Finite Group Databasebeta

← #30594492

Subgroups — #30594492

Order 15616.

270 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 62 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#21461698C211yesmaximal, characteristic
3#21445856C211yesmaximal, characteristic
4C2×D61⋊C16C412yes—
5C2×#14519847—21no—
6#16840733—21no—
7#16840657—21no—
8C22⋊#11758187—21no—
9#16840638C412yes—
10C22×C8×D61C2211yescharacteristic
11C2×#14519712—21no—
12#16839725—21no—
13#16839527C411yescharacteristic
14C61×#341C411yescharacteristic
15C2×#11758213—22no—
16D61⋊C16—42no—
17C2×#11758187—22no—
18#14519847—42no—
19#14519834—41no—
20C22⋊#92420—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×D61Q1611yescharacteristic
35C22×C4×C61C22⋊C411yescharacteristic
36C22×Dic61SD1611yescharacteristic
37C2×C4×D61—41no—
38C2×C4×D61—41no—
39C2×C4×D61C22⋊C411yescharacteristic
40C2×C4×D61C4⋊C411yescharacteristic
41C2×C4×D61D811yescharacteristic
42C2×C4×D61SD1611yescharacteristic
43C2×#92420—42no—
44#11758213—42no—
45#11758213—42no—
46M16×C61—41no—
47M16×C61—41no—
48C2×C8×C61—41no—
49C2×C8×C61—41no—
50C2×C8×C61C4211yescharacteristic
51C2×C8×C61C4⋊C411yescharacteristic
52#11758194—41no—
53#11758194—41no—
54C2×#92418—22no—
55C2×#92418—41no—
56C2×#92418C22⋊C411yescharacteristic
57C2×#92418C4⋊C411yescharacteristic
58C8×D61—22no—
59C8×D61—22no—
60C8×D61—41no—
61C8×D61—41no—
62#11758187—42no—
63C23×C61#10311yescharacteristic
64C22×D61—22no—
65C22×D61—41no—
66C22×D61—41no—
67C22×D61#10311yescharacteristic
68C22×D61#10711yescharacteristic
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61#9511yescharacteristic
72C2×C4×C61#10211yescharacteristic
73C2×Dic61—41no—
74C2×Dic61#10211yescharacteristic
75C2×Dic61#10611yescharacteristic
76C4×D61—21no—
77C4×D61—21no—
78C4×D61—21no—
79C4×D61—21no—
80C4×D61—41no—
81C4×D61—41no—
82#92420—82no—
83C8×C61—21no—
84C8×C61—21no—
85C8×C61—81no—
86#92418—21no—
87#92418—81no—
88#92418#9912yes—
89#7231—611nomaximal, Sylow
90C22×C61—21no—
91C22×C61—21no—
92C22×C61—21no—
93C22×C61#34011yescharacteristic
94C2×D61—21no—
95C2×D61—21no—
96C2×D61—21no—
97C2×D61—21no—
98C2×D61—21no—
99C2×D61—44no—
100C2×D61#36812yes—
101C4×C61—21no—
102C4×C61H(3,ℤ/4)11yescharacteristic
103C4×C61#34211yescharacteristic
104Dic61—21no—
105Dic61—21no—
106C2×C22⋊C16—611no—
107#1810—611no—
108#1810—611no—
109C2×C61—41no—
110C2×C61#128911yescharacteristic
111C2×C61#138111yescharacteristic
112C2×C61#138511yescharacteristic
113D61—22no—
114D61—41no—
115C23×C8—611no—
116C22×C16—612no—
117C2×#108—1221no—
118C2×#108—1221no—
119#407—1221no—
120#407—1221no—
121C22⋊C16—1221no—
122C22⋊C16—1221no—
123#341—612no—
124#341—611no—
125#341#692311yescharacteristic
126C61#723111yescharacteristic, complemented, Sylow
127C23×C4—611no—
128C2×M16—21no—
129C2×M16—1222no—
130C2×M16—1221no—
131C22×C8—611no—
132C22×C8—611no—
133C22×C8—611no—
134C22×C8—611no—
135C22×C8—611no—
136C22×C8—2442no—
137C22×C8C2×#692311yescharacteristic
138C2×C16—1222no—
139C2×C16—2442no—
140#108—2442no—
141#108—2442no—
142C22⋊C8—2441no—
143C22⋊C8—2441no—
144C22⋊C8—2441no—
145C22⋊C8—2441no—
146C24—611no—
147C22×C4—611no—
148C22×C4—611no—
149C22×C4—611no—
150C22×C4—611no—
151C22×C4—611no—
152C22×C4—2441no—
153C22×C4—2441no—
154C22×C4C22⋊#692311yescharacteristic
155M16—41no—
156M16—41no—
157M16—2441no—
158M16—2441no—
159M16—2442no—
160M16—2442no—
161C2×C8—41no—
162C2×C8—41no—
163C2×C8—611no—
164C2×C8—611no—
165C2×C8—1222no—
166C2×C8—1222no—
167C2×C8—1222no—
168C2×C8—2441no—
169C2×C8—2441no—
170C2×C8—2442no—
171C2×C8—2441no—
172C2×C8C4×#692311yescharacteristic
173C2×C8C4⋊#692311yescharacteristic
174C16—2442no—
175C23—611no—
176C23—611no—
177C23—1222no—
178C23—2441no—
179C23—2441no—
180C23#1451984011yescharacteristic
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—611no—
184C2×C4—611no—
185C2×C4—1221no—
186C2×C4—1221no—
187C2×C4—1221no—
188C2×C4—1221no—
189C2×C4—2441no—
190C2×C4—2441no—
191C2×C4—2441no—
192C2×C4(C2×#6923)⋊C411yescharacteristic
193C2×C4#1451983911yescharacteristic
194C8—21no—
195C8—21no—
196C8—81no—
197C8—612no—
198C8—1221no—
199C8—4881no—
200C8—4882no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—612no—
205C22—1221no—
206C22—1221no—
207C22—1221no—
208C22—1221no—
209C22—1221no—
210C22—2444no—
211C22#1684063511yescharacteristic
212C4—21no—
213C4—1221no—
214C4—1221no—
215C4#1684062911yescharacteristic
216C4#1684063911yescharacteristic
217C2—41no—
218C2—1222no—
219C2—2441no—
220C2#2146068111yescharacteristic
221C2#2146087811yescharacteristic
222C2#2146088811yescharacteristic
subgroupG/H
centerC22#16840635
commutatorC2×C8×C61C42
FrattiniC22×C8C2×#6923
FittingC61×#341C4
socleC22×C61#340
prime radicalC23×D61Q16
cosocleC22×C8×D61C22
hypercenter#341#6923
hypocenterC61#7231
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
126. C61#7231semidirect

Maximal subgroups

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

subgroupindex
D61⋊(C22⋊C16)2
#214616982
#214458562
#723161