
266C22×C61C22×C22⋊C411yescharacteristic
267C22×C61C23×C811yescharacteristic
268C22×C61C22×M1611yescharacteristic
269C2×D61—22no—
270C2×D61—22no—
271C2×D61—42no—
272C2×D61—42no—
273C2×D61C2×C22⋊C814yes—
274C4×C61—22no—
275C4×C61—22no—
276C4×C61—21no—
277C4×C61—21no—
278C4×C61—41no—
279C4×C61—41no—
280Dic61—22no—
281Dic61—22no—
282Dic61—22no—
283Dic61—22no—
284Dic61—41no—
285Dic61—41no—
286Dic61C2×C22⋊C814yes—
287C2×#520—611no—
288#2972—612no—
289#1461—612no—
290#1459—612no—
291#1459—611no—
292#1459D6111yescharacteristic, complemented
293#1458—612no—
294C2×#324—612no—
295C2×#324—612no—
296C2×C61—21no—
297C2×C61—21no—
298C2×C61—24no—
299C2×C61—42no—
300C2×C61C22×C22⋊C811yescharacteristic
301C2×C61#288311yescharacteristic
302C2×C61#288911yescharacteristic
303D61—24no—
304C22×#41—611no—
305#520—1224no—
306#520—1224no—
307C2×C4×Q8—611no—
308C2×C4×Q8—611no—
309C2×C4×D4—611no—
310C2×C4×D4—611no—
311C2×C4×D4—611no—
312C2×C4×D4—611no—
313C2×C4×D4—611no—
314C2×C4×D4C2×D6111yescharacteristic
315C2×#117—611no—
316C2×#117—611no—
317C2×#117—611no—
318C22×C4⋊C4—611no—
319C22×C4⋊C4—611no—
320C22×C4⋊C4—611no—
321C8×D4—1224no—
322C8×D4—1224no—
323#431—614no—
324C2×C22⋊C8—612no—
325C2×C22⋊C8—614no—
326C2×C22⋊C8C2×D6112yes—
327#324—612no—
328#324—614no—
329#324—614no—
330#324C2×D6112yes—
331#323—612no—
332#323C2×D6112yes—
333C61#1735111yescharacteristic, complemented, Sylow
334C2×#41—618no—
335C2×#41—1224no—
336C2×#41—1224no—
337C22×Q8—611no—
338C22×D4—611no—
339C22×D4—611no—
340C22×D4C4×D6111yescharacteristic
341C23×C4—611no—
342C23×C4—611no—
343C23×C4—611no—
344C23×C4—611no—
345C23×C4—611no—
346C23×C4—611no—
347C23×C4—611no—
348C23×C4C4×D6111yescharacteristic
349C23×C4C22×D6111yescharacteristic
350C22×C8—22no—
351C22×C8—1224no—
352C22×C8—1222no—
353C4×Q8—1222no—
354C4×Q8—1222no—
355C4×Q8—1224no—
356C4×D4—22no—
357C4×D4—22no—
358C4×D4—614no—
359C4×D4—614no—
360C4×D4—1224no—
361C4×D4—1224no—
362C4×D4—1222no—
363C4×D4—1222no—
364C4×D4—1224no—
365#117—1222no—
366#117—1222no—
367#117—1224no—
368#117—1224no—
369C2×C4⋊C4—611no—
370C2×C4⋊C4—611no—
371C2×C4⋊C4—611no—
372C2×C4⋊C4—611no—
373C2×C4⋊C4—611no—
374C2×C4⋊C4—611no—
375C2×C4⋊C4—611no—
376C2×C4⋊C4—611no—
377C2×C4⋊C4—611no—
378C2×C4⋊C4—1224no—
379C2×C4⋊C4—1222no—
380C2×C4⋊C4—1222no—
381C2×C4⋊C4—1222no—
382C2×C4⋊C4—1222no—
383C2×C4⋊C4C22×D6111yescharacteristic
384C2×C22⋊C4—611no—
385C2×C22⋊C4—611no—
386C2×C22⋊C4—611no—
387C2×C22⋊C4—611no—
388C2×C22⋊C4C4×D6111yescharacteristic
389C2×C22⋊C4C22×D6111yescharacteristic
390C2×C42—611no—
391C2×C42—611no—
392C2×C42—611no—
393C2×C42—611no—
394C2×C42—611no—
395C2×C42C4×D6111yescharacteristic
396C4⋊C8—1224no—
397C22⋊C8—22no—
398C22⋊C8—614no—
399C22⋊C8—1224no—
400C22⋊C8—1222no—
401C22⋊C8C22×D6114yes—
402C4×C8—1224no—
403C24—611no—
404C24C2×C4×D6111yescharacteristic
405C24C2×C4×D6111yescharacteristic
406#41—12232no—
407C2×Q8—614no—
408C2×Q8—1222no—
409C2×Q8—1222no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—614no—
413C2×D4—614no—
414C2×D4—614no—
415C2×D4—614no—
416C2×D4—1222no—
417C2×D4—1222no—
418C2×D4C8×D6114yescomplemented
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—81no—
422C22×C4—81no—
423C22×C4—611no—
424C22×C4—611no—
425C22×C4—611no—
426C22×C4—614no—
427C22×C4—614no—
428C22×C4—611no—
429C22×C4—611no—
430C22×C4—614no—
431C22×C4—614no—
432C22×C4—611no—
433C22×C4—611no—
434C22×C4—1222no—
435C22×C4—1222no—
436C22×C4—1222no—
437C22×C4—1222no—
438C22×C4—1222no—
439C22×C4—1222no—
440C22×C4—1222no—
441C22×C4—1222no—
442C22×C4—1222no—
443C22×C4—4881no—
444C22×C4—4881no—
445C22×C4—4881no—
446C22×C4—4881no—
447C22×C4C2×C4×D6111yescharacteristic
448C22×C4C2×C4×D6111yescharacteristic
449C22×C4C2×C4×D6111yescharacteristic
450C22×C4C2×C4×D6111yescharacteristic
451C22×C4D4×D6112yes—
452C22×C4D4×D6112yes—
453C22×C4C23×D6111yescharacteristic
454C2×C8—24no—
455C2×C8—82no—
456C2×C8—1224no—
457C2×C8—4884no—
458C2×C8—4882no—
459C4⋊C4—22no—
460C4⋊C4—612no—
461C4⋊C4—612no—
462C4⋊C4—1222no—
463C4⋊C4—1222no—
464C4⋊C4—1222no—
465C4⋊C4—1222no—
466C4⋊C4—1222no—
467C4⋊C4—1222no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—614no—
475C22⋊C4—612no—
476C22⋊C4—612no—
477C22⋊C4—1222no—
478C22⋊C4—1222no—
479C42—21no—
480C42—21no—
481C42—614no—
482C42—1222no—
483C42—1222no—
484C42—1222no—
485C42—1222no—
486C23—21no—
487C23—21no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—612no—
493C23—612no—
494C23—612no—
495C23—2441no—
496C23—2441no—
497C23C22⋊C4×D6112yes—
498C23C2×C8×D6112yes—
499C23C2×C8×D6112yes—
500C23M16×D6112yes—
501C23C22×C4×D6111yescharacteristic
502Q8—1228no—
503D4—28no—
504D4—6116no—
505D4—1228no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—81no—
517C2×C4—81no—
518C2×C4—612no—
519C2×C4—612no—
520C2×C4—612no—
521C2×C4—612no—
522C2×C4—612no—
523C2×C4—612no—
524C2×C4—612no—
525C2×C4—1228no—
526C2×C4—1228no—
527C2×C4—1221no—
528C2×C4—1221no—
529C2×C4—1228no—
530C2×C4—1221no—
531C2×C4—1221no—
532C2×C4—1221no—
533C2×C4—1221no—
534C2×C4—4882no—
535C2×C4—4882no—
536C2×C4—4882no—
537C2×C4—2444no—
538C2×C4—2441no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4C22⋊C4×D6111yescharacteristic
543C2×C4C22⋊C4×D6111yescharacteristic
544C2×C4C2×C8×D6112yes—
545C2×C4C2×D4×D6112yes—
546C8—44no—
547C8—2444no—
548C22—21no—
549C22—22no—
550C22—21no—
551C22—22no—
552C22—22no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—41no—
558C22—41no—
559C22—614no—
560C22—1222no—
561C22—1222no—
562C22—2442no—
563C22—2442no—
564C22C22⋊C8×D6114yes—
565C22C2×C22⋊C4×D6111yescharacteristic
566C22C22×C8×D6111yescharacteristic
567C22C2×M16×D6111yescharacteristic
568C4—22no—
569C4—22no—
570C4—21no—
571C4—21no—
572C4—41no—
573C4—41no—
574C4—614no—
575C4—1222no—
576C4—1222no—
577C4—1222no—
578C4—1222no—
579C4—2441no—
580C4—2441no—
581C2—21no—
582C2—21no—
583C2—24no—
584C2—42no—
585C2—1224no—
586C2C2×C22⋊C8×D6111yescharacteristic
587C2#2145427711yescharacteristic
588C2#2145430011yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC22×C61C23×C8
FrattiniC22×C4C23×D61
FittingC61×#1459C2
socleC22×C61C22×C22⋊C4
prime radicalC22×#11758224C4
cosocleC22×C4×C61C24
hypercenter#1459D61
hypocenterC61#17351
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1459

Complements

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

NH ≅ G/Ntype
2. #21454841C2semidirect
3. #21444141C2semidirect
4. #21444137C2semidirect
5. #21444134C2semidirect
6. #21444130C2semidirect
7. C2×#16839487C2semidirect
8. #324×D61C2semidirect
9. C61×#1459C2semidirect
41. C2×#11758224C8semidirect
113. C2×D4×C61C2×C8semidirect
129. C2×C22⋊D61C2×C8semidirect
139. C22×Dic61C2×C8semidirect
140. C22×Dic61C2×C8semidirect
154. C2×C4×D61C2×C8semidirect
158. C2×Dic122C2×C8semidirect
292. #1459D61semidirect
333. C61#17351semidirect
418. C2×D4C8×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402412
#214548412
#214441412
#214441372
#214441342
#214441302
C2×#168394872
#324×D612
C61×#14592
#1735161