Finite Group Databasebeta

← #30594886

Subgroups — #30594886

Order 15616.

202 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 42 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#21446036C211yesmaximal, characteristic
4#16840628—21no—
5#16840607—21no—
6#16840240C411yescharacteristic
7#16839804—21no—
8#16839669C2211yescharacteristic
9#16839523—21no—
10C2×#101×C61C411yescharacteristic
11C22×#92420—41no—
12C22⋊#92420—41no—
13Q8×Dic61—41no—
14Q8×Dic61—41no—
15#14519736—21no—
16#14519736—41no—
17C2×C4⋊Dic61D411yescharacteristic
18C2×C4×Dic61D411yescharacteristic
19#14519711—41no—
20#14519709—41no—
21#14519684—41no—
22C22×Q8×C61C2×C411yescharacteristic
23C2×M16×C61—21no—
24#101×C61—21no—
25#101×C61C812yescomplemented
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—
39M16×C61—22no—
40M16×C61—41no—
41C2×C8×C61—41no—
42C22⋊Dic61—41no—
43C4⋊Dic61—21no—
44C4⋊Dic61—21no—
45C4⋊Dic61—41no—
46C4⋊Dic61—41no—
47C4⋊Dic61—41no—
48C4×Dic61—41no—
49C4×Dic61—42no—
50C4×Dic61—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×C61C22⋊C811yescharacteristic
62C2×C4×C61#10111yescharacteristic
63C2×Dic61—21no—
64C2×Dic61—21no—
65C2×Dic61—41no—
66C2×Dic61—41no—
67C2×Dic61—41no—
68C2×Dic61—41no—
69C2×Dic61—41no—
70C2×Dic61—81no—
71#92420—82no—
72#92420—161no—
73C8×C61—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—
84Dic61—41no—
85Dic61—41no—
86Dic61—81no—
87Dic61—81no—
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—611no—
98#428—1221no—
99C2×#101#692311yescharacteristic
100#391—611no—
101#339—1221no—
102#336—1221no—
103#324—1221no—
104C61#737611yescharacteristic, complemented, Sylow
105C22×Q8C2×#692311yescharacteristic
106C2×M16—21no—
107C22×C8—2441no—
108C4×Q8—2441no—
109C4×Q8—2441no—
110#117—1221no—
111#117—2441no—
112C2×C4⋊C4—611no—
113C2×C42—611no—
114#107—2441no—
115#106—2441no—
116#101—21no—
117#101#9242012yescomplemented
118C22⋊C8—2441no—
119#95—2441no—
120C2×Q8—21no—
121C2×Q8—41no—
122C2×Q8—41no—
123C2×Q8C2×#9242011yescharacteristic
124C2×Q8#1175821711yescharacteristic
125C22×C4—21no—
126C22×C4—1221no—
127C22×C4—1221no—
128C22×C4C22⋊#692311yescharacteristic
129M16—22no—
130M16—41no—
131C2×C8—41no—
132C2×C8—4881no—
133C2×C8—4881no—
134C2×C8—4881no—
135C2×C8—2442no—
136C4⋊C4—1221no—
137C4⋊C4—1221no—
138C4⋊C4—2441no—
139C4⋊C4—2441no—
140C4⋊C4—2441no—
141C22⋊C4—2441no—
142C42—2441no—
143C42—2441no—
144C42—2442no—
145C23#1451983611yescharacteristic
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—1221no—
156C2×C4—1221no—
157C2×C4—4881no—
158C2×C4—2441no—
159C2×C4—2441no—
160C2×C4—2441no—
161C2×C4—2441no—
162C2×C4—2441no—
163C2×C4C22⋊#9242011yescharacteristic
164C2×C4#1451983811yescharacteristic
165C8—42no—
166C8—9761no—
167C8—4882no—
168C22—21no—
169C22—21no—
170C22#1684060711yescharacteristic
171C22#1684066311yescharacteristic
172C22#1684066511yescharacteristic
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—4881no—
178C4—4881no—
179C4—4881no—
180C4—2441no—
181C4—2441no—
182C2—21no—
183C2—21no—
184C2#2146076311yescharacteristic
185C2#2146094311yescharacteristic
186C2#2146094511yescharacteristic
subgroupG/H
centerC22#16840663
commutatorC2×Q8×C61C2×C8
FrattiniC22×Q8C2×#6923
FittingC2×#101×C61C4
socleC22×C61AΣL(1,𝔽16)
prime radicalC23×C61#99
cosocle#16839669C22
hypercenterC2×#101#6923
hypocenterC61#7376
LCSG ▷ C2×Q8×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C22×Q8 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
25. #101×C61C8semidirect
104. C61#7376semidirect
117. #101#92420semidirect

Maximal subgroups

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

subgroupindex
#214607492
#214606392
#214460362
#737661