Finite Group Databasebeta

← #30594001

Subgroups — #30594001

Order 15616.

608 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 78 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#21461642C212yesmaximal
2#21445728C211yesmaximal, characteristic
3C2×#14519834—22no—
4C2×#14519834C414yes—
5C2×C22⋊#92420—22no—
6C23×C4×D61C2211yescharacteristic
7C2×C22⋊#92418C411yescharacteristic
8C2×#14519689—22no—
9C2×C22⋊C8×C61C411yescharacteristic
10C22×#92420—24no—
11#14519834—42no—
12#14519834—42no—
13#14519834—44no—
14C22⋊#92420—44no—
15C24×D61Q811yescharacteristic
16C23×Dic61D411yescharacteristic
17C22×C4×D61—44no—
18C22×C4×D61—41no—
19C22×C4×D61—41no—
20C22×C4×D61C2×C412yes—
21C22×C4×D61D412yes—
22C22×#92418—21no—
23C22⋊#92418—41no—
24#14519689—44no—
25C23×C4×C61C2×C411yescharacteristic
26C22×C8×C61—21no—
27C22⋊C8×C61—41no—
28C24×C61C4⋊C411yescharacteristic
29C23×D61—21no—
30C23×D61—21no—
31C23×D61—24no—
32C23×D61—41no—
33C23×D61—42no—
34C23×D61—41no—
35C23×D61C4⋊C412yes—
36C22×C4×C61—21no—
37C22×C4×C61—21no—
38C22×C4×C61—42no—
39C22×C4×C61C4211yescharacteristic
40C22×C4×C61C22⋊C411yescharacteristic
41C22×Dic61—24no—
42C22×Dic61—41no—
43C22×Dic61C22⋊C412yes—
44C2×C4×D61—22no—
45C2×C4×D61—22no—
46C2×C4×D61—24no—
47C2×C4×D61—24no—
48C2×C4×D61—42no—
49C2×C4×D61—42no—
50C2×C4×D61—42no—
51C2×C4×D61—48no—
52C2×C4×D61—48no—
53C2×#92420—44no—
54C2×#92420—44no—
55C2×#92420—44no—
56C2×C8×C61—42no—
57C2×C8×C61—41no—
58C2×#92418—42no—
59C2×#92418—41no—
60C23×C61—21no—
61C23×C61—22no—
62C23×C61—22no—
63C23×C61—21no—
64C23×C61#9511yescharacteristic
65C23×C61#10811yescharacteristic
66C23×C61#10811yescharacteristic
67C22×D61—22no—
68C22×D61—22no—
69C22×D61—22no—
70C22×D61—22no—
71C22×D61—22no—
72C22×D61—22no—
73C22×D61—44no—
74C22×D61—44no—
75C22×D61—44no—
76C22×D61—48no—
77C22×D61—42no—
78C22×D61—42no—
79C22×D61—44no—
80C22×D61#10814yes—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61—21no—
84C2×C4×C61—42no—
85C2×C4×C61—42no—
86C2×C4×C61#9911yescharacteristic
87C2×C4×C61#9911yescharacteristic
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—44no—
91C2×Dic61#9914yes—
92C4×D61—44no—
93C4×D61—44no—
94C4×D61—48no—
95#92420—84no—
96C8×C61—81no—
97#92418—81no—
98#7047—611nomaximal, Sylow
99C22×C61—21no—
100C22×C61—21no—
101C22×C61—22no—
102C22×C61—22no—
103C22×C61—42no—
104C22×C61—41no—
105C22×C61—41no—
106C22×C61#33811yescharacteristic
107C22×C61#34112yes—
108C22×C61#34111yescharacteristic
109C22×C61#34212yes—
110C22×C61#34211yescharacteristic
111C2×D61—24no—
112C2×D61—24no—
113C2×D61—24no—
114C2×D61—48no—
115C2×D61—48no—
116C2×D61—42no—
117C2×D61—42no—
118C2×D61—42no—
119C2×D61—42no—
120C4×C61—21no—
121C4×C61—21no—
122C4×C61—41no—
123Dic61—24no—
124#1779—612no—
125#1779—611no—
126C2×C61—41no—
127C2×C61—41no—
128C2×C61#129312yes—
129C2×C61#129311yescharacteristic
130C2×C61#129811yescharacteristic
131C2×C61#129812yes—
132C2×C61#130411yescharacteristic
133D61—44no—
134C24×C4—611no—
135C2×C22⋊C8—614no—
136C2×C22⋊C8—611no—
137C2×C22⋊C8—1222no—
138C2×C22⋊C8—1222no—
139C2×C22⋊C8—1222no—
140C2×C22⋊C8#692311yescharacteristic
141C61#704711yescharacteristic, complemented, Sylow
142C25—611no—
143C23×C4—611no—
144C23×C4—612no—
145C23×C4—612no—
146C23×C4—2441no—
147C23×C4—2441no—
148C23×C4—2444no—
149C23×C4C2×#692311yescharacteristic
150C22×C8—21no—
151C22×C8—1224no—
152C22×C8—1221no—
153C22⋊C8—41no—
154C22⋊C8—2444no—
155C22⋊C8—2444no—
156C22⋊C8—2442no—
157C22⋊C8—2442no—
158C22⋊C8—2441no—
159C22⋊C8—2444no—
160C24—612no—
161C24—1224no—
162C24—1221no—
163C24—1221no—
164C24—2442no—
165C24—2441no—
166C24—2441no—
167C24C4⋊#692311yescharacteristic
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—42no—
171C22×C4—612no—
172C22×C4—1224no—
173C22×C4—1224no—
174C22×C4—1224no—
175C22×C4—1222no—
176C22×C4—1222no—
177C22×C4—2442no—
178C22×C4—2442no—
179C22×C4—2442no—
180C22×C4—2448no—
181C22×C4—2448no—
182C22×C4—2441no—
183C22×C4C4×#692311yescharacteristic
184C22×C4C22⋊#692311yescharacteristic
185C2×C8—42no—
186C2×C8—41no—
187C2×C8—2442no—
188C2×C8—2444no—
189C2×C8—2444no—
190C2×C8—2444no—
191C2×C8—2441no—
192C23—21no—
193C23—22no—
194C23—22no—
195C23—21no—
196C23—614no—
197C23—1222no—
198C23—1222no—
199C23—1222no—
200C23—1222no—
201C23—1222no—
202C23—1222no—
203C23—2444no—
204C23—2444no—
205C23—2442no—
206C23—2442no—
207C23—2444no—
208C23—2448no—
209C23—2444no—
210C23(C2×#6923)⋊C411yescharacteristic
211C23#1451984711yescharacteristic
212C23#1451984811yescharacteristic
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—614no—
219C2×C4—1222no—
220C2×C4—1222no—
221C2×C4—2444no—
222C2×C4—2444no—
223C2×C4—2448no—
224C2×C4—2444no—
225C2×C4#1451983511yescharacteristic
226C2×C4#1451983611yescharacteristic
227C8—81no—
228C8—4881no—
229C8—4884no—
230C22—21no—
231C22—21no—
232C22—22no—
233C22—22no—
234C22—42no—
235C22—41no—
236C22—41no—
237C22—1224no—
238C22—1224no—
239C22—1224no—
240C22—2448no—
241C22—2448no—
242C22—2442no—
243C22—2442no—
244C22—2442no—
245C22—2442no—
246C22#1684063111yescharacteristic
247C22#1684063712yes—
248C22#1684063811yescharacteristic
249C22#1684063912yes—
250C22#1684064011yescharacteristic
251C4—21no—
252C4—21no—
253C4—41no—
254C4—1224no—
255C2—41no—
256C2—41no—
257C2—2444no—
258C2#2146069012yes—
259C2#2146069111yescharacteristic
260C2#2146070111yescharacteristic
261C2#2146070212yes—
262C2#2146071811yescharacteristic
subgroupG/H
centerC23(C2×#6923)⋊C4
commutatorC22×C4×C61C42
FrattiniC23×C4C2×#6923
FittingC2×C22⋊C8×C61C4
socleC23×C61#95
prime radicalC24×D61Q8
cosocleC23×C4×D61C22
hypercenterC2×C22⋊C8#6923
hypocenterC61#7047
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
141. C61#7047semidirect

Maximal subgroups

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

subgroupindex
#214616422
#214457282
#704761