Finite Group Databasebeta

← #30604035

Subgroups — #30604035

Order 15616.

364 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 86 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#21462055C212yesmaximal, complemented
2#21460766C212yesmaximal, complemented
3#21460754C212yesmaximal, complemented
4#21454534C211yesmaximal, characteristic
5C2×#14519851—22no—
6#16840658—22no—
7#16840658C2214yes—
8C2×#14519785C411yescharacteristic
9C2×#14519784C2211yescharacteristic
10#16840308C411yescharacteristic
11#16839836—22no—
12#16839830—22no—
13#16839785C2211yescharacteristic
14#16839728C2211yescharacteristic
15C2×#14519687C411yescharacteristic
16C61×#408C411yescharacteristic
17#14519851—24no—
18#14519851—42no—
19C2×#11758187—42no—
20C2×#11758222C2×C411yescharacteristic
21#14519785—42no—
22#14519784—42no—
23C2×#11758194D412yes—
24C2×#11758194C2311yescharacteristic
25C2×#11758189—21no—
26C22×#92418C2×C411yescharacteristic
27C22×#92418D412yes—
28C2×C8×D61—21no—
29#14519775C811yescharacteristic
30#14519773C811yescharacteristic
31#14519766C811yescharacteristic
32#14519764C811yescharacteristic
33#14519749—22no—
34C4×C22⋊D61—22no—
35C2×C4×Dic61C2×C411yescharacteristic
36#14519706—22no—
37#14519689—22no—
38#14519687—21no—
39#14519687—21no—
40C2×#41×C61C2×C411yescharacteristic
41C2×M16×C61C2×C411yescharacteristic
42C22×C8×C61C2×C411yescharacteristic
43C22⋊C8×C61—22no—
44#41×C61—41no—
45#41×C61—41no—
46C2×Q8×C61C2×C811yescharacteristic
47C2×D4×C61C2×C811yescharacteristic
48C2×D4×C61M1612yes—
49C22×C4×C61C22⋊C412yes—
50C22×C4×C61C22×C411yescharacteristic
51C2×C22⋊D61—21no—
52C2×C22⋊D61—22no—
53C22×Dic61—21no—
54#11758222—41no—
55#11758222—41no—
56C2×D244C2×C811yescharacteristic
57C2×C4×D61—21no—
58C2×Dic122C2×C811yescharacteristic
59M16×C61—41no—
60C2×C8×C61—21no—
61C2×C8×C61—21no—
62C2×C8×C61—41no—
63C22⋊Dic61—22no—
64#11758198—22no—
65#11758196—22no—
66C4×Dic61—21no—
67C4×Dic61C2×C811yescharacteristic
68C4×Dic61C2×C811yescharacteristic
69#11758194—42no—
70#11758194—41no—
71C2×#92418—22no—
72C2×#92418—22no—
73C2×#92418—22no—
74C2×#92418C22⋊C411yescharacteristic
75C2×#92418C22⋊C411yescharacteristic
76C2×#92418C2×D412yes—
77#11758189—42no—
78C8×D61—42no—
79#11758187—44no—
80C23×C61C22⋊C812yes—
81C23×C61C2×M1611yescharacteristic
82C22×D61—21no—
83Q8×C61—41no—
84D4×C61—41no—
85D4×C61—42no—
86C2×C4×C61—21no—
87C2×C4×C61—22no—
88C2×C4×C61—21no—
89C2×C4×C61—22no—
90C2×C4×C61C22⋊C812yes—
91C2×C4×C61C2×C22⋊C411yescharacteristic
92C2×C4×C61C22×C811yescharacteristic
93C22⋊D61—42no—
94C22⋊D61—82no—
95C2×Dic61—21no—
96C2×Dic61—21no—
97C2×Dic61—21no—
98C2×Dic61—81no—
99D244—41no—
100C4×D61—41no—
101C4×D61—41no—
102Dic122—41no—
103C8×C61—41no—
104C8×C61—41no—
105#92418—22no—
106#92418—21no—
107#92418#9912yes—
108#11486—611nomaximal, Sylow
109C22×C61—21no—
110C22×C61—22no—
111C22×C61—41no—
112C22×C61—42no—
113C22×C61C2×C22⋊C811yescharacteristic
114C2×D61—42no—
115C2×D61—41no—
116C4×C61—21no—
117C4×C61—22no—
118C4×C61C2×#9911yescharacteristic
119C4×C61#41311yescharacteristic
120Dic61—41no—
121Dic61—41no—
122Dic61—41no—
123#2932—611no—
124#2115—612no—
125#1327—612no—
126#1321—612no—
127C2×C61—21no—
128C2×C61—41no—
129C2×C61—42no—
130C2×C61#145911yescharacteristic
131D61—81no—
132C2×#131—611no—
133C2×#131—611no—
134#532—611no—
135C2×M32—1222no—
136#435—1222no—
137#435—1222no—
138#423—611no—
139#408—611no—
140#408#692311yescharacteristic
141C2×#97—611no—
142#349—614no—
143#349—1222no—
144C61#1148611yescharacteristic, complemented, Sylow
145C2×#41—611no—
146C2×#41C2×#692311yescharacteristic
147#131—2442no—
148#131—2442no—
149C2×M16—612no—
150C2×M16—611no—
151C2×M16—1221no—
152C2×M16C2×#692311yescharacteristic
153C22×C8—612no—
154C22×C8—611no—
155C22×C8—1221no—
156C22×C8C2×#692311yescharacteristic
157C4⋊Q8—611no—
158#127—611no—
159#124—611no—
160#124—611no—
161#121—1222no—
162C4×D4—1222no—
163C2×C42—611no—
164M32—1224no—
165M32—2442no—
166C2×C16—2442no—
167C4⋊C8—1222no—
168C22⋊C8—22no—
169C22⋊C8—1222no—
170#97—1221no—
171#97—1221no—
172#41—41no—
173#41—41no—
174#41—2441no—
175#41—2441no—
176C2×Q8—611no—
177C2×Q8D61⋊C811yescharacteristic
178C2×D4—611no—
179C2×D4—1222no—
180C2×D4—1221no—
181C2×D4D61⋊C811yescharacteristic
182C2×D4#1175821312yes—
183C22×C4—1221no—
184C22×C4—1221no—
185C22×C4C22⋊#692312yes—
186C22×C4C22×#692311yescharacteristic
187M16—41no—
188M16—2442no—
189M16—2441no—
190M16—2442no—
191C2×C8—21no—
192C2×C8—21no—
193C2×C8—41no—
194C2×C8—611no—
195C2×C8—611no—
196C2×C8—612no—
197C2×C8—1222no—
198C2×C8—1222no—
199C2×C8—1222no—
200C2×C8—2442no—
201C4⋊C4—1222no—
202C22⋊C4—1222no—
203C22⋊C4—1222no—
204C42—611no—
205C42—611no—
206C42—1221no—
207C16—2444no—
208C23—1221no—
209C23#1451983412yes—
210C23C2×#1175821311yescharacteristic
211Q8—41no—
212Q8—2441no—
213D4—41no—
214D4—42no—
215D4—4882no—
216D4—2441no—
217D4—2442no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—1221no—
223C2×C4—1221no—
224C2×C4—1221no—
225C2×C4—4881no—
226C2×C4—2441no—
227C2×C4—2441no—
228C2×C4#1451983412yes—
229C2×C4C2×C22⋊#692311yescharacteristic
230C2×C4C2×D61⋊C811yescharacteristic
231C8—41no—
232C8—41no—
233C8—612no—
234C8—1222no—
235C8—1221no—
236C22—21no—
237C22—22no—
238C22—41no—
239C22—42no—
240C22—2442no—
241C22—2441no—
242C22C2×#1451983411yescharacteristic
243C4—22no—
244C4—21no—
245C4—2441no—
246C4—2441no—
247C4—2441no—
248C4D61⋊#9911yescharacteristic
249C4#1684074911yescharacteristic
250C2—21no—
251C2—41no—
252C2—42no—
253C2—4881no—
254C2#2146105711yescharacteristic
subgroupG/H
centerC4D61⋊#99
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#408C4
socleC2×C61#1459
prime radical#16840308C4
cosocleC2×#11758194C23
hypercenter#408#6923
hypocenterC61#11486
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #21462055C2semidirect
2. #21460766C2semidirect
3. #21460754C2semidirect
144. C61#11486semidirect

Maximal subgroups

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

subgroupindex
#214620552
#214607662
#214607542
#214545342
#1148661