Finite Group Databasebeta

← #30602159

Subgroups — #30602159

Order 15616.

486 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 124 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#21461752C211yesmaximal, characteristic
2C4×#14519832C211yesmaximal, characteristic
3#21460655C214yesmaximal
4#21448374C211yesmaximal, characteristic
5C2×#14519844—22no—
6C2×C4⋊#92420C2212yes—
7C2×#14519832—22no—
8C2×C4×#92420C2212yes—
9C2×#14519769C411yescharacteristic
10#16839658C412yes—
11#16839644—22no—
12C4⋊C4×Dic61C2212yes—
13#16839613—22no—
14C42×Dic61C2211yescharacteristic
15C61×#382C411yescharacteristic
16C22×#92420—22no—
17C22×#92420—22no—
18#14519844—44no—
19C4⋊#92420—24no—
20#14519832—28no—
21C4×#92420—22no—
22C4×#92420Q814yes—
23#14519769—24no—
24C2×C4⋊Dic61C2×C412yes—
25C2×#11758196—22no—
26C2×#11758196—22no—
27C2×C4×Dic61—22no—
28C2×C4×Dic61C2×C411yescharacteristic
29C2×C4×Dic61D412yes—
30C2×C4×Dic61D412yes—
31C2×C4×Dic61C2311yescharacteristic
32#14519684—22no—
33#14519684—22no—
34C2×C4⋊C4×C61C2×C412yes—
35C2×C42×C61C2×C411yescharacteristic
36#95×C61—22no—
37C22×C4×C61—22no—
38C22×C4×C61C22⋊C412yes—
39C22×C4×C61C22×C411yescharacteristic
40C22×Dic61—22no—
41C22×Dic61C22⋊C412yes—
42C22×Dic61C2×D411yescharacteristic
43C22×Dic61C2×D411yescharacteristic
44C2×#92420—28no—
45C2×#92420—24no—
46C2×#92420—42no—
47C2×#92420—44no—
48C4⋊C4×C61—24no—
49C42×C61—22no—
50C4⋊Dic61—22no—
51C4⋊Dic61M1614yes—
52#11758196—28no—
53#11758196—44no—
54C4×Dic61—22no—
55C4×Dic61—24no—
56C4×Dic61—22no—
57C4×Dic61—22no—
58C4×Dic61—42no—
59C4×Dic61—42no—
60C4×Dic61C2×Q812yes—
61C4×Dic61#4112yes—
62C23×C61C2×C22⋊C411yescharacteristic
63C2×C4×C61—22no—
64C2×C4×C61—22no—
65C2×C4×C61—22no—
66C2×C4×C61—42no—
67C2×C4×C61—42no—
68C2×C4×C61—42no—
69C2×C4×C61C4×Q812yes—
70C2×C4×C61C2×M1612yes—
71C2×C4×C61#13112yes—
72C2×Dic61—22no—
73C2×Dic61—22no—
74C2×Dic61—22no—
75C2×Dic61—24no—
76C2×Dic61—42no—
77C2×Dic61—42no—
78C2×Dic61#10414yes—
79C2×Dic61C22⋊Q812yes—
80C2×Dic61#12411yescharacteristic
81C2×Dic61C4⋊Q811yescharacteristic
82C2×Dic61AGL(1,ℤ/8)12yes—
83C2×Dic61#13712yes—
84#92420—28no—
85#92420—82no—
86#9876—611nomaximal, Sylow
87C22×C61#39111yescharacteristic
88C22×C61#40711yescharacteristic
89C22×C61#40811yescharacteristic
90C22×C61#41712yes—
91C22×C61C2×#10412yes—
92C4×C61—42no—
93C4×C61—82no—
94C4×C61#44614yes—
95Dic61—22no—
96Dic61—24no—
97Dic61—44no—
98Dic61#49011yescharacteristic
99Dic61#49111yescharacteristic
100Dic61#50112yes—
101C4×#125—611no—
102#1842—611no—
103C4×#97—611no—
104#1279—614no—
105C2×C61#148312yes—
106C2×C61#148912yes—
107C2×C61#198511yescharacteristic
108C2×C61#199211yescharacteristic
109C2×C61#199411yescharacteristic
110C2×#125—611no—
111C2×C4⋊C8—612no—
112C2×C4⋊C8—1222no—
113C2×#97—1222no—
114C2×C4×C8—612no—
115#389—612no—
116#387—1222no—
117#382#692311yescharacteristic
118C4×C4⋊C4—612no—
119C4×C4⋊C4—1222no—
120C43—611no—
121C61#987611yescharacteristic, complemented, Sylow
122C22×C8—1222no—
123C22×C8—1222no—
124#125—1224no—
125C2×C4⋊C4—612no—
126C2×C4⋊C4—1222no—
127C2×C4⋊C4—1222no—
128C2×C4⋊C4C2×#692312yes—
129C2×C42—611no—
130C2×C42—612no—
131C2×C42—612no—
132C2×C42—611no—
133C2×C42—1222no—
134C2×C42C2×#692311yescharacteristic
135C4⋊C8—1224no—
136C4⋊C8—2444no—
137#97—1228no—
138C4×C8—614no—
139C4×C8—1222no—
140#95—22no—
141#95—1222no—
142#95—1222no—
143C22×C4—22no—
144C22×C4—611no—
145C22×C4—611no—
146C22×C4—612no—
147C22×C4—1222no—
148C22×C4C22⋊#692312yes—
149C22×C4C22×#692311yescharacteristic
150C2×C8—1224no—
151C2×C8—1228no—
152C2×C8—2442no—
153C2×C8—2444no—
154C4⋊C4—24no—
155C4⋊C4—614no—
156C4⋊C4—1228no—
157C4⋊C4—1222no—
158C4⋊C4—2444no—
159C42—22no—
160C42—612no—
161C42—612no—
162C42—1224no—
163C42—1222no—
164C42—1222no—
165C42—1222no—
166C42—2442no—
167C42—2442no—
168C23C2×C22⋊#692311yescharacteristic
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—611no—
176C2×C4—611no—
177C2×C4—612no—
178C2×C4—612no—
179C2×C4—612no—
180C2×C4—614no—
181C2×C4—1222no—
182C2×C4—1222no—
183C2×C4—1222no—
184C2×C4—1224no—
185C2×C4—2442no—
186C2×C4—2442no—
187C2×C4Q8×#692312yes—
188C2×C4D61⋊M1612yes—
189C2×C4#1451986412yes—
190C8—1228no—
191C8—4882no—
192C22(C2×#6923)⋊Q811yescharacteristic
193C22#1684073411yescharacteristic
194C22#1684073611yescharacteristic
195C22#1684075312yes—
196C22D61⋊#10412yes—
197C4—42no—
198C4—82no—
199C4—611no—
200C4—611no—
201C4—612no—
202C4—1224no—
203C4—1222no—
204C4—2444no—
205C4#1684081414yes—
206C2#2146113512yes—
207C2#2146115612yes—
208C2#2146199111yescharacteristic
209C2#2146200211yescharacteristic
210C2#2146200511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#382C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#382#6923
hypocenterC61#9876
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
121. C61#9876semidirect

Maximal subgroups

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

subgroupindex
#214617522
C4×#145198322
#214606552
#214483742
#987661