Finite Group Databasebeta

← #30594401

Subgroups — #30594401

Order 15616.

284 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C4×#14519838C211yesmaximal, characteristic
2#21461061C211yesmaximal, characteristic
3#21446755C211yesmaximal, characteristic
4#16840779—21no—
5C2×#14519838C412yes—
6C4×#11758217—21no—
7#16840642—21no—
8#16840608—21no—
9#16840607C412yes—
10C2×C4×Dic122C2211yescharacteristic
11C2×C4⋊#92418C411yescharacteristic
12#16839516—21no—
13#16839516—21no—
14C2×C4×C8×C61C411yescharacteristic
15C2×#11758217—22no—
16#14519844—41no—
17#14519838—22no—
18#14519838C814yescomplemented
19C22⋊#92420—22no—
20#14519832—41no—
21C4×#92420—41no—
22C4×#92420—41no—
23C22×Dic122C2×C411yescharacteristic
24C22×#92418—21no—
25C4×Dic122—41no—
26C4×Dic122—41no—
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×#11758196D411yescharacteristic
29C2×#11758196Q811yescharacteristic
30C2×C4×Dic61D411yescharacteristic
31C2×C4×Dic61D411yescharacteristic
32C4⋊#92418—41no—
33C22×C8×C61—21no—
34C2×C42×C61C2×C411yescharacteristic
35C4×C8×C61—41no—
36C22×C4×C61C4211yescharacteristic
37C22×C4×C61C22⋊C411yescharacteristic
38C22×C4×C61C4⋊C411yescharacteristic
39C22×Dic61C22⋊C411yescharacteristic
40C22×Dic61C22⋊C411yescharacteristic
41C22×Dic61C4⋊C411yescharacteristic
42C22×Dic61C4⋊C411yescharacteristic
43C2×Dic122—41no—
44C2×Dic122—41no—
45C2×Dic122C2×C812yes—
46C2×Dic122M1612yes—
47#11758217—24no—
48#11758217—42no—
49C2×#92420—42no—
50C2×#92420—42no—
51C2×C8×C61—22no—
52C2×C8×C61—41no—
53C2×C8×C61—41no—
54C42×C61—21no—
55C42×C61—21no—
56C4⋊Dic61—41no—
57#11758196—41no—
58#11758196—41no—
59C4×Dic61—21no—
60C4×Dic61—21no—
61C4×Dic61—21no—
62C4×Dic61—21no—
63C2×#92418—42no—
64C2×#92418—41no—
65C23×C61#9511yescharacteristic
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—41no—
72C2×C4×C61C4×C811yescharacteristic
73C2×C4×C61#9711yescharacteristic
74C2×C4×C61#9911yescharacteristic
75C2×C4×C61#9911yescharacteristic
76C2×Dic61—21no—
77C2×Dic61—21no—
78C2×Dic61—21no—
79C2×Dic61—21no—
80C2×Dic61—21no—
81C2×Dic61—21no—
82C2×Dic61—41no—
83C2×Dic61—41no—
84C2×Dic61C22⋊C812yes—
85C2×Dic61C4⋊C812yes—
86Dic122—42no—
87Dic122—42no—
88#92420—44no—
89#92420—82no—
90C8×C61—42no—
91#92418—81no—
92#7206—611nomaximal, Sylow
93C22×C61—21no—
94C22×C61—21no—
95C22×C61#33611yescharacteristic
96C22×C61#34211yescharacteristic
97C22×C61#34411yescharacteristic
98C4×C61—21no—
99C4×C61—21no—
100C4×C61—21no—
101C4×C61—41no—
102C4×C61#35511yescharacteristic
103C4×C61#35611yescharacteristic
104Dic61—22no—
105Dic61—22no—
106Dic61—41no—
107Dic61—41no—
108#1984—611no—
109C4×#101—611no—
110#1461—611no—
111C2×C61—21no—
112C2×C61—21no—
113C2×C61#128211yescharacteristic
114C2×C61#139411yescharacteristic
115C2×C61#139511yescharacteristic
116C2×C4×Q8—611no—
117#431—1221no—
118C2×C4⋊C8—611no—
119C2×#101—612no—
120C4×M16—1221no—
121C2×C4×C8#692311yescharacteristic
122#343—1221no—
123#336—1221no—
124#336—1221no—
125#324—612no—
126#324—1221no—
127C61#720611yescharacteristic, complemented, Sylow
128C22×Q8—611no—
129C2×M16—1222no—
130C22×C8—21no—
131C22×C8—1221no—
132C4×Q8—2441no—
133C4×Q8—2441no—
134C2×C4⋊C4—611no—
135C2×C4⋊C4—611no—
136C2×C4⋊C4—611no—
137C2×C42—611no—
138C2×C42—611no—
139C2×C42C2×#692311yescharacteristic
140C4⋊C8—2441no—
141C4⋊C8—2441no—
142#101—614no—
143#101—1222no—
144C22⋊C8—1222no—
145#97—2441no—
146C4×C8—41no—
147C4×C8—2441no—
148C4×C8—2441no—
149C2×Q8—612no—
150C2×Q8—612no—
151C2×Q8—2441no—
152C2×Q8—2441no—
153C22×C4—611no—
154C22×C4—611no—
155C22×C4—611no—
156C22×C4—611no—
157C22×C4C4×#692311yescharacteristic
158C22×C4C4⋊#692311yescharacteristic
159C22×C4C22⋊#692311yescharacteristic
160M16—1224no—
161M16—2442no—
162C2×C8—22no—
163C2×C8—41no—
164C2×C8—41no—
165C2×C8—2442no—
166C2×C8—2442no—
167C2×C8—2441no—
168C2×C8—2442no—
169C4⋊C4—2441no—
170C4⋊C4—2441no—
171C4⋊C4—2441no—
172C42—21no—
173C42—21no—
174C42—1221no—
175C42—1221no—
176C42—1221no—
177C42—1221no—
178C23(C2×#6923)⋊C411yescharacteristic
179Q8—2442no—
180Q8—2442no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—612no—
188C2×C4—612no—
189C2×C4—1221no—
190C2×C4—1221no—
191C2×C4—1221no—
192C2×C4—1221no—
193C2×C4—1221no—
194C2×C4—1221no—
195C2×C4—2441no—
196C2×C4—2441no—
197C2×C4C8×#692311yescharacteristic
198C2×C4#1451983111yescharacteristic
199C2×C4#1451983511yescharacteristic
200C2×C4#1451983611yescharacteristic
201C8—42no—
202C8—4882no—
203C8—4881no—
204C8—2444no—
205C22—21no—
206C22—21no—
207C22(C2×#6923)⋊C811yescharacteristic
208C22#1684064011yescharacteristic
209C22#1684064411yescharacteristic
210C4—21no—
211C4—21no—
212C4—21no—
213C4—41no—
214C4—1222no—
215C4—1222no—
216C4—2441no—
217C4—2441no—
218C4#1684067111yescharacteristic
219C4#1684067311yescharacteristic
220C2—21no—
221C2—21no—
222C2#2146066111yescharacteristic
223C2#2146091611yescharacteristic
224C2#2146091911yescharacteristic
subgroupG/H
centerC2×C4#14519836
commutatorC2×C4×C61C4×C8
FrattiniC2×C42C2×#6923
FittingC2×C4×C8×C61C4
socleC22×C61#342
prime radicalC23×C61#95
cosocleC2×C4×Dic122C22
hypercenterC2×C4×C8#6923
hypocenterC61#7206
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
18. #14519838C8semidirect
127. C61#7206semidirect

Maximal subgroups

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

subgroupindex
C4×#145198382
#214610612
#214467552
#720661