Finite Group Databasebeta

← #29567529

Subgroups — #29567529

Order 15616.

252 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 43 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#21443946C211yesmaximal, characteristic
2#21443753C211yesmaximal, characteristic
3C61×#2016C211yesmaximal, characteristic
4C2×#14519696—21no—
5#16839488—21no—
6C22×Q16×C61—21no—
7C2×C4⋊Q8×C61C411yescharacteristic
8C2×#103×C61—21no—
9C61×#391C2211yescharacteristic
10C61×#336C411yescharacteristic
11C2×#11758194—41no—
12#14519696—22no—
13#14519696—41no—
14C22⋊#92418—41no—
15C22×Q8×C61—21no—
16C22×Q8×C61D411yescharacteristic
17C2×Q16×C61—42no—
18C2×Q16×C61—42no—
19C2×Q16×C61—41no—
20C2×Q16×C61—41no—
21C22×C8×C61—21no—
22C4⋊Q8×C61—42no—
23C2×C4⋊C4×C61—41no—
24C2×C4⋊C4×C61D411yescharacteristic
25C2×C42×C61C2×C411yescharacteristic
26#103×C61—42no—
27#95×C61—41no—
28C2×Q8×C61—21no—
29C2×Q8×C61—22no—
30C2×Q8×C61—41no—
31C2×Q8×C61—41no—
32C2×Q8×C61—41no—
33C2×Q8×C61—41no—
34C2×Q8×C61—41no—
35C2×Q8×C61—41no—
36C2×Q8×C61—41no—
37C2×Q8×C61D811yescharacteristic
38C2×Q8×C61SD1611yescharacteristic
39C22×C4×C61—21no—
40C22×C4×C61—21no—
41C22×C4×C61—21no—
42C22×C4×C61—41no—
43C22×C4×C61C22⋊C411yescharacteristic
44Q16×C61—44no—
45Q16×C61—44no—
46C2×C8×C61—22no—
47C2×C8×C61—41no—
48C2×C8×C61—41no—
49C4⋊C4×C61—41no—
50C4⋊C4×C61—42no—
51C4⋊C4×C61—42no—
52C42×C61—41no—
53#11758194—42no—
54#11758194—81no—
55C2×#92418—81no—
56C2×#92418—81no—
57C23×C61#9911yescharacteristic
58Q8×C61—41no—
59Q8×C61—41no—
60Q8×C61—42no—
61Q8×C61—42no—
62Q8×C61—81no—
63Q8×C61—81no—
64Q8×C61—81no—
65C2×C4×C61—21no—
66C2×C4×C61—21no—
67C2×C4×C61—22no—
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—41no—
71C2×C4×C61—41no—
72C2×C4×C61—41no—
73C2×C4×C61—41no—
74C2×C4×C61—42no—
75C2×C4×C61—41no—
76C2×C4×C61—81no—
77C2×C4×C61—81no—
78C2×C4×C61—81no—
79C2×C4×C61#10211yescharacteristic
80C2×C4×C61#10411yescharacteristic
81C8×C61—42no—
82#92418—82no—
83#92418—161no—
84#7405—611nomaximal, Sylow
85C22×C61—21no—
86C22×C61—21no—
87C22×C61#32711yescharacteristic
88C22×C61AΣL(1,𝔽16)11yescharacteristic
89C22×C61#35311yescharacteristic
90C4×C61—21no—
91C4×C61—21no—
92C4×C61—42no—
93C4×C61—41no—
94C4×C61—41no—
95C4×C61—82no—
96C4×C61—81no—
97#2016D6111yescharacteristic
98#1394—611no—
99#1319—611no—
100C2×C61—21no—
101C2×C61—21no—
102C2×C61#134311yescharacteristic
103C2×C61#140711yescharacteristic
104C2×C61#141111yescharacteristic
105C22×Q16—21no—
106C2×C4⋊Q8Dic6111yescharacteristic
107C2×#103—21no—
108C2×#101—1221no—
109#391C2×D6111yescharacteristic
110#336Dic6111yescharacteristic
111#324—1221no—
112C61#740511yescharacteristic, complemented, Sylow
113C22×Q8—21no—
114C22×Q8C22⋊D6111yescharacteristic
115C2×Q16—42no—
116C2×Q16—42no—
117C2×Q16—41no—
118C2×Q16—41no—
119C2×M16—2441no—
120C22×C8—21no—
121C4⋊Q8—42no—
122C2×C4⋊C4—41no—
123C2×C4⋊C4C22⋊D6111yescharacteristic
124C2×C42C2×Dic6111yescharacteristic
125#103—42no—
126#101—1222no—
127#101—2441no—
128C22⋊C8—2441no—
129#95—41no—
130C2×Q8—21no—
131C2×Q8—22no—
132C2×Q8—41no—
133C2×Q8—41no—
134C2×Q8—41no—
135C2×Q8—41no—
136C2×Q8—41no—
137C2×Q8—41no—
138C2×Q8—41no—
139C2×Q8#1175819911yescharacteristic
140C2×Q8#1175820011yescharacteristic
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—41no—
145C22×C4C22⋊Dic6111yescharacteristic
146Q16—44no—
147Q16—44no—
148M16—4881no—
149M16—2442no—
150C2×C8—22no—
151C2×C8—41no—
152C2×C8—41no—
153C2×C8—4881no—
154C2×C8—4881no—
155C4⋊C4—41no—
156C4⋊C4—42no—
157C4⋊C4—42no—
158C42—41no—
159C23#1451969211yescharacteristic
160Q8—41no—
161Q8—41no—
162Q8—42no—
163Q8—42no—
164Q8—81no—
165Q8—81no—
166Q8—81no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—42no—
177C2×C4—41no—
178C2×C4—81no—
179C2×C4—81no—
180C2×C4—81no—
181C2×C4#1451969811yescharacteristic
182C2×C4#1451970411yescharacteristic
183C8—42no—
184C8—9761no—
185C8—4882no—
186C22—21no—
187C22—21no—
188C22#1683949611yescharacteristic
189C22#1683954911yescharacteristic
190C22#1683955511yescharacteristic
191C4—21no—
192C4—21no—
193C4—42no—
194C4—41no—
195C4—41no—
196C4—81no—
197C4—82no—
198C2—21no—
199C2—21no—
200C2#2144381611yescharacteristic
201C2#2144397911yescharacteristic
202C2#2144398811yescharacteristic
subgroupG/H
centerC22#16839555
commutatorC2×C42×C61C2×C4
Frattini#391C2×D61
FittingC61×#2016C2
socleC22×C61#353
prime radicalC23×C61#99
cosocleC61×#391C22
hypercenter#2016D61
hypocenterC61#7405
LCSG ▷ C2×C42×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #391 ◁ #2016

Complements

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

NH ≅ G/Ntype
112. C61#7405semidirect

Maximal subgroups

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

subgroupindex
#214439462
#214437532
C61×#20162
#740561