Finite Group Databasebeta

← #30604694

Subgroups — #30604694

Order 15616.

318 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 82 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#21462020C211yesmaximal, characteristic
2#21461380C211yesmaximal, characteristic
3#21460779C214yesmaximal, complemented
4#21456403C211yesmaximal, characteristic
5C2×D61⋊C16—21no—
6#16840784—21no—
7#16840651C2212yes—
8#16840650—21no—
9#16840625—21no—
10#16840623C2212yes—
11#16840317—21no—
12#16840167C411yescharacteristic
13#16840112—21no—
14#16840000—21no—
15#16840000C412yes—
16Q16×Dic61—21no—
17Q16×Dic61C2212yes—
18C4×C8×D61C2211yescharacteristic
19C61×#494C411yescharacteristic
20D61⋊C16—24no—
21C2×#11758187—22no—
22C4⋊#92420—22no—
23#14519834—41no—
24#14519832—41no—
25C2×C8×D61C2×C411yescharacteristic
26C2×C8×D61D411yescharacteristic
27#14519777—21no—
28#14519768—41no—
29#14519757—41no—
30#14519753—22no—
31Q8×Dic61—22no—
32#14519742—41no—
33#14519735—41no—
34C42×D61D411yescharacteristic
35#14519711—21no—
36#14519711C2×C412yes—
37#14519701—22no—
38#14519701—22no—
39C4×#92418D411yescharacteristic
40C8×Dic61D411yescharacteristic
41C8×Dic61C2311yescharacteristic
42C2×Q16×C61—21no—
43C2×Q16×C61C2×C412yes—
44C4⋊Q8×C61—21no—
45C4×C8×C61C2×C411yescharacteristic
46C2×Q8×C61—22no—
47C2×C4×D61C22⋊C411yescharacteristic
48C2×C4×D61D811yescharacteristic
49C2×C4×D61SD1611yescharacteristic
50C2×Dic122—41no—
51C2×#92420—42no—
52Q16×C61—24no—
53Q16×C61—42no—
54C2×C8×C61C22⋊C411yescharacteristic
55C2×C8×C61C22×C411yescharacteristic
56C4⋊C4×C61—41no—
57C4⋊C4×C61—41no—
58C42×C61C22⋊C411yescharacteristic
59#11758198—42no—
60C4⋊Dic61—22no—
61C4⋊Dic61—41no—
62C4⋊Dic61—42no—
63#11758196—42no—
64C4×Dic61—42no—
65C4×Dic61D811yescharacteristic
66C4×Dic61SD1611yescharacteristic
67C4×Dic61C2×D411yescharacteristic
68C2×#92418C22⋊C411yescharacteristic
69C2×#92418C2×D411yescharacteristic
70C8×D61—22no—
71C8×D61—22no—
72#11758187—24no—
73C22×D61#10211yescharacteristic
74Q8×C61—42no—
75Q8×C61—42no—
76C2×C4×C61—42no—
77C2×C4×C61#10211yescharacteristic
78C2×C4×C61#10211yescharacteristic
79C2×C4×C61C2×C22⋊C411yescharacteristic
80C2×Dic61—42no—
81C2×Dic61#10211yescharacteristic
82C2×Dic61C2×D811yescharacteristic
83C2×Dic61C2×SD1611yescharacteristic
84C4×D61—22no—
85C4×D61—21no—
86C4×D61—21no—
87C4×D61—41no—
88Dic122—82no—
89#92420—82no—
90C8×C61#10412yes—
91C8×C61#13112yes—
92#92418—21no—
93#92418—21no—
94#11679—611nomaximal, Sylow
95C22×C61C2×#10211yescharacteristic
96C2×D61—21no—
97C2×D61—21no—
98C2×D61#36212yes—
99C4×C61—21no—
100C4×C61—21no—
101C4×C61—82no—
102C4×C61#40811yescharacteristic
103C4×C61C2×#10411yescharacteristic
104Dic61—21no—
105Dic61—21no—
106Dic61—21no—
107Dic61—82no—
108#3170—611no—
109C2×#346—611no—
110#1568—611no—
111#1334—614no—
112C2×C61#149211yescharacteristic
113C2×C61#214511yescharacteristic
114C2×C61C2×#36211yescharacteristic
115D61—22no—
116#533—1221no—
117C22×C16—1221no—
118#500—611no—
119#494#692311yescharacteristic
120#487—1221no—
121#467—612no—
122#467—1221no—
123C4×Q16—612no—
124C4×Q16—1221no—
125#432—1221no—
126C2×C4×C8—611no—
127#346—612no—
128#346—1221no—
129#335—1221no—
130#334—612no—
131C61#1167911yescharacteristic, complemented, Sylow
132C2×Q16—21no—
133C2×Q16C2×#692312yes—
134C22×C8—611no—
135C22×C8—611no—
136C4⋊Q8—21no—
137C4⋊Q8—1221no—
138#125—2441no—
139C22⋊Q8—1222no—
140C22⋊Q8—2441no—
141C4×Q8—1222no—
142C4×Q8—2441no—
143#117—2441no—
144C2×C42—611no—
145C2×C16—1222no—
146C2×C16—1224no—
147#107—612no—
148#107—1221no—
149C4⋊C8—1222no—
150#103—1222no—
151#103—1222no—
152C22⋊C8—2441no—
153#97—2441no—
154C4×C8—611no—
155C4×C8—611no—
156C4×C8—611no—
157C4×C8C2×#692311yescharacteristic
158C2×Q8—22no—
159C2×Q8—2441no—
160C22×C4—611no—
161C22×C4—611no—
162C22×C4—611no—
163Q16—24no—
164Q16—42no—
165C2×C8—611no—
166C2×C8—611no—
167C2×C8—1222no—
168C2×C8—1222no—
169C2×C8—2442no—
170C2×C8C22⋊#692311yescharacteristic
171C2×C8C22×#692311yescharacteristic
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—1222no—
175C4⋊C4—2442no—
176C4⋊C4—2442no—
177C4⋊C4—2441no—
178C22⋊C4—2442no—
179C42—611no—
180C42—611no—
181C42—611no—
182C42—2442no—
183C42C22⋊#692311yescharacteristic
184C16—1224no—
185C23—611no—
186Q8—42no—
187Q8—42no—
188Q8—4882no—
189C2×C4—42no—
190C2×C4—611no—
191C2×C4—611no—
192C2×C4—611no—
193C2×C4—1222no—
194C2×C4—1221no—
195C2×C4—1221no—
196C2×C4—2441no—
197C2×C4—2442no—
198C2×C4#1451983911yescharacteristic
199C2×C4#1451983911yescharacteristic
200C2×C4C2×C22⋊#692311yescharacteristic
201C8—1221no—
202C8—1221no—
203C8—4882no—
204C8#1451984112yes—
205C8#1451986412yes—
206C22—612no—
207C22—1221no—
208C22—1221no—
209C22C2×#1451983911yescharacteristic
210C4—21no—
211C4—21no—
212C4—82no—
213C4—1221no—
214C4—1221no—
215C4—1221no—
216C4—4882no—
217C4#1684073611yescharacteristic
218C4C2×#1451984111yescharacteristic
219C2—1222no—
220C2#2146116511yescharacteristic
221C2#2146214111yescharacteristic
222C2D61⋊#36211yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#494C4
socleC22×C61C2×#102
prime radicalC22×D61#102
cosocleC8×Dic61C23
hypercenter#494#6923
hypocenterC61#11679
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #494

Complements

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

NH ≅ G/Ntype
3. #21460779C2semidirect
131. C61#11679semidirect

Maximal subgroups

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

subgroupindex
#214620202
#214613802
#214607792
#214564032
#1167961