Finite Group Databasebeta

← #30594558

Subgroups — #30594558

Order 15616.

328 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 74 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#21461524C211yesmaximal, characteristic
2#21461052C211yesmaximal, characteristic
3#21445800C211yesmaximal, characteristic
4C2×D61⋊M16—21no—
5#16840778—21no—
6#16840642—21no—
7#16840642C412yes—
8#16840608—21no—
9#16840606C412yes—
10C2×#14519734C2211yescharacteristic
11C2×C4⋊#92418C411yescharacteristic
12C2×#14519689—21no—
13#16839516—21no—
14C2×C4⋊C8×C61C411yescharacteristic
15C2×#11758213—41no—
16D61⋊M16—22no—
17D61⋊M16—22no—
18D61⋊M16—41no—
19D61⋊M16—41no—
20C2×#11758217—22no—
21C2×D61⋊C8—41no—
22C4⋊#92420—41no—
23C22⋊#92420—22no—
24C4×#92420—41no—
25C22×C4×D61D411yescharacteristic
26C22×#92418—21no—
27#14519734—41no—
28#14519734—41no—
29C2×#11758196C2×C411yescharacteristic
30C2×#11758196D411yescharacteristic
31C2×#11758198C2×C411yescharacteristic
32C2×#11758198Q811yescharacteristic
33C2×C4×Dic61D411yescharacteristic
34C4⋊#92418—41no—
35#14519689—41no—
36#14519689—41no—
37C22×C8×C61—21no—
38C2×C42×C61C2×C411yescharacteristic
39C4⋊C8×C61—41no—
40C23×D61C4⋊C411yescharacteristic
41C22×C4×C61C4211yescharacteristic
42C22×C4×C61C22⋊C411yescharacteristic
43C22×C4×C61C4⋊C411yescharacteristic
44C22×Dic61C22⋊C411yescharacteristic
45C22×Dic61C22⋊C411yescharacteristic
46C22×Dic61C4⋊C411yescharacteristic
47C2×C4×D61—21no—
48C2×C4×D61—21no—
49C2×C4×D61—21no—
50C2×C4×D61—21no—
51C2×C4×D61D811yescharacteristic
52C2×C4×D61SD1611yescharacteristic
53C2×C4×D61SD1611yescharacteristic
54C2×C4×D61Q1611yescharacteristic
55#11758217—24no—
56#11758217—42no—
57C2×#92420—42no—
58C2×#92420—42no—
59#11758213—42no—
60#11758213—42no—
61D61⋊C8—42no—
62D61⋊C8—42no—
63C2×C8×C61—41no—
64C2×C8×C61—41no—
65C2×C8×C61—41no—
66C42×C61—21no—
67C42×C61—21no—
68#11758198—41no—
69#11758198—41no—
70#11758196—41no—
71#11758196—41no—
72C4×Dic61—21no—
73C4×Dic61—21no—
74C2×#92418—41no—
75C2×#92418—41no—
76C2×#92418—41no—
77C23×C61#9511yescharacteristic
78C22×D61—21no—
79C22×D61—21no—
80C22×D61—41no—
81C22×D61—41no—
82C22×D61#10611yescharacteristic
83C22×D61#10711yescharacteristic
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—41no—
87C2×C4×C61—41no—
88C2×C4×C61#9911yescharacteristic
89C2×C4×C61#9911yescharacteristic
90C2×C4×C61#10211yescharacteristic
91C2×C4×C61#10311yescharacteristic
92C2×C4×C61#10411yescharacteristic
93C2×C4×C61#10411yescharacteristic
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—21no—
97C2×Dic61—21no—
98C2×Dic61—41no—
99C2×Dic61—41no—
100C2×Dic61#10211yescharacteristic
101C2×Dic61#10311yescharacteristic
102C4×D61—21no—
103C4×D61—21no—
104C4×D61—21no—
105C4×D61—21no—
106C4×D61—21no—
107C4×D61—21no—
108C4×D61—21no—
109C4×D61—21no—
110#92420—44no—
111#92420—82no—
112C8×C61—81no—
113#92418—81no—
114#7253—611nomaximal, Sylow
115C22×C61—21no—
116C22×C61—21no—
117C22×C61#33911yescharacteristic
118C22×C61#34011yescharacteristic
119C22×C61#34211yescharacteristic
120C2×D61—21no—
121C2×D61—21no—
122C2×D61—41no—
123C2×D61—41no—
124C2×D61—41no—
125C2×D61—41no—
126C2×D61—81no—
127C4×C61—41no—
128C4×C61—41no—
129C4×C61#32711yescharacteristic
130C4×C61#32711yescharacteristic
131C4×C61#32811yescharacteristic
132C4×C61#32811yescharacteristic
133Dic61—21no—
134Dic61—21no—
135Dic61—41no—
136Dic61—41no—
137#1798—611no—
138#1742—611no—
139#1458—611no—
140C2×C61—21no—
141C2×C61—21no—
142C2×C61#129411yescharacteristic
143C2×C61#139211yescharacteristic
144C2×C61#139511yescharacteristic
145D61—41no—
146D61—41no—
147C22×M16—1221no—
148C2×#117—611no—
149#431—1221no—
150C2×C4⋊C8—611no—
151C2×C4⋊C8#692311yescharacteristic
152C2×C22⋊C8—1221no—
153#343—612no—
154#343—1221no—
155#336—1221no—
156#324—1221no—
157#323—612no—
158C61#725311yescharacteristic, complemented, Sylow
159C23×C4—611no—
160C2×M16—1222no—
161C2×M16—1222no—
162C2×M16—1222no—
163C2×M16—2441no—
164C2×M16—2441no—
165C2×M16—2441no—
166C22×C8—21no—
167C22×C8—1221no—
168C22×C8—2441no—
169#117—2441no—
170#117—2441no—
171C2×C4⋊C4—611no—
172C2×C4⋊C4—611no—
173C2×C22⋊C4—611no—
174C2×C22⋊C4—611no—
175C2×C42—611no—
176C2×C42C2×#692311yescharacteristic
177C4⋊C8—41no—
178C4⋊C8—2441no—
179C4⋊C8—2441no—
180C22⋊C8—1222no—
181C22⋊C8—2441no—
182C22⋊C8—2441no—
183C4×C8—2441no—
184C24—611no—
185C22×C4—611no—
186C22×C4—611no—
187C22×C4—611no—
188C22×C4—611no—
189C22×C4—611no—
190C22×C4—611no—
191C22×C4—611no—
192C22×C4—1221no—
193C22×C4—1221no—
194C22×C4—1221no—
195C22×C4—1221no—
196C22×C4C4×#692311yescharacteristic
197C22×C4C4⋊#692311yescharacteristic
198C22×C4C22⋊#692311yescharacteristic
199M16—1224no—
200M16—2442no—
201M16—2442no—
202M16—2442no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8—41no—
206C2×C8—2442no—
207C2×C8—2441no—
208C2×C8—2441no—
209C2×C8—2441no—
210C2×C8—2442no—
211C2×C8—2442no—
212C2×C8—2442no—
213C4⋊C4—2441no—
214C4⋊C4—2441no—
215C22⋊C4—2441no—
216C22⋊C4—2441no—
217C42—21no—
218C42—21no—
219C42—1221no—
220C42—1221no—
221C23—611no—
222C23—611no—
223C23—1221no—
224C23—1221no—
225C23—2441no—
226C23—2441no—
227C23(C2×#6923)⋊C411yescharacteristic
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—611no—
233C2×C4—611no—
234C2×C4—1221no—
235C2×C4—1221no—
236C2×C4—1221no—
237C2×C4—1221no—
238C2×C4—1221no—
239C2×C4—1221no—
240C2×C4—1221no—
241C2×C4—1221no—
242C2×C4—1221no—
243C2×C4—1221no—
244C2×C4—1221no—
245C2×C4—1221no—
246C2×C4—2441no—
247C2×C4—2441no—
248C2×C4#1451983511yescharacteristic
249C2×C4#1451983611yescharacteristic
250C2×C4#1451983911yescharacteristic
251C2×C4#1451984011yescharacteristic
252C2×C4#1451984111yescharacteristic
253C2×C4#1451984211yescharacteristic
254C8—81no—
255C8—4882no—
256C8—4881no—
257C8—2444no—
258C22—21no—
259C22—21no—
260C22—1221no—
261C22—1221no—
262C22—4881no—
263C22—2441no—
264C22—2441no—
265C22—2441no—
266C22—2441no—
267C22#1684063211yescharacteristic
268C22#1684063511yescharacteristic
269C22#1684064011yescharacteristic
270C4—41no—
271C4—41no—
272C4—1221no—
273C4—1221no—
274C4—2441no—
275C4—2441no—
276C4#1684061311yescharacteristic
277C4#1684061411yescharacteristic
278C4#1684061511yescharacteristic
279C4#1684061611yescharacteristic
280C2—21no—
281C2—21no—
282C2—2441no—
283C2—2441no—
284C2#2146069211yescharacteristic
285C2#2146091111yescharacteristic
286C2#2146091911yescharacteristic
subgroupG/H
centerC2×C4#14519836
commutatorC22×C4×C61C42
FrattiniC2×C42C2×#6923
FittingC2×C4⋊C8×C61C4
socleC22×C61#342
prime radicalC23×D61C4⋊C4
cosocleC2×#14519734C22
hypercenterC2×C4⋊C8#6923
hypocenterC61#7253
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
158. C61#7253semidirect

Maximal subgroups

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

subgroupindex
#214615242
#214610522
#214458002
#725361