Finite Group Databasebeta

← #30595901

Subgroups — #30595901

Order 15616.

388 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 98 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#21461747C211yesmaximal, characteristic
2#21461735C211yesmaximal, characteristic
3#21460637C214yesmaximal
4#21454180C211yesmaximal, characteristic
5C2×#14519844—21no—
6#16840628—21no—
7#16840628—21no—
8#16840628—21no—
9#16840628C2212yes—
10#16840628C2212yes—
11C2×#14519768—21no—
12#16839661—21no—
13#16839661C2212yes—
14#16839658—21no—
15#16839658C412yes—
16#16839632C411yescharacteristic
17#16839627—21no—
18C42×Dic61C2211yescharacteristic
19C61×#384C411yescharacteristic
20C22×#92420—22no—
21C22×#92420—22no—
22#14519844—42no—
23#14519768—44no—
24C2×C4⋊Dic61—21no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61—22no—
27C2×C4⋊Dic61C2×C412yes—
28C2×#11758196—22no—
29C2×C4×Dic61C2×C411yescharacteristic
30C2×C4×Dic61D411yescharacteristic
31C2×C4×Dic61D411yescharacteristic
32C2×C4×Dic61D411yescharacteristic
33C2×C4×Dic61D411yescharacteristic
34C2×C4×Dic61C2311yescharacteristic
35#14519684—22no—
36#14519684—22no—
37C2×C4⋊C4×C61—21no—
38C2×C4⋊C4×C61—21no—
39C2×C4⋊C4×C61C2×C412yes—
40C2×C42×C61C2×C411yescharacteristic
41C22×C4×C61—22no—
42C22×C4×C61C22⋊C411yescharacteristic
43C22×C4×C61C22⋊C411yescharacteristic
44C22×C4×C61C22×C411yescharacteristic
45C22×Dic61—22no—
46C22×Dic61C22⋊C411yescharacteristic
47C22×Dic61C22⋊C411yescharacteristic
48C22×Dic61C2×D411yescharacteristic
49C22×Dic61C2×D411yescharacteristic
50C2×#92420—42no—
51C2×#92420—42no—
52C2×#92420—42no—
53C2×#92420—42no—
54C2×#92420—42no—
55C2×#92420—42no—
56C4⋊C4×C61—24no—
57C4⋊C4×C61—42no—
58C4⋊C4×C61—42no—
59C42×C61—22no—
60C4⋊Dic61—42no—
61C4⋊Dic61—42no—
62C4⋊Dic61—44no—
63C4⋊Dic61—42no—
64#11758196—44no—
65C4×Dic61—22no—
66C4×Dic61—22no—
67C4×Dic61—41no—
68C4×Dic61—41no—
69C4×Dic61—41no—
70C4×Dic61SD1612yes—
71C4×Dic61Q1612yes—
72C23×C61C2×C22⋊C411yescharacteristic
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—42no—
80C2×C4×C61—42no—
81C2×C4×C61—42no—
82C2×C4×C61#10112yes—
83C2×C4×C61#10312yes—
84C2×C4×C61#13112yes—
85C2×Dic61—21no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61—21no—
91C2×Dic61—21no—
92C2×Dic61—21no—
93C2×Dic61—21no—
94C2×Dic61—42no—
95C2×Dic61—42no—
96C2×Dic61—42no—
97C2×Dic61#10312yes—
98C2×Dic61C2×SD1611yescharacteristic
99C2×Dic61C2×Q1611yescharacteristic
100C2×Dic61AGL(1,ℤ/8)12yes—
101#92420—82no—
102#92420—82no—
103#7720—611nomaximal, Sylow
104C22×C61#40811yescharacteristic
105C22×C61#41011yescharacteristic
106C22×C61C2×#10111yescharacteristic
107C22×C61C2×#10311yescharacteristic
108C22×C61#41811yescharacteristic
109C22×C61#42111yescharacteristic
110C22×C61#42111yescharacteristic
111C4×C61—22no—
112C4×C61—22no—
113C4×C61—22no—
114C4×C61—82no—
115Dic61—22no—
116Dic61—22no—
117Dic61—21no—
118Dic61—21no—
119Dic61—41no—
120Dic61—82no—
121#2859—611no—
122#1839—611no—
123#1831—611no—
124#1271—614no—
125C2×C61#147011yescharacteristic
126C2×C61#148111yescharacteristic
127C2×C61#149611yescharacteristic
128C2×C61#151411yescharacteristic
129C2×C61#151811yescharacteristic
130C2×C61#153411yescharacteristic
131C2×C61#154911yescharacteristic
132C2×#125—1221no—
133C2×C4⋊C8—1221no—
134#389—612no—
135#389—612no—
136#389—1221no—
137#389—1221no—
138#384—611no—
139#384#692311yescharacteristic
140#382—1221no—
141C43—611no—
142#336—612no—
143#336—612no—
144#336—1221no—
145#336—1221no—
146#336—1221no—
147C61#772011yescharacteristic, complemented, Sylow
148C22×C8—1222no—
149C22×C8—1222no—
150#125—2444no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—612no—
154C2×C4⋊C4—1222no—
155C2×C4⋊C4—1222no—
156C2×C4⋊C4—1221no—
157C2×C4⋊C4—1221no—
158C2×C4⋊C4C2×#692312yes—
159C2×C42—611no—
160C2×C42—611no—
161C2×C42—611no—
162C2×C42—611no—
163C2×C42—611no—
164C2×C42—611no—
165C2×C42C2×#692311yescharacteristic
166C4⋊C8—2442no—
167#95—1222no—
168#95—1222no—
169C22×C4—22no—
170C22×C4—611no—
171C22×C4—611no—
172C22×C4—611no—
173C22×C4—611no—
174C22×C4—1222no—
175C22×C4C22⋊#692311yescharacteristic
176C22×C4C22⋊#692311yescharacteristic
177C22×C4C22×#692311yescharacteristic
178C2×C8—2442no—
179C2×C8—2442no—
180C2×C8—2442no—
181C2×C8—2442no—
182C2×C8—2442no—
183C2×C8—2442no—
184C4⋊C4—24no—
185C4⋊C4—42no—
186C4⋊C4—42no—
187C4⋊C4—2442no—
188C4⋊C4—2442no—
189C4⋊C4—2442no—
190C4⋊C4—2444no—
191C4⋊C4—2444no—
192C42—22no—
193C42—612no—
194C42—612no—
195C42—1222no—
196C42—1222no—
197C42—2441no—
198C42—2441no—
199C42—2441no—
200C23C2×C22⋊#692311yescharacteristic
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—612no—
211C2×C4—611no—
212C2×C4—611no—
213C2×C4—612no—
214C2×C4—1221no—
215C2×C4—1221no—
216C2×C4—1221no—
217C2×C4—1221no—
218C2×C4—1221no—
219C2×C4—1221no—
220C2×C4—1221no—
221C2×C4—1221no—
222C2×C4—1221no—
223C2×C4—2442no—
224C2×C4—2442no—
225C2×C4—2442no—
226C2×C4#1451983812yes—
227C2×C4#1451984012yes—
228C2×C4#1451986412yes—
229C8—4882no—
230C8—4882no—
231C22#1684073611yescharacteristic
232C22#1684074311yescharacteristic
233C22C2×#1451983811yescharacteristic
234C22C2×#1451984011yescharacteristic
235C22#1684075411yescharacteristic
236C22#1684076011yescharacteristic
237C22#1684076111yescharacteristic
238C4—22no—
239C4—22no—
240C4—22no—
241C4—82no—
242C4—1221no—
243C4—1221no—
244C4—1222no—
245C4—1222no—
246C4—4882no—
247C4—2441no—
248C2#2146109211yescharacteristic
249C2#2146112811yescharacteristic
250C2#2146117911yescharacteristic
251C2#2146124011yescharacteristic
252C2#2146125111yescharacteristic
253C2#2146130111yescharacteristic
254C2#2146133411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#384C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#384#6923
hypocenterC61#7720
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
147. C61#7720semidirect

Maximal subgroups

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

subgroupindex
#214617472
#214617352
#214606372
#214541802
#772061