Finite Group Databasebeta

← #30595151

Subgroups — #30595151

Order 15616.

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

normal subgroups only

This group has 298 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×#16840670C211yesmaximal, characteristic
2C2×#16840617C211yesmaximal, characteristic
3#21446205C211yesmaximal, characteristic
4C2×#14519838—21no—
5C2×#14519832—21no—
6#16840670—21no—
7#16840670C412yescomplemented
8#16840617—21no—
9#16840617C412yescomplemented
10C2×#14519764C2211yescharacteristic
11#16840237C411yescharacteristic
12#16839772—21no—
13#16839523—21no—
14C2×#100×C61C411yescharacteristic
15C2×#11758217—41no—
16C22×#92420—41no—
17#14519838—22no—
18#14519838—41no—
19#14519832—22no—
20#14519832—41no—
21C22×Dic122D411yescharacteristic
22#14519764—41no—
23#14519764C2×C411yescharacteristic
24#14519764C2×C411yescharacteristic
25#14519764D411yescharacteristic
26#14519764Q811yescharacteristic
27D4×Dic61—42no—
28#14519736—21no—
29C2×C22⋊Dic61—41no—
30C2×C22⋊Dic61—41no—
31C2×C4×Dic61D411yescharacteristic
32#14519702—42no—
33C22×D4×C61C2×C411yescharacteristic
34C2×M16×C61—21no—
35#100×C61—41no—
36C24×C61—21no—
37C2×D4×C61—21no—
38C2×D4×C61—41no—
39C2×D4×C61—41no—
40C2×D4×C61C4211yescharacteristic
41C2×D4×C61C4⋊C411yescharacteristic
42C22×C4×C61C22⋊C411yescharacteristic
43C22×Dic61—21no—
44C22×Dic61—21no—
45C22×Dic61—42no—
46C2×Dic122—21no—
47C2×Dic122—41no—
48C2×Dic122—41no—
49C2×Dic122C22⋊C411yescharacteristic
50C2×Dic122C4⋊C411yescharacteristic
51#11758217—42no—
52#11758217—81no—
53C2×#92420—42no—
54C2×#92420—44no—
55C2×#92420—81no—
56M16×C61—41no—
57M16×C61—41no—
58C2×C8×C61—41no—
59C22⋊Dic61—41no—
60C22⋊Dic61—41no—
61C22⋊Dic61—41no—
62C22⋊Dic61—41no—
63C22⋊Dic61—42no—
64C22⋊Dic61—41no—
65C4⋊Dic61—22no—
66C4×Dic61—21no—
67C4×Dic61—41no—
68C4×Dic61C22⋊C411yescharacteristic
69C4×Dic61C4⋊C411yescharacteristic
70C23×C61—21no—
71C23×C61—21no—
72C23×C61—41no—
73C23×C61—41no—
74C23×C61—82no—
75C23×C61#9911yescharacteristic
76D4×C61—41no—
77D4×C61—41no—
78D4×C61—42no—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61#9511yescharacteristic
82C2×C4×C61#9911yescharacteristic
83C2×Dic61—21no—
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—21no—
87C2×Dic61—42no—
88C2×Dic61—41no—
89C2×Dic61—41no—
90C2×Dic61—42no—
91C2×Dic61—162no—
92Dic122—41no—
93Dic122—41no—
94Dic122—81no—
95#92420—44no—
96#92420—82no—
97C8×C61—81no—
98#7487—611nomaximal, Sylow
99C22×C61—22no—
100C22×C61—41no—
101C22×C61—41no—
102C22×C61—81no—
103C22×C61—81no—
104C22×C61—82no—
105C22×C61—161no—
106C22×C61#34211yescharacteristic
107C22×C61AΣL(1,𝔽16)11yescharacteristic
108C22×C61#35211yescharacteristic
109C4×C61—21no—
110C4×C61—21no—
111Dic61—41no—
112Dic61—41no—
113Dic61—41no—
114Dic61—41no—
115Dic61—82no—
116C2×#355—611no—
117#1885—611no—
118C2×#329—611no—
119C2×C61—21no—
120C2×C61—21no—
121C2×C61—81no—
122C2×C61—81no—
123C2×C61#139011yescharacteristic
124C2×C61#140312yes—
125C2×#124—611no—
126#518—611no—
127#419—1221no—
128C2×#101—1221no—
129C2×#100#692311yescharacteristic
130C2×#97—1221no—
131#355—612no—
132#355—1221no—
133#339—1221no—
134#329—612no—
135#329—1221no—
136C61#748711yescharacteristic, complemented, Sylow
137C22×Q8—611no—
138C22×D4C2×#692311yescharacteristic
139C2×M16—21no—
140C2×M16—2441no—
141C22×C8—2441no—
142#124—611no—
143#124—611no—
144#124—611no—
145#124—611no—
146#124—2441no—
147C4×D4—2442no—
148#117—1221no—
149C2×C22⋊C4—2441no—
150C2×C22⋊C4—2441no—
151C2×C42—611no—
152#103—2442no—
153#101—1222no—
154#101—2441no—
155#100—41no—
156#97—1222no—
157#97—2441no—
158C24—21no—
159C2×Q8—611no—
160C2×Q8—611no—
161C2×Q8—1221no—
162C2×Q8—2441no—
163C2×Q8—2441no—
164C2×D4—21no—
165C2×D4—41no—
166C2×D4—41no—
167C2×D4C4×#692311yescharacteristic
168C2×D4C4⋊#692311yescharacteristic
169C22×C4—1221no—
170C22×C4—1221no—
171C22×C4—2442no—
172C22×C4C22⋊#692311yescharacteristic
173M16—41no—
174M16—41no—
175M16—4881no—
176M16—2442no—
177C2×C8—41no—
178C2×C8—4881no—
179C2×C8—2442no—
180C2×C8—2444no—
181C4⋊C4—1222no—
182C22⋊C4—2441no—
183C22⋊C4—2441no—
184C22⋊C4—2441no—
185C22⋊C4—2441no—
186C22⋊C4—2442no—
187C22⋊C4—2441no—
188C42—611no—
189C42—611no—
190C42—1221no—
191C42—2441no—
192C23—21no—
193C23—21no—
194C23—41no—
195C23—41no—
196C23—82no—
197C23#1451983611yescharacteristic
198Q8—4881no—
199Q8—2441no—
200Q8—2441no—
201D4—41no—
202D4—41no—
203D4—42no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—1221no—
207C2×C4—1221no—
208C2×C4—1221no—
209C2×C4—1221no—
210C2×C4—9762no—
211C2×C4—2442no—
212C2×C4—2442no—
213C2×C4—2441no—
214C2×C4—2441no—
215C2×C4(C2×#6923)⋊C411yescharacteristic
216C2×C4#1451983511yescharacteristic
217C8—81no—
218C8—4882no—
219C8—2444no—
220C22—22no—
221C22—41no—
222C22—41no—
223C22—81no—
224C22—81no—
225C22—82no—
226C22—161no—
227C22#1684064011yescharacteristic
228C22#1684066311yescharacteristic
229C22#1684066511yescharacteristic
230C4—21no—
231C4—21no—
232C4—4882no—
233C4—2441no—
234C4—2441no—
235C4—2441no—
236C4—2441no—
237C2—21no—
238C2—21no—
239C2—81no—
240C2—81no—
241C2#2146090411yescharacteristic
242C2#2146094112yes—
subgroupG/H
centerC22#16840663
commutatorC2×D4×C61C42
FrattiniC22×D4C2×#6923
FittingC2×#100×C61C4
socleC22×C61AΣL(1,𝔽16)
prime radicalC22×D4×C61C2×C4
cosocleC2×#14519764C22
hypercenterC2×#100#6923
hypocenterC61#7487
LCSG ▷ C2×D4×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C22×D4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
7. #16840670C4semidirect
9. #16840617C4semidirect
136. C61#7487semidirect

Maximal subgroups

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

subgroupindex
C2×#168406702
C2×#168406172
#214462052
#748761