Finite Group Databasebeta

← #30594496

Subgroups — #30594496

Order 15616.

292 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 64 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)C211yesmaximal, characteristic
2#21461695C211yesmaximal, characteristic
3#21445856C211yesmaximal, characteristic
4C2×D61⋊C16C412yescomplemented
5C2×#14519845—21no—
6#16840704—21no—
7#16840657—21no—
8C22⋊#11758187—21no—
9#16840636C412yes—
10C22×C8×D61C2211yescharacteristic
11C2×#14519712—21no—
12#16839725—21no—
13#16839527C411yescharacteristic, complemented
14C61×#341C411yescharacteristic, complemented
15C2×C4⋊#6923—22no—
16C2×C22⋊#6923—41no—
17D61⋊C16—42no—
18C2×#11758187—22no—
19#14519845—42no—
20(C2×#6923)⋊C4—41no—
21C22×C4×D61D411yescharacteristic
22C2×#11758194—21no—
23C22×#92418D411yescharacteristic
24C2×C8×D61—42no—
25C2×C8×D61C2×C411yescharacteristic
26C2×C8×D61C2×C411yescharacteristic
27C2×C8×D61D411yescharacteristic
28C2×C8×D61Q811yescharacteristic
29#14519712—42no—
30#14519689—41no—
31#14519689—41no—
32C2×M16×C61—21no—
33C22×C8×C61C2×C411yescharacteristic
34C23×D61SD1611yescharacteristic
35C22×#6923—42no—
36C22×C4×C61C22⋊C411yescharacteristic
37C22×Dic61Q1611yescharacteristic
38C2×C4×D61—41no—
39C2×C4×D61—41no—
40C2×C4×D61C22⋊C411yescharacteristic
41C2×C4×D61C4⋊C411yescharacteristic
42C2×C4×D61D811yescharacteristic
43C2×C4×D61SD1611yescharacteristic
44C22⋊#6923—82no—
45C4⋊#6923—42no—
46C4⋊#6923—42no—
47M16×C61—41no—
48M16×C61—41no—
49C2×C8×C61—41no—
50C2×C8×C61—41no—
51C2×C8×C61C4211yescharacteristic
52C2×C8×C61C4⋊C411yescharacteristic
53#11758194—41no—
54#11758194—41no—
55C2×#92418—22no—
56C2×#92418—41no—
57C2×#92418C22⋊C411yescharacteristic
58C2×#92418C4⋊C411yescharacteristic
59C8×D61—22no—
60C8×D61—22no—
61C8×D61—41no—
62C8×D61—41no—
63#11758187—42no—
64C23×C61#10311yescharacteristic
65C22×D61—22no—
66C22×D61—22no—
67C22×D61—41no—
68C22×D61#10211yescharacteristic
69C22×D61#10611yescharacteristic
70C2×#6923—82no—
71C2×#6923—82no—
72C2×#6923—82no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61#9511yescharacteristic
76C2×C4×C61#10211yescharacteristic
77C2×Dic61—41no—
78C2×Dic61#10311yescharacteristic
79C2×Dic61#10711yescharacteristic
80C4×D61—21no—
81C4×D61—21no—
82C4×D61—21no—
83C4×D61—21no—
84C4×D61—41no—
85C4×D61—41no—
86C8×C61—21no—
87C8×C61—21no—
88C8×C61—81no—
89#92418—21no—
90#92418—81no—
91#92418#9912yes—
92#7232—611nomaximal, Sylow
93C22×C61—21no—
94C22×C61—21no—
95C22×C61—21no—
96C22×C61#34011yescharacteristic
97C2×D61—21no—
98C2×D61—21no—
99C2×D61—21no—
100C2×D61—21no—
101C2×D61—44no—
102C2×D61#35912yes—
103C2×D61#36512yes—
104#6923—162no—
105C4×C61—21no—
106C4×C61H(3,ℤ/4)11yescharacteristic
107C4×C61#34211yescharacteristic
108Dic61—21no—
109Dic61—21no—
110C2×C22⋊C16—611no—
111#1810—611no—
112#1807—611no—
113C2×C61—41no—
114C2×C61#128911yescharacteristic
115C2×C61#138211yescharacteristic
116C2×C61#138311yescharacteristic
117D61—22no—
118D61—22no—
119C23×C8—611no—
120C22×C16—612no—
121C2×#108—1221no—
122C2×#106—1221no—
123#407—1221no—
124#380—1221no—
125C22⋊C16—1221no—
126C22⋊C16—1221no—
127#341—611no—
128#341#692311yescharacteristic, complemented
129#340—612no—
130C61#723211yescharacteristic, complemented, Sylow
131C23×C4—611no—
132C2×M16—21no—
133C2×M16—1221no—
134C22×C8—611no—
135C22×C8—611no—
136C22×C8—611no—
137C22×C8—611no—
138C22×C8—611no—
139C22×C8—2442no—
140C22×C8C2×#692311yescharacteristic
141C2×C4⋊C4—1222no—
142C2×C22⋊C4—2441no—
143C2×C16—1222no—
144C2×C16—2442no—
145#108—2442no—
146#106—2442no—
147C22⋊C8—2441no—
148C22⋊C8—2441no—
149#95—2441no—
150C24—611no—
151C22×C4—611no—
152C22×C4—611no—
153C22×C4—611no—
154C22×C4—611no—
155C22×C4—611no—
156C22×C4—2441no—
157C22×C4—2441no—
158C22×C4—2442no—
159C22×C4C22⋊#692311yescharacteristic
160M16—41no—
161M16—41no—
162M16—2441no—
163M16—2441no—
164C2×C8—41no—
165C2×C8—41no—
166C2×C8—611no—
167C2×C8—611no—
168C2×C8—1222no—
169C2×C8—1222no—
170C2×C8—1222no—
171C2×C8—2441no—
172C2×C8—2441no—
173C2×C8—2441no—
174C2×C8C4×#692311yescharacteristic
175C2×C8C4⋊#692311yescharacteristic
176C4⋊C4—2442no—
177C4⋊C4—2442no—
178C22⋊C4—4882no—
179C16—2442no—
180C23—611no—
181C23—611no—
182C23—1222no—
183C23—1222no—
184C23—2441no—
185C23#1451984011yescharacteristic
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—611no—
189C2×C4—611no—
190C2×C4—1221no—
191C2×C4—1221no—
192C2×C4—1221no—
193C2×C4—1221no—
194C2×C4—4882no—
195C2×C4—4882no—
196C2×C4—4882no—
197C2×C4—2441no—
198C2×C4—2441no—
199C2×C4—2441no—
200C2×C4(C2×#6923)⋊C411yescharacteristic
201C2×C4#1451983911yescharacteristic
202C8—21no—
203C8—21no—
204C8—81no—
205C8—612no—
206C8—1221no—
207C8—4881no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—612no—
212C22—612no—
213C22—1221no—
214C22—1221no—
215C22—1221no—
216C22—1221no—
217C22—2444no—
218C22#1684063511yescharacteristic
219C4—21no—
220C4—1221no—
221C4—1221no—
222C4—9762no—
223C4#1684062911yescharacteristic
224C4#1684063911yescharacteristic
225C2—41no—
226C2—1222no—
227C2—1222no—
228C2#2146068111yescharacteristic
229C2#2146088211yescharacteristic
230C2#2146088511yescharacteristic
subgroupG/H
centerC22#16840635
commutatorC2×C8×C61C42
FrattiniC22×C8C2×#6923
FittingC61×#341C4
socleC22×C61#340
prime radicalC23×D61SD16
cosocleC22×C8×D61C22
hypercenter#341#6923
hypocenterC61#7232
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #341

Complements

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

NH ≅ G/Ntype
4. C2×D61⋊C16C4semidirect
13. #16839527C4semidirect
14. C61×#341C4semidirect
128. #341#6923semidirect
130. C61#7232semidirect

Maximal subgroups

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

subgroupindex
D61⋊(C22⋊C16)2
#214616952
#214458562
#723261