Finite Group Databasebeta

← #29577858

Subgroups — #29577858

Order 15616.

474 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 135 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#21454900C211yesmaximal, characteristic
2#21445815C211yesmaximal, characteristic
3#21444248C212yesmaximal
4#21443677C212yesmaximal
5C61×#2581C211yesmaximal, characteristic
6Q8×#92418—24no—
7#16839815—22no—
8#16839815C2212yes—
9#16839786C2212yes—
10C2×#14519696—21no—
11#16839531—21no—
12Q8⋊#92418—24no—
13C2×C4×Q8×C61C2211yescharacteristic
14C2×C4×Q8×C61C2211yescharacteristic
15C61×#400C412yes—
16C61×#395C412yes—
17C61×#391—21no—
18C61×#389—21no—
19C61×#387—22no—
20C61×#382C2211yescharacteristic
21C2×#11758194—22no—
22C4⋊#92418—24no—
23C4⋊#92418—22no—
24C4⋊#92418—22no—
25C4⋊#92418—22no—
26#14519696—42no—
27C22⋊#92418—22no—
28C4×#92418—24no—
29C4×#92418D414yes—
30C22×Q8×C61C2×C411yescharacteristic
31C22×Q8×C61D411yescharacteristic
32C4×Q8×C61—22no—
33C4×Q8×C61—22no—
34C4×Q8×C61—22no—
35C4×Q8×C61—22no—
36C2×C4⋊C4×C61—22no—
37C2×C4⋊C4×C61—21no—
38C2×C4⋊C4×C61—21no—
39C2×C4⋊C4×C61C2×C411yescharacteristic
40C2×C4⋊C4×C61C2×C412yes—
41C2×C4⋊C4×C61D411yescharacteristic
42C2×C42×C61—21no—
43C2×C42×C61D412yes—
44C2×C42×C61C2311yescharacteristic
45#95×C61—22no—
46#95×C61—22no—
47#95×C61—22no—
48#95×C61—21no—
49#95×C61C2×C412yes—
50C2×Q8×C61—22no—
51C2×Q8×C61—22no—
52C2×Q8×C61—22no—
53C2×Q8×C61—42no—
54C2×Q8×C61SD1612yes—
55C2×Q8×C61Q1612yes—
56C22×C4×C61—21no—
57C22×C4×C61—22no—
58C22×C4×C61—21no—
59C22×C4×C61C22⋊C412yes—
60C22×C4×C61C22⋊C412yes—
61C22×C4×C61C22×C411yescharacteristic
62C22×C4×C61C2×D411yescharacteristic
63C22×C4×C61C2×D411yescharacteristic
64C4⋊C4×C61—24no—
65C4⋊C4×C61—22no—
66C4⋊C4×C61—22no—
67C4⋊C4×C61—44no—
68C4⋊C4×C61—41no—
69C4⋊C4×C61—41no—
70C4⋊C4×C61—42no—
71C42×C61—22no—
72C42×C61—22no—
73C42×C61—42no—
74C42×C61C2×D412yes—
75C42×C61#4112yes—
76#11758194—42no—
77#11758194—42no—
78C2×#92418—24no—
79C2×#92418—42no—
80C23×C61C2×C22⋊C411yescharacteristic
81Q8×C61—24no—
82Q8×C61—24no—
83Q8×C61—24no—
84Q8×C61—42no—
85C2×C4×C61—22no—
86C2×C4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61—41no—
90C2×C4×C61—41no—
91C2×C4×C61—41no—
92C2×C4×C61—41no—
93C2×C4×C61—42no—
94C2×C4×C61—42no—
95C2×C4×C61—42no—
96C2×C4×C61—42no—
97C2×C4×C61—41no—
98C2×C4×C61—42no—
99C2×C4×C61#10314yes—
100C2×C4×C61C4×D412yes—
101C2×C4×C61#12011yescharacteristic
102C2×C4×C61#12112yes—
103C2×C4×C61#12311yescharacteristic
104C2×C4×C61C2×SD1611yescharacteristic
105C2×C4×C61C2×Q1611yescharacteristic
106C2×C4×C61#13512yes—
107#92418—44no—
108#92418—82no—
109#9484—611nomaximal, Sylow
110C22×C61—21no—
111C22×C61—21no—
112C22×C61#38611yescharacteristic
113C22×C61C2×#10311yescharacteristic
114C22×C61#41611yescharacteristic
115C4×C61—22no—
116C4×C61—24no—
117C4×C61—21no—
118C4×C61—21no—
119C4×C61—42no—
120C4×C61—42no—
121C4×C61—82no—
122C4×C61—81no—
123C4×C61#46512yes—
124C4×C61#46712yes—
125#2982—611no—
126#2581D6111yescharacteristic
127#1801—611no—
128#1487—612no—
129#1286—612no—
130C2×C61—21no—
131C2×C61—21no—
132C2×C61#189111yescharacteristic
133C2×C61#189211yescharacteristic
134C2×C61#191211yescharacteristic
135C2×C4×Q8C2×D6111yescharacteristic
136C2×C4×Q8C2×D6111yescharacteristic
137C8×Q8—1224no—
138#431—612no—
139#431—1222no—
140#423—612no—
141C2×#101—1221no—
142#400Dic6112yes—
143#395Dic6112yes—
144#391—21no—
145#389—21no—
146#387—22no—
147#382C2×D6111yescharacteristic
148#343—1221no—
149Q8⋊C8—1224no—
150C61#948411yescharacteristic, complemented, Sylow
151C22×Q8C2×Dic6111yescharacteristic
152C22×Q8C22⋊D6111yescharacteristic
153C2×M16—1222no—
154C4×Q8—22no—
155C4×Q8—22no—
156C4×Q8—22no—
157C4×Q8—22no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4C2×Dic6111yescharacteristic
162C2×C4⋊C4C2×Dic6112yes—
163C2×C4⋊C4C22⋊D6111yescharacteristic
164C2×C42—21no—
165C2×C42C22⋊D6112yes—
166C2×C42C22×D6111yescharacteristic
167C4⋊C8—1224no—
168C4⋊C8—1222no—
169C4⋊C8—1222no—
170C4⋊C8—1222no—
171#101—2442no—
172C22⋊C8—1222no—
173C4×C8—614no—
174C4×C8—1224no—
175#95—22no—
176#95—22no—
177#95—22no—
178#95—21no—
179#95C2×Dic6112yes—
180C2×Q8—22no—
181C2×Q8—22no—
182C2×Q8—22no—
183C2×Q8—42no—
184C2×Q8#1175820112yes—
185C2×Q8#1175820212yes—
186C22×C4—21no—
187C22×C4—22no—
188C22×C4—21no—
189C22×C4C22⋊Dic6112yes—
190C22×C4C22⋊Dic6112yes—
191C22×C4C22×Dic6111yescharacteristic
192C22×C4C2×C22⋊D6111yescharacteristic
193C22×C4C2×C22⋊D6111yescharacteristic
194M16—2442no—
195M16—2442no—
196C2×C8—1224no—
197C2×C8—2442no—
198C4⋊C4—24no—
199C4⋊C4—22no—
200C4⋊C4—22no—
201C4⋊C4—44no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—42no—
205C42—22no—
206C42—22no—
207C42—42no—
208C42D4×D6112yes—
209C42#1175822412yes—
210C23C2×C22⋊Dic6111yescharacteristic
211Q8—24no—
212Q8—24no—
213Q8—24no—
214Q8—42no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—41no—
229C2×C4#1451970114yes—
230C2×C4D4×Dic6112yes—
231C2×C4#1451974511yescharacteristic
232C2×C4#1451974912yes—
233C2×C4#1451975811yescharacteristic
234C2×C4C2×#1175820111yescharacteristic
235C2×C4C2×#1175820211yescharacteristic
236C2×C4#1451979712yes—
237C8—4882no—
238C8—2444no—
239C22—21no—
240C22—21no—
241C22#1683964211yescharacteristic
242C22C2×#1451970111yescharacteristic
243C22#1683975811yescharacteristic
244C4—22no—
245C4—24no—
246C4—21no—
247C4—21no—
248C4—42no—
249C4—42no—
250C4—82no—
251C4—81no—
252C4#1683999312yes—
253C4#1684000112yes—
254C2—21no—
255C2—21no—
256C2#2144623811yescharacteristic
257C2#2144624311yescharacteristic
258C2#2144635711yescharacteristic
subgroupG/H
centerC22#16839642
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2581C2
socleC22×C61#386
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#2581D61
hypocenterC61#9484
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2581

Complements

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

NH ≅ G/Ntype
150. C61#9484semidirect

Maximal subgroups

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

subgroupindex
#214549002
#214458152
#214442482
#214436772
C61×#25812
#948461