Finite Group Databasebeta

← #30594538

Subgroups — #30594538

Order 15616.

244 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 52 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#21461990C211yesmaximal, characteristic
2#21461083C211yesmaximal, characteristic
3#21444161C211yesmaximal, characteristic
4#16840782—21no—
5C2×#14519844C411yescharacteristic
6C2×C4×#92420C411yescharacteristic
7#16840628—21no—
8#16840628—21no—
9#16840608—21no—
10#16840608C412yes—
11C2×#14519742C2211yescharacteristic
12#16839816—21no—
13#16839488C411yescharacteristic
14#16839487—21no—
15C61×#324C411yescharacteristic
16C22×#92420—21no—
17C22×#92420—21no—
18#14519844—41no—
19#14519844—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—
33#14519687—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—22no—
44C2×Dic122—41no—
45C2×Dic122—41no—
46C2×#92420—22no—
47C2×#92420—41no—
48C2×#92420—41no—
49C2×#92420—42no—
50C2×#92420—42no—
51C2×#92420—41no—
52C2×C8×C61—41no—
53C4⋊C4×C61—41no—
54#11758196—41no—
55#11758196—41no—
56C4×Dic61—21no—
57C4×Dic61—21no—
58C4×Dic61—21no—
59C4×Dic61—21no—
60C4×Dic61—21no—
61C4×Dic61—21no—
62C2×#92418—41no—
63C23×C61#9511yescharacteristic
64C2×C4×C61—21no—
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×Dic61—21no—
72C2×Dic61—21no—
73C2×Dic61—21no—
74C2×Dic61—21no—
75C2×Dic61—21no—
76C2×Dic61—21no—
77C2×Dic61—21no—
78C2×Dic61—21no—
79C2×Dic61—41no—
80C2×Dic61#9911yescharacteristic
81C2×Dic61#9911yescharacteristic
82C2×Dic61#10812yes—
83Dic122—44no—
84#92420—42no—
85#92420—82no—
86#92420—81no—
87C8×C61—81no—
88#92418—81no—
89#7248—611nomaximal, Sylow
90C22×C61—21no—
91C22×C61—21no—
92C22×C61#33811yescharacteristic
93C22×C61#34111yescharacteristic
94C22×C61#34211yescharacteristic
95C4×C61—41no—
96C4×C61—41no—
97C4×C61—41no—
98Dic61—22no—
99Dic61—21no—
100Dic61—41no—
101Dic61—41no—
102Dic61#35511yescharacteristic
103Dic61#35611yescharacteristic
104#1984—611no—
105#1467—611no—
106#1467—611no—
107C2×C61—21no—
108C2×C61—21no—
109C2×C61#129311yescharacteristic
110C2×C61#139111yescharacteristic
111C2×C61#139411yescharacteristic
112C2×C4×Q8—611no—
113#432—1221no—
114#432—1221no—
115C2×C4⋊C8—611no—
116C2×C4×C8—611no—
117#336—1221no—
118#336—1221no—
119#324—612no—
120#324—611no—
121#324—1221no—
122#324—1221no—
123#324#692311yescharacteristic
124C61#724811yescharacteristic, complemented, Sylow
125C22×Q8—611no—
126C22×C8—1221no—
127C22×C8—1221no—
128C4×Q8—2441no—
129C4×Q8—2441no—
130C2×C4⋊C4—611no—
131C2×C4⋊C4—611no—
132C2×C4⋊C4C2×#692311yescharacteristic
133C2×C42—611no—
134C2×C42—611no—
135C2×C42—611no—
136C4⋊C8—2441no—
137C4⋊C8—2441no—
138C4⋊C8—2441no—
139C22⋊C8—21no—
140C22⋊C8—1222no—
141C22⋊C8—1221no—
142#97—2441no—
143#97—2441no—
144C4×C8—2441no—
145C2×Q8—1222no—
146C2×Q8—2441no—
147C2×Q8—2441no—
148C22×C4—611no—
149C22×C4—611no—
150C22×C4—611no—
151C22×C4—611no—
152C22×C4C4×#692311yescharacteristic
153C22×C4C4⋊#692311yescharacteristic
154C22×C4C22⋊#692311yescharacteristic
155C2×C8—41no—
156C2×C8—1222no—
157C2×C8—2441no—
158C2×C8—2441no—
159C2×C8—2442no—
160C2×C8—2442no—
161C2×C8—2441no—
162C2×C8—2441no—
163C4⋊C4—41no—
164C4⋊C4—2441no—
165C4⋊C4—2441no—
166C42—1221no—
167C42—1221no—
168C42—1221no—
169C42—1221no—
170C42—1221no—
171C42—1221no—
172C23(C2×#6923)⋊C411yescharacteristic
173Q8—2444no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—611no—
182C2×C4—612no—
183C2×C4—611no—
184C2×C4—1221no—
185C2×C4—1221no—
186C2×C4—1221no—
187C2×C4—1221no—
188C2×C4—1221no—
189C2×C4—1221no—
190C2×C4—1221no—
191C2×C4—1221no—
192C2×C4—2441no—
193C8—81no—
194C8—4881no—
195C8—4881no—
196C8—4882no—
197C8—2442no—
198C22—21no—
199C22—21no—
200C22#1684063111yescharacteristic
201C22#1684063711yescharacteristic
202C22#1684063911yescharacteristic
203C4—41no—
204C4—41no—
205C4—41no—
206C4—611no—
207C4—611no—
208C4—1221no—
209C4—1222no—
210C4—2441no—
211C4—2441no—
212C2—21no—
213C2—21no—
214C2#2146069011yescharacteristic
215C2#2146090611yescharacteristic
216C2#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#7248
LCSG ▷ C22×C4×C61 ▷ C22×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
124. C61#7248semidirect

Maximal subgroups

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

subgroupindex
#214619902
#214610832
#214441612
#724861