Finite Group Databasebeta

← #30595166

Subgroups — #30595166

Order 15616.

276 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 50 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
2C2×#16840622C211yesmaximal, characteristic
3#21446212C211yesmaximal, characteristic
4C2×#14519844—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—
16C22×#92420—41no—
17#14519844—22no—
18#14519844—41no—
19#14519838—22no—
20#14519838—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—82no—
54C2×#92420—81no—
55C4⋊C4×C61—22no—
56C4⋊C4×C61—42no—
57C22⋊C4×C61—41no—
58C42×C61—41no—
59C42×C61—42no—
60#11758196—41no—
61#11758196—41no—
62#11758196—41no—
63#11758196—41no—
64C4×Dic61—21no—
65C4×Dic61C22⋊C411yescharacteristic
66C4×Dic61C4⋊C411yescharacteristic
67#11758194—41no—
68#11758194—41no—
69C2×#92418—41no—
70C23×C61#9911yescharacteristic
71Q8×C61—42no—
72Q8×C61—41no—
73Q8×C61—41no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—41no—
79C2×C4×C61—41no—
80C2×C4×C61—42no—
81C2×C4×C61#9511yescharacteristic
82C2×C4×C61#9911yescharacteristic
83C2×Dic61—22no—
84C2×Dic61—22no—
85C2×Dic61—21no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—41no—
90C2×Dic61—41no—
91Dic122—41no—
92Dic122—41no—
93Dic122—81no—
94#92420—82no—
95#92420—82no—
96#92418—81no—
97#7491—611nomaximal, Sylow
98C22×C61—22no—
99C22×C61#34211yescharacteristic
100C22×C61AΣL(1,𝔽16)11yescharacteristic
101C22×C61#35211yescharacteristic
102C4×C61—21no—
103C4×C61—21no—
104C4×C61—41no—
105C4×C61—41no—
106C4×C61—82no—
107Dic61—21no—
108Dic61—22no—
109Dic61—21no—
110Dic61—41no—
111Dic61—41no—
112C2×#356—611no—
113#1886—611no—
114C2×#333—611no—
115C2×C61—21no—
116C2×C61—21no—
117C2×C61#139011yescharacteristic
118C2×C61#140512yes—
119C2×C4⋊Q8—611no—
120#519#692311yescharacteristic
121C2×C4⋊C8—1221no—
122#419—1221no—
123C2×#101—611no—
124C2×#101—1221no—
125#356—612no—
126#356—1221no—
127#339—1221no—
128#333—612no—
129#333—1221no—
130C61#749111yescharacteristic, complemented, Sylow
131C22×Q8—611no—
132C22×Q8C2×#692311yescharacteristic
133C2×M16—1221no—
134C2×M16—2441no—
135C22×C8—2441no—
136C4⋊Q8—611no—
137C4⋊Q8—611no—
138C4⋊Q8—611no—
139C4⋊Q8—611no—
140C4⋊Q8—2441no—
141C4×Q8—42no—
142#117—21no—
143#117—41no—
144C2×C4⋊C4—2441no—
145C2×C42—611no—
146C4⋊C8—1222no—
147C4⋊C8—2441no—
148#103—2442no—
149#101—1222no—
150#101—2441no—
151#101—2441no—
152C2×Q8—21no—
153C2×Q8—41no—
154C2×Q8—41no—
155C2×Q8—611no—
156C2×Q8—611no—
157C2×Q8—1221no—
158C2×Q8—2441no—
159C2×Q8—2441no—
160C2×Q8C4×#692311yescharacteristic
161C2×Q8C4⋊#692311yescharacteristic
162C22×C4—21no—
163C22×C4—1221no—
164C22×C4—1221no—
165C22×C4C22⋊#692311yescharacteristic
166M16—4881no—
167M16—2441no—
168M16—2442no—
169M16—2441no—
170C2×C8—4882no—
171C2×C8—4881no—
172C2×C8—2441no—
173C2×C8—2442no—
174C4⋊C4—22no—
175C4⋊C4—42no—
176C4⋊C4—2441no—
177C4⋊C4—2441no—
178C4⋊C4—2441no—
179C4⋊C4—2441no—
180C22⋊C4—41no—
181C42—41no—
182C42—42no—
183C42—611no—
184C42—611no—
185C42—1221no—
186C23#1451983511yescharacteristic
187Q8—41no—
188Q8—41no—
189Q8—42no—
190Q8—4881no—
191Q8—2441no—
192Q8—2441no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—42no—
200C2×C4—1222no—
201C2×C4—1222no—
202C2×C4—1221no—
203C2×C4—1221no—
204C2×C4—1221no—
205C2×C4—1221no—
206C2×C4—2441no—
207C2×C4—2441no—
208C2×C4(C2×#6923)⋊C411yescharacteristic
209C2×C4#1451983611yescharacteristic
210C8—4881no—
211C8—4882no—
212C8—4882no—
213C22—22no—
214C22#1684064011yescharacteristic
215C22#1684066211yescharacteristic
216C22#1684066411yescharacteristic
217C4—21no—
218C4—21no—
219C4—41no—
220C4—41no—
221C4—82no—
222C4—1221no—
223C4—1222no—
224C4—1221no—
225C4—2441no—
226C4—2441no—
227C2—21no—
228C2—21no—
229C2#2146090311yescharacteristic
230C2#2146094412yes—
subgroupG/H
centerC22#16840662
commutatorC2×Q8×C61C42
FrattiniC22×Q8C2×#6923
FittingC61×#519C4
socleC22×C61AΣL(1,𝔽16)
prime radicalC23×C61#99
cosocleC2×#14519775C22
hypercenter#519#6923
hypocenterC61#7491
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
7. #16840672C4semidirect
9. #16840622C4semidirect
130. C61#7491semidirect

Maximal subgroups

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

subgroupindex
C2×#168406722
C2×#168406222
#214462122
#749161