Finite Group Databasebeta

← #30593994

Subgroups — #30593994

Order 15616.

352 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 82 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#21461711C211yesmaximal, characteristic
2#21461674C211yesmaximal, characteristic
3#21445798C211yesmaximal, characteristic
4C2×C4⋊#92420—21no—
5C2×#14519834—21no—
6C2×#14519834C412yes—
7#16840628—21no—
8#16840628—21no—
9#16840628C412yes—
10C2×C42×D61C2211yescharacteristic
11C2×#14519706—21no—
12C2×#14519689—21no—
13#16839517C411yescharacteristic
14C61×#336C411yescharacteristic
15C22×#92420—22no—
16C22×#92420—22no—
17C4⋊#92420—42no—
18#14519834—41no—
19#14519834—41no—
20#14519834—42no—
21C22×C4×D61C2×C411yescharacteristic
22C22×C4×D61D411yescharacteristic
23C22×C4×D61Q811yescharacteristic
24C22×#92418—21no—
25C2×C4×Dic61C2×C411yescharacteristic
26C2×C4×Dic61D411yescharacteristic
27C2×C4×Dic61D411yescharacteristic
28C42×D61—42no—
29#14519706—42no—
30#14519689—41no—
31#14519689—41no—
32C22×C8×C61—21no—
33C2×C42×C61C2×C411yescharacteristic
34C23×D61C4⋊C411yescharacteristic
35C22×C4×C61C4211yescharacteristic
36C22×C4×C61C22⋊C411yescharacteristic
37C22×C4×C61C4⋊C411yescharacteristic
38C22×Dic61C22⋊C411yescharacteristic
39C22×Dic61C22⋊C411yescharacteristic
40C22×Dic61C4⋊C411yescharacteristic
41C2×C4×D61—21no—
42C2×C4×D61—21no—
43C2×C4×D61—22no—
44C2×C4×D61—22no—
45C2×C4×D61—41no—
46C2×C4×D61—41no—
47C2×C4×D61—41no—
48C2×C4×D61—41no—
49C2×C4×D61—41no—
50C2×C4×D61D811yescharacteristic
51C2×C4×D61SD1611yescharacteristic
52C2×C4×D61SD1611yescharacteristic
53C2×C4×D61Q1611yescharacteristic
54C2×#92420—42no—
55C2×#92420—42no—
56C2×#92420—42no—
57C2×#92420—42no—
58C2×#92420—42no—
59C2×#92420—42no—
60C2×C8×C61—41no—
61C2×C8×C61—41no—
62C2×C8×C61—41no—
63C42×C61—41no—
64C4×Dic61—22no—
65C4×Dic61—22no—
66C4×Dic61—41no—
67C2×#92418—41no—
68C2×#92418—41no—
69C2×#92418—41no—
70C23×C61#9511yescharacteristic
71C22×D61—21no—
72C22×D61—21no—
73C22×D61—21no—
74C22×D61—21no—
75C22×D61—21no—
76C22×D61—21no—
77C22×D61#10611yescharacteristic
78C22×D61#10711yescharacteristic
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61#10211yescharacteristic
87C2×C4×C61#10311yescharacteristic
88C2×C4×C61#10811yescharacteristic
89C2×C4×C61#10811yescharacteristic
90C2×Dic61—21no—
91C2×Dic61—21no—
92C2×Dic61—21no—
93C2×Dic61—21no—
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61#9912yes—
97C2×Dic61#10211yescharacteristic
98C2×Dic61#10311yescharacteristic
99C2×Dic61#10812yes—
100C4×D61—41no—
101C4×D61—41no—
102C4×D61—41no—
103C4×D61—41no—
104C4×D61—42no—
105C4×D61—42no—
106C4×D61—44no—
107#92420—82no—
108#92420—82no—
109C8×C61—81no—
110#92418—81no—
111#7044—611nomaximal, Sylow
112C22×C61H(3,ℤ/4)11yescharacteristic
113C22×C61#34011yescharacteristic
114C22×C61#34111yescharacteristic
115C22×C61#34111yescharacteristic
116C22×C61#34211yescharacteristic
117C22×C61#34411yescharacteristic
118C22×C61#34411yescharacteristic
119C2×D61—21no—
120C2×D61—21no—
121C2×D61—21no—
122C2×D61—21no—
123C2×D61—21no—
124C2×D61—21no—
125C2×D61—41no—
126C2×D61—41no—
127C2×D61—41no—
128C2×D61—41no—
129C4×C61—21no—
130C4×C61—21no—
131C4×C61—21no—
132C4×C61—21no—
133C4×C61—41no—
134Dic61—21no—
135Dic61—21no—
136Dic61—22no—
137Dic61—22no—
138#1817—611no—
139#1797—611no—
140#1797—611no—
141C2×C61#128711yescharacteristic
142C2×C61#128711yescharacteristic
143C2×C61#128911yescharacteristic
144C2×C61#129811yescharacteristic
145C2×C61#130111yescharacteristic
146C2×C61#130111yescharacteristic
147C2×C61#130611yescharacteristic
148D61—41no—
149D61—41no—
150C22×C42—611no—
151C2×C4⋊C8—1221no—
152C2×C4⋊C8—1221no—
153C2×C22⋊C8—612no—
154C2×C22⋊C8—1221no—
155C2×C22⋊C8—1221no—
156#336—612no—
157#336—611no—
158#336—1221no—
159#336—1221no—
160#336#692311yescharacteristic
161C61#704411yescharacteristic, complemented, Sylow
162C23×C4—611no—
163C23×C4—611no—
164C23×C4—611no—
165C22×C8—21no—
166C22×C8—1222no—
167C22×C8—1222no—
168C22×C8—1221no—
169C2×C42—611no—
170C2×C42—611no—
171C2×C42—611no—
172C2×C42—2442no—
173C2×C42C2×#692311yescharacteristic
174C4⋊C8—2442no—
175C4⋊C8—2442no—
176C22⋊C8—2441no—
177C22⋊C8—2441no—
178C22⋊C8—2441no—
179C22⋊C8—2441no—
180C22⋊C8—2442no—
181C24—611no—
182C22×C4—611no—
183C22×C4—611no—
184C22×C4—611no—
185C22×C4—611no—
186C22×C4—611no—
187C22×C4—611no—
188C22×C4—611no—
189C22×C4—1222no—
190C22×C4—1222no—
191C22×C4—1221no—
192C22×C4—1221no—
193C22×C4—2441no—
194C22×C4—2441no—
195C22×C4—2441no—
196C22×C4—2441no—
197C22×C4—2441no—
198C22×C4C4×#692311yescharacteristic
199C22×C4C4⋊#692311yescharacteristic
200C22×C4C22⋊#692311yescharacteristic
201C2×C8—41no—
202C2×C8—41no—
203C2×C8—41no—
204C2×C8—2441no—
205C2×C8—2441no—
206C2×C8—2442no—
207C2×C8—2442no—
208C2×C8—2442no—
209C2×C8—2442no—
210C2×C8—2442no—
211C2×C8—2442no—
212C2×C8—2441no—
213C42—41no—
214C42—1222no—
215C42—1222no—
216C42—2441no—
217C23—611no—
218C23—611no—
219C23—1221no—
220C23—1221no—
221C23—1221no—
222C23—1221no—
223C23—1221no—
224C23—1221no—
225C23(C2×#6923)⋊C411yescharacteristic
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—611no—
234C2×C4—611no—
235C2×C4—612no—
236C2×C4—612no—
237C2×C4—1221no—
238C2×C4—1221no—
239C2×C4—1221no—
240C2×C4—1221no—
241C2×C4—1221no—
242C2×C4—1221no—
243C2×C4—2441no—
244C2×C4—2441no—
245C2×C4—2441no—
246C2×C4—2441no—
247C2×C4—2442no—
248C2×C4—2442no—
249C2×C4—2444no—
250C2×C4#1451983911yescharacteristic
251C2×C4#1451984011yescharacteristic
252C2×C4#1451984711yescharacteristic
253C2×C4#1451984811yescharacteristic
254C8—81no—
255C8—4881no—
256C8—4882no—
257C8—4882no—
258C22—1221no—
259C22—1221no—
260C22—1221no—
261C22—1221no—
262C22—1221no—
263C22—1221no—
264C22—2441no—
265C22—2441no—
266C22—2441no—
267C22—2441no—
268C22#1684062911yescharacteristic
269C22#1684063511yescharacteristic
270C22#1684063711yescharacteristic
271C22#1684063811yescharacteristic
272C22#1684063911yescharacteristic
273C22#1684064411yescharacteristic
274C22#1684064511yescharacteristic
275C4—21no—
276C4—21no—
277C4—21no—
278C4—21no—
279C4—41no—
280C4—1221no—
281C4—1221no—
282C4—1222no—
283C4—1222no—
284C2—2441no—
285C2—2441no—
286C2#2146067511yescharacteristic
287C2#2146067611yescharacteristic
288C2#2146068111yescharacteristic
289C2#2146070211yescharacteristic
290C2#2146070911yescharacteristic
291C2#2146071111yescharacteristic
292C2#2146072311yescharacteristic
subgroupG/H
centerC23(C2×#6923)⋊C4
commutatorC22×C4×C61C42
FrattiniC2×C42C2×#6923
FittingC61×#336C4
socleC23×C61#95
prime radicalC23×D61C4⋊C4
cosocleC2×C42×D61C22
hypercenter#336#6923
hypocenterC61#7044
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
161. C61#7044semidirect

Maximal subgroups

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

subgroupindex
#214617112
#214616742
#214457982
#704461