Finite Group Databasebeta

← #29593901

Subgroups — #29593901

Order 15616.

294 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 65 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#21458805C211yesmaximal, characteristic
2#21448047C211yesmaximal, characteristic, complemented
3#21447956C211yesmaximal, characteristic
4#21445214C211yesmaximal, characteristic, complemented
5#21443867C211yesmaximal, characteristic, complemented
6#21443799C211yesmaximal, characteristic, complemented
7C61×#1331C211yesmaximal, characteristic
8#16840482—21no—
9#16840167C2211yescharacteristic
10#16840145—21no—
11#16840142C2211yescharacteristic
12#16839983—22no—
13#16839973—21no—
14#16839967—21no—
15C8×Dic122C2211yescharacteristic
16#16839856—21no—
17#16839587—21no—
18C4⋊#11758185C2211yescharacteristic
19#16839567—22no—
20#16839563—21no—
21#16839509—21no—
22C4×D8×C61C2211yescharacteristic
23C4×C16×C61C2211yescharacteristic
24C61×#335C2211yescharacteristic
25C2×Dic244—21no—
26C2×Dic244—41no—
27C2×Dic244D412yes—
28C2×#11758200—22no—
29#14519777—21no—
30#14519777—21no—
31#14519770—42no—
32#14519764—22no—
33#14519756—41no—
34C4×Dic122D411yescharacteristic
35#14519742—22no—
36#14519736—41no—
37C2×#11758185—21no—
38#14519711—21no—
39#14519711—21no—
40C4⋊#92418D411yescharacteristic
41#14519706—21no—
42#14519702—41no—
43#14519700—22no—
44C8×Dic61—21no—
45C2×D8×C61D411yescharacteristic
46C4×D4×C61—21no—
47C2×C16×C61—21no—
48#107×C61D411yescharacteristic
49C4⋊C8×C61—21no—
50#102×C61—21no—
51C4×C8×C61C2311yescharacteristic
52C2×D4×C61—21no—
53C22×C4×C61—41no—
54C2×Dic122—22no—
55C2×Dic122—41no—
56C2×Dic122D811yescharacteristic
57D8×C61—21no—
58D8×C61—21no—
59C2×C8×C61—41no—
60C2×C8×C61C2×D411yescharacteristic
61C2×C8×C61C2×D411yescharacteristic
62C4⋊C4×C61—21no—
63C22⋊C4×C61—41no—
64C42×C61C2×D411yescharacteristic
65C22⋊Dic61—42no—
66C22⋊Dic61—42no—
67#11758200—82no—
68C4⋊Dic61—41no—
69C4⋊Dic61—41no—
70C4⋊Dic61—41no—
71C4⋊Dic61—41no—
72C4⋊Dic61D811yescharacteristic
73#11758196—21no—
74#11758196—42no—
75C4×Dic61—21no—
76C4×Dic61—42no—
77C2×#92418—21no—
78Dic244—42no—
79Dic244—41no—
80Dic244—41no—
81Dic244—82no—
82C16×C61—41no—
83#11758185—41no—
84C23×C61—41no—
85D4×C61—41no—
86D4×C61—41no—
87C2×C4×C61—41no—
88C2×C4×C61—81no—
89C2×C4×C61—81no—
90C2×C4×C61#12011yescharacteristic
91C2×C4×C61C2×D811yescharacteristic
92C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
93C2×Dic61—21no—
94C2×Dic61—21no—
95C2×Dic61—42no—
96C2×Dic61—81no—
97Dic122—21no—
98Dic122—21no—
99Dic122—42no—
100Dic122—42no—
101Dic122—81no—
102Dic122—81no—
103C8×C61—21no—
104C8×C61—81no—
105C8×C61#13511yescharacteristic
106C8×C61#13711yescharacteristic
107#92418—41no—
108#12383—611nomaximal, Sylow
109C22×C61—81no—
110C22×C61—81no—
111C22×C61—81no—
112C22×C61#44711yescharacteristic
113C4×C61—21no—
114C4×C61—81no—
115C4×C61#45211yescharacteristic
116C4×C61#45511yescharacteristic
117C4×C61#50811yescharacteristic
118C4×C61#50911yescharacteristic
119Dic61—41no—
120Dic61—41no—
121Dic61—82no—
122Dic61—161no—
123#3393—611no—
124#2241—611no—
125#2224—611no—
126#1674—611no—
127#1362—611no—
128Q8⋊C16—611no—
129#1331D6111yescharacteristic
130C2×C61—161no—
131C2×C61#164111yescharacteristic
132C2×C61#218611yescharacteristic
133C2×C61#219511yescharacteristic
134#556—1221no—
135#500—611no—
136#495—1221no—
137#494—611no—
138#464—1222no—
139#462—1221no—
140#461—1221no—
141C8×Q8—611no—
142C4×Q16—1221no—
143C4×D8C2×D6111yescharacteristic
144#366—1221no—
145C4⋊C16—611no—
146#358—1222no—
147#357—1221no—
148C4×C16C2×D6111yescharacteristic
149#335C2×D6111yescharacteristic
150#332—1221no—
151C61#1238311yescharacteristic, complemented, Sylow
152C2×Q16—612no—
153C2×Q16—1221no—
154C2×Q16—2441no—
155C2×SD16—1222no—
156C2×D8D24411yescharacteristic
157C4⋊Q8—1221no—
158C4⋊Q8—1221no—
159#126—2442no—
160#124—1222no—
161C22⋊Q8—2441no—
162C4×Q8—611no—
163C4×Q8—1222no—
164C4×D4—21no—
165#117—2441no—
166C2×C16—21no—
167C2×C16—1221no—
168#107—1221no—
169#107—1221no—
170#107D24411yescharacteristic
171C4⋊C8—21no—
172C4⋊C8—611no—
173C4⋊C8—1221no—
174#103—1222no—
175#103—2441no—
176#102—21no—
177C4×C8—1221no—
178C4×C8C22×D6111yescharacteristic
179C2×Q8—611no—
180C2×Q8—1222no—
181C2×Q8—2441no—
182C2×D4—21no—
183C22×C4—41no—
184Q16—4882no—
185Q16—2442no—
186Q16—2441no—
187Q16—2441no—
188SD16—4882no—
189D8—21no—
190D8—21no—
191C2×C8—41no—
192C2×C8—1221no—
193C2×C8C2×D24411yescharacteristic
194C2×C8D4×D6111yescharacteristic
195C4⋊C4—21no—
196C4⋊C4—611no—
197C4⋊C4—1221no—
198C4⋊C4—2442no—
199C4⋊C4—2441no—
200C4⋊C4—2441no—
201C4⋊C4—2441no—
202C4⋊C4—2441no—
203C22⋊C4—41no—
204C22⋊C4—2442no—
205C22⋊C4—2442no—
206C42—1221no—
207C42—2442no—
208C42D4×D6111yescharacteristic
209C16—41no—
210C16—2441no—
211C23—41no—
212Q8—1221no—
213Q8—1221no—
214Q8—4881no—
215Q8—4881no—
216Q8—2442no—
217Q8—2442no—
218D4—41no—
219D4—41no—
220C2×C4—41no—
221C2×C4—81no—
222C2×C4—81no—
223C2×C4—1221no—
224C2×C4—1221no—
225C2×C4—4881no—
226C2×C4—2442no—
227C2×C4#1451974711yescharacteristic
228C2×C4D8×D6111yescharacteristic
229C2×C4#1451980411yescharacteristic
230C8—21no—
231C8—81no—
232C8—2441no—
233C8#1451979911yescharacteristic
234C8#1451981011yescharacteristic
235C22—81no—
236C22—81no—
237C22—81no—
238C22#1683989711yescharacteristic
239C4—21no—
240C4—81no—
241C4—9761no—
242C4—4882no—
243C4—2441no—
244C4—2441no—
245C4#1683992611yescharacteristic
246C4#1683994111yescharacteristic
247C4#1684019311yescharacteristic
248C4#1684019611yescharacteristic
249C2—161no—
250C2#2144501511yescharacteristic
251C2#2144774311yescharacteristic
252C2#2144779811yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1331C2
socleC22×C61#447
prime radicalC2×D8×C61D4
hypercenter#1331D61
hypocenterC61#12383
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1331

Complements

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

NH ≅ G/Ntype
2. #21448047C2semidirect
4. #21445214C2semidirect
5. #21443867C2semidirect
6. #21443799C2semidirect
151. C61#12383semidirect

Maximal subgroups

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

subgroupindex
#214588052
#214480472
#214479562
#214452142
#214438672
#214437992
C61×#13312
#1238361