Finite Group Databasebeta

← #29566639

Subgroups — #29566639

Order 15616.

354 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 47 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#21445730C211yesmaximal, characteristic
2#21443743C211yesmaximal, characteristic, complemented
3C61×#1314C211yesmaximal, characteristic, complemented
4C22×#11758222C411yescharacteristic
5C2×C22⋊#92418C411yescharacteristic
6C2×#14519689—21no—
7C2×#14519689—21no—
8C22⋊#11758185—21no—
9C2×C22⋊C8×C61C2211yescharacteristic
10C61×C22⋊C16—21no—
11C2×#11758222—42no—
12C2×#11758222—42no—
13C2×#11758222—41no—
14C2×#11758222—41no—
15C22×Dic122C811yescharacteristic
16C22×D244C811yescharacteristic
17C22×C22⋊D61—21no—
18C22×C4×D61—21no—
19C22×#92418—21no—
20C2×#11758185—41no—
21C22⋊#92418—41no—
22#14519689—42no—
23#14519689—42no—
24C23×C4×C61C2×C411yescharacteristic
25C22×C8×C61D411yescharacteristic
26C22×C8×C61D411yescharacteristic
27C2×C16×C61—41no—
28C22⋊C8×C61—41no—
29C24×C61M1611yescharacteristic
30C23×D61—21no—
31C22×C4×C61—21no—
32C22×C4×C61—21no—
33C22×C4×C61—41no—
34C22×C4×C61—41no—
35C22×C4×C61C22⋊C411yescharacteristic
36C22×C4×C61C2×C811yescharacteristic
37C2×C22⋊D61—42no—
38C2×C22⋊D61—42no—
39C2×C22⋊D61—42no—
40C22×Dic61—21no—
41#11758222—44no—
42#11758222—42no—
43#11758222—42no—
44#11758222—44no—
45#11758222—42no—
46#11758222—42no—
47C2×D244—41no—
48C2×D244—42no—
49C2×C4×D61—22no—
50C2×C4×D61—22no—
51C2×C4×D61—41no—
52C2×C4×D61—41no—
53C2×C4×D61—41no—
54C2×C4×D61—41no—
55C2×Dic122—41no—
56C2×Dic122—42no—
57C2×C8×C61—21no—
58C2×C8×C61—21no—
59C2×C8×C61—41no—
60C2×C8×C61—41no—
61C2×#92418—41no—
62C2×#92418—41no—
63C2×#92418—41no—
64C16×C61—81no—
65#11758185—81no—
66C23×C61—21no—
67C23×C61—21no—
68C23×C61—21no—
69C23×C61—41no—
70C23×C61—41no—
71C23×C61C22⋊C811yescharacteristic
72C22×D61—22no—
73C22×D61—41no—
74C22×D61—41no—
75C22×D61—41no—
76C22×D61—41no—
77C22×D61—41no—
78C22×D61—41no—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—42no—
83C2×C4×C61—41no—
84C2×C4×C61—41no—
85C2×C4×C61—41no—
86C2×C4×C61#9911yescharacteristic
87C2×C4×C61#10011yescharacteristic
88C22⋊D61—44no—
89C22⋊D61—44no—
90C2×Dic61—22no—
91C2×Dic61—41no—
92C2×Dic61—41no—
93D244—42no—
94D244—42no—
95C4×D61—42no—
96C4×D61—42no—
97C4×D61—42no—
98C4×D61—42no—
99Dic122—42no—
100Dic122—42no—
101C8×C61—41no—
102C8×C61—41no—
103#92418—81no—
104#7058—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×C61#35011yescharacteristic
114C22×C61#35011yescharacteristic
115C2×D61—42no—
116C2×D61—42no—
117C2×D61—42no—
118C2×D61—81no—
119C2×D61—81no—
120C2×D61—81no—
121C2×D61—81no—
122C4×C61—21no—
123C4×C61—41no—
124C4×C61AΣL(1,𝔽16)11yescharacteristic
125C4×C61AΣL(1,𝔽16)11yescharacteristic
126Dic61—42no—
127#1780—611no—
128#1314—611no—
129#1314D6111yescharacteristic, complemented
130C2×C61—21no—
131C2×C61—21no—
132C2×C61—81no—
133C2×C61#131511yescharacteristic
134C2×C61#131611yescharacteristic
135C2×C61#132111yescharacteristic
136D61—82no—
137C22×#41—611no—
138C2×C22⋊C8—611no—
139C2×C22⋊C8—1221no—
140C2×C22⋊C8—1221no—
141C2×C22⋊C8C2×D6111yescharacteristic
142C22⋊C16—21no—
143C22⋊C16—1221no—
144C61#705811yescharacteristic, complemented, Sylow
145C2×#41—2441no—
146C2×#41—2441no—
147C2×#41—2442no—
148C2×#41—2442no—
149C22×Q8—611no—
150C22×D4—611no—
151C22×D4—1221no—
152C23×C4—1221no—
153C23×C4C4×D6111yescharacteristic
154C22×C8—1221no—
155C22×C8D24411yescharacteristic
156C22×C8C22⋊D6111yescharacteristic
157C2×C16—41no—
158C2×C16—2441no—
159C22⋊C8—41no—
160C22⋊C8—2442no—
161C22⋊C8—2442no—
162C22⋊C8—2441no—
163C24—1221no—
164C24#1175818911yescharacteristic
165#41—2444no—
166#41—2444no—
167#41—2442no—
168#41—2442no—
169#41—2442no—
170#41—2442no—
171C2×Q8—2441no—
172C2×Q8—2442no—
173C2×D4—2441no—
174C2×D4—2442no—
175C2×D4—2442no—
176C2×D4—2442no—
177C2×D4—2442no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4—1222no—
183C22×C4—1222no—
184C22×C4—1221no—
185C22×C4—2441no—
186C22×C4—2441no—
187C22×C4—2441no—
188C22×C4—2441no—
189C22×C4C8×D6111yescharacteristic
190C22×C4#1175819811yescharacteristic
191C2×C8—21no—
192C2×C8—21no—
193C2×C8—41no—
194C2×C8—41no—
195C2×C8—2441no—
196C2×C8—2441no—
197C2×C8—2441no—
198C16—81no—
199C16—4881no—
200C23—21no—
201C23—21no—
202C23—21no—
203C23—41no—
204C23—41no—
205C23—1222no—
206C23—2441no—
207C23—2441no—
208C23—2441no—
209C23—2441no—
210C23—2441no—
211C23—2441no—
212C23#1451968911yescharacteristic
213Q8—2442no—
214Q8—2442no—
215D4—2442no—
216D4—2442no—
217D4—2444no—
218D4—2444no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—42no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—1222no—
227C2×C4—2442no—
228C2×C4—2442no—
229C2×C4—2441no—
230C2×C4—2441no—
231C2×C4—2442no—
232C2×C4—2442no—
233C2×C4#1451969111yescharacteristic
234C2×C4#1451969311yescharacteristic
235C8—41no—
236C8—41no—
237C8—4881no—
238C22—21no—
239C22—21no—
240C22—41no—
241C22—41no—
242C22—41no—
243C22—81no—
244C22—81no—
245C22—4881no—
246C22—4881no—
247C22—4881no—
248C22—4881no—
249C22—2442no—
250C22—2442no—
251C22—2442no—
252C22#1683948511yescharacteristic
253C22#1683954511yescharacteristic
254C22#1683954711yescharacteristic
255C4—21no—
256C4—41no—
257C4—2442no—
258C4#1683954811yescharacteristic
259C4#1683955011yescharacteristic
260C2—21no—
261C2—21no—
262C2—81no—
263C2—4882no—
264C2#2144374411yescharacteristic
265C2#2144374611yescharacteristic
266C2#2144375611yescharacteristic
subgroupG/H
centerC2×C4#14519691
commutatorC22×C4×C61C2×C8
FrattiniC2×C22⋊C8C2×D61
FittingC61×#1314C2
socleC22×C61#323
prime radicalC22×#11758222C4
cosocleC2×C22⋊C8×C61C22
hypercenter#1314D61
hypocenterC61#7058
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #1314

Complements

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

NH ≅ G/Ntype
2. #21443743C2semidirect
3. C61×#1314C2semidirect
129. #1314D61semidirect
144. C61#7058semidirect

Maximal subgroups

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

subgroupindex
#214457302
#214437432
C61×#13142
#705861