Finite Group Databasebeta

← #29567441

Subgroups — #29567441

Order 15616.

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

normal subgroups only

This group has 202 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#21446033C211yesmaximal, characteristic
2#21443645C211yesmaximal, characteristic
3C61×#1319C211yesmaximal, characteristic
4#16840240C411yescharacteristic
5#16839802—21no—
6C2×#14519696C411yescharacteristic
7#16839522—21no—
8#16839517—21no—
9C61×#391C2211yescharacteristic
10C61×#324—21no—
11C2×#11758194—21no—
12C22×#92418—41no—
13Q8×Dic61—41no—
14Q8×Dic61—41no—
15#14519736—21no—
16#14519736—41no—
17#14519710—41no—
18#14519708—41no—
19#14519696—21no—
20#14519696C812yescomplemented
21C22×Q8×C61C2×C411yescharacteristic
22C2×C4⋊C4×C61D411yescharacteristic
23C2×C42×C61D411yescharacteristic
24C22⋊C8×C61—41no—
25#95×C61—41no—
26C2×Q8×C61—21no—
27C2×Q8×C61—41no—
28C2×Q8×C61—41no—
29C2×Q8×C61C2×C811yescharacteristic
30C2×Q8×C61M1611yescharacteristic
31C22×C4×C61—21no—
32C22×C4×C61—21no—
33C22×C4×C61—21no—
34C22×C4×C61C22⋊C411yescharacteristic
35C2×C8×C61—81no—
36C4⋊C4×C61—41no—
37C42×C61—41no—
38C22⋊Dic61—41no—
39C4⋊Dic61—21no—
40C4⋊Dic61—21no—
41C4⋊Dic61—41no—
42C4⋊Dic61—41no—
43C4×Dic61—41no—
44C4×Dic61—42no—
45#11758194—22no—
46#11758194—41no—
47C2×#92418—41no—
48C2×#92418—42no—
49C2×#92418—81no—
50C2×#92418—81no—
51C23×C61#9911yescharacteristic
52Q8×C61—42no—
53Q8×C61—41no—
54Q8×C61—41no—
55C2×C4×C61—21no—
56C2×C4×C61—21no—
57C2×C4×C61—21no—
58C2×C4×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61—21no—
61C2×C4×C61—41no—
62C2×C4×C61—41no—
63C2×C4×C61—41no—
64C2×C4×C61—41no—
65C2×C4×C61—41no—
66C2×C4×C61—81no—
67C2×C4×C61C22⋊C811yescharacteristic
68C2×C4×C61#10111yescharacteristic
69C2×Dic61—41no—
70C2×Dic61—41no—
71C8×C61—161no—
72#92418—42no—
73#92418—82no—
74#7376—611nomaximal, Sylow
75C22×C61—21no—
76C22×C61—21no—
77C22×C61#32411yescharacteristic
78C22×C61AΣL(1,𝔽16)11yescharacteristic
79C22×C61#35211yescharacteristic
80C4×C61—21no—
81C4×C61—21no—
82C4×C61—41no—
83C4×C61—41no—
84C4×C61—41no—
85C4×C61—41no—
86C4×C61—81no—
87Dic61—81no—
88Dic61—81no—
89#1857—611no—
90#1319D6111yescharacteristic
91#1272—611no—
92C2×C61—21no—
93C2×C61—21no—
94C2×C61#132611yescharacteristic
95C2×C61#140411yescharacteristic
96C2×C61#140511yescharacteristic
97#519—611no—
98#428—1221no—
99C2×#101—611no—
100#391C2×D6111yescharacteristic
101#339—1221no—
102#336—1221no—
103#324—21no—
104C61#737611yescharacteristic, complemented, Sylow
105C22×Q8C4×D6111yescharacteristic
106C2×M16—1221no—
107C22×C8—2441no—
108C4×Q8—2441no—
109C4×Q8—2441no—
110#117—1221no—
111#117—2441no—
112C2×C4⋊C4C22⋊D6111yescharacteristic
113C2×C42D24411yescharacteristic
114#107—2441no—
115#106—2441no—
116#101—612no—
117#101—1221no—
118C22⋊C8—41no—
119#95—41no—
120C2×Q8—21no—
121C2×Q8—41no—
122C2×Q8—41no—
123C2×Q8C8×D6111yescharacteristic
124C2×Q8#1175818911yescharacteristic
125C22×C4—21no—
126C22×C4—21no—
127C22×C4—21no—
128C22×C4#1175819811yescharacteristic
129M16—1222no—
130M16—2441no—
131C2×C8—81no—
132C2×C8—4881no—
133C2×C8—4881no—
134C2×C8—2442no—
135C2×C8—2441no—
136C4⋊C4—41no—
137C4⋊C4—1221no—
138C4⋊C4—1221no—
139C4⋊C4—2441no—
140C4⋊C4—2441no—
141C22⋊C4—2441no—
142C42—41no—
143C42—2441no—
144C42—2442no—
145C23#1451969111yescharacteristic
146Q8—41no—
147Q8—41no—
148Q8—42no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—81no—
161C2×C4—2441no—
162C2×C4—2441no—
163C2×C4#1451968911yescharacteristic
164C2×C4#1451969511yescharacteristic
165C8—161no—
166C8—4882no—
167C8—2442no—
168C22—21no—
169C22—21no—
170C22#1683948711yescharacteristic
171C22#1683954811yescharacteristic
172C22#1683955311yescharacteristic
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—41no—
178C4—41no—
179C4—81no—
180C4—4881no—
181C4—4881no—
182C2—21no—
183C2—21no—
184C2#2144376611yescharacteristic
185C2#2144396911yescharacteristic
186C2#2144397211yescharacteristic
subgroupG/H
centerC22#16839548
commutatorC2×Q8×C61C2×C8
Frattini#391C2×D61
FittingC61×#1319C2
socleC22×C61AΣL(1,𝔽16)
prime radicalC23×C61#99
cosocleC61×#391C22
hypercenter#1319D61
hypocenterC61#7376
LCSG ▷ C2×Q8×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #391 ◁ #1319

Complements

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

NH ≅ G/Ntype
20. #14519696C8semidirect
104. C61#7376semidirect

Maximal subgroups

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

subgroupindex
#214460332
#214436452
C61×#13192
#737661