Finite Group Databasebeta

← #29580974

Subgroups — #29580974

Order 15616.

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

normal subgroups only

This group has 468 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#21457164C211yesmaximal, characteristic
2#21455949C212yesmaximal
3#21444433C212yesmaximal
4#21443689C211yesmaximal, characteristic
5C61×#1985C211yesmaximal, characteristic
6#16840319C2212yes—
7#16840092—22no—
8#16840058—22no—
9#16840047—22no—
10#16840003—22no—
11#16839973—22no—
12#16839972—22no—
13#16839918—22no—
14#16839867—24no—
15#16839819C2212yes—
16#16839503—24no—
17C2×C4×Q8×C61C2211yescharacteristic
18C2×C4⋊C8×C61C2211yescharacteristic
19C2×#97×C61C2211yescharacteristic
20C61×#336—22no—
21C2×Dic244—22no—
22C2×#11758202—24no—
23#14519777D412yes—
24#14519777D412yes—
25#14519769—22no—
26#14519756—22no—
27#14519756—22no—
28C4×Dic122—22no—
29C4×Dic122—22no—
30#14519736—22no—
31#14519711—22no—
32#14519708—24no—
33C4⋊#92418—22no—
34#14519702—24no—
35#14519701—24no—
36#14519700—24no—
37C22⋊#92418—22no—
38#14519688D414yes—
39C22×Q8×C61D411yescharacteristic
40C22×C8×C61—21no—
41C22×C8×C61D412yes—
42C4×Q8×C61—22no—
43C4×Q8×C61—22no—
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61D411yescharacteristic
46C2×C42×C61—21no—
47C2×C42×C61C2311yescharacteristic
48C4⋊C8×C61—22no—
49#97×C61—22no—
50C2×Q8×C61—22no—
51C2×Q8×C61—42no—
52C22×C4×C61—21no—
53C22×C4×C61—21no—
54C22×C4×C61C2×D411yescharacteristic
55C22×C4×C61C2×D411yescharacteristic
56C22×C4×C61#4111yescharacteristic
57C2×Dic122—22no—
58C2×Dic122—22no—
59C2×C8×C61—22no—
60C2×C8×C61—22no—
61C2×C8×C61—41no—
62C2×C8×C61—41no—
63C2×C8×C61—42no—
64C4⋊C4×C61—22no—
65C4⋊C4×C61—42no—
66C42×C61—41no—
67C42×C61—41no—
68C42×C61C2×D412yes—
69C42×C61C2×D412yes—
70C22⋊Dic61—42no—
71#11758202—48no—
72C4⋊Dic61—22no—
73C4⋊Dic61—22no—
74C4⋊Dic61—22no—
75C4⋊Dic61—22no—
76#11758196—42no—
77#11758196—42no—
78C4×Dic61—42no—
79C2×#92418—24no—
80Dic244—82no—
81C23×C61#12111yescharacteristic
82Q8×C61—24no—
83Q8×C61—42no—
84C2×C4×C61—22no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—22no—
88C2×C4×C61—41no—
89C2×C4×C61—41no—
90C2×C4×C61—41no—
91C2×C4×C61—41no—
92C2×C4×C61—42no—
93C2×C4×C61#12012yes—
94C2×C4×C61#12011yescharacteristic
95C2×C4×C61#12112yes—
96C2×C4×C61#12711yescharacteristic
97C2×Dic61—42no—
98C2×Dic61—42no—
99Dic122—44no—
100Dic122—42no—
101Dic122—42no—
102C8×C61—42no—
103C8×C61—42no—
104#92418—44no—
105#10031—611nomaximal, Sylow
106C22×C61—21no—
107C22×C61—21no—
108C22×C61#39211yescharacteristic
109C22×C61#47312yes—
110C4×C61—21no—
111C4×C61—22no—
112C4×C61—22no—
113C4×C61—42no—
114C4×C61—81no—
115C4×C61#45511yescharacteristic
116C4×C61#45611yescharacteristic
117Dic61—82no—
118Dic61—82no—
119#3249—611no—
120#3113—612no—
121#1985D6111yescharacteristic
122#1531—612no—
123#1290—611no—
124C2×C61—22no—
125C2×C61#200711yescharacteristic
126C2×C61#201011yescharacteristic
127C2×C61#202011yescharacteristic
128#533—612no—
129C2×C4×Q8C2×D6111yescharacteristic
130#483—1222no—
131#477—1222no—
132#475—1222no—
133#467—1222no—
134#462—1222no—
135#462—1222no—
136#451—1222no—
137#441—1224no—
138#432—612no—
139C2×C4⋊C8C2×D6111yescharacteristic
140C2×#97C2×D6111yescharacteristic
141#336—22no—
142#330—1224no—
143C61#1003111yescharacteristic, complemented, Sylow
144C22×Q8D24411yescharacteristic
145C2×Q16—1222no—
146C2×Q16—1224no—
147C22×C8—21no—
148C22×C8C22⋊D6112yes—
149C4⋊Q8—612no—
150C4⋊Q8—612no—
151#125—1222no—
152C22⋊Q8—1222no—
153C22⋊Q8—1222no—
154C4×Q8—22no—
155C4×Q8—22no—
156C4×Q8—1222no—
157C4×Q8—1222no—
158#117—1222no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4D24411yescharacteristic
161C2×C42—21no—
162C2×C42C22×D6111yescharacteristic
163#107—1222no—
164#106—1224no—
165C4⋊C8—22no—
166C4⋊C8—1222no—
167#103—1224no—
168#103—1224no—
169#103—1224no—
170C22⋊C8—1222no—
171#97—22no—
172#97—614no—
173C2×Q8—22no—
174C2×Q8—42no—
175C2×Q8—1222no—
176C2×Q8—1222no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4C2×D24411yescharacteristic
180C22×C4#1175822211yescharacteristic
181C22×C4C2×C22⋊D6111yescharacteristic
182Q16—4882no—
183Q16—2448no—
184C2×C8—22no—
185C2×C8—22no—
186C2×C8—41no—
187C2×C8—41no—
188C2×C8—42no—
189C2×C8—1224no—
190C4⋊C4—22no—
191C4⋊C4—42no—
192C4⋊C4—1222no—
193C4⋊C4—1222no—
194C4⋊C4—1222no—
195C4⋊C4—1222no—
196C4⋊C4—2442no—
197C4⋊C4—2442no—
198C22⋊C4—2442no—
199C42—41no—
200C42—41no—
201C42—2442no—
202C42D4×D6112yes—
203C42D4×D6112yes—
204C23#1451975111yescharacteristic
205Q8—24no—
206Q8—42no—
207Q8—2444no—
208Q8—2442no—
209Q8—2442no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—41no—
219C2×C4—2442no—
220C2×C4—2442no—
221C2×C4#1451974511yescharacteristic
222C2×C4#1451974712yes—
223C2×C4#1451975012yes—
224C2×C4#1451977311yescharacteristic
225C8—42no—
226C8—42no—
227C8—2444no—
228C22—21no—
229C22—21no—
230C22#1683967111yescharacteristic
231C22#1684003712yes—
232C4—22no—
233C4—21no—
234C4—22no—
235C4—42no—
236C4—81no—
237C4—4882no—
238C4—4882no—
239C4#1683993911yescharacteristic
240C4#1683994411yescharacteristic
241C2—22no—
242C2#2144686511yescharacteristic
243C2#2144688611yescharacteristic
244C2#2144694011yescharacteristic
subgroupG/H
centerC22#16839671
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1985C2
socleC22×C61#392
prime radicalC23×C61#121
hypercenter#1985D61
hypocenterC61#10031
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1985

Complements

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

NH ≅ G/Ntype
143. C61#10031semidirect

Maximal subgroups

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

subgroupindex
#214571642
#214559492
#214444332
#214436892
C61×#19852
#1003161