Finite Group Databasebeta

← #29590090

Subgroups — #29590090

Order 15616.

360 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 75 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#21454724C211yesmaximal, characteristic
2#21447630C211yesmaximal, characteristic, complemented
3#21444121C211yesmaximal, characteristic, complemented
4#21443795C211yesmaximal, characteristic, complemented
5#21443794C211yesmaximal, characteristic, complemented
6#21443793C211yesmaximal, characteristic, complemented
7C61×#1335C211yesmaximal, characteristic, complemented
8#16840559C411yescharacteristic
9#16840527—21no—
10#16839884C411yescharacteristic
11#16839883C411yescharacteristic
12#16839882—21no—
13#16839880C2211yescharacteristic
14#16839876—21no—
15#16839809C411yescharacteristic
16#104×D61—21no—
17C4×#11758189—21no—
18C4×#11758189C2211yescharacteristic
19#16839583C2211yescharacteristic, complemented
20#16839543—21no—
21#16839539—21no—
22#16839483—21no—
23#16839483C2211yescharacteristic, complemented
24C61×#443C2211yescharacteristic
25C61×#364C2211yescharacteristic, complemented
26C82×C61C2211yescharacteristic, complemented
27#41×D61—21no—
28#14519809—21no—
29#14519806—21no—
30#14519804—21no—
31#14519801—21no—
32#14519799C2×C411yescharacteristic
33#14519797—21no—
34#14519785—21no—
35#14519785—41no—
36#14519784—21no—
37#14519783—21no—
38#14519783—41no—
39C2×#11758189—22no—
40C2×#11758189—41no—
41C2×#11758189C2×C411yescharacteristic
42C2×#11758189D411yescharacteristic
43M16×D61—21no—
44M16×D61—41no—
45C42×D61D411yescharacteristic
46#14519717—21no—
47#14519713C2×C411yescharacteristic
48#14519712—21no—
49#14519705—21no—
50#14519704—21no—
51#14519703—21no—
52#14519687—22no—
53#14519687C2×C411yescharacteristic
54#14519687D411yescharacteristic
55C4×#92418—21no—
56C4×#92418D411yescharacteristic
57#135×C61C2×C411yescharacteristic
58#131×C61—21no—
59M32×C61—21no—
60#108×C61C2×C411yescharacteristic
61#104×C61—21no—
62C4×C8×C61—21no—
63C4×C8×C61C2311yescharacteristic
64#41×C61—21no—
65#11758226—21no—
66Q8×D61—21no—
67#11758224—21no—
68#11758224—41no—
69D4×D61—21no—
70D4×D61—41no—
71#11758222—21no—
72#11758222—41no—
73C2×C4×D61—21no—
74C2×C4×D61—41no—
75C2×C4×D61C22⋊C411yescharacteristic
76Q16×C61M1611yescharacteristic, complemented
77SD16×C61—21no—
78D8×C61M1611yescharacteristic, complemented
79M16×C61—21no—
80M16×C61—41no—
81C2×C8×C61—22no—
82C2×C8×C61—41no—
83C2×C8×C61C22×C411yescharacteristic
84C2×C8×C61C2×D411yescharacteristic
85C42×C61C2×D411yescharacteristic
86#11758202—21no—
87#11758201—21no—
88#11758200—21no—
89#11758199—21no—
90C4×Dic61—21no—
91C4×Dic61C22⋊C411yescharacteristic
92#11758194—21no—
93#11758194—41no—
94C2×#92418—22no—
95C2×#92418—41no—
96C2×#92418C22⋊C411yescharacteristic
97C2×#92418C22⋊C411yescharacteristic
98Dic244M1611yescharacteristic, complemented
99D488M1611yescharacteristic, complemented
100#11758190—21no—
101#11758189—21no—
102#11758189—21no—
103#11758189—21no—
104#11758189—21no—
105#11758189—41no—
106#11758189—44no—
107#11758189—41no—
108#11758189—41no—
109C8×D61—41no—
110C8×D61—41no—
111C8×D61—41no—
112C16×C61—41no—
113#11758185—41no—
114C22×D61—41no—
115C22×D61#10411yescharacteristic
116Q8×C61—21no—
117D4×C61—21no—
118D4×C61—41no—
119C2×C4×C61—21no—
120C2×C4×C61—41no—
121C2×C4×C61C2×C22⋊C411yescharacteristic
122C22⋊D61—41no—
123C22⋊D61—41no—
124C22⋊D61—41no—
125C2×Dic61—21no—
126C2×Dic61—41no—
127C2×Dic61#10411yescharacteristic
128D244—21no—
129D244—41no—
130C4×D61—21no—
131C4×D61—21no—
132C4×D61—41no—
133C4×D61—42no—
134C4×D61—41no—
135C4×D61—41no—
136Dic122—21no—
137Dic122—41no—
138C8×C61—24no—
139C8×C61—41no—
140C8×C61C2×M1611yescharacteristic
141C8×C61C2×M1611yescharacteristic
142C8×C61AGL(1,ℤ/8)11yescharacteristic
143C8×C61AGL(1,ℤ/8)11yescharacteristic
144#92418—21no—
145#92418—21no—
146#92418—42no—
147#92418—41no—
148#11669—611nomaximal, Sylow
149C22×C61—41no—
150C22×C61C2×#10411yescharacteristic
151C2×D61—21no—
152C2×D61—41no—
153C2×D61—41no—
154C2×D61—161no—
155C4×C61—22no—
156C4×C61—41no—
157C4×C61#40711yescharacteristic
158C4×C61#41811yescharacteristic
159Dic61—21no—
160Dic61—41no—
161Dic61—41no—
162#2956—611no—
163#2165—611no—
164#1455—611no—
165#1336—611no—
166#1336—611no—
167#1335—611no—
168#1335D6111yescharacteristic, complemented
169C2×C61—21no—
170C2×C61—81no—
171C2×C61#149011yescharacteristic
172D61—41no—
173D61—81no—
174#575—611no—
175#568—1221no—
176#444—611no—
177#444—611no—
178#444—1221no—
179#443—611no—
180#443—1221no—
181#443C2×D6111yescharacteristic
182#430—611no—
183C2×#104—1221no—
184C4×M16—611no—
185C4×M16—1221no—
186#364—611no—
187#364C2×D6111yescharacteristic, complemented
188#349—1221no—
189#347—1221no—
190#322—611no—
191#322—1221no—
192C82C2×D6111yescharacteristic, complemented
193C61#1166911yescharacteristic, complemented, Sylow
194C2×#41—1221no—
195#137—1221no—
196#137—1221no—
197AGL(1,ℤ/8)—1221no—
198AGL(1,ℤ/8)—1221no—
199#135—611no—
200#135—1221no—
201#135C4×D6111yescharacteristic
202#131—21no—
203#131—1221no—
204#131—1221no—
205#131—1221no—
206#131—2441no—
207#131—2441no—
208C2×M16—611no—
209C2×M16—611no—
210C2×M16—1222no—
211C2×M16—1221no—
212C2×M16—2441no—
213C2×M16—2441no—
214C2×C42—611no—
215M32—21no—
216M32—1221no—
217#108—611no—
218#108—1221no—
219#108C4×D6111yescharacteristic
220#104—21no—
221#104—1221no—
222#104—1221no—
223#104—1221no—
224#97—611no—
225#97—611no—
226#97—1222no—
227C4×C8—21no—
228C4×C8—611no—
229C4×C8—1221no—
230C4×C8C22×D6111yescharacteristic
231#41—21no—
232#41—1221no—
233#41—1221no—
234#41—1221no—
235#41—2441no—
236#41—2441no—
237C2×Q8—1221no—
238C2×D4—1221no—
239C2×D4—2441no—
240C22×C4—611no—
241C22×C4—1221no—
242C22×C4—2441no—
243Q16—611no—
244Q16—1221no—
245Q16#1175818911yescharacteristic, complemented
246SD16—21no—
247SD16—1221no—
248SD16—1221no—
249SD16—1221no—
250D8—611no—
251D8—1221no—
252D8#1175818911yescharacteristic, complemented
253M16—21no—
254M16—41no—
255M16—1221no—
256M16—1221no—
257M16—1221no—
258M16—1221no—
259M16—1221no—
260M16—2444no—
261M16—2441no—
262M16—2441no—
263M16—2441no—
264M16—2441no—
265C2×C8—22no—
266C2×C8—41no—
267C2×C8—611no—
268C2×C8—611no—
269C2×C8—1222no—
270C2×C8—2441no—
271C2×C8—2441no—
272C2×C8—2441no—
273C2×C8—2441no—
274C2×C8C2×C4×D6111yescharacteristic
275C2×C8D4×D6111yescharacteristic
276C42—611no—
277C42—1221no—
278C42D4×D6111yescharacteristic
279C16—41no—
280C16—2441no—
281C23—611no—
282C23—2441no—
283Q8—21no—
284Q8—1221no—
285Q8—2441no—
286D4—21no—
287D4—41no—
288D4—1221no—
289D4—2441no—
290D4—2441no—
291D4—2441no—
292D4—2441no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—611no—
296C2×C4—1221no—
297C2×C4—1221no—
298C2×C4—1221no—
299C2×C4—2442no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4C22⋊C4×D6111yescharacteristic
305C8—24no—
306C8—41no—
307C8—1221no—
308C8—1221no—
309C8—2442no—
310C8—2441no—
311C8M16×D6111yescharacteristic
312C8C2×#1175818911yescharacteristic
313C8#1451980111yescharacteristic
314C8#1451980411yescharacteristic
315C22—41no—
316C22—1221no—
317C22—9761no—
318C22—2441no—
319C22—2441no—
320C22#104×D6111yescharacteristic
321C4—22no—
322C4—41no—
323C4—1221no—
324C4—2441no—
325C4—2441no—
326C4#1683972411yescharacteristic
327C4#1683976511yescharacteristic
328C2—21no—
329C2—81no—
330C2—4881no—
331C2—2441no—
332C2#2144426011yescharacteristic
subgroupG/H
centerC4#16839765
commutatorC2×C8×C61C22×C4
FrattiniC4×C8C22×D61
FittingC61×#1335C2
socleC2×C61#1490
prime radical#16840559C4
cosocleC4×C8×C61C23
hypercenter#1335D61
hypocenterC61#11669
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C8 ◁ C4×C8 ◁ #1335

Complements

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

NH ≅ G/Ntype
2. #21447630C2semidirect
3. #21444121C2semidirect
4. #21443795C2semidirect
5. #21443794C2semidirect
6. #21443793C2semidirect
7. C61×#1335C2semidirect
19. #16839583C22semidirect
23. #16839483C22semidirect
25. C61×#364C22semidirect
26. C82×C61C22semidirect
76. Q16×C61M16semidirect
78. D8×C61M16semidirect
98. Dic244M16semidirect
99. D488M16semidirect
168. #1335D61semidirect
187. #364C2×D61semidirect
192. C82C2×D61semidirect
193. C61#11669semidirect
245. Q16#11758189semidirect
252. D8#11758189semidirect

Maximal subgroups

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

subgroupindex
#214547242
#214476302
#214441212
#214437952
#214437942
#214437932
C61×#13352
#1166961