Finite Group Databasebeta

← D61⋊#1323 #30603872

Subgroups — D61⋊#1323 #30603872

Order 15616.

394 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 98 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⋊(C22⋊C16)C212yesmaximal
2#21460758C212yesmaximal, complemented
3#21460757C212yesmaximal, complemented
4#424×D61C211yesmaximal, characteristic
5C2×D61⋊C16—22no—
6#16840657—22no—
7C22⋊#11758187C2214yes—
8C2×M16×D61C411yescharacteristic
9C22×C8×D61C2211yescharacteristic
10#117×D61C411yescharacteristic
11#16839790C2211yescharacteristic
12#16839789C2211yescharacteristic
13#16839788C411yescharacteristic
14#16839787—22no—
15C4⋊C8×D61—22no—
16C61×#424C411yescharacteristic
17D61⋊C16—44no—
18C2×#11758187—24no—
19C22×C4×D61C2×C411yescharacteristic
20C2×#11758194C2×C411yescharacteristic
21C2×#11758189—21no—
22M16×D61—42no—
23C22×#92418C2311yescharacteristic
24C2×C8×D61—21no—
25C2×C8×D61—42no—
26C2×C8×D61D412yes—
27C2×C8×D61D412yes—
28#14519736C2×C411yescharacteristic
29#14519735C812yes—
30#14519734—21no—
31#14519733—21no—
32C4⋊C4×D61C812yes—
33C22⋊C4×D61—21no—
34C42×D61—21no—
35C4⋊#92418—22no—
36#14519706—22no—
37#14519706—22no—
38C2×M16×C61C2×C411yescharacteristic
39C22×C8×C61C2×C411yescharacteristic
40#117×C61C2×C411yescharacteristic
41C4⋊C8×C61—22no—
42C23×D61M1611yescharacteristic
43C22×C4×C61C22×C411yescharacteristic
44C22×Dic61M1611yescharacteristic
45C2×C4×D61—22no—
46C2×C4×D61—22no—
47C2×C4×D61—22no—
48C2×C4×D61C22⋊C411yescharacteristic
49C2×C4×D61C22⋊C411yescharacteristic
50C2×C4×D61C2×C811yescharacteristic
51C2×C4×D61C2×C811yescharacteristic
52M16×C61—41no—
53C2×C8×C61—21no—
54C2×C8×C61—41no—
55C2×C8×C61C22⋊C412yes—
56C4⋊C4×C61C2×C812yes—
57C22⋊C4×C61—21no—
58C42×C61—21no—
59C22⋊Dic61—21no—
60#11758198—22no—
61C4⋊Dic61C2×C812yes—
62#11758196—22no—
63C4×Dic61—21no—
64C4×Dic61—22no—
65#11758194—41no—
66C2×#92418—21no—
67C2×#92418—41no—
68C2×#92418C2×D412yes—
69#11758189—42no—
70C8×D61—24no—
71C8×D61—42no—
72C8×D61—42no—
73#11758187—44no—
74C23×C61C2×M1611yescharacteristic
75C22×D61—22no—
76C22×D61—24no—
77C22×D61C22⋊C811yescharacteristic
78C22×D61C22⋊C811yescharacteristic
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—22no—
82C2×C4×C61C2×C22⋊C411yescharacteristic
83C2×C4×C61C22×C811yescharacteristic
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61C22⋊C811yescharacteristic
87C2×Dic61C22⋊C811yescharacteristic
88C4×D61—22no—
89C4×D61—21no—
90C4×D61—21no—
91C4×D61—22no—
92C4×D61—44no—
93C4×D61#9912yes—
94C4×D61#10112yes—
95C8×C61—22no—
96C8×C61—41no—
97#92418—22no—
98#92418—41no—
99C2×#1323—611nomaximal, Sylow
100C22×C61—22no—
101C22×C61—21no—
102C22×C61C2×C22⋊C811yescharacteristic
103C2×D61—22no—
104C2×D61—21no—
105C2×D61—44no—
106C2×D61#32412yes—
107C2×D61#35014yes—
108C4×C61—21no—
109C4×C61—42no—
110C4×C61C2×#9911yescharacteristic
111C4×C61C2×#10111yescharacteristic
112Dic61—21no—
113Dic61—42no—
114Dic61#32412yes—
115C2×#424—611no—
116C2×C22⋊C16—612no—
117#1323—612no—
118#1323—612no—
119C2×C61—41no—
120C2×C61C2×#32411yescharacteristic
121C2×C61C2×#35012yes—
122D61—41no—
123D61#132314yescomplemented
124C22×M16—611no—
125C23×C8—611no—
126C2×#117—611no—
127C22×C16—1222no—
128#424—611no—
129#424—611no—
130#424—611no—
131#424—1222no—
132#424#692311yescharacteristic
133C2×C4⋊C8—1222no—
134C22⋊C16—614no—
135C22⋊C16—1222no—
136C61C2×#132311yescharacteristic, complemented, Sylow
137C23×C4—611no—
138C2×M16—611no—
139C2×M16—1221no—
140C2×M16—2442no—
141C2×M16C2×#692311yescharacteristic
142C22×C8—611no—
143C22×C8—612no—
144C22×C8—612no—
145C22×C8—1221no—
146C22×C8—2442no—
147C22×C8C2×#692311yescharacteristic
148#117—611no—
149#117—612no—
150#117—1221no—
151#117—1221no—
152#117C2×#692311yescharacteristic
153C2×C4⋊C4—612no—
154C2×C22⋊C4—1221no—
155C2×C42—1221no—
156C2×C16—1224no—
157C2×C16—2444no—
158C4⋊C8—22no—
159C4⋊C8—1222no—
160C4⋊C8—1222no—
161C4⋊C8—1222no—
162C24—611no—
163C22×C4—611no—
164C22×C4—611no—
165C22×C4—611no—
166C22×C4—611no—
167C22×C4—611no—
168C22×C4—1222no—
169C22×C4—1222no—
170C22×C4—1222no—
171C22×C4C22×#692311yescharacteristic
172M16—41no—
173M16—2442no—
174M16—2441no—
175C2×C8—21no—
176C2×C8—41no—
177C2×C8—612no—
178C2×C8—1224no—
179C2×C8—1221no—
180C2×C8—2442no—
181C2×C8—2442no—
182C2×C8—2441no—
183C2×C8C22⋊#692312yes—
184C4⋊C4—612no—
185C4⋊C4—1222no—
186C4⋊C4D61⋊C812yes—
187C22⋊C4—21no—
188C22⋊C4—1222no—
189C22⋊C4—1221no—
190C42—21no—
191C42—1222no—
192C42—1221no—
193C16—2444no—
194C23—611no—
195C23—611no—
196C23—1222no—
197C23—1224no—
198C23D61⋊M1611yescharacteristic
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—611no—
203C2×C4—612no—
204C2×C4—612no—
205C2×C4—611no—
206C2×C4—1222no—
207C2×C4—1222no—
208C2×C4—1222no—
209C2×C4—1221no—
210C2×C4—1221no—
211C2×C4—1222no—
212C2×C4—2444no—
213C2×C4C2×C22⋊#692311yescharacteristic
214C2×C4C2×D61⋊C811yescharacteristic
215C8—22no—
216C8—41no—
217C8—1222no—
218C8—2441no—
219C22—22no—
220C22—21no—
221C22—614no—
222C22—612no—
223C22—1222no—
224C22—1221no—
225C22—2444no—
226C22D61⋊(C22⋊C8)11yescharacteristic
227C4—21no—
228C4—42no—
229C4—612no—
230C4—1221no—
231C4—2442no—
232C4D61⋊#9911yescharacteristic
233C4D61⋊#10111yescharacteristic
234C2—41no—
235C2—614no—
236C2—2441no—
237C2D61⋊#32411yescharacteristic
238C2D61⋊#35012yes—
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#424C4
socleC22×C61C2×C22⋊C8
prime radicalC23×D61M16
cosocleC22×#92418C23
hypercenter#424#6923
hypocenterC61C2×#1323
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #424

Complements

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

NH ≅ G/Ntype
2. #21460758C2semidirect
3. #21460757C2semidirect
123. D61#1323semidirect
136. C61C2×#1323semidirect

Maximal subgroups

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

subgroupindex
D61⋊(C22⋊C16)2
#214607582
#214607572
#424×D612
C2×#132361