Finite Group Databasebeta

← #30594885

Subgroups — #30594885

Order 15616.

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

normal subgroups only

This group has 228 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#21460747C211yesmaximal, characteristic
2#21460635C211yesmaximal, characteristic
3#21446029C211yesmaximal, characteristic
4#16840628—21no—
5#16840607—21no—
6#16839805—21no—
7C2×#14519694C411yescharacteristic
8#16839665C2211yescharacteristic
9#16839521—21no—
10C61×#518C411yescharacteristic
11C22×#92420—41no—
12C22⋊#92420—41no—
13C2×#11758194—21no—
14C2×C4⋊Dic61D411yescharacteristic
15C2×C22⋊Dic61—41no—
16C2×C4×Dic61D411yescharacteristic
17#14519710—41no—
18#14519708—41no—
19#14519694—21no—
20#14519694C812yescomplemented
21C22×D4×C61C2×C411yescharacteristic
22C4×D4×C61—41no—
23C4×D4×C61—41no—
24#117×C61—21no—
25C2×C22⋊C4×C61—41no—
26C24×C61—21no—
27C2×D4×C61—21no—
28C2×D4×C61—41no—
29C2×D4×C61—41no—
30C2×D4×C61C2×C811yescharacteristic
31C2×D4×C61M1611yescharacteristic
32C22×C4×C61—41no—
33C22×C4×C61—41no—
34C22×C4×C61C22⋊C411yescharacteristic
35C22×Dic61—21no—
36C22×Dic61—21no—
37C2×#92420—42no—
38C2×#92420—81no—
39C2×#92420—81no—
40C2×#92420—81no—
41C4⋊C4×C61—21no—
42C4⋊C4×C61—21no—
43C22⋊C4×C61—42no—
44C22⋊C4×C61—41no—
45C42×C61—41no—
46C22⋊Dic61—81no—
47C22⋊Dic61—81no—
48C4⋊Dic61—41no—
49C4×Dic61—41no—
50#11758194—22no—
51#11758194—41no—
52C2×#92418—41no—
53C23×C61—21no—
54C23×C61—21no—
55C23×C61—41no—
56C23×C61—41no—
57C23×C61—81no—
58C23×C61—81no—
59C23×C61#9911yescharacteristic
60D4×C61—41no—
61D4×C61—41no—
62D4×C61—42no—
63C2×C4×C61—21no—
64C2×C4×C61—21no—
65C2×C4×C61—41no—
66C2×C4×C61—41no—
67C2×C4×C61—161no—
68C2×C4×C61—161no—
69C2×C4×C61C22⋊C811yescharacteristic
70C2×C4×C61#10111yescharacteristic
71C2×Dic61—21no—
72C2×Dic61—21no—
73C2×Dic61—41no—
74C2×Dic61—41no—
75C2×Dic61—41no—
76C2×Dic61—81no—
77#92420—82no—
78#92420—161no—
79#92418—42no—
80#7375—611nomaximal, Sylow
81C22×C61—21no—
82C22×C61—21no—
83C22×C61—41no—
84C22×C61—41no—
85C22×C61—81no—
86C22×C61—81no—
87C22×C61—81no—
88C22×C61—81no—
89C22×C61—161no—
90C22×C61#32411yescharacteristic
91C22×C61AΣL(1,𝔽16)11yescharacteristic
92C22×C61#35211yescharacteristic
93C4×C61—21no—
94C4×C61—21no—
95C4×C61—81no—
96C4×C61—81no—
97Dic61—41no—
98Dic61—41no—
99Dic61—81no—
100#1856—611no—
101#1318—611no—
102#1270—611no—
103C2×C61—21no—
104C2×C61—21no—
105C2×C61—81no—
106C2×C61—81no—
107C2×C61#132611yescharacteristic
108C2×C61#140211yescharacteristic
109C2×C61#140311yescharacteristic
110#518#692311yescharacteristic
111#428—1221no—
112C2×#100—611no—
113#390—611no—
114#339—1221no—
115#336—1221no—
116#324—1221no—
117C61#737511yescharacteristic, complemented, Sylow
118C22×D4C2×#692311yescharacteristic
119C2×M16—1221no—
120C22×C8—2441no—
121C4×D4—41no—
122C4×D4—41no—
123#117—21no—
124C2×C4⋊C4—611no—
125C2×C22⋊C4—41no—
126C2×C22⋊C4—2441no—
127C2×C42—611no—
128#107—2441no—
129#106—2441no—
130#100—612no—
131#100—1221no—
132C22⋊C8—2441no—
133C24—21no—
134C2×D4—21no—
135C2×D4—41no—
136C2×D4—41no—
137C2×D4D61⋊C811yescharacteristic
138C2×D4#1175821311yescharacteristic
139C22×C4—41no—
140C22×C4—41no—
141C22×C4—1221no—
142C22×C4—1221no—
143C22×C4C22⋊#692311yescharacteristic
144M16—1222no—
145M16—2441no—
146C2×C8—4881no—
147C2×C8—4881no—
148C2×C8—4881no—
149C2×C8—2442no—
150C2×C8—2441no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—2441no—
154C22⋊C4—42no—
155C22⋊C4—41no—
156C22⋊C4—4881no—
157C22⋊C4—4881no—
158C42—41no—
159C42—2441no—
160C23—21no—
161C23—21no—
162C23—41no—
163C23—41no—
164C23—81no—
165C23—81no—
166C23#1451983511yescharacteristic
167D4—41no—
168D4—41no—
169D4—42no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—161no—
175C2×C4—161no—
176C2×C4—1221no—
177C2×C4—1221no—
178C2×C4—4881no—
179C2×C4—2441no—
180C2×C4—2441no—
181C2×C4—2441no—
182C2×C4#1451983411yescharacteristic
183C2×C4#1451983811yescharacteristic
184C8—9761no—
185C8—4882no—
186C8—2442no—
187C22—21no—
188C22—21no—
189C22—41no—
190C22—41no—
191C22—81no—
192C22—81no—
193C22—81no—
194C22—81no—
195C22—161no—
196C22#1684060811yescharacteristic
197C22#1684066211yescharacteristic
198C22#1684066411yescharacteristic
199C4—21no—
200C4—21no—
201C4—81no—
202C4—81no—
203C4—4881no—
204C4—2441no—
205C4—2441no—
206C2—21no—
207C2—21no—
208C2—81no—
209C2—81no—
210C2#2146076411yescharacteristic
211C2#2146093811yescharacteristic
212C2#2146094011yescharacteristic
subgroupG/H
centerC22#16840662
commutatorC2×D4×C61C2×C8
FrattiniC22×D4C2×#6923
FittingC61×#518C4
socleC22×C61AΣL(1,𝔽16)
prime radicalC22×D4×C61C2×C4
cosocle#16839665C22
hypercenter#518#6923
hypocenterC61#7375
LCSG ▷ C2×D4×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C22×D4 ◁ #518

Complements

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

NH ≅ G/Ntype
20. #14519694C8semidirect
117. C61#7375semidirect

Maximal subgroups

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

subgroupindex
#214607472
#214606352
#214460292
#737561