Finite Group Databasebeta

← #29567361

Subgroups — #29567361

Order 15616.

356 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 39 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#21445736C211yesmaximal, characteristic
2#21443749C211yesmaximal, characteristic, complemented
3C61×#1317C211yesmaximal, characteristic, complemented
4C22×#11758222C411yescharacteristic
5C2×#14519691—21no—
6C2×#14519691—21no—
7#16839625C411yescharacteristic
8#16839486—21no—
9C61×#381C2211yescharacteristic
10C61×#323—21no—
11C2×#11758222—41no—
12C2×#11758222—41no—
13C2×#11758222—42no—
14C2×#11758222—42no—
15C22×Dic122C811yescharacteristic, complemented
16C22×D244C811yescharacteristic, complemented
17C22×C22⋊D61—21no—
18C22×C4×D61—21no—
19C2×C22⋊Dic61—21no—
20#14519691—42no—
21#14519691—42no—
22C22⋊#92418—41no—
23#14519684—41no—
24C23×C4×C61C2×C411yescharacteristic
25C2×C22⋊C4×C61D411yescharacteristic
26C2×C22⋊C4×C61D411yescharacteristic
27C22⋊C8×C61—41no—
28#95×C61—41no—
29C24×C61C22⋊C411yescharacteristic
30C23×D61—21no—
31C22×C4×C61—21no—
32C22×C4×C61—21no—
33C22×C4×C61—21no—
34C22×C4×C61—21no—
35C22×C4×C61—41no—
36C22×C4×C61—41no—
37C22×C4×C61C2×C811yescharacteristic
38C22×C4×C61M1611yescharacteristic
39C2×C22⋊D61—22no—
40C2×C22⋊D61—22no—
41C2×C22⋊D61—41no—
42C2×C22⋊D61—41no—
43C2×C22⋊D61—41no—
44C2×C22⋊D61—41no—
45C22×Dic61—21no—
46C22×Dic61—41no—
47#11758222—44no—
48#11758222—42no—
49#11758222—42no—
50#11758222—44no—
51#11758222—42no—
52#11758222—42no—
53C2×D244—41no—
54C2×D244—42no—
55C2×C4×D61—42no—
56C2×C4×D61—42no—
57C2×C4×D61—42no—
58C2×Dic122—41no—
59C2×Dic122—42no—
60C2×C8×C61—81no—
61C22⋊C4×C61—41no—
62C22⋊C4×C61—41no—
63C22⋊Dic61—41no—
64C22⋊Dic61—41no—
65C2×#92418—81no—
66C23×C61—21no—
67C23×C61—21no—
68C23×C61—81no—
69C23×C61C22⋊C811yescharacteristic
70C23×C61#9911yescharacteristic
71C23×C61#10011yescharacteristic
72C22×D61—22no—
73C22×D61—41no—
74C22×D61—41no—
75C22×D61—82no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—42no—
79C2×C4×C61—41no—
80C2×C4×C61—41no—
81C2×C4×C61—41no—
82C2×C4×C61—41no—
83C2×C4×C61—41no—
84C2×C4×C61—41no—
85C2×C4×C61—81no—
86C2×C4×C61—81no—
87C22⋊D61—42no—
88C22⋊D61—42no—
89C22⋊D61—42no—
90C22⋊D61—42no—
91C2×Dic61—22no—
92C2×Dic61—41no—
93C2×Dic61—41no—
94C2×Dic61—81no—
95C2×Dic61—82no—
96D244—42no—
97D244—42no—
98C4×D61—44no—
99C4×D61—44no—
100Dic122—42no—
101Dic122—42no—
102C8×C61—161no—
103#92418—161no—
104#7339—611nomaximal, Sylow
105C22×C61—21no—
106C22×C61—21no—
107C22×C61—41no—
108C22×C61—41no—
109C22×C61—41no—
110C22×C61—81no—
111C22×C61—81no—
112C22×C61#32311yescharacteristic
113C22×C61AΣL(1,𝔽16)11yescharacteristic
114C22×C61AΣL(1,𝔽16)11yescharacteristic
115C2×D61—42no—
116C2×D61—82no—
117C2×D61—82no—
118C2×D61—82no—
119C4×C61—41no—
120C4×C61—41no—
121C4×C61—81no—
122C4×C61—81no—
123Dic61—42no—
124Dic61—161no—
125#1782—611no—
126#1317—611no—
127#1317D6111yescharacteristic, complemented
128C2×C61—21no—
129C2×C61—21no—
130C2×C61—21no—
131C2×C61—41no—
132C2×C61—41no—
133C2×C61#131611yescharacteristic
134D61—82no—
135C22×#41—611no—
136C2×#99—1221no—
137C2×#99—1221no—
138#381—611no—
139#381C2×D6111yescharacteristic
140#323—21no—
141#323—1221no—
142C61#733911yescharacteristic, complemented, Sylow
143C2×#41—2441no—
144C2×#41—2441no—
145C2×#41—2442no—
146C2×#41—2442no—
147C22×Q8—611no—
148C22×D4—611no—
149C22×D4—1221no—
150C23×C4—1221no—
151C23×C4C4×D6111yescharacteristic
152C2×C22⋊C4—1221no—
153C2×C22⋊C4D24411yescharacteristic
154C2×C22⋊C4C22⋊D6111yescharacteristic
155#99—2442no—
156#99—2442no—
157C22⋊C8—41no—
158C22⋊C8—2441no—
159#95—41no—
160#95—2441no—
161C24—1221no—
162C24#1175819811yescharacteristic
163#41—2444no—
164#41—2444no—
165#41—2442no—
166#41—2442no—
167#41—2442no—
168#41—2442no—
169C2×Q8—2441no—
170C2×Q8—2442no—
171C2×D4—1222no—
172C2×D4—1222no—
173C2×D4—2441no—
174C2×D4—2442no—
175C2×D4—2441no—
176C2×D4—2441no—
177C2×D4—2441no—
178C2×D4—2441no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4—1221no—
186C22×C4—2442no—
187C22×C4—2442no—
188C22×C4—2442no—
189C22×C4—2441no—
190C22×C4C8×D6111yescharacteristic
191C22×C4#1175818911yescharacteristic
192C2×C8—81no—
193C2×C8—4881no—
194C22⋊C4—41no—
195C22⋊C4—41no—
196C22⋊C4—2441no—
197C22⋊C4—2441no—
198C23—21no—
199C23—21no—
200C23—81no—
201C23—1222no—
202C23—4882no—
203C23—2441no—
204C23—2441no—
205C23#1451968911yescharacteristic
206C23#1451969111yescharacteristic
207C23#1451969311yescharacteristic
208Q8—2442no—
209Q8—2442no—
210D4—2442no—
211D4—2442no—
212D4—2442no—
213D4—2442no—
214D4—2442no—
215D4—2442no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—42no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—81no—
226C2×C4—81no—
227C2×C4—1222no—
228C2×C4—4881no—
229C2×C4—4882no—
230C2×C4—2444no—
231C2×C4—2444no—
232C2×C4—2441no—
233C2×C4—2441no—
234C8—161no—
235C8—9761no—
236C22—21no—
237C22—21no—
238C22—41no—
239C22—41no—
240C22—41no—
241C22—81no—
242C22—81no—
243C22—4882no—
244C22—4882no—
245C22—4882no—
246C22—2442no—
247C22#1683948511yescharacteristic
248C22#1683954811yescharacteristic
249C22#1683955011yescharacteristic
250C4—41no—
251C4—41no—
252C4—81no—
253C4—81no—
254C4—9761no—
255C4—2442no—
256C2—21no—
257C2—21no—
258C2—21no—
259C2—41no—
260C2—41no—
261C2—4882no—
262C2#2144374611yescharacteristic
subgroupG/H
centerC2#21443746
commutatorC22×C4×C61C2×C8
Frattini#381C2×D61
FittingC61×#1317C2
socleC2×C61#1316
prime radicalC22×#11758222C4
cosocleC61×#381C22
hypercenter#1317D61
hypocenterC61#7339
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ #381 ◁ #1317

Complements

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

NH ≅ G/Ntype
2. #21443749C2semidirect
3. C61×#1317C2semidirect
15. C22×Dic122C8semidirect
16. C22×D244C8semidirect
127. #1317D61semidirect
142. C61#7339semidirect

Maximal subgroups

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

subgroupindex
#214457362
#214437492
C61×#13172
#733961