Finite Group Databasebeta

← #29837577

Subgroups — #29837577

Order 15616.

476 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458188C211yesmaximal, characteristic, complemented
2#21448095C211yesmaximal, characteristic, complemented
3#21448027C211yesmaximal, characteristic, complemented
4#21448016C211yesmaximal, characteristic, complemented
5#21448007C211yesmaximal, characteristic, complemented
6#21448002C211yesmaximal, characteristic, complemented
7#21447980C211yesmaximal, characteristic, complemented
8#21447976C211yesmaximal, characteristic, complemented
9#21447930C211yesmaximal, characteristic, complemented
10#21447930C211yesmaximal, characteristic, complemented
11C4×#14519721C211yesmaximal, characteristic, complemented
12#21447651C211yesmaximal, characteristic, complemented
13#21447608C211yesmaximal, characteristic, complemented
14#21447605C211yesmaximal, characteristic, complemented
15C61×#3339C211yesmaximal, characteristic
16#16840452—21no—
17C2×#14519721C2211yescharacteristic
18C2×#14519717C2211yescharacteristic
19C2×#14519717C2211yescharacteristic
20#16840164C2211yescharacteristic
21#16840104—21no—
22#16840093—21no—
23#16840070—21no—
24#16840003C2211yescharacteristic
25#16840003C2211yescharacteristic
26C4×Dic244C2211yescharacteristic
27#16839800C2211yescharacteristic
28C2×#14519711C2211yescharacteristic
29#16839589C2211yescharacteristic
30#16839589C2211yescharacteristic
31#16839589C2211yescharacteristic
32#16839589C2211yescharacteristic
33#16839589C2211yescharacteristic
34#16839587C2211yescharacteristic
35#16839587C2211yescharacteristic
36#16839587C2211yescharacteristic
37#16839587C2211yescharacteristic
38C4⋊#11758185C2211yescharacteristic
39#16839565C2211yescharacteristic
40#16839565C2211yescharacteristic
41#16839565C2211yescharacteristic
42#16839563C2211yescharacteristic
43#16839563C2211yescharacteristic
44#16839563C2211yescharacteristic
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×Dic244C2311yescharacteristic
60#14519770—41no—
61#14519769—21no—
62#14519767—41no—
63#14519758—41no—
64#14519756—21no—
65#14519756—21no—
66C4×Dic122—21no—
67#14519736—21no—
68#14519733—41no—
69C2×C4⋊Dic61—21no—
70#14519721—22no—
71#14519717—22no—
72#14519717—22no—
73C2×#11758185C2311yescharacteristic
74C2×#11758185C2311yescharacteristic
75C2×#11758185C2311yescharacteristic
76C2×#11758185C2311yescharacteristic
77#14519711—21no—
78#14519711C2311yescharacteristic
79#14519711C2311yescharacteristic
80#14519711C2311yescharacteristic
81#14519709—21no—
82#14519709—21no—
83#14519702—21no—
84#14519702—21no—
85#14519702—21no—
86C2×D8×C61C2311yescharacteristic
87C22×C8×C61C2311yescharacteristic
88C22×C8×C61C2311yescharacteristic
89#126×C61—41no—
90#125×C61—21no—
91#123×C61—41no—
92#121×C61—21no—
93#121×C61—21no—
94#121×C61—41no—
95C4×D4×C61—21no—
96C4×D4×C61—41no—
97C4×D4×C61D411yescharacteristic
98#117×C61—21no—
99C2×C4⋊C4×C61—21no—
100#107×C61—21no—
101#107×C61C2311yescharacteristic
102#107×C61C2311yescharacteristic
103#107×C61C2311yescharacteristic
104#106×C61—21no—
105#106×C61—21no—
106C4⋊C8×C61D411yescharacteristic
107#102×C61—21no—
108#102×C61—21no—
109#102×C61—21no—
110C22⋊C8×C61D411yescharacteristic
111C22⋊C8×C61D411yescharacteristic
112C4×C8×C61C2311yescharacteristic
113C2×D4×C61—21no—
114C2×D4×C61—41no—
115C2×D4×C61—41no—
116C2×D4×C61D811yescharacteristic
117C22×C4×C61—41no—
118C22×C4×C61—41no—
119C22×C4×C61C2×D411yescharacteristic
120C22×C4×C61C2×D411yescharacteristic
121C22×Dic61—41no—
122C2×Dic122—21no—
123D8×C61—21no—
124D8×C61—21no—
125C2×C8×C61—21no—
126C2×C8×C61—21no—
127C2×C8×C61—21no—
128C2×C8×C61—21no—
129C2×C8×C61C2×D411yescharacteristic
130C2×C8×C61C2×D411yescharacteristic
131C2×C8×C61C2×D411yescharacteristic
132C2×C8×C61C2411yescharacteristic
133C4⋊C4×C61—21no—
134C4⋊C4×C61—21no—
135C4⋊C4×C61—21no—
136C4⋊C4×C61—41no—
137C4⋊C4×C61—41no—
138C4⋊C4×C61—41no—
139C4⋊C4×C61D811yescharacteristic
140C22⋊C4×C61—41no—
141C22⋊C4×C61—41no—
142C22⋊C4×C61—41no—
143C22⋊C4×C61—41no—
144C22⋊C4×C61D811yescharacteristic
145C22⋊C4×C61D811yescharacteristic
146C42×C61—41no—
147C42×C61C2×D411yescharacteristic
148C22⋊Dic61—41no—
149C22⋊Dic61—41no—
150C22⋊Dic61—41no—
151C4⋊Dic61—21no—
152C4⋊Dic61—21no—
153C4⋊Dic61—21no—
154C4⋊Dic61—41no—
155#11758196—41no—
156#11758196—41no—
157#11758196—41no—
158#11758196—41no—
159#11758196—41no—
160C4×Dic61—41no—
161C4×Dic61—41no—
162Dic244—21no—
163Dic244—21no—
164#11758185—21no—
165#11758185—21no—
166#11758185—21no—
167#11758185#4112yes—
168C23×C61—41no—
169C23×C61C2×D811yescharacteristic
170C23×C61C2×D811yescharacteristic
171D4×C61—41no—
172D4×C61—41no—
173D4×C61—41no—
174D4×C61—82no—
175D4×C61—161no—
176C2×C4×C61—21no—
177C2×C4×C61—21no—
178C2×C4×C61—21no—
179C2×C4×C61—21no—
180C2×C4×C61—41no—
181C2×C4×C61—41no—
182C2×C4×C61—41no—
183C2×C4×C61—161no—
184C2×C4×C61—161no—
185C2×C4×C61C2×D811yescharacteristic
186C2×C4×C61C2×D811yescharacteristic
187C2×C4×C61C2×D811yescharacteristic
188C2×C4×C61C2×D811yescharacteristic
189C2×C4×C61C22×D411yescharacteristic
190C2×Dic61—41no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—41no—
194C2×Dic61—82no—
195Dic122—41no—
196Dic122—41no—
197C8×C61—21no—
198C8×C61—21no—
199C8×C61—21no—
200C8×C61C2×#4111yescharacteristic
201C8×C612−1+411yescharacteristic
202#33918—611nomaximal, Sylow
203C22×C61—21no—
204C22×C61—21no—
205C22×C61—21no—
206C22×C61—21no—
207C22×C61—21no—
208C22×C61—21no—
209C22×C61—81no—
210C22×C61—81no—
211C22×C61—81no—
212C22×C61C22×D811yescharacteristic
213C4×C61—21no—
214C4×C61—21no—
215C4×C61—21no—
216C4×C61—21no—
217C4×C61—81no—
218C4×C61—81no—
219C4×C61—81no—
220C4×C61#54711yescharacteristic
221C4×C61#57811yescharacteristic
222Dic61—81no—
223Dic61—81no—
224Dic61—81no—
225Dic61—81no—
226#3339D6111yescharacteristic
227#3336—611no—
228#2253—611no—
229#2237—611no—
230#2235—611no—
231#2234—611no—
232#2233—611no—
233#2229—611no—
234#2228—611no—
235#2220—611no—
236#2220—611no—
237C4×SD32—611no—
238#2169—611no—
239#2159—611no—
240#2159—611no—
241C2×C61—41no—
242C2×C61—41no—
243C2×C61—161no—
244C2×C61#333411yescharacteristic
245C2×C61#341411yescharacteristic
246C2×C61#341611yescharacteristic
247#553—21no—
248#552—1221no—
249C2×SD32—611no—
250C2×M32—611no—
251C2×M32—611no—
252#499—611no—
253#499C2×D6111yescharacteristic
254#485—1221no—
255#483—1221no—
256#482—21no—
257#481—21no—
258#479—1221no—
259#478—21no—
260#467—611no—
261#467—611no—
262#466C2×D6111yescharacteristic
263#466C2×D6111yescharacteristic
264C4×Q16—611no—
265C4×D8C2×D6111yescharacteristic
266C8×D4C2×D6111yescharacteristic
267#427—611no—
268#427C2×D6111yescharacteristic
269C2×#107—611no—
270C2×#107C2×D6111yescharacteristic
271#367—611no—
272#367—611no—
273#367—611no—
274#367—611no—
275#367—611no—
276#366—611no—
277#366—611no—
278#366—611no—
279#366—611no—
280C4⋊C16—611no—
281#358—611no—
282#358—611no—
283#358—611no—
284#357—611no—
285#357—611no—
286#357—611no—
287C22⋊C16—611no—
288C22⋊C16—611no—
289C4×C16—611no—
290C61#3391811yescharacteristic, complemented, Sylow
291C2×Q16—611no—
292C2×D8C22×D6111yescharacteristic
293C22×C8C22×D6111yescharacteristic
294C22×C8C22×D6111yescharacteristic
295#126—41no—
296#126—2441no—
297#125—21no—
298#125—1221no—
299#125—2441no—
300#123—41no—
301#123—2441no—
302C22⋊Q8—1221no—
303C22⋊Q8—1221no—
304#121—21no—
305#121—21no—
306#121—41no—
307C4×Q8—1221no—
308C4×D4—21no—
309C4×D4—41no—
310C4×D4C22⋊D6111yescharacteristic
311#117—21no—
312#117—1221no—
313#117—2441no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—1221no—
316SD32—1222no—
317M32—1222no—
318M32—1222no—
319C2×C16—611no—
320C2×C16—611no—
321C2×C16—611no—
322C2×C16—611no—
323#107—21no—
324#107—611no—
325#107—611no—
326#107—611no—
327#107—1221no—
328#107C22×D6111yescharacteristic
329#107C22×D6111yescharacteristic
330#107C22×D6111yescharacteristic
331#106—21no—
332#106—21no—
333#106—1221no—
334#106—1221no—
335C4⋊C8C22⋊D6111yescharacteristic
336#103—1221no—
337#103—1221no—
338#103—1221no—
339#102—21no—
340#102—21no—
341#102—21no—
342C22⋊C8C22⋊D6111yescharacteristic
343C22⋊C8C22⋊D6111yescharacteristic
344C4×C8C22×D6111yescharacteristic
345C2×Q8—1221no—
346C2×D4—21no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4#1175819911yescharacteristic
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—2441no—
353C22×C4C2×C22⋊D6111yescharacteristic
354C22×C4C2×C22⋊D6111yescharacteristic
355Q16—1221no—
356Q16—1221no—
357D8—21no—
358D8—21no—
359C2×C8—21no—
360C2×C8—21no—
361C2×C8—21no—
362C2×C8—21no—
363C2×C8C2×C22⋊D6111yescharacteristic
364C2×C8C2×C22⋊D6111yescharacteristic
365C2×C8C2×C22⋊D6111yescharacteristic
366C2×C8C23×D6111yescharacteristic
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—1221no—
374C4⋊C4—1221no—
375C4⋊C4—1221no—
376C4⋊C4—2441no—
377C4⋊C4—2441no—
378C4⋊C4—2441no—
379C4⋊C4—2441no—
380C4⋊C4—2441no—
381C4⋊C4—2441no—
382C4⋊C4#1175819911yescharacteristic
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—2441no—
388C22⋊C4—2441no—
389C22⋊C4—2441no—
390C22⋊C4#1175819911yescharacteristic
391C22⋊C4#1175819911yescharacteristic
392C42—41no—
393C42—2441no—
394C42—2441no—
395C42C2×C22⋊D6111yescharacteristic
396C16—612no—
397C16—1221no—
398C16—1221no—
399C16—1221no—
400C23—41no—
401C23C2×#1175819911yescharacteristic
402C23C2×#1175819911yescharacteristic
403Q8—2441no—
404Q8—2441no—
405D4—41no—
406D4—41no—
407D4—41no—
408D4—82no—
409D4—161no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—161no—
418C2×C4—161no—
419C2×C4—4882no—
420C2×C4—2441no—
421C2×C4—2441no—
422C2×C4—2441no—
423C2×C4—2441no—
424C2×C4C2×#1175819911yescharacteristic
425C2×C4C2×#1175819911yescharacteristic
426C2×C4C2×#1175819911yescharacteristic
427C2×C4C2×#1175819911yescharacteristic
428C2×C4C22×C22⋊D6111yescharacteristic
429C8—21no—
430C8—21no—
431C8—21no—
432C8#41×D6111yescharacteristic
433C8#1451982411yescharacteristic
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—81no—
441C22—81no—
442C22—81no—
443C22C22×#1175819911yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—81no—
449C4—81no—
450C4—81no—
451C4—4881no—
452C4—4881no—
453C4—4881no—
454C4—4881no—
455C4#1684041111yescharacteristic
456C4#1684057711yescharacteristic
457C2—41no—
458C2—41no—
459C2—161no—
460C2#2145816211yescharacteristic
461C2#2145895311yescharacteristic
462C2#2145896611yescharacteristic
subgroupG/H
centerC22C22×#11758199
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
Fitting, prime radicalC61×#3339C2
socleC22×C61C22×D8
hypercenter#3339D61
hypocenterC61#33918
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. #21458188C2semidirect
2. #21448095C2semidirect
3. #21448027C2semidirect
4. #21448016C2semidirect
5. #21448007C2semidirect
6. #21448002C2semidirect
7. #21447980C2semidirect
8. #21447976C2semidirect
9. #21447930C2semidirect
10. #21447930C2semidirect
11. C4×#14519721C2semidirect
12. #21447651C2semidirect
13. #21447608C2semidirect
14. #21447605C2semidirect
290. C61#33918semidirect

Maximal subgroups

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

subgroupindex
#214581882
#214480952
#214480272
#214480162
#214480072
#214480022
#214479802
#214479762
#214479302
C4×#145197212
#214476512
#214476082
#214476052
C61×#33392
#3391861