Finite Group Databasebeta

← #30594755

Subgroups — #30594755

Order 15616.

328 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 52 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#21461798C211yesmaximal, characteristic
2#21461684C211yesmaximal, characteristic
3#21444154C211yesmaximal, characteristic
4C22×#11758217C411yescharacteristic
5#16840765—21no—
6C2×#14519837C412yes—
7C2×#14519834—21no—
8C2×C22⋊#92420C411yescharacteristic
9#16840642—21no—
10#16840628—21no—
11C2×#14519737C2211yescharacteristic
12#16839724—21no—
13#16839487—21no—
14#16839486C411yescharacteristic
15C61×#323C411yescharacteristic
16C2×#11758217—22no—
17C2×#11758217—42no—
18C2×#11758217—41no—
19C22×#92420—21no—
20C22×#92420—21no—
21#14519844—41no—
22C4⋊#92420—41no—
23#14519837—42no—
24#14519834—42no—
25C22⋊#92420—41no—
26C22×C22⋊D61C2×C411yescharacteristic
27C23×Dic61C2×C411yescharacteristic
28C22×C4×D61D411yescharacteristic
29C2×#11758189—41no—
30#14519737—41no—
31#14519737—41no—
32C2×#11758196D411yescharacteristic
33C2×#11758198Q811yescharacteristic
34C2×C4×Dic61D411yescharacteristic
35C22⋊#92418—21no—
36#14519689—41no—
37C2×C22⋊C4×C61C2×C411yescharacteristic
38C22⋊C8×C61—21no—
39C24×C61C4211yescharacteristic
40C23×D61C4⋊C411yescharacteristic
41C22×C4×C61C22⋊C411yescharacteristic
42C22×C4×C61C4⋊C411yescharacteristic
43C2×C22⋊D61—21no—
44C2×C22⋊D61—21no—
45C2×C22⋊D61—41no—
46C2×C22⋊D61—41no—
47C22×Dic61—21no—
48C22×Dic61—21no—
49C22×Dic61—41no—
50C22×Dic61—41no—
51C22×Dic61C22⋊C411yescharacteristic
52C22×Dic61C22⋊C411yescharacteristic
53C22×Dic61C4⋊C411yescharacteristic
54C2×C4×D61—21no—
55C2×C4×D61—21no—
56C2×C4×D61—41no—
57C2×C4×D61—41no—
58#11758217—42no—
59#11758217—42no—
60#11758217—42no—
61#11758217—42no—
62C2×#92420—22no—
63C2×#92420—41no—
64C2×#92420—41no—
65C2×#92420—41no—
66C2×#92420—42no—
67C2×#92420—41no—
68C2×#92420—41no—
69C2×C8×C61—41no—
70C22⋊C4×C61—41no—
71#11758198—41no—
72#11758196—41no—
73C4×Dic61—21no—
74C4×Dic61—21no—
75C2×#92418—41no—
76#11758189—81no—
77#11758189—81no—
78C23×C61—21no—
79C23×C61—21no—
80C23×C61—21no—
81C23×C61—41no—
82C23×C61—41no—
83C23×C61#9511yescharacteristic
84C22×D61—21no—
85C22×D61—21no—
86C22×D61—21no—
87C22×D61—41no—
88C22×D61—41no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—41no—
92C2×C4×C61—41no—
93C22⋊D61—42no—
94C22⋊D61—42no—
95C2×Dic61—21no—
96C2×Dic61—21no—
97C2×Dic61—21no—
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61—42no—
101C2×Dic61—41no—
102C2×Dic61—41no—
103C2×Dic61—41no—
104C2×Dic61#9911yescharacteristic
105C2×Dic61#9911yescharacteristic
106C2×Dic61#10011yescharacteristic
107C2×Dic61#10111yescharacteristic
108C4×D61—41no—
109C4×D61—41no—
110C4×D61—81no—
111#92420—42no—
112#92420—81no—
113#92420—82no—
114C8×C61—81no—
115#92418—81no—
116#7321—611nomaximal, Sylow
117C22×C61—21no—
118C22×C61—21no—
119C22×C61—41no—
120C22×C61—41no—
121C22×C61—41no—
122C22×C61—81no—
123C22×C61—81no—
124C22×C61#34211yescharacteristic
125C22×C61#34311yescharacteristic
126C22×C61#34411yescharacteristic
127C2×D61—42no—
128C2×D61—41no—
129C2×D61—41no—
130C2×D61—41no—
131C2×D61—81no—
132C4×C61—41no—
133C4×C61—41no—
134Dic61—21no—
135Dic61—21no—
136Dic61—21no—
137Dic61—41no—
138Dic61AΣL(1,𝔽16)11yescharacteristic
139Dic61#35211yescharacteristic
140#1870—611no—
141#1800—611no—
142#1465—611no—
143C2×C61—21no—
144C2×C61—21no—
145C2×C61—81no—
146C2×C61#130511yescharacteristic
147C2×C61#139011yescharacteristic
148C2×C61#139211yescharacteristic
149D61—81no—
150C22×M16—611no—
151C2×C4×D4—611no—
152#423—1221no—
153C2×#100—612no—
154#407—1221no—
155C2×C22⋊C8—611no—
156C2×C22⋊C8—1221no—
157#343—1221no—
158#336—1221no—
159#324—1221no—
160#323—611no—
161#323#692311yescharacteristic
162C61#732111yescharacteristic, complemented, Sylow
163C22×D4—611no—
164C23×C4—611no—
165C23×C4—611no—
166C2×M16—1222no—
167C2×M16—2441no—
168C2×M16—2442no—
169C2×M16—2441no—
170C22×C8—1221no—
171C22×C8—1221no—
172C4×D4—2441no—
173C4×D4—2441no—
174C2×C4⋊C4—611no—
175C2×C22⋊C4—611no—
176C2×C22⋊C4C2×#692311yescharacteristic
177C2×C42—611no—
178C4⋊C8—2441no—
179C4⋊C8—2441no—
180#100—2442no—
181C22⋊C8—21no—
182C22⋊C8—1221no—
183C22⋊C8—2441no—
184C22⋊C8—2442no—
185C22⋊C8—2441no—
186C24—611no—
187C24C4×#692311yescharacteristic
188C2×D4—1221no—
189C2×D4—1221no—
190C2×D4—2441no—
191C2×D4—2441no—
192C22×C4—611no—
193C22×C4—611no—
194C22×C4—611no—
195C22×C4—1221no—
196C22×C4—1221no—
197C22×C4—1221no—
198C22×C4—1221no—
199C22×C4—2441no—
200C22×C4—2441no—
201C22×C4—2441no—
202C22×C4—2441no—
203C22×C4C4⋊#692311yescharacteristic
204C22×C4C22⋊#692311yescharacteristic
205M16—4881no—
206M16—4881no—
207M16—2442no—
208M16—2442no—
209M16—2442no—
210M16—2442no—
211C2×C8—41no—
212C2×C8—1222no—
213C2×C8—2441no—
214C2×C8—2441no—
215C2×C8—2441no—
216C2×C8—2442no—
217C2×C8—2441no—
218C2×C8—2441no—
219C2×C8—2441no—
220C4⋊C4—2441no—
221C22⋊C4—41no—
222C22⋊C4—2441no—
223C42—1221no—
224C42—1221no—
225C23—21no—
226C23—21no—
227C23—21no—
228C23—41no—
229C23—41no—
230C23—1221no—
231C23—1221no—
232C23—1221no—
233C23—2441no—
234C23—2441no—
235C23(C2×#6923)⋊C411yescharacteristic
236D4—2442no—
237D4—2442no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—611no—
243C2×C4—611no—
244C2×C4—611no—
245C2×C4—611no—
246C2×C4—1221no—
247C2×C4—1221no—
248C2×C4—1221no—
249C2×C4—1221no—
250C2×C4—1221no—
251C2×C4—4881no—
252C2×C4—2441no—
253C2×C4—2441no—
254C2×C4—2441no—
255C2×C4—2441no—
256C2×C4—2442no—
257C2×C4—2441no—
258C8—81no—
259C8—4881no—
260C8—4881no—
261C8—4882no—
262C8—2442no—
263C22—21no—
264C22—21no—
265C22—41no—
266C22—41no—
267C22—41no—
268C22—81no—
269C22—81no—
270C22—4881no—
271C22—2442no—
272C22—2441no—
273C22—2441no—
274C22—2441no—
275C22#1684063911yescharacteristic
276C22#1684064111yescharacteristic
277C22#1684064411yescharacteristic
278C4—41no—
279C4—41no—
280C4—611no—
281C4—611no—
282C4—1221no—
283C4—1221no—
284C4—1221no—
285C4—2441no—
286C2—21no—
287C2—21no—
288C2—81no—
289C2—4881no—
290C2#2146072111yescharacteristic
291C2#2146090211yescharacteristic
292C2#2146090911yescharacteristic
subgroupG/H
centerC22#16840639
commutatorC24×C61C42
FrattiniC2×C22⋊C4C2×#6923
FittingC61×#323C4
socleC22×C61#342
prime radicalC22×C22⋊D61C2×C4
cosocleC2×#14519737C22
hypercenter#323#6923
hypocenterC61#7321
LCSG ▷ C24×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #323

Complements

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

NH ≅ G/Ntype
162. C61#7321semidirect

Maximal subgroups

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

subgroupindex
#214617982
#214616842
#214441542
#732161