Finite Group Databasebeta

← #29739116

Subgroups — #29739116

Order 15616.

708 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21451053C211yesmaximal, characteristic, complemented
2#21447347C211yesmaximal, characteristic
3#21447340C211yesmaximal, characteristic
4#21447207C211yesmaximal, characteristic
5#21447193C211yesmaximal, characteristic
6#21446587C211yesmaximal, characteristic, complemented
7#21446577C211yesmaximal, characteristic, complemented
8#21446575C211yesmaximal, characteristic, complemented
9#21446543C211yesmaximal, characteristic, complemented
10#21446411C211yesmaximal, characteristic, complemented
11#21446404C211yesmaximal, characteristic, complemented
12#21445985C211yesmaximal, characteristic, complemented
13#21445829C211yesmaximal, characteristic
14#21445644C211yesmaximal, characteristic
15C61×#2354C211yesmaximal, characteristic
16C2×#14519710C2211yescharacteristic
17C2×#14519710C2211yescharacteristic
18C2×#14519710C2211yescharacteristic
19C2×#14519710C2211yescharacteristic
20C2×#14519708C2211yescharacteristic
21C2×#14519708C2211yescharacteristic
22C2×C4⋊#92418C2211yescharacteristic
23C2×C4⋊#92418C2211yescharacteristic
24C2×C4⋊#92418C2211yescharacteristic
25C2×#14519698C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519688C2211yescharacteristic
30#16839701—21no—
31#16839695—21no—
32#16839660C2211yescharacteristic
33#16839660C2211yescharacteristic
34#16839649—21no—
35#16839645—21no—
36#16839632C2211yescharacteristic
37#16839628C2211yescharacteristic
38#16839628C2211yescharacteristic
39C4×C4⋊Dic61C2211yescharacteristic
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48C2×C4×D4×C61C2211yescharacteristic
49C2×#117×C61—21no—
50C61×#390C2211yescharacteristic
51C61×#390C2211yescharacteristic
52C61×#388—21no—
53C61×#388—21no—
54C61×#384C2211yescharacteristic
55C61×#380—21no—
56C4×C4⋊C4×C61C2211yescharacteristic
57C4×C4⋊C4×C61C2211yescharacteristic
58C4×C4⋊C4×C61C2211yescharacteristic
59C22×#92418C2311yescharacteristic
60C22×#92418C2311yescharacteristic
61C22×#92418C2311yescharacteristic
62C22×#92418C2311yescharacteristic
63C2×C4⋊Dic61—21no—
64C2×C4⋊Dic61—21no—
65C2×C4⋊Dic61C2311yescharacteristic
66C2×C4⋊Dic61C2311yescharacteristic
67C2×C4⋊Dic61C2311yescharacteristic
68C2×C4⋊Dic61C2311yescharacteristic
69C2×#11758196—21no—
70C2×#11758196—21no—
71C2×C4×Dic61—21no—
72#14519710—22no—
73#14519710—41no—
74#14519710—41no—
75#14519710—41no—
76#14519708—22no—
77#14519708—41no—
78C4⋊#92418—22no—
79C4⋊#92418—22no—
80C4⋊#92418—22no—
81#14519698—22no—
82#14519698—22no—
83#14519698—41no—
84#14519698—41no—
85#14519688—22no—
86#14519684—21no—
87#14519684—21no—
88#14519684—21no—
89#14519684—21no—
90#14519684—21no—
91#14519684—21no—
92#14519684—21no—
93C22×D4×C61C2311yescharacteristic
94C23×C4×C61—21no—
95C4×D4×C61—22no—
96C4×D4×C61Q814yes—
97#117×C61—44no—
98C2×C4⋊C4×C61—21no—
99C2×C4⋊C4×C61—21no—
100C2×C4⋊C4×C61D411yescharacteristic
101C2×C4⋊C4×C61D411yescharacteristic
102C2×C4⋊C4×C61C2311yescharacteristic
103C2×C4⋊C4×C61C2311yescharacteristic
104C2×C4⋊C4×C61C2311yescharacteristic
105C2×C22⋊C4×C61—21no—
106C2×C22⋊C4×C61—21no—
107C2×C22⋊C4×C61—21no—
108C2×C22⋊C4×C61—21no—
109C2×C22⋊C4×C61—21no—
110C2×C42×C61—21no—
111C2×C42×C61—21no—
112C2×C42×C61C2311yescharacteristic
113C2×C42×C61C2311yescharacteristic
114C2×C42×C61C2311yescharacteristic
115#95×C61—21no—
116#95×C61—21no—
117#95×C61D411yescharacteristic
118#95×C61D411yescharacteristic
119C24×C61—21no—
120C2×D4×C61—21no—
121C2×D4×C61—21no—
122C2×D4×C61—21no—
123C2×D4×C61—21no—
124C2×D4×C61—21no—
125C2×D4×C61C2×Q812yes—
126C22×C4×C61—21no—
127C22×C4×C61—24no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—42no—
131C22×C4×C61—42no—
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2411yescharacteristic
139C22×Dic61—21no—
140C22×Dic61—21no—
141C22×Dic61—21no—
142C22×Dic61—21no—
143C4⋊C4×C61—22no—
144C4⋊C4×C61—21no—
145C4⋊C4×C61—21no—
146C4⋊C4×C61—21no—
147C4⋊C4×C61—21no—
148C4⋊C4×C61—21no—
149C4⋊C4×C61—41no—
150C4⋊C4×C61—42no—
151C4⋊C4×C61—81no—
152C4⋊C4×C61C2×Q812yes—
153C22⋊C4×C61—24no—
154C22⋊C4×C61—42no—
155C22⋊C4×C61—42no—
156C22⋊C4×C61—81no—
157C22⋊C4×C61—81no—
158C42×C61—21no—
159C42×C61—21no—
160C42×C61—21no—
161C42×C61—21no—
162C42×C61—42no—
163C42×C61—42no—
164C42×C61C2×Q812yes—
165C42×C61#4112yes—
166C4⋊Dic61—21no—
167C4⋊Dic61—21no—
168C4⋊Dic61—21no—
169C4⋊Dic61—21no—
170C4⋊Dic61—21no—
171C4⋊Dic61—21no—
172C4⋊Dic61—21no—
173C4⋊Dic61—21no—
174C4⋊Dic61—42no—
175C4⋊Dic61—81no—
176#11758196—42no—
177#11758196—81no—
178C4×Dic61—81no—
179C2×#92418—21no—
180C2×#92418—21no—
181C2×#92418—21no—
182C2×#92418—21no—
183C2×#92418—21no—
184C2×#92418—21no—
185C2×#92418—21no—
186C2×#92418—21no—
187C2×#92418—21no—
188C2×#92418—21no—
189C2×#92418#4112yes—
190C2×#92418#4112yes—
191C23×C61—22no—
192C23×C61—41no—
193C23×C61—41no—
194C23×C61—41no—
195C23×C61—41no—
196C23×C61—41no—
197C23×C61—41no—
198C23×C61C22×D411yescharacteristic
199D4×C61—22no—
200D4×C61—22no—
201D4×C61—41no—
202D4×C61—41no—
203C2×C4×C61—21no—
204C2×C4×C61—21no—
205C2×C4×C61—21no—
206C2×C4×C61—21no—
207C2×C4×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—22no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—48no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61C22⋊Q812yes—
229C2×C4×C61C22⋊Q812yes—
230C2×C4×C61AGL(1,ℤ/8)12yes—
231C2×C4×C61C22×Q811yescharacteristic
232C2×C4×C61C2×#4111yescharacteristic
233C2×C4×C61C2×#4111yescharacteristic
234C2×C4×C61C2×#4111yescharacteristic
235C2×C4×C61H(5,𝔽2)11yescharacteristic
236C2×C4×C612−1+411yescharacteristic
237C2×Dic61—41no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249#92418—22no—
250#92418—22no—
251#92418—41no—
252#92418—41no—
253#26098—611nomaximal, Sylow
254C22×C61—42no—
255C22×C61—42no—
256C22×C61—42no—
257C22×C61—81no—
258C22×C61—81no—
259C22×C61—81no—
260C22×C61—81no—
261C22×C61C2×C22⋊Q811yescharacteristic
262C22×C61#54711yescharacteristic
263C22×C61#55011yescharacteristic
264C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
265C22×C61#57511yescharacteristic
266C22×C61#57611yescharacteristic
267C22×C61#57811yescharacteristic
268C4×C61—22no—
269C4×C61—22no—
270C4×C61—22no—
271C4×C61—42no—
272C4×C61—41no—
273C4×C61—41no—
274C4×C61—41no—
275C4×C61—81no—
276C4×C61—81no—
277C4×C61#53311yescharacteristic
278C4×C61#54411yescharacteristic
279C4×C61#55211yescharacteristic
280C4×C61#55311yescharacteristic
281Dic61—81no—
282Dic61—81no—
283Dic61—81no—
284Dic61—81no—
285#2570—611no—
286#2354D6111yescharacteristic
287#2093—611no—
288#2092—611no—
289#2067—611no—
290#2065—611no—
291#1949—611no—
292#1947—611no—
293#1947—611no—
294#1940—611no—
295#1921—611no—
296#1920—611no—
297#1847—611no—
298#1804—611no—
299#1762—611no—
300C2×C61—82no—
301C2×C61#244111yescharacteristic
302C2×C61#307711yescharacteristic
303C2×C61#308311yescharacteristic
304C2×C61#334311yescharacteristic
305C2×C61#334711yescharacteristic
306C2×C61#339911yescharacteristic
307C2×C61#340211yescharacteristic
308C2×C4×D4C2×D6111yescharacteristic
309C2×#117—21no—
310C2×#107—611no—
311C2×#107—611no—
312C2×#107—611no—
313C2×#107—611no—
314C2×#106—611no—
315C2×#106—611no—
316C2×C4⋊C8—611no—
317C2×C4⋊C8—611no—
318C2×C4⋊C8—611no—
319C2×#102—611no—
320C2×#102—611no—
321C2×#102—611no—
322C2×#102—611no—
323C2×#97—611no—
324#400—1221no—
325#398—1221no—
326#390C2×D6111yescharacteristic
327#390C2×D6111yescharacteristic
328#389—611no—
329#389—611no—
330#388—21no—
331#388—21no—
332#387—1221no—
333#387—1221no—
334#384—611no—
335#384C2×D6111yescharacteristic
336#382—611no—
337#382—611no—
338#380—21no—
339C4×C4⋊C4—611no—
340C4×C4⋊C4C2×D6111yescharacteristic
341C4×C4⋊C4C2×D6111yescharacteristic
342C4×C4⋊C4C2×D6111yescharacteristic
343#340—611no—
344#340—611no—
345#340—611no—
346#340—611no—
347#340—611no—
348#340—611no—
349#336—611no—
350#336—611no—
351C61#2609811yescharacteristic, complemented, Sylow
352C22×D4C22×D6111yescharacteristic
353C23×C4—21no—
354C22×C8—611no—
355C22×C8—611no—
356C22×C8—611no—
357C22×C8—611no—
358C4×D4—22no—
359C4×D4Dic12214yes—
360#117—44no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—611no—
364C2×C4⋊C4—611no—
365C2×C4⋊C4—611no—
366C2×C4⋊C4—611no—
367C2×C4⋊C4—1221no—
368C2×C4⋊C4—1221no—
369C2×C4⋊C4—1221no—
370C2×C4⋊C4—1221no—
371C2×C4⋊C4C22⋊D6111yescharacteristic
372C2×C4⋊C4C22⋊D6111yescharacteristic
373C2×C4⋊C4C22×D6111yescharacteristic
374C2×C4⋊C4C22×D6111yescharacteristic
375C2×C4⋊C4C22×D6111yescharacteristic
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—1221no—
384C2×C42C22×D6111yescharacteristic
385C2×C42C22×D6111yescharacteristic
386C2×C42C22×D6111yescharacteristic
387#107—1222no—
388#107—2441no—
389#107—2441no—
390#107—2441no—
391#106—1222no—
392#106—2441no—
393C4⋊C8—1222no—
394C4⋊C8—1222no—
395C4⋊C8—1222no—
396#102—1222no—
397#102—1222no—
398#102—2441no—
399#102—2441no—
400#97—1222no—
401#95—21no—
402#95—21no—
403#95—1221no—
404#95—1221no—
405#95—1221no—
406#95—1221no—
407#95—1221no—
408#95—1221no—
409#95—1221no—
410#95C22⋊D6111yescharacteristic
411#95C22⋊D6111yescharacteristic
412C24—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4C2×Dic12212yes—
419C22×C4—21no—
420C22×C4—24no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—1221no—
426C22×C4—1221no—
427C22×C4—1221no—
428C22×C4—1221no—
429C22×C4C2×C22⋊D6111yescharacteristic
430C22×C4C2×C22⋊D6111yescharacteristic
431C22×C4C2×C22⋊D6111yescharacteristic
432C22×C4C2×C22⋊D6111yescharacteristic
433C22×C4C2×C22⋊D6111yescharacteristic
434C22×C4C2×C22⋊D6111yescharacteristic
435C22×C4C23×D6111yescharacteristic
436C2×C8—612no—
437C2×C8—612no—
438C2×C8—1221no—
439C2×C8—1221no—
440C2×C8—1221no—
441C2×C8—1221no—
442C2×C8—1221no—
443C2×C8—1221no—
444C2×C8—1221no—
445C2×C8—1221no—
446C2×C8—1221no—
447C2×C8—1221no—
448C4⋊C4—21no—
449C4⋊C4—22no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—41no—
455C4⋊C4—42no—
456C4⋊C4—81no—
457C4⋊C4—1221no—
458C4⋊C4—1221no—
459C4⋊C4—1221no—
460C4⋊C4—1221no—
461C4⋊C4—1221no—
462C4⋊C4—1221no—
463C4⋊C4—1221no—
464C4⋊C4—1221no—
465C4⋊C4—4881no—
466C4⋊C4—4881no—
467C4⋊C4—2442no—
468C4⋊C4—2442no—
469C4⋊C4C2×Dic12212yes—
470C22⋊C4—24no—
471C22⋊C4—42no—
472C22⋊C4—42no—
473C22⋊C4—81no—
474C22⋊C4—81no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—42no—
480C42—42no—
481C42—4881no—
482C42C2×Dic12212yes—
483C42#1175822212yes—
484C23—22no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23C22×C22⋊D6111yescharacteristic
492D4—22no—
493D4—22no—
494D4—41no—
495D4—41no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—48no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—2441no—
522C2×C4—2441no—
523C2×C4—2441no—
524C2×C4—2441no—
525C2×C4—2441no—
526C2×C4—2441no—
527C2×C4—2441no—
528C2×C4—2441no—
529C2×C4—2441no—
530C2×C4—2441no—
531C2×C4—2441no—
532C2×C4—2441no—
533C2×C4#1451975612yes—
534C2×C4#1451975612yes—
535C2×C4#1451980312yes—
536C2×C4C22×Dic12211yescharacteristic
537C2×C4#41×D6111yescharacteristic
538C2×C4#41×D6111yescharacteristic
539C2×C4C2×#1175822211yescharacteristic
540C2×C4#1451982311yescharacteristic
541C2×C4#1451982411yescharacteristic
542C8—1222no—
543C8—1222no—
544C8—2441no—
545C8—2441no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22C2×#1451975611yescharacteristic
554C22#1684041111yescharacteristic
555C22#1684043111yescharacteristic
556C22C2×#1451980311yescharacteristic
557C22#1684056011yescharacteristic
558C22#1684056511yescharacteristic
559C22#1684057711yescharacteristic
560C4—22no—
561C4—22no—
562C4—22no—
563C4—42no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—81no—
568C4—81no—
569C4—4881no—
570C4—4881no—
571C4—4881no—
572C4—4881no—
573C4#1684031511yescharacteristic
574C4#1684039011yescharacteristic
575C4#1684045111yescharacteristic
576C4#1684045611yescharacteristic
577C2—82no—
578C2#2144952611yescharacteristic
579C2#2145561611yescharacteristic
580C2#2145567011yescharacteristic
581C2#2145825311yescharacteristic
582C2#2145831911yescharacteristic
583C2#2145886111yescharacteristic
584C2#2145889411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2354C2
socleC23×C61C22×D4
prime radicalC22×D4×C61C23
hypercenter#2354D61
hypocenterC61#26098
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2354

Complements

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

NH ≅ G/Ntype
1. #21451053C2semidirect
6. #21446587C2semidirect
7. #21446577C2semidirect
8. #21446575C2semidirect
9. #21446543C2semidirect
10. #21446411C2semidirect
11. #21446404C2semidirect
12. #21445985C2semidirect
351. C61#26098semidirect

Maximal subgroups

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

subgroupindex
#214510532
#214473472
#214473402
#214472072
#214471932
#214465872
#214465772
#214465752
#214465432
#214464112
#214464042
#214459852
#214458292
#214456442
C61×#23542
#2609861