Finite Group Databasebeta

← #30604663

Subgroups — #30604663

Order 15616.

348 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 74 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#21462189C211yesmaximal, characteristic, complemented
2#21461038C211yesmaximal, characteristic, complemented
3#21460783C212yesmaximal, complemented
4#21460781C212yesmaximal, complemented
5#21454729C211yesmaximal, characteristic
6#16840779—21no—
7#16840684C2212yescomplemented
8#16840658—21no—
9#16840655—21no—
10#92420⋊C8—21no—
11#16840603C2211yescharacteristic, complemented
12C8×#92420C2211yescharacteristic, complemented
13#16840529—21no—
14#16839884—21no—
15#16839884C412yes—
16#16839879—21no—
17#16839879C2212yes—
18#16839811C411yescharacteristic
19C2×#14519704—21no—
20M16×Dic61C2211yescharacteristic
21C61×#575C411yescharacteristic
22#14519851—22no—
23#14519844—22no—
24C22⋊#92420—22no—
25C4×#92420—21no—
26C4×#92420—21no—
27#14519784—22no—
28#14519784—22no—
29#14519784—42no—
30C2×#11758194—21no—
31C2×#11758194—42no—
32C2×#11758194D411yescharacteristic
33C2×C4×Dic61D411yescharacteristic
34#14519713—21no—
35#14519713C2×C412yes—
36#14519704—22no—
37#14519704—22no—
38#14519687C2×C411yescharacteristic
39#14519687D411yescharacteristic
40C8×Dic61D411yescharacteristic
41C8×Dic61C2311yescharacteristic
42C2×#41×C61—21no—
43#137×C61—22no—
44AGL(1,ℤ/8)×C61—22no—
45#135×C61—21no—
46#135×C61C2×C412yes—
47C2×M16×C61C2×C411yescharacteristic
48#41×C61—22no—
49#41×C61—22no—
50#41×C61—41no—
51#41×C61—41no—
52C2×Q8×C61—21no—
53C2×D4×C61—21no—
54C2×D4×C61—41no—
55C22×C4×C61—41no—
56C22×C4×C61C22⋊C411yescharacteristic
57C22×Dic61—21no—
58C2×#92420—22no—
59C2×#92420—22no—
60Q16×C61—21no—
61Q16×C61M1612yes—
62SD16×C61—22no—
63SD16×C61—22no—
64D8×C61—21no—
65D8×C61M1612yes—
66M16×C61—22no—
67C2×C8×C61C22⋊C411yescharacteristic
68C2×C8×C61C22×C411yescharacteristic
69C4×Dic61—21no—
70C4×Dic61C22⋊C411yescharacteristic
71C4×Dic61C2×D411yescharacteristic
72#11758194—22no—
73#11758194—22no—
74#11758194—42no—
75#11758194—41no—
76#11758194—42no—
77C2×#92418—42no—
78C2×#92418—41no—
79C2×#92418—42no—
80C2×#92418C22⋊C411yescharacteristic
81C2×#92418C2×D411yescharacteristic
82#11758187—42no—
83C23×C61—41no—
84C23×C61#10411yescharacteristic
85Q8×C61—22no—
86Q8×C61—41no—
87D4×C61—22no—
88D4×C61—41no—
89D4×C61—42no—
90D4×C61—42no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—42no—
94C2×C4×C61—41no—
95C2×C4×C61—42no—
96C2×C4×C61#10411yescharacteristic
97C2×C4×C61C2×C22⋊C411yescharacteristic
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61—42no—
101#92420—42no—
102#92420—42no—
103C8×C61—21no—
104C8×C61C2×M1612yes—
105#92418—21no—
106#92418—42no—
107#92418AGL(1,ℤ/8)12yes—
108#11670—611nomaximal, Sylow
109C22×C61—21no—
110C22×C61—41no—
111C22×C61—42no—
112C22×C61—161no—
113C22×C61C2×#10411yescharacteristic
114C4×C61—21no—
115C4×C61—42no—
116C4×C61#40711yescharacteristic
117C4×C61#41811yescharacteristic
118Dic61—22no—
119Dic61—41no—
120#2956—611no—
121#2165—611no—
122#1453—611no—
123#1336—612no—
124#1335—612no—
125C2×C61—21no—
126C2×C61—41no—
127C2×C61—82no—
128C2×C61#149011yescharacteristic
129#575#692311yescharacteristic
130#568—1221no—
131#444—612no—
132#444—1221no—
133#443—612no—
134#443—1221no—
135#431—1221no—
136#430—611no—
137C2×#104—1221no—
138C4×M16—611no—
139#364—612no—
140#349—1221no—
141#347—1221no—
142#322—611no—
143#322—1221no—
144C82—611no—
145C61#1167011yescharacteristic, complemented, Sylow
146C2×#41—21no—
147#137—22no—
148AGL(1,ℤ/8)—22no—
149#135—21no—
150#135C2×#692312yes—
151#131—1222no—
152#131—1222no—
153#131—2442no—
154C2×M16—611no—
155C2×M16—1221no—
156C2×M16—2442no—
157C2×M16C2×#692311yescharacteristic
158C2×C42—611no—
159M32—1222no—
160#108—612no—
161#108—1221no—
162C4⋊C8—1222no—
163#104—1222no—
164#104—1222no—
165C22⋊C8—1222no—
166#97—611no—
167#97—611no—
168C4×C8—611no—
169C4×C8—611no—
170C4×C8—1221no—
171C4×C8—1221no—
172#41—22no—
173#41—22no—
174#41—41no—
175#41—41no—
176C2×Q8—21no—
177C2×D4—21no—
178C2×D4—41no—
179C22×C4—41no—
180C22×C4—1221no—
181C22×C4C22⋊#692311yescharacteristic
182Q16—21no—
183Q16#1175821712yes—
184SD16—22no—
185SD16—22no—
186D8—21no—
187D8#1175821712yes—
188M16—22no—
189M16—1222no—
190M16—1222no—
191M16—2442no—
192M16—2442no—
193M16—2441no—
194C2×C8—611no—
195C2×C8—611no—
196C2×C8—1222no—
197C2×C8—1222no—
198C2×C8—2442no—
199C2×C8—2442no—
200C2×C8—2441no—
201C2×C8C22⋊#692311yescharacteristic
202C2×C8C22×#692311yescharacteristic
203C42—611no—
204C42—611no—
205C42—1221no—
206C16—2442no—
207C23—41no—
208C23#1451984111yescharacteristic
209Q8—22no—
210Q8—41no—
211D4—22no—
212D4—41no—
213D4—42no—
214D4—42no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—42no—
218C2×C4—41no—
219C2×C4—42no—
220C2×C4—1221no—
221C2×C4—1221no—
222C2×C4—2442no—
223C2×C4#1451984111yescharacteristic
224C2×C4C2×C22⋊#692311yescharacteristic
225C8—21no—
226C8—612no—
227C8—1221no—
228C8—2442no—
229C8—2442no—
230C8—2442no—
231C8C2×#1175821712yes—
232C22—21no—
233C22—41no—
234C22—42no—
235C22—161no—
236C22C2×#1451984111yescharacteristic
237C4—21no—
238C4—42no—
239C4—1222no—
240C4—2441no—
241C4#1684073211yescharacteristic
242C4#1684075411yescharacteristic
243C2—21no—
244C2—41no—
245C2—82no—
246C2#2146115811yescharacteristic
subgroupG/H
centerC4#16840754
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
Fitting, prime radicalC61×#575C4
socleC2×C61#1490
cosocleC8×Dic61C23
hypercenter#575#6923
hypocenterC61#11670
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #21462189C2semidirect
2. #21461038C2semidirect
3. #21460783C2semidirect
4. #21460781C2semidirect
7. #16840684C22semidirect
11. #16840603C22semidirect
12. C8×#92420C22semidirect
145. C61#11670semidirect

Maximal subgroups

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

subgroupindex
#214621892
#214610382
#214607832
#214607812
#214547292
#1167061