Finite Group Databasebeta

← #30595219

Subgroups — #30595219

Order 15616.

274 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 42 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#21462091C211yesmaximal, characteristic
2#21461956C211yesmaximal, characteristic
3#21447483C211yesmaximal, characteristic
4#16840766C411yescharacteristic, complemented
5C2×#14519842—21no—
6C2×#14519841—21no—
7#16840743—21no—
8#16840698C411yescharacteristic, complemented
9#16840669C412yescomplemented
10#16840666—21no—
11#16840311C2211yescharacteristic
12#16839734—21no—
13#16839557C411yescharacteristic, complemented
14#16839554—21no—
15C61×#354C411yescharacteristic, complemented
16C2×#11758213—21no—
17#14519856—41no—
18C2×C4×#6923—21no—
19C4⋊#92420—41no—
20#14519842—42no—
21#14519841—42no—
22#14519836—22no—
23#14519836—41no—
24(C2×#6923)⋊C4—41no—
25C2×#11758226D411yescharacteristic
26C2×#11758224D411yescharacteristic
27#14519775Q811yescharacteristic
28#14519773D411yescharacteristic
29#14519765C2×C411yescharacteristic
30#14519750—41no—
31#14519737—41no—
32#14519733—41no—
33C42×D61C2×C411yescharacteristic
34#14519692—21no—
35#14519691—41no—
36#124×C61C2×C411yescharacteristic
37#99×C61—21no—
38C22×#6923—41no—
39C2×Q8×C61C4⋊C411yescharacteristic
40C2×D4×C61C22⋊C411yescharacteristic
41C2×C22⋊D61—21no—
42C2×C22⋊D61—41no—
43C22×Dic61—21no—
44#11758226—41no—
45#11758226—41no—
46#11758224—41no—
47#11758224—41no—
48C2×D244—21no—
49C2×D244C22⋊C411yescharacteristic
50C2×C4×D61—21no—
51C2×C4×D61—21no—
52C2×C4×D61C22⋊C411yescharacteristic
53C2×Dic122C4⋊C411yescharacteristic
54C22⋊#6923—42no—
55C2×#92420—41no—
56C4⋊#6923—81no—
57C4×#6923—22no—
58C4×#6923—41no—
59C4×#6923—81no—
60#11758213—41no—
61#11758213—41no—
62C22⋊C4×C61—41no—
63C22⋊C4×C61—41no—
64C42×C61C4211yescharacteristic
65C22⋊Dic61—41no—
66#11758198—41no—
67#11758196—41no—
68#11758196—81no—
69C4×Dic61—21no—
70C4×Dic61—81no—
71C4×Dic61C4⋊C411yescharacteristic
72C23×C61—21no—
73C22×D61—21no—
74C22×D61#9911yescharacteristic
75C2×#6923—42no—
76C2×#6923—82no—
77C2×#6923—82no—
78Q8×C61—41no—
79D4×C61—41no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—81no—
83C2×C4×C61#9511yescharacteristic
84C22⋊D61—81no—
85C22⋊D61—82no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—41no—
89C2×Dic61—41no—
90C2×Dic61—81no—
91C2×Dic61#9911yescharacteristic
92D244—41no—
93D244—81no—
94C4×D61—21no—
95C4×D61—21no—
96C4×D61—41no—
97C4×D61—41no—
98C4×D61—81no—
99Dic122—41no—
100#92420—81no—
101#7506—611nomaximal, Sylow
102C22×C61—41no—
103C22×C61—81no—
104C22×C61#34211yescharacteristic
105C2×D61—21no—
106C2×D61—41no—
107C2×D61—41no—
108C2×D61—81no—
109#6923—82no—
110#6923—162no—
111C4×C61—21no—
112C4×C61—41no—
113C4×C61—41no—
114C4×C61—161no—
115Dic61—41no—
116Dic61—41no—
117Dic61—161no—
118Dic61#35311yescharacteristic
119Dic61#35411yescharacteristic
120#2126—611no—
121#2126—611no—
122#1963—611no—
123C2×C61—21no—
124C2×C61—81no—
125C2×C61#139311yescharacteristic
126D61—41no—
127D61—81no—
128#532—611no—
129#423—611no—
130C2×#104—1221no—
131C2×#104—1221no—
132#410—1221no—
133#410—1221no—
134#376—611no—
135#354—612no—
136#354—611no—
137#354#692311yescharacteristic, complemented
138#353—1221no—
139#353—1221no—
140C61#750611yescharacteristic, complemented, Sylow
141C2×#41—611no—
142C2×#41—611no—
143C2×M16—1221no—
144C4⋊Q8—611no—
145#127—611no—
146#124—611no—
147#124C2×#692311yescharacteristic
148#121—2441no—
149C4×D4—2441no—
150#117—2441no—
151#117—2441no—
152C2×C42—611no—
153C2×C42—1221no—
154C4⋊C8—2441no—
155#104—2442no—
156#104—2442no—
157#99—21no—
158#99—1222no—
159#99—1221no—
160#99—2441no—
161#99—2441no—
162#95—2441no—
163#41—2441no—
164#41—2441no—
165#41—2441no—
166#41—2441no—
167C2×Q8—611no—
168C2×Q8C4⋊#692311yescharacteristic
169C2×D4—611no—
170C2×D4—1221no—
171C2×D4—1221no—
172C2×D4—2441no—
173C2×D4C22⋊#692311yescharacteristic
174C22×C4—611no—
175C22×C4—1221no—
176C22×C4—1221no—
177C22×C4—1221no—
178C22×C4—2441no—
179M16—2441no—
180M16—2441no—
181C2×C8—2441no—
182C4⋊C4—4881no—
183C4⋊C4—4881no—
184C4⋊C4—2441no—
185C22⋊C4—41no—
186C22⋊C4—41no—
187C22⋊C4—2441no—
188C22⋊C4—2441no—
189C22⋊C4—2442no—
190C42—611no—
191C42—1221no—
192C42—1222no—
193C42—4881no—
194C42—4881no—
195C42—2441no—
196C42C4×#692311yescharacteristic
197C23—21no—
198C23—611no—
199C23—1221no—
200Q8—41no—
201Q8—2441no—
202D4—41no—
203D4—4881no—
204D4—4881no—
205D4—4882no—
206D4—2441no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—81no—
210C2×C4—611no—
211C2×C4—1221no—
212C2×C4—1221no—
213C2×C4—1221no—
214C2×C4—1221no—
215C2×C4—4881no—
216C2×C4—4881no—
217C2×C4—4882no—
218C2×C4—4882no—
219C2×C4—2441no—
220C2×C4—2441no—
221C2×C4—2441no—
222C2×C4—2441no—
223C2×C4—2442no—
224C2×C4(C2×#6923)⋊C411yescharacteristic
225C8—4881no—
226C22—41no—
227C22—81no—
228C22—1221no—
229C22—4881no—
230C22—2441no—
231C22—2441no—
232C22#1684063911yescharacteristic
233C4—21no—
234C4—41no—
235C4—41no—
236C4—161no—
237C4—611no—
238C4—611no—
239C4—9761no—
240C4—9762no—
241C4—4882no—
242C4—2441no—
243C4—2441no—
244C2—21no—
245C2—81no—
246C2—4881no—
247C2—2441no—
248C2#2146091211yescharacteristic
subgroupG/H
centerC2#21460912
commutatorC42×C61C42
Frattini#124C2×#6923
FittingC61×#354C4
socleC2×C61#1393
prime radical, cosocle#16840311C22
hypercenter#354#6923
hypocenterC61#7506
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #354

Complements

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

NH ≅ G/Ntype
4. #16840766C4semidirect
8. #16840698C4semidirect
9. #16840669C4semidirect
13. #16839557C4semidirect
15. C61×#354C4semidirect
137. #354#6923semidirect
140. C61#7506semidirect

Maximal subgroups

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

subgroupindex
#214620912
#214619562
#214474832
#750661