Finite Group Databasebeta

← #29836919

Subgroups — #29836919

Order 15616.

558 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457562C211yesmaximal, characteristic, complemented
2#21448053C211yesmaximal, characteristic, complemented
3#21448027C211yesmaximal, characteristic, complemented
4#21448004C211yesmaximal, characteristic, complemented
5#21447980C211yesmaximal, characteristic, complemented
6#21447913C211yesmaximal, characteristic, complemented
7#21447903C211yesmaximal, characteristic, complemented
8#21447874C211yesmaximal, characteristic, complemented
9#21447740C211yesmaximal, characteristic, complemented
10#21447735C211yesmaximal, characteristic, complemented
11C4×#14519721C211yesmaximal, characteristic, complemented
12D4×#11758185C211yesmaximal, characteristic, complemented
13#21447524C211yesmaximal, characteristic, complemented
14C2×#16839565C211yesmaximal, characteristic, complemented
15C61×#3339C211yesmaximal, characteristic, complemented
16C2×#14519799C2211yescharacteristic
17C22×Dic244C2211yescharacteristic
18#16840421—21no—
19C2×#14519721C2211yescharacteristic
20C2×#14519721C2211yescharacteristic
21C2×#14519718C2211yescharacteristic
22C22×#11758185C2211yescharacteristic
23C22×#11758185C2211yescharacteristic
24#16840146C2211yescharacteristic
25#16840003C2211yescharacteristic
26#16839998C2211yescharacteristic
27#16839985—21no—
28#16839926—21no—
29#16839903—21no—
30C4×Dic244C2211yescharacteristic
31#16839589C2211yescharacteristic
32#16839589C2211yescharacteristic
33#16839587C2211yescharacteristic
34C4⋊#11758185C2211yescharacteristic
35#16839565C2211yescharacteristic
36#16839565C2211yescharacteristic
37#16839565C2211yescharacteristic
38#16839565C2211yescharacteristic
39#16839565C2211yescharacteristic
40#16839565C2211yescharacteristic
41#16839563C2211yescharacteristic
42#16839562C2211yescharacteristic
43#16839562C2211yescharacteristic
44#16839562C2211yescharacteristic
45C22⋊#11758185C2211yescharacteristic
46C22⋊#11758185C2211yescharacteristic
47C4×#11758185C2211yescharacteristic
48C61×#553—21no—
49C61×#499C2211yescharacteristic
50C61×#482—21no—
51C61×#481—21no—
52C61×#478—21no—
53C61×#466C2211yescharacteristic
54C61×#466C2211yescharacteristic
55C4×D8×C61C2211yescharacteristic
56C8×D4×C61C2211yescharacteristic
57C61×#427C2211yescharacteristic
58C2×#107×C61C2211yescharacteristic
59C2×#11758222—21no—
60C22×Dic122—21no—
61#14519799—22no—
62#14519799—41no—
63C2×Dic244—22no—
64C2×Dic244—21no—
65C2×Dic244—41no—
66C2×Dic244C2311yescharacteristic
67C2×Dic244C2311yescharacteristic
68C2×#11758190—21no—
69C2×#11758190—21no—
70C2×D488C2311yescharacteristic
71#14519765—21no—
72#14519763—41no—
73#14519756—21no—
74#14519755—41no—
75#14519751—21no—
76#14519749—41no—
77C4×Dic122—21no—
78#14519737—41no—
79#14519721—22no—
80#14519721—41no—
81#14519718—41no—
82C2×#11758185—41no—
83C2×#11758185—41no—
84C2×#11758185C2311yescharacteristic
85C2×#11758185C2311yescharacteristic
86C2×#11758185C2311yescharacteristic
87C2×#11758185C2311yescharacteristic
88#14519711C2311yescharacteristic
89#14519702—21no—
90#14519702—21no—
91#14519699—21no—
92C2×D8×C61C2311yescharacteristic
93C22×C8×C61C2311yescharacteristic
94C22×C8×C61C2311yescharacteristic
95#126×C61—41no—
96#125×C61—21no—
97#123×C61—41no—
98#121×C61—21no—
99#121×C61—21no—
100#121×C61—41no—
101C4×D4×C61—21no—
102C4×D4×C61—41no—
103C4×D4×C61D411yescharacteristic
104#117×C61—21no—
105C2×C4⋊C4×C61—21no—
106#107×C61—21no—
107#107×C61C2311yescharacteristic
108#107×C61C2311yescharacteristic
109#107×C61C2311yescharacteristic
110#106×C61—21no—
111#106×C61—21no—
112C4⋊C8×C61D411yescharacteristic
113#102×C61—21no—
114#102×C61—21no—
115#102×C61—21no—
116C22⋊C8×C61D411yescharacteristic
117C22⋊C8×C61D411yescharacteristic
118C4×C8×C61C2311yescharacteristic
119C2×D4×C61—21no—
120C2×D4×C61—41no—
121C2×D4×C61—41no—
122C2×D4×C61D811yescharacteristic
123C22×C4×C61—41no—
124C22×C4×C61—41no—
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61C2×D411yescharacteristic
127C2×C22⋊D61—41no—
128C2×C22⋊D61—41no—
129C22×Dic61—41no—
130#11758222—42no—
131#11758222—81no—
132C2×D244—21no—
133C2×C4×D61—41no—
134C2×Dic122—21no—
135C2×Dic122—21no—
136C2×Dic122—42no—
137C2×Dic122—41no—
138C2×Dic122—81no—
139D8×C61—21no—
140D8×C61—21no—
141C2×C8×C61—21no—
142C2×C8×C61—21no—
143C2×C8×C61—21no—
144C2×C8×C61—21no—
145C2×C8×C61C2×D411yescharacteristic
146C2×C8×C61C2×D411yescharacteristic
147C2×C8×C61C2×D411yescharacteristic
148C2×C8×C61C2411yescharacteristic
149C4⋊C4×C61—21no—
150C4⋊C4×C61—21no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—41no—
153C4⋊C4×C61—41no—
154C4⋊C4×C61—41no—
155C4⋊C4×C61D811yescharacteristic
156C22⋊C4×C61—41no—
157C22⋊C4×C61—41no—
158C22⋊C4×C61—41no—
159C22⋊C4×C61—41no—
160C22⋊C4×C61D811yescharacteristic
161C22⋊C4×C61D811yescharacteristic
162C42×C61—41no—
163C42×C61C2×D411yescharacteristic
164C22⋊Dic61—41no—
165#11758198—41no—
166#11758198—41no—
167#11758198—41no—
168C4⋊Dic61—21no—
169#11758196—41no—
170#11758196—41no—
171C4×Dic61—41no—
172Dic244—21no—
173Dic244—21no—
174Dic244—21no—
175Dic244—42no—
176Dic244#4112yes—
177D488—21no—
178D488—21no—
179#11758190—42no—
180#11758190—81no—
181#11758185—21no—
182#11758185—21no—
183#11758185—21no—
184#11758185—21no—
185C23×C61—41no—
186C23×C61C2×D811yescharacteristic
187C23×C61C2×D811yescharacteristic
188C22×D61—41no—
189D4×C61—22no—
190D4×C61—41no—
191D4×C61—41no—
192D4×C61—82no—
193D4×C61—161no—
194C2×C4×C61—21no—
195C2×C4×C61—21no—
196C2×C4×C61—21no—
197C2×C4×C61—21no—
198C2×C4×C61—41no—
199C2×C4×C61—41no—
200C2×C4×C61—41no—
201C2×C4×C61—161no—
202C2×C4×C61—161no—
203C2×C4×C61C2×D811yescharacteristic
204C2×C4×C61C2×D811yescharacteristic
205C2×C4×C61C2×D811yescharacteristic
206C2×C4×C61C2×D811yescharacteristic
207C2×C4×C61C22×D411yescharacteristic
208C22⋊D61—82no—
209C22⋊D61—82no—
210C2×Dic61—41no—
211C2×Dic61—41no—
212C2×Dic61—41no—
213C2×Dic61—82no—
214D244—41no—
215D244—41no—
216C4×D61—82no—
217Dic122—22no—
218Dic122—41no—
219Dic122—41no—
220Dic122—41no—
221Dic122—82no—
222C8×C61—21no—
223C8×C61—21no—
224C8×C61—21no—
225C8×C61C2×#4111yescharacteristic
226C8×C61H(5,𝔽2)11yescharacteristic
227#33868—611nomaximal, Sylow
228C22×C61—21no—
229C22×C61—21no—
230C22×C61—21no—
231C22×C61—21no—
232C22×C61—21no—
233C22×C61—81no—
234C22×C61—81no—
235C22×C61—81no—
236C22×C61#50812yes—
237C22×C61C22×D811yescharacteristic
238C2×D61—81no—
239C2×D61—81no—
240C2×D61—81no—
241C4×C61—21no—
242C4×C61—21no—
243C4×C61—21no—
244C4×C61—21no—
245C4×C61—81no—
246C4×C61—81no—
247C4×C61—81no—
248C4×C61#54611yescharacteristic
249C4×C61#57711yescharacteristic
250Dic61—42no—
251Dic61—81no—
252Dic61—81no—
253#3339D6111yescharacteristic, complemented
254#3285—611no—
255#2242—611no—
256#2237—611no—
257#2233—611no—
258#2229—611no—
259#2217—611no—
260#2215—611no—
261#2210—611no—
262#2186—611no—
263#2185—611no—
264C4×SD32—611no—
265D4×C16—611no—
266#2138—611no—
267C2×#358—611no—
268C2×C61—22no—
269C2×C61—41no—
270C2×C61—161no—
271C2×C61#329411yescharacteristic
272C2×C61C2×#50811yescharacteristic
273C2×C61#341611yescharacteristic
274D61—161no—
275C2×#135—611no—
276C22×Q16—611no—
277#553—21no—
278#548—1221no—
279C2×SD32—611no—
280C2×SD32—611no—
281C2×D16—611no—
282C22×C16—611no—
283C22×C16—611no—
284#499C2×D6111yescharacteristic
285#495—611no—
286#482—21no—
287#481—21no—
288#478—21no—
289#467—611no—
290#466—611no—
291#466C2×D6111yescharacteristic
292#466C2×D6111yescharacteristic
293#464—1221no—
294#452—1221no—
295#448—1221no—
296C4×Q16—611no—
297C4×D8C2×D6111yescharacteristic
298C8×D4C2×D6111yescharacteristic
299#427C2×D6111yescharacteristic
300C2×#107C2×D6111yescharacteristic
301#367—611no—
302#367—611no—
303#366—611no—
304C4⋊C16—611no—
305#358—611no—
306#358—611no—
307#358—611no—
308#358—611no—
309#358—611no—
310#358—611no—
311#357—611no—
312#357—611no—
313#357—611no—
314#357—611no—
315C22⋊C16—611no—
316C22⋊C16—611no—
317C4×C16—611no—
318C61#3386811yescharacteristic, complemented, Sylow
319C2×#41—1221no—
320C22×Q8—1221no—
321#135—1222no—
322#135—2441no—
323C2×Q16—611no—
324C2×Q16—611no—
325C2×Q16—1222no—
326C2×Q16—1221no—
327C2×Q16—2441no—
328C2×SD16—1221no—
329C2×SD16—1221no—
330C2×D8—611no—
331C2×D8C22×D6111yescharacteristic
332C22×C8C22×D6111yescharacteristic
333C22×C8C22×D6111yescharacteristic
334#126—41no—
335#125—21no—
336#124—1221no—
337#124—2441no—
338#123—41no—
339C22⋊Q8—1221no—
340C22⋊Q8—2441no—
341#121—21no—
342#121—21no—
343#121—41no—
344#121—1221no—
345#121—2441no—
346C4×Q8—1221no—
347C4×D4—21no—
348C4×D4—41no—
349C4×D4—2441no—
350C4×D4C22⋊D6111yescharacteristic
351#117—21no—
352C2×C4⋊C4—21no—
353SD32—1222no—
354SD32—2441no—
355D16—2441no—
356C2×C16—611no—
357C2×C16—611no—
358C2×C16—611no—
359C2×C16—611no—
360C2×C16—2441no—
361C2×C16—2441no—
362#107—21no—
363#107—611no—
364#107C22×D6111yescharacteristic
365#107C22×D6111yescharacteristic
366#107C22×D6111yescharacteristic
367#106—21no—
368#106—21no—
369C4⋊C8C22⋊D6111yescharacteristic
370#103—1221no—
371#103—1221no—
372#102—21no—
373#102—21no—
374#102—21no—
375#102—1221no—
376C22⋊C8C22⋊D6111yescharacteristic
377C22⋊C8C22⋊D6111yescharacteristic
378C4×C8C22×D6111yescharacteristic
379#41—4881no—
380#41—2442no—
381C2×Q8—1221no—
382C2×Q8—1221no—
383C2×Q8—4881no—
384C2×Q8—2442no—
385C2×Q8—2441no—
386C2×D4—21no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—1221no—
390C2×D4—2441no—
391C2×D4—2441no—
392C2×D4#1175819911yescharacteristic
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—2441no—
396C22×C4—2441no—
397C22×C4C2×C22⋊D6111yescharacteristic
398C22×C4C2×C22⋊D6111yescharacteristic
399Q16—612no—
400Q16—1221no—
401Q16—1221no—
402Q16—1221no—
403Q16—2442no—
404SD16—4881no—
405SD16—2442no—
406D8—21no—
407D8—21no—
408D8—1221no—
409D8—1221no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8—21no—
414C2×C8C2×C22⋊D6111yescharacteristic
415C2×C8C2×C22⋊D6111yescharacteristic
416C2×C8C2×C22⋊D6111yescharacteristic
417C2×C8C23×D6111yescharacteristic
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—41no—
422C4⋊C4—41no—
423C4⋊C4—41no—
424C4⋊C4—1221no—
425C4⋊C4—2441no—
426C4⋊C4—2441no—
427C4⋊C4#1175819911yescharacteristic
428C22⋊C4—41no—
429C22⋊C4—41no—
430C22⋊C4—41no—
431C22⋊C4—41no—
432C22⋊C4—2441no—
433C22⋊C4—2441no—
434C22⋊C4—2441no—
435C22⋊C4—2441no—
436C22⋊C4#1175819911yescharacteristic
437C22⋊C4#1175819911yescharacteristic
438C42—41no—
439C42—2441no—
440C42C2×C22⋊D6111yescharacteristic
441C16—1221no—
442C16—1221no—
443C16—1221no—
444C16—1221no—
445C23—41no—
446C23—2441no—
447C23C2×#1175819911yescharacteristic
448C23C2×#1175819911yescharacteristic
449Q8—1222no—
450Q8—4882no—
451Q8—2441no—
452Q8—2441no—
453Q8—2441no—
454D4—22no—
455D4—41no—
456D4—41no—
457D4—82no—
458D4—161no—
459D4—4882no—
460D4—4882no—
461D4—2441no—
462D4—2441no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—161no—
471C2×C4—161no—
472C2×C4—4882no—
473C2×C4—4882no—
474C2×C4—2441no—
475C2×C4—2441no—
476C2×C4—2441no—
477C2×C4C2×#1175819911yescharacteristic
478C2×C4C2×#1175819911yescharacteristic
479C2×C4C2×#1175819911yescharacteristic
480C2×C4C2×#1175819911yescharacteristic
481C2×C4C22×C22⋊D6111yescharacteristic
482C8—21no—
483C8—21no—
484C8—21no—
485C8#41×D6111yescharacteristic
486C8#1451982311yescharacteristic
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—81no—
493C22—81no—
494C22—81no—
495C22—4881no—
496C22—4881no—
497C22—4881no—
498C22#1684019212yes—
499C22C22×#1175819911yescharacteristic
500C4—21no—
501C4—21no—
502C4—21no—
503C4—21no—
504C4—81no—
505C4—81no—
506C4—81no—
507C4—4881no—
508C4—4881no—
509C4—2442no—
510C4#1684040011yescharacteristic
511C4#1684057011yescharacteristic
512C2—22no—
513C2—41no—
514C2—161no—
515C2—9761no—
516C2#2145762611yescharacteristic
517C2C2×#1684019211yescharacteristic
518C2#2145896611yescharacteristic
subgroupG/H
centerC22C22×#11758199
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#3339C2
socleC22×C61C22×D8
hypercenter#3339D61
hypocenterC61#33868
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3339

Complements

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

NH ≅ G/Ntype
1. #21457562C2semidirect
2. #21448053C2semidirect
3. #21448027C2semidirect
4. #21448004C2semidirect
5. #21447980C2semidirect
6. #21447913C2semidirect
7. #21447903C2semidirect
8. #21447874C2semidirect
9. #21447740C2semidirect
10. #21447735C2semidirect
11. C4×#14519721C2semidirect
12. D4×#11758185C2semidirect
13. #21447524C2semidirect
14. C2×#16839565C2semidirect
15. C61×#3339C2semidirect
253. #3339D61semidirect
318. C61#33868semidirect

Maximal subgroups

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

subgroupindex
#214575622
#214480532
#214480272
#214480042
#214479802
#214479132
#214479032
#214478742
#214477402
#214477352
C4×#145197212
D4×#117581852
#214475242
C2×#168395652
C61×#33392
#3386861