Finite Group Databasebeta

← #29573464

Subgroups — #29573464

Order 15616.

404 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 99 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#21448316C211yesmaximal, characteristic
2#21444131C212yesmaximal
3#21443652C211yesmaximal, characteristic, complemented
4#21443647C212yesmaximal, complemented
5C61×#1276C211yesmaximal, characteristic, complemented
6C2×#14519734C2211yescharacteristic
7#16839815C2212yes—
8#16839653—22no—
9#16839646—22no—
10C4×#11758196C412yes—
11C4×#11758198C412yes—
12#16839608C2211yescharacteristic
13#16839487—22no—
14#16839485—22no—
15C61×#431C2212yes—
16C43×C61C2211yescharacteristic
17C22×C4×D61C2×C411yescharacteristic
18#14519734—22no—
19#14519734—21no—
20#14519734—21no—
21C2×#11758196—22no—
22C2×#11758196D412yes—
23C2×#11758198—22no—
24C2×#11758198D412yes—
25C2×C4×Dic61C2×C412yes—
26C2×C4×Dic61C2×C411yescharacteristic
27C4⋊#92418—22no—
28C22⋊#92418—22no—
29C4×#92418—22no—
30#14519684—22no—
31#14519684—22no—
32#14519684—22no—
33C2×C42×C61—22no—
34C2×C42×C61C2×C412yes—
35C2×C42×C61C2311yescharacteristic
36C4⋊C8×C61—22no—
37C22⋊C8×C61—22no—
38C4×C8×C61—22no—
39C23×D61C22⋊C411yescharacteristic
40C22×C4×C61—22no—
41C22×C4×C61C22×C411yescharacteristic
42C22×C4×C61C2×D412yes—
43C22×Dic61—22no—
44C22×Dic61C22⋊C411yescharacteristic
45C22×Dic61C22⋊C412yes—
46C2×C4×D61—21no—
47C2×C4×D61—21no—
48C2×C4×D61—22no—
49C2×C4×D61—22no—
50C2×C8×C61—42no—
51C42×C61—22no—
52C42×C61—22no—
53C42×C61—44no—
54C42×C61#4112yes—
55C42×C61#4111yescharacteristic
56C42×C61#4111yescharacteristic
57#11758198—22no—
58#11758198—22no—
59#11758198—44no—
60#11758196—22no—
61#11758196—22no—
62#11758196—44no—
63C4×Dic61—21no—
64C4×Dic61—21no—
65C4×Dic61—22no—
66C4×Dic61—22no—
67C2×#92418—42no—
68C23×C61C2×C22⋊C411yescharacteristic
69C22×D61—21no—
70C22×D61—22no—
71C22×D61—42no—
72C2×C4×C61—24no—
73C2×C4×C61—42no—
74C2×C4×C61—42no—
75C2×C4×C61—42no—
76C2×C4×C61#11711yescharacteristic
77C2×C4×C61#11711yescharacteristic
78C2×C4×C61#12312yes—
79C2×C4×C61#12312yes—
80C2×C4×C61#13112yes—
81C2×C4×C61#13112yes—
82C2×Dic61—22no—
83C2×Dic61—21no—
84C2×Dic61—22no—
85C2×Dic61—42no—
86C2×Dic61—42no—
87C2×Dic61—42no—
88C2×Dic61—42no—
89C4×D61—41no—
90C4×D61—42no—
91C4×D61—41no—
92C8×C61—82no—
93#92418—82no—
94#8732—611nomaximal, Sylow
95C22×C61—22no—
96C22×C61#38111yescharacteristic
97C22×C61#40812yes—
98C2×D61—41no—
99C2×D61—42no—
100C2×D61—82no—
101C4×C61—22no—
102C4×C61—22no—
103C4×C61—44no—
104C4×C61#43311yescharacteristic
105C4×C61#43312yes—
106C4×C61#43311yescharacteristic
107Dic61—41no—
108Dic61—42no—
109Dic61—82no—
110#2298—611no—
111#1458—612no—
112#1276—611no—
113#1276D6111yescharacteristic, complemented
114#1274—612no—
115C2×C61—22no—
116C2×C61#181811yescharacteristic
117C2×C61#182712yes—
118D61—81no—
119C2×#117—611no—
120#431—612no—
121#431C2×D6112yes—
122#388—1222no—
123#387—1222no—
124C4×C4⋊C4—612no—
125C4×C22⋊C4—612no—
126#376—611no—
127C43C2×D6111yescharacteristic
128#324—1222no—
129#323—1222no—
130C61#873211yescharacteristic, complemented, Sylow
131C23×C4—611no—
132#117—1222no—
133#117—1221no—
134#117—1221no—
135C2×C4⋊C4—612no—
136C2×C4⋊C4—1222no—
137C2×C22⋊C4—612no—
138C2×C22⋊C4—1222no—
139C2×C42—22no—
140C2×C42—611no—
141C2×C42—612no—
142C2×C42C4×D6112yes—
143C2×C42C22×D6111yescharacteristic
144C4⋊C8—22no—
145C4⋊C8—1222no—
146C22⋊C8—22no—
147C22⋊C8—1222no—
148C4×C8—22no—
149C4×C8—1222no—
150#95—1222no—
151#95—1222no—
152#95—1222no—
153C24—611no—
154C22×C4—22no—
155C22×C4—611no—
156C22×C4—612no—
157C22×C4—1221no—
158C22×C4—1221no—
159C22×C4—1222no—
160C22×C4—1222no—
161C22×C4—1222no—
162C22×C4C2×C4×D6111yescharacteristic
163C22×C4D4×D6112yes—
164C2×C8—42no—
165C2×C8—2442no—
166C4⋊C4—1222no—
167C4⋊C4—1222no—
168C4⋊C4—2444no—
169C22⋊C4—1222no—
170C22⋊C4—1222no—
171C22⋊C4—2444no—
172C42—22no—
173C42—22no—
174C42—44no—
175C42—1221no—
176C42—1221no—
177C42—1222no—
178C42—1222no—
179C42#1175822212yes—
180C42#1175822411yescharacteristic
181C42#1175822611yescharacteristic
182C23—1222no—
183C23—1221no—
184C23—2442no—
185C23C22⋊C4×D6111yescharacteristic
186C2×C4—24no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—1222no—
191C2×C4—1222no—
192C2×C4—1221no—
193C2×C4—2442no—
194C2×C4—2442no—
195C2×C4—2442no—
196C2×C4—2441no—
197C2×C4—2442no—
198C2×C4—2441no—
199C2×C4—2442no—
200C2×C4#1451973411yescharacteristic
201C2×C4#1451973511yescharacteristic
202C2×C4#1451975912yes—
203C2×C4#1451976212yes—
204C2×C4#1451978312yes—
205C2×C4#1451978512yes—
206C8—82no—
207C8—4882no—
208C22—22no—
209C22—4882no—
210C22—2441no—
211C22—2442no—
212C22#1683962411yescharacteristic
213C22#1683972712yes—
214C4—22no—
215C4—22no—
216C4—44no—
217C4—4882no—
218C4—2441no—
219C4—2442no—
220C4#1683982111yescharacteristic
221C4#1683982212yes—
222C4#1683982411yescharacteristic
223C2—22no—
224C2—4881no—
225C2#2144588911yescharacteristic
226C2#2144592212yes—
subgroupG/H
centerC2×C4#14519735
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1276C2
socleC22×C61#381
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1276D61
hypocenterC61#8732
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
3. #21443652C2semidirect
4. #21443647C2semidirect
5. C61×#1276C2semidirect
113. #1276D61semidirect
130. C61#8732semidirect

Maximal subgroups

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

subgroupindex
#214483162
#214441312
#214436522
#214436472
C61×#12762
#873261