Finite Group Databasebeta

← #29739120

Subgroups — #29739120

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#21448766C211yesmaximal, characteristic
3#21447346C211yesmaximal, characteristic
4#21447339C211yesmaximal, characteristic
5#21447206C211yesmaximal, characteristic
6#21447192C211yesmaximal, characteristic
7#21446589C211yesmaximal, characteristic, complemented
8#21446578C211yesmaximal, characteristic, complemented
9#21446578C211yesmaximal, characteristic, complemented
10#21446412C211yesmaximal, characteristic, complemented
11#21446405C211yesmaximal, characteristic, complemented
12#21445987C211yesmaximal, characteristic, complemented
13#21445830C211yesmaximal, characteristic
14#21445645C211yesmaximal, characteristic
15C61×#1940C211yesmaximal, characteristic, complemented
16C2×C4×D244C2211yescharacteristic
17C2×#14519735—21no—
18C2×#14519711C2211yescharacteristic
19C2×#14519711C2211yescharacteristic
20C2×#14519711C2211yescharacteristic
21C2×#14519711C2211yescharacteristic
22C2×#14519709C2211yescharacteristic
23C2×#14519709C2211yescharacteristic
24C2×#14519699C2211yescharacteristic
25C2×#14519699C2211yescharacteristic
26C2×#14519699C2211yescharacteristic
27C2×#14519699C2211yescharacteristic
28#16839701—21no—
29#16839695—21no—
30#16839664C2211yescharacteristic
31#16839664C2211yescharacteristic
32#16839660C2211yescharacteristic
33#16839660C2211yescharacteristic
34#16839654—21no—
35#16839654—21no—
36#16839649—21no—
37#16839645—21no—
38#16839632C2211yescharacteristic
39#16839632C2211yescharacteristic
40#16839628C2211yescharacteristic
41#16839628C2211yescharacteristic
42#16839619—21no—
43C4×C4⋊Dic61C2211yescharacteristic
44C4×C4⋊Dic61C2211yescharacteristic
45C4×C4⋊Dic61C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52C2×C4⋊C8×C61C2211yescharacteristic
53C2×C4⋊C8×C61C2211yescharacteristic
54C2×C4⋊C8×C61C2211yescharacteristic
55C2×#97×C61C2211yescharacteristic
56C4×C4⋊C4×C61C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C22×D244C2311yescharacteristic
60C22×C4×D61—21no—
61C4×D244—22no—
62C4×D244Q814yes—
63#14519735—44no—
64C2×C4⋊Dic61—21no—
65C2×C4⋊Dic61—21no—
66C2×C4⋊Dic61—21no—
67C2×C4⋊Dic61—21no—
68C2×C4⋊Dic61C2311yescharacteristic
69C2×C4⋊Dic61C2311yescharacteristic
70C2×C4⋊Dic61C2311yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758198—21no—
78C2×#11758198—21no—
79C2×#11758198—21no—
80C2×#11758198—21no—
81C2×#11758198—21no—
82C2×C4×Dic61—21no—
83C2×C4×Dic61—21no—
84C2×C4×Dic61—21no—
85#14519711—22no—
86#14519711—41no—
87#14519711—41no—
88#14519711—41no—
89#14519709—22no—
90#14519709—41no—
91#14519699—22no—
92#14519699—22no—
93#14519699—41no—
94#14519699—41no—
95#14519684—21no—
96#14519684—21no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104C22×C8×C61C2311yescharacteristic
105C22×C8×C61C2311yescharacteristic
106C22×C8×C61C2311yescharacteristic
107C22×C8×C61C2311yescharacteristic
108C2×C4⋊C4×C61D411yescharacteristic
109C2×C4⋊C4×C61D411yescharacteristic
110C2×C42×C61C2311yescharacteristic
111C2×C42×C61C2311yescharacteristic
112C2×C42×C61C2311yescharacteristic
113C4⋊C8×C61—22no—
114C4⋊C8×C61—22no—
115C4⋊C8×C61—22no—
116#97×C61—22no—
117#95×C61D411yescharacteristic
118#95×C61D411yescharacteristic
119C23×D61—21no—
120C22×C4×C61C2×D411yescharacteristic
121C22×C4×C61C2×D411yescharacteristic
122C22×C4×C61C2×D411yescharacteristic
123C22×C4×C61C2×D411yescharacteristic
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61C2411yescharacteristic
127C22×Dic61—21no—
128C22×Dic61—21no—
129C22×Dic61—21no—
130C22×Dic61—21no—
131C22×Dic61—21no—
132C22×Dic61—21no—
133C22×Dic61—21no—
134C2×D244—21no—
135C2×D244—21no—
136C2×D244—21no—
137C2×D244—21no—
138C2×D244—21no—
139C2×D244C2×Q812yes—
140C2×C4×D61—24no—
141C2×C4×D61—42no—
142C2×C4×D61—42no—
143C2×C8×C61—21no—
144C2×C8×C61—21no—
145C2×C8×C61—21no—
146C2×C8×C61—21no—
147C2×C8×C61—21no—
148C2×C8×C61—21no—
149C2×C8×C61—21no—
150C2×C8×C61—21no—
151C2×C8×C61—21no—
152C2×C8×C61—21no—
153C2×C8×C61#4112yes—
154C2×C8×C61#4112yes—
155C4⋊C4×C61—22no—
156C4⋊C4×C61—41no—
157C42×C61—21no—
158C42×C61—21no—
159C42×C61—21no—
160C42×C61—21no—
161C42×C61C2×Q812yes—
162C42×C61#4112yes—
163#11758198—24no—
164#11758198—42no—
165#11758198—42no—
166#11758198—81no—
167#11758198—81no—
168C4⋊Dic61—21no—
169C4⋊Dic61—21no—
170C4⋊Dic61—21no—
171C4⋊Dic61—21no—
172C4⋊Dic61—21no—
173C4⋊Dic61—21no—
174C4⋊Dic61—21no—
175C4⋊Dic61—21no—
176C4⋊Dic61—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—42no—
182C4⋊Dic61—42no—
183C4⋊Dic61—81no—
184C4⋊Dic61—81no—
185C4⋊Dic61C2×Q812yes—
186#11758196—42no—
187#11758196—81no—
188C4×Dic61—42no—
189C4×Dic61—42no—
190C4×Dic61—81no—
191C23×C61C22×D411yescharacteristic
192C22×D61—22no—
193C22×D61—41no—
194C22×D61—41no—
195C22×D61—41no—
196C22×D61—41no—
197C22×D61—41no—
198C22×D61—41no—
199C2×C4×C61—21no—
200C2×C4×C61—21no—
201C2×C4×C61—21no—
202C2×C4×C61—21no—
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—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61C22⋊Q812yes—
215C2×C4×C61C22⋊Q812yes—
216C2×C4×C61AGL(1,ℤ/8)12yes—
217C2×C4×C61C22×Q811yescharacteristic
218C2×C4×C61C2×#4111yescharacteristic
219C2×C4×C61C2×#4111yescharacteristic
220C2×C4×C61C2×#4111yescharacteristic
221C2×C4×C61H(5,𝔽2)11yescharacteristic
222C2×C4×C612−1+411yescharacteristic
223C2×Dic61—22no—
224C2×Dic61—41no—
225C2×Dic61—41no—
226C2×Dic61—41no—
227C2×Dic61—41no—
228C2×Dic61—41no—
229C2×Dic61—41no—
230C2×Dic61—41no—
231C2×Dic61—41no—
232C2×Dic61—41no—
233C2×Dic61—41no—
234C2×Dic61—41no—
235C2×Dic61—41no—
236C2×Dic61—41no—
237C2×Dic61—41no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244D244—22no—
245D244—22no—
246D244—41no—
247D244—41no—
248C4×D61—48no—
249C8×C61—22no—
250C8×C61—22no—
251C8×C61—41no—
252C8×C61—41no—
253#26098—611nomaximal, Sylow
254C22×C61C2×C22⋊Q811yescharacteristic
255C22×C61#54711yescharacteristic
256C22×C61#55011yescharacteristic
257C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
258C22×C61#57511yescharacteristic
259C22×C61#57611yescharacteristic
260C22×C61#57811yescharacteristic
261C2×D61—42no—
262C2×D61—42no—
263C2×D61—42no—
264C2×D61—81no—
265C2×D61—81no—
266C2×D61—81no—
267C2×D61—81no—
268C4×C61—22no—
269C4×C61—22no—
270C4×C61—22no—
271C4×C61—41no—
272C4×C61—41no—
273C4×C61—41no—
274C4×C61#53311yescharacteristic
275C4×C61#54411yescharacteristic
276C4×C61#55211yescharacteristic
277C4×C61#55311yescharacteristic
278Dic61—42no—
279Dic61—81no—
280Dic61—81no—
281Dic61—81no—
282Dic61—81no—
283Dic61—81no—
284Dic61—81no—
285#2570—611no—
286#2354—611no—
287#2093—611no—
288#2092—611no—
289#2067—611no—
290#2065—611no—
291#1949—611no—
292#1947—611no—
293#1947—611no—
294#1940D6111yescharacteristic, complemented
295#1921—611no—
296#1920—611no—
297#1847—611no—
298#1804—611no—
299#1762—611no—
300C2×C61#244111yescharacteristic
301C2×C61#307711yescharacteristic
302C2×C61#308311yescharacteristic
303C2×C61#334311yescharacteristic
304C2×C61#334711yescharacteristic
305C2×C61#339911yescharacteristic
306C2×C61#340211yescharacteristic
307D61—82no—
308C2×C4×D4—611no—
309C2×#117—1221no—
310C2×#107—611no—
311C2×#107—611no—
312C2×#107—611no—
313C2×#107—611no—
314C2×#106—611no—
315C2×#106—611no—
316C2×C4⋊C8C2×D6111yescharacteristic
317C2×C4⋊C8C2×D6111yescharacteristic
318C2×C4⋊C8C2×D6111yescharacteristic
319C2×#102—611no—
320C2×#102—611no—
321C2×#102—611no—
322C2×#102—611no—
323C2×#97C2×D6111yescharacteristic
324#400—1221no—
325#398—1221no—
326#390—611no—
327#390—611no—
328#389—611no—
329#389—611no—
330#388—1221no—
331#388—1221no—
332#387—1221no—
333#387—1221no—
334#384—611no—
335#384—611no—
336#382—611no—
337#382—611no—
338#380—1221no—
339C4×C4⋊C4—611no—
340C4×C4⋊C4—611no—
341C4×C4⋊C4—611no—
342C4×C4⋊C4C2×D6111yescharacteristic
343#340—611no—
344#340—611no—
345#340—611no—
346#340—611no—
347#340—611no—
348#340—611no—
349#336C2×D6111yescharacteristic
350#336C2×D6111yescharacteristic
351C61#2609811yescharacteristic, complemented, Sylow
352C22×D4—611no—
353C23×C4—1221no—
354C22×C8C22×D6111yescharacteristic
355C22×C8C22×D6111yescharacteristic
356C22×C8C22×D6111yescharacteristic
357C22×C8C22×D6111yescharacteristic
358C4×D4—614no—
359C4×D4—1222no—
360#117—2444no—
361C2×C4⋊C4—611no—
362C2×C4⋊C4—611no—
363C2×C4⋊C4—611no—
364C2×C4⋊C4—611no—
365C2×C4⋊C4—611no—
366C2×C4⋊C4—611no—
367C2×C4⋊C4—611no—
368C2×C4⋊C4—1221no—
369C2×C4⋊C4—1221no—
370C2×C4⋊C4—1221no—
371C2×C4⋊C4—1221no—
372C2×C4⋊C4—1221no—
373C2×C4⋊C4—1221no—
374C2×C4⋊C4D24411yescharacteristic
375C2×C4⋊C4D24411yescharacteristic
376C2×C22⋊C4—1221no—
377C2×C22⋊C4—1221no—
378C2×C22⋊C4—1221no—
379C2×C22⋊C4—1221no—
380C2×C22⋊C4—1221no—
381C2×C42—1221no—
382C2×C42—1221no—
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—22no—
394C4⋊C8—22no—
395C4⋊C8—22no—
396#102—1222no—
397#102—1222no—
398#102—2441no—
399#102—2441no—
400#97—22no—
401#95—1221no—
402#95—1221no—
403#95—1221no—
404#95—1221no—
405#95—1221no—
406#95—1221no—
407#95—1221no—
408#95—1221no—
409#95—1221no—
410#95D24411yescharacteristic
411#95D24411yescharacteristic
412C24—1221no—
413C2×D4—612no—
414C2×D4—1221no—
415C2×D4—1221no—
416C2×D4—1221no—
417C2×D4—1221no—
418C2×D4—1221no—
419C22×C4—1221no—
420C22×C4—1224no—
421C22×C4—1221no—
422C22×C4—1221no—
423C22×C4—1221no—
424C22×C4—1221no—
425C22×C4—1221no—
426C22×C4—1221no—
427C22×C4—2442no—
428C22×C4—2442no—
429C22×C4C2×D24411yescharacteristic
430C22×C4C2×D24411yescharacteristic
431C22×C4C2×D24411yescharacteristic
432C22×C4C2×D24411yescharacteristic
433C22×C4C2×D24411yescharacteristic
434C22×C4C2×D24411yescharacteristic
435C22×C4C23×D6111yescharacteristic
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8#1175822412yes—
447C2×C8#1175822612yes—
448C4⋊C4—22no—
449C4⋊C4—41no—
450C4⋊C4—612no—
451C4⋊C4—1221no—
452C4⋊C4—1221no—
453C4⋊C4—1221no—
454C4⋊C4—1221no—
455C4⋊C4—1221no—
456C4⋊C4—1221no—
457C4⋊C4—1221no—
458C4⋊C4—1221no—
459C4⋊C4—1221no—
460C4⋊C4—1221no—
461C4⋊C4—1221no—
462C4⋊C4—1221no—
463C4⋊C4—1221no—
464C4⋊C4—4881no—
465C4⋊C4—4881no—
466C4⋊C4—4881no—
467C4⋊C4—2442no—
468C4⋊C4—2442no—
469C4⋊C4—2442no—
470C22⋊C4—1224no—
471C22⋊C4—4881no—
472C22⋊C4—4881no—
473C22⋊C4—2442no—
474C22⋊C4—2442no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—4881no—
480C42—2442no—
481C42—2442no—
482C42#1175822412yes—
483C42Q8×D6112yes—
484C23—1222no—
485C23—2441no—
486C23—2441no—
487C23—2441no—
488C23—2441no—
489C23—2441no—
490C23—2441no—
491C23C22×D24411yescharacteristic
492D4—1222no—
493D4—1222no—
494D4—2441no—
495D4—2441no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
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—1222no—
512C2×C4—2448no—
513C2×C4—2441no—
514C2×C4—2441no—
515C2×C4—2441no—
516C2×C4—2441no—
517C2×C4—2441no—
518C2×C4—2441no—
519C2×C4—2441no—
520C2×C4—2441no—
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#1451975712yes—
534C2×C4#1451975712yes—
535C2×C4#1451980512yes—
536C2×C4C2×Q8×D6111yescharacteristic
537C2×C4C2×#1175822411yescharacteristic
538C2×C4C2×#1175822411yescharacteristic
539C2×C4C2×#1175822611yescharacteristic
540C2×C4#1451982311yescharacteristic
541C2×C4#1451982411yescharacteristic
542C8—22no—
543C8—22no—
544C8—41no—
545C8—41no—
546C22—4881no—
547C22—4881no—
548C22—4881no—
549C22—4881no—
550C22—2442no—
551C22—2442no—
552C22—2442no—
553C22C2×#1451975711yescharacteristic
554C22#1684041611yescharacteristic
555C22#1684043411yescharacteristic
556C22C2×#1451980511yescharacteristic
557C22#1684056211yescharacteristic
558C22#1684056711yescharacteristic
559C22#1684057911yescharacteristic
560C4—22no—
561C4—22no—
562C4—22no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—4881no—
567C4—4881no—
568C4—4881no—
569C4—4881no—
570C4—4881no—
571C4—4881no—
572C4—2442no—
573C4#1684031711yescharacteristic
574C4#1684039211yescharacteristic
575C4#1684045411yescharacteristic
576C4#1684046411yescharacteristic
577C2—4882no—
578C2#2144953011yescharacteristic
579C2#2145561811yescharacteristic
580C2#2145567211yescharacteristic
581C2#2145826111yescharacteristic
582C2#2145832111yescharacteristic
583C2#2145886311yescharacteristic
584C2#2145890011yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1940C2
socleC23×C61C22×D4
prime radicalC22×D244C23
hypercenter#1940D61
hypocenterC61#26098
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1940

Complements

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

NH ≅ G/Ntype
1. #21451053C2semidirect
7. #21446589C2semidirect
8. #21446578C2semidirect
9. #21446578C2semidirect
10. #21446412C2semidirect
11. #21446405C2semidirect
12. #21445987C2semidirect
15. C61×#1940C2semidirect
294. #1940D61semidirect
351. C61#26098semidirect

Maximal subgroups

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

subgroupindex
#214510532
#214487662
#214473462
#214473392
#214472062
#214471922
#214465892
#214465782
#214464122
#214464052
#214459872
#214458302
#214456452
C61×#19402
#2609861