Finite Group Databasebeta

← #30594887

Subgroups — #30594887

Order 15616.

202 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 40 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#21460749C211yesmaximal, characteristic
2#21460639C211yesmaximal, characteristic
3#21446034C211yesmaximal, characteristic
4#16840628—21no—
5#16840607—21no—
6#16839805—21no—
7C2×#14519696C411yescharacteristic
8#16839669C2211yescharacteristic
9#16839521—21no—
10C61×#519C411yescharacteristic
11C22×#92420—41no—
12C22⋊#92420—41no—
13C2×#11758194—21no—
14C2×C4⋊Dic61D411yescharacteristic
15C2×C4×Dic61D411yescharacteristic
16#14519710—41no—
17#14519708—41no—
18#14519696—21no—
19#14519696C812yescomplemented
20#14519684—41no—
21C22×Q8×C61C2×C411yescharacteristic
22C4×Q8×C61—41no—
23C4×Q8×C61—41no—
24#117×C61—21no—
25#117×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×C61C22⋊C411yescharacteristic
33C22×Dic61—21no—
34C22×Dic61—21no—
35C2×#92420—42no—
36C2×#92420—81no—
37C2×#92420—81no—
38C2×#92420—81no—
39C4⋊C4×C61—21no—
40C4⋊C4×C61—21no—
41C4⋊C4×C61—41no—
42C4⋊C4×C61—41no—
43C22⋊C4×C61—41no—
44C42×C61—41no—
45C42×C61—42no—
46C4⋊Dic61—41no—
47C4×Dic61—41no—
48#11758194—22no—
49#11758194—41no—
50C2×#92418—41no—
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—41no—
60C2×C4×C61—41no—
61C2×C4×C61—41no—
62C2×C4×C61—41no—
63C2×C4×C61C22⋊C811yescharacteristic
64C2×C4×C61#10111yescharacteristic
65C2×Dic61—21no—
66C2×Dic61—21no—
67C2×Dic61—41no—
68C2×Dic61—41no—
69C2×Dic61—41no—
70C2×Dic61—81no—
71#92420—82no—
72#92420—161no—
73#92418—42no—
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—81no—
85C4×C61—81no—
86Dic61—41no—
87Dic61—41no—
88Dic61—81no—
89#1857—611no—
90#1319—611no—
91#1272—611no—
92C2×C61—21no—
93C2×C61—21no—
94C2×C61#132611yescharacteristic
95C2×C61#140411yescharacteristic
96C2×C61#140511yescharacteristic
97#519#692311yescharacteristic
98#428—1221no—
99C2×#101—611no—
100#391—611no—
101#339—1221no—
102#336—1221no—
103#324—1221no—
104C61#737611yescharacteristic, complemented, Sylow
105C22×Q8C2×#692311yescharacteristic
106C2×M16—1221no—
107C22×C8—2441no—
108C4×Q8—41no—
109C4×Q8—41no—
110#117—21no—
111#117—41no—
112C2×C4⋊C4—611no—
113C2×C42—611no—
114#107—2441no—
115#106—2441no—
116#101—612no—
117#101—1221no—
118C22⋊C8—2441no—
119#95—2441no—
120C2×Q8—21no—
121C2×Q8—41no—
122C2×Q8—41no—
123C2×Q8D61⋊C811yescharacteristic
124C2×Q8#1175821311yescharacteristic
125C22×C4—21no—
126C22×C4—1221no—
127C22×C4—1221no—
128C22×C4C22⋊#692311yescharacteristic
129M16—1222no—
130M16—2441no—
131C2×C8—4881no—
132C2×C8—4881no—
133C2×C8—4881no—
134C2×C8—2442no—
135C2×C8—2441no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—41no—
139C4⋊C4—41no—
140C4⋊C4—2441no—
141C22⋊C4—41no—
142C42—41no—
143C42—42no—
144C42—2441no—
145C23#1451983511yescharacteristic
146Q8—41no—
147Q8—41no—
148Q8—42no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—1221no—
158C2×C4—1221no—
159C2×C4—4881no—
160C2×C4—2441no—
161C2×C4—2441no—
162C2×C4—2441no—
163C2×C4#1451983411yescharacteristic
164C2×C4#1451983811yescharacteristic
165C8—9761no—
166C8—4882no—
167C8—2442no—
168C22—21no—
169C22—21no—
170C22#1684060811yescharacteristic
171C22#1684066211yescharacteristic
172C22#1684066411yescharacteristic
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—81no—
178C4—81no—
179C4—4881no—
180C4—2441no—
181C4—2441no—
182C2—21no—
183C2—21no—
184C2#2146076411yescharacteristic
185C2#2146094211yescharacteristic
186C2#2146094411yescharacteristic
subgroupG/H
centerC22#16840662
commutatorC2×Q8×C61C2×C8
FrattiniC22×Q8C2×#6923
FittingC61×#519C4
socleC22×C61AΣL(1,𝔽16)
prime radicalC23×C61#99
cosocle#16839669C22
hypercenter#519#6923
hypocenterC61#7376
LCSG ▷ C2×Q8×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C22×Q8 ◁ #519

Complements

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

NH ≅ G/Ntype
19. #14519696C8semidirect
104. C61#7376semidirect

Maximal subgroups

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

subgroupindex
#214607492
#214606392
#214460342
#737661