Finite Group Databasebeta

← #29597467

Subgroups — #29597467

Order 15616.

458 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 127 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#21455474C211yesmaximal, characteristic
2#21447540C212yesmaximal, complemented
3#21445865C211yesmaximal, characteristic
4#21443921C212yesmaximal, complemented
5C61×#3407C211yesmaximal, characteristic
6C22×Dic244C2211yescharacteristic
7#16840333—21no—
8#16840020C414yescomplemented
9#16840003—22no—
10#16839800C2212yes—
11#16839800C2211yescharacteristic
12#16839772—21no—
13#16839736—21no—
14#16839567—24no—
15#16839519—21no—
16C2×#131×C61C2211yescharacteristic
17C61×#504—24no—
18C2×M32×C61—22no—
19C2×M32×C61C2212yes—
20C22×Dic122—21no—
21C2×Dic244—22no—
22C2×Dic244—22no—
23C2×Dic244—21no—
24C2×Dic244C2×C412yes—
25#14519775—41no—
26#14519764—41no—
27#14519758—42no—
28#14519756—24no—
29#14519736—21no—
30#14519736—22no—
31#14519711—21no—
32#14519711—22no—
33#14519709—22no—
34#14519709C2×C412yes—
35#14519702—24no—
36#14519692—42no—
37C2×#41×C61D411yescharacteristic
38#131×C61—22no—
39#131×C61—22no—
40C2×M16×C61C2×C412yes—
41C2×M16×C61D411yescharacteristic
42C22×C8×C61D412yes—
43C22×C8×C61C2311yescharacteristic
44M32×C61—24no—
45M32×C61—22no—
46M32×C61—22no—
47C2×C16×C61—24no—
48C2×C16×C61D414yes—
49#41×C61—22no—
50#41×C61—22no—
51C2×Q8×C61SD1611yescharacteristic
52C2×D4×C61D812yes—
53C2×D4×C61SD1611yescharacteristic
54C22×C4×C61C22⋊C412yes—
55C22×C4×C61C2×D411yescharacteristic
56C22×Dic61—41no—
57C2×Dic122—22no—
58C2×Dic122—42no—
59C2×Dic122—42no—
60C2×Dic122—41no—
61M16×C61—22no—
62M16×C61—24no—
63C2×C8×C61—22no—
64C2×C8×C61—22no—
65C2×C8×C61C22⋊C412yes—
66C2×C8×C61C22×C411yescharacteristic
67C2×C8×C61C2×D412yes—
68C2×C8×C61C2×D411yescharacteristic
69C2×C8×C61#4112yes—
70C22⋊Dic61—44no—
71C22⋊Dic61—41no—
72C22⋊Dic61—42no—
73C4⋊Dic61—22no—
74C4⋊Dic61—42no—
75#11758196—44no—
76C4×Dic61—41no—
77C4×Dic61—42no—
78Dic244—24no—
79Dic244—41no—
80Dic244—41no—
81C16×C61—24no—
82C23×C61#10212yes—
83C23×C61C2×D811yescharacteristic
84Q8×C61—22no—
85D4×C61—24no—
86D4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61#10212yes—
90C2×C4×C61C2×C22⋊C411yescharacteristic
91C2×C4×C61#12112yes—
92C2×C4×C61C2×SD1611yescharacteristic
93C2×C4×C61#13512yes—
94C2×Dic61—42no—
95C2×Dic61—42no—
96C2×Dic61—82no—
97C2×Dic61—82no—
98Dic122—42no—
99Dic122—42no—
100Dic122—82no—
101C8×C61—22no—
102C8×C61C4×D412yes—
103C8×C61#12011yescharacteristic
104C8×C61#12311yescharacteristic
105#13075—611nomaximal, Sylow
106C22×C61—22no—
107C22×C61—41no—
108C22×C61—42no—
109C22×C61C2×#10211yescharacteristic
110C22×C61#46612yes—
111C4×C61—22no—
112C4×C61#38611yescharacteristic
113C4×C61#41611yescharacteristic
114C4×C61#46512yes—
115Dic61—82no—
116Dic61—82no—
117Dic61—162no—
118#3407D6111yescharacteristic
119#3059—611no—
120#2141—612no—
121#1812—611no—
122#1384—612no—
123C2×C61—21no—
124C2×C61—22no—
125C2×C61—42no—
126C2×C61#189311yescharacteristic
127C22×Q16—611no—
128C2×#131C2×D6111yescharacteristic
129#536—1221no—
130#504—24no—
131C2×M32—22no—
132C2×M32C2×D6112yes—
133#470—614no—
134#467—1222no—
135#427—611no—
136#427—612no—
137#419—1221no—
138#410—1221no—
139#358—1224no—
140H(3,ℤ/4)—1221no—
141C61#1307511yescharacteristic, complemented, Sylow
142C2×#41D24411yescharacteristic
143C22×Q8—1221no—
144C2×Q16—612no—
145C2×Q16—1222no—
146C2×Q16—1222no—
147C2×Q16—1221no—
148#131—22no—
149#131—22no—
150C2×M16C4×D6112yes—
151C2×M16D24411yescharacteristic
152C22×C8C22⋊D6112yes—
153C22×C8C22×D6111yescharacteristic
154C4⋊Q8—2441no—
155#124—2441no—
156#123—2442no—
157C22⋊Q8—1224no—
158#117—1221no—
159#117—1222no—
160M32—24no—
161M32—22no—
162M32—22no—
163C2×C16—24no—
164C2×C16C22⋊D6114yes—
165#107—1221no—
166#107—1222no—
167#106—612no—
168#106—1222no—
169#103—1224no—
170#99—2442no—
171#41—22no—
172#41—22no—
173C2×Q8—1222no—
174C2×Q8—2442no—
175C2×Q8—2442no—
176C2×Q8—2441no—
177C2×Q8#1175819011yescharacteristic
178C2×D4#1175819011yescharacteristic
179C2×D4D48812yes—
180C22×C4—2441no—
181C22×C4#1175819812yes—
182C22×C4C2×D24411yescharacteristic
183Q16—1224no—
184Q16—2441no—
185Q16—2441no—
186M16—22no—
187M16—24no—
188C2×C8—22no—
189C2×C8—22no—
190C2×C8#1175819812yes—
191C2×C8C2×C4×D6111yescharacteristic
192C2×C8#1175822212yes—
193C2×C8C2×C22⋊D6112yes—
194C2×C8C2×C22⋊D6111yescharacteristic
195C4⋊C4—1222no—
196C4⋊C4—2442no—
197C4⋊C4—2444no—
198C22⋊C4—2442no—
199C22⋊C4—2444no—
200C22⋊C4—2441no—
201C42—2442no—
202C42—2441no—
203C16—24no—
204C23#1451969912yes—
205C23C2×D48811yescharacteristic
206Q8—22no—
207Q8—4882no—
208Q8—2442no—
209Q8—2442no—
210D4—24no—
211D4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—4882no—
215C2×C4—4882no—
216C2×C4—2442no—
217C2×C4—2442no—
218C2×C4#1451969912yes—
219C2×C4C2×#1175819811yescharacteristic
220C2×C4#1451975112yes—
221C2×C4C2×#1175819011yescharacteristic
222C2×C4#1451979912yes—
223C8—22no—
224C8C4×C22⋊D6112yes—
225C8#1451974611yescharacteristic
226C8#1451976011yescharacteristic
227C22—22no—
228C22—41no—
229C22—42no—
230C22C2×#1451969911yescharacteristic
231C22#1683999812yes—
232C4—22no—
233C4—9762no—
234C4—4882no—
235C4—4882no—
236C4#1683964111yescharacteristic
237C4#1683975911yescharacteristic
238C4#1683999112yes—
239C2—22no—
240C2—21no—
241C2—42no—
242C2#2144624711yescharacteristic
subgroupG/H
centerC2#21446247
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#3407C2
socleC2×C61#1893
prime radicalC2×#41×C61D4
cosocleC22×C8×C61C23
hypercenter#3407D61
hypocenterC61#13075
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#131 ◁ #3407

Complements

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

NH ≅ G/Ntype
2. #21447540C2semidirect
4. #21443921C2semidirect
8. #16840020C4semidirect
141. C61#13075semidirect

Maximal subgroups

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

subgroupindex
#214554742
#214475402
#214458652
#214439212
C61×#34072
#1307561