Finite Group Databasebeta

← #29835273

Subgroups — #29835273

Order 15616.

524 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456437C211yesmaximal, characteristic, complemented
2#21454722C211yesmaximal, characteristic, complemented
3#21448036C211yesmaximal, characteristic, complemented
4#21448034C211yesmaximal, characteristic, complemented
5#21447988C212yesmaximal, complemented
6#21447890C212yesmaximal, complemented
7#21447765C211yesmaximal, characteristic
8#21447714C212yesmaximal, complemented
9#21447711C212yesmaximal, complemented
10#21447632C211yesmaximal, characteristic, complemented
11C61×#2191C211yesmaximal, characteristic, complemented
12C2×#14519784—21no—
13#16840385—21no—
14#16840197C2212yes—
15#16840159C2211yescharacteristic, complemented
16#16840147C2211yescharacteristic, complemented
17#16840123—21no—
18#16840015C2211yescharacteristic
19#16839993—21no—
20#16839884—21no—
21#16839884C2212yes—
22#16839879—21no—
23#16839879C2212yes—
24#16839873C2211yescharacteristic, complemented
25#16839869C2211yescharacteristic, complemented
26#16839847—21no—
27#16839811C2211yescharacteristic
28#16839779—21no—
29#16839720C2211yescharacteristic
30#16839585C2212yescomplemented
31#16839584C2212yescomplemented
32#16839582C2212yescomplemented
33#16839578C2212yescomplemented
34#16839576C2212yescomplemented
35#16839572C2212yes—
36#16839544C2211yescharacteristic
37#16839539C2212yescomplemented
38C61×#575C2211yescharacteristic
39C61×#510C2212yes—
40C61×#470C2211yescharacteristic
41C61×#360C2212yes—
42C61×#349C2211yescharacteristic
43C2×#11758201—21no—
44C2×D488C2311yescharacteristic
45#14519784—22no—
46#14519784—22no—
47#14519784—41no—
48#14519784—41no—
49C2×#11758194—21no—
50C2×#11758194—41no—
51C22×#92418—41no—
52C22×#92418D411yescharacteristic
53#14519776—21no—
54#14519772—41no—
55#14519766—21no—
56#14519763—41no—
57#14519759—41no—
58#14519757—41no—
59#14519751—21no—
60Q8×Dic61—21no—
61#14519739—21no—
62#14519736D411yescharacteristic
63#14519720—22no—
64#14519718—22no—
65#14519717C2312yes—
66#14519713—21no—
67#14519713C2312yes—
68#14519709C2311yescharacteristic
69#14519708—21no—
70#14519704—22no—
71#14519704—22no—
72#14519701—21no—
73#14519699—21no—
74#14519697—21no—
75#14519687D411yescharacteristic
76#14519687C2311yescharacteristic
77C8×Dic61D411yescharacteristic
78C8×Dic61C2311yescharacteristic
79C2×#41×C61—21no—
80#137×C61—22no—
81AGL(1,ℤ/8)×C61—22no—
82#135×C61—21no—
83#135×C61C2312yes—
84C2×Q16×C61C2311yescharacteristic
85C2×M16×C61C2311yescharacteristic
86C22⋊Q8×C61—21no—
87Q32×C61—22no—
88SD32×C61—22no—
89M32×C61C2312yes—
90#106×C61C2311yescharacteristic
91#103×C61—21no—
92#41×C61—22no—
93#41×C61—22no—
94#41×C61—41no—
95#41×C61—41no—
96C2×Q8×C61—21no—
97C2×Q8×C61—21no—
98C2×D4×C61—21no—
99C2×D4×C61—41no—
100C22×C4×C61—41no—
101C22×C4×C61C2×D411yescharacteristic
102C2×C22⋊D61—41no—
103C2×D244—21no—
104C2×C4×D61—41no—
105C2×Dic122—41no—
106Q16×C61—21no—
107Q16×C61—22no—
108Q16×C61#4112yes—
109SD16×C61—22no—
110SD16×C61—22no—
111D8×C61—21no—
112D8×C61#4112yes—
113M16×C61—22no—
114C2×C8×C61C2×D411yescharacteristic
115C2×C8×C61C2411yescharacteristic
116C4⋊C4×C61—21no—
117C4⋊C4×C61—41no—
118C22⋊C4×C61—41no—
119C22⋊Dic61—21no—
120#11758201—41no—
121#11758201—41no—
122#11758198—41no—
123#11758198—41no—
124#11758198—41no—
125#11758198—41no—
126C4⋊Dic61—21no—
127C4⋊Dic61—21no—
128C4⋊Dic61—41no—
129#11758196—41no—
130C4×Dic61—41no—
131C4×Dic61C2×D411yescharacteristic
132C4×Dic61C2×D411yescharacteristic
133#11758194—22no—
134#11758194—42no—
135#11758194—41no—
136#11758194—42no—
137C2×#92418—21no—
138C2×#92418—21no—
139C2×#92418—42no—
140C2×#92418—41no—
141C2×#92418—42no—
142C2×#92418C2×D411yescharacteristic
143C2×#92418C2×D411yescharacteristic
144D488—22no—
145C16×C61—22no—
146#11758185—22no—
147C23×C61—41no—
148C23×C61AGL(1,ℤ/8)11yescharacteristic
149C22×D61—41no—
150Q8×C61—22no—
151Q8×C61—41no—
152Q8×C61—41no—
153Q8×C61—41no—
154D4×C61—22no—
155D4×C61—41no—
156D4×C61—42no—
157D4×C61—42no—
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61—42no—
161C2×C4×C61—41no—
162C2×C4×C61—42no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C61C22×D411yescharacteristic
167C22⋊D61—161no—
168C2×Dic61—21no—
169C2×Dic61—21no—
170C2×Dic61—41no—
171D244—41no—
172D244—41no—
173C4×D61—161no—
174Dic122—161no—
175C8×C61—21no—
176C8×C61C2×#4112yes—
177#92418—21no—
178#92418—42no—
179#92418AGL(1,ℤ/8)11yescharacteristic
180#92418AGL(1,ℤ/8)11yescharacteristic
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—42no—
192C4×C61—81no—
193C4×C61—81no—
194C4×C61#52511yescharacteristic
195C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
196Dic61—41no—
197Dic61—41no—
198Dic61—81no—
199#3173—611no—
200#2955—611no—
201#2239—611no—
202#2238—611no—
203#2230—612no—
204#2212—612no—
205#2191D6111yescharacteristic, complemented
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—1221no—
217#542—1221no—
218#510C2×D6112yes—
219#509—612no—
220#498—611no—
221#495—611no—
222#489—1221no—
223#470C2×D6111yescharacteristic
224#469—611no—
225#465—1221no—
226#444—612no—
227#444—1221no—
228#443—612no—
229#443—1221no—
230#442—611no—
231#441—611no—
232C4×SD16—1221no—
233#430—611no—
234#421—1221no—
235#405—611no—
236#365—612no—
237#365—612no—
238#364—612no—
239#362—612no—
240#361—612no—
241#360—612no—
242#360C2×D6112yes—
243#349—611no—
244#349C2×D6111yescharacteristic
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×Q16C22×D6111yescharacteristic
253C2×SD16—1221no—
254C2×D8—611no—
255#131—1222no—
256#131—1222no—
257#131—2441no—
258#131—2441no—
259C2×M16—1221no—
260C2×M16—2441no—
261C2×M16C22×D6111yescharacteristic
262C22×C8—611no—
263C22×C8—2441no—
264C4⋊Q8—1221no—
265#126—2441no—
266#124—1221no—
267#124—2441no—
268#123—2441no—
269C22⋊Q8—21no—
270C22⋊Q8—2441no—
271#121—1221no—
272C4×Q8—1221no—
273C4×D4—1221no—
274#117—611no—
275Q32—22no—
276SD32—22no—
277SD32—1222no—
278D16—1222no—
279M32—612no—
280M32C22×D6112yes—
281#108—612no—
282#108—1221no—
283#106—611no—
284#106—1221no—
285#106C22×D6111yescharacteristic
286#104—1222no—
287#104—1222no—
288#103—21no—
289#103—1221no—
290#102—1221no—
291#102—1221no—
292#97—611no—
293#97—611no—
294C4×C8—611no—
295C4×C8—611no—
296#41—22no—
297#41—22no—
298#41—41no—
299#41—41no—
300C2×Q8—21no—
301C2×Q8—21no—
302C2×Q8—2441no—
303C2×D4—21no—
304C2×D4—41no—
305C2×D4—1221no—
306C2×D4—2441no—
307C22×C4—41no—
308C22×C4—2441no—
309C22×C4D4×D6111yescharacteristic
310Q16—21no—
311Q16—22no—
312Q16#1175822412yes—
313SD16—22no—
314SD16—22no—
315SD16—2441no—
316SD16—2441no—
317D8—21no—
318D8—1222no—
319D8#1175822412yes—
320M16—22no—
321M16—1222no—
322M16—2442no—
323M16—2442no—
324M16—2441no—
325C2×C8—611no—
326C2×C8—611no—
327C2×C8—1221no—
328C2×C8—1221no—
329C2×C8—2442no—
330C2×C8—2442no—
331C2×C8—2441no—
332C2×C8D4×D6111yescharacteristic
333C2×C8C23×D6111yescharacteristic
334C4⋊C4—21no—
335C4⋊C4—41no—
336C4⋊C4—1221no—
337C4⋊C4—1221no—
338C4⋊C4—2441no—
339C4⋊C4—2441no—
340C22⋊C4—41no—
341C22⋊C4—1221no—
342C22⋊C4—2441no—
343C22⋊C4—2441no—
344C22⋊C4—2441no—
345C22⋊C4—2441no—
346C42—611no—
347C42—611no—
348C42—2441no—
349C16—22no—
350C16—1222no—
351C23—41no—
352C23—2441no—
353C23#1451980111yescharacteristic
354Q8—22no—
355Q8—41no—
356Q8—41no—
357Q8—41no—
358Q8—9761no—
359D4—22no—
360D4—41no—
361D4—42no—
362D4—42no—
363D4—9761no—
364D4—2441no—
365D4—2441no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—1221no—
374C2×C4—1221no—
375C2×C4—9761no—
376C2×C4—2441no—
377C2×C4#1451980111yescharacteristic
378C2×C4C2×D4×D6111yescharacteristic
379C8—21no—
380C8—611no—
381C8—611no—
382C8—1221no—
383C8—2442no—
384C8C2×#1175822412yes—
385C22—21no—
386C22—41no—
387C22—42no—
388C22—82no—
389C22—4881no—
390C22—4881no—
391C22—4881no—
392C22C2×#1451980111yescharacteristic
393C4—21no—
394C4—42no—
395C4—81no—
396C4—81no—
397C4—4881no—
398C4—2441no—
399C4—2441no—
400C4#1684026811yescharacteristic
401C4AGL(1,ℤ/8)×D6111yescharacteristic
402C2—21no—
403C2—41no—
404C2—82no—
405C2—9761no—
406C2#2145590511yescharacteristic
subgroupG/H
centerC2#21455905
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2191C2
socleC2×C61#3109
prime radical#21447765C2
hypercenter#2191D61
hypocenterC61#33691
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #2191

Complements

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

NH ≅ G/Ntype
1. #21456437C2semidirect
2. #21454722C2semidirect
3. #21448036C2semidirect
4. #21448034C2semidirect
5. #21447988C2semidirect
6. #21447890C2semidirect
8. #21447714C2semidirect
9. #21447711C2semidirect
10. #21447632C2semidirect
11. C61×#2191C2semidirect
15. #16840159C22semidirect
16. #16840147C22semidirect
24. #16839873C22semidirect
25. #16839869C22semidirect
30. #16839585C22semidirect
31. #16839584C22semidirect
32. #16839582C22semidirect
33. #16839578C22semidirect
34. #16839576C22semidirect
37. #16839539C22semidirect
205. #2191D61semidirect
246. C61#33691semidirect

Maximal subgroups

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

subgroupindex
#214564372
#214547222
#214480362
#214480342
#214479882
#214478902
#214477652
#214477142
#214477112
#214476322
C61×#21912
#3369161