Finite Group Databasebeta

← #30595363

Subgroups — #30595363

Order 15616.

444 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 118 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#21461533C212yesmaximal
2#21460638C214yesmaximal
3#21448374C211yesmaximal, characteristic
4C2×C4×#92420—22no—
5#16840628—22no—
6#16840628C2214yes—
7C2×#14519769C411yescharacteristic
8#16839658C2212yes—
9#16839644—22no—
10C4⋊C4×Dic61C412yes—
11#16839613—22no—
12C42×Dic61C2211yescharacteristic
13C61×#382C411yescharacteristic
14C22×#92420—24no—
15C4×#92420—28no—
16#14519769—22no—
17#14519769C814yescomplemented
18C2×C4⋊Dic61C2×C412yes—
19C2×#11758196—22no—
20C2×#11758196—22no—
21C2×C4×Dic61—22no—
22C2×C4×Dic61C2×C411yescharacteristic
23C2×C4×Dic61D412yes—
24C2×C4×Dic61D412yes—
25C2×C4×Dic61C2311yescharacteristic
26#14519684—22no—
27#14519684—22no—
28C2×C4⋊C4×C61C2×C412yes—
29C2×C42×C61C2×C411yescharacteristic
30#95×C61—22no—
31C22×C4×C61—22no—
32C22×C4×C61C22⋊C412yes—
33C22×C4×C61C22×C411yescharacteristic
34C22×Dic61—22no—
35C22×Dic61C22⋊C411yescharacteristic
36C22×Dic61C22⋊C411yescharacteristic
37C22×Dic61C2×D412yes—
38C2×#92420—28no—
39C2×#92420—44no—
40C2×#92420—44no—
41C4⋊C4×C61—42no—
42C42×C61C2×C812yes—
43C42×C61M1612yes—
44C4⋊Dic61—22no—
45C4⋊Dic61C2×C814yes—
46#11758196—28no—
47#11758196—44no—
48C4×Dic61—22no—
49C4×Dic61—24no—
50C4×Dic61—24no—
51C4×Dic61—41no—
52C4×Dic61—44no—
53C23×C61C2×C22⋊C411yescharacteristic
54C2×C4×C61—21no—
55C2×C4×C61—21no—
56C2×C4×C61—22no—
57C2×C4×C61—22no—
58C2×C4×C61—42no—
59C2×C4×C61—42no—
60C2×C4×C61—42no—
61C2×C4×C61C22⋊C814yes—
62C2×C4×C61C22×C811yescharacteristic
63C2×C4×C61C2×M1611yescharacteristic
64C2×Dic61—22no—
65C2×Dic61—22no—
66C2×Dic61—24no—
67C2×Dic61—21no—
68C2×Dic61—22no—
69C2×Dic61—42no—
70C2×Dic61—42no—
71C2×Dic61#10112yes—
72C2×Dic61#10414yes—
73C2×Dic61#13514yes—
74#92420—48no—
75#7568—611nomaximal, Sylow
76C22×C61C2×C22⋊C811yescharacteristic
77C22×C61#41011yescharacteristic
78C22×C61C2×#10111yescharacteristic
79C22×C61#41612yes—
80C22×C61C2×#10412yes—
81C4×C61—21no—
82C4×C61—21no—
83C4×C61—24no—
84C4×C61—82no—
85Dic61—24no—
86Dic61—41no—
87Dic61—44no—
88Dic61#33014yes—
89C4×#125—611no—
90#1744—612no—
91#1271—614no—
92C2×C61#146111yescharacteristic
93C2×C61#147612yes—
94C2×C61#150012yes—
95C2×C61C2×#33011yescharacteristic
96C2×C61#154411yescharacteristic
97C2×#125—611no—
98C2×C4×C8—1222no—
99#389—612no—
100#387—1222no—
101#382#692311yescharacteristic
102C4×C4⋊C4—612no—
103C4×C4⋊C4—1222no—
104C43—611no—
105#336—614no—
106#336—1222no—
107C61#756811yescharacteristic, complemented, Sylow
108C22×C8—1224no—
109#125—614no—
110#125—1222no—
111C2×C4⋊C4—612no—
112C2×C4⋊C4—1222no—
113C2×C4⋊C4—1222no—
114C2×C4⋊C4C2×#692312yes—
115C2×C42—612no—
116C2×C42—612no—
117C2×C42—611no—
118C2×C42—611no—
119C2×C42—1222no—
120C2×C42C2×#692311yescharacteristic
121C4×C8—1228no—
122#95—22no—
123#95—1222no—
124#95—1222no—
125C22×C4—22no—
126C22×C4—611no—
127C22×C4—612no—
128C22×C4—611no—
129C22×C4—1222no—
130C22×C4C22⋊#692312yes—
131C22×C4C22×#692311yescharacteristic
132C2×C8—1228no—
133C2×C8—2444no—
134C2×C8—2444no—
135C4⋊C4—42no—
136C4⋊C4—614no—
137C4⋊C4—1228no—
138C4⋊C4—1222no—
139C4⋊C4—2444no—
140C42—1224no—
141C42—1222no—
142C42—1224no—
143C42—2441no—
144C42—2444no—
145C42D61⋊C812yes—
146C42#1175821312yes—
147C23C2×C22⋊#692311yescharacteristic
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—42no—
153C2×C4—42no—
154C2×C4—42no—
155C2×C4—612no—
156C2×C4—614no—
157C2×C4—614no—
158C2×C4—1222no—
159C2×C4—1222no—
160C2×C4—1224no—
161C2×C4—1221no—
162C2×C4—1222no—
163C2×C4—2442no—
164C2×C4—2442no—
165C2×C4#1451983414yes—
166C2×C4C2×D61⋊C811yescharacteristic
167C2×C4C2×#1175821311yescharacteristic
168C8—2448no—
169C22C2×#1451983411yescharacteristic
170C22#1684074211yescharacteristic
171C22D61⋊#10111yescharacteristic
172C22#1684075212yes—
173C22D61⋊#10412yes—
174C4—21no—
175C4—21no—
176C4—24no—
177C4—82no—
178C4—614no—
179C4—1224no—
180C4—2441no—
181C4—2444no—
182C2#2146106311yescharacteristic
183C2#2146111212yes—
184C2#2146119112yes—
185C2D61⋊#33011yescharacteristic
186C2#2146132511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#382C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#382#6923
hypocenterC61#7568
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
17. #14519769C8semidirect
107. C61#7568semidirect

Maximal subgroups

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

subgroupindex
#214615332
#214606382
#214483742
#756861