Finite Group Databasebeta

← #29573465

Subgroups — #29573465

Order 15616.

404 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 115 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#21444133C212yesmaximal
2#21443652C212yesmaximal, complemented
3#21443648C212yesmaximal, complemented
4C61×#2298C211yesmaximal, characteristic
5#16839815C2214yes—
6#16839488—22no—
7#16839486—22no—
8C2×#117×C61C2211yescharacteristic
9C61×#388—22no—
10C61×#387—22no—
11C4×C4⋊C4×C61C412yes—
12C4×C22⋊C4×C61C412yes—
13C61×#376C2211yescharacteristic
14C43×C61C2211yescharacteristic
15C4⋊#92418—24no—
16C22⋊#92418—24no—
17C4×#92418—24no—
18C23×C4×C61C2×C411yescharacteristic
19#117×C61—22no—
20#117×C61—22no—
21C2×C4⋊C4×C61—22no—
22C2×C4⋊C4×C61D412yes—
23C2×C22⋊C4×C61—22no—
24C2×C22⋊C4×C61D412yes—
25C2×C42×C61—22no—
26C2×C42×C61C2×C412yes—
27C2×C42×C61C2×C412yes—
28C2×C42×C61C2×C411yescharacteristic
29C2×C42×C61C2311yescharacteristic
30#95×C61—22no—
31#95×C61—22no—
32#95×C61—22no—
33C24×C61C22⋊C411yescharacteristic
34C22×C4×C61—22no—
35C22×C4×C61—21no—
36C22×C4×C61—21no—
37C22×C4×C61—24no—
38C22×C4×C61—22no—
39C22×C4×C61C22⋊C411yescharacteristic
40C22×C4×C61C22⋊C412yes—
41C22×C4×C61C22×C411yescharacteristic
42C22×C4×C61C2×D412yes—
43C4⋊C4×C61—24no—
44C4⋊C4×C61—44no—
45C22⋊C4×C61—24no—
46C22⋊C4×C61—44no—
47C42×C61—21no—
48C42×C61—21no—
49C42×C61—24no—
50C42×C61—24no—
51C42×C61—44no—
52C42×C61#4112yes—
53C42×C61#4112yes—
54C2×#92418—44no—
55C23×C61—21no—
56C23×C61—22no—
57C23×C61—42no—
58C23×C61C2×C22⋊C411yescharacteristic
59C2×C4×C61—24no—
60C2×C4×C61—22no—
61C2×C4×C61—21no—
62C2×C4×C61—22no—
63C2×C4×C61—42no—
64C2×C4×C61—42no—
65C2×C4×C61—42no—
66C2×C4×C61—42no—
67C2×C4×C61—42no—
68C2×C4×C61—42no—
69C2×C4×C61—42no—
70C2×C4×C61—42no—
71C2×C4×C61—42no—
72C2×C4×C61#11711yescharacteristic
73C2×C4×C61#11711yescharacteristic
74C2×C4×C61#12314yes—
75C2×C4×C61#13114yes—
76#92418—84no—
77#8732—611nomaximal, Sylow
78C22×C61—22no—
79C22×C61—41no—
80C22×C61—42no—
81C22×C61—82no—
82C22×C61#38111yescharacteristic
83C22×C61#40812yes—
84C4×C61—24no—
85C4×C61—44no—
86C4×C61—41no—
87C4×C61—42no—
88C4×C61—82no—
89C4×C61#43312yes—
90C4×C61#43312yes—
91#2298D6111yescharacteristic
92#1458—612no—
93#1276—612no—
94#1274—612no—
95C2×C61—22no—
96C2×C61—81no—
97C2×C61#181811yescharacteristic
98C2×C61#182712yes—
99C2×#117C2×D6111yescharacteristic
100#431—614no—
101#388—22no—
102#387—22no—
103C4×C4⋊C4Dic6112yes—
104C4×C22⋊C4Dic6112yes—
105#376C2×D6111yescharacteristic
106C43C2×D6111yescharacteristic
107#324—1222no—
108#323—1222no—
109C61#873211yescharacteristic, complemented, Sylow
110C23×C4C2×Dic6111yescharacteristic
111#117—22no—
112#117—22no—
113C2×C4⋊C4—22no—
114C2×C4⋊C4C22⋊D6112yes—
115C2×C22⋊C4—22no—
116C2×C22⋊C4C22⋊D6112yes—
117C2×C42—22no—
118C2×C42C2×Dic6112yes—
119C2×C42C2×Dic6112yes—
120C2×C42C2×Dic6111yescharacteristic
121C2×C42C22×D6111yescharacteristic
122C4⋊C8—1224no—
123C22⋊C8—1224no—
124C4×C8—1224no—
125#95—22no—
126#95—22no—
127#95—22no—
128C24C22⋊Dic6111yescharacteristic
129C22×C4—22no—
130C22×C4—21no—
131C22×C4—21no—
132C22×C4—24no—
133C22×C4—22no—
134C22×C4C22⋊Dic6111yescharacteristic
135C22×C4C22⋊Dic6112yes—
136C22×C4C22×Dic6111yescharacteristic
137C22×C4C2×C22⋊D6112yes—
138C2×C8—2444no—
139C4⋊C4—24no—
140C4⋊C4—44no—
141C22⋊C4—24no—
142C22⋊C4—44no—
143C42—21no—
144C42—21no—
145C42—24no—
146C42—24no—
147C42—44no—
148C42#1175822212yes—
149C42#1175822212yes—
150C23—21no—
151C23—22no—
152C23—42no—
153C23C2×C22⋊Dic6111yescharacteristic
154C2×C4—24no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—21no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4#1451973611yescharacteristic
168C2×C4#1451973611yescharacteristic
169C2×C4#1451976014yes—
170C2×C4#1451978414yes—
171C8—4884no—
172C22—22no—
173C22—41no—
174C22—42no—
175C22—82no—
176C22#1683962511yescharacteristic
177C22#1683972912yes—
178C4—24no—
179C4—44no—
180C4—41no—
181C4—42no—
182C4—82no—
183C4#1683982312yes—
184C4#1683982312yes—
185C2—22no—
186C2—81no—
187C2#2144589011yescharacteristic
188C2#2144592312yes—
subgroupG/H
centerC2×C4#14519736
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2298C2
socleC22×C61#381
prime radicalC24×C61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#2298D61
hypocenterC61#8732
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ #376 ◁ #2298

Complements

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

NH ≅ G/Ntype
2. #21443652C2semidirect
3. #21443648C2semidirect
109. C61#8732semidirect

Maximal subgroups

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

subgroupindex
#214441332
#214436522
#214436482
C61×#22982
#873261