Finite Group Databasebeta

← #30604347

Subgroups — #30604347

Order 15616.

374 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 74 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#21461081C211yesmaximal, characteristic
2#21461061C211yesmaximal, characteristic
3#21460762C214yesmaximal
4#21451028C211yesmaximal, characteristic
5#16840783—21no—
6#16840779—21no—
7#16840608—21no—
8#16840608—21no—
9#16840607C2212yes—
10#16840607C2212yes—
11C2×C4×Dic122C2211yescharacteristic
12#16839681—21no—
13#16839681—21no—
14#16839667C412yes—
15#16839658—21no—
16#16839658—21no—
17#16839631C2212yes—
18C4×C4⋊Dic61C411yescharacteristic
19C2×C4⋊Q8×C61C411yescharacteristic
20#14519844—41no—
21C4⋊#92420—41no—
22C22⋊#92420—22no—
23C22⋊#92420—22no—
24#14519832—41no—
25C4×#92420—41no—
26C22×Dic122C2×C411yescharacteristic
27C4×Dic122—41no—
28C4×Dic122—41no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61C2311yescharacteristic
31C2×#11758196—22no—
32C2×#11758196—22no—
33C2×#11758196D411yescharacteristic
34C2×#11758196D411yescharacteristic
35C2×C4×Dic61C2×C412yes—
36C2×C4×Dic61D411yescharacteristic
37C2×C4×Dic61D411yescharacteristic
38#14519684—21no—
39#14519684—22no—
40#14519684—22no—
41C22×Q8×C61—21no—
42C4⋊Q8×C61—41no—
43C4⋊Q8×C61—41no—
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61C2×C412yes—
46C2×C42×C61C2×C411yescharacteristic
47C2×Q8×C61—42no—
48C2×Q8×C61—82no—
49C22×C4×C61—22no—
50C22×C4×C61C22⋊C411yescharacteristic
51C22×C4×C61C22⋊C411yescharacteristic
52C22×C4×C61C22×C411yescharacteristic
53C22×Dic61—22no—
54C22×Dic61C22⋊C411yescharacteristic
55C22×Dic61C22⋊C411yescharacteristic
56C22×Dic61C2×D411yescharacteristic
57C22×Dic61C2×D411yescharacteristic
58C2×Dic122—22no—
59C2×Dic122—22no—
60C2×Dic122—41no—
61C2×#92420—42no—
62C2×#92420—42no—
63C4⋊C4×C61—42no—
64C4⋊C4×C61—41no—
65C4⋊C4×C61—41no—
66C42×C61—21no—
67C42×C61—21no—
68C4⋊Dic61—24no—
69C4⋊Dic61—41no—
70#11758196—41no—
71#11758196—41no—
72#11758196—82no—
73#11758196—82no—
74C4×Dic61—21no—
75C4×Dic61—21no—
76C4×Dic61—21no—
77C4×Dic61—21no—
78C4×Dic61—24no—
79C23×C61C2×C22⋊C411yescharacteristic
80Q8×C61—84no—
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—22no—
84C2×C4×C61—21no—
85C2×C4×C61—41no—
86C2×C4×C61—42no—
87C2×C4×C61—42no—
88C2×C4×C61—42no—
89C2×C4×C61#9911yescharacteristic
90C2×C4×C61#9911yescharacteristic
91C2×C4×C61#13112yes—
92C2×Dic61—21no—
93C2×Dic61—21no—
94C2×Dic61—24no—
95C2×Dic61—21no—
96C2×Dic61—21no—
97C2×Dic61—21no—
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61—42no—
101C2×Dic61—42no—
102C2×Dic61—41no—
103C2×Dic61—41no—
104C2×Dic61#10112yes—
105Dic122—44no—
106#92420—82no—
107#92420—82no—
108#11574—611nomaximal, Sylow
109C22×C61—21no—
110C22×C61—21no—
111C22×C61#40811yescharacteristic
112C22×C61C2×#9911yescharacteristic
113C22×C61C2×#10111yescharacteristic
114C4×C61—21no—
115C4×C61—22no—
116C4×C61—41no—
117C4×C61—82no—
118C4×C61#35612yes—
119Dic61—22no—
120Dic61—44no—
121Dic61—41no—
122Dic61—41no—
123Dic61—41no—
124#2567—611no—
125#1467—611no—
126#1461—611no—
127#1325—614no—
128C2×C61—21no—
129C2×C61—21no—
130C2×C61#147211yescharacteristic
131C2×C61#212811yescharacteristic
132C2×C61C2×#35611yescharacteristic
133C2×C4⋊Q8#692311yescharacteristic
134C2×C4×Q8—611no—
135#432—1221no—
136#431—1221no—
137#395—1221no—
138#395—1221no—
139#391—612no—
140#389—1221no—
141#389—1221no—
142#384—612no—
143C4×C4⋊C4—611no—
144#324—612no—
145#324—612no—
146#324—1221no—
147#324—1221no—
148C61#1157411yescharacteristic, complemented, Sylow
149C22×Q8—21no—
150C22×Q8—611no—
151C4⋊Q8—41no—
152C4⋊Q8—41no—
153C4×Q8—2441no—
154C4×Q8—2441no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—611no—
157C2×C4⋊C4—611no—
158C2×C4⋊C4—611no—
159C2×C4⋊C4—1221no—
160C2×C4⋊C4—1222no—
161C2×C4⋊C4—1222no—
162C2×C4⋊C4C2×#692312yes—
163C2×C42—611no—
164C2×C42—611no—
165C2×C42—612no—
166C2×C42C2×#692311yescharacteristic
167C4⋊C8—2441no—
168C4⋊C8—2441no—
169C22⋊C8—1222no—
170C22⋊C8—1222no—
171#97—2441no—
172C4×C8—2441no—
173#95—1222no—
174#95—1222no—
175#95—1221no—
176C2×Q8—42no—
177C2×Q8—82no—
178C2×Q8—1222no—
179C2×Q8—1222no—
180C2×Q8—2441no—
181C22×C4—22no—
182C22×C4—611no—
183C22×C4—611no—
184C22×C4—611no—
185C22×C4—611no—
186C22×C4—1222no—
187C22×C4C22⋊#692311yescharacteristic
188C22×C4C22⋊#692311yescharacteristic
189C22×C4C22×#692311yescharacteristic
190C2×C8—2442no—
191C2×C8—2442no—
192C4⋊C4—42no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—1224no—
196C4⋊C4—4882no—
197C4⋊C4—4882no—
198C4⋊C4—2441no—
199C4⋊C4—2441no—
200C4⋊C4—2441no—
201C42—21no—
202C42—21no—
203C42—1221no—
204C42—1221no—
205C42—1221no—
206C42—1221no—
207C42—1224no—
208C23C2×C22⋊#692311yescharacteristic
209Q8—84no—
210Q8—2444no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—41no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—612no—
220C2×C4—1221no—
221C2×C4—1221no—
222C2×C4—1224no—
223C2×C4—1221no—
224C2×C4—1221no—
225C2×C4—1221no—
226C2×C4—1221no—
227C2×C4—1221no—
228C2×C4—2442no—
229C2×C4—2442no—
230C2×C4—2441no—
231C2×C4—2441no—
232C2×C4#1451983511yescharacteristic
233C2×C4#1451983511yescharacteristic
234C2×C4#1451986512yes—
235C8—4882no—
236C8—4882no—
237C22—21no—
238C22—21no—
239C22#1684073711yescharacteristic
240C22C2×#1451983511yescharacteristic
241C22D61⋊#10111yescharacteristic
242C4—21no—
243C4—22no—
244C4—41no—
245C4—82no—
246C4—1222no—
247C4—2444no—
248C4—2441no—
249C4—2441no—
250C4—2441no—
251C4#1684067212yes—
252C2—21no—
253C2—21no—
254C2#2146109911yescharacteristic
255C2#2146209811yescharacteristic
256C2C2×#1684067211yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4⋊Q8×C61C4
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4⋊Dic61C23
hypercenterC2×C4⋊Q8#6923
hypocenterC61#11574
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
148. C61#11574semidirect

Maximal subgroups

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

subgroupindex
#214610812
#214610612
#214607622
#214510282
#1157461