Finite Group Databasebeta

← #29833422

Subgroups — #29833422

Order 15616.

652 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458953C211yesmaximal, characteristic
2C2×#16839879C211yesmaximal, characteristic, complemented
3C2×#16839878C211yesmaximal, characteristic, complemented
4#21447702C214yesmaximal, complemented
5#21447697C214yesmaximal, complemented
6#21447613C211yesmaximal, characteristic, complemented
7#21447548C211yesmaximal, characteristic, complemented
8M32×Dic61C211yesmaximal, characteristic, complemented
9C61×#2143C211yesmaximal, characteristic, complemented
10C2×#14519799C2211yescharacteristic
11C2×#14519785—21no—
12C2×#14519784—21no—
13#16840203C412yescomplemented
14#16840202C412yescomplemented
15#16840198C412yescomplemented
16#16840197C412yescomplemented
17#16840192C2214yes—
18C2×#14519717C2211yescharacteristic
19#16839879—21no—
20#16839879—21no—
21#16839879C2212yescomplemented
22#16839879C2212yescomplemented
23#16839878—21no—
24#16839878—21no—
25#16839878C2212yescomplemented
26#16839878C2212yescomplemented
27C2×#14519713C2211yescharacteristic
28C2×#14519704—21no—
29C2×#14519703—21no—
30C2×C8×Dic61C2211yescharacteristic
31#16839591C2214yescomplemented
32#16839570C2214yescomplemented
33#16839537C2212yescomplemented
34C16×Dic61C2212yescomplemented
35C2×#135×C61C2211yescharacteristic
36C2×M32×C61C2211yescharacteristic
37C2×#108×C61C2211yescharacteristic
38C61×#359C2214yescomplemented
39C2×#11758222—21no—
40#14519799—21no—
41#14519799—21no—
42#14519799C2×C412yes—
43#14519799C2312yes—
44C2×Dic244C2×C411yescharacteristic
45C2×#11758190—21no—
46C2×D488C2×C411yescharacteristic
47#14519785—22no—
48#14519785—22no—
49#14519785—41no—
50#14519785—41no—
51#14519784—22no—
52#14519784—22no—
53#14519784—41no—
54#14519784—41no—
55C2×#11758194—21no—
56C2×#11758194—41no—
57C2×#11758189—41no—
58C22×#92418—41no—
59C22×#92418D411yescharacteristic
60C2×C8×D61—41no—
61C2×C4×Dic61D411yescharacteristic
62#14519723C2×C414yescomplemented
63#14519721C2×C414yescomplemented
64#14519720C2×C414yescomplemented
65#14519718C2×C414yescomplemented
66#14519717C2×C412yes—
67#14519717C2×C412yes—
68C2×#11758185C2312yes—
69#14519713—21no—
70#14519713C2312yes—
71#14519704—22no—
72#14519704—22no—
73#14519703—22no—
74#14519703—22no—
75C8×Dic61D411yescharacteristic
76C8×Dic61D411yescharacteristic
77C8×Dic61C2311yescharacteristic
78C8×Dic61C2311yescharacteristic
79C2×#41×C61—21no—
80#135×C61—21no—
81#135×C61—21no—
82#135×C61C2×C412yes—
83#135×C61C2312yes—
84C2×Q16×C61C2×C411yescharacteristic
85C2×SD16×C61—21no—
86C2×D8×C61C2×C411yescharacteristic
87C2×M16×C61—21no—
88C22×C8×C61C2311yescharacteristic
89M32×C61—21no—
90M32×C61—21no—
91C2×C16×C61C2312yes—
92#108×C61—21no—
93#108×C61C2312yes—
94#41×C61—22no—
95#41×C61—22no—
96#41×C61—41no—
97#41×C61—41no—
98C2×Q8×C61—21no—
99C2×D4×C61—21no—
100C2×D4×C61—41no—
101C22×C4×C61—41no—
102C22×C4×C61C2×D411yescharacteristic
103C2×C22⋊D61—41no—
104C22×Dic61—21no—
105#11758222—22no—
106#11758222—22no—
107#11758222—41no—
108#11758222—41no—
109C2×D244—21no—
110C2×C4×D61—41no—
111C2×Dic122—21no—
112Q16×C61—21no—
113Q16×C61C22×C412yes—
114SD16×C61—22no—
115SD16×C61—22no—
116D8×C61—21no—
117D8×C61C22×C412yes—
118M16×C61—22no—
119M16×C61—41no—
120C2×C8×C61—41no—
121C2×C8×C61C22×C411yescharacteristic
122C2×C8×C61C22×C411yescharacteristic
123C2×C8×C61C2×D411yescharacteristic
124C2×C8×C61#4111yescharacteristic
125C2×C8×C61#4111yescharacteristic
126C2×C8×C61C2411yescharacteristic
127C4×Dic61—21no—
128C4×Dic61C2×D411yescharacteristic
129C4×Dic61C2×D411yescharacteristic
130#11758194—22no—
131#11758194—41no—
132#11758194—42no—
133#11758194—42no—
134C2×#92418—41no—
135C2×#92418—42no—
136C2×#92418—42no—
137C2×#92418D811yescharacteristic
138C2×#92418D811yescharacteristic
139C2×#92418D811yescharacteristic
140C2×#92418D811yescharacteristic
141C2×#92418C2×D411yescharacteristic
142C2×#92418C2×D411yescharacteristic
143Dic244—21no—
144Dic244C22×C412yes—
145D488—21no—
146D488C22×C412yes—
147#11758190—22no—
148#11758190—22no—
149#11758189—42no—
150#11758189—42no—
151C8×D61—42no—
152C8×D61—42no—
153C16×C61—22no—
154#11758185C22×C414yes—
155C23×C61—41no—
156C23×C61#13511yescharacteristic
157C22×D61—41no—
158Q8×C61—22no—
159Q8×C61—41no—
160D4×C61—22no—
161D4×C61—42no—
162D4×C61—42no—
163D4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—42no—
166C2×C4×C61—42no—
167C2×C4×C61C4×D411yescharacteristic
168C2×C4×C61C4×D411yescharacteristic
169C2×C4×C61C2×D811yescharacteristic
170C2×C4×C61C2×D811yescharacteristic
171C2×C4×C61#13511yescharacteristic
172C2×C4×C61C22×D411yescharacteristic
173C22⋊D61—42no—
174C22⋊D61—42no—
175C2×Dic61—21no—
176C2×Dic61—21no—
177C2×Dic61—42no—
178C2×Dic61—41no—
179D244—22no—
180D244—41no—
181C4×D61—42no—
182C4×D61—42no—
183Dic122—22no—
184Dic122—41no—
185C8×C61—42no—
186C8×C61C4×D411yescharacteristic
187C8×C61C4×D411yescharacteristic
188C8×C61C23×C411yescharacteristic
189C8×C61C2×#4111yescharacteristic
190#92418—42no—
191#92418C2×D811yescharacteristic
192#92418C2×D811yescharacteristic
193#92418C2×D811yescharacteristic
194#92418C2×D811yescharacteristic
195#33463—611nomaximal, Sylow
196C22×C61—41no—
197C22×C61—42no—
198C22×C61—82no—
199C22×C61C4×D811yescharacteristic
200C22×C61C4×D811yescharacteristic
201C22×C61C2×#13511yescharacteristic
202C2×D61—42no—
203C2×D61—82no—
204C4×C61—42no—
205C4×C61C4×D811yescharacteristic
206C4×C61C4×D811yescharacteristic
207C4×C61C2×C4×D411yescharacteristic
208C4×C61C22×D811yescharacteristic
209Dic61—22no—
210Dic61—41no—
211Dic61—42no—
212#3414—611no—
213C2×#443—611no—
214C2×#443—611no—
215#2179—614no—
216#2178—614no—
217#2161—611no—
218#2143—611no—
219#2143D6111yescharacteristic, complemented
220C4×M32—611no—
221C2×C61—21no—
222C2×C61—21no—
223C2×C61—21no—
224C2×C61—82no—
225C2×C61C2×C4×D811yescharacteristic
226D61—82no—
227C2×#135—611no—
228C2×#135C2×D6111yescharacteristic
229C2×#131—1221no—
230C2×#131—1221no—
231#510—612no—
232#510—612no—
233#509—612no—
234#509—612no—
235#508—614no—
236C2×M32—611no—
237C2×M32C2×D6111yescharacteristic
238#443—612no—
239#443—612no—
240#443—612no—
241#443—612no—
242#443—1221no—
243#443—1221no—
244#443—1221no—
245#443—1221no—
246C2×#108—611no—
247C2×#108C2×D6111yescharacteristic
248C2×#104—1221no—
249C2×#104—1221no—
250C2×C4×C8—611no—
251#368—614no—
252#359—614no—
253#359C2×D6114yescomplemented
254#346—612no—
255C4×C16—612no—
256C61#3346311yescharacteristic, complemented, Sylow
257C2×#41—21no—
258C2×#41—1221no—
259#135—21no—
260#135—21no—
261#135—612no—
262#135—612no—
263#135—1221no—
264#135—1221no—
265#135C4×D6112yes—
266#135C22×D6112yes—
267C2×Q16—611no—
268C2×Q16C4×D6111yescharacteristic
269C2×SD16—21no—
270C2×SD16—1221no—
271C2×D8—611no—
272C2×D8C4×D6111yescharacteristic
273#131—1222no—
274#131—1222no—
275#131—1222no—
276#131—1222no—
277#131—2441no—
278#131—2441no—
279#131—2441no—
280#131—2441no—
281C2×M16—21no—
282C2×M16—1221no—
283C2×M16—2441no—
284C2×M16—2441no—
285C22×C8—611no—
286C22×C8—2441no—
287C22×C8—2441no—
288C22×C8C22×D6111yescharacteristic
289C2×C42—611no—
290Q32—614no—
291SD32—614no—
292SD32—614no—
293D16—614no—
294M32—21no—
295M32—21no—
296M32—612no—
297M32—612no—
298C2×C16—612no—
299C2×C16C22×D6112yes—
300#108—21no—
301#108—612no—
302#108—1221no—
303#108C22×D6112yes—
304#104—1222no—
305#104—1222no—
306#104—1222no—
307#104—1222no—
308C4×C8—611no—
309C4×C8—611no—
310C4×C8—611no—
311C4×C8—611no—
312#41—22no—
313#41—22no—
314#41—41no—
315#41—41no—
316#41—1222no—
317#41—1222no—
318#41—2441no—
319#41—2441no—
320C2×Q8—21no—
321C2×Q8—1221no—
322C2×D4—21no—
323C2×D4—41no—
324C2×D4—1221no—
325C2×D4—2441no—
326C22×C4—41no—
327C22×C4—1221no—
328C22×C4—2441no—
329C22×C4D4×D6111yescharacteristic
330Q16—21no—
331Q16—612no—
332Q16—1221no—
333Q16C2×C4×D6112yes—
334SD16—22no—
335SD16—22no—
336SD16—1222no—
337SD16—1222no—
338D8—21no—
339D8—612no—
340D8—1221no—
341D8C2×C4×D6112yes—
342M16—22no—
343M16—41no—
344M16—1222no—
345M16—2442no—
346M16—2442no—
347M16—2442no—
348M16—2442no—
349M16—2441no—
350C2×C8—41no—
351C2×C8—611no—
352C2×C8—611no—
353C2×C8—611no—
354C2×C8—611no—
355C2×C8—611no—
356C2×C8—611no—
357C2×C8—2442no—
358C2×C8—2442no—
359C2×C8—2442no—
360C2×C8—2442no—
361C2×C8—2441no—
362C2×C8C2×C4×D6111yescharacteristic
363C2×C8C2×C4×D6111yescharacteristic
364C2×C8D4×D6111yescharacteristic
365C2×C8#1175822411yescharacteristic
366C2×C8#1175822411yescharacteristic
367C2×C8C23×D6111yescharacteristic
368C42—611no—
369C42—611no—
370C42—1221no—
371C16—22no—
372C16—614no—
373C23—41no—
374C23—2441no—
375C23#1451979811yescharacteristic
376Q8—22no—
377Q8—41no—
378Q8—1222no—
379Q8—2441no—
380D4—22no—
381D4—42no—
382D4—42no—
383D4—41no—
384D4—1222no—
385D4—2442no—
386D4—2442no—
387D4—2441no—
388C2×C4—41no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—1221no—
392C2×C4—1221no—
393C2×C4—2442no—
394C2×C4—2441no—
395C2×C4—2442no—
396C2×C4—2442no—
397C2×C4#1451973711yescharacteristic
398C2×C4#1451973711yescharacteristic
399C2×C4D8×D6111yescharacteristic
400C2×C4D8×D6111yescharacteristic
401C2×C4#1451979811yescharacteristic
402C2×C4C2×D4×D6111yescharacteristic
403C8—42no—
404C8—611no—
405C8—611no—
406C8—611no—
407C8—611no—
408C8—2442no—
409C8#1451973711yescharacteristic
410C8#1451973711yescharacteristic
411C8C22×C4×D6111yescharacteristic
412C8C2×#1175822411yescharacteristic
413C22—41no—
414C22—42no—
415C22—82no—
416C22—4882no—
417C22—2442no—
418C22#1683984211yescharacteristic
419C22#1683984211yescharacteristic
420C22C2×#1451979811yescharacteristic
421C4—42no—
422C4—1222no—
423C4—2441no—
424C4—2442no—
425C4#1683984211yescharacteristic
426C4#1683984211yescharacteristic
427C4C2×#1451973711yescharacteristic
428C4C2×D8×D6111yescharacteristic
429C2—21no—
430C2—21no—
431C2—21no—
432C2—82no—
433C2—4882no—
434C2C2×#1683984211yescharacteristic
subgroupG/H
centerC4C2×D8×D61
commutatorC8×C61C23×C4
FrattiniC2×C8C23×D61
FittingC61×#2143C2
socleC2×C61C2×C4×D8
prime radical#21458953C2
cosocleC2×C8×C61C24
hypercenter#2143D61
hypocenterC61#33463
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #2143

Complements

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

NH ≅ G/Ntype
2. C2×#16839879C2semidirect
3. C2×#16839878C2semidirect
4. #21447702C2semidirect
5. #21447697C2semidirect
6. #21447613C2semidirect
7. #21447548C2semidirect
8. M32×Dic61C2semidirect
9. C61×#2143C2semidirect
13. #16840203C4semidirect
14. #16840202C4semidirect
15. #16840198C4semidirect
16. #16840197C4semidirect
21. #16839879C22semidirect
22. #16839879C22semidirect
25. #16839878C22semidirect
26. #16839878C22semidirect
31. #16839591C22semidirect
32. #16839570C22semidirect
33. #16839537C22semidirect
34. C16×Dic61C22semidirect
38. C61×#359C22semidirect
62. #14519723C2×C4semidirect
63. #14519721C2×C4semidirect
64. #14519720C2×C4semidirect
65. #14519718C2×C4semidirect
219. #2143D61semidirect
253. #359C2×D61semidirect
256. C61#33463semidirect

Maximal subgroups

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

subgroupindex
#214589532
C2×#168398792
C2×#168398782
#214477022
#214476972
#214476132
#214475482
M32×Dic612
C61×#21432
#3346361