Finite Group Databasebeta

← #29584215

Subgroups — #29584215

Order 15616.

342 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 81 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#21457213C211yesmaximal, characteristic
2#21445956C211yesmaximal, characteristic
3#21444556C212yesmaximal
4#21444273C212yesmaximal
5C61×#1309C211yesmaximal, characteristic
6#16840319C2212yes—
7#16840048—22no—
8#16840020—22no—
9#16839973—22no—
10#16839786C2211yescharacteristic
11C2×C4×#92418C2211yescharacteristic
12#16839526—22no—
13#16839509—22no—
14#16839507—22no—
15#16839492—24no—
16C61×#423C2212yes—
17C61×#423C2211yescharacteristic
18C2×Dic244—22no—
19C2×#11758194—21no—
20C22×#92418—21no—
21#14519777D412yes—
22#14519777D412yes—
23#14519769—22no—
24#14519756—22no—
25#14519756—22no—
26C4×Dic122—22no—
27C4×Dic122—22no—
28#14519736—22no—
29#14519709—22no—
30C4⋊#92418—22no—
31#14519702—24no—
32C4×#92418—21no—
33C4×#92418D412yes—
34C2×M16×C61—22no—
35C2×M16×C61D412yes—
36C2×C42×C61C2311yescharacteristic
37C4⋊C8×C61—22no—
38C4⋊C8×C61—22no—
39C4⋊C8×C61—22no—
40C22×C4×C61C2×D411yescharacteristic
41C22×C4×C61#4112yes—
42C2×Dic122—22no—
43C2×Dic122—22no—
44M16×C61—42no—
45M16×C61—82no—
46C2×C8×C61—22no—
47C2×C8×C61—42no—
48C42×C61C2×D412yes—
49C42×C61C2×D411yescharacteristic
50C42×C61#4111yescharacteristic
51C22⋊Dic61—42no—
52C4⋊Dic61—22no—
53C4⋊Dic61—22no—
54C4⋊Dic61—22no—
55C4⋊Dic61—22no—
56#11758196—42no—
57#11758196—42no—
58C4×Dic61—42no—
59#11758194—42no—
60C2×#92418—22no—
61C2×#92418—41no—
62C2×#92418—41no—
63C2×#92418—41no—
64Dic244—82no—
65C23×C61#12411yescharacteristic
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61—22no—
69C2×C4×C61—22no—
70C2×C4×C61#12011yescharacteristic
71C2×C4×C61#12111yescharacteristic
72C2×C4×C61#12112yes—
73C2×C4×C61#12312yes—
74C2×Dic61—42no—
75C2×Dic61—42no—
76Dic122—42no—
77Dic122—42no—
78Dic122—42no—
79Dic122—42no—
80C8×C61—42no—
81C8×C61—82no—
82#92418—42no—
83#92418—81no—
84#10535—611nomaximal, Sylow
85C22×C61—22no—
86C22×C61—21no—
87C22×C61#39411yescharacteristic
88C4×C61—22no—
89C4×C61—21no—
90C4×C61#45411yescharacteristic
91C4×C61#45511yescharacteristic
92C4×C61#47112yes—
93C4×C61#47312yes—
94Dic61—82no—
95Dic61—82no—
96#3255—611no—
97#1837—611no—
98#1561—612no—
99#1493—612no—
100#1309D6111yescharacteristic
101C2×C61—41no—
102C2×C61#204011yescharacteristic
103C2×C61#205212yes—
104#533—612no—
105#475—1222no—
106#470—1222no—
107#462—1222no—
108#423—611no—
109#423C2×D6112yes—
110#423C2×D6111yescharacteristic
111C2×C4×C8—611no—
112#341—1222no—
113#332—1222no—
114#332—1222no—
115Q8⋊C8—1224no—
116C61#1053511yescharacteristic, complemented, Sylow
117C2×Q16—1222no—
118C2×M16—22no—
119C2×M16—1221no—
120C2×M16D24412yes—
121C22×C8—1221no—
122C4⋊Q8—612no—
123C4⋊Q8—612no—
124#125—1222no—
125C22⋊Q8—1222no—
126C22⋊Q8—1222no—
127C4×Q8—1222no—
128C4×Q8—1222no—
129#117—1222no—
130C2×C42C22×D6111yescharacteristic
131#106—1222no—
132C4⋊C8—22no—
133C4⋊C8—22no—
134C4⋊C8—22no—
135C4⋊C8—1222no—
136#103—1224no—
137C4×C8—612no—
138C4×C8—1221no—
139C2×Q8—1222no—
140C2×Q8—1222no—
141C22×C4C2×D24411yescharacteristic
142C22×C4#1175822212yes—
143Q16—4882no—
144M16—42no—
145M16—82no—
146M16—2442no—
147C2×C8—22no—
148C2×C8—42no—
149C2×C8—1222no—
150C2×C8—2441no—
151C2×C8—2441no—
152C2×C8—2441no—
153C4⋊C4—1222no—
154C4⋊C4—1222no—
155C4⋊C4—1222no—
156C4⋊C4—1222no—
157C4⋊C4—2442no—
158C4⋊C4—2442no—
159C22⋊C4—2442no—
160C42—2442no—
161C42D4×D6112yes—
162C42D4×D6111yescharacteristic
163C42#1175822611yescharacteristic
164C23#1451976511yescharacteristic
165Q8—2442no—
166Q8—2442no—
167Q8—2442no—
168Q8—2442no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—2442no—
174C2×C4—2442no—
175C2×C4#1451974711yescharacteristic
176C2×C4#1451975012yes—
177C2×C4#1451975211yescharacteristic
178C2×C4#1451976212yes—
179C8—42no—
180C8—82no—
181C8—4881no—
182C8—2442no—
183C22—21no—
184C22—22no—
185C22#1683968011yescharacteristic
186C4—21no—
187C4—22no—
188C4—4882no—
189C4—4882no—
190C4#1683993711yescharacteristic
191C4#1683994211yescharacteristic
192C4#1684002412yes—
193C4#1684003612yes—
194C2—41no—
195C2#2144704911yescharacteristic
196C2#2144712112yes—
subgroupG/H
centerC22#16839680
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1309C2
socleC22×C61#394
prime radicalC23×C61#124
hypercenter#1309D61
hypocenterC61#10535
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1309

Complements

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

NH ≅ G/Ntype
116. C61#10535semidirect

Maximal subgroups

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

subgroupindex
#214572132
#214459562
#214445562
#214442732
C61×#13092
#1053561