Finite Group Databasebeta

← #30594444

Subgroups — #30594444

Order 15616.

276 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 52 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#21461720C211yesmaximal, characteristic
2#21461072C211yesmaximal, characteristic
3#21445588C211yesmaximal, characteristic
4#16840782—21no—
5#16840734—21no—
6#16840642—21no—
7#16840642C412yes—
8#16840608—21no—
9#16840606C412yes—
10C2×#14519734C2211yescharacteristic
11C2×#14519689—21no—
12C2×C4×#92418C411yescharacteristic
13#16839516—21no—
14C2×#97×C61C411yescharacteristic
15C2×#11758217—22no—
16#14519844—41no—
17#14519834—41no—
18#14519834—41no—
19C22⋊#92420—22no—
20#14519832—41no—
21C22×C4×D61D411yescharacteristic
22C22×#92418—21no—
23#14519734—41no—
24#14519734—41no—
25C2×#11758196C2×C411yescharacteristic
26C2×#11758196D411yescharacteristic
27C2×#11758198C2×C411yescharacteristic
28C2×#11758198Q811yescharacteristic
29C2×C4×Dic61D411yescharacteristic
30#14519689—24no—
31C4×#92418—41no—
32C22×C8×C61—21no—
33C2×C42×C61C2×C411yescharacteristic
34#97×C61—41no—
35C23×D61C4⋊C411yescharacteristic
36C22×C4×C61C4211yescharacteristic
37C22×C4×C61C22⋊C411yescharacteristic
38C22×C4×C61C4⋊C411yescharacteristic
39C22×Dic61C22⋊C411yescharacteristic
40C22×Dic61C22⋊C411yescharacteristic
41C22×Dic61C4⋊C411yescharacteristic
42C2×C4×D61—21no—
43C2×C4×D61—21no—
44C2×C4×D61—22no—
45C2×C4×D61—41no—
46#11758217—42no—
47#11758217—42no—
48C2×#92420—42no—
49C2×#92420—42no—
50C2×C8×C61—22no—
51C2×C8×C61—41no—
52C2×C8×C61—41no—
53C42×C61—21no—
54C42×C61—21no—
55#11758198—41no—
56#11758198—41no—
57#11758196—41no—
58#11758196—41no—
59C4×Dic61—21no—
60C4×Dic61—21no—
61C2×#92418—22no—
62C2×#92418—41no—
63C2×#92418—41no—
64C23×C61#9511yescharacteristic
65C22×D61—21no—
66C22×D61—21no—
67C22×D61—21no—
68C22×D61—41no—
69C22×D61—41no—
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—41no—
75C2×C4×C61—41no—
76C2×C4×C61#9911yescharacteristic
77C2×C4×C61#9911yescharacteristic
78C2×Dic61—21no—
79C2×Dic61—21no—
80C2×Dic61—21no—
81C2×Dic61—21no—
82C2×Dic61—41no—
83C2×Dic61—41no—
84C2×Dic61#10412yes—
85C4×D61—42no—
86C4×D61—42no—
87#92420—82no—
88#92420—82no—
89C8×C61—42no—
90#92418—42no—
91#7216—611nomaximal, Sylow
92C22×C61—21no—
93C22×C61—21no—
94C22×C61H(3,ℤ/4)11yescharacteristic
95C22×C61#33911yescharacteristic
96C22×C61#34211yescharacteristic
97C2×D61—42no—
98C2×D61—41no—
99C2×D61—41no—
100C2×D61—41no—
101C2×D61—81no—
102C4×C61—21no—
103C4×C61—21no—
104C4×C61—41no—
105C4×C61—41no—
106Dic61—22no—
107Dic61—41no—
108Dic61—41no—
109#1822—611no—
110#1750—611no—
111#1464—611no—
112C2×C61—21no—
113C2×C61—21no—
114C2×C61#128411yescharacteristic
115C2×C61#139211yescharacteristic
116C2×C61#139511yescharacteristic
117D61—81no—
118C2×#117—611no—
119#432—1221no—
120#407—1221no—
121C2×C22⋊C8—1221no—
122C2×#97#692311yescharacteristic
123C2×C4×C8—611no—
124#343—612no—
125#343—1221no—
126#336—1221no—
127#324—1221no—
128#323—612no—
129C61#721611yescharacteristic, complemented, Sylow
130C23×C4—611no—
131C2×M16—1222no—
132C22×C8—21no—
133C22×C8—1221no—
134#117—2441no—
135#117—2441no—
136C2×C4⋊C4—611no—
137C2×C4⋊C4—611no—
138C2×C22⋊C4—611no—
139C2×C22⋊C4—611no—
140C2×C42—611no—
141C2×C42C2×#692311yescharacteristic
142C4⋊C8—2441no—
143C22⋊C8—1224no—
144C22⋊C8—1222no—
145C22⋊C8—2441no—
146C22⋊C8—2441no—
147#97—41no—
148#97—2441no—
149C4×C8—2441no—
150C24—611no—
151C22×C4—611no—
152C22×C4—611no—
153C22×C4—611no—
154C22×C4—1222no—
155C22×C4—1221no—
156C22×C4—1221no—
157C22×C4—2441no—
158C22×C4C4×#692311yescharacteristic
159C22×C4C4⋊#692311yescharacteristic
160C22×C4C22⋊#692311yescharacteristic
161M16—2442no—
162M16—2442no—
163C2×C8—22no—
164C2×C8—41no—
165C2×C8—41no—
166C2×C8—1222no—
167C2×C8—2442no—
168C2×C8—2442no—
169C2×C8—2441no—
170C2×C8—2441no—
171C4⋊C4—2441no—
172C4⋊C4—2441no—
173C22⋊C4—2441no—
174C22⋊C4—2441no—
175C42—21no—
176C42—21no—
177C42—1221no—
178C42—1221no—
179C23—1221no—
180C23—1221no—
181C23—1221no—
182C23—2441no—
183C23—2441no—
184C23(C2×#6923)⋊C411yescharacteristic
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—612no—
192C2×C4—1221no—
193C2×C4—1221no—
194C2×C4—1221no—
195C2×C4—1221no—
196C2×C4—2442no—
197C2×C4—2442no—
198C2×C4—2441no—
199C2×C4—2441no—
200C2×C4#1451983511yescharacteristic
201C2×C4#1451983611yescharacteristic
202C8—42no—
203C8—4882no—
204C8—4882no—
205C8—2442no—
206C22—21no—
207C22—21no—
208C22—4881no—
209C22—2442no—
210C22—2441no—
211C22—2441no—
212C22—2441no—
213C22#1684062911yescharacteristic
214C22#1684063311yescharacteristic
215C22#1684064011yescharacteristic
216C4—21no—
217C4—21no—
218C4—41no—
219C4—41no—
220C4—1222no—
221C4—2441no—
222C4—2441no—
223C2—21no—
224C2—21no—
225C2—4881no—
226C2#2146066711yescharacteristic
227C2#2146091111yescharacteristic
228C2#2146092011yescharacteristic
subgroupG/H
centerC22#16840640
commutatorC22×C4×C61C42
FrattiniC2×C42C2×#6923
FittingC2×#97×C61C4
socleC22×C61#342
prime radicalC23×D61C4⋊C4
cosocleC2×#14519734C22
hypercenterC2×#97#6923
hypocenterC61#7216
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
129. C61#7216semidirect

Maximal subgroups

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

subgroupindex
#214617202
#214610722
#214455882
#721661