Finite Group Databasebeta

← D61⋊#1413 #30608400

Subgroups — D61⋊#1413 #30608400

Order 15616.

314 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 58 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⋊#356C212yesmaximal
2#21460963C212yesmaximal, complemented
3#21460962C211yesmaximal, characteristic, complemented
4#21460961C211yesmaximal, characteristic, complemented
5#491×D61C211yesmaximal, characteristic
6D61⋊#101—22no—
7#16840673C2212yes—
8#16840673C2212yes—
9#16840672—22no—
10C4⋊Q8×D61C2211yescharacteristic
11#125×D61C411yescharacteristic
12#16840132C2211yescharacteristic
13#16840131C2211yescharacteristic
14#16840130C411yescharacteristic
15#16840129—22no—
16#103×D61—22no—
17#97×D61C411yescharacteristic
18C61×#491C411yescharacteristic
19D61⋊M16—42no—
20#14519838—22no—
21#14519838—22no—
22#14519838—42no—
23C2×Q8×D61D412yes—
24C2×C8×D61—21no—
25#14519777C2311yescharacteristic
26#14519776—41no—
27#14519775D412yes—
28#14519769C2×C411yescharacteristic
29#14519768—21no—
30#14519767—41no—
31C4⋊C4×D61—21no—
32C4⋊C4×D61—41no—
33C4⋊C4×D61—41no—
34C42×D61C2×C411yescharacteristic
35#14519702—22no—
36#14519701—22no—
37#14519700—22no—
38#14519688C2×C411yescharacteristic
39#14519687—21no—
40C4⋊Q8×C61C2×C411yescharacteristic
41#125×C61C2×C411yescharacteristic
42#103×C61—22no—
43#97×C61C2×C411yescharacteristic
44C2×Q8×C61C22⋊C412yes—
45Q8×D61—42no—
46Q8×D61—42no—
47C2×C4×D61—22no—
48C2×C4×D61—21no—
49C2×C4×D61—41no—
50C2×C4×D61C22⋊C411yescharacteristic
51C2×Dic122—22no—
52C2×Dic122C2×D412yes—
53#11758217—42no—
54#11758217—42no—
55#11758213—82no—
56D61⋊C8—82no—
57C2×C8×C61—21no—
58C4⋊C4×C61—21no—
59C4⋊C4×C61—41no—
60C4⋊C4×C61—41no—
61C42×C61C22×C411yescharacteristic
62C4⋊Dic61—21no—
63C4⋊Dic61—41no—
64C4⋊Dic61—41no—
65#11758196—42no—
66#11758196—41no—
67#11758196—41no—
68#11758196—41no—
69C4×Dic61—21no—
70C4×Dic61C22⋊C411yescharacteristic
71C2×#92418—21no—
72C8×D61—41no—
73C8×D61—41no—
74C22×D61#9911yescharacteristic
75Q8×C61—42no—
76C2×C4×C61—21no—
77C2×C4×C61—22no—
78C2×C4×C61—41no—
79C2×C4×C61C2×C22⋊C411yescharacteristic
80C2×Dic61—21no—
81C2×Dic61—22no—
82C2×Dic61—41no—
83C2×Dic61#9911yescharacteristic
84C4×D61—21no—
85C4×D61—21no—
86C4×D61—42no—
87C4×D61—42no—
88C4×D61—42no—
89C4×D61—82no—
90Dic122—42no—
91Dic122—82no—
92#92420—82no—
93#92420—82no—
94C8×C61—41no—
95#92418—41no—
96C2×#1413—611nomaximal, Sylow
97C22×C61C2×#9911yescharacteristic
98C2×D61—22no—
99C2×D61#35411yescharacteristic
100C2×D61#35411yescharacteristic
101C4×C61—21no—
102C4×C61—41no—
103C4×C61—42no—
104C4×C61—81no—
105Dic61—21no—
106Dic61—41no—
107Dic61—42no—
108Dic61—81no—
109C2×#491—611no—
110C2×#356—612no—
111#1413—611no—
112#1413—611no—
113#1413—612no—
114C2×C61—21no—
115C2×C61C2×#35411yescharacteristic
116D61—21no—
117D61#141312yescomplemented
118C2×C4⋊Q8—611no—
119C2×#125—611no—
120#491—611no—
121#491—611no—
122#491—611no—
123#491—1222no—
124#491#692311yescharacteristic
125C2×#103—1222no—
126C2×#101—1222no—
127C2×#97—611no—
128#356—612no—
129#356—612no—
130#356—1222no—
131C61C2×#141311yescharacteristic, complemented, Sylow
132C22×Q8—612no—
133C2×M16—2442no—
134C22×C8—1221no—
135C4⋊Q8—612no—
136C4⋊Q8—611no—
137C4⋊Q8—2441no—
138C4⋊Q8C2×#692311yescharacteristic
139#125—611no—
140#125—1221no—
141#125—2441no—
142#125C2×#692311yescharacteristic
143C2×C4⋊C4—1221no—
144C2×C4⋊C4—2441no—
145C2×C4⋊C4—2441no—
146C2×C42—611no—
147#103—22no—
148#103—1222no—
149#103—1222no—
150#103—1222no—
151#101—1222no—
152#101—1222no—
153#101—2442no—
154#97—611no—
155#97—1221no—
156#97C2×#692311yescharacteristic
157C2×Q8—612no—
158C2×Q8—1222no—
159C2×Q8—2442no—
160C2×Q8—2442no—
161C2×Q8C22⋊#692312yes—
162C22×C4—611no—
163C22×C4—1221no—
164C22×C4—1222no—
165C22×C4—2441no—
166M16—4882no—
167M16—2442no—
168M16—2442no—
169C2×C8—21no—
170C2×C8—1221no—
171C2×C8—4882no—
172C2×C8—2441no—
173C2×C8—2441no—
174C4⋊C4—21no—
175C4⋊C4—41no—
176C4⋊C4—41no—
177C4⋊C4—1221no—
178C4⋊C4—2442no—
179C4⋊C4—2441no—
180C4⋊C4—2441no—
181C4⋊C4—2441no—
182C4⋊C4—2441no—
183C4⋊C4—2441no—
184C42—611no—
185C42—1221no—
186C42C22×#692311yescharacteristic
187C23—611no—
188Q8—42no—
189Q8—4882no—
190Q8—2442no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—41no—
194C2×C4—611no—
195C2×C4—1221no—
196C2×C4—1221no—
197C2×C4—1221no—
198C2×C4—1222no—
199C2×C4—4882no—
200C2×C4—2442no—
201C2×C4—2442no—
202C2×C4—2442no—
203C2×C4—2441no—
204C2×C4C2×C22⋊#692311yescharacteristic
205C8—41no—
206C8—4882no—
207C8—4882no—
208C8—2441no—
209C22—611no—
210C22—611no—
211C22—1222no—
212C22D61⋊#9911yescharacteristic
213C4—21no—
214C4—41no—
215C4—42no—
216C4—81no—
217C4—1221no—
218C4—4881no—
219C4—2441no—
220C4—2442no—
221C2—21no—
222C2—612no—
223C2—1221no—
224C2D61⋊#35411yescharacteristic
subgroupG/H
centerC2D61⋊#354
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#491C4
socleC2×C61C2×#354
prime radicalC22×D61#99
cosocle#14519777C23
hypercenter#491#6923
hypocenterC61C2×#1413
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #21460963C2semidirect
3. #21460962C2semidirect
4. #21460961C2semidirect
117. D61#1413semidirect
131. C61C2×#1413semidirect

Maximal subgroups

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

subgroupindex
D61⋊#3562
#214609632
#214609622
#214609612
#491×D612
C2×#141361