Finite Group Databasebeta

← #30603916

Subgroups — #30603916

Order 15616.

364 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 86 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
1D61⋊#349C212yesmaximal
2#21460766C212yesmaximal, complemented
3#21460765C212yesmaximal, complemented
4#21454381C211yesmaximal, characteristic
5D61⋊M32—22no—
6#16840659—22no—
7#16840658C2214yes—
8C2×M16×D61C411yescharacteristic
9C2×M16×D61C2211yescharacteristic
10C2×#14519734C411yescharacteristic
11#16839787—22no—
12#16839787—22no—
13#16839786C2211yescharacteristic
14#16839785C411yescharacteristic
15#16839785C2211yescharacteristic
16C61×#423C411yescharacteristic
17#14519852—42no—
18#14519851—24no—
19D61⋊C16—42no—
20C22×C4×D61C2×C411yescharacteristic
21C2×#11758194C2×C411yescharacteristic
22C2×#11758194C2311yescharacteristic
23C2×#11758189—21no—
24C2×#11758189D412yes—
25M16×D61—42no—
26M16×D61—42no—
27C2×C8×D61—21no—
28C2×C8×D61D412yes—
29#14519734—21no—
30#14519734—21no—
31#14519734C812yes—
32#14519734C812yes—
33C2×#11758196—21no—
34C2×#11758198—21no—
35C2×C4×Dic61C2×C411yescharacteristic
36C4⋊#92418—22no—
37#14519706—22no—
38#14519706—22no—
39C2×M16×C61C2×C411yescharacteristic
40C2×M16×C61C2×C411yescharacteristic
41C2×C42×C61C2×C411yescharacteristic
42C4⋊C8×C61—22no—
43C23×D61M1611yescharacteristic
44C22×C4×C61—21no—
45C22×C4×C61C22×C411yescharacteristic
46C22×Dic61—21no—
47C22×Dic61M1611yescharacteristic
48C2×C4×D61—22no—
49C2×C4×D61—22no—
50C2×C4×D61C22⋊C411yescharacteristic
51C2×C4×D61C22⋊C411yescharacteristic
52C2×C4×D61C2×C811yescharacteristic
53C2×C4×D61C2×C811yescharacteristic
54M16×C61—41no—
55M16×C61—41no—
56C2×C8×C61—21no—
57C2×C8×C61C22⋊C412yes—
58C42×C61—21no—
59C42×C61C2×C812yes—
60#11758198—22no—
61#11758198—22no—
62#11758196—22no—
63#11758196—22no—
64C4×Dic61—21no—
65C4×Dic61C2×C812yes—
66#11758194—41no—
67#11758194—41no—
68C2×#92418—21no—
69C2×#92418C2×D412yes—
70#11758189—42no—
71#11758189—42no—
72C8×D61—22no—
73C8×D61—22no—
74C8×D61—42no—
75#11758187—44no—
76C23×C61C2×M1611yescharacteristic
77C22×D61—22no—
78C22×D61—81no—
79C22×D61C22⋊C811yescharacteristic
80C22×D61C22⋊C811yescharacteristic
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—22no—
84C2×C4×C61—81no—
85C2×C4×C61C2×C22⋊C411yescharacteristic
86C2×C4×C61C22×C811yescharacteristic
87C2×Dic61—22no—
88C2×Dic61—22no—
89C2×Dic61—81no—
90C2×Dic61C22⋊C811yescharacteristic
91C2×Dic61C22⋊C811yescharacteristic
92C4×D61—22no—
93C4×D61—21no—
94C4×D61—21no—
95C4×D61—22no—
96C4×D61#9912yes—
97C4×D61#10112yes—
98C8×C61—22no—
99C8×C61—41no—
100#92418—22no—
101#92418—41no—
102#11456—611nomaximal, Sylow
103C22×C61—21no—
104C22×C61—41no—
105C22×C61C2×C22⋊C811yescharacteristic
106C2×D61—21no—
107C2×D61—41no—
108C2×D61—41no—
109C2×D61—82no—
110C2×D61#32412yes—
111C4×C61—21no—
112C4×C61—42no—
113C4×C61C2×#9911yescharacteristic
114C4×C61C2×#10111yescharacteristic
115Dic61—21no—
116Dic61—42no—
117Dic61#32412yes—
118#2905—611no—
119C2×#349—612no—
120#1327—612no—
121#1327—612no—
122C2×C61—21no—
123C2×C61—41no—
124C2×C61C2×#32411yescharacteristic
125D61—22no—
126D61—41no—
127C22×M16—611no—
128C22×M16—611no—
129C2×#117—611no—
130C2×M32—1222no—
131#424—1222no—
132#424—1222no—
133#423—611no—
134#423—611no—
135#423—611no—
136#423#692311yescharacteristic
137#349—614no—
138#349—1222no—
139C61#1145611yescharacteristic, complemented, Sylow
140C23×C4—611no—
141C2×M16—611no—
142C2×M16—612no—
143C2×M16—611no—
144C2×M16—1221no—
145C2×M16—2442no—
146C2×M16—2442no—
147C2×M16C2×#692311yescharacteristic
148C2×M16C2×#692311yescharacteristic
149C22×C8—612no—
150C22×C8—1221no—
151#117—612no—
152#117—612no—
153#117—1221no—
154#117—1221no—
155C2×C4⋊C4—1221no—
156C2×C22⋊C4—1221no—
157C2×C42—611no—
158C2×C42C2×#692311yescharacteristic
159M32—1224no—
160M32—2442no—
161C2×C16—2442no—
162C4⋊C8—22no—
163C4⋊C8—1222no—
164C4⋊C8—1222no—
165C4⋊C8—1222no—
166C24—611no—
167C22×C4—21no—
168C22×C4—611no—
169C22×C4—611no—
170C22×C4—611no—
171C22×C4—611no—
172C22×C4—611no—
173C22×C4—1222no—
174C22×C4—1222no—
175C22×C4—1221no—
176C22×C4C22×#692311yescharacteristic
177M16—41no—
178M16—41no—
179M16—2442no—
180M16—2442no—
181M16—2441no—
182M16—2441no—
183C2×C8—21no—
184C2×C8—612no—
185C2×C8—1222no—
186C2×C8—1222no—
187C2×C8—1221no—
188C2×C8—2442no—
189C2×C8C22⋊#692312yes—
190C4⋊C4—1222no—
191C4⋊C4—1222no—
192C22⋊C4—1222no—
193C22⋊C4—1222no—
194C42—21no—
195C42—612no—
196C42—1221no—
197C42D61⋊C812yes—
198C16—2444no—
199C23—611no—
200C23—611no—
201C23—1222no—
202C23—4881no—
203C23D61⋊M1611yescharacteristic
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—81no—
208C2×C4—611no—
209C2×C4—612no—
210C2×C4—612no—
211C2×C4—611no—
212C2×C4—1222no—
213C2×C4—1222no—
214C2×C4—1222no—
215C2×C4—1221no—
216C2×C4—1221no—
217C2×C4—1222no—
218C2×C4—4881no—
219C2×C4C2×C22⋊#692311yescharacteristic
220C2×C4C2×D61⋊C811yescharacteristic
221C8—22no—
222C8—41no—
223C8—1222no—
224C8—2441no—
225C22—21no—
226C22—41no—
227C22—612no—
228C22—1221no—
229C22—4882no—
230C22—2441no—
231C22—2441no—
232C22D61⋊(C22⋊C8)11yescharacteristic
233C4—21no—
234C4—42no—
235C4—612no—
236C4—1221no—
237C4—2442no—
238C4D61⋊#9911yescharacteristic
239C4D61⋊#10111yescharacteristic
240C2—21no—
241C2—41no—
242C2—1222no—
243C2—2441no—
244C2D61⋊#32411yescharacteristic
subgroupG/H
centerC4D61⋊#99
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#423C4
socleC2×C61C2×#324
prime radicalC23×D61M16
cosocleC2×#11758194C23
hypercenter#423#6923
hypocenterC61#11456
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #423

Complements

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

NH ≅ G/Ntype
2. #21460766C2semidirect
3. #21460765C2semidirect
139. C61#11456semidirect

Maximal subgroups

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

subgroupindex
D61⋊#3492
#214607662
#214607652
#214543812
#1145661