Finite Group Databasebeta

← #29645833

Subgroups — #29645833

Order 15616.

1278 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840243C211yesmaximal, characteristic
2#21454841C212yesmaximal, complemented
3#21444141C212yesmaximal, complemented
4#21444136C212yesmaximal, complemented
5#21444135C212yesmaximal, complemented
6#21444132C212yesmaximal, complemented
7C2×#16839488C211yesmaximal, characteristic, complemented
8#324×D61C212yesmaximal, complemented
9C2×C61×#324C211yesmaximal, characteristic, complemented
10C22×#11758222C411yescharacteristic
11#16840243—24no—
12#16840243—24no—
13C2×#14519742C411yescharacteristic
14C2×#14519742C2211yescharacteristic
15C2×#14519739C411yescharacteristic
16C2×#14519739C2211yescharacteristic
17C2×C4×C22⋊D61C411yescharacteristic
18C2×C4×C22⋊D61C411yescharacteristic
19C2×C4×C22⋊D61C2211yescharacteristic
20C2×C4×C22⋊D61C2211yescharacteristic
21C2×#14519736C411yescharacteristic
22C2×#14519735C411yescharacteristic
23C2×#14519735C2211yescharacteristic
24C2×C4⋊C4×D61C411yescharacteristic
25C2×C4⋊C4×D61C2211yescharacteristic
26C8×C22⋊D61—24no—
27#16839825—24no—
28#16839812C2214yes—
29C2×C22⋊#92418C2212yes—
30C22⋊C8×D61C2214yes—
31#16839488C2212yes—
32#16839488C2212yes—
33#16839487C2214yes—
34#16839485C2214yes—
35C22×C4⋊C4×C61C2211yescharacteristic
36C2×C22⋊C8×C61C2212yes—
37C61×#324C2212yes—
38C61×#324C2212yes—
39C2×#11758222—22no—
40C2×#11758222—22no—
41C2×#11758222—24no—
42C2×#11758222C818yescomplemented
43C22×Dic122C2×C411yescharacteristic
44C22×D244C2×C411yescharacteristic
45C22×C22⋊D61C2×C411yescharacteristic
46C22×C22⋊D61C2×C411yescharacteristic
47C22×C4×D61C2×C411yescharacteristic
48C22×C4×D61C2×C411yescharacteristic
49C22×C4×D61C2×C411yescharacteristic
50C22×C4×D61C2×C411yescharacteristic
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61C2311yescharacteristic
53C22×#92418—22no—
54C2×C8×D61—24no—
55#14519742—24no—
56#14519742—24no—
57#14519739—24no—
58#14519739—24no—
59C4×C22⋊D61—22no—
60C4×C22⋊D61—22no—
61C4×C22⋊D61—22no—
62C4×C22⋊D61—22no—
63C4×C22⋊D61—22no—
64C4×C22⋊D61—22no—
65C4×C22⋊D61D414yes—
66C4×C22⋊D61D414yes—
67#14519736—22no—
68#14519736—22no—
69#14519735—24no—
70#14519735—24no—
71C2×C4⋊Dic61C2×C411yescharacteristic
72C2×C4⋊Dic61C2×C411yescharacteristic
73C2×#11758196C2×C411yescharacteristic
74C2×#11758196C2×C411yescharacteristic
75C2×#11758196C2×C411yescharacteristic
76C2×#11758196C2311yescharacteristic
77C4⋊C4×D61—24no—
78C4⋊C4×D61—24no—
79C2×C22⋊Dic61C2×C411yescharacteristic
80C2×C22⋊Dic61C2×C411yescharacteristic
81C2×#11758198C2×C411yescharacteristic
82C2×#11758198C2×C411yescharacteristic
83C2×#11758198C2×C411yescharacteristic
84C2×#11758198C2311yescharacteristic
85C2×C4×Dic61C2×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—
96C23×C4×C61C2×C411yescharacteristic
97C23×C4×C61C2×C411yescharacteristic
98C23×C4×C61C2311yescharacteristic
99C22×C8×C61—22no—
100C2×C4⋊C4×C61—22no—
101C2×C4⋊C4×C61—22no—
102C2×C4⋊C4×C61C2×C411yescharacteristic
103C2×C4⋊C4×C61C2×C411yescharacteristic
104C2×C4⋊C4×C61C2311yescharacteristic
105C2×C4⋊C4×C61C2311yescharacteristic
106C22⋊C8×C61—22no—
107C22⋊C8×C61C2314yes—
108C24×C61C22×C411yescharacteristic
109C23×D61C22×C411yescharacteristic
110C23×D61C22×C411yescharacteristic
111C22×C4×C61—21no—
112C22×C4×C61—21no—
113C22×C4×C61—22no—
114C22×C4×C61—21no—
115C22×C4×C61—21no—
116C22×C4×C61—81no—
117C22×C4×C61—81no—
118C22×C4×C61C2×C814yescomplemented
119C22×C4×C61C22×C411yescharacteristic
120C22×C4×C61C22×C411yescharacteristic
121C22×C4×C61C22×C411yescharacteristic
122C22×C4×C61C22×C411yescharacteristic
123C22×C4×C61C22×C411yescharacteristic
124C22×C4×C61C2×D412yes—
125C22×C4×C61C2×D412yes—
126C22×C4×C61C2411yescharacteristic
127C2×C22⋊D61—21no—
128C2×C22⋊D61—21no—
129C2×C22⋊D61—22no—
130C2×C22⋊D61C22⋊C412yes—
131C2×C22⋊D61C22⋊C412yes—
132C2×C22⋊D61C2×C814yes—
133C2×C22⋊D61C2×C814yescomplemented
134C2×C22⋊D61M1614yes—
135C22×Dic61C22×C411yescharacteristic
136C22×Dic61C22×C411yescharacteristic
137C22×Dic61C22×C411yescharacteristic
138C22×Dic61C22×C411yescharacteristic
139C22×Dic61C22×C411yescharacteristic
140C22×Dic61C22×C411yescharacteristic
141#11758222—216no—
142#11758222—216no—
143C2×D244—22no—
144C2×D244—22no—
145C2×D244C2×C814yescomplemented
146C2×C4×D61—22no—
147C2×C4×D61—22no—
148C2×C4×D61—22no—
149C2×C4×D61—22no—
150C2×C4×D61—22no—
151C2×C4×D61—22no—
152C2×C4×D61—22no—
153C2×C4×D61—81no—
154C2×C4×D61—81no—
155C2×C4×D61—81no—
156C2×C4×D61—81no—
157C2×C4×D61C2×C814yescomplemented
158C2×C4×D61C2×C814yescomplemented
159C2×C4×D61C2×D414yes—
160C2×Dic122—22no—
161C2×Dic122—22no—
162C2×Dic122C2×C814yescomplemented
163C2×C8×C61—24no—
164C2×C8×C61—82no—
165C4⋊C4×C61—22no—
166C4⋊C4×C61—22no—
167C4⋊C4×C61—22no—
168C4⋊C4×C61—22no—
169C22⋊Dic61—21no—
170C22⋊Dic61—21no—
171C22⋊Dic61C22⋊C412yes—
172C22⋊Dic61C22⋊C412yes—
173#11758198—22no—
174#11758198—22no—
175#11758198—22no—
176#11758198C22⋊C414yes—
177C4⋊Dic61—22no—
178C4⋊Dic61—22no—
179#11758196—22no—
180#11758196—22no—
181#11758196—22no—
182#11758196C22⋊C414yes—
183C4×Dic61—22no—
184C4×Dic61—22no—
185C4×Dic61—22no—
186C4×Dic61—22no—
187C4×Dic61—22no—
188C4×Dic61C2×D414yes—
189C2×#92418—24no—
190C2×#92418—82no—
191C8×D61—84no—
192C23×C61—41no—
193C23×C61—41no—
194C23×C61C2×C22⋊C411yescharacteristic
195C23×C61C2×C22⋊C411yescharacteristic
196C23×C61C22×C812yes—
197C23×C61C2×M1612yes—
198C23×C61C23×C411yescharacteristic
199C22×D61—21no—
200C22×D61—21no—
201C22×D61—41no—
202C22×D61—41no—
203C22×D61—41no—
204C22×D61—41no—
205C22×D61C2×C22⋊C412yes—
206C22×D61C22×C812yes—
207C22×D61C22×C812yes—
208C22×D61C2×M1612yes—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—24no—
214C2×C4×C61—24no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—42no—
218C2×C4×C61—42no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—81no—
224C2×C4×C61—81no—
225C2×C4×C61C2×C22⋊C412yes—
226C2×C4×C61C22×C812yes—
227C2×C4×C61C22×C812yes—
228C2×C4×C61C22×D412yes—
229C22⋊D61—24no—
230C22⋊D61—24no—
231C22⋊D61C22⋊C818yes—
232C22⋊D61C22⋊C818yes—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—41no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240C2×Dic61—41no—
241C2×Dic61C2×C22⋊C412yes—
242C2×Dic61C2×C22⋊C412yes—
243C2×Dic61C2×C22⋊C412yes—
244C2×Dic61C22×C812yes—
245C2×Dic61C22×C812yes—
246C2×Dic61C2×M1612yes—
247D244—28no—
248C4×D61—28no—
249C4×D61—28no—
250C4×D61—44no—
251C4×D61—82no—
252C4×D61—82no—
253C4×D61—82no—
254Dic122—28no—
255C8×C61—44no—
256#92418—44no—
257#17351—611nomaximal, Sylow
258C22×C61—21no—
259C22×C61—21no—
260C22×C61—21no—
261C22×C61—21no—
262C22×C61—21no—
263C22×C61—21no—
264C22×C61—42no—
265C22×C61—42no—
266C22×C61C2×C22⋊C812yes—
267C22×C61C2×C22⋊C812yes—
268C22×C61C22×C22⋊C411yescharacteristic
269C22×C61C23×C811yescharacteristic
270C22×C61C22×M1611yescharacteristic
271C2×D61—22no—
272C2×D61—22no—
273C2×D61—22no—
274C2×D61—42no—
275C2×D61—42no—
276C2×D61—42no—
277C2×D61—41no—
278C2×D61—41no—
279C2×D61—42no—
280C2×D61C2×C22⋊C814yes—
281C4×C61—22no—
282C4×C61—22no—
283C4×C61—22no—
284C4×C61—22no—
285C4×C61—41no—
286C4×C61—41no—
287Dic61—22no—
288Dic61—22no—
289Dic61—22no—
290Dic61—41no—
291Dic61—41no—
292Dic61C2×C22⋊C814yes—
293C2×#520—611no—
294#2972—612no—
295#1461—612no—
296#1459—612no—
297#1459—612no—
298#1458—612no—
299C2×#324—612no—
300C2×#324—611no—
301C2×#324D6111yescharacteristic, complemented
302C2×C61—21no—
303C2×C61—21no—
304C2×C61—22no—
305C2×C61—22no—
306C2×C61C22×C22⋊C811yescharacteristic
307C2×C61#288311yescharacteristic
308C2×C61#288911yescharacteristic
309D61—24no—
310D61—42no—
311C22×#41—611no—
312#520—1224no—
313#520—1224no—
314C2×C4×Q8—611no—
315C2×C4×Q8—611no—
316C2×C4×D4—611no—
317C2×C4×D4—611no—
318C2×C4×D4—611no—
319C2×C4×D4—611no—
320C2×C4×D4—611no—
321C2×C4×D4—611no—
322C2×#117—611no—
323C2×#117—611no—
324C2×#117—611no—
325C22×C4⋊C4—611no—
326C22×C4⋊C4—611no—
327C22×C4⋊C4C2×D6111yescharacteristic
328C8×D4—1224no—
329C8×D4—1224no—
330#431—614no—
331C2×C22⋊C8—612no—
332C2×C22⋊C8—614no—
333C2×C22⋊C8C2×D6112yes—
334#324—612no—
335#324—612no—
336#324—614no—
337#324C2×D6112yes—
338#324C2×D6112yes—
339#323—614no—
340C61#1735111yescharacteristic, complemented, Sylow
341C2×#41—618no—
342C2×#41—1222no—
343C2×#41—1222no—
344C2×#41—1224no—
345C22×Q8—611no—
346C22×D4—611no—
347C22×D4—611no—
348C22×D4—611no—
349C23×C4—611no—
350C23×C4—611no—
351C23×C4—611no—
352C23×C4—611no—
353C23×C4—611no—
354C23×C4—611no—
355C23×C4C4×D6111yescharacteristic
356C23×C4C4×D6111yescharacteristic
357C23×C4C22×D6111yescharacteristic
358C22×C8—22no—
359C22×C8—1224no—
360C22×C8—1222no—
361C4×Q8—1224no—
362C4×Q8—1224no—
363C4×D4—614no—
364C4×D4—614no—
365C4×D4—1224no—
366C4×D4—1222no—
367C4×D4—1222no—
368C4×D4—1224no—
369C4×D4—1222no—
370C4×D4—1222no—
371C4×D4—1222no—
372C4×D4—1222no—
373#117—1224no—
374#117—1224no—
375#117—1222no—
376#117—1222no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—611no—
380C2×C4⋊C4—611no—
381C2×C4⋊C4—611no—
382C2×C4⋊C4—611no—
383C2×C4⋊C4—611no—
384C2×C4⋊C4—611no—
385C2×C4⋊C4—1224no—
386C2×C4⋊C4—1224no—
387C2×C4⋊C4C4×D6111yescharacteristic
388C2×C4⋊C4C4×D6111yescharacteristic
389C2×C4⋊C4C22×D6111yescharacteristic
390C2×C4⋊C4C22×D6111yescharacteristic
391C2×C22⋊C4—611no—
392C2×C22⋊C4—611no—
393C2×C22⋊C4—611no—
394C2×C22⋊C4—611no—
395C2×C22⋊C4—611no—
396C2×C22⋊C4—611no—
397C2×C42—611no—
398C2×C42—611no—
399C2×C42—611no—
400C2×C42—611no—
401C2×C42—611no—
402C2×C42—611no—
403C4⋊C8—1224no—
404C22⋊C8—22no—
405C22⋊C8—614no—
406C22⋊C8—1224no—
407C22⋊C8—1222no—
408C22⋊C8C22×D6114yes—
409C4×C8—1224no—
410C24—611no—
411C24—611no—
412C24C2×C4×D6111yescharacteristic
413#41—12216no—
414#41—12216no—
415C2×Q8—614no—
416C2×Q8—1222no—
417C2×Q8—1222no—
418C2×D4—612no—
419C2×D4—612no—
420C2×D4—614no—
421C2×D4—614no—
422C2×D4—614no—
423C2×D4—614no—
424C2×D4—1222no—
425C2×D4—1222no—
426C2×D4—1221no—
427C2×D4—1221no—
428C2×D4—1222no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—81no—
435C22×C4—81no—
436C22×C4—611no—
437C22×C4—611no—
438C22×C4—611no—
439C22×C4—611no—
440C22×C4—614no—
441C22×C4—614no—
442C22×C4—614no—
443C22×C4—611no—
444C22×C4—611no—
445C22×C4—1222no—
446C22×C4—1222no—
447C22×C4—1222no—
448C22×C4—1222no—
449C22×C4—1222no—
450C22×C4—1222no—
451C22×C4—1222no—
452C22×C4—4881no—
453C22×C4—4881no—
454C22×C4—4881no—
455C22×C4—4881no—
456C22×C4C8×D6114yescomplemented
457C22×C4C2×C4×D6111yescharacteristic
458C22×C4C2×C4×D6111yescharacteristic
459C22×C4C2×C4×D6111yescharacteristic
460C22×C4C2×C4×D6111yescharacteristic
461C22×C4C2×C4×D6111yescharacteristic
462C22×C4D4×D6112yes—
463C22×C4D4×D6112yes—
464C22×C4C23×D6111yescharacteristic
465C2×C8—24no—
466C2×C8—82no—
467C2×C8—1224no—
468C2×C8—4884no—
469C2×C8—4882no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—614no—
475C4⋊C4—1222no—
476C4⋊C4—1222no—
477C4⋊C4—1222no—
478C4⋊C4—1222no—
479C4⋊C4—1222no—
480C22⋊C4—612no—
481C22⋊C4—612no—
482C22⋊C4—614no—
483C22⋊C4—1222no—
484C22⋊C4—1222no—
485C22⋊C4—1221no—
486C22⋊C4—1221no—
487C22⋊C4—1222no—
488C42—614no—
489C42—1222no—
490C42—1222no—
491C42—1222no—
492C42—1222no—
493C42—1222no—
494C23—41no—
495C23—41no—
496C23—612no—
497C23—612no—
498C23—612no—
499C23—612no—
500C23—1221no—
501C23—1221no—
502C23—2441no—
503C23—2441no—
504C23—2441no—
505C23—2441no—
506C23C22⋊C4×D6111yescharacteristic
507C23C22⋊C4×D6111yescharacteristic
508C23C2×C8×D6112yes—
509C23M16×D6112yes—
510C23C22×C4×D6111yescharacteristic
511Q8—1228no—
512D4—618no—
513D4—618no—
514D4—1228no—
515D4—1224no—
516D4—1224no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—612no—
534C2×C4—612no—
535C2×C4—612no—
536C2×C4—612no—
537C2×C4—612no—
538C2×C4—612no—
539C2×C4—1228no—
540C2×C4—1228no—
541C2×C4—1221no—
542C2×C4—1221no—
543C2×C4—1221no—
544C2×C4—1221no—
545C2×C4—4882no—
546C2×C4—4882no—
547C2×C4—4882no—
548C2×C4—2444no—
549C2×C4—2441no—
550C2×C4—2441no—
551C2×C4—2441no—
552C2×C4—2441no—
553C2×C4C22⋊C4×D6112yes—
554C2×C4C2×C8×D6112yes—
555C2×C4C2×C8×D6112yes—
556C2×C4C2×D4×D6112yes—
557C8—44no—
558C8—2444no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—21no—
565C22—42no—
566C22—42no—
567C22—614no—
568C22—1222no—
569C22—1222no—
570C22—1222no—
571C22—2442no—
572C22—2442no—
573C22—2442no—
574C22—2442no—
575C22—2441no—
576C22—2441no—
577C22C22⋊C8×D6112yes—
578C22C22⋊C8×D6112yes—
579C22C2×C22⋊C4×D6111yescharacteristic
580C22C22×C8×D6111yescharacteristic
581C22C2×M16×D6111yescharacteristic
582C4—22no—
583C4—22no—
584C4—22no—
585C4—22no—
586C4—41no—
587C4—41no—
588C4—614no—
589C4—1222no—
590C4—1222no—
591C4—1222no—
592C4—2441no—
593C4—2441no—
594C2—21no—
595C2—21no—
596C2—22no—
597C2—22no—
598C2—1224no—
599C2—2442no—
600C2C2×C22⋊C8×D6111yescharacteristic
601C2#2145427711yescharacteristic
602C2#2145429911yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC22×C61C23×C8
FrattiniC22×C4C23×D61
FittingC2×C61×#324C2
socleC22×C61C22×C22⋊C4
prime radicalC22×#11758222C4
cosocleC22×C4×C61C24
hypercenterC2×#324D61
hypocenterC61#17351
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. #21454841C2semidirect
3. #21444141C2semidirect
4. #21444136C2semidirect
5. #21444135C2semidirect
6. #21444132C2semidirect
7. C2×#16839488C2semidirect
8. #324×D61C2semidirect
9. C2×C61×#324C2semidirect
42. C2×#11758222C8semidirect
118. C22×C4×C61C2×C8semidirect
133. C2×C22⋊D61C2×C8semidirect
145. C2×D244C2×C8semidirect
157. C2×C4×D61C2×C8semidirect
158. C2×C4×D61C2×C8semidirect
162. C2×Dic122C2×C8semidirect
301. C2×#324D61semidirect
340. C61#17351semidirect
456. C22×C4C8×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402432
#214548412
#214441412
#214441362
#214441352
#214441322
C2×#168394882
#324×D612
C2×C61×#3242
#1735161