Finite Group Databasebeta

← #29836819

Subgroups — #29836819

Order 15616.

646 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458972C211yesmaximal, characteristic, complemented
2#21458960C211yesmaximal, characteristic, complemented
3#21457606C212yesmaximal, complemented
4#21448080C211yesmaximal, characteristic, complemented
5#21447944C211yesmaximal, characteristic, complemented
6#21447939C211yesmaximal, characteristic, complemented
7#21447889C212yesmaximal, complemented
8#21447792C212yesmaximal, complemented
9#21447785C212yesmaximal, complemented
10#21447701C211yesmaximal, characteristic, complemented
11C61×#2170C211yesmaximal, characteristic, complemented
12#16840579C2212yescomplemented
13#16840569—22no—
14#16840567C2212yes—
15#16840205—22no—
16#16840205C2212yescomplemented
17#16840200—22no—
18#16840200C2212yes—
19#16840194—21no—
20#16840194—21no—
21#16840194C2211yescharacteristic
22C2×Dic488—21no—
23C2×Dic488C2211yescharacteristic, complemented
24C2×#14519722C2212yescomplemented
25C2×D976—21no—
26C2×D976C2211yescharacteristic
27#16840146C2212yescomplemented
28#16840037C2212yes—
29#16840032C2212yescomplemented
30#16840026—22no—
31#16839941—22no—
32#16839936—22no—
33#16839880C2212yescomplemented
34#16839592C2211yescharacteristic, complemented
35#16839579C2212yescomplemented
36#16839576C2212yescomplemented
37#16839570C2212yescomplemented
38C61×#504C2211yescharacteristic
39C61×#504C2211yescharacteristic, complemented
40C61×#443C2211yescharacteristic
41C61×#364C2211yescharacteristic, complemented
42C61×#350C2211yescharacteristic
43C61×#350C2211yescharacteristic, complemented
44C4×C16×C61C2211yescharacteristic, complemented
45#14519824—22no—
46#14519823—22no—
47#14519810—22no—
48#14519810—42no—
49#14519809—42no—
50#14519807—22no—
51#14519805—22no—
52#14519805—42no—
53#14519802—22no—
54#14519801—42no—
55#14519799—22no—
56#14519799—22no—
57#14519799C2312yes—
58#14519798—42no—
59C2×Dic244—22no—
60C2×Dic244C2312yes—
61C2×#11758190—22no—
62SD16×D61—42no—
63C2×D488—22no—
64C2×D488C2312yes—
65#14519783—22no—
66#14519765—22no—
67Dic488—22no—
68Dic488—21no—
69Dic488—21no—
70Dic488D411yescharacteristic
71#14519722—22no—
72#14519722—22no—
73#14519722—42no—
74#14519722D412yes—
75D976—22no—
76D976—21no—
77D976—21no—
78D976D411yescharacteristic
79#14519713C2312yes—
80#14519705—22no—
81#14519695—22no—
82#14519693—22no—
83#135×C61D411yescharacteristic
84#131×C61C2311yescharacteristic
85#131×C61C2311yescharacteristic
86M32×C61—21no—
87M32×C61—21no—
88M32×C61C2311yescharacteristic
89M32×C61C2311yescharacteristic
90C2×C16×C61—21no—
91C2×C16×C61—21no—
92C2×C16×C61C2311yescharacteristic
93C2×C16×C61C2311yescharacteristic
94#108×C61D411yescharacteristic
95#104×C61D411yescharacteristic
96#104×C61D411yescharacteristic
97C4×C8×C61C2311yescharacteristic
98#41×C61C2×D411yescharacteristic
99#41×C61C2×D411yescharacteristic
100#11758226—42no—
101Q8×D61—42no—
102#11758224—42no—
103#11758224—82no—
104D4×D61—42no—
105D4×D61—82no—
106#11758222—22no—
107#11758222—42no—
108#11758222—42no—
109C2×D244—22no—
110C2×D244—42no—
111C2×Dic122—22no—
112C2×Dic122—42no—
113Q16×C61D811yescharacteristic
114SD16×C61D811yescharacteristic
115SD16×C61D811yescharacteristic
116D8×C61D811yescharacteristic
117M16×C61—21no—
118M16×C61—21no—
119M16×C61C2×D411yescharacteristic
120M16×C61C2×D411yescharacteristic
121C2×C8×C61—21no—
122C2×C8×C61—21no—
123C2×C8×C61C2×D411yescharacteristic
124C2×C8×C61C2411yescharacteristic
125C42×C61C2×D411yescharacteristic
126#11758202—42no—
127#11758201—42no—
128#11758200—42no—
129#11758199—42no—
130#11758198—82no—
131#11758194—22no—
132Dic244—22no—
133Dic244—22no—
134Dic244—42no—
135Dic244C2×D412yes—
136D488—22no—
137D488—22no—
138D488—42no—
139D488C2×D412yes—
140#11758190—22no—
141#11758190—42no—
142#11758190—42no—
143#11758190—42no—
144#11758190—42no—
145#11758189—42no—
146C8×D61—42no—
147C16×C61—21no—
148C16×C61—21no—
149C16×C61—21no—
150C16×C61C2×D411yescharacteristic
151C16×C61C2×D411yescharacteristic
152C22×D61—42no—
153C22×D61—82no—
154Q8×C61C2×D811yescharacteristic
155Q8×C61C2×D811yescharacteristic
156D4×C61—21no—
157D4×C61—21no—
158D4×C61C2×D811yescharacteristic
159D4×C61C2×D811yescharacteristic
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61C22×D411yescharacteristic
164C22⋊D61—42no—
165C22⋊D61—82no—
166C22⋊D61—82no—
167C2×Dic61—42no—
168C2×Dic61—82no—
169D244—22no—
170D244—42no—
171D244—42no—
172D244—82no—
173C4×D61—42no—
174C4×D61—82no—
175C4×D61—82no—
176Dic122—22no—
177Dic122—42no—
178Dic122—42no—
179Dic122—82no—
180C8×C61—21no—
181C8×C61—21no—
182C8×C61C2×D811yescharacteristic
183C8×C61C2×D811yescharacteristic
184C8×C61C22×D411yescharacteristic
185C8×C61H(5,𝔽2)11yescharacteristic
186#92418—42no—
187#33859—611nomaximal, Sylow
188C22×C61—21no—
189C22×C61—21no—
190C22×C61#57611yescharacteristic
191C2×D61—42no—
192C2×D61—82no—
193C2×D61—162no—
194C2×D61—322no—
195C4×C61—21no—
196C4×C61—21no—
197C4×C61—41no—
198C4×C61D4211yescharacteristic
199C4×C61C22×D811yescharacteristic
200Dic61—42no—
201Dic61—82no—
202#3417—611no—
203#3415—611no—
204#3290—612no—
205#2249—611no—
206#2222—611no—
207#2221—611no—
208#2212—612no—
209#2194—612no—
210#2193—612no—
211#2178—611no—
212#2170D6111yescharacteristic, complemented
213C2×C61—21no—
214C2×C61—41no—
215C2×C61—41no—
216C2×C61D4×D811yescharacteristic
217D61—82no—
218D61—162no—
219#578—612no—
220#577—1222no—
221#576—612no—
222#510—612no—
223#510—1222no—
224#509—612no—
225#509—1222no—
226#508—611no—
227#508—1221no—
228#508—1221no—
229C2×Q32—611no—
230C2×Q32—1221no—
231C2×SD32—612no—
232C2×D16—611no—
233C2×D16—1221no—
234#504C2×D6111yescharacteristic
235#504C2×D6111yescharacteristic, complemented
236#495—612no—
237#473—612no—
238#472—612no—
239#471—1222no—
240#455—1222no—
241#454—1222no—
242#443—612no—
243#443C2×D6111yescharacteristic
244#368—611no—
245#364C2×D6111yescharacteristic, complemented
246#362—612no—
247#361—612no—
248#359—612no—
249#350C2×D6111yescharacteristic
250#350C2×D6111yescharacteristic, complemented
251C4×C16C2×D6111yescharacteristic, complemented
252C61#3385911yescharacteristic, complemented, Sylow
2532−1+4—1222no—
254H(5,𝔽2)—1222no—
255#137—1222no—
256#137—1222no—
257#137—2442no—
258#137—2442no—
259AGL(1,ℤ/8)—1222no—
260AGL(1,ℤ/8)—1222no—
261AGL(1,ℤ/8)—2442no—
262AGL(1,ℤ/8)—2442no—
263#135—612no—
264#135—1222no—
265#135—1222no—
266#135—2442no—
267#135D24411yescharacteristic
268C2×Q16—612no—
269C2×Q16—1222no—
270C2×SD16—1222no—
271C2×SD16—2442no—
272C2×D8—612no—
273C2×D8—1222no—
274#131—1222no—
275#131C22×D6111yescharacteristic
276#131C22×D6111yescharacteristic
277#124—1222no—
278Q32—611no—
279Q32—1222no—
280Q32—1221no—
281Q32—1221no—
282SD32—612no—
283SD32—1222no—
284SD32—1222no—
285SD32—2442no—
286D16—611no—
287D16—1222no—
288D16—1221no—
289D16—1221no—
290M32—21no—
291M32—21no—
292M32C22×D6111yescharacteristic
293M32C22×D6111yescharacteristic
294C2×C16—21no—
295C2×C16—21no—
296C2×C16C22×D6111yescharacteristic
297C2×C16C22×D6111yescharacteristic
298#108—612no—
299#108D24411yescharacteristic
300#104—1222no—
301#104D24411yescharacteristic
302#104D24411yescharacteristic
303#101—1222no—
304#100—1222no—
305C4×C8C22×D6111yescharacteristic
306#41—1222no—
307#41—4882no—
308#41—2442no—
309#41—2442no—
310#41—2442no—
311#41—2442no—
312#41C2×D24411yescharacteristic
313#41C2×D24411yescharacteristic
314C2×Q8—1222no—
315C2×Q8—2442no—
316C2×Q8—2442no—
317C2×D4—1222no—
318C2×D4—4882no—
319C2×D4—2442no—
320C2×D4—2442no—
321Q16—612no—
322Q16—1222no—
323Q16—1222no—
324Q16—2442no—
325Q16—2442no—
326Q16D48811yescharacteristic
327SD16—1222no—
328SD16—2442no—
329SD16—2442no—
330SD16—2442no—
331SD16—2442no—
332SD16—2442no—
333SD16—2442no—
334SD16D48811yescharacteristic
335SD16D48811yescharacteristic
336D8—612no—
337D8—1222no—
338D8—1222no—
339D8—2442no—
340D8—2442no—
341D8D48811yescharacteristic
342M16—21no—
343M16—21no—
344M16—1222no—
345M16—2442no—
346M16C2×D24411yescharacteristic
347M16C2×D24411yescharacteristic
348C2×C8—21no—
349C2×C8—21no—
350C2×C8—2442no—
351C2×C8C2×D24411yescharacteristic
352C2×C8C23×D6111yescharacteristic
353C22⋊C4—4882no—
354C42C2×D24411yescharacteristic
355C16—21no—
356C16—21no—
357C16—21no—
358C16D4×D6111yescharacteristic
359C16D4×D6111yescharacteristic
360C23—4882no—
361C23—2442no—
362Q8—1222no—
363Q8—4882no—
364Q8—2442no—
365Q8—2442no—
366Q8C2×D48811yescharacteristic
367Q8C2×D48811yescharacteristic
368D4—21no—
369D4—21no—
370D4—1222no—
371D4—4882no—
372D4—4882no—
373D4—4882no—
374D4—2442no—
375D4—2442no—
376D4—2442no—
377D4C2×D48811yescharacteristic
378D4C2×D48811yescharacteristic
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—4882no—
383C2×C4—4882no—
384C2×C4—4882no—
385C2×C4—2442no—
386C2×C4—2442no—
387C2×C4C22×D24411yescharacteristic
388C8—21no—
389C8—21no—
390C8—2442no—
391C8C2×D48811yescharacteristic
392C8C2×D48811yescharacteristic
393C8C2×D4×D6111yescharacteristic
394C8#1451982311yescharacteristic
395C22—21no—
396C22—21no—
397C22—19522no—
398C22—9762no—
399C22—4882no—
400C22—2442no—
401C22#1684056711yescharacteristic
402C4—21no—
403C4—21no—
404C4—41no—
405C4—4882no—
406C4—2442no—
407C4D4×D24411yescharacteristic
408C4C22×D48811yescharacteristic
409C2—21no—
410C2—41no—
411C2—41no—
412C2—9762no—
413C2—4882no—
414C2D4×D48811yescharacteristic
subgroupG/H
centerC2D4×D488
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2170C2
socleC2×C61D4×D8
hypercenter#2170D61
hypocenterC61#33859
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443 ◁ #2170

Complements

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

NH ≅ G/Ntype
1. #21458972C2semidirect
2. #21458960C2semidirect
3. #21457606C2semidirect
4. #21448080C2semidirect
5. #21447944C2semidirect
6. #21447939C2semidirect
7. #21447889C2semidirect
8. #21447792C2semidirect
9. #21447785C2semidirect
10. #21447701C2semidirect
11. C61×#2170C2semidirect
12. #16840579C22semidirect
16. #16840205C22semidirect
23. C2×Dic488C22semidirect
24. C2×#14519722C22semidirect
27. #16840146C22semidirect
29. #16840032C22semidirect
33. #16839880C22semidirect
34. #16839592C22semidirect
35. #16839579C22semidirect
36. #16839576C22semidirect
37. #16839570C22semidirect
39. C61×#504C22semidirect
41. C61×#364C22semidirect
43. C61×#350C22semidirect
44. C4×C16×C61C22semidirect
212. #2170D61semidirect
235. #504C2×D61semidirect
245. #364C2×D61semidirect
250. #350C2×D61semidirect
251. C4×C16C2×D61semidirect
252. C61#33859semidirect

Maximal subgroups

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

subgroupindex
#214589722
#214589602
#214576062
#214480802
#214479442
#214479392
#214478892
#214477922
#214477852
#214477012
C61×#21702
#3385961