Finite Group Databasebeta

← D61⋊#1328 #30603919

Subgroups — D61⋊#1328 #30603919

Order 15616.

378 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 88 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#21460768C212yesmaximal, complemented
3#21460767C212yesmaximal, complemented
4#424×D61C211yesmaximal, characteristic
5D61⋊M32—22no—
6#16840659—22no—
7#16840658C2214yes—
8C2×M16×D61C2211yescharacteristic
9C22×C8×D61C411yescharacteristic
10#117×D61C411yescharacteristic
11#16839790C411yescharacteristic
12#16839789C2211yescharacteristic
13#16839788C2211yescharacteristic
14#16839787—22no—
15C4⋊C8×D61—22no—
16C61×#424C411yescharacteristic
17#14519852—42no—
18#14519851—24no—
19D61⋊C16—42no—
20C22×C4×D61C2×C411yescharacteristic
21C2×#11758194C2311yescharacteristic
22C2×#11758189D412yes—
23M16×D61—41no—
24M16×D61—41no—
25C22×#92418C2×C411yescharacteristic
26C2×C8×D61—21no—
27C2×C8×D61—21no—
28C2×C8×D61—41no—
29C2×C8×D61—41no—
30C2×C8×D61D412yes—
31#14519736C2×C411yescharacteristic
32#14519735—21no—
33#14519734—21no—
34#14519733C812yes—
35C4⋊C4×D61—21no—
36C22⋊C4×D61C812yes—
37C42×D61—21no—
38C4⋊#92418—22no—
39#14519706—22no—
40#14519706—22no—
41C2×M16×C61C2×C411yescharacteristic
42C22×C8×C61C2×C411yescharacteristic
43#117×C61C2×C411yescharacteristic
44C4⋊C8×C61—22no—
45C23×D61C2×C811yescharacteristic
46C22×C4×C61C22×C411yescharacteristic
47C22×Dic61C2×C811yescharacteristic
48C2×C4×D61—21no—
49C2×C4×D61—21no—
50C2×C4×D61—21no—
51C2×C4×D61—21no—
52C2×C4×D61—22no—
53C2×C4×D61C22⋊C411yescharacteristic
54C2×C4×D61C22⋊C411yescharacteristic
55C2×C4×D61M1611yescharacteristic
56C2×C4×D61M1611yescharacteristic
57M16×C61—41no—
58C2×C8×C61—21no—
59C2×C8×C61—41no—
60C2×C8×C61C22⋊C412yes—
61C4⋊C4×C61—21no—
62C22⋊C4×C61C2×C812yes—
63C42×C61—21no—
64C22⋊Dic61C2×C812yes—
65#11758198—22no—
66C4⋊Dic61—21no—
67#11758196—22no—
68C4×Dic61—21no—
69C4×Dic61—22no—
70#11758194—41no—
71C2×#92418—21no—
72C2×#92418—41no—
73C2×#92418C2×D412yes—
74#11758189—42no—
75C8×D61—22no—
76C8×D61—22no—
77C8×D61—42no—
78C8×D61—41no—
79C8×D61—41no—
80#11758187—44no—
81C23×C61C22×C811yescharacteristic
82C22×D61—21no—
83C22×D61—21no—
84C22×D61—42no—
85C22×D61C22⋊C811yescharacteristic
86C22×D61C22⋊C811yescharacteristic
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—22no—
90C2×C4×C61C2×C22⋊C411yescharacteristic
91C2×C4×C61C2×M1611yescharacteristic
92C2×Dic61—21no—
93C2×Dic61—21no—
94C2×Dic61—22no—
95C2×Dic61C22⋊C811yescharacteristic
96C2×Dic61C22⋊C811yescharacteristic
97C4×D61—21no—
98C4×D61—21no—
99C4×D61—21no—
100C4×D61—21no—
101C4×D61—21no—
102C4×D61—21no—
103C4×D61—44no—
104C4×D61#9911yescharacteristic
105C4×D61#9911yescharacteristic
106C4×D61#10111yescharacteristic
107C4×D61#10111yescharacteristic
108C8×C61—22no—
109C8×C61—41no—
110#92418—22no—
111#92418—41no—
112C2×#1328—611nomaximal, Sylow
113C22×C61—21no—
114C22×C61—41no—
115C22×C61C2×C22⋊C811yescharacteristic
116C2×D61—22no—
117C2×D61—21no—
118C2×D61—42no—
119C2×D61—42no—
120C2×D61—41no—
121C2×D61#32411yescharacteristic
122C2×D61#32411yescharacteristic
123C4×C61—21no—
124C4×C61—42no—
125C4×C61C2×#9911yescharacteristic
126C4×C61C2×#10111yescharacteristic
127Dic61—21no—
128Dic61—42no—
129Dic61#32411yescharacteristic
130Dic61#32411yescharacteristic
131C2×#424—611no—
132C2×#349—612no—
133#1328—612no—
134#1328—612no—
135C2×C61—21no—
136C2×C61—41no—
137C2×C61C2×#32411yescharacteristic
138D61—21no—
139D61—41no—
140D61#132812yescomplemented
141C22×M16—611no—
142C23×C8—611no—
143C2×#117—611no—
144C2×M32—1222no—
145#424—611no—
146#424—611no—
147#424—611no—
148#424—1222no—
149#424#692311yescharacteristic
150C2×C4⋊C8—1222no—
151#349—614no—
152#349—1222no—
153C61C2×#132811yescharacteristic, complemented, Sylow
154C23×C4—611no—
155C2×M16—611no—
156C2×M16—612no—
157C2×M16—2441no—
158C2×M16—2441no—
159C2×M16C2×#692311yescharacteristic
160C22×C8—612no—
161C22×C8—611no—
162C22×C8—1221no—
163C22×C8—1221no—
164C22×C8—2441no—
165C22×C8—2441no—
166C22×C8C2×#692311yescharacteristic
167#117—611no—
168#117—612no—
169#117—1221no—
170#117—1221no—
171#117C2×#692311yescharacteristic
172C2×C4⋊C4—1221no—
173C2×C22⋊C4—612no—
174C2×C42—1221no—
175M32—1224no—
176M32—2442no—
177C2×C16—2442no—
178C4⋊C8—22no—
179C4⋊C8—1222no—
180C4⋊C8—1222no—
181C4⋊C8—1222no—
182C24—611no—
183C22×C4—611no—
184C22×C4—611no—
185C22×C4—611no—
186C22×C4—611no—
187C22×C4—611no—
188C22×C4—1221no—
189C22×C4—1221no—
190C22×C4—1221no—
191C22×C4—1221no—
192C22×C4—1222no—
193C22×C4C22×#692311yescharacteristic
194M16—41no—
195M16—2442no—
196M16—2441no—
197C2×C8—21no—
198C2×C8—41no—
199C2×C8—612no—
200C2×C8—1222no—
201C2×C8—1222no—
202C2×C8—1221no—
203C2×C8—2441no—
204C2×C8—2441no—
205C2×C8—2442no—
206C2×C8—2441no—
207C2×C8C22⋊#692312yes—
208C4⋊C4—21no—
209C4⋊C4—1222no—
210C4⋊C4—1221no—
211C22⋊C4—612no—
212C22⋊C4—1222no—
213C22⋊C4D61⋊C812yes—
214C42—21no—
215C42—1222no—
216C42—1221no—
217C16—2444no—
218C23—611no—
219C23—611no—
220C23—1221no—
221C23—1221no—
222C23—2442no—
223C23C2×D61⋊C811yescharacteristic
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—611no—
228C2×C4—611no—
229C2×C4—611no—
230C2×C4—611no—
231C2×C4—611no—
232C2×C4—611no—
233C2×C4—1221no—
234C2×C4—1221no—
235C2×C4—1221no—
236C2×C4—1221no—
237C2×C4—1221no—
238C2×C4—1221no—
239C2×C4—1221no—
240C2×C4—1221no—
241C2×C4—1222no—
242C2×C4—2444no—
243C2×C4C2×C22⋊#692311yescharacteristic
244C2×C4D61⋊M1611yescharacteristic
245C8—22no—
246C8—41no—
247C8—1222no—
248C8—2441no—
249C22—21no—
250C22—41no—
251C22—611no—
252C22—611no—
253C22—1222no—
254C22—1221no—
255C22—2441no—
256C22—2442no—
257C22—2442no—
258C22D61⋊(C22⋊C8)11yescharacteristic
259C4—21no—
260C4—42no—
261C4—611no—
262C4—611no—
263C4—1221no—
264C4—2442no—
265C4D61⋊#9911yescharacteristic
266C4D61⋊#10111yescharacteristic
267C2—21no—
268C2—41no—
269C2—612no—
270C2—1221no—
271C2—2441no—
272C2D61⋊#32411yescharacteristic
subgroupG/H
centerC4D61⋊#99
commutatorC23×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#424C4
socleC2×C61C2×#324
prime radicalC23×D61C2×C8
cosocleC2×#11758194C23
hypercenter#424#6923
hypocenterC61C2×#1328
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #424

Complements

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

NH ≅ G/Ntype
2. #21460768C2semidirect
3. #21460767C2semidirect
140. D61#1328semidirect
153. C61C2×#1328semidirect

Maximal subgroups

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

subgroupindex
D61⋊#3492
#214607682
#214607672
#424×D612
C2×#132861