Finite Group Databasebeta

← #29590099

Subgroups — #29590099

Order 15616.

348 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 83 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#21454730C211yesmaximal, characteristic
2#21447631C211yesmaximal, characteristic, complemented
3#21443796C212yesmaximal, complemented
4#21443793C212yesmaximal, complemented
5C61×#1453C211yesmaximal, characteristic, complemented
6#16840562C411yescharacteristic
7#16840528—21no—
8#16839885—21no—
9#16839885C412yes—
10#16839880—21no—
11#16839880C2212yes—
12#16839811C411yescharacteristic
13C2×#14519705—21no—
14#16839583C2212yescomplemented
15#16839544—21no—
16#16839540—21no—
17C61×#431—21no—
18C4×M16×C61C2211yescharacteristic
19C61×#322—21no—
20C61×#322C2211yescharacteristic, complemented
21C82×C61C2211yescharacteristic, complemented
22C2×#11758222—21no—
23#14519810—22no—
24#14519805—22no—
25#14519799—21no—
26#14519799C2×C412yes—
27#14519785—42no—
28#14519783—22no—
29#14519783—22no—
30C2×#11758194—21no—
31M16×D61—42no—
32#14519717—22no—
33#14519713—21no—
34#14519713C2×C412yes—
35#14519705—22no—
36#14519705—22no—
37C2×M16×C61C2×C411yescharacteristic
38C2×M16×C61D411yescharacteristic
39C2×C42×C61D411yescharacteristic
40C4⋊C8×C61—22no—
41C22⋊C8×C61—22no—
42#97×C61C2×C411yescharacteristic
43#97×C61D411yescharacteristic
44C4×C8×C61—21no—
45C4×C8×C61—21no—
46C4×C8×C61D411yescharacteristic
47C4×C8×C61C2311yescharacteristic
48C22×C4×C61—21no—
49C22×C4×C61C22⋊C411yescharacteristic
50C2×C22⋊D61—41no—
51#11758222—22no—
52#11758222—22no—
53#11758222—41no—
54#11758222—41no—
55C2×D244—21no—
56C2×C4×D61—41no—
57C2×Dic122—21no—
58M16×C61—22no—
59M16×C61—22no—
60C2×C8×C61—22no—
61C2×C8×C61—22no—
62C2×C8×C61C22⋊C411yescharacteristic
63C2×C8×C61C22⋊C411yescharacteristic
64C2×C8×C61C22×C411yescharacteristic
65C2×C8×C61C2×D411yescharacteristic
66C42×C61—21no—
67C42×C61C22⋊C411yescharacteristic
68C42×C61C2×D411yescharacteristic
69#11758194—22no—
70#11758194—41no—
71C2×#92418—41no—
72Dic244—21no—
73Dic244M1612yes—
74D488—21no—
75D488M1612yes—
76#11758190—22no—
77#11758190—22no—
78#11758189—42no—
79#11758189—42no—
80C8×D61—42no—
81C8×D61—42no—
82#11758185—42no—
83C23×C61#10411yescharacteristic
84C22×D61—41no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—42no—
90C2×C4×C61#10411yescharacteristic
91C2×C4×C61C2×C22⋊C411yescharacteristic
92C22⋊D61—42no—
93C22⋊D61—42no—
94C2×Dic61—41no—
95D244—22no—
96D244—41no—
97C4×D61—42no—
98C4×D61—42no—
99Dic122—22no—
100Dic122—41no—
101C8×C61—21no—
102C8×C61—21no—
103C8×C61—42no—
104C8×C61—42no—
105C8×C61C2×M1612yes—
106C8×C61AGL(1,ℤ/8)12yes—
107#92418—42no—
108#11670—611nomaximal, Sylow
109C22×C61—21no—
110C22×C61—41no—
111C22×C61C2×#10411yescharacteristic
112C2×D61—42no—
113C2×D61—161no—
114C4×C61—22no—
115C4×C61—21no—
116C4×C61—41no—
117C4×C61#40711yescharacteristic
118C4×C61#41811yescharacteristic
119Dic61—42no—
120#2956—611no—
121#2165—611no—
122#1453D6111yescharacteristic, complemented
123#1336—612no—
124#1335—612no—
125C2×C61—21no—
126C2×C61—41no—
127C2×C61#149011yescharacteristic
128D61—82no—
129#575—611no—
130#568—1221no—
131#444—612no—
132#444—1221no—
133#443—612no—
134#443—1221no—
135#431—21no—
136#430—611no—
137C2×#104—1221no—
138C4×M16C2×D6111yescharacteristic
139#364—612no—
140#349—1221no—
141#347—1221no—
142#322—21no—
143#322C2×D6111yescharacteristic, complemented
144C82C2×D6111yescharacteristic, complemented
145C61#1167011yescharacteristic, complemented, Sylow
146C2×#41—1221no—
147#137—1222no—
148AGL(1,ℤ/8)—1222no—
149#135—612no—
150#135—1221no—
151#131—1222no—
152#131—1222no—
153#131—2442no—
154C2×M16—1221no—
155C2×M16—2442no—
156C2×M16C4×D6111yescharacteristic
157C2×M16D24411yescharacteristic
158C2×C42C22⋊D6111yescharacteristic
159M32—1222no—
160#108—612no—
161#108—1221no—
162C4⋊C8—22no—
163#104—1222no—
164#104—1222no—
165C22⋊C8—22no—
166#97C4×D6111yescharacteristic
167#97D24411yescharacteristic
168C4×C8—21no—
169C4×C8—21no—
170C4×C8C22⋊D6111yescharacteristic
171C4×C8C22×D6111yescharacteristic
172#41—1222no—
173#41—1222no—
174#41—2441no—
175#41—2441no—
176C2×Q8—1221no—
177C2×D4—1221no—
178C2×D4—2441no—
179C22×C4—21no—
180C22×C4—2441no—
181C22×C4#1175819811yescharacteristic
182Q16—612no—
183Q16—1221no—
184SD16—1222no—
185SD16—1222no—
186D8—612no—
187D8—1221no—
188M16—22no—
189M16—22no—
190M16—1222no—
191M16—2442no—
192M16—2441no—
193M16—2442no—
194C2×C8—22no—
195C2×C8—22no—
196C2×C8—2442no—
197C2×C8—2441no—
198C2×C8—2442no—
199C2×C8#1175819811yescharacteristic
200C2×C8#1175819811yescharacteristic
201C2×C8C2×C4×D6111yescharacteristic
202C2×C8C2×D24411yescharacteristic
203C42—21no—
204C42#1175819811yescharacteristic
205C42C2×C22⋊D6111yescharacteristic
206C16—2442no—
207C23—2441no—
208C23#1451970511yescharacteristic
209Q8—1222no—
210Q8—2441no—
211D4—1222no—
212D4—2441no—
213D4—2442no—
214D4—2442no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—42no—
220C2×C4—2442no—
221C2×C4—2441no—
222C2×C4—2442no—
223C2×C4#1451970511yescharacteristic
224C2×C4C2×#1175819811yescharacteristic
225C8—21no—
226C8—21no—
227C8—42no—
228C8—42no—
229C8—2442no—
230C8M16×D6112yes—
231C8#1451980512yes—
232C22—21no—
233C22—41no—
234C22—9761no—
235C22—2442no—
236C22C2×#1451970511yescharacteristic
237C4—22no—
238C4—21no—
239C4—41no—
240C4—2442no—
241C4#1683972511yescharacteristic
242C4#1683976811yescharacteristic
243C2—21no—
244C2—41no—
245C2—4882no—
246C2#2144426311yescharacteristic
subgroupG/H
centerC4#16839768
commutatorC2×C8×C61C22×C4
FrattiniC4×C8C22×D61
FittingC61×#1453C2
socleC2×C61#1490
prime radical#16840562C4
cosocleC4×C8×C61C23
hypercenter#1453D61
hypocenterC61#11670
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C8 ◁ C4×M16 ◁ #1453

Complements

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

NH ≅ G/Ntype
2. #21447631C2semidirect
3. #21443796C2semidirect
4. #21443793C2semidirect
5. C61×#1453C2semidirect
14. #16839583C22semidirect
20. C61×#322C22semidirect
21. C82×C61C22semidirect
122. #1453D61semidirect
143. #322C2×D61semidirect
144. C82C2×D61semidirect
145. C61#11670semidirect

Maximal subgroups

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

subgroupindex
#214547302
#214476312
#214437962
#214437932
C61×#14532
#1167061