Finite Group Databasebeta

← #29837101

Subgroups — #29837101

Order 15616.

570 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458211C211yesmaximal, characteristic, complemented
2#21457505C211yesmaximal, characteristic
3#21448058C211yesmaximal, characteristic, complemented
4#21448023C211yesmaximal, characteristic, complemented
5#21448001C211yesmaximal, characteristic, complemented
6#21447933C211yesmaximal, characteristic, complemented
7#21447911C211yesmaximal, characteristic, complemented
8#21447882C211yesmaximal, characteristic, complemented
9#21447760C211yesmaximal, characteristic, complemented
10#21447749C211yesmaximal, characteristic, complemented
11#21447683C211yesmaximal, characteristic, complemented
12#21447643C211yesmaximal, characteristic, complemented
13#21447528C211yesmaximal, characteristic, complemented
14#357×D61C211yesmaximal, characteristic, complemented
15C61×#2224C211yesmaximal, characteristic, complemented
16C2×#14519796C2211yescharacteristic
17C2×D8×D61C2211yescharacteristic
18#16840473—21no—
19#16840407—21no—
20C2×Dic488C2211yescharacteristic, complemented
21C2×#14519722C2211yescharacteristic
22C2×#14519721C2211yescharacteristic
23C2×#14519716C2211yescharacteristic, complemented
24C2×C16×D61C2211yescharacteristic
25#16840146C2211yescharacteristic
26#16840099—21no—
27#16840099—21no—
28#16840054—21no—
29#16840004C2211yescharacteristic
30#16840004C2211yescharacteristic
31#16840004C2211yescharacteristic, complemented
32#16839999C2211yescharacteristic
33#16839977—21no—
34#16839914—21no—
35#16839908—21no—
36C4×Dic244C2211yescharacteristic, complemented
37C8×D244C2211yescharacteristic
38#107×D61C2211yescharacteristic
39#107×D61C2211yescharacteristic, complemented
40#16839587C2211yescharacteristic, complemented
41#16839567C2211yescharacteristic, complemented
42#16839565C2211yescharacteristic, complemented
43#16839565C2211yescharacteristic, complemented
44#16839565C2211yescharacteristic, complemented
45#16839564C2211yescharacteristic
46#16839563C2211yescharacteristic
47#16839562C2211yescharacteristic
48#16839562C2211yescharacteristic
49#16839541C2211yescharacteristic
50#16839541C2211yescharacteristic, complemented
51#16839538C2211yescharacteristic, complemented
52C61×#500C2211yescharacteristic, complemented
53C4×D8×C61C2211yescharacteristic
54C61×#366C2211yescharacteristic, complemented
55C61×#366C2211yescharacteristic, complemented
56C61×C4⋊C16C2211yescharacteristic, complemented
57C61×#357C2211yescharacteristic
58C61×#357C2211yescharacteristic
59C2×#11758224—21no—
60C2×D4×D61—21no—
61#14519796—22no—
62#14519796—41no—
63C2×Dic244C2311yescharacteristic
64C2×Dic244C2311yescharacteristic
65C2×#11758190—21no—
66C2×#11758200—21no—
67C2×D488C2311yescharacteristic
68C2×#11758199—21no—
69D8×D61—22no—
70D8×D61—41no—
71C2×C8×D61C2311yescharacteristic
72C2×C8×D61C2311yescharacteristic
73#14519768—41no—
74#14519765—21no—
75#14519761—41no—
76#14519757—21no—
77#14519757—21no—
78#14519757—21no—
79#14519753—41no—
80#14519753—41no—
81#14519752—21no—
82#14519751—41no—
83#14519747—41no—
84C4×Dic122—21no—
85C4×D244D411yescharacteristic
86#14519739—41no—
87C4⋊C4×D61—21no—
88C4⋊C4×D61—21no—
89C2×#11758198—41no—
90Dic488—41no—
91#14519722—41no—
92#14519721—22no—
93#14519716—41no—
94C2×#11758185C2311yescharacteristic
95C2×#11758185C2311yescharacteristic
96C16×D61—41no—
97#14519711C2311yescharacteristic
98#14519710—21no—
99#14519710—21no—
100C4⋊#92418D411yescharacteristic
101#14519702—21no—
102#14519700—21no—
103#14519700—21no—
104#14519700—21no—
105#14519697—21no—
106#14519689D411yescharacteristic
107#14519689D411yescharacteristic
108C2×D8×C61C2311yescharacteristic
109C4⋊Q8×C61—21no—
110C4×D4×C61—21no—
111C2×C16×C61C2311yescharacteristic
112C2×C16×C61C2311yescharacteristic
113#107×C61—21no—
114#107×C61C2311yescharacteristic
115#107×C61C2311yescharacteristic
116#107×C61C2311yescharacteristic
117#102×C61—21no—
118C4×C8×C61C2311yescharacteristic
119C23×D61—41no—
120C2×Q8×C61—41no—
121C2×D4×C61—21no—
122C22×C4×C61—41no—
123C2×C22⋊D61—41no—
124C2×C22⋊D61—41no—
125C22×Dic61—41no—
126#11758224—42no—
127#11758224—81no—
128D4×D61—42no—
129D4×D61—81no—
130C2×D244—21no—
131C2×D244—41no—
132C2×D244D811yescharacteristic
133C2×C4×D61—41no—
134C2×C4×D61—41no—
135C2×C4×D61C2×D411yescharacteristic
136C2×C4×D61C2×D411yescharacteristic
137C2×Dic122—21no—
138C2×Dic122—21no—
139D8×C61—21no—
140D8×C61#4112yes—
141C2×C8×C61C2×D411yescharacteristic
142C2×C8×C61C2411yescharacteristic
143C4⋊C4×C61—21no—
144C4⋊C4×C61—21no—
145C4⋊C4×C61—21no—
146C4⋊C4×C61—41no—
147C22⋊C4×C61—41no—
148C42×C61C2×D411yescharacteristic
149#11758200—42no—
150#11758199—42no—
151#11758198—41no—
152#11758198—41no—
153#11758198—41no—
154#11758198—41no—
155#11758198—41no—
156#11758198—41no—
157#11758198D811yescharacteristic
158#11758198D811yescharacteristic
159C4⋊Dic61—21no—
160C4⋊Dic61—41no—
161C4⋊Dic61—41no—
162C4⋊Dic61—41no—
163C4⋊Dic61D811yescharacteristic
164#11758196—41no—
165#11758196—41no—
166#11758196—41no—
167C4×Dic61—41no—
168C2×#92418C2×D411yescharacteristic
169C2×#92418C2×D411yescharacteristic
170Dic244—21no—
171Dic244—21no—
172Dic244—21no—
173Dic244—21no—
174D488—21no—
175D488—21no—
176#11758190—81no—
177C8×D61—21no—
178C8×D61—21no—
179C8×D61—21no—
180C8×D61—21no—
181C16×C61—21no—
182C16×C61—21no—
183#11758185—21no—
184#11758185—21no—
185C23×C61—41no—
186C22×D61—41no—
187C22×D61—82no—
188C22×D61—82no—
189C22×D61—161no—
190C22×D61C2×D811yescharacteristic
191C22×D61C2×D811yescharacteristic
192Q8×C61—161no—
193D4×C61—22no—
194D4×C61—41no—
195C2×C4×C61—41no—
196C2×C4×C61—41no—
197C2×C4×C61—41no—
198C2×C4×C61—161no—
199C2×C4×C61C2×D811yescharacteristic
200C2×C4×C61C2×D811yescharacteristic
201C2×C4×C61C22×D411yescharacteristic
202C22⋊D61—82no—
203C22⋊D61—82no—
204C2×Dic61—41no—
205C2×Dic61—41no—
206C2×Dic61—41no—
207C2×Dic61—82no—
208C2×Dic61C2×D811yescharacteristic
209C2×Dic61C2×D811yescharacteristic
210D244—22no—
211D244—41no—
212D244—41no—
213D244—161no—
214C4×D61—21no—
215C4×D61—21no—
216C4×D61—21no—
217C4×D61—21no—
218C4×D61—161no—
219C4×D61—161no—
220Dic122—41no—
221Dic122—41no—
222Dic122—41no—
223Dic122—41no—
224C8×C61—21no—
225C8×C61C2×#4111yescharacteristic
226C8×C61H(5,𝔽2)11yescharacteristic
227#92418—21no—
228#92418—21no—
229#33881—611nomaximal, Sylow
230C22×C61—42no—
231C22×C61—81no—
232C22×C61—81no—
233C22×C61C22×D811yescharacteristic
234C2×D61—21no—
235C2×D61—21no—
236C2×D61—21no—
237C2×D61—21no—
238C2×D61—21no—
239C2×D61—81no—
240C2×D61—81no—
241C2×D61—81no—
242C2×D61—164no—
243C2×D61#51012yes—
244C4×C61—21no—
245C4×C61—21no—
246C4×C61—81no—
247C4×C61—81no—
248C4×C61—81no—
249C4×C61#54611yescharacteristic
250C4×C61#57711yescharacteristic
251Dic61—21no—
252Dic61—21no—
253Dic61—81no—
254Dic61—81no—
255Dic61—81no—
256#3338—611no—
257#3280—611no—
258#2243—611no—
259#2236—611no—
260#2232—611no—
261#2224D6111yescharacteristic, complemented
262#2220—611no—
263#2216—611no—
264#2211—611no—
265#2189—611no—
266#2187—611no—
267#2175—611no—
268#2168—611no—
269#2139—611no—
270C2×#357—611no—
271C2×C61—82no—
272C2×C61#329411yescharacteristic
273C2×C61C2×#51011yescharacteristic
274C2×C61#341511yescharacteristic
275D61—22no—
276D61—41no—
277D61—161no—
278C2×#135—611no—
279C22×D8—611no—
280#554—1221no—
281#546—1221no—
282C2×Q32—611no—
283C2×SD32—611no—
284C2×SD32—611no—
285C2×M32—611no—
286C22×C16—611no—
287#500C2×D6111yescharacteristic, complemented
288#495—611no—
289#484—1221no—
290#484—1221no—
291#477—1221no—
292#467—611no—
293#467—611no—
294#467—611no—
295#466—611no—
296#463—1221no—
297#450—1221no—
298#449—1221no—
299C4×Q16—611no—
300C4×D8C2×D6111yescharacteristic
301C8×D4—611no—
302C2×#107—611no—
303C2×#107—611no—
304#366—611no—
305#366C2×D6111yescharacteristic, complemented
306#366C2×D6111yescharacteristic, complemented
307C4⋊C16C2×D6111yescharacteristic, complemented
308#358—611no—
309#358—611no—
310#358—611no—
311#358—611no—
312#357—611no—
313#357—611no—
314#357—611no—
315#357—611no—
316#357C2×D6111yescharacteristic
317#357C2×D6111yescharacteristic
318C22⋊C16—611no—
319C22⋊C16—611no—
320#346—611no—
321C61#3388111yescharacteristic, complemented, Sylow
322C2×#41—1221no—
323C22×D4—1221no—
324#135—1222no—
325#135—2441no—
326C2×Q16—611no—
327C2×Q16—611no—
328C2×SD16—1221no—
329C2×SD16—1221no—
330C2×D8—611no—
331C2×D8—1221no—
332C2×D8—1222no—
333C2×D8—2441no—
334C2×D8C22×D6111yescharacteristic
335C22×C8—611no—
336C22×C8—611no—
337C4⋊Q8—21no—
338#125—2441no—
339#124—1221no—
340#123—2441no—
341C22⋊Q8—1221no—
342C22⋊Q8—1221no—
343C22⋊Q8—1221no—
344C22⋊Q8—2441no—
345C22⋊Q8—2441no—
346#121—1221no—
347#121—2441no—
348#120—2441no—
349C4×Q8—1221no—
350C4×D4—21no—
351C4×D4—611no—
352C4×D4—2441no—
353C2×C4⋊C4—1221no—
354C2×C4⋊C4—1221no—
355C2×C22⋊C4—2441no—
356Q32—2441no—
357SD32—1222no—
358SD32—2441no—
359M32—2441no—
360C2×C16—611no—
361C2×C16—611no—
362C2×C16—2441no—
363C2×C16C22×D6111yescharacteristic
364C2×C16C22×D6111yescharacteristic
365#107—21no—
366#107—611no—
367#107—1221no—
368#107—1221no—
369#107C22×D6111yescharacteristic
370#107C22×D6111yescharacteristic
371#107C22×D6111yescharacteristic
372C4⋊C8—611no—
373#103—1221no—
374#103—1221no—
375#103—1221no—
376#103—1221no—
377#102—21no—
378#102—1221no—
379C22⋊C8—611no—
380C22⋊C8—611no—
381C4×C8C22×D6111yescharacteristic
382C24—2441no—
383#41—4881no—
384#41—2442no—
385C2×Q8—41no—
386C2×Q8—1221no—
387C2×Q8—1221no—
388C2×D4—21no—
389C2×D4—611no—
390C2×D4—1221no—
391C2×D4—4881no—
392C2×D4—2441no—
393C2×D4—2441no—
394C2×D4—2442no—
395C2×D4—2441no—
396C22×C4—41no—
397C22×C4—611no—
398C22×C4—611no—
399C22×C4—2441no—
400C22×C4—2441no—
401C22×C4—2441no—
402Q16—1221no—
403Q16—1221no—
404Q16—1221no—
405Q16—1221no—
406SD16—4881no—
407SD16—2442no—
408D8—21no—
409D8—1221no—
410D8—1221no—
411D8—2442no—
412D8#1175822612yes—
413C2×C8—611no—
414C2×C8—611no—
415C2×C8—1221no—
416C2×C8—1221no—
417C2×C8—1221no—
418C2×C8—1221no—
419C2×C8D4×D6111yescharacteristic
420C2×C8C23×D6111yescharacteristic
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—41no—
425C4⋊C4—611no—
426C4⋊C4—1221no—
427C4⋊C4—2441no—
428C4⋊C4—2441no—
429C4⋊C4—2441no—
430C4⋊C4—2441no—
431C4⋊C4—2441no—
432C4⋊C4—2441no—
433C22⋊C4—41no—
434C22⋊C4—611no—
435C22⋊C4—611no—
436C22⋊C4—2441no—
437C22⋊C4—2441no—
438C22⋊C4—2441no—
439C22⋊C4—2441no—
440C22⋊C4—2441no—
441C22⋊C4—2441no—
442C42—2441no—
443C42D4×D6111yescharacteristic
444C16—21no—
445C16—21no—
446C16—1221no—
447C16—1221no—
448C23—41no—
449C23—611no—
450C23—611no—
451C23—9761no—
452C23—4882no—
453C23—4882no—
454C23—2441no—
455Q8—161no—
456Q8—2441no—
457Q8—2441no—
458Q8—2441no—
459Q8—2441no—
460D4—22no—
461D4—41no—
462D4—1222no—
463D4—9761no—
464D4—4882no—
465D4—4882no—
466D4—2441no—
467D4—2441no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—161no—
472C2×C4—611no—
473C2×C4—611no—
474C2×C4—1221no—
475C2×C4—1221no—
476C2×C4—1221no—
477C2×C4—1221no—
478C2×C4—9761no—
479C2×C4—9761no—
480C2×C4—4882no—
481C2×C4—2441no—
482C2×C4—2441no—
483C2×C4—2441no—
484C2×C4D8×D6111yescharacteristic
485C2×C4D8×D6111yescharacteristic
486C2×C4C2×D4×D6111yescharacteristic
487C8—21no—
488C8—1221no—
489C8—1221no—
490C8C2×#1175822611yescharacteristic
491C8#1451982311yescharacteristic
492C22—42no—
493C22—81no—
494C22—81no—
495C22—612no—
496C22—1221no—
497C22—1221no—
498C22—1221no—
499C22—1221no—
500C22—1221no—
501C22—9764no—
502C22—4881no—
503C22—4881no—
504C22—4881no—
505C22C2×D8×D6111yescharacteristic
506C4—21no—
507C4—21no—
508C4—81no—
509C4—81no—
510C4—81no—
511C4—1221no—
512C4—1221no—
513C4—4881no—
514C4—4881no—
515C4—4881no—
516C4#1684040311yescharacteristic
517C4#1684057111yescharacteristic
518C2—82no—
519C2—1222no—
520C2—9761no—
521C2—2441no—
522C2#2145762911yescharacteristic
523C2#510×D6111yescharacteristic
524C2#2145895611yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2224C2
socleC22×C61C22×D8
prime radical#21457505C2
hypercenter#2224D61
hypocenterC61#33881
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2224

Complements

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

NH ≅ G/Ntype
1. #21458211C2semidirect
3. #21448058C2semidirect
4. #21448023C2semidirect
5. #21448001C2semidirect
6. #21447933C2semidirect
7. #21447911C2semidirect
8. #21447882C2semidirect
9. #21447760C2semidirect
10. #21447749C2semidirect
11. #21447683C2semidirect
12. #21447643C2semidirect
13. #21447528C2semidirect
14. #357×D61C2semidirect
15. C61×#2224C2semidirect
20. C2×Dic488C22semidirect
23. C2×#14519716C22semidirect
31. #16840004C22semidirect
36. C4×Dic244C22semidirect
39. #107×D61C22semidirect
40. #16839587C22semidirect
41. #16839567C22semidirect
42. #16839565C22semidirect
43. #16839565C22semidirect
44. #16839565C22semidirect
50. #16839541C22semidirect
51. #16839538C22semidirect
52. C61×#500C22semidirect
54. C61×#366C22semidirect
55. C61×#366C22semidirect
56. C61×C4⋊C16C22semidirect
261. #2224D61semidirect
287. #500C2×D61semidirect
305. #366C2×D61semidirect
306. #366C2×D61semidirect
307. C4⋊C16C2×D61semidirect
321. C61#33881semidirect

Maximal subgroups

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

subgroupindex
#214582112
#214575052
#214480582
#214480232
#214480012
#214479332
#214479112
#214478822
#214477602
#214477492
#214476832
#214476432
#214475282
#357×D612
C61×#22242
#3388161