Finite Group Databasebeta

← #29698654

Subgroups — #29698654

Order 15616.

938 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839825C211yesmaximal, characteristic
2#21448750C211yesmaximal, characteristic
3#21448744C211yesmaximal, characteristic
4#21446588C211yesmaximal, characteristic, complemented
5#21446586C211yesmaximal, characteristic, complemented
6#21446019C211yesmaximal, characteristic, complemented
7#21446017C211yesmaximal, characteristic, complemented
8#21446014C211yesmaximal, characteristic, complemented
9#21445948C211yesmaximal, characteristic, complemented
10#21445846C211yesmaximal, characteristic, complemented
11#21445841C211yesmaximal, characteristic, complemented
12#106×Dic61C211yesmaximal, characteristic, complemented
13#21445534C211yesmaximal, characteristic, complemented
14C2×#16839524C211yesmaximal, characteristic, complemented
15C61×#1853C211yesmaximal, characteristic, complemented
16C23×#92418C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C2×C4×C22⋊D61C2211yescharacteristic
19C2×#14519735C2211yescharacteristic
20C2×#14519735C2211yescharacteristic
21C22×C4⋊Dic61C2211yescharacteristic
22#16839825C418yescomplemented
23C2×#14519710C2211yescharacteristic
24C2×#14519710C2211yescharacteristic
25C2×#14519709C2211yescharacteristic
26C2×#14519709C2211yescharacteristic
27C2×#14519706C2211yescharacteristic
28C2×#14519689C2211yescharacteristic
29C2×C8×Dic61C2211yescharacteristic
30#16839654—21no—
31#16839652—21no—
32#16839649—21no—
33#16839643—21no—
34#16839641—21no—
35#16839639—21no—
36#16839627C2211yescharacteristic
37#16839627C2211yescharacteristic
38#16839622C2211yescharacteristic
39#16839619C2211yescharacteristic
40#16839619C2211yescharacteristic
41C4⋊C4×Dic61C2211yescharacteristic
42C4⋊C4×Dic61C2211yescharacteristic
43C22⋊C4×Dic61—21no—
44C4×C22⋊Dic61—21no—
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53C22×C4⋊C4×C61C2211yescharacteristic
54C2×#106×C61C2211yescharacteristic
55C2×#106×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C61×#380C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C22×C22⋊D61D411yescharacteristic
61C23×Dic61—21no—
62C22×C4×D61C2311yescharacteristic
63C22×#92418—41no—
64C22×#92418—41no—
65C22×#92418C2×C414yes—
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C2×C8×D61—41no—
69C2×C8×D61—41no—
70C2×C8×D61C2×C414yescomplemented
71C4×C22⋊D61C2×C414yes—
72C4×C22⋊D61Q814yes—
73#14519735—22no—
74#14519735—22no—
75#14519735—41no—
76#14519735—41no—
77C2×C4⋊Dic61—22no—
78C2×C4⋊Dic61—21no—
79C2×C4⋊Dic61—41no—
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×#11758196D411yescharacteristic
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61D411yescharacteristic
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×#11758198D411yescharacteristic
92C2×C4×Dic61—21no—
93C2×C4×Dic61—21no—
94C2×C4×Dic61—21no—
95C2×C4×Dic61—21no—
96C2×C4×Dic61C2311yescharacteristic
97#14519710—41no—
98#14519710—41no—
99#14519709—22no—
100#14519709—41no—
101#14519706C2×C414yescomplemented
102#14519689C2×C414yescomplemented
103C8×Dic61C2×C414yescomplemented
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113C23×C4×C61—21no—
114C23×C4×C61C2311yescharacteristic
115C22×C8×C61C2311yescharacteristic
116C22×C8×C61C2311yescharacteristic
117C2×C4⋊C4×C61—22no—
118C2×C4⋊C4×C61—21no—
119C2×C4⋊C4×C61—41no—
120C2×C4⋊C4×C61C2311yescharacteristic
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C22⋊C4×C61—21no—
125#106×C61—22no—
126#106×C61—41no—
127C22⋊C8×C61C2×C414yes—
128#95×C61—21no—
129C24×C61C2×D411yescharacteristic
130C23×D61C2×D411yescharacteristic
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—42no—
140C22×C4×C61—42no—
141C22×C4×C61—81no—
142C22×C4×C61C22×C412yes—
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×Q812yes—
145C22×C4×C61C2411yescharacteristic
146C2×C22⋊D61—22no—
147C2×C22⋊D61—22no—
148C2×C22⋊D61C4⋊C414yes—
149C22×Dic61—21no—
150C22×Dic61—21no—
151C22×Dic61—21no—
152C22×Dic61—21no—
153C22×Dic61—42no—
154C22×Dic61—42no—
155C22×Dic61—81no—
156C22×Dic61C2×D411yescharacteristic
157C22×Dic61C2×D411yescharacteristic
158C22×Dic61C2×D411yescharacteristic
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×C4×D61—21no—
163C2×C4×D61C22×C412yes—
164C2×C4×D61C2×Q812yes—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61C22×C412yes—
170C2×C8×C61C22×C412yes—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—42no—
179C4⋊C4×C61#4112yes—
180C22⋊C4×C61—42no—
181C22⋊Dic61—42no—
182C22⋊Dic61C4⋊C414yes—
183#11758198—42no—
184#11758198—42no—
185#11758198—81no—
186#11758198—81no—
187#11758198C4⋊C414yes—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—42no—
196C4⋊Dic61#4112yes—
197#11758196C4⋊C414yes—
198C4×Dic61—42no—
199C4×Dic61—42no—
200C4×Dic61—81no—
201C4×Dic61—81no—
202C4×Dic61C22×C412yes—
203C4×Dic61C2×Q812yes—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—44no—
209C2×#92418C22×C412yes—
210C2×#92418C22×C412yes—
211C8×D61—44no—
212C23×C61—21no—
213C23×C61—21no—
214C23×C61—21no—
215C23×C61—21no—
216C23×C61C2×C4⋊C412yes—
217C23×C61#13512yes—
218C23×C61#13512yes—
219C23×C61C22×D411yescharacteristic
220C22×D61—21no—
221C22×D61—21no—
222C22×D61—21no—
223C22×D61—21no—
224C22×D61—21no—
225C22×D61—21no—
226C22×D61C2×C4⋊C412yes—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—22no—
230C2×C4×C61—22no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—22no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—84no—
246C2×C4×C61C2×C4⋊C412yes—
247C2×C4×C61C23×C411yescharacteristic
248C2×C4×C61C22×Q811yescharacteristic
249C2×C4×C61C2×#4111yescharacteristic
250C2×C4×C61C2×#4111yescharacteristic
251C2×C4×C61H(5,𝔽2)11yescharacteristic
252C2×C4×C61H(5,𝔽2)11yescharacteristic
253C22⋊D61—28no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—22no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270C2×Dic61—41no—
271C2×Dic61—41no—
272C2×Dic61—84no—
273C2×Dic61C2×C4⋊C412yes—
274C2×Dic61C2×C4⋊C412yes—
275C2×Dic61C2×C4⋊C412yes—
276C4×D61—22no—
277C4×D61—22no—
278C4×D61—22no—
279C4×D61—22no—
280C8×C61—22no—
281C8×C61—22no—
282#92418—22no—
283#92418—22no—
284#22706—611nomaximal, Sylow
285C22×C61—22no—
286C22×C61—22no—
287C22×C61—22no—
288C22×C61—22no—
289C22×C61—22no—
290C22×C61—22no—
291C22×C61#42714yes—
292C22×C61C22×C4⋊C411yescharacteristic
293C22×C61#54611yescharacteristic
294C22×C61#54611yescharacteristic
295C22×C61C2×#13511yescharacteristic
296C22×C61C2×#13511yescharacteristic
297C22×C61#57711yescharacteristic
298C22×C61#57711yescharacteristic
299C2×D61—22no—
300C2×D61—22no—
301C2×D61—22no—
302C2×D61—41no—
303C2×D61—41no—
304C2×D61—41no—
305C2×D61—41no—
306C4×C61—22no—
307C4×C61—42no—
308C4×C61—81no—
309C4×C61—81no—
310C4×C61—81no—
311C4×C61C4×#4111yescharacteristic
312C4×C61#51811yescharacteristic
313C4×C61#55411yescharacteristic
314C4×C61#55411yescharacteristic
315Dic61—22no—
316Dic61—22no—
317Dic61—22no—
318Dic61—42no—
319Dic61—81no—
320Dic61—81no—
321Dic61—81no—
322C2×C8×D4—611no—
323#2352—611no—
324#2352—611no—
325#1949—611no—
326#1949—611no—
327#1854—611no—
328#1854—611no—
329#1853—611no—
330#1853D6111yescharacteristic, complemented
331#1835—611no—
332#1808—611no—
333#1807—611no—
334C4×#106—611no—
335#1735—611no—
336C2×#340—611no—
337C2×C61—24no—
338C2×C61#234911yescharacteristic
339C2×C61C2×#42711yescharacteristic
340C2×C61#291211yescharacteristic
341C2×C61#329611yescharacteristic
342C2×C61#329611yescharacteristic
343C2×C61#330111yescharacteristic
344C2×C61#330111yescharacteristic
345D61—42no—
346C23×C8—611no—
347C23×C8—611no—
348C2×C4×D4—611no—
349C2×#117—611no—
350C2×#117—611no—
351C22×C4⋊C4—611no—
352C22×C4⋊C4C2×D6111yescharacteristic
353C8×D4—618no—
354C2×#107—611no—
355C2×#107—611no—
356C2×#106—611no—
357C2×#106—611no—
358C2×#106C2×D6111yescharacteristic
359C2×#106C2×D6111yescharacteristic
360C2×C4⋊C8—611no—
361C2×C22⋊C8—611no—
362C2×C22⋊C8C2×D6111yescharacteristic
363C2×C4×C8—611no—
364#388—1221no—
365#388—1221no—
366#387—1221no—
367#387—1221no—
368#386—1221no—
369#386—1221no—
370#382—611no—
371#382—611no—
372#380—611no—
373#380—611no—
374#380—611no—
375#380C2×D6111yescharacteristic
376C4×C4⋊C4—611no—
377C4×C4⋊C4—611no—
378C4×C22⋊C4—1221no—
379C4×C22⋊C4—1221no—
380#340—611no—
381#340—611no—
382#340—611no—
383#340—611no—
384#340—611no—
385#340—611no—
386#340—611no—
387#340—611no—
388#340C2×D6111yescharacteristic
389#340C2×D6111yescharacteristic
390C61#2270611yescharacteristic, complemented, Sylow
391C22×D4—611no—
392C23×C4—21no—
393C23×C4—611no—
394C23×C4—1221no—
395C23×C4C22×D6111yescharacteristic
396C22×C8—611no—
397C22×C8—611no—
398C22×C8—614no—
399C22×C8—614no—
400C22×C8—2441no—
401C22×C8—2441no—
402C22×C8—2441no—
403C22×C8—2441no—
404C22×C8C22×D6111yescharacteristic
405C22×C8C22×D6111yescharacteristic
406C4×D4—614no—
407C4×D4—614no—
408#117—1222no—
409#117—1222no—
410#117—2441no—
411#117—2441no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—41no—
415C2×C4⋊C4—611no—
416C2×C4⋊C4—611no—
417C2×C4⋊C4—611no—
418C2×C4⋊C4—611no—
419C2×C4⋊C4—611no—
420C2×C4⋊C4—1222no—
421C2×C4⋊C4—1221no—
422C2×C4⋊C4—2441no—
423C2×C4⋊C4C22×D6111yescharacteristic
424C2×C4⋊C4C22×D6111yescharacteristic
425C2×C4⋊C4C22×D6111yescharacteristic
426C2×C4⋊C4C22×D6111yescharacteristic
427C2×C22⋊C4—21no—
428C2×C22⋊C4—611no—
429C2×C22⋊C4—611no—
430C2×C22⋊C4—1221no—
431C2×C22⋊C4—1221no—
432C2×C22⋊C4—1221no—
433C2×C22⋊C4—1221no—
434C2×C22⋊C4—1221no—
435C2×C42—611no—
436C2×C42—1221no—
437C2×C42—1221no—
438C2×C42—1221no—
439C2×C42—1221no—
440#107—2441no—
441#107—2441no—
442#106—22no—
443#106—41no—
444#106—1222no—
445#106—2441no—
446C4⋊C8—614no—
447C22⋊C8—614no—
448C22⋊C8C4×D6114yes—
449C4×C8—614no—
450#95—21no—
451#95—1221no—
452#95—1221no—
453#95—1221no—
454#95—1221no—
455#95—1221no—
456#95—1221no—
457#95—1221no—
458#95—1221no—
459#95—1221no—
460C24—611no—
461C24D4×D6111yescharacteristic
462C2×D4—614no—
463C2×D4—1222no—
464C2×D4—1222no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—81no—
476C22×C4—611no—
477C22×C4—611no—
478C22×C4—611no—
479C22×C4—612no—
480C22×C4—612no—
481C22×C4—1221no—
482C22×C4—1221no—
483C22×C4—1221no—
484C22×C4—1221no—
485C22×C4—1221no—
486C22×C4—1221no—
487C22×C4—1221no—
488C22×C4—1221no—
489C22×C4—4881no—
490C22×C4—2442no—
491C22×C4—2442no—
492C22×C4C2×C4×D6112yes—
493C22×C4D4×D6111yescharacteristic
494C22×C4Q8×D6112yes—
495C22×C4C23×D6111yescharacteristic
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—612no—
501C2×C8—612no—
502C2×C8—1221no—
503C2×C8—1221no—
504C2×C8—1221no—
505C2×C8—1221no—
506C2×C8—2444no—
507C2×C8—2444no—
508C2×C8C2×C4×D6112yes—
509C2×C8C2×C4×D6112yes—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—42no—
518C4⋊C4—614no—
519C4⋊C4—612no—
520C4⋊C4—1221no—
521C4⋊C4—1221no—
522C4⋊C4—1221no—
523C4⋊C4—1221no—
524C4⋊C4—1221no—
525C4⋊C4—1221no—
526C4⋊C4—1221no—
527C4⋊C4—2442no—
528C4⋊C4#1175822412yes—
529C22⋊C4—42no—
530C22⋊C4—614no—
531C22⋊C4—614no—
532C22⋊C4—4881no—
533C22⋊C4—4881no—
534C22⋊C4—2442no—
535C22⋊C4—2442no—
536C22⋊C4—2442no—
537C42—612no—
538C42—612no—
539C42—4881no—
540C42—4881no—
541C42—2442no—
542C42—2442no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—612no—
548C23—1221no—
549C23—1221no—
550C23—1221no—
551C23—1221no—
552C23—1221no—
553C23—1221no—
554C23C4⋊C4×D6112yes—
555C23#1451979812yes—
556C23#1451979812yes—
557C23C2×D4×D6111yescharacteristic
558D4—1228no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—84no—
578C2×C4—612no—
579C2×C4—612no—
580C2×C4—612no—
581C2×C4—1221no—
582C2×C4—1221no—
583C2×C4—1221no—
584C2×C4—1221no—
585C2×C4—1221no—
586C2×C4—1221no—
587C2×C4—1222no—
588C2×C4—1222no—
589C2×C4—1222no—
590C2×C4—1222no—
591C2×C4—1222no—
592C2×C4—4884no—
593C2×C4—2441no—
594C2×C4—2441no—
595C2×C4—2441no—
596C2×C4—2441no—
597C2×C4—2441no—
598C2×C4—2441no—
599C2×C4—2441no—
600C2×C4—2441no—
601C2×C4—2441no—
602C2×C4—2441no—
603C2×C4—2441no—
604C2×C4C4⋊C4×D6112yes—
605C2×C4C22×C4×D6111yescharacteristic
606C2×C4C2×Q8×D6111yescharacteristic
607C2×C4#41×D6111yescharacteristic
608C2×C4C2×#1175822411yescharacteristic
609C2×C4#1451982211yescharacteristic
610C2×C4#1451982311yescharacteristic
611C8—22no—
612C8—22no—
613C8—1222no—
614C8—1222no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—1222no—
622C22—1222no—
623C22—1222no—
624C22—2441no—
625C22—2441no—
626C22—2441no—
627C22—2441no—
628C22#1683979714yes—
629C22C2×C4⋊C4×D6111yescharacteristic
630C22#1684039911yescharacteristic
631C22#1684040411yescharacteristic
632C22C2×#1451979811yescharacteristic
633C22C2×#1451979811yescharacteristic
634C22#1684057111yescharacteristic
635C22#1684057211yescharacteristic
636C4—22no—
637C4—42no—
638C4—81no—
639C4—81no—
640C4—81no—
641C4—1222no—
642C4—1222no—
643C4—1222no—
644C4—4881no—
645C4—4881no—
646C4—4881no—
647C4—2442no—
648C4C4×#1175822411yescharacteristic
649C4#1684023411yescharacteristic
650C4#1684046611yescharacteristic
651C4#1684047011yescharacteristic
652C2—24no—
653C2—2442no—
654C2#2144872511yescharacteristic
655C2C2×#1683979711yescharacteristic
656C2#2145441311yescharacteristic
657C2#2145765211yescharacteristic
658C2#2145765811yescharacteristic
659C2#2145771911yescharacteristic
660C2#2145772511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1853C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
cosocleC22×C4×C61C24
hypercenter#1853D61
hypocenterC61#22706
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1853

Complements

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

NH ≅ G/Ntype
4. #21446588C2semidirect
5. #21446586C2semidirect
6. #21446019C2semidirect
7. #21446017C2semidirect
8. #21446014C2semidirect
9. #21445948C2semidirect
10. #21445846C2semidirect
11. #21445841C2semidirect
12. #106×Dic61C2semidirect
13. #21445534C2semidirect
14. C2×#16839524C2semidirect
15. C61×#1853C2semidirect
22. #16839825C4semidirect
70. C2×C8×D61C2×C4semidirect
101. #14519706C2×C4semidirect
102. #14519689C2×C4semidirect
103. C8×Dic61C2×C4semidirect
330. #1853D61semidirect
390. C61#22706semidirect

Maximal subgroups

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

subgroupindex
C2×#168398252
#214487502
#214487442
#214465882
#214465862
#214460192
#214460172
#214460142
#214459482
#214458462
#214458412
#106×Dic612
#214455342
C2×#168395242
C61×#18532
#2270661