Finite Group Databasebeta

← #30604199

Subgroups — #30604199

Order 15616.

424 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 70 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#21461082C212yesmaximal, complemented
2#21460762C212yesmaximal, complemented
3#21460748C212yesmaximal
4#21448533C211yesmaximal, characteristic
5#16840782—22no—
6#16840607—22no—
7#16840607C2214yes—
8C2×#14519766C411yescharacteristic
9C2×Q8×Dic61C2211yescharacteristic
10C2×#14519739C411yescharacteristic
11#16839664C2211yescharacteristic
12#16839651—22no—
13#16839636—22no—
14#16839631C2211yescharacteristic
15#16839608C411yescharacteristic
16C61×#391C411yescharacteristic
17#14519844—42no—
18C22⋊#92420—24no—
19#14519832—42no—
20C22×D244C2×C411yescharacteristic
21C22×C4×D61—21no—
22#14519766—22no—
23#14519766—22no—
24Q8×Dic61—42no—
25#14519739—42no—
26C2×C4⋊Dic61D412yes—
27C2×C4⋊Dic61C2311yescharacteristic
28C2×#11758196—22no—
29C2×#11758198—22no—
30C2×#11758198—21no—
31C2×#11758198—22no—
32C2×C4×Dic61C2×C411yescharacteristic
33C2×C4×Dic61C2×C411yescharacteristic
34C2×C4×Dic61D412yes—
35#14519684—21no—
36#14519684—21no—
37C22×Q8×C61C2×C411yescharacteristic
38C2×C4⋊C4×C61C2×C411yescharacteristic
39C2×C42×C61C2×C411yescharacteristic
40#95×C61—22no—
41C23×D61—21no—
42C2×Q8×C61—21no—
43C2×Q8×C61—21no—
44C2×Q8×C61—41no—
45C2×Q8×C61—41no—
46C22×C4×C61—21no—
47C22×C4×C61—21no—
48C22×C4×C61C22⋊C412yes—
49C22×C4×C61C22×C411yescharacteristic
50C22×Dic61—21no—
51C22×Dic61C22⋊C411yescharacteristic
52C22×Dic61C22⋊C411yescharacteristic
53C22×Dic61C2×D412yes—
54C2×D244—21no—
55C2×D244—41no—
56C2×D244—41no—
57C2×D244M1612yes—
58C2×C4×D61—42no—
59C2×C4×D61—82no—
60C2×#92420—44no—
61C4⋊C4×C61—41no—
62C42×C61—41no—
63#11758198—28no—
64#11758198—42no—
65#11758198—82no—
66C4⋊Dic61—42no—
67C4⋊Dic61—41no—
68#11758196—82no—
69C4×Dic61—21no—
70C4×Dic61—22no—
71C4×Dic61—22no—
72C4×Dic61—22no—
73C4×Dic61M1612yes—
74C23×C61C2×C22⋊C411yescharacteristic
75C22×D61—22no—
76C22×D61—42no—
77C22×D61—42no—
78C22×D61—41no—
79C22×D61—41no—
80Q8×C61—42no—
81Q8×C61—42no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61—22no—
87C2×C4×C61—42no—
88C2×C4×C61—41no—
89C2×C4×C61—41no—
90C2×C4×C61—41no—
91C2×C4×C61—41no—
92C2×C4×C61C2×M1611yescharacteristic
93C2×C4×C61C2×M1611yescharacteristic
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—21no—
97C2×Dic61—41no—
98C2×Dic61—41no—
99C2×Dic61—41no—
100C2×Dic61—42no—
101C2×Dic61—41no—
102C2×Dic61#9912yes—
103D244—42no—
104D244—42no—
105C4×D61—84no—
106#92420—84no—
107#11534—611nomaximal, Sylow
108C22×C61—21no—
109C22×C61—21no—
110C22×C61#40711yescharacteristic
111C22×C61C2×#9911yescharacteristic
112C22×C61#41311yescharacteristic
113C2×D61—44no—
114C2×D61—42no—
115C2×D61—82no—
116C2×D61—81no—
117C2×D61—81no—
118C4×C61—21no—
119C4×C61—21no—
120C4×C61—42no—
121C4×C61—81no—
122C4×C61—81no—
123Dic61—22no—
124Dic61—42no—
125Dic61—42no—
126Dic61—41no—
127#2326—611no—
128#1467—612no—
129#1325—612no—
130#1318—612no—
131C2×C61—21no—
132C2×C61—21no—
133C2×C61#146511yescharacteristic
134C2×C61#212811yescharacteristic
135C2×C61#213311yescharacteristic
136D61—82no—
137C2×#124—611no—
138C2×C4×Q8—611no—
139C2×C4×D4—611no—
140#432—1222no—
141#391#692311yescharacteristic
142#390—611no—
143#388—1222no—
144#385—1222no—
145#384—611no—
146#376—611no—
147#324—614no—
148#324—1222no—
149C61#1153411yescharacteristic, complemented, Sylow
150C22×Q8C2×#692311yescharacteristic
151C22×D4—611no—
152C23×C4—1221no—
153#124—1222no—
154#124—1222no—
155C4×Q8—2442no—
156C4×D4—2442no—
157C2×C4⋊C4—612no—
158C2×C4⋊C4—611no—
159C2×C4⋊C4—1222no—
160C2×C4⋊C4C2×#692311yescharacteristic
161C2×C22⋊C4—1222no—
162C2×C22⋊C4—1222no—
163C2×C22⋊C4—1221no—
164C2×C42—611no—
165C2×C42—612no—
166C2×C42—611no—
167C2×C42C2×#692311yescharacteristic
168C4⋊C8—2442no—
169C22⋊C8—1224no—
170#97—2442no—
171#95—22no—
172#95—1221no—
173#95—1221no—
174C24—1221no—
175C2×Q8—21no—
176C2×Q8—21no—
177C2×Q8—41no—
178C2×Q8—41no—
179C2×D4—612no—
180C2×D4—1221no—
181C2×D4—2441no—
182C2×D4—2441no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—611no—
186C22×C4—611no—
187C22×C4—612no—
188C22×C4—1221no—
189C22×C4—4882no—
190C22×C4—2442no—
191C22×C4C22⋊#692312yes—
192C22×C4C22×#692311yescharacteristic
193C2×C8—2444no—
194C4⋊C4—41no—
195C4⋊C4—4882no—
196C4⋊C4—2441no—
197C4⋊C4—2442no—
198C22⋊C4—1228no—
199C22⋊C4—4882no—
200C22⋊C4—2442no—
201C42—41no—
202C42—612no—
203C42—1222no—
204C42—1222no—
205C42—1222no—
206C42—1221no—
207C23—1222no—
208C23—2442no—
209C23—2442no—
210C23—2441no—
211C23—2441no—
212C23C2×C22⋊#692311yescharacteristic
213Q8—42no—
214Q8—42no—
215D4—2442no—
216D4—2442no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—41no—
223C2×C4—42no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—612no—
228C2×C4—1222no—
229C2×C4—1222no—
230C2×C4—1221no—
231C2×C4—4884no—
232C2×C4—2441no—
233C2×C4—2441no—
234C2×C4—2441no—
235C2×C4—2442no—
236C2×C4—2441no—
237C2×C4D61⋊M1611yescharacteristic
238C2×C4D61⋊M1611yescharacteristic
239C8—4884no—
240C22—21no—
241C22—21no—
242C22—4882no—
243C22—4881no—
244C22—4881no—
245C22—2444no—
246C22—2442no—
247C22#1684073411yescharacteristic
248C22D61⋊#9911yescharacteristic
249C22#1684074911yescharacteristic
250C4—21no—
251C4—21no—
252C4—42no—
253C4—81no—
254C4—81no—
255C4—1222no—
256C4—2442no—
257C4—2442no—
258C4—2441no—
259C2—21no—
260C2—21no—
261C2—4882no—
262C2#2146107711yescharacteristic
263C2#2146209911yescharacteristic
264C2#2146211711yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#391C4
socleC22×C61C2×#99
prime radicalC22×D244C2×C4
cosocleC2×C4⋊Dic61C23
hypercenter#391#6923
hypocenterC61#11534
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #391

Complements

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

NH ≅ G/Ntype
1. #21461082C2semidirect
2. #21460762C2semidirect
149. C61#11534semidirect

Maximal subgroups

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

subgroupindex
#214610822
#214607622
#214607482
#214485332
#1153461