Finite Group Databasebeta

← D61×#1355 #29591182

Subgroups — D61×#1355 #29591182

Order 15616.

366 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 71 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#490×D61C211yesmaximal, characteristic
2#347×D61C212yesmaximal, complemented
3#21443852C211yesmaximal, characteristic, complemented
4#21443851C212yesmaximal, complemented
5C61×#1355C211yesmaximal, characteristic, complemented
6#127×D61C411yescharacteristic
7#125×D61C411yescharacteristic
8M32×D61—22no—
9#16840128C411yescharacteristic
10#16840127C2211yescharacteristic
11#16840126C411yescharacteristic
12#16840125—22no—
13#102×D61—22no—
14#97×D61C2211yescharacteristic
15#16839540C2212yescomplemented
16#16839539—22no—
17C61×#490C2211yescharacteristic
18C61×#347C2212yescomplemented
19C2×D4×D61—21no—
20C2×D4×D61—41no—
21C2×C8×D61D412yes—
22#14519774C2×C411yescharacteristic
23#14519773—21no—
24#14519773—41no—
25#14519769C2×C411yescharacteristic
26#14519768—21no—
27#14519767—41no—
28C4⋊C4×D61—21no—
29C4⋊C4×D61—41no—
30C42×D61C2×C411yescharacteristic
31#14519717—22no—
32#14519716—24no—
33C16×D61—24no—
34#14519699—22no—
35#14519698—22no—
36#14519697—22no—
37#14519688C2×C411yescharacteristic
38#14519687D412yes—
39#127×C61C2×C411yescharacteristic
40#125×C61C2×C411yescharacteristic
41M32×C61—22no—
42#102×C61—22no—
43#97×C61C2311yescharacteristic
44C23×D61—41no—
45C2×D4×C61—21no—
46C2×D4×C61—41no—
47C2×C22⋊D61—42no—
48C2×C22⋊D61—41no—
49D4×D61—42no—
50D4×D61—42no—
51D4×D61—84no—
52C2×D244—21no—
53C2×D244—41no—
54C2×C4×D61—21no—
55C2×C4×D61—41no—
56C2×C4×D61C22⋊C411yescharacteristic
57C2×C8×C61C2×D412yes—
58C4⋊C4×C61—21no—
59C4⋊C4×C61—41no—
60C42×C61C22×C411yescharacteristic
61C4⋊Dic61—21no—
62C4⋊Dic61—41no—
63#11758196—41no—
64#11758196—41no—
65#11758196—41no—
66C4×Dic61—21no—
67C4×Dic61C22⋊C411yescharacteristic
68C2×#92418C22⋊C412yes—
69C8×D61—22no—
70C8×D61—22no—
71C16×C61—24no—
72#11758185—24no—
73C23×C61—41no—
74C22×D61—41no—
75C22×D61—84no—
76C22×D61—81no—
77C22×D61—81no—
78C22×D61#10011yescharacteristic
79D4×C61—42no—
80D4×C61—82no—
81C2×C4×C61—21no—
82C2×C4×C61—41no—
83C2×C4×C61C2×C22⋊C411yescharacteristic
84C22⋊D61—84no—
85C22⋊D61—82no—
86C2×Dic61—21no—
87C2×Dic61—41no—
88C2×Dic61#10011yescharacteristic
89D244—42no—
90D244—82no—
91C4×D61—42no—
92C4×D61—82no—
93C4×D61#10412yes—
94C4×D61#10412yes—
95C8×C61—22no—
96#92418—22no—
97C2×#1355—611nomaximal, Sylow
98C22×C61—82no—
99C22×C61—81no—
100C22×C61C2×#10011yescharacteristic
101C2×D61—22no—
102C2×D61—82no—
103C2×D61—81no—
104C2×D61—162no—
105C2×D61—162no—
106C2×D61#32911yescharacteristic
107C2×D61#32911yescharacteristic
108C4×C61—41no—
109C4×C61—81no—
110C4×C61C2×#10412yes—
111Dic61—41no—
112Dic61—81no—
113Dic61#32912yes—
114C2×#490—611no—
115C2×#347—612no—
116#1355—611no—
117#1355—612no—
118#1355D6111yescharacteristic, direct product factor
119C2×C61—21no—
120C2×C61—161no—
121C2×C61C2×#32911yescharacteristic
122D61—21no—
123D61—161no—
124D61#135512yesdirect product factor
125C2×#127—611no—
126C2×#125—611no—
127C2×M32—1222no—
128#490—611no—
129#490—611no—
130#490—611no—
131#490—1222no—
132#490C2×D6111yescharacteristic
133C2×#102—1222no—
134C2×#97—611no—
135#347—612no—
136#347—1222no—
137#347C2×D6112yescomplemented
138C61C2×#135511yescharacteristic, complemented, Sylow
139C22×D4—1221no—
140C22×D4—2441no—
141C22×C8—612no—
142#127—611no—
143#127—1221no—
144#127—2441no—
145#127C4×D6111yescharacteristic
146#125—611no—
147#125—1221no—
148#125—2441no—
149#125C4×D6111yescharacteristic
150C2×C4⋊C4—1221no—
151C2×C4⋊C4—2441no—
152C2×C42—611no—
153M32—22no—
154M32—1224no—
155M32—1222no—
156C2×C16—1224no—
157#102—22no—
158#102—1222no—
159#102—1222no—
160#102—1222no—
161#97—612no—
162#97—611no—
163#97C22×D6111yescharacteristic
164C24—2441no—
165C2×D4—21no—
166C2×D4—41no—
167C2×D4—1221no—
168C2×D4—4884no—
169C2×D4—2441no—
170C2×D4—2442no—
171C2×D4—2442no—
172C2×D4—2441no—
173C2×D4—2442no—
174C22×C4—611no—
175C22×C4—1221no—
176C22×C4—2441no—
177C2×C8—612no—
178C2×C8—1222no—
179C2×C8—1222no—
180C2×C8D4×D6112yes—
181C4⋊C4—21no—
182C4⋊C4—41no—
183C4⋊C4—1221no—
184C4⋊C4—2441no—
185C4⋊C4—2441no—
186C4⋊C4—2441no—
187C4⋊C4—2441no—
188C42—611no—
189C42—1221no—
190C42C2×C4×D6111yescharacteristic
191C16—24no—
192C16—1224no—
193C23—41no—
194C23—611no—
195C23—4881no—
196C23—4881no—
197C23—4884no—
198C23—2441no—
199D4—42no—
200D4—82no—
201D4—4882no—
202D4—4882no—
203D4—4884no—
204D4—2442no—
205C2×C4—21no—
206C2×C4—41no—
207C2×C4—611no—
208C2×C4—612no—
209C2×C4—612no—
210C2×C4—1221no—
211C2×C4—4882no—
212C2×C4—2442no—
213C2×C4—2441no—
214C2×C4C22⋊C4×D6111yescharacteristic
215C8—22no—
216C8—1222no—
217C22—82no—
218C22—81no—
219C22—611no—
220C22—611no—
221C22—1222no—
222C22—9762no—
223C22—9762no—
224C22—4882no—
225C22—4881no—
226C22#100×D6111yescharacteristic
227C4—41no—
228C4—81no—
229C4—612no—
230C4—4881no—
231C4—2441no—
232C4#104×D6112yes—
233C2—21no—
234C2—161no—
235C2—612no—
236C2—1221no—
237C2—9761no—
238C2#329×D6111yescharacteristic
subgroupG/H
centerC2#329×D61
commutatorC42×C61C22×C4
Frattini#97C22×D61
FittingC61×#1355C2
socleC2×C61C2×#329
prime radical#127×D61C4
cosocle#97×C61C23
hypercenter#1355D61
hypocenterC61C2×#1355
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #1355

Complements

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

NH ≅ G/Ntype
2. #347×D61C2semidirect
3. #21443852C2semidirect
4. #21443851C2semidirect
5. C61×#1355C2semidirect
15. #16839540C22semidirect
18. C61×#347C22semidirect
118. #1355D61direct (N × H)
124. D61#1355direct (N × H)
137. #347C2×D61semidirect
138. C61C2×#1355semidirect

Maximal subgroups

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

subgroupindex
#490×D612
#347×D612
#214438522
#214438512
C61×#13552
C2×#135561