Finite Group Databasebeta

← #29584177

Subgroups — #29584177

Order 15616.

326 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 77 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#21445959C211yesmaximal, characteristic
2#21444549C212yesmaximal
3#21444434C212yesmaximal
4#21443730C211yesmaximal, characteristic
5C61×#3255C211yesmaximal, characteristic
6#16839819C2212yes—
7#16839786C2211yescharacteristic
8C2×#14519688C2211yescharacteristic
9#16839526—22no—
10#16839511—22no—
11#16839508—22no—
12#16839504—24no—
13C61×#533C2212yes—
14C61×#475—22no—
15C61×#470—22no—
16C61×#462—22no—
17C61×#423C2211yescharacteristic
18C2×#11758194—21no—
19C22×#92418—21no—
20C4⋊#92418—22no—
21C4⋊#92418—22no—
22C22⋊#92418—22no—
23#14519688—21no—
24#14519688—22no—
25#14519688D412yes—
26C2×Q16×C61—22no—
27C2×M16×C61D412yes—
28C4⋊Q8×C61D412yes—
29C4⋊Q8×C61D412yes—
30#125×C61—22no—
31C22⋊Q8×C61—22no—
32C22⋊Q8×C61—22no—
33C4×Q8×C61—22no—
34C4×Q8×C61—22no—
35#117×C61—22no—
36C2×C42×C61C2311yescharacteristic
37#106×C61—22no—
38C4⋊C8×C61—22no—
39#103×C61—24no—
40C2×Q8×C61—22no—
41C2×Q8×C61—22no—
42C22×C4×C61C2×D411yescharacteristic
43C22×C4×C61#4112yes—
44Q16×C61—82no—
45M16×C61—42no—
46C2×C8×C61—22no—
47C4⋊C4×C61—22no—
48C4⋊C4×C61—22no—
49C4⋊C4×C61—22no—
50C4⋊C4×C61—22no—
51C4⋊C4×C61—42no—
52C4⋊C4×C61—42no—
53C22⋊C4×C61—42no—
54C42×C61—42no—
55C42×C61C2×D412yes—
56C42×C61C2×D411yescharacteristic
57C42×C61#4111yescharacteristic
58#11758194—42no—
59C2×#92418—22no—
60C2×#92418—41no—
61C2×#92418—41no—
62C2×#92418—41no—
63C2×#92418—42no—
64C23×C61#12411yescharacteristic
65Q8×C61—42no—
66Q8×C61—42no—
67Q8×C61—82no—
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—42no—
71C2×C4×C61—42no—
72C2×C4×C61—42no—
73C2×C4×C61#12011yescharacteristic
74C2×C4×C61#12111yescharacteristic
75C2×C4×C61#12112yes—
76C2×C4×C61#12312yes—
77C8×C61—42no—
78#92418—42no—
79#92418—82no—
80#92418—81no—
81#10529—611nomaximal, Sylow
82C22×C61—22no—
83C22×C61—21no—
84C22×C61#39411yescharacteristic
85C4×C61—22no—
86C4×C61—22no—
87C4×C61—21no—
88C4×C61—82no—
89C4×C61—82no—
90C4×C61#45411yescharacteristic
91C4×C61#45511yescharacteristic
92#3255D6111yescharacteristic
93#1838—611no—
94#1559—612no—
95#1531—612no—
96#1307—611no—
97C2×C61—41no—
98C2×C61#204011yescharacteristic
99C2×C61#204912yes—
100#533C2×D6112yes—
101#475—22no—
102#470—22no—
103#462—22no—
104#432—612no—
105#423—611no—
106#423C2×D6111yescharacteristic
107C2×#97—611no—
108#341—1222no—
109#333—1222no—
110#332—1222no—
111#330—1224no—
112C61#1052911yescharacteristic, complemented, Sylow
113C2×Q16—22no—
114C2×M16—1221no—
115C2×M16C22⋊D6112yes—
116C22×C8—1221no—
117C4⋊Q8C22⋊D6112yes—
118C4⋊Q8C22⋊D6112yes—
119#125—22no—
120C22⋊Q8—22no—
121C22⋊Q8—22no—
122C4×Q8—22no—
123C4×Q8—22no—
124#117—22no—
125C2×C42C22×D6111yescharacteristic
126#106—22no—
127C4⋊C8—22no—
128C4⋊C8—1222no—
129C4⋊C8—1222no—
130#103—24no—
131C22⋊C8—1222no—
132#97—612no—
133#97—1222no—
134#97—1221no—
135C2×Q8—22no—
136C2×Q8—22no—
137C22×C4#1175822412yes—
138C22×C4C2×C22⋊D6111yescharacteristic
139Q16—82no—
140M16—42no—
141M16—2442no—
142C2×C8—22no—
143C2×C8—1222no—
144C2×C8—2441no—
145C2×C8—2442no—
146C2×C8—2441no—
147C2×C8—2441no—
148C4⋊C4—22no—
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—42no—
153C4⋊C4—42no—
154C22⋊C4—42no—
155C42—42no—
156C42D4×D6111yescharacteristic
157C42#1175822411yescharacteristic
158C42C2×C22⋊D6112yes—
159C23#1451976411yescharacteristic
160Q8—42no—
161Q8—42no—
162Q8—82no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4#1451974611yescharacteristic
169C2×C4#1451974811yescharacteristic
170C2×C4#1451974912yes—
171C2×C4#1451975812yes—
172C8—42no—
173C8—4882no—
174C8—4881no—
175C8—2442no—
176C22—21no—
177C22—22no—
178C22#1683967611yescharacteristic
179C4—21no—
180C4—22no—
181C4—22no—
182C4—82no—
183C4—82no—
184C4#1683993511yescharacteristic
185C4#1683994011yescharacteristic
186C2—41no—
187C2#2144704511yescharacteristic
188C2#2144709612yes—
subgroupG/H
centerC22#16839676
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#3255C2
socleC22×C61#394
prime radicalC23×C61#124
hypercenter#3255D61
hypocenterC61#10529
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3255

Complements

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

NH ≅ G/Ntype
112. C61#10529semidirect

Maximal subgroups

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

subgroupindex
#214459592
#214445492
#214444342
#214437302
C61×#32552
#1052961