Finite Group Databasebeta

← #29837623

Subgroups — #29837623

Order 15616.

488 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458222C211yesmaximal, characteristic, complemented
2#21448095C211yesmaximal, characteristic, complemented
3#21448010C211yesmaximal, characteristic, complemented
4#21448007C211yesmaximal, characteristic, complemented
5#21447999C211yesmaximal, characteristic, complemented
6#21447997C211yesmaximal, characteristic, complemented
7#21447976C211yesmaximal, characteristic, complemented
8#21447973C211yesmaximal, characteristic, complemented
9#21447920C211yesmaximal, characteristic, complemented
10#21447920C211yesmaximal, characteristic, complemented
11C4×#14519718C211yesmaximal, characteristic, complemented
12#21447651C211yesmaximal, characteristic, complemented
13#21447608C211yesmaximal, characteristic, complemented
14#21447605C211yesmaximal, characteristic, complemented
15C61×#3339C211yesmaximal, characteristic, complemented
16#16840458—21no—
17C2×#14519718C2211yescharacteristic
18C2×#14519717C2211yescharacteristic
19C2×#14519717C2211yescharacteristic
20#16840164C2211yescharacteristic
21#16840087—21no—
22#16840081—21no—
23#16840063—21no—
24#16839998C2211yescharacteristic
25#16839998C2211yescharacteristic
26C4×D488C2211yescharacteristic
27#16839800C2211yescharacteristic
28C2×#14519711C2211yescharacteristic
29#16839589C2211yescharacteristic
30#16839589C2211yescharacteristic
31#16839589C2211yescharacteristic
32#16839589C2211yescharacteristic
33#16839587C2211yescharacteristic
34#16839587C2211yescharacteristic
35#16839587C2211yescharacteristic
36#16839587C2211yescharacteristic
37#16839587C2211yescharacteristic
38C4⋊#11758185C2211yescharacteristic
39#16839563C2211yescharacteristic
40#16839563C2211yescharacteristic
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×D488C2311yescharacteristic
60#14519772—41no—
61#14519769—21no—
62#14519759—41no—
63#14519751—21no—
64#14519751—21no—
65#14519749—41no—
66C4×D244—21no—
67#14519737—41no—
68#14519736—21no—
69C2×C4⋊Dic61—21no—
70#14519718—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#14519699—21no—
84#14519699—21no—
85#14519699—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
121C2×C22⋊D61—41no—
122C2×C22⋊D61—41no—
123C22×Dic61—41no—
124C2×D244—21no—
125C2×C4×D61—41no—
126D8×C61—21no—
127D8×C61—21no—
128C2×C8×C61—21no—
129C2×C8×C61—21no—
130C2×C8×C61—21no—
131C2×C8×C61—21no—
132C2×C8×C61C2×D411yescharacteristic
133C2×C8×C61C2×D411yescharacteristic
134C2×C8×C61C2×D411yescharacteristic
135C2×C8×C61C2411yescharacteristic
136C4⋊C4×C61—21no—
137C4⋊C4×C61—21no—
138C4⋊C4×C61—21no—
139C4⋊C4×C61—41no—
140C4⋊C4×C61—41no—
141C4⋊C4×C61—41no—
142C4⋊C4×C61D811yescharacteristic
143C22⋊C4×C61—41no—
144C22⋊C4×C61—41no—
145C22⋊C4×C61—41no—
146C22⋊C4×C61—41no—
147C22⋊C4×C61D811yescharacteristic
148C22⋊C4×C61D811yescharacteristic
149C42×C61—41no—
150C42×C61C2×D411yescharacteristic
151C22⋊Dic61—41no—
152#11758198—41no—
153#11758198—41no—
154#11758198—41no—
155C4⋊Dic61—21no—
156C4⋊Dic61—21no—
157C4⋊Dic61—21no—
158C4⋊Dic61—41no—
159#11758196—41no—
160#11758196—41no—
161C4×Dic61—41no—
162D488—21no—
163D488—21no—
164#11758185—21no—
165#11758185—21no—
166#11758185—21no—
167#11758185#4112yes—
168C23×C61—41no—
169C23×C61C2×D811yescharacteristic
170C23×C61C2×D811yescharacteristic
171C22×D61—41no—
172D4×C61—41no—
173D4×C61—41no—
174D4×C61—41no—
175D4×C61—82no—
176D4×C61—161no—
177C2×C4×C61—21no—
178C2×C4×C61—21no—
179C2×C4×C61—21no—
180C2×C4×C61—21no—
181C2×C4×C61—41no—
182C2×C4×C61—41no—
183C2×C4×C61—41no—
184C2×C4×C61—161no—
185C2×C4×C61—161no—
186C2×C4×C61C2×D811yescharacteristic
187C2×C4×C61C2×D811yescharacteristic
188C2×C4×C61C2×D811yescharacteristic
189C2×C4×C61C2×D811yescharacteristic
190C2×C4×C61C22×D411yescharacteristic
191C22⋊D61—82no—
192C22⋊D61—161no—
193C2×Dic61—41no—
194C2×Dic61—41no—
195C2×Dic61—41no—
196C2×Dic61—161no—
197D244—41no—
198D244—41no—
199C4×D61—161no—
200C8×C61—21no—
201C8×C61—21no—
202C8×C61—21no—
203C8×C61C2×#4111yescharacteristic
204C8×C612−1+411yescharacteristic
205#33922—611nomaximal, Sylow
206C22×C61—21no—
207C22×C61—21no—
208C22×C61—21no—
209C22×C61—21no—
210C22×C61—21no—
211C22×C61—21no—
212C22×C61—81no—
213C22×C61—81no—
214C22×C61—81no—
215C22×C61C22×D811yescharacteristic
216C2×D61—81no—
217C2×D61—81no—
218C2×D61—81no—
219C4×C61—21no—
220C4×C61—21no—
221C4×C61—21no—
222C4×C61—21no—
223C4×C61—81no—
224C4×C61—81no—
225C4×C61—81no—
226C4×C61#54711yescharacteristic
227C4×C61#57811yescharacteristic
228Dic61—81no—
229Dic61—81no—
230Dic61—81no—
231#3339—611no—
232#3339D6111yescharacteristic, complemented
233#2253—611no—
234#2234—611no—
235#2234—611no—
236#2232—611no—
237#2232—611no—
238#2228—611no—
239#2228—611no—
240#2218—611no—
241#2218—611no—
242C4×D16—611no—
243#2169—611no—
244#2159—611no—
245#2159—611no—
246C2×C61—41no—
247C2×C61—41no—
248C2×C61—161no—
249C2×C61#333411yescharacteristic
250C2×C61#341411yescharacteristic
251C2×C61#341511yescharacteristic
252D61—161no—
253#553—21no—
254#553—1221no—
255C2×D16—611no—
256C2×M32—611no—
257C2×M32—611no—
258#499—611no—
259#499C2×D6111yescharacteristic
260#482—21no—
261#482—1221no—
262#481—21no—
263#481—1221no—
264#478—21no—
265#478—1221no—
266#466—611no—
267#466—611no—
268#466C2×D6111yescharacteristic
269#466C2×D6111yescharacteristic
270C4×D8—611no—
271C4×D8C2×D6111yescharacteristic
272C8×D4C2×D6111yescharacteristic
273#427—611no—
274#427C2×D6111yescharacteristic
275C2×#107—611no—
276C2×#107C2×D6111yescharacteristic
277#367—611no—
278#367—611no—
279#367—611no—
280#367—611no—
281#366—611no—
282#366—611no—
283#366—611no—
284#366—611no—
285#366—611no—
286C4⋊C16—611no—
287#357—611no—
288#357—611no—
289#357—611no—
290#357—611no—
291#357—611no—
292#357—611no—
293C22⋊C16—611no—
294C22⋊C16—611no—
295C4×C16—611no—
296C61#3392211yescharacteristic, complemented, Sylow
297C2×D8—611no—
298C2×D8C22×D6111yescharacteristic
299C22×C8C22×D6111yescharacteristic
300C22×C8C22×D6111yescharacteristic
301#126—41no—
302#126—2441no—
303#125—21no—
304#125—1221no—
305#123—41no—
306#123—2441no—
307#121—21no—
308#121—21no—
309#121—41no—
310#121—1221no—
311#121—1221no—
312#121—2441no—
313C4×D4—21no—
314C4×D4—41no—
315C4×D4—1221no—
316C4×D4—2441no—
317C4×D4C22⋊D6111yescharacteristic
318#117—21no—
319#117—1221no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—1221no—
322D16—1222no—
323M32—1222no—
324M32—1222no—
325C2×C16—611no—
326C2×C16—611no—
327C2×C16—611no—
328C2×C16—611no—
329#107—21no—
330#107—611no—
331#107—611no—
332#107—611no—
333#107—1221no—
334#107C22×D6111yescharacteristic
335#107C22×D6111yescharacteristic
336#107C22×D6111yescharacteristic
337#106—21no—
338#106—21no—
339#106—1221no—
340#106—1221no—
341C4⋊C8C22⋊D6111yescharacteristic
342#102—21no—
343#102—21no—
344#102—21no—
345#102—1221no—
346#102—1221no—
347#102—1221no—
348C22⋊C8C22⋊D6111yescharacteristic
349C22⋊C8C22⋊D6111yescharacteristic
350C4×C8C22×D6111yescharacteristic
351C2×D4—21no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4—1221no—
355C2×D4—2441no—
356C2×D4—2441no—
357C2×D4#1175819911yescharacteristic
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—2441no—
361C22×C4—2441no—
362C22×C4C2×C22⋊D6111yescharacteristic
363C22×C4C2×C22⋊D6111yescharacteristic
364D8—21no—
365D8—21no—
366D8—1221no—
367D8—1221no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8C2×C22⋊D6111yescharacteristic
373C2×C8C2×C22⋊D6111yescharacteristic
374C2×C8C2×C22⋊D6111yescharacteristic
375C2×C8C23×D6111yescharacteristic
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—1221no—
383C4⋊C4—1221no—
384C4⋊C4—1221no—
385C4⋊C4—2441no—
386C4⋊C4—2441no—
387C4⋊C4—2441no—
388C4⋊C4#1175819911yescharacteristic
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—2441no—
394C22⋊C4—2441no—
395C22⋊C4—2441no—
396C22⋊C4—2441no—
397C22⋊C4#1175819911yescharacteristic
398C22⋊C4#1175819911yescharacteristic
399C42—41no—
400C42—2441no—
401C42C2×C22⋊D6111yescharacteristic
402C16—612no—
403C16—1221no—
404C16—1221no—
405C16—1221no—
406C23—41no—
407C23—2441no—
408C23C2×#1175819911yescharacteristic
409C23C2×#1175819911yescharacteristic
410D4—41no—
411D4—41no—
412D4—41no—
413D4—82no—
414D4—161no—
415D4—9761no—
416D4—4882no—
417D4—2441no—
418D4—2441no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—161no—
427C2×C4—161no—
428C2×C4—9761no—
429C2×C4—9761no—
430C2×C4—2441no—
431C2×C4—2441no—
432C2×C4—2441no—
433C2×C4C2×#1175819911yescharacteristic
434C2×C4C2×#1175819911yescharacteristic
435C2×C4C2×#1175819911yescharacteristic
436C2×C4C2×#1175819911yescharacteristic
437C2×C4C22×C22⋊D6111yescharacteristic
438C8—21no—
439C8—21no—
440C8—21no—
441C8#41×D6111yescharacteristic
442C8#1451982411yescharacteristic
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22—4881no—
453C22—4881no—
454C22—4881no—
455C22C22×#1175819911yescharacteristic
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—81no—
461C4—81no—
462C4—81no—
463C4—4881no—
464C4—4881no—
465C4—4881no—
466C4#1684041111yescharacteristic
467C4#1684057711yescharacteristic
468C2—41no—
469C2—41no—
470C2—161no—
471C2—9761no—
472C2#2145816211yescharacteristic
473C2#2145895311yescharacteristic
474C2#2145895811yescharacteristic
subgroupG/H
centerC22C22×#11758199
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#3339C2
socleC22×C61C22×D8
hypercenter#3339D61
hypocenterC61#33922
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. #21458222C2semidirect
2. #21448095C2semidirect
3. #21448010C2semidirect
4. #21448007C2semidirect
5. #21447999C2semidirect
6. #21447997C2semidirect
7. #21447976C2semidirect
8. #21447973C2semidirect
9. #21447920C2semidirect
10. #21447920C2semidirect
11. C4×#14519718C2semidirect
12. #21447651C2semidirect
13. #21447608C2semidirect
14. #21447605C2semidirect
15. C61×#3339C2semidirect
232. #3339D61semidirect
296. C61#33922semidirect

Maximal subgroups

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

subgroupindex
#214582222
#214480952
#214480102
#214480072
#214479992
#214479972
#214479762
#214479732
#214479202
C4×#145197182
#214476512
#214476082
#214476052
C61×#33392
#3392261