Finite Group Databasebeta

← #29583153

Subgroups — #29583153

Order 15616.

364 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 93 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#21446800C211yesmaximal, characteristic
2#21444317C212yesmaximal
3#21443722C212yesmaximal
4#21443648C211yesmaximal, characteristic
5C61×#2402C211yesmaximal, characteristic
6#16840319C2211yescharacteristic
7#16839815C2212yes—
8#16839786C2211yescharacteristic
9#16839522—22no—
10#16839498—22no—
11#16839498—22no—
12C61×#400—22no—
13C61×#398—22no—
14C4×C4⋊C4×C61—22no—
15C4×C4⋊C4×C61C2212yes—
16C61×#376C2211yescharacteristic
17C2×#11758194—21no—
18#14519777Q812yes—
19#14519769—21no—
20#14519756—22no—
21C4×Dic122—22no—
22#14519736—21no—
23C4⋊#92418—22no—
24C4⋊#92418—22no—
25C22⋊#92418—22no—
26C4×#92418—22no—
27C2×C4⋊C4×C61—22no—
28C2×C4⋊C4×C61—22no—
29C2×C4⋊C4×C61—22no—
30C2×C42×C61—22no—
31C2×C42×C61D412yes—
32C2×C42×C61C2311yescharacteristic
33#95×C61—22no—
34#95×C61—22no—
35#95×C61—22no—
36#95×C61D412yes—
37#95×C61D412yes—
38C22×C4×C61—22no—
39C22×C4×C61—22no—
40C22×C4×C61—22no—
41C22×C4×C61C2×D412yes—
42C22×C4×C61C2×D411yescharacteristic
43C2×Dic122—22no—
44C4⋊C4×C61—44no—
45C4⋊C4×C61—44no—
46C4⋊C4×C61—44no—
47C42×C61—22no—
48C42×C61—22no—
49C42×C61—42no—
50C42×C61—42no—
51C42×C61C2×Q811yescharacteristic
52C42×C61#4112yes—
53C42×C61#4111yescharacteristic
54C22⋊Dic61—41no—
55C4⋊Dic61—22no—
56C4⋊Dic61—22no—
57#11758196—42no—
58C4×Dic61—41no—
59#11758194—42no—
60C2×#92418—42no—
61C2×#92418—41no—
62C23×C61#12011yescharacteristic
63C2×C4×C61—24no—
64C2×C4×C61—42no—
65C2×C4×C61—42no—
66C2×C4×C61—42no—
67C2×C4×C61—42no—
68C2×C4×C61—42no—
69C2×C4×C61—42no—
70C2×C4×C61—42no—
71C2×C4×C61—42no—
72C2×C4×C61—42no—
73C2×C4×C61C22⋊Q812yes—
74C2×C4×C61C22⋊Q811yescharacteristic
75C2×C4×C61#12412yes—
76C2×C4×C61#12411yescharacteristic
77C2×C4×C61#13512yes—
78C2×C4×C61#13712yes—
79C2×Dic61—42no—
80Dic122—82no—
81#92418—82no—
82#92418—81no—
83#10373—611nomaximal, Sylow
84C22×C61—22no—
85C22×C61#39311yescharacteristic
86C22×C61#45212yes—
87C4×C61—22no—
88C4×C61—22no—
89C4×C61—44no—
90C4×C61—82no—
91C4×C61—82no—
92C4×C61#47912yes—
93C4×C61#48811yescharacteristic
94C4×C61#49111yescharacteristic
95Dic61—82no—
96#2402D6111yescharacteristic
97#1995—611no—
98#1503—612no—
99#1303—612no—
100#1274—611no—
101C2×C61—22no—
102C2×C61#202611yescharacteristic
103C2×C61#203112yes—
104#533—611no—
105#431—612no—
106#423—611no—
107#400—22no—
108#398—22no—
109C4×C4⋊C4—22no—
110C4×C4⋊C4C2×D6112yes—
111#376C2×D6111yescharacteristic
112#339—1222no—
113#328—1222no—
114#328—1222no—
115C61#1037311yescharacteristic, complemented, Sylow
116C2×M16—1221no—
117C4⋊Q8—612no—
118#125—1221no—
119C22⋊Q8—1222no—
120C4×Q8—1222no—
121#117—1221no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—22no—
125C2×C42—22no—
126C2×C42C22⋊D6112yes—
127C2×C42C22×D6111yescharacteristic
128C4⋊C8—1222no—
129C4⋊C8—1222no—
130C22⋊C8—1222no—
131C4×C8—1222no—
132#95—22no—
133#95—22no—
134#95—22no—
135#95C22⋊D6112yes—
136#95C22⋊D6112yes—
137C2×Q8—1222no—
138C22×C4—22no—
139C22×C4—22no—
140C22×C4—22no—
141C22×C4C2×C22⋊D6112yes—
142C22×C4C2×C22⋊D6111yescharacteristic
143M16—2442no—
144C2×C8—2442no—
145C2×C8—2441no—
146C4⋊C4—44no—
147C4⋊C4—44no—
148C4⋊C4—44no—
149C4⋊C4—1222no—
150C4⋊C4—1222no—
151C4⋊C4—2442no—
152C22⋊C4—2441no—
153C42—22no—
154C42—22no—
155C42—42no—
156C42—42no—
157C42—2441no—
158C42Q8×D6111yescharacteristic
159C42#1175822611yescharacteristic
160C42#1175822612yes—
161C23#1451974611yescharacteristic
162Q8—4882no—
163C2×C4—24no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—2442no—
174C2×C4#1451975312yes—
175C2×C4#1451975311yescharacteristic
176C2×C4#1451976612yes—
177C2×C4#1451976611yescharacteristic
178C2×C4#1451979712yes—
179C2×C4#1451980712yes—
180C8—4882no—
181C8—4881no—
182C22—22no—
183C22#1683967311yescharacteristic
184C22#1683992412yes—
185C4—22no—
186C4—22no—
187C4—44no—
188C4—82no—
189C4—82no—
190C4—4882no—
191C4#1684006612yes—
192C4#1684011911yescharacteristic
193C4#1684013211yescharacteristic
194C2—22no—
195C2#2144696711yescharacteristic
196C2#2144698812yes—
subgroupG/H
centerC2×C4#14519766
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2402C2
socleC22×C61#393
prime radicalC23×C61#120
hypercenter#2402D61
hypocenterC61#10373
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2402

Complements

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

NH ≅ G/Ntype
115. C61#10373semidirect

Maximal subgroups

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

subgroupindex
#214468002
#214443172
#214437222
#214436482
C61×#24022
#1037361