Finite Group Databasebeta

← #30598941

Subgroups — #30598941

Order 15616.

476 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 118 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#21461735C212yesmaximal
2C2×#16840622C212yesmaximal
3#21460697C212yesmaximal
4C4×#14519775C211yesmaximal, characteristic
5C2×#14519844C2214yes—
6#16840628—22no—
7#16840628—22no—
8#16840622—24no—
9C2×#14519775C2211yescharacteristic
10C2×C4×Dic122C411yescharacteristic
11#16839669C411yescharacteristic
12#16839667C411yescharacteristic
13#16839657—22no—
14#16839631C2211yescharacteristic
15C4×#11758196—22no—
16C42×Dic61C2211yescharacteristic
17C2×C4×Q8×C61C411yescharacteristic
18C22×#92420—24no—
19#14519844—24no—
20#14519844—24no—
21C22×Dic122C2×C411yescharacteristic
22#14519775—22no—
23#14519775D412yes—
24#14519775Q812yes—
25C4×Dic122—42no—
26C2×C4⋊Dic61C2×C411yescharacteristic
27C2×#11758196—22no—
28C2×#11758196—21no—
29C2×#11758196—22no—
30C2×C4×Dic61—21no—
31C2×C4×Dic61C2×C411yescharacteristic
32C2×C4×Dic61D412yes—
33C2×C4×Dic61D412yes—
34C2×C4×Dic61C2311yescharacteristic
35#14519684—22no—
36#14519684—22no—
37C22×Q8×C61C2×C411yescharacteristic
38C4×Q8×C61—42no—
39C2×C4⋊C4×C61—21no—
40C2×C4⋊C4×C61C2×C411yescharacteristic
41C2×C42×C61—21no—
42C2×C42×C61C2×C411yescharacteristic
43C2×Q8×C61—21no—
44C2×Q8×C61—41no—
45C2×Q8×C61—41no—
46C2×Q8×C61C4⋊C412yes—
47C22×C4×C61—21no—
48C22×C4×C61—21no—
49C22×C4×C61C22⋊C411yescharacteristic
50C22×C4×C61C22⋊C411yescharacteristic
51C22×C4×C61C22×C411yescharacteristic
52C22×Dic61—21no—
53C22×Dic61—21no—
54C22×Dic61C22⋊C412yes—
55C22×Dic61C2×D412yes—
56C2×Dic122—21no—
57C2×Dic122—41no—
58C2×Dic122—41no—
59C2×Dic122C4⋊C412yes—
60C2×#92420—44no—
61C2×#92420—44no—
62C2×#92420—44no—
63C4⋊C4×C61—42no—
64C4⋊C4×C61—41no—
65C42×C61—22no—
66C42×C61—42no—
67C4⋊Dic61—41no—
68#11758196—24no—
69#11758196—24no—
70#11758196—42no—
71#11758196—44no—
72C4×Dic61—24no—
73C4×Dic61—24no—
74C4×Dic61—41no—
75C4×Dic61—42no—
76C4×Dic61C2×D411yescharacteristic
77C4×Dic61C2×Q811yescharacteristic
78C4×Dic61#4112yes—
79C23×C61C2×C22⋊C411yescharacteristic
80Q8×C61—42no—
81Q8×C61—42no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61—21no—
87C2×C4×C61—22no—
88C2×C4×C61—41no—
89C2×C4×C61—41no—
90C2×C4×C61—41no—
91C2×C4×C61—42no—
92C2×C4×C61#10012yes—
93C2×C4×C61C2×C4⋊C411yescharacteristic
94C2×C4×C61#11711yescharacteristic
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61—22no—
98C2×Dic61—22no—
99C2×Dic61—41no—
100C2×Dic61—41no—
101C2×Dic61—41no—
102C2×Dic61—42no—
103C2×Dic61#12112yes—
104C2×Dic61C22⋊Q812yes—
105C2×Dic61#13514yes—
106C2×Dic61#13714yes—
107Dic122—42no—
108Dic122—42no—
109#92420—84no—
110#8594—611nomaximal, Sylow
111C22×C61#38011yescharacteristic
112C22×C61C2×#10011yescharacteristic
113C22×C61#41311yescharacteristic
114C22×C61#41612yes—
115C22×C61#41912yes—
116C4×C61—21no—
117C4×C61—21no—
118C4×C61—22no—
119C4×C61—41no—
120C4×C61—42no—
121C4×C61—81no—
122Dic61—42no—
123Dic61—42no—
124Dic61—81no—
125Dic61#46414yes—
126Dic61#47914yes—
127C4×C4⋊Q8—611no—
128#1831—612no—
129C2×#333—612no—
130#1296—612no—
131C2×C61#154311yescharacteristic
132C2×C61#155412yes—
133C2×C61#155811yescharacteristic
134C2×C61#180011yescharacteristic
135C2×C61#180512yes—
136C2×C4⋊Q8—611no—
137C2×C4×Q8—611no—
138C2×C4×Q8#692311yescharacteristic
139C2×C4⋊C8—614no—
140#391—611no—
141#391—611no—
142#389—1222no—
143#384—611no—
144C4×C4⋊C4—1222no—
145C43—611no—
146#336—1222no—
147#336—1222no—
148#333—1224no—
149C61#859411yescharacteristic, complemented, Sylow
150C22×Q8—611no—
151C22×Q8C2×#692311yescharacteristic
152C22×C8—1224no—
153C4⋊Q8—612no—
154C4⋊Q8—612no—
155C4⋊Q8—1222no—
156C4×Q8—42no—
157C4×Q8—2442no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—611no—
160C2×C4⋊C4—1222no—
161C2×C4⋊C4—1222no—
162C2×C4⋊C4—1221no—
163C2×C4⋊C4C2×#692311yescharacteristic
164C2×C42—21no—
165C2×C42—611no—
166C2×C42—612no—
167C2×C42—612no—
168C2×C42—611no—
169C2×C42—1221no—
170C2×C42C2×#692311yescharacteristic
171C4⋊C8—1224no—
172C4⋊C8—1224no—
173#95—1222no—
174#95—1222no—
175C2×Q8—21no—
176C2×Q8—41no—
177C2×Q8—41no—
178C2×Q8—612no—
179C2×Q8—1221no—
180C2×Q8—2441no—
181C2×Q8—2441no—
182C2×Q8C4⋊#692312yes—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—612no—
186C22×C4—612no—
187C22×C4—1221no—
188C22×C4—1221no—
189C22×C4C22⋊#692311yescharacteristic
190C22×C4C22⋊#692311yescharacteristic
191C22×C4C22×#692311yescharacteristic
192C2×C8—2444no—
193C2×C8—2444no—
194C2×C8—2444no—
195C4⋊C4—41no—
196C4⋊C4—42no—
197C4⋊C4—1224no—
198C4⋊C4—1224no—
199C4⋊C4—2441no—
200C4⋊C4—2442no—
201C4⋊C4—2444no—
202C42—22no—
203C42—42no—
204C42—611no—
205C42—611no—
206C42—612no—
207C42—1224no—
208C42—1224no—
209C42—2441no—
210C42—2442no—
211C23C2×C22⋊#692311yescharacteristic
212Q8—42no—
213Q8—42no—
214Q8—2442no—
215Q8—2442no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—42no—
226C2×C4—612no—
227C2×C4—612no—
228C2×C4—614no—
229C2×C4—614no—
230C2×C4—1222no—
231C2×C4—1222no—
232C2×C4—1222no—
233C2×C4—1222no—
234C2×C4—2441no—
235C2×C4—2442no—
236C2×C4—2441no—
237C2×C4—2441no—
238C2×C4#1451983712yes—
239C2×C4C2×C4⋊#692311yescharacteristic
240C2×C4#1451985611yescharacteristic
241C8—4884no—
242C22#1684070411yescharacteristic
243C22C2×#1451983711yescharacteristic
244C22#1684074811yescharacteristic
245C22#1684075212yes—
246C22#1684075512yes—
247C4—22no—
248C4—21no—
249C4—21no—
250C4—41no—
251C4—42no—
252C4—81no—
253C4—614no—
254C4—614no—
255C4—4881no—
256C4—2442no—
257C4—2442no—
258C2#2146132211yescharacteristic
259C2#2146134412yes—
260C2#2146135211yescharacteristic
261C2#2146168311yescharacteristic
262C2#2146169012yes—
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4×Q8×C61C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4×Q8#6923
hypocenterC61#8594
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
149. C61#8594semidirect

Maximal subgroups

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

subgroupindex
#214617352
C2×#168406222
#214606972
C4×#145197752
#859461