Finite Group Databasebeta

← #30605517

Subgroups — #30605517

Order 15616.

284 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 62 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#21462194C211yesmaximal, characteristic, complemented
2#21462041C211yesmaximal, characteristic, complemented
3#21460824C212yesmaximal, complemented
4#21460821C212yesmaximal, complemented
5#21456444C211yesmaximal, characteristic
6D61⋊M32—21no—
7#16840684—21no—
8#16840659—21no—
9#16840655—21no—
10#16840654C2212yes—
11#16840654C2212yes—
12#16840373C411yescharacteristic
13#16840366C411yescharacteristic
14#16840164C411yescharacteristic
15#16840130C2211yescharacteristic
16#16840126C2211yescharacteristic
17#16840005—21no—
18#16839988—21no—
19#16839863—21no—
20SD16×Dic61—21no—
21#16839716C2211yescharacteristic
22C61×#492C411yescharacteristic
23#14519852—22no—
24#14519851—22no—
25#14519851—22no—
26D61⋊C16—22no—
27C2×#11758189D411yescharacteristic
28C2×C8×D61D411yescharacteristic
29#14519772—41no—
30#14519769C2×C411yescharacteristic
31#14519769C2×C411yescharacteristic
32#14519767—41no—
33#14519758—41no—
34#14519753—21no—
35#14519749—41no—
36#14519748—21no—
37Q8×Dic61—21no—
38D4×Dic61—21no—
39#14519734C2×C411yescharacteristic
40#14519711—21no—
41#14519709—21no—
42#14519701—21no—
43#14519701—21no—
44#14519698—21no—
45#14519698—21no—
46#14519688C2311yescharacteristic
47#14519687D411yescharacteristic
48C8×Dic61D411yescharacteristic
49C2×SD16×C61—21no—
50C2×SD16×C61—21no—
51C4⋊Q8×C61C2×C411yescharacteristic
52#127×C61C2×C411yescharacteristic
53C4×C8×C61C2×C411yescharacteristic
54C2×Q8×C61—21no—
55C2×D4×C61—21no—
56C2×D4×C61—41no—
57C2×C22⋊D61—41no—
58C22×Dic61—41no—
59C2×C4×D61C22⋊C411yescharacteristic
60SD16×C61—42no—
61SD16×C61—41no—
62SD16×C61—41no—
63C2×C8×C61C22⋊C411yescharacteristic
64C2×C8×C61C22⋊C411yescharacteristic
65C4⋊C4×C61—41no—
66C42×C61C22×C411yescharacteristic
67C22⋊Dic61—41no—
68C22⋊Dic61—41no—
69#11758198—21no—
70#11758198—41no—
71C4⋊Dic61—21no—
72C4⋊Dic61—21no—
73C4⋊Dic61—41no—
74#11758196—21no—
75#11758196—41no—
76#11758196—41no—
77#11758196—41no—
78C4×Dic61—41no—
79C4×Dic61C22⋊C411yescharacteristic
80C2×#92418C2×D411yescharacteristic
81C2×#92418C2×D411yescharacteristic
82#11758189—41no—
83C8×D61—21no—
84C8×D61—21no—
85#11758187—24no—
86#11758187—42no—
87C23×C61—41no—
88C22×D61#10011yescharacteristic
89Q8×C61—41no—
90Q8×C61—41no—
91D4×C61—41no—
92D4×C61—41no—
93D4×C61—161no—
94C2×C4×C61—21no—
95C2×C4×C61—41no—
96C2×C4×C61C2×C22⋊C411yescharacteristic
97C22⋊D61—161no—
98C2×Dic61—21no—
99C2×Dic61—41no—
100C2×Dic61—41no—
101C2×Dic61—161no—
102C2×Dic61#10011yescharacteristic
103C4×D61—21no—
104C4×D61—21no—
105C8×C61—21no—
106C8×C61#10411yescharacteristic
107C8×C61#10411yescharacteristic
108#92418—21no—
109#92418—21no—
110#11912—611nomaximal, Sylow
111C22×C61—81no—
112C22×C61—81no—
113C22×C61—81no—
114C22×C61C2×#10011yescharacteristic
115C2×D61—21no—
116C2×D61—41no—
117C4×C61—41no—
118C4×C61—81no—
119C4×C61C2×#10411yescharacteristic
120C4×C61#42111yescharacteristic
121Dic61—21no—
122Dic61—41no—
123Dic61—81no—
124Dic61—81no—
125#3174—611no—
126#2166—611no—
127#2110—611no—
128#1356—612no—
129#1355—612no—
130C2×C61—21no—
131C2×C61—161no—
132C2×C61#153011yescharacteristic
133D61—41no—
134#541—611no—
135#540—611no—
136C2×M32—1221no—
137#499—611no—
138#492#692311yescharacteristic
139#491—611no—
140#490—611no—
141#468—1221no—
142#465—1221no—
143#440—1221no—
144C4×SD16—1221no—
145#405—611no—
146#364—1221no—
147#349—1221no—
148#347—612no—
149#347—612no—
150#347—1221no—
151C61#1191211yescharacteristic, complemented, Sylow
152C2×SD16—21no—
153C2×SD16—21no—
154C2×M16—611no—
155C22×C8—611no—
156C4⋊Q8C2×#692311yescharacteristic
157#127C2×#692311yescharacteristic
158#126—2441no—
159#125—611no—
160#125—611no—
161#125—2441no—
162#123—2441no—
163C22⋊Q8—1221no—
164#121—1221no—
165#121—2441no—
166C4×Q8—1221no—
167C4×D4—1221no—
168#117—611no—
169M32—1222no—
170M32—1222no—
171M32—1222no—
172C2×C16—1222no—
173#107—1221no—
174#106—1221no—
175#103—1221no—
176#103—1221no—
177#102—1221no—
178#102—1221no—
179#97—611no—
180#97—611no—
181C4×C8—611no—
182C4×C8C2×#692311yescharacteristic
183C2×Q8—21no—
184C2×D4—21no—
185C2×D4—41no—
186C2×D4—2441no—
187C22×C4—611no—
188C22×C4—2441no—
189SD16—42no—
190SD16—41no—
191SD16—41no—
192M16—2441no—
193C2×C8—611no—
194C2×C8—611no—
195C2×C8—1221no—
196C2×C8—1221no—
197C2×C8C22⋊#692311yescharacteristic
198C2×C8C22⋊#692311yescharacteristic
199C4⋊C4—41no—
200C4⋊C4—1221no—
201C4⋊C4—1221no—
202C4⋊C4—1221no—
203C4⋊C4—2441no—
204C4⋊C4—2441no—
205C4⋊C4—2441no—
206C4⋊C4—2441no—
207C22⋊C4—1221no—
208C22⋊C4—2441no—
209C22⋊C4—2441no—
210C22⋊C4—2441no—
211C42—611no—
212C42—2441no—
213C42C22×#692311yescharacteristic
214C16—1224no—
215C16—2442no—
216C23—41no—
217C23—611no—
218Q8—41no—
219Q8—41no—
220D4—41no—
221D4—41no—
222D4—161no—
223D4—9761no—
224C2×C4—21no—
225C2×C4—41no—
226C2×C4—611no—
227C2×C4—1221no—
228C2×C4—1221no—
229C2×C4—1221no—
230C2×C4—9761no—
231C2×C4—2441no—
232C2×C4—2441no—
233C2×C4C2×C22⋊#692311yescharacteristic
234C8—21no—
235C8—1221no—
236C8—1221no—
237C8#1451984111yescharacteristic
238C8#1451984111yescharacteristic
239C22—81no—
240C22—81no—
241C22—81no—
242C22—1221no—
243C22—2441no—
244C22D61⋊#10011yescharacteristic
245C4—41no—
246C4—81no—
247C4—1221no—
248C4—4881no—
249C4—4881no—
250C4—2441no—
251C4C2×#1451984111yescharacteristic
252C4#1684076011yescharacteristic
253C2—21no—
254C2—161no—
255C2—2441no—
256C2#2146128911yescharacteristic
subgroupG/H
centerC2#21461289
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#492C4
socleC2×C61#1530
prime radical#16840366C4
cosocle#14519688C23
hypercenter#492#6923
hypocenterC61#11912
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #21462194C2semidirect
2. #21462041C2semidirect
3. #21460824C2semidirect
4. #21460821C2semidirect
151. C61#11912semidirect

Maximal subgroups

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

subgroupindex
#214621942
#214620412
#214608242
#214608212
#214564442
#1191261