Finite Group Databasebeta

← #29573533

Subgroups — #29573533

Order 15616.

566 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 99 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#21448405C211yesmaximal, characteristic
2#21445743C211yesmaximal, characteristic
3#21443728C214yesmaximal
4C61×#1784C211yesmaximal, characteristic
5C2×#14519736C412yes—
6C2×#14519696—22no—
7#16839726C2212yes—
8#16839669—22no—
9#16839669—22no—
10#16839625C412yes—
11#16839625C2212yes—
12C23×Q8×C61C2211yescharacteristic
13C2×#101×C61—22no—
14C61×#407C2212yes—
15C2×#11758194—22no—
16#14519736—44no—
17C2×C4⋊Dic61—22no—
18C2×C22⋊Dic61C2×C414yes—
19C2×C4×Dic61—22no—
20#14519696—44no—
21C22⋊#92418—24no—
22#14519684—24no—
23#14519684—22no—
24#14519684—22no—
25C22×Q8×C61—24no—
26C22×Q8×C61—44no—
27C22×Q8×C61D412yes—
28C22×Q8×C61D412yes—
29C23×C4×C61C2×C411yescharacteristic
30C23×C4×C61C2×C411yescharacteristic
31C23×C4×C61C2311yescharacteristic
32C2×M16×C61—22no—
33#101×C61—44no—
34C22⋊C8×C61—24no—
35C24×C61C22×C411yescharacteristic
36C2×Q8×C61—24no—
37C2×Q8×C61—24no—
38C2×Q8×C61—24no—
39C2×Q8×C61—24no—
40C2×Q8×C61—42no—
41C2×Q8×C61—42no—
42C2×Q8×C61—416no—
43C22×C4×C61—22no—
44C22×C4×C61—24no—
45C22×C4×C61—22no—
46C22×C4×C61—42no—
47C22×C4×C61—42no—
48C22×C4×C61C22⋊C412yes—
49C22×C4×C61C22⋊C412yes—
50C22×C4×C61C2×D411yescharacteristic
51C22×C4×C61C2×D411yescharacteristic
52C22×C4×C61#4114yes—
53C22×Dic61—24no—
54M16×C61—44no—
55C2×C8×C61—42no—
56C22⋊Dic61—44no—
57C4⋊Dic61—44no—
58C4×Dic61—44no—
59#11758194—44no—
60C2×#92418—42no—
61C23×C61—22no—
62C23×C61—42no—
63C23×C61C2×C22⋊C411yescharacteristic
64C23×C61#11712yes—
65Q8×C61—48no—
66Q8×C61—48no—
67C2×C4×C61—28no—
68C2×C4×C61—22no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61—44no—
76C2×C4×C61—44no—
77C2×C4×C61#9914yes—
78C2×C4×C61#12312yes—
79C2×C4×C61#12312yes—
80C2×Dic61—48no—
81C2×Dic61—44no—
82C8×C61—82no—
83#92418—82no—
84#8753—611nomaximal, Sylow
85C22×C61—22no—
86C22×C61—22no—
87C22×C61—24no—
88C22×C61—44no—
89C22×C61#38111yescharacteristic
90C22×C61C2×#9912yes—
91C4×C61—22no—
92C4×C61—22no—
93C4×C61—24no—
94C4×C61—42no—
95Dic61—84no—
96#2310—611no—
97#1784—611no—
98#1784D6111yescharacteristic
99#1306—614no—
100C2×C61—22no—
101C2×C61—42no—
102C2×C61#181911yescharacteristic
103C2×C61#183012yes—
104C23×Q8C2×D6111yescharacteristic
105C2×#117—612no—
106C2×#101—22no—
107C2×#101—1222no—
108#407—612no—
109#407C2×D6112yes—
110#391—1222no—
111#391—1222no—
112#381—612no—
113#381—612no—
114C61#875311yescharacteristic, complemented, Sylow
115C22×Q8—24no—
116C22×Q8—44no—
117C22×Q8D24412yes—
118C22×Q8C22⋊D6112yes—
119C23×C4C4×D6111yescharacteristic
120C23×C4C4×D6111yescharacteristic
121C23×C4C22×D6111yescharacteristic
122C2×M16—22no—
123C2×M16—1222no—
124#117—2444no—
125C2×C4⋊C4—1222no—
126C2×C22⋊C4—614no—
127C2×C42—1222no—
128#101—44no—
129#101—2444no—
130C22⋊C8—24no—
131C22⋊C8—1224no—
132#95—1224no—
133#95—1222no—
134#95—1222no—
135C24C2×C4×D6111yescharacteristic
136C2×Q8—24no—
137C2×Q8—24no—
138C2×Q8—24no—
139C2×Q8—24no—
140C2×Q8—42no—
141C2×Q8—42no—
142C2×Q8—416no—
143C22×C4—22no—
144C22×C4—24no—
145C22×C4—22no—
146C22×C4—42no—
147C22×C4—42no—
148C22×C4—1224no—
149C22×C4#1175819812yes—
150C22×C4#1175819812yes—
151C22×C4C2×D24411yescharacteristic
152C22×C4#1175822414yes—
153C22×C4C2×C22⋊D6111yescharacteristic
154M16—44no—
155M16—2444no—
156C2×C8—42no—
157C2×C8—2442no—
158C4⋊C4—2444no—
159C22⋊C4—2444no—
160C42—2444no—
161C23—22no—
162C23—42no—
163C23C2×#1175819811yescharacteristic
164C23#1451973312yes—
165Q8—48no—
166Q8—48no—
167C2×C4—28no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—44no—
176C2×C4—44no—
177C2×C4—2448no—
178C2×C4—2444no—
179C2×C4#1451969114yes—
180C2×C4#1451975812yes—
181C2×C4#1451976112yes—
182C8—82no—
183C8—4882no—
184C22—22no—
185C22—22no—
186C22—24no—
187C22—44no—
188C22#1683962311yescharacteristic
189C22C2×#1451969112yes—
190C4—22no—
191C4—22no—
192C4—24no—
193C4—42no—
194C4—4884no—
195C2—22no—
196C2—42no—
197C2#2144589111yescharacteristic
198C2#2144593112yes—
subgroupG/H
centerC22#16839623
commutator, prime radicalC24×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1784C2
socleC22×C61#381
cosocleC23×C4×C61C23
hypercenter#1784D61
hypocenterC61#8753
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1784

Complements

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

NH ≅ G/Ntype
114. C61#8753semidirect

Maximal subgroups

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

subgroupindex
#214484052
#214457432
#214437282
C61×#17842
#875361