Finite Group Databasebeta

← #30595348

Subgroups — #30595348

Order 15616.

550 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 550 conjugacy classes of subgroups — too many to draw. Only its 128 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×C22⋊#92420C212yesmaximal
2#21460638C214yesmaximal, complemented
3#21448301C211yesmaximal, characteristic
4C2×C22⋊#92420—22no—
5C2×C4×#92420—22no—
6#16840628C2214yes—
7C2×#14519736C411yescharacteristic
8C22×C4×Dic61C2211yescharacteristic
9#16839658C412yes—
10#16839658C2212yes—
11#16839634—22no—
12C4×#11758196—22no—
13C2×#117×C61C411yescharacteristic
14C22×#92420—24no—
15C22⋊#92420—28no—
16C4×#92420—44no—
17C23×Dic61D412yes—
18#14519736—22no—
19#14519736C814yescomplemented
20C2×C4⋊Dic61C2×C412yes—
21C2×#11758196—22no—
22C2×#11758196—22no—
23C2×C22⋊Dic61—21no—
24C2×C4×Dic61—21no—
25C2×C4×Dic61—42no—
26C2×C4×Dic61C2×C411yescharacteristic
27C2×C4×Dic61D412yes—
28C2×C4×Dic61C2311yescharacteristic
29#14519684—22no—
30#14519684—22no—
31C23×C4×C61C2×C411yescharacteristic
32#117×C61—42no—
33C2×C4⋊C4×C61C2×C412yes—
34C2×C22⋊C4×C61—21no—
35C2×C42×C61—21no—
36C24×C61C22⋊C411yescharacteristic
37C22×C4×C61—22no—
38C22×C4×C61—22no—
39C22×C4×C61—22no—
40C22×C4×C61C22⋊C411yescharacteristic
41C22×C4×C61C2×C812yes—
42C22×C4×C61M1612yes—
43C22×C4×C61C22×C411yescharacteristic
44C22×Dic61—22no—
45C22×Dic61—24no—
46C22×Dic61—24no—
47C22×Dic61—42no—
48C22×Dic61C22⋊C412yes—
49C22×Dic61C2×D412yes—
50C2×#92420—28no—
51C2×#92420—44no—
52C2×#92420—44no—
53C4⋊C4×C61—42no—
54C22⋊C4×C61—42no—
55C42×C61—42no—
56C22⋊Dic61—24no—
57C4⋊Dic61—22no—
58C4⋊Dic61C2×C814yes—
59#11758196—44no—
60#11758196—44no—
61C4×Dic61—24no—
62C4×Dic61—24no—
63C4×Dic61—41no—
64C4×Dic61—41no—
65C23×C61—21no—
66C23×C61—21no—
67C23×C61—22no—
68C23×C61—22no—
69C23×C61C22⋊C812yes—
70C23×C61C2×C22⋊C411yescharacteristic
71C2×C4×C61—21no—
72C2×C4×C61—21no—
73C2×C4×C61—24no—
74C2×C4×C61—24no—
75C2×C4×C61—42no—
76C2×C4×C61—42no—
77C2×C4×C61—42no—
78C2×C4×C61C22⋊C812yes—
79C2×C4×C61#9912yes—
80C2×C4×C61#10112yes—
81C2×C4×C61C22×C811yescharacteristic
82C2×C4×C61C2×M1611yescharacteristic
83C2×Dic61—22no—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61—22no—
87C2×Dic61—24no—
88C2×Dic61—48no—
89C2×Dic61—42no—
90C2×Dic61—42no—
91C2×Dic61#10414yes—
92C2×Dic61#13514yes—
93#92420—48no—
94#7564—611nomaximal, Sylow
95C22×C61—22no—
96C22×C61—24no—
97C22×C61—41no—
98C22×C61—42no—
99C22×C61—41no—
100C22×C61C2×C22⋊C811yescharacteristic
101C22×C61C2×#9911yescharacteristic
102C22×C61C2×#10111yescharacteristic
103C22×C61#41612yes—
104C22×C61C2×#10412yes—
105C4×C61—21no—
106C4×C61—21no—
107C4×C61—82no—
108C4×C61#32414yes—
109Dic61—24no—
110Dic61—24no—
111Dic61—44no—
112#2296—611no—
113C4×C22⋊C8—612no—
114#1271—614no—
115C2×C61—42no—
116C2×C61C2×#32411yescharacteristic
117C2×C61#147612yes—
118C2×C61#150112yes—
119C2×C61#152611yescharacteristic
120C2×C61#154411yescharacteristic
121C2×#117—611no—
122C2×#117#692311yescharacteristic
123C22×C42—611no—
124C2×C22⋊C8—1222no—
125C2×C4×C8—1222no—
126#389—612no—
127#389—612no—
128#385—1222no—
129C4×C4⋊C4—1222no—
130#336—614no—
131C61#756411yescharacteristic, complemented, Sylow
132C23×C4—612no—
133C23×C4C2×#692311yescharacteristic
134C22×C8—1224no—
135#117—42no—
136#117—614no—
137#117—1222no—
138C2×C4⋊C4—612no—
139C2×C4⋊C4—1222no—
140C2×C4⋊C4—1222no—
141C2×C4⋊C4C2×#692312yes—
142C2×C22⋊C4—21no—
143C2×C22⋊C4—1221no—
144C2×C42—21no—
145C2×C42—612no—
146C2×C42—611no—
147C2×C42—611no—
148C2×C42—1221no—
149C2×C42—2442no—
150C22⋊C8—1228no—
151C4×C8—2444no—
152#95—1222no—
153#95—1222no—
154C24C22⋊#692311yescharacteristic
155C22×C4—22no—
156C22×C4—22no—
157C22×C4—22no—
158C22×C4—612no—
159C22×C4—612no—
160C22×C4—1224no—
161C22×C4—1224no—
162C22×C4—1222no—
163C22×C4—2442no—
164C22×C4D61⋊C812yes—
165C22×C4#1175821312yes—
166C22×C4C22⋊#692311yescharacteristic
167C22×C4C22×#692311yescharacteristic
168C2×C8—1228no—
169C2×C8—2444no—
170C2×C8—2444no—
171C4⋊C4—42no—
172C4⋊C4—614no—
173C4⋊C4—1222no—
174C4⋊C4—2444no—
175C4⋊C4—2444no—
176C22⋊C4—42no—
177C22⋊C4—1224no—
178C42—42no—
179C42—1224no—
180C42—1224no—
181C42—2441no—
182C42—2441no—
183C23—21no—
184C23—21no—
185C23—22no—
186C23—22no—
187C23#1451983412yes—
188C23C2×C22⋊#692311yescharacteristic
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—24no—
192C2×C4—24no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—614no—
197C2×C4—614no—
198C2×C4—1222no—
199C2×C4—1222no—
200C2×C4—1222no—
201C2×C4—1222no—
202C2×C4—1224no—
203C2×C4—2448no—
204C2×C4—2442no—
205C2×C4—2442no—
206C2×C4#1451983412yes—
207C2×C4#1451983512yes—
208C2×C4#1451983812yes—
209C2×C4C2×D61⋊C811yescharacteristic
210C2×C4C2×#1175821311yescharacteristic
211C8—2448no—
212C22—22no—
213C22—24no—
214C22—41no—
215C22—41no—
216C22—42no—
217C22C2×#1451983411yescharacteristic
218C22C2×#1451983511yescharacteristic
219C22C2×#1451983811yescharacteristic
220C22#1684075212yes—
221C22D61⋊#10412yes—
222C4—21no—
223C4—21no—
224C4—82no—
225C4—1224no—
226C4—1224no—
227C4—2444no—
228C4#1684060814yes—
229C2—42no—
230C2C2×#1684060811yescharacteristic
231C2#2146111212yes—
232C2#2146119412yes—
233C2#2146127611yescharacteristic
234C2#2146132411yescharacteristic
subgroupG/H
centerC22×C4C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC2×#117×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×#117#6923
hypocenterC61#7564
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #21460638C2semidirect
19. #14519736C8semidirect
131. C61#7564semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊#924202
#214606382
#214483012
#756461