Finite Group Databasebeta

← #30594661

Subgroups — #30594661

Order 15616.

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

normal subgroups only

This group has 250 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
1#21461992C211yesmaximal, characteristic
2#21461063C211yesmaximal, characteristic
3#21444141C211yesmaximal, characteristic
4#16840778—21no—
5C2×C4⋊#92420C411yescharacteristic
6C2×#14519832C411yescharacteristic
7#16840628—21no—
8#16840628—21no—
9#16840608—21no—
10#16840608C412yes—
11C2×#14519742C2211yescharacteristic
12#16839812—21no—
13#16839488C411yescharacteristic
14#16839487—21no—
15C61×#324C411yescharacteristic
16C22×#92420—21no—
17C22×#92420—21no—
18C4⋊#92420—41no—
19C4⋊#92420—41no—
20C22⋊#92420—22no—
21#14519832—41no—
22C4×#92420—41no—
23C22×Dic122Q811yescharacteristic
24#14519742—41no—
25#14519742—41no—
26C2×#11758196C2×C411yescharacteristic
27C2×#11758196D411yescharacteristic
28C2×C4×Dic61C2×C411yescharacteristic
29C2×C4×Dic61D411yescharacteristic
30C2×C4×Dic61D411yescharacteristic
31#14519706—41no—
32C22⋊#92418—21no—
33C8×Dic61—41no—
34C2×C4⋊C4×C61C2×C411yescharacteristic
35C22⋊C8×C61—21no—
36C22×C4×C61C4211yescharacteristic
37C22×C4×C61C22⋊C411yescharacteristic
38C22×C4×C61C4⋊C411yescharacteristic
39C22×Dic61C22⋊C411yescharacteristic
40C22×Dic61C22⋊C411yescharacteristic
41C22×Dic61C4⋊C411yescharacteristic
42C22×Dic61C4⋊C411yescharacteristic
43C2×Dic122—21no—
44C2×Dic122—21no—
45C2×Dic122—22no—
46C2×Dic122—41no—
47C2×#92420—22no—
48C2×#92420—41no—
49C2×#92420—41no—
50C2×#92420—42no—
51C2×#92420—42no—
52C2×#92420—41no—
53C2×C8×C61—41no—
54C4⋊C4×C61—41no—
55#11758196—41no—
56#11758196—41no—
57C4×Dic61—21no—
58C4×Dic61—21no—
59C4×Dic61—21no—
60C4×Dic61—21no—
61C4×Dic61—21no—
62C4×Dic61—21no—
63C2×#92418—41no—
64C23×C61#9511yescharacteristic
65C2×C4×C61—21no—
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—41no—
70C2×C4×C61—41no—
71C2×C4×C61#10811yescharacteristic
72C2×C4×C61#10811yescharacteristic
73C2×Dic61—21no—
74C2×Dic61—21no—
75C2×Dic61—21no—
76C2×Dic61—21no—
77C2×Dic61—21no—
78C2×Dic61—21no—
79C2×Dic61—21no—
80C2×Dic61—21no—
81C2×Dic61—41no—
82C2×Dic61#9911yescharacteristic
83C2×Dic61#9911yescharacteristic
84C2×Dic61#10812yes—
85Dic122—42no—
86Dic122—42no—
87#92420—42no—
88#92420—82no—
89#92420—81no—
90C8×C61—81no—
91#92418—81no—
92#7286—611nomaximal, Sylow
93C22×C61—21no—
94C22×C61—21no—
95C22×C61#34111yescharacteristic
96C22×C61#34111yescharacteristic
97C22×C61#34211yescharacteristic
98C4×C61—21no—
99C4×C61—21no—
100C4×C61—41no—
101C4×C61—41no—
102Dic61—22no—
103Dic61—21no—
104Dic61—41no—
105Dic61—41no—
106Dic61#35511yescharacteristic
107Dic61#35611yescharacteristic
108#1985—611no—
109#1461—611no—
110#1461—611no—
111C2×C61—21no—
112C2×C61—21no—
113C2×C61#129811yescharacteristic
114C2×C61#139111yescharacteristic
115C2×C61#139411yescharacteristic
116C2×C4×Q8—611no—
117#431—1221no—
118#431—1221no—
119C2×C4⋊C8—611no—
120C2×#97—611no—
121#336—1221no—
122#336—1221no—
123#324—612no—
124#324—611no—
125#324—1221no—
126#324—1221no—
127#324#692311yescharacteristic
128C61#728611yescharacteristic, complemented, Sylow
129C22×Q8—611no—
130C22×C8—1221no—
131C22×C8—1221no—
132C4×Q8—2441no—
133C4×Q8—2441no—
134C2×C4⋊C4—611no—
135C2×C4⋊C4—611no—
136C2×C4⋊C4C2×#692311yescharacteristic
137C2×C42—611no—
138C2×C42—611no—
139C2×C42—611no—
140C4⋊C8—2441no—
141C4⋊C8—2441no—
142C4⋊C8—2441no—
143C22⋊C8—21no—
144C22⋊C8—1222no—
145C22⋊C8—1221no—
146#97—2441no—
147C4×C8—2441no—
148C4×C8—2441no—
149C2×Q8—1222no—
150C2×Q8—1221no—
151C2×Q8—1221no—
152C2×Q8—2441no—
153C22×C4—611no—
154C22×C4—611no—
155C22×C4—611no—
156C22×C4—611no—
157C22×C4C4×#692311yescharacteristic
158C22×C4C4⋊#692311yescharacteristic
159C22×C4C22⋊#692311yescharacteristic
160C2×C8—41no—
161C2×C8—1222no—
162C2×C8—2441no—
163C2×C8—2441no—
164C2×C8—2442no—
165C2×C8—2442no—
166C2×C8—2441no—
167C2×C8—2441no—
168C4⋊C4—41no—
169C4⋊C4—2441no—
170C4⋊C4—2441no—
171C42—1221no—
172C42—1221no—
173C42—1221no—
174C42—1221no—
175C42—1221no—
176C42—1221no—
177C23(C2×#6923)⋊C411yescharacteristic
178Q8—2442no—
179Q8—2442no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—611no—
187C2×C4—612no—
188C2×C4—611no—
189C2×C4—1221no—
190C2×C4—1221no—
191C2×C4—1221no—
192C2×C4—1221no—
193C2×C4—1221no—
194C2×C4—1221no—
195C2×C4—1221no—
196C2×C4—1221no—
197C2×C4—2441no—
198C2×C4#1451984711yescharacteristic
199C2×C4#1451984811yescharacteristic
200C8—81no—
201C8—4881no—
202C8—4881no—
203C8—4882no—
204C8—2442no—
205C22—21no—
206C22—21no—
207C22#1684063711yescharacteristic
208C22#1684063811yescharacteristic
209C22#1684063911yescharacteristic
210C4—21no—
211C4—21no—
212C4—41no—
213C4—41no—
214C4—611no—
215C4—611no—
216C4—1221no—
217C4—1222no—
218C4—2441no—
219C4—2441no—
220C2—21no—
221C2—21no—
222C2#2146070211yescharacteristic
223C2#2146090611yescharacteristic
224C2#2146091511yescharacteristic
subgroupG/H
centerC22#16840639
commutatorC22×C4×C61C42
FrattiniC2×C4⋊C4C2×#6923
FittingC61×#324C4
socleC22×C61#342
prime radicalC23×C61#95
cosocleC2×#14519742C22
hypercenter#324#6923
hypocenterC61#7286
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #324

Complements

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

NH ≅ G/Ntype
128. C61#7286semidirect

Maximal subgroups

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

subgroupindex
#214619922
#214610632
#214441412
#728661