Finite Group Databasebeta

← #30595199

Subgroups — #30595199

Order 15616.

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

normal subgroups only

This group has 294 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#21461954C211yesmaximal, characteristic
3#21447483C211yesmaximal, characteristic
4#16840767C411yescharacteristic, complemented
5C2×#14519842—21no—
6C2×#14519841—21no—
7#16840743—21no—
8C42×#6923C411yescharacteristic, 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—
19C2×C4×#6923—41no—
20#14519844—41no—
21#14519842—42no—
22#14519841—42no—
23#14519836—22no—
24#14519836—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—44no—
60C4×#6923—81no—
61#11758213—41no—
62#11758213—41no—
63C22⋊C4×C61—41no—
64C22⋊C4×C61—41no—
65C42×C61C4211yescharacteristic
66C22⋊Dic61—41no—
67#11758198—41no—
68#11758196—41no—
69#11758196—81no—
70C4×Dic61—21no—
71C4×Dic61—81no—
72C4×Dic61C4⋊C411yescharacteristic
73C23×C61—21no—
74C22×D61—21no—
75C22×D61#9911yescharacteristic
76C2×#6923—42no—
77C2×#6923—44no—
78C2×#6923—82no—
79Q8×C61—41no—
80D4×C61—41no—
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—81no—
84C2×C4×C61#9511yescharacteristic
85C22⋊D61—82no—
86C22⋊D61—81no—
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—41no—
90C2×Dic61—41no—
91C2×Dic61—81no—
92C2×Dic61#9911yescharacteristic
93D244—41no—
94D244—81no—
95C4×D61—21no—
96C4×D61—21no—
97C4×D61—42no—
98C4×D61—41no—
99C4×D61—41no—
100Dic122—41no—
101#92420—81no—
102#7500—611nomaximal, Sylow
103C22×C61—41no—
104C22×C61—81no—
105C22×C61#34211yescharacteristic
106C2×D61—21no—
107C2×D61—41no—
108C2×D61—41no—
109C2×D61—81no—
110#6923—44no—
111#6923—162no—
112C4×C61—21no—
113C4×C61—41no—
114C4×C61—41no—
115C4×C61—161no—
116Dic61—22no—
117Dic61—41no—
118Dic61—161no—
119Dic61#35311yescharacteristic
120Dic61#35411yescharacteristic
121#2126—611no—
122#2126—611no—
123#1962—611no—
124C2×C61—21no—
125C2×C61—81no—
126C2×C61#139311yescharacteristic
127D61—41no—
128D61—81no—
129#532—611no—
130#423—611no—
131C2×#104—1221no—
132C2×#104—1221no—
133#410—1221no—
134#410—1221no—
135C43—611no—
136#354—612no—
137#354—611no—
138#354#692311yescharacteristic, complemented
139#353—1221no—
140#353—1221no—
141C61#750011yescharacteristic, complemented, Sylow
142C2×#41—611no—
143C2×#41—611no—
144C2×M16—1221no—
145C4⋊Q8—611no—
146#127—611no—
147#124—611no—
148#124C2×#692311yescharacteristic
149#121—2441no—
150C4×D4—2441no—
151#117—2441no—
152#117—2441no—
153C2×C42—611no—
154C2×C42—1221no—
155C2×C42—2441no—
156C4⋊C8—2441no—
157#104—2442no—
158#104—2442no—
159#99—21no—
160#99—1222no—
161#99—1221no—
162#99—2441no—
163#99—2441no—
164#41—2441no—
165#41—2441no—
166#41—2441no—
167#41—2441no—
168C2×Q8—611no—
169C2×Q8C4⋊#692311yescharacteristic
170C2×D4—611no—
171C2×D4—1221no—
172C2×D4—1221no—
173C2×D4—2441no—
174C2×D4C22⋊#692311yescharacteristic
175C22×C4—611no—
176C22×C4—1221no—
177C22×C4—1221no—
178C22×C4—1221no—
179C22×C4—2441no—
180M16—2441no—
181M16—2441no—
182C2×C8—2441no—
183C4⋊C4—4881no—
184C4⋊C4—4881no—
185C4⋊C4—2441no—
186C22⋊C4—41no—
187C22⋊C4—41no—
188C22⋊C4—2441no—
189C22⋊C4—2441no—
190C22⋊C4—2442no—
191C42—611no—
192C42—1221no—
193C42—1222no—
194C42—4881no—
195C42—4881no—
196C42—2441no—
197C42—2444no—
198C42C4×#692311yescharacteristic
199C23—21no—
200C23—611no—
201C23—1221no—
202Q8—41no—
203Q8—2441no—
204D4—41no—
205D4—4881no—
206D4—4882no—
207D4—4881no—
208D4—2441no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—81no—
212C2×C4—611no—
213C2×C4—1221no—
214C2×C4—1221no—
215C2×C4—1221no—
216C2×C4—1221no—
217C2×C4—4881no—
218C2×C4—4882no—
219C2×C4—2441no—
220C2×C4—2441no—
221C2×C4—2442no—
222C2×C4—2441no—
223C2×C4—2441no—
224C2×C4—2442no—
225C2×C4—2444no—
226C2×C4(C2×#6923)⋊C411yescharacteristic
227C8—4881no—
228C22—41no—
229C22—81no—
230C22—1221no—
231C22—4881no—
232C22—2441no—
233C22—2441no—
234C22#1684063911yescharacteristic
235C4—21no—
236C4—41no—
237C4—41no—
238C4—161no—
239C4—611no—
240C4—611no—
241C4—1222no—
242C4—9761no—
243C4—9762no—
244C4—2444no—
245C4—2441no—
246C2—21no—
247C2—81no—
248C2—4881no—
249C2—2441no—
250C2#2146091211yescharacteristic
subgroupG/H
centerC2#21460912
commutatorC42×C61C42
Frattini#124C2×#6923
FittingC61×#354C4
socleC2×C61#1393
prime radical, cosocle#16840311C22
hypercenter#354#6923
hypocenterC61#7500
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. #16840767C4semidirect
8. C42×#6923C4semidirect
9. #16840669C4semidirect
13. #16839557C4semidirect
15. C61×#354C4semidirect
138. #354#6923semidirect
141. C61#7500semidirect

Maximal subgroups

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

subgroupindex
#214620912
#214619542
#214474832
#750061