Finite Group Databasebeta

← #30595134

Subgroups — #30595134

Order 15616.

262 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 46 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
1C2×#16840672C211yesmaximal, characteristic
2#21461352C211yesmaximal, characteristic
3#21446212C211yesmaximal, characteristic
4#16840782—21no—
5C2×#14519838—21no—
6#16840672—21no—
7#16840672C412yescomplemented
8#16840622—21no—
9#16840622C412yescomplemented
10C2×#14519775C2211yescharacteristic
11#16839770—21no—
12C2×#14519696C411yescharacteristic
13#16839521—21no—
14C61×#519C411yescharacteristic
15C2×#11758217—41no—
16#14519844—22no—
17#14519838—22no—
18#14519838—41no—
19C22⋊#92420—41no—
20#14519832—41no—
21C22×Dic122D411yescharacteristic
22C2×#11758194—21no—
23#14519775—41no—
24#14519775C2×C411yescharacteristic
25#14519775C2×C411yescharacteristic
26#14519775D411yescharacteristic
27#14519775Q811yescharacteristic
28C2×#11758196—41no—
29C2×C4×Dic61D411yescharacteristic
30#14519700—42no—
31#14519696—41no—
32C22×Q8×C61C2×C411yescharacteristic
33C4×Q8×C61—42no—
34#117×C61—21no—
35#117×C61—41no—
36C2×Q8×C61—21no—
37C2×Q8×C61—41no—
38C2×Q8×C61—41no—
39C2×Q8×C61C4211yescharacteristic
40C2×Q8×C61C4⋊C411yescharacteristic
41C22×C4×C61—21no—
42C22×C4×C61C22⋊C411yescharacteristic
43C22×Dic61—21no—
44C22×Dic61—21no—
45C2×Dic122—21no—
46C2×Dic122—41no—
47C2×Dic122—41no—
48C2×Dic122C22⋊C411yescharacteristic
49C2×Dic122C4⋊C411yescharacteristic
50#11758217—42no—
51#11758217—81no—
52C2×#92420—42no—
53C2×#92420—81no—
54C4⋊C4×C61—22no—
55C4⋊C4×C61—42no—
56C22⋊C4×C61—41no—
57C42×C61—41no—
58C42×C61—42no—
59#11758196—41no—
60#11758196—41no—
61#11758196—41no—
62#11758196—41no—
63C4×Dic61—21no—
64C4×Dic61C22⋊C411yescharacteristic
65C4×Dic61C4⋊C411yescharacteristic
66#11758194—41no—
67#11758194—41no—
68C2×#92418—41no—
69C23×C61#9911yescharacteristic
70Q8×C61—42no—
71Q8×C61—41no—
72Q8×C61—41no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—41no—
78C2×C4×C61—41no—
79C2×C4×C61—42no—
80C2×C4×C61#9511yescharacteristic
81C2×C4×C61#9911yescharacteristic
82C2×Dic61—21no—
83C2×Dic61—21no—
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—42no—
87C2×Dic61—41no—
88C2×Dic61—41no—
89Dic122—41no—
90Dic122—41no—
91Dic122—81no—
92#92420—82no—
93#92420—82no—
94#92418—81no—
95#7483—611nomaximal, Sylow
96C22×C61—41no—
97C22×C61#34211yescharacteristic
98C22×C61AΣL(1,𝔽16)11yescharacteristic
99C22×C61#35211yescharacteristic
100C4×C61—21no—
101C4×C61—21no—
102C4×C61—41no—
103C4×C61—41no—
104C4×C61—82no—
105Dic61—22no—
106Dic61—41no—
107Dic61—41no—
108Dic61—41no—
109C2×#356—611no—
110#1886—611no—
111#1558—611no—
112C2×C61—21no—
113C2×C61—21no—
114C2×C61—21no—
115C2×C61#139011yescharacteristic
116C2×C4⋊Q8—611no—
117#519#692311yescharacteristic
118#432—1221no—
119#419—1221no—
120C2×#101—611no—
121C2×#101—1221no—
122#356—612no—
123#356—1221no—
124#339—1221no—
125#333—612no—
126#333—1221no—
127C61#748311yescharacteristic, complemented, Sylow
128C22×Q8—611no—
129C22×Q8C2×#692311yescharacteristic
130C2×M16—1221no—
131C2×M16—2441no—
132C4⋊Q8—611no—
133C4⋊Q8—611no—
134C4⋊Q8—611no—
135C4⋊Q8—611no—
136C4⋊Q8—2441no—
137C4×Q8—42no—
138#117—21no—
139#117—41no—
140C2×C4⋊C4—2441no—
141C2×C42—611no—
142C4⋊C8—1222no—
143#103—2442no—
144#101—1222no—
145#101—2441no—
146#101—2441no—
147C22⋊C8—2441no—
148#97—2441no—
149C2×Q8—21no—
150C2×Q8—41no—
151C2×Q8—41no—
152C2×Q8—611no—
153C2×Q8—611no—
154C2×Q8—1221no—
155C2×Q8—2441no—
156C2×Q8—2441no—
157C2×Q8C4×#692311yescharacteristic
158C2×Q8C4⋊#692311yescharacteristic
159C22×C4—21no—
160C22×C4—1221no—
161C22×C4—1221no—
162C22×C4C22⋊#692311yescharacteristic
163M16—4881no—
164M16—2441no—
165M16—2442no—
166M16—2441no—
167C2×C8—4881no—
168C2×C8—2441no—
169C2×C8—2442no—
170C4⋊C4—22no—
171C4⋊C4—42no—
172C4⋊C4—2441no—
173C4⋊C4—2441no—
174C4⋊C4—2441no—
175C4⋊C4—2441no—
176C22⋊C4—41no—
177C42—41no—
178C42—42no—
179C42—611no—
180C42—611no—
181C42—1221no—
182C23#1451983511yescharacteristic
183Q8—41no—
184Q8—41no—
185Q8—42no—
186Q8—4881no—
187Q8—2441no—
188Q8—2441no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—42no—
196C2×C4—1221no—
197C2×C4—1221no—
198C2×C4—1221no—
199C2×C4—1221no—
200C2×C4—2442no—
201C2×C4—2441no—
202C2×C4—2441no—
203C2×C4(C2×#6923)⋊C411yescharacteristic
204C2×C4#1451983611yescharacteristic
205C8—4881no—
206C8—4882no—
207C8—4882no—
208C22—41no—
209C22#1684064011yescharacteristic
210C22#1684066211yescharacteristic
211C22#1684066411yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—41no—
216C4—82no—
217C4—1222no—
218C4—2441no—
219C4—2441no—
220C4—2441no—
221C2—21no—
222C2—21no—
223C2—21no—
224C2#2146090311yescharacteristic
subgroupG/H
centerC2#21460903
commutatorC2×Q8×C61C42
FrattiniC22×Q8C2×#6923
FittingC61×#519C4
socleC2×C61#1390
prime radicalC23×C61#99
cosocleC2×#14519775C22
hypercenter#519#6923
hypocenterC61#7483
LCSG ▷ C2×Q8×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C22×Q8 ◁ #519

Complements

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

NH ≅ G/Ntype
7. #16840672C4semidirect
9. #16840622C4semidirect
127. C61#7483semidirect

Maximal subgroups

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

subgroupindex
C2×#168406722
#214613522
#214462122
#748361