Finite Group Databasebeta

← #30605019

Subgroups — #30605019

Order 15616.

316 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 60 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#21462195C211yesmaximal, characteristic, complemented
2#21461541C211yesmaximal, characteristic, complemented
3#21460794C211yesmaximal, characteristic, complemented
4#21460793C211yesmaximal, characteristic, complemented
5#21460790C211yesmaximal, characteristic, complemented
6#21460789C211yesmaximal, characteristic, complemented
7#21456467C211yesmaximal, characteristic
8#16840725—21no—
9#16840685—21no—
10#16840659C2211yescharacteristic
11#16840659C2211yescharacteristic
12#16840655—21no—
13#16840631C2211yescharacteristic
14#16840630C2211yescharacteristic
15#16840629—21no—
16#16840363—21no—
17#16840162C411yescharacteristic, complemented
18#16840137C411yescharacteristic, complemented
19#16840125—21no—
20#16840016C2211yescharacteristic
21#16840012C2211yescharacteristic
22#16839997—21no—
23#16839875C411yescharacteristic, complemented
24C4×#11758199—21no—
25#16839719C2211yescharacteristic
26C61×#442C411yescharacteristic, complemented
27D61⋊M16—21no—
28#14519856—21no—
29#14519851—21no—
30#14519851—21no—
31#14519831—22no—
32C8×#6923—22no—
33C2×D488C2×C411yescharacteristic
34C2×#11758199—21no—
35C2×#11758189C2311yescharacteristic
36C2×C8×D61D411yescharacteristic
37#14519773—21no—
38#14519768—21no—
39#14519760—41no—
40#14519759—41no—
41#14519752—21no—
42#14519751—41no—
43#14519750—41no—
44#14519748—21no—
45C4×D244—21no—
46#14519734D411yescharacteristic
47#14519710—21no—
48#14519709C2×C411yescharacteristic
49#14519699—21no—
50#14519698—21no—
51#14519697—21no—
52#14519687D411yescharacteristic
53C4×#92418D411yescharacteristic
54C8×Dic61C2×C411yescharacteristic
55C2×D8×C61C2×C411yescharacteristic
56C4×D4×C61—21no—
57#106×C61C2×C411yescharacteristic
58#102×C61—21no—
59#97×C61C2×C411yescharacteristic
60C2×D4×C61—21no—
61C22×C4×C61—41no—
62C2×C22⋊D61—41no—
63C2×C22⋊D61—41no—
64C2×C22⋊D61—41no—
65C2×D244—21no—
66C2×D244—41no—
67C2×C4×D61—41no—
68C2×C4×D61C2×D411yescharacteristic
69C22⋊#6923—41no—
70#11758217—41no—
71C4⋊#6923—41no—
72C4×#6923—22no—
73#11758213—41no—
74D61⋊C8—22no—
75D8×C61—41no—
76C2×C8×C61C22⋊C411yescharacteristic
77C2×C8×C61C22×C411yescharacteristic
78C4⋊C4×C61—21no—
79C22⋊C4×C61—41no—
80C42×C61C22⋊C411yescharacteristic
81C22⋊Dic61—41no—
82#11758199—41no—
83#11758199—41no—
84#11758198—21no—
85#11758198—41no—
86#11758198—41no—
87C4⋊Dic61—21no—
88C4⋊Dic61—41no—
89#11758196—21no—
90#11758196—41no—
91C4×Dic61C22⋊C411yescharacteristic
92C2×#92418C22⋊C411yescharacteristic
93C2×#92418C2×D411yescharacteristic
94D488—41no—
95#11758189—41no—
96C8×D61—21no—
97C8×D61—21no—
98#11758187—41no—
99#11758187—41no—
100C23×C61—41no—
101C22×D61—41no—
102C22×D61AGL(1,ℤ/8)11yescharacteristic
103C2×#6923—42no—
104D4×C61—41no—
105D4×C61—41no—
106C2×C4×C61—21no—
107C2×C4×C61—41no—
108C2×C4×C61—161no—
109C2×C4×C61C2×C22⋊C411yescharacteristic
110C22⋊D61—161no—
111C22⋊D61—161no—
112C22⋊D61—161no—
113C2×Dic61—21no—
114C2×Dic61—41no—
115C2×Dic61AGL(1,ℤ/8)11yescharacteristic
116D244—41no—
117D244—41no—
118D244—161no—
119C4×D61—21no—
120C4×D61—21no—
121C4×D61—161no—
122#92420—42no—
123C8×C61—21no—
124C8×C61—21no—
125#92418—21no—
126#92418#10411yescharacteristic
127#92418#10411yescharacteristic
128#11770—611nomaximal, Sylow
129C22×C61—81no—
130C22×C61—81no—
131C22×C61—81no—
132C22×C61#41811yescharacteristic
133C2×D61—21no—
134C2×D61—41no—
135C2×D61—81no—
136C2×D61—81no—
137C2×D61—81no—
138#6923—82no—
139C4×C61—41no—
140C4×C61—81no—
141C4×C61#41011yescharacteristic
142C4×C61C2×#10411yescharacteristic
143Dic61—21no—
144Dic61—41no—
145Dic61—81no—
146#3176—611no—
147#2166—611no—
148#1747—611no—
149#1341—611no—
150#1341—611no—
151#1339—611no—
152#1339—611no—
153C2×C61—21no—
154C2×C61—161no—
155C2×C61#150511yescharacteristic
156D61—41no—
157D61—161no—
158#540—1221no—
159#499—611no—
160#493—611no—
161#490—1221no—
162#469—611no—
163#469—611no—
164#466—1221no—
165#442—611no—
166#442#692311yescharacteristic, complemented
167C4×D8—1221no—
168#405—611no—
169#405—1221no—
170#364—1221no—
171#349—611no—
172#349—611no—
173#347—1221no—
174#338—611no—
175H(3,ℤ/4)—611no—
176H(3,ℤ/4)—1221no—
177C61#1177011yescharacteristic, complemented, Sylow
178C2×D8—611no—
179C2×D8—1221no—
180C2×D8C2×#692311yescharacteristic
181C2×M16—611no—
182C2×M16—1221no—
183C22×C8—611no—
184#127—1221no—
185#125—1221no—
186#123—2441no—
187#123—2441no—
188#121—1221no—
189#121—1221no—
190#121—2441no—
191#121—2441no—
192C4×D4—21no—
193C4×D4—1221no—
194#117—611no—
195#117—1221no—
196M32—1221no—
197M32—1221no—
198#107—1221no—
199#106—611no—
200#106C2×#692311yescharacteristic
201#102—21no—
202#102—1221no—
203#102—1221no—
204#102—1221no—
205#97—611no—
206#97—1222no—
207#97C2×#692311yescharacteristic
208C4×C8—611no—
209C4×C8—611no—
210C4×C8—1222no—
211C2×D4—21no—
212C2×D4—1221no—
213C2×D4—2441no—
214C2×D4—2441no—
215C2×D4—2441no—
216C2×D4—2441no—
217C22×C4—41no—
218C22×C4—611no—
219C22×C4—2441no—
220D8—41no—
221D8—2441no—
222D8—2441no—
223D8—2441no—
224M16—2441no—
225M16—2441no—
226M16—2441no—
227C2×C8—611no—
228C2×C8—611no—
229C2×C8—1221no—
230C2×C8—1221no—
231C2×C8—1222no—
232C2×C8C22⋊#692311yescharacteristic
233C2×C8C22×#692311yescharacteristic
234C4⋊C4—21no—
235C4⋊C4—1221no—
236C4⋊C4—1221no—
237C4⋊C4—2441no—
238C4⋊C4—2441no—
239C4⋊C4—2441no—
240C22⋊C4—41no—
241C22⋊C4—1221no—
242C22⋊C4—2441no—
243C22⋊C4—2441no—
244C22⋊C4—2441no—
245C22⋊C4—2441no—
246C42—611no—
247C42—1222no—
248C42C22⋊#692311yescharacteristic
249C16—2441no—
250C16—2441no—
251C23—41no—
252C23—611no—
253C23—2441no—
254D4—41no—
255D4—41no—
256D4—9761no—
257D4—9761no—
258D4—9761no—
259D4—9761no—
260D4—2441no—
261D4—2441no—
262C2×C4—21no—
263C2×C4—41no—
264C2×C4—161no—
265C2×C4—611no—
266C2×C4—1221no—
267C2×C4—1221no—
268C2×C4—1221no—
269C2×C4—9761no—
270C2×C4—2442no—
271C2×C4—2441no—
272C2×C4C2×C22⋊#692311yescharacteristic
273C8—21no—
274C8—21no—
275C8—611no—
276C8—611no—
277C8—1221no—
278C8—2442no—
279C22—81no—
280C22—81no—
281C22—81no—
282C22—1221no—
283C22—4881no—
284C22—4881no—
285C22—4881no—
286C22—2441no—
287C22#1684075411yescharacteristic
288C4—41no—
289C4—81no—
290C4—1221no—
291C4—4881no—
292C4—4882no—
293C4—2441no—
294C4#1684074111yescharacteristic
295C4D61⋊#10411yescharacteristic
296C2—21no—
297C2—161no—
298C2—9761no—
299C2—2441no—
300C2#2146120911yescharacteristic
subgroupG/H
centerC2#21461209
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#442C4
socleC2×C61#1505
prime radical#21456467C2
cosocleC2×#11758189C23
hypercenter#442#6923
hypocenterC61#11770
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #21462195C2semidirect
2. #21461541C2semidirect
3. #21460794C2semidirect
4. #21460793C2semidirect
5. #21460790C2semidirect
6. #21460789C2semidirect
17. #16840162C4semidirect
18. #16840137C4semidirect
23. #16839875C4semidirect
26. C61×#442C4semidirect
166. #442#6923semidirect
177. C61#11770semidirect

Maximal subgroups

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

subgroupindex
#214621952
#214615412
#214607942
#214607932
#214607902
#214607892
#214564672
#1177061