Finite Group Databasebeta

← #30608375

Subgroups — #30608375

Order 15616.

398 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 56 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, complemented
2#21460957C212yesmaximal, complemented
3#21460954C212yesmaximal, complemented
4#21456273C211yesmaximal, characteristic
5D61⋊#101—22no—
6#16840673C2214yes—
7#16840672—22no—
8C2×#14519806—22no—
9#16840310C411yescharacteristic
10C4⋊Q8×D61C2211yescharacteristic
11#16840153—22no—
12#16840142C2211yescharacteristic
13#16840141C411yescharacteristic
14#16840134C2211yescharacteristic
15C4×#11758189C411yescharacteristic
16C61×#492C411yescharacteristic
17D61⋊M16—42no—
18#14519838—24no—
19#14519838—42no—
20C2×#11758224—21no—
21C2×Q8×D61D412yes—
22#14519806—44no—
23#14519806—44no—
24C2×Dic244—22no—
25C2×#11758202—22no—
26C2×#11758200—22no—
27C2×#11758189—21no—
28#14519777C2×C411yescharacteristic
29#14519777C2311yescharacteristic
30#14519776—41no—
31#14519775D412yes—
32#14519764—21no—
33#14519748—41no—
34D4×Dic61—41no—
35C4⋊C4×D61—41no—
36C42×D61C2×C411yescharacteristic
37#14519687—21no—
38C4×#92418C2×C411yescharacteristic
39C2×SD16×C61—22no—
40C4⋊Q8×C61C2×C411yescharacteristic
41#127×C61C2×C411yescharacteristic
42C4×C8×C61C2×C411yescharacteristic
43C2×Q8×C61C22⋊C412yes—
44C2×D4×C61—21no—
45C2×D4×C61—41no—
46C2×C22⋊D61—41no—
47C22×Dic61—41no—
48Q8×D61—42no—
49Q8×D61—42no—
50#11758224—42no—
51#11758224—42no—
52C2×C4×D61—22no—
53C2×C4×D61—21no—
54C2×C4×D61C22⋊C411yescharacteristic
55C2×Dic122—21no—
56C2×Dic122—22no—
57C2×Dic122C2×D412yes—
58#11758217—44no—
59#11758213—82no—
60D61⋊C8—82no—
61SD16×C61—44no—
62C2×C8×C61—21no—
63C4⋊C4×C61—41no—
64C42×C61C22×C411yescharacteristic
65C22⋊Dic61—42no—
66#11758202—44no—
67#11758200—44no—
68C4⋊Dic61—41no—
69C4⋊Dic61—41no—
70#11758196—42no—
71C4×Dic61—21no—
72C4×Dic61C22⋊C411yescharacteristic
73C2×#92418—21no—
74Dic244—44no—
75#11758189—24no—
76C23×C61—41no—
77C22×D61#9911yescharacteristic
78Q8×C61—42no—
79D4×C61—42no—
80D4×C61—82no—
81C2×C4×C61—21no—
82C2×C4×C61—22no—
83C2×C4×C61C2×C22⋊C411yescharacteristic
84C22⋊D61—82no—
85C2×Dic61—21no—
86C2×Dic61—22no—
87C2×Dic61—41no—
88C2×Dic61—81no—
89C2×Dic61—81no—
90C2×Dic61#9911yescharacteristic
91C4×D61—22no—
92C4×D61—42no—
93C4×D61—42no—
94C4×D61—42no—
95Dic122—42no—
96Dic122—42no—
97Dic122—82no—
98#92420—84no—
99C8×C61—22no—
100#92418—22no—
101#13590—611nomaximal, Sylow
102C22×C61—82no—
103C22×C61—81no—
104C22×C61C2×#9911yescharacteristic
105C2×D61—41no—
106C2×D61#35312yes—
107C4×C61—22no—
108C4×C61—21no—
109C4×C61—42no—
110Dic61—21no—
111Dic61—41no—
112Dic61—42no—
113Dic61—81no—
114#3152—611no—
115C2×#356—612no—
116#1411—612no—
117#1410—612no—
118C2×C61—21no—
119C2×C61—161no—
120C2×C61C2×#35311yescharacteristic
121D61—22no—
122C2×#137—1222no—
123#532—611no—
124C2×C4⋊Q8—611no—
125#497—1222no—
126#494—611no—
127#494—611no—
128#492—611no—
129#492#692311yescharacteristic
130C2×#101—1222no—
131C4×M16—611no—
132#356—614no—
133#356—1222no—
134C61#1359011yescharacteristic, complemented, Sylow
135C2×#41—1221no—
136C22×Q8—612no—
137#137—2444no—
138#137—2444no—
139C2×Q16—1222no—
140C2×Q16—1222no—
141C2×SD16—22no—
142C2×SD16—1222no—
143C2×M16—1221no—
144C2×M16—2442no—
145C4⋊Q8—612no—
146C4⋊Q8—611no—
147C4⋊Q8—611no—
148C4⋊Q8—2441no—
149C4⋊Q8C2×#692311yescharacteristic
150#127C2×#692311yescharacteristic
151#124—1221no—
152#121—2441no—
153C4×D4—2441no—
154C2×C4⋊C4—2441no—
155C2×C42—611no—
156#101—1224no—
157#101—2442no—
158#97—1221no—
159C4×C8—611no—
160C4×C8C2×#692311yescharacteristic
161#41—2442no—
162#41—2442no—
163C2×Q8—612no—
164C2×Q8—1222no—
165C2×Q8—1221no—
166C2×Q8—2442no—
167C2×Q8—2442no—
168C2×Q8C22⋊#692312yes—
169C2×D4—21no—
170C2×D4—41no—
171C2×D4—2441no—
172C22×C4—611no—
173C22×C4—1221no—
174C22×C4—1222no—
175C22×C4—2441no—
176Q16—2444no—
177Q16—2444no—
178SD16—44no—
179SD16—2444no—
180M16—1224no—
181M16—4882no—
182M16—2444no—
183C2×C8—21no—
184C2×C8—1221no—
185C2×C8—4882no—
186C4⋊C4—41no—
187C4⋊C4—2442no—
188C4⋊C4—2441no—
189C4⋊C4—2441no—
190C22⋊C4—2442no—
191C42—611no—
192C42—1221no—
193C42C22×#692311yescharacteristic
194C23—41no—
195C23—611no—
196Q8—42no—
197Q8—4882no—
198Q8—2442no—
199Q8—2442no—
200D4—42no—
201D4—82no—
202D4—4882no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—611no—
206C2×C4—1222no—
207C2×C4—1221no—
208C2×C4—1222no—
209C2×C4—4881no—
210C2×C4—4881no—
211C2×C4—2442no—
212C2×C4—2442no—
213C2×C4—2442no—
214C2×C4—2441no—
215C2×C4C2×C22⋊#692311yescharacteristic
216C8—22no—
217C8—1222no—
218C8—4884no—
219C22—82no—
220C22—81no—
221C22—612no—
222C22—2441no—
223C22D61⋊#9911yescharacteristic
224C4—22no—
225C4—21no—
226C4—42no—
227C4—1221no—
228C4—4881no—
229C4—2441no—
230C4—2442no—
231C2—21no—
232C2—161no—
233C2—1222no—
234C2D61⋊#35311yescharacteristic
subgroupG/H
centerC2D61⋊#353
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#492C4
socleC2×C61C2×#353
prime radical#16840310C4
cosocle#14519777C23
hypercenter#492#6923
hypocenterC61#13590
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #492

Complements

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

NH ≅ G/Ntype
1. D61⋊#356C2semidirect
2. #21460957C2semidirect
3. #21460954C2semidirect
134. C61#13590semidirect

Maximal subgroups

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

subgroupindex
D61⋊#3562
#214609572
#214609542
#214562732
#1359061