Finite Group Databasebeta

← #30594763

Subgroups — #30594763

Order 15616.

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

normal subgroups only

This group has 256 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#21461991C211yesmaximal, characteristic
2#21461686C211yesmaximal, characteristic
3#21444161C211yesmaximal, characteristic
4#16840765—21no—
5C2×#14519844C411yescharacteristic
6C2×#14519838C412yes—
7C2×#14519832C411yescharacteristic
8#16840642—21no—
9#16840628—21no—
10#16840628—21no—
11C2×#14519742C2211yescharacteristic
12#16839816—21no—
13#16839488C411yescharacteristic
14#16839487—21no—
15C61×#324C411yescharacteristic
16C2×#11758217—22no—
17C22×#92420—21no—
18C22×#92420—21no—
19#14519844—41no—
20#14519844—41no—
21C4⋊#92420—41no—
22#14519838—42no—
23#14519832—41no—
24C22×Dic122C2×C411yescharacteristic
25#14519742—41no—
26#14519742—41no—
27C2×#11758196D411yescharacteristic
28C2×#11758196Q811yescharacteristic
29C2×C4×Dic61C2×C411yescharacteristic
30C2×C4×Dic61D411yescharacteristic
31C2×C4×Dic61D411yescharacteristic
32#14519706—41no—
33C22⋊#92418—21no—
34#14519687—41no—
35C2×C4⋊C4×C61C2×C411yescharacteristic
36C22⋊C8×C61—21no—
37C22×C4×C61C4211yescharacteristic
38C22×C4×C61C22⋊C411yescharacteristic
39C22×C4×C61C4⋊C411yescharacteristic
40C22×Dic61C22⋊C411yescharacteristic
41C22×Dic61C22⋊C411yescharacteristic
42C22×Dic61C4⋊C411yescharacteristic
43C22×Dic61C4⋊C411yescharacteristic
44C2×Dic122—21no—
45C2×Dic122—21no—
46C2×Dic122—41no—
47C2×Dic122—41no—
48#11758217—42no—
49#11758217—42no—
50C2×#92420—22no—
51C2×#92420—41no—
52C2×#92420—41no—
53C2×#92420—42no—
54C2×#92420—42no—
55C2×#92420—41no—
56C2×C8×C61—41no—
57C4⋊C4×C61—41no—
58#11758196—41no—
59#11758196—41no—
60C4×Dic61—21no—
61C4×Dic61—21no—
62C4×Dic61—21no—
63C4×Dic61—21no—
64C4×Dic61—21no—
65C4×Dic61—21no—
66C2×#92418—41no—
67C23×C61#9511yescharacteristic
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—21no—
73C2×C4×C61—41no—
74C2×C4×C61—41no—
75C2×Dic61—21no—
76C2×Dic61—21no—
77C2×Dic61—21no—
78C2×Dic61—21no—
79C2×Dic61—21no—
80C2×Dic61—21no—
81C2×Dic61—21no—
82C2×Dic61—21no—
83C2×Dic61—41no—
84C2×Dic61#9911yescharacteristic
85C2×Dic61#9911yescharacteristic
86C2×Dic61#10011yescharacteristic
87C2×Dic61#10111yescharacteristic
88Dic122—42no—
89Dic122—42no—
90#92420—42no—
91#92420—82no—
92#92420—81no—
93C8×C61—81no—
94#92418—81no—
95#7323—611nomaximal, Sylow
96C22×C61—21no—
97C22×C61—21no—
98C22×C61#34211yescharacteristic
99C22×C61#34311yescharacteristic
100C22×C61#34411yescharacteristic
101C4×C61—41no—
102C4×C61—41no—
103C4×C61—41no—
104Dic61—21no—
105Dic61—21no—
106Dic61—21no—
107Dic61—41no—
108Dic61—41no—
109Dic61#35511yescharacteristic
110Dic61#35611yescharacteristic
111#1985—611no—
112#1801—611no—
113#1467—611no—
114C2×C61—21no—
115C2×C61—21no—
116C2×C61#130511yescharacteristic
117C2×C61#139411yescharacteristic
118C2×C61#139511yescharacteristic
119C2×C4×Q8—611no—
120#432—1221no—
121#423—1221no—
122C2×C4⋊C8—611no—
123C2×#101—612no—
124C2×#97—611no—
125#343—1221no—
126#336—1221no—
127#336—1221no—
128#324—611no—
129#324—1221no—
130#324#692311yescharacteristic
131C61#732311yescharacteristic, complemented, Sylow
132C22×Q8—611no—
133C2×M16—1222no—
134C22×C8—1221no—
135C22×C8—1221no—
136C4×Q8—2441no—
137C4×Q8—2441no—
138C2×C4⋊C4—611no—
139C2×C4⋊C4—611no—
140C2×C4⋊C4C2×#692311yescharacteristic
141C2×C42—611no—
142C2×C42—611no—
143C2×C42—611no—
144C4⋊C8—2441no—
145C4⋊C8—2441no—
146C4⋊C8—2441no—
147C4⋊C8—2441no—
148#101—2442no—
149C22⋊C8—21no—
150C22⋊C8—1221no—
151#97—2441no—
152#97—2441no—
153C2×Q8—1221no—
154C2×Q8—1221no—
155C2×Q8—2441no—
156C2×Q8—2441no—
157C22×C4—611no—
158C22×C4—611no—
159C22×C4—611no—
160C22×C4—611no—
161C22×C4C4×#692311yescharacteristic
162C22×C4C4⋊#692311yescharacteristic
163C22×C4C22⋊#692311yescharacteristic
164M16—2442no—
165M16—2442no—
166C2×C8—41no—
167C2×C8—1222no—
168C2×C8—2441no—
169C2×C8—2441no—
170C2×C8—2442no—
171C2×C8—2442no—
172C2×C8—2441no—
173C2×C8—2441no—
174C4⋊C4—41no—
175C4⋊C4—2441no—
176C4⋊C4—2441no—
177C42—1221no—
178C42—1221no—
179C42—1221no—
180C42—1221no—
181C42—1221no—
182C42—1221no—
183C23(C2×#6923)⋊C411yescharacteristic
184Q8—2442no—
185Q8—2442no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—611no—
194C2×C4—611no—
195C2×C4—611no—
196C2×C4—611no—
197C2×C4—1221no—
198C2×C4—1221no—
199C2×C4—1221no—
200C2×C4—1221no—
201C2×C4—1221no—
202C2×C4—1221no—
203C2×C4—1221no—
204C2×C4—1221no—
205C2×C4—2441no—
206C8—81no—
207C8—4881no—
208C8—4881no—
209C8—4882no—
210C8—2442no—
211C22—21no—
212C22—21no—
213C22#1684063911yescharacteristic
214C22#1684064111yescharacteristic
215C22#1684064411yescharacteristic
216C4—41no—
217C4—41no—
218C4—41no—
219C4—611no—
220C4—611no—
221C4—1221no—
222C4—1221no—
223C4—1221no—
224C4—2441no—
225C4—2441no—
226C2—21no—
227C2—21no—
228C2#2146072111yescharacteristic
229C2#2146091511yescharacteristic
230C2#2146091811yescharacteristic
subgroupG/H
centerC22#16840639
commutatorC22×C4×C61C42
FrattiniC2×C4⋊C4C2×#6923
FittingC61×#324C4
socleC22×C61#342
prime radicalC23×C61#95
cosocleC2×#14519742C22
hypercenter#324#6923
hypocenterC61#7323
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #324

Complements

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

NH ≅ G/Ntype
131. C61#7323semidirect

Maximal subgroups

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

subgroupindex
#214619912
#214616862
#214441612
#732361