Finite Group Databasebeta

← #29582293

Subgroups — #29582293

Order 15616.

574 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 105 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#21456937C212yesmaximal, complemented
2#21446639C211yesmaximal, characteristic, complemented
3#21444379C212yesmaximal, complemented
4#21443664C211yesmaximal, characteristic, complemented
5C61×#3150C211yesmaximal, characteristic
6C2×#14519777C2211yescharacteristic
7#16840165—22no—
8#16840108—22no—
9#16840073—24no—
10#16840042—24no—
11#16839815C2212yes—
12C2×#14519702—22no—
13#16839628C2211yescharacteristic
14#16839496—24no—
15C2×#135×C61—22no—
16C61×#532C2212yes—
17C61×#497—22no—
18C61×#496—22no—
19C2×#97×C61C2211yescharacteristic
20C22×Dic122—21no—
21#14519777—22no—
22#14519777—21no—
23#14519777D412yes—
24C2×C4⋊Dic61—22no—
25C2×C4⋊Dic61—21no—
26#14519710—28no—
27C4⋊#92418—22no—
28#14519702—44no—
29#14519698—28no—
30C22⋊#92418D414yes—
31C4×#92418—22no—
32#14519684—22no—
33C2×#41×C61—22no—
34#135×C61—44no—
35#135×C61—44no—
36C2×Q16×C61—22no—
37C2×SD16×C61—24no—
38C2×D8×C61—22no—
39C22×C8×C61D412yes—
40C4⋊Q8×C61D412yes—
41#127×C61D412yes—
42#124×C61—22no—
43#121×C61—22no—
44#121×C61—22no—
45C4×D4×C61—22no—
46C4×D4×C61—22no—
47C2×C42×C61C2311yescharacteristic
48#97×C61—22no—
49#41×C61—44no—
50#41×C61—44no—
51C2×Q8×C61—22no—
52C2×D4×C61—22no—
53C2×D4×C61—22no—
54C2×D4×C61—22no—
55C2×D4×C61—42no—
56C22×C4×C61—42no—
57C22×C4×C61C2×D412yes—
58C22×C4×C61C2×D411yescharacteristic
59C22×Dic61—41no—
60C22×Dic61—41no—
61C2×Dic122—22no—
62C2×Dic122—42no—
63C2×Dic122—42no—
64C2×Dic122—41no—
65Q16×C61—44no—
66SD16×C61—48no—
67D8×C61—44no—
68C2×C8×C61—22no—
69C2×C8×C61—22no—
70C2×C8×C61D814yes—
71C4⋊C4×C61—22no—
72C4⋊C4×C61—22no—
73C22⋊C4×C61—42no—
74C22⋊C4×C61—42no—
75C42×C61C2×D411yescharacteristic
76C42×C61C2×D412yes—
77C42×C61#4111yescharacteristic
78C4⋊Dic61—24no—
79C4⋊Dic61—42no—
80C4⋊Dic61—42no—
81C2×#92418—24no—
82C23×C61—42no—
83C23×C61#12711yescharacteristic
84Q8×C61—44no—
85D4×C61—44no—
86D4×C61—44no—
87D4×C61—82no—
88D4×C61—82no—
89D4×C61—82no—
90C2×C4×C61—42no—
91C2×C4×C61—42no—
92C2×C4×C61—84no—
93C2×C4×C61#12012yes—
94C2×C4×C61#12011yescharacteristic
95C2×C4×C61#12112yes—
96C2×C4×C61#12111yescharacteristic
97C2×C4×C61C2×D812yes—
98C2×C4×C61AGL(1,ℤ/8)12yes—
99C2×Dic61—42no—
100C2×Dic61—81no—
101C2×Dic61—81no—
102C2×Dic61—82no—
103C2×Dic61—81no—
104Dic122—44no—
105Dic122—82no—
106C8×C61—24no—
107#92418—44no—
108#10225—611nomaximal, Sylow
109C22×C61—22no—
110C22×C61—82no—
111C22×C61—82no—
112C22×C61—82no—
113C22×C61#39211yescharacteristic
114C22×C61#49311yescharacteristic
115C22×C61#49611yescharacteristic
116C4×C61—22no—
117C4×C61—22no—
118C4×C61—82no—
119C4×C61#44712yes—
120C4×C61#45912yes—
121Dic61—82no—
122Dic61—161no—
123#3226—612no—
124#3150D6111yescharacteristic
125#1960—611no—
126#1517—612no—
127#1281—611no—
128C2×C61—21no—
129C2×C61—21no—
130C2×C61—162no—
131C2×C61#200912yes—
132C2×C61#201111yescharacteristic
133C2×#135—22no—
134#532C2×D6112yes—
135C2×C4⋊Q8—611no—
136#500—1222no—
137#497—22no—
138#496—22no—
139#486—1222no—
140#480—1224no—
141#474—1224no—
142#431—612no—
143C2×#103—1222no—
144C2×#97C2×D6111yescharacteristic
145#382—611no—
146#327—1224no—
147C61#1022511yescharacteristic, complemented, Sylow
148C2×#41—22no—
149C22×Q8—1221no—
150#135—44no—
151#135—44no—
152C2×Q16—22no—
153C2×SD16—24no—
154C2×D8—22no—
155C22×C8C22⋊D6112yes—
156C4⋊Q8—612no—
157C4⋊Q8—1221no—
158C4⋊Q8—1222no—
159C4⋊Q8C22⋊D6112yes—
160#127C22⋊D6112yes—
161#124—22no—
162#121—22no—
163#121—22no—
164C4×D4—22no—
165C4×D4—22no—
166C2×C4⋊C4—1222no—
167C2×C4⋊C4—1221no—
168C2×C42C22×D6111yescharacteristic
169#107—1228no—
170C4⋊C8—1222no—
171#103—2444no—
172#102—1228no—
173C22⋊C8—614no—
174#97—22no—
175C4×C8—1222no—
176#95—1222no—
177#41—44no—
178#41—44no—
179C2×Q8—22no—
180C2×Q8—1222no—
181C2×Q8—2442no—
182C2×Q8—2442no—
183C2×Q8—2441no—
184C2×D4—22no—
185C2×D4—22no—
186C2×D4—22no—
187C2×D4—42no—
188C22×C4—42no—
189C22×C4—2441no—
190C22×C4—2441no—
191C22×C4D4×D6112yes—
192C22×C4C2×C22⋊D6111yescharacteristic
193Q16—44no—
194SD16—48no—
195D8—44no—
196C2×C8—22no—
197C2×C8—22no—
198C2×C8—1224no—
199C2×C8#1175819914yes—
200C4⋊C4—22no—
201C4⋊C4—22no—
202C4⋊C4—1224no—
203C4⋊C4—2442no—
204C4⋊C4—2442no—
205C22⋊C4—42no—
206C22⋊C4—42no—
207C42D4×D6111yescharacteristic
208C42#1175822411yescharacteristic
209C42C2×C22⋊D6112yes—
210C23—42no—
211C23#1451977311yescharacteristic
212Q8—44no—
213Q8—4882no—
214Q8—2444no—
215D4—44no—
216D4—44no—
217D4—82no—
218D4—82no—
219D4—82no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—84no—
223C2×C4—4882no—
224C2×C4—4881no—
225C2×C4—4881no—
226C2×C4—4881no—
227C2×C4—2442no—
228C2×C4#1451974512yes—
229C2×C4#1451974611yescharacteristic
230C2×C4#1451974811yescharacteristic
231C2×C4#1451974912yes—
232C2×C4C2×#1175819912yes—
233C2×C4#1451980312yes—
234C8—24no—
235C8—2444no—
236C22—22no—
237C22—82no—
238C22—82no—
239C22—82no—
240C22#1683967011yescharacteristic
241C22#1684013811yescharacteristic
242C22#1684014911yescharacteristic
243C4—22no—
244C4—22no—
245C4—82no—
246C4—9761no—
247C4—4882no—
248C4#1683989612yes—
249C4#1683995412yes—
250C2—21no—
251C2—21no—
252C2—162no—
253C2#2144687612yes—
254C2#2144689011yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
Fitting, prime radicalC61×#3150C2
socleC22×C61#392
hypercenter#3150D61
hypocenterC61#10225
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3150

Complements

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

NH ≅ G/Ntype
1. #21456937C2semidirect
2. #21446639C2semidirect
3. #21444379C2semidirect
4. #21443664C2semidirect
147. C61#10225semidirect

Maximal subgroups

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

subgroupindex
#214569372
#214466392
#214443792
#214436642
C61×#31502
#1022561