Finite Group Databasebeta

← #29835272

Subgroups — #29835272

Order 15616.

524 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456436C211yesmaximal, characteristic, complemented
2#21448038C211yesmaximal, characteristic, complemented
3#21448033C211yesmaximal, characteristic, complemented
4#21447990C212yesmaximal, complemented
5#21447888C212yesmaximal, complemented
6#21447770C211yesmaximal, characteristic, complemented
7#21447765C211yesmaximal, characteristic
8#21447717C212yesmaximal, complemented
9#21447710C212yesmaximal, complemented
10#21447635C211yesmaximal, characteristic, complemented
11C61×#2955C211yesmaximal, characteristic, complemented
12#16840383—21no—
13#16840202C2212yes—
14#16840197C2212yes—
15#16840160C2211yescharacteristic, complemented
16#16840146C2211yescharacteristic, complemented
17#16840122—21no—
18#16840020C2211yescharacteristic
19#16840015C2211yescharacteristic
20#16839991—21no—
21#16839875C2211yescharacteristic, complemented
22#16839870C2211yescharacteristic, complemented
23C4×#11758190—21no—
24#16839586C2212yescomplemented
25#16839586C2212yescomplemented
26#16839583C2212yescomplemented
27#16839577C2212yescomplemented
28#16839574C2212yescomplemented
29#16839572C2212yes—
30#16839572C2212yes—
31#16839544C2211yescharacteristic
32#16839544C2211yescharacteristic
33#16839540C2212yescomplemented
34C61×#575C2211yescharacteristic
35C2×#131×C61—21no—
36C61×#444—21no—
37C61×#444C2212yes—
38C61×#443—21no—
39C61×#443C2212yes—
40C61×#430C2211yescharacteristic
41C61×#421—21no—
42C61×#405C2211yescharacteristic
43C2×Dic244C2311yescharacteristic
44C2×#11758190—21no—
45C2×D488C2311yescharacteristic
46#14519777—21no—
47#14519772—41no—
48#14519765—21no—
49#14519763—41no—
50#14519759—41no—
51#14519756—21no—
52#14519755—41no—
53#14519751—21no—
54C4×Dic122—21no—
55C4×D244—21no—
56#14519723—22no—
57#14519721—22no—
58#14519720—22no—
59#14519718—22no—
60#14519717C2312yes—
61#14519717C2312yes—
62#14519709—21no—
63#14519709C2311yescharacteristic
64#14519709C2311yescharacteristic
65#14519702—21no—
66#14519702—21no—
67#14519699—21no—
68#14519699—21no—
69C2×#41×C61—21no—
70#137×C61—22no—
71AGL(1,ℤ/8)×C61—22no—
72#135×C61—21no—
73#135×C61C2312yes—
74#131×C61—22no—
75#131×C61—22no—
76#131×C61—41no—
77#131×C61—41no—
78C2×M16×C61—21no—
79C2×M16×C61—41no—
80C2×M16×C61C2311yescharacteristic
81C22×C8×C61—41no—
82C22×C8×C61D411yescharacteristic
83#117×C61D411yescharacteristic
84#108×C61—21no—
85#108×C61C2312yes—
86#104×C61—22no—
87#104×C61—22no—
88#97×C61D411yescharacteristic
89#97×C61C2311yescharacteristic
90C4×C8×C61D411yescharacteristic
91C4×C8×C61C2311yescharacteristic
92#41×C61—22no—
93#41×C61—22no—
94#41×C61—41no—
95#41×C61—41no—
96C2×Q8×C61—21no—
97C2×D4×C61—21no—
98C2×D4×C61—41no—
99C22×C4×C61—41no—
100C22×C4×C61C2×D411yescharacteristic
101C2×C22⋊D61—41no—
102C2×D244—21no—
103C2×C4×D61—41no—
104C2×Dic122—21no—
105C2×Dic122—41no—
106Q16×C61—21no—
107Q16×C61#4112yes—
108SD16×C61—22no—
109SD16×C61—22no—
110D8×C61—21no—
111D8×C61#4112yes—
112M16×C61—22no—
113M16×C61—22no—
114M16×C61—42no—
115M16×C61—41no—
116M16×C61—42no—
117C2×C8×C61—21no—
118C2×C8×C61—21no—
119C2×C8×C61—42no—
120C2×C8×C61—41no—
121C2×C8×C61—42no—
122C2×C8×C61C2×D411yescharacteristic
123C2×C8×C61C2×D411yescharacteristic
124C2×C8×C61C2×D411yescharacteristic
125C2×C8×C61C2411yescharacteristic
126C4⋊C4×C61—21no—
127C22⋊C4×C61—21no—
128C42×C61C2×D411yescharacteristic
129C42×C61C2×D411yescharacteristic
130C22⋊Dic61—41no—
131#11758198—41no—
132#11758198—41no—
133#11758198—41no—
134#11758198—41no—
135C4⋊Dic61—21no—
136C4⋊Dic61—21no—
137C4⋊Dic61—41no—
138#11758196—41no—
139#11758196—41no—
140C4×Dic61—41no—
141Dic244—22no—
142D488—22no—
143#11758190—41no—
144#11758190—41no—
145#11758185—22no—
146#11758185—22no—
147C23×C61—41no—
148C23×C61AGL(1,ℤ/8)11yescharacteristic
149C22×D61—41no—
150Q8×C61—22no—
151Q8×C61—41no—
152D4×C61—22no—
153D4×C61—41no—
154D4×C61—42no—
155D4×C61—42no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61—42no—
161C2×C4×C61—41no—
162C2×C4×C61—42no—
163C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C61C22×D411yescharacteristic
165C22⋊D61—161no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169D244—41no—
170D244—41no—
171C4×D61—161no—
172Dic122—41no—
173Dic122—41no—
174Dic122—161no—
175C8×C61—21no—
176C8×C61—21no—
177C8×C61—42no—
178C8×C61AGL(1,ℤ/8)11yescharacteristic
179C8×C61AGL(1,ℤ/8)11yescharacteristic
180C8×C61C2×#4112yes—
181#33691—611nomaximal, Sylow
182C22×C61—21no—
183C22×C61—41no—
184C22×C61—42no—
185C22×C61—82no—
186C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
187C2×D61—81no—
188C2×D61—81no—
189C2×D61—81no—
190C4×C61—21no—
191C4×C61—41no—
192C4×C61—41no—
193C4×C61—42no—
194C4×C61#52511yescharacteristic
195C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
196Dic61—81no—
197Dic61—81no—
198Dic61—81no—
199#3173—611no—
200#2955D6111yescharacteristic, complemented
201#2239—611no—
202#2238—611no—
203#2230—612no—
204#2212—612no—
205#2191—611no—
206#2190—611no—
207AGL(1,ℤ/16)—612no—
208#2180—612no—
209#2166—611no—
210C2×C61—21no—
211C2×C61—41no—
212C2×C61—82no—
213C2×C61#310911yescharacteristic
214D61—161no—
215#575C2×D6111yescharacteristic
216C2×#131—21no—
217#542—1221no—
218#510—612no—
219#509—612no—
220#498—611no—
221#495—611no—
222#489—1221no—
223#470—611no—
224#469—611no—
225#465—1221no—
226#444—21no—
227#444C2×D6112yes—
228#443—21no—
229#443C2×D6112yes—
230#442—611no—
231#441—611no—
232C4×SD16—1221no—
233#430C2×D6111yescharacteristic
234#421—21no—
235#405C2×D6111yescharacteristic
236#365—612no—
237#365—612no—
238#364—612no—
239#362—612no—
240#361—612no—
241#360—612no—
242#360—612no—
243#349—611no—
244#349—611no—
245#347—612no—
246C61#3369111yescharacteristic, complemented, Sylow
247C2×#41—21no—
248#137—22no—
249AGL(1,ℤ/8)—22no—
250#135—21no—
251#135C22×D6112yes—
252C2×Q16—611no—
253C2×SD16—1221no—
254C2×D8—611no—
255#131—22no—
256#131—22no—
257#131—41no—
258#131—41no—
259C2×M16—21no—
260C2×M16—41no—
261C2×M16C22×D6111yescharacteristic
262C22×C8—41no—
263C22×C8C22⋊D6111yescharacteristic
264C4⋊Q8—1221no—
265#126—2441no—
266#124—1221no—
267#124—2441no—
268#123—2441no—
269C22⋊Q8—1221no—
270C22⋊Q8—2441no—
271#121—1221no—
272C4×Q8—1221no—
273C4×D4—1221no—
274#117C22⋊D6111yescharacteristic
275Q32—1222no—
276SD32—1222no—
277SD32—1222no—
278D16—1222no—
279M32—612no—
280M32—612no—
281#108—21no—
282#108C22×D6112yes—
283#106—611no—
284#106—611no—
285#106—1221no—
286#104—22no—
287#104—22no—
288#103—1221no—
289#103—1221no—
290#102—1221no—
291#102—1221no—
292#97C22⋊D6111yescharacteristic
293#97C22×D6111yescharacteristic
294C4×C8C22⋊D6111yescharacteristic
295C4×C8C22×D6111yescharacteristic
296#41—22no—
297#41—22no—
298#41—41no—
299#41—41no—
300C2×Q8—21no—
301C2×Q8—1221no—
302C2×Q8—2441no—
303C2×D4—21no—
304C2×D4—41no—
305C2×D4—1221no—
306C2×D4—2441no—
307C22×C4—41no—
308C22×C4—2441no—
309C22×C4C2×C22⋊D6111yescharacteristic
310Q16—21no—
311Q16—1222no—
312Q16#1175822212yes—
313SD16—22no—
314SD16—22no—
315SD16—2441no—
316SD16—2441no—
317D8—21no—
318D8—1222no—
319D8#1175822212yes—
320M16—22no—
321M16—22no—
322M16—42no—
323M16—41no—
324M16—42no—
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—42no—
328C2×C8—41no—
329C2×C8—42no—
330C2×C8C2×C22⋊D6111yescharacteristic
331C2×C8C2×C22⋊D6111yescharacteristic
332C2×C8C2×C22⋊D6111yescharacteristic
333C2×C8C23×D6111yescharacteristic
334C4⋊C4—21no—
335C4⋊C4—1221no—
336C4⋊C4—1221no—
337C4⋊C4—2441no—
338C4⋊C4—2441no—
339C4⋊C4—2441no—
340C22⋊C4—21no—
341C22⋊C4—2441no—
342C22⋊C4—2441no—
343C22⋊C4—2441no—
344C22⋊C4—2441no—
345C22⋊C4—2441no—
346C42—2441no—
347C42C2×C22⋊D6111yescharacteristic
348C42C2×C22⋊D6111yescharacteristic
349C16—1222no—
350C16—1222no—
351C23—41no—
352C23—2441no—
353C23#1451980211yescharacteristic
354Q8—22no—
355Q8—41no—
356Q8—9761no—
357Q8—2441no—
358Q8—2441no—
359D4—22no—
360D4—41no—
361D4—42no—
362D4—42no—
363D4—9761no—
364D4—2441no—
365D4—2441no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—9761no—
374C2×C4—2441no—
375C2×C4—2441no—
376C2×C4—2441no—
377C2×C4#1451980211yescharacteristic
378C2×C4C22×C22⋊D6111yescharacteristic
379C8—21no—
380C8—21no—
381C8—42no—
382C8#1451980311yescharacteristic
383C8#1451980311yescharacteristic
384C8C2×#1175822212yes—
385C22—21no—
386C22—41no—
387C22—42no—
388C22—82no—
389C22—4881no—
390C22—4881no—
391C22—4881no—
392C22C2×#1451980211yescharacteristic
393C4—21no—
394C4—41no—
395C4—41no—
396C4—42no—
397C4—4881no—
398C4—4881no—
399C4—4881no—
400C4#1684027311yescharacteristic
401C4C2×#1451980311yescharacteristic
402C2—21no—
403C2—41no—
404C2—82no—
405C2—9761no—
406C2#2145591011yescharacteristic
subgroupG/H
centerC2#21455910
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2955C2
socleC2×C61#3109
prime radical#21447765C2
hypercenter#2955D61
hypocenterC61#33691
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #405 ◁ #2955

Complements

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

NH ≅ G/Ntype
1. #21456436C2semidirect
2. #21448038C2semidirect
3. #21448033C2semidirect
4. #21447990C2semidirect
5. #21447888C2semidirect
6. #21447770C2semidirect
8. #21447717C2semidirect
9. #21447710C2semidirect
10. #21447635C2semidirect
11. C61×#2955C2semidirect
15. #16840160C22semidirect
16. #16840146C22semidirect
21. #16839875C22semidirect
22. #16839870C22semidirect
24. #16839586C22semidirect
25. #16839586C22semidirect
26. #16839583C22semidirect
27. #16839577C22semidirect
28. #16839574C22semidirect
33. #16839540C22semidirect
200. #2955D61semidirect
246. C61#33691semidirect

Maximal subgroups

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

subgroupindex
#214564362
#214480382
#214480332
#214479902
#214478882
#214477702
#214477652
#214477172
#214477102
#214476352
C61×#29552
#3369161