Finite Group Databasebeta

← #29589318

Subgroups — #29589318

Order 15616.

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

normal subgroups only

This group has 368 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#21454521C211yesmaximal, characteristic
2#21447438C212yesmaximal, complemented
3#21443772C211yesmaximal, characteristic, complemented
4#21443754C212yesmaximal, complemented
5C61×#1328C211yesmaximal, characteristic, complemented
6C2×#14519785C2211yescharacteristic
7C22×#11758189C411yescharacteristic
8#16840274C411yescharacteristic
9M32×D61—22no—
10#16839839—22no—
11#16839832—22no—
12#16839728C411yescharacteristic
13#16839725C2211yescharacteristic
14#16839718C411yescharacteristic
15#16839544C2212yes—
16#16839543—22no—
17C61×#424C2211yescharacteristic
18C61×#349C2212yes—
19C2×#11758222C2×C411yescharacteristic
20C22×C4×D61C2×C411yescharacteristic
21#14519785—42no—
22C2×#11758194C2×C411yescharacteristic
23C2×#11758189—21no—
24C2×#11758189—21no—
25C2×#11758189—42no—
26C2×#11758189D412yes—
27C22×#92418C2×C411yescharacteristic
28C2×C8×D61D412yes—
29#14519761C812yes—
30#14519757—21no—
31#14519752—21no—
32#14519747C812yes—
33C4×D244—22no—
34#14519717—22no—
35#14519716—42no—
36C16×D61—42no—
37#14519689—22no—
38#14519689—22no—
39#14519688—21no—
40C4×#92418—21no—
41C2×M16×C61C2311yescharacteristic
42C22×C8×C61C2×C411yescharacteristic
43#117×C61C2×C411yescharacteristic
44M32×C61—22no—
45C4⋊C8×C61—22no—
46C23×D61C2×C811yescharacteristic
47C22×C4×C61C22×C411yescharacteristic
48C2×C22⋊D61C2×C812yes—
49C22×Dic61C2×C811yescharacteristic
50#11758222—41no—
51#11758222—41no—
52C2×D244—22no—
53C2×D244M1611yescharacteristic
54C2×C4×D61—21no—
55C2×C4×D61—21no—
56C2×C4×D61—41no—
57C2×C4×D61—41no—
58C2×C4×D61C22⋊C412yes—
59C2×Dic122M1611yescharacteristic
60M16×C61—41no—
61C2×C8×C61—21no—
62C2×C8×C61—41no—
63C2×C8×C61C2×D412yes—
64C4⋊C4×C61—21no—
65C22⋊C4×C61C2×C812yes—
66C42×C61—21no—
67#11758198—22no—
68#11758198—22no—
69C4⋊Dic61—22no—
70#11758194—41no—
71C2×#92418—22no—
72C2×#92418—21no—
73C2×#92418C22⋊C411yescharacteristic
74C2×#92418C22⋊C411yescharacteristic
75#11758189—42no—
76#11758189—42no—
77#11758189—42no—
78C8×D61—22no—
79C8×D61—22no—
80C16×C61—42no—
81#11758185—42no—
82C23×C61C22×C811yescharacteristic
83C22×D61—21no—
84C22×D61—41no—
85C22×D61—81no—
86C22×D61C22⋊C812yes—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—22no—
90C2×C4×C61C2×C22⋊C411yescharacteristic
91C2×C4×C61C2×M1611yescharacteristic
92C22⋊D61—42no—
93C2×Dic61—21no—
94C2×Dic61—41no—
95C2×Dic61C22⋊C812yes—
96D244—41no—
97D244—82no—
98C4×D61—22no—
99C4×D61—22no—
100C4×D61—42no—
101C4×D61—41no—
102C4×D61—41no—
103Dic122—41no—
104C8×C61—22no—
105C8×C61—41no—
106#92418—21no—
107#92418—41no—
108#92418#9912yes—
109#11484—611nomaximal, Sylow
110C22×C61—21no—
111C22×C61—41no—
112C22×C61C2×C22⋊C811yescharacteristic
113C2×D61—22no—
114C2×D61—42no—
115C2×D61—41no—
116C2×D61—41no—
117C2×D61—41no—
118C2×D61—82no—
119C4×C61—21no—
120C4×C61—42no—
121C4×C61C2×#9911yescharacteristic
122C4×C61#41311yescharacteristic
123Dic61—22no—
124Dic61—41no—
125#2930—611no—
126#2115—612no—
127#1328—611no—
128#1328D6111yescharacteristic, complemented
129#1320—612no—
130C2×C61—21no—
131C2×C61—41no—
132C2×C61#145911yescharacteristic
133D61—42no—
134D61—81no—
135C2×#131—611no—
136C22×M16—611no—
137#525—611no—
138C2×M32—1222no—
139#436—1222no—
140#435—1222no—
141#424C2×D6111yescharacteristic
142#408—611no—
143#407—611no—
144#405—611no—
145#349—612no—
146#349—1222no—
147#349C2×D6112yes—
148C61#1148411yescharacteristic, complemented, Sylow
149C2×#41—611no—
150C23×C4—611no—
151#131—2442no—
152C2×M16—612no—
153C2×M16—611no—
154C2×M16—1221no—
155C2×M16—1221no—
156C2×M16—2442no—
157C2×M16C22×D6111yescharacteristic
158C22×C8—611no—
159C22×C8—612no—
160C22×C8C4×D6111yescharacteristic
161#123—612no—
162C22⋊Q8—1221no—
163#121—1221no—
164#120—612no—
165C4×D4—1222no—
166#117C4×D6111yescharacteristic
167M32—22no—
168M32—1222no—
169M32—2442no—
170C2×C16—2442no—
171C4⋊C8—22no—
172C22⋊C8—1222no—
173C22⋊C8—1222no—
174#97—1221no—
175C4×C8—1221no—
176C24—611no—
177#41—2441no—
178#41—2441no—
179C2×Q8—611no—
180C2×D4—612no—
181C2×D4—611no—
182C2×D4—1222no—
183C22×C4—612no—
184C22×C4—611no—
185C22×C4—1221no—
186C22×C4—1221no—
187C22×C4—2441no—
188C22×C4—2441no—
189C22×C4C2×C4×D6111yescharacteristic
190M16—41no—
191M16—2442no—
192M16—2442no—
193M16—2442no—
194M16—2441no—
195C2×C8—21no—
196C2×C8—41no—
197C2×C8—611no—
198C2×C8—611no—
199C2×C8—1222no—
200C2×C8—1222no—
201C2×C8—1222no—
202C2×C8—1221no—
203C2×C8D4×D6112yes—
204C4⋊C4—21no—
205C4⋊C4—1222no—
206C22⋊C4—1222no—
207C22⋊C4—1222no—
208C22⋊C4C8×D6112yes—
209C42—21no—
210C16—42no—
211C16—2442no—
212C23—612no—
213C23—1221no—
214C23—4881no—
215C23—2441no—
216C23C2×C8×D6111yescharacteristic
217Q8—2441no—
218D4—4882no—
219D4—2441no—
220D4—2442no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—612no—
225C2×C4—1222no—
226C2×C4—1222no—
227C2×C4—1221no—
228C2×C4—2442no—
229C2×C4—2441no—
230C2×C4—2441no—
231C2×C4—2441no—
232C2×C4C22⋊C4×D6111yescharacteristic
233C2×C4M16×D6111yescharacteristic
234C8—22no—
235C8—41no—
236C8—612no—
237C8—1221no—
238C8—2441no—
239C22—21no—
240C22—41no—
241C22—1222no—
242C22—4882no—
243C22—2441no—
244C22—2441no—
245C22—2442no—
246C22—2441no—
247C22C22⋊C8×D6111yescharacteristic
248C4—21no—
249C4—42no—
250C4—1222no—
251C4—2441no—
252C4#99×D6111yescharacteristic
253C4#1683974511yescharacteristic
254C2—21no—
255C2—41no—
256C2—4881no—
257C2—2442no—
258C2#2144413611yescharacteristic
subgroupG/H
centerC4#99×D61
commutatorC23×C61C22×C8
FrattiniC2×M16C22×D61
FittingC61×#1328C2
socleC2×C61#1459
prime radical#16840274C4
cosocleC2×M16×C61C23
hypercenter#1328D61
hypocenterC61#11484
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1328

Complements

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

NH ≅ G/Ntype
2. #21447438C2semidirect
3. #21443772C2semidirect
4. #21443754C2semidirect
5. C61×#1328C2semidirect
128. #1328D61semidirect
148. C61#11484semidirect

Maximal subgroups

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

subgroupindex
#214545212
#214474382
#214437722
#214437542
C61×#13282
#1148461