Finite Group Databasebeta

← #29567231

Subgroups — #29567231

Order 15616.

324 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 75 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#21446117C211yesmaximal, characteristic
2#21444137C211yesmaximal, characteristic
3C61×#1460C211yesmaximal, characteristic
4C22×#11758194C411yescharacteristic
5C2×C22⋊#92418—21no—
6C2×C22⋊#92418—21no—
7C2×C22⋊#92418C411yescharacteristic
8#16839517—21no—
9#16839488C412yes—
10#16839486—21no—
11C2×C4×D4×C61C2211yescharacteristic
12C61×#431—21no—
13C61×#323—21no—
14C61×#323C412yes—
15C2×#11758194—42no—
16C2×#11758194—41no—
17C22×#92418—21no—
18C22×#92418—21no—
19C22×#92418—41no—
20C22⋊#92418—22no—
21C22⋊#92418—42no—
22C22⋊#92418—41no—
23C22⋊#92418—41no—
24C22×D4×C61Q811yescharacteristic
25C23×C4×C61C2×C411yescharacteristic
26C23×C4×C61D411yescharacteristic
27C4×D4×C61—41no—
28C4×D4×C61—41no—
29C2×C4⋊C4×C61C2×C411yescharacteristic
30C2×C22⋊C4×C61C2×C411yescharacteristic
31C2×C22⋊C4×C61D411yescharacteristic
32C2×C42×C61D411yescharacteristic
33C4⋊C8×C61—41no—
34C22⋊C8×C61—22no—
35C4×C8×C61—41no—
36C24×C61C4⋊C411yescharacteristic
37C24×C61C4⋊C411yescharacteristic
38C2×D4×C61—22no—
39C2×D4×C61—22no—
40C2×D4×C61—41no—
41C22×C4×C61—21no—
42C22×C4×C61—21no—
43C22×C4×C61—21no—
44C22×C4×C61—21no—
45C22×C4×C61—41no—
46C22×C4×C61—41no—
47C22×C4×C61—41no—
48C22×C4×C61—41no—
49C22×C4×C61C4211yescharacteristic
50C22×C4×C61C22⋊C411yescharacteristic
51C22×C4×C61C22⋊C411yescharacteristic
52C22×C4×C61C22⋊C411yescharacteristic
53C22×C4×C61C4⋊C411yescharacteristic
54C2×C8×C61—42no—
55C4⋊C4×C61—41no—
56C22⋊C4×C61—41no—
57C22⋊C4×C61—41no—
58C42×C61—21no—
59C42×C61—21no—
60#11758194—42no—
61#11758194—42no—
62C2×#92418—22no—
63C2×#92418—41no—
64C2×#92418—41no—
65C2×#92418—42no—
66C2×#92418—41no—
67C2×#92418—41no—
68C2×#92418—41no—
69C2×#92418—81no—
70C2×#92418—81no—
71C23×C61—21no—
72C23×C61—21no—
73C23×C61—21no—
74C23×C61—21no—
75C23×C61—21no—
76C23×C61—41no—
77C23×C61—41no—
78C23×C61—41no—
79C23×C61—41no—
80C23×C61#9511yescharacteristic
81C23×C61#10812yes—
82D4×C61—44no—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—42no—
91C2×C4×C61—41no—
92C2×C4×C61—41no—
93C2×C4×C61—41no—
94C2×C4×C61—41no—
95C2×C4×C61—41no—
96C2×C4×C61—41no—
97C2×C4×C61—41no—
98C2×C4×C61—81no—
99C2×C4×C61#9911yescharacteristic
100C2×C4×C61#9911yescharacteristic
101C2×C4×C61#10812yes—
102C8×C61—82no—
103#92418—42no—
104#92418—81no—
105#92418—82no—
106#7285—611nomaximal, Sylow
107C22×C61—21no—
108C22×C61—21no—
109C22×C61—22no—
110C22×C61—42no—
111C22×C61—41no—
112C22×C61—41no—
113C22×C61—41no—
114C22×C61—41no—
115C22×C61—41no—
116C22×C61—81no—
117C22×C61—81no—
118C22×C61—81no—
119C22×C61#34111yescharacteristic
120C22×C61#34111yescharacteristic
121C22×C61#34211yescharacteristic
122C4×C61—22no—
123C4×C61—21no—
124C4×C61—41no—
125C4×C61—41no—
126C4×C61—41no—
127C4×C61AΣL(1,𝔽16)11yescharacteristic
128C4×C61#35211yescharacteristic
129#1870—611no—
130#1460D6111yescharacteristic
131#1459—611no—
132C2×C61—21no—
133C2×C61—21no—
134C2×C61—42no—
135C2×C61—81no—
136C2×C61#129811yescharacteristic
137C2×C61#139011yescharacteristic
138C2×C61#139511yescharacteristic
139C22×M16—611no—
140C2×C4×D4C2×D6111yescharacteristic
141#431—21no—
142C2×C22⋊C8—611no—
143C2×C22⋊C8—1221no—
144C2×C22⋊C8—1221no—
145#336—1221no—
146#324—612no—
147#323—21no—
148#323—1221no—
149#323Dic6112yes—
150C61#728511yescharacteristic, complemented, Sylow
151C22×D4Dic12211yescharacteristic
152C23×C4C4×D6111yescharacteristic
153C23×C4D24411yescharacteristic
154C2×M16—2442no—
155C2×M16—2441no—
156C22×C8—1221no—
157C22×C8—1221no—
158C22×C8—2441no—
159C4×D4—41no—
160C4×D4—41no—
161C2×C4⋊C4C4×D6111yescharacteristic
162C2×C22⋊C4C2×Dic6111yescharacteristic
163C2×C22⋊C4C22⋊D6111yescharacteristic
164C2×C42C22⋊D6111yescharacteristic
165C4⋊C8—41no—
166C22⋊C8—22no—
167C22⋊C8—1222no—
168C22⋊C8—2442no—
169C22⋊C8—2441no—
170C22⋊C8—2441no—
171C4×C8—41no—
172C24#1175819611yescharacteristic
173C24C4⋊Dic6111yescharacteristic
174C2×D4—22no—
175C2×D4—22no—
176C2×D4—41no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4C4×Dic6111yescharacteristic
186C22×C4#1175819611yescharacteristic
187C22×C4#1175819811yescharacteristic
188C22×C4#1175819811yescharacteristic
189C22×C4C22⋊Dic6111yescharacteristic
190M16—2442no—
191M16—2442no—
192C2×C8—42no—
193C2×C8—1222no—
194C2×C8—4881no—
195C2×C8—4881no—
196C2×C8—2442no—
197C2×C8—2441no—
198C2×C8—2441no—
199C2×C8—2441no—
200C2×C8—2441no—
201C2×C8—2441no—
202C4⋊C4—41no—
203C22⋊C4—41no—
204C22⋊C4—41no—
205C42—21no—
206C42—21no—
207C23—21no—
208C23—21no—
209C23—21no—
210C23—21no—
211C23—21no—
212C23—41no—
213C23—41no—
214C23—41no—
215C23—41no—
216C23#1451968411yescharacteristic
217C23#1451971312yes—
218D4—44no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—42no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—81no—
235C2×C4#1451969111yescharacteristic
236C2×C4#1451969111yescharacteristic
237C2×C4#1451971212yes—
238C8—82no—
239C8—4881no—
240C8—4882no—
241C8—2442no—
242C22—21no—
243C22—21no—
244C22—22no—
245C22—42no—
246C22—41no—
247C22—41no—
248C22—41no—
249C22—41no—
250C22—41no—
251C22—81no—
252C22—81no—
253C22—81no—
254C22#1683952611yescharacteristic
255C22#1683952711yescharacteristic
256C22#1683952811yescharacteristic
257C4—21no—
258C4—22no—
259C4—41no—
260C4—41no—
261C4—41no—
262C4#1683955011yescharacteristic
263C4#1683955311yescharacteristic
264C2—21no—
265C2—21no—
266C2—42no—
267C2—81no—
268C2#2144370711yescharacteristic
269C2#2144393811yescharacteristic
270C2#2144394711yescharacteristic
subgroupG/H
centerC2×C4#14519691
commutatorC22×C4×C61C42
FrattiniC2×C4×D4C2×D61
FittingC61×#1460C2
socleC22×C61#342
prime radicalC22×D4×C61Q8
cosocleC2×C4×D4×C61C22
hypercenter#1460D61
hypocenterC61#7285
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1460

Complements

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

NH ≅ G/Ntype
150. C61#7285semidirect

Maximal subgroups

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

subgroupindex
#214461172
#214441372
C61×#14602
#728561