Finite Group Databasebeta

← D61⋊#1411 #30608368

Subgroups — D61⋊#1411 #30608368

Order 15616.

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

normal subgroups only

This group has 398 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#21460957C212yesmaximal, complemented
3#21460956C212yesmaximal, complemented
4#494×D61C211yesmaximal, characteristic
5D61⋊#101—22no—
6#16840673C2214yes—
7#16840672—22no—
8C2×Q16×D61—22no—
9C4⋊Q8×D61C411yescharacteristic
10C4⋊Q8×D61C2211yescharacteristic
11#16840142C2211yescharacteristic
12#16840141C411yescharacteristic
13#16840141C2211yescharacteristic
14#16840140—22no—
15C4×C8×D61C411yescharacteristic
16C61×#494C411yescharacteristic
17D61⋊M16—42no—
18#14519838—24no—
19#14519838—42no—
20C2×Q8×D61—21no—
21C2×Q8×D61D412yes—
22C2×Dic244—22no—
23C2×#11758202—22no—
24C2×#11758202—22no—
25Q16×D61—44no—
26Q16×D61—44no—
27C2×C8×D61—21no—
28#14519777C2×C411yescharacteristic
29#14519777C2311yescharacteristic
30#14519776—41no—
31#14519776—41no—
32#14519775—21no—
33#14519775D412yes—
34C4⋊C4×D61—41no—
35C4⋊C4×D61—41no—
36C42×D61C2×C411yescharacteristic
37C4×#92418C2×C411yescharacteristic
38C8×Dic61—21no—
39C2×Q16×C61—22no—
40C4⋊Q8×C61C2×C411yescharacteristic
41C4⋊Q8×C61C2×C411yescharacteristic
42C4×C8×C61C2×C411yescharacteristic
43C2×Q8×C61—21no—
44C2×Q8×C61C22⋊C412yes—
45Q8×D61—42no—
46Q8×D61—42no—
47Q8×D61—42no—
48Q8×D61—42no—
49C2×C4×D61—21no—
50C2×C4×D61—22no—
51C2×C4×D61—41no—
52C2×C4×D61C22⋊C411yescharacteristic
53C2×Dic122—21no—
54C2×Dic122—22no—
55C2×Dic122—41no—
56C2×Dic122C2×D412yes—
57#11758217—44no—
58#11758213—82no—
59D61⋊C8—82no—
60Q16×C61—44no—
61C2×C8×C61—21no—
62C4⋊C4×C61—41no—
63C4⋊C4×C61—41no—
64C42×C61C22×C411yescharacteristic
65#11758202—44no—
66#11758202—44no—
67C4⋊Dic61—41no—
68C4⋊Dic61—41no—
69#11758196—42no—
70#11758196—42no—
71C4×Dic61—21no—
72C4×Dic61C22⋊C411yescharacteristic
73C2×#92418—21no—
74Dic244—44no—
75C8×D61—22no—
76C8×D61—22no—
77C22×D61#9911yescharacteristic
78Q8×C61—42no—
79Q8×C61—42no—
80C2×C4×C61—21no—
81C2×C4×C61—22no—
82C2×C4×C61—41no—
83C2×C4×C61C2×C22⋊C411yescharacteristic
84C2×Dic61—21no—
85C2×Dic61—22no—
86C2×Dic61—41no—
87C2×Dic61#9911yescharacteristic
88C4×D61—24no—
89C4×D61—21no—
90C4×D61—21no—
91C4×D61—42no—
92C4×D61—42no—
93C4×D61—81no—
94C4×D61—81no—
95Dic122—42no—
96Dic122—42no—
97Dic122—82no—
98Dic122—82no—
99#92420—84no—
100C8×C61—22no—
101#92418—22no—
102C2×#1411—611nomaximal, Sylow
103C22×C61C2×#9911yescharacteristic
104C2×D61—22no—
105C2×D61#35311yescharacteristic
106C2×D61#35311yescharacteristic
107C4×C61—22no—
108C4×C61—21no—
109C4×C61—42no—
110C4×C61—81no—
111Dic61—22no—
112Dic61—21no—
113Dic61—42no—
114Dic61—81no—
115C2×#494—611no—
116C2×#356—612no—
117#1411—612no—
118#1411—612no—
119C2×C61—21no—
120C2×C61C2×#35311yescharacteristic
121D61—21no—
122D61#141112yescomplemented
123C22×Q16—1222no—
124C2×C4⋊Q8—611no—
125C2×C4⋊Q8—611no—
126#494—611no—
127#494—611no—
128#494—611no—
129#494—1222no—
130#494#692311yescharacteristic
131C2×#101—1222no—
132C2×C4×C8—611no—
133#356—614no—
134#356—1222no—
135C61C2×#141111yescharacteristic, complemented, Sylow
136C22×Q8—612no—
137C22×Q8—1221no—
138C2×Q16—22no—
139C2×Q16—1222no—
140C2×Q16—1222no—
141C2×Q16—1222no—
142C2×Q16—2444no—
143C2×Q16—2444no—
144C2×M16—2442no—
145C22×C8—1221no—
146C4⋊Q8—612no—
147C4⋊Q8—611no—
148C4⋊Q8—611no—
149C4⋊Q8—1221no—
150C4⋊Q8—2441no—
151C4⋊Q8—2441no—
152C4⋊Q8C2×#692311yescharacteristic
153C4⋊Q8C2×#692311yescharacteristic
154C2×C4⋊C4—2441no—
155C2×C4⋊C4—2441no—
156C2×C42—611no—
157#101—1224no—
158#101—2442no—
159C4×C8—611no—
160C4×C8—1221no—
161C4×C8C2×#692311yescharacteristic
162C2×Q8—21no—
163C2×Q8—612no—
164C2×Q8—1222no—
165C2×Q8—1221no—
166C2×Q8—2441no—
167C2×Q8—2442no—
168C2×Q8—2442no—
169C2×Q8—2442no—
170C2×Q8—2442no—
171C2×Q8C22⋊#692312yes—
172C22×C4—611no—
173C22×C4—1221no—
174C22×C4—1222no—
175C22×C4—2441no—
176Q16—44no—
177Q16—2444no—
178Q16—2444no—
179Q16—2444no—
180M16—4882no—
181M16—2444no—
182C2×C8—21no—
183C2×C8—1222no—
184C2×C8—1222no—
185C2×C8—1221no—
186C2×C8—4882no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—2442no—
190C4⋊C4—2441no—
191C4⋊C4—2441no—
192C4⋊C4—2442no—
193C42—611no—
194C42—1221no—
195C42C22×#692311yescharacteristic
196C23—611no—
197Q8—42no—
198Q8—42no—
199Q8—4882no—
200Q8—4882no—
201Q8—2442no—
202Q8—2442no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—41no—
206C2×C4—611no—
207C2×C4—1221no—
208C2×C4—1221no—
209C2×C4—1224no—
210C2×C4—1221no—
211C2×C4—1222no—
212C2×C4—4881no—
213C2×C4—4881no—
214C2×C4—2442no—
215C2×C4—2442no—
216C2×C4—2441no—
217C2×C4C2×C22⋊#692311yescharacteristic
218C8—22no—
219C8—1222no—
220C8—4884no—
221C22—611no—
222C22—611no—
223C22—1222no—
224C22D61⋊#9911yescharacteristic
225C4—22no—
226C4—21no—
227C4—42no—
228C4—81no—
229C4—1222no—
230C4—1221no—
231C4—4881no—
232C4—2442no—
233C2—21no—
234C2—612no—
235C2—1221no—
236C2D61⋊#35311yescharacteristic
subgroupG/H
centerC2D61⋊#353
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#494C4
socleC2×C61C2×#353
prime radicalC22×D61#99
cosocle#14519777C23
hypercenter#494#6923
hypocenterC61C2×#1411
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #494

Complements

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

NH ≅ G/Ntype
2. #21460957C2semidirect
3. #21460956C2semidirect
122. D61#1411semidirect
135. C61C2×#1411semidirect

Maximal subgroups

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

subgroupindex
D61⋊#3562
#214609572
#214609562
#494×D612
C2×#141161