Finite Group Databasebeta

← #29580975

Subgroups — #29580975

Order 15616.

468 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 85 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#21455950C212yesmaximal
3#21446758C211yesmaximal, characteristic
4#21444435C212yesmaximal
5C61×#1290C211yesmaximal, characteristic
6#16840319C2212yes—
7C2×C4×Dic122C2211yescharacteristic
8#16840093—22no—
9#16840058—22no—
10#16840048—22no—
11#16840003—22no—
12#16839973—22no—
13#16839973—22no—
14#16839920—22no—
15#16839870—24no—
16C2×#14519688C2211yescharacteristic
17#16839516—22no—
18#16839503—24no—
19C61×#432C2212yes—
20C2×C4⋊C8×C61C2211yescharacteristic
21C22×Dic122D411yescharacteristic
22C2×Dic244—24no—
23C2×Dic244—22no—
24C22×#92418—21no—
25#14519777D412yes—
26#14519777D412yes—
27#14519769—22no—
28#14519756—22no—
29#14519756—22no—
30C4×Dic122—22no—
31C4×Dic122—22no—
32C4×Dic122—22no—
33C4×Dic122—22no—
34#14519736—22no—
35C2×C4⋊Dic61D411yescharacteristic
36C2×#11758196—21no—
37C2×C4×Dic61—21no—
38#14519711—22no—
39#14519709—24no—
40#14519702—24no—
41#14519702—24no—
42#14519702—24no—
43#14519688—22no—
44C22×C8×C61D412yes—
45C2×C42×C61C2311yescharacteristic
46C4⋊C8×C61—22no—
47C4⋊C8×C61—22no—
48C22⋊C8×C61—22no—
49#97×C61D414yes—
50C22×C4×C61C2×D411yescharacteristic
51C22×C4×C61C2×D411yescharacteristic
52C22×C4×C61#4111yescharacteristic
53C22×Dic61—21no—
54C22×Dic61—21no—
55C2×Dic122—22no—
56C2×Dic122—22no—
57C2×Dic122—22no—
58C2×Dic122—42no—
59C2×C8×C61—24no—
60C2×C8×C61—22no—
61C2×C8×C61—42no—
62C42×C61C2×D412yes—
63C42×C61C2×D412yes—
64C22⋊Dic61—42no—
65C4⋊Dic61—22no—
66C4⋊Dic61—22no—
67C4⋊Dic61—22no—
68C4⋊Dic61—22no—
69C4⋊Dic61—22no—
70#11758196—42no—
71#11758196—42no—
72#11758196—42no—
73C4×Dic61—41no—
74C4×Dic61—42no—
75C4×Dic61—41no—
76C2×#92418—22no—
77C2×#92418—41no—
78C2×#92418—41no—
79Dic244—48no—
80Dic244—82no—
81C23×C61#12111yescharacteristic
82C2×C4×C61—22no—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—41no—
86C2×C4×C61#12012yes—
87C2×C4×C61#12011yescharacteristic
88C2×C4×C61#12112yes—
89C2×C4×C61#12711yescharacteristic
90C2×Dic61—22no—
91C2×Dic61—41no—
92C2×Dic61—41no—
93C2×Dic61—41no—
94C2×Dic61—42no—
95C2×Dic61—42no—
96C2×Dic61—42no—
97Dic122—24no—
98Dic122—42no—
99Dic122—44no—
100Dic122—42no—
101Dic122—42no—
102C8×C61—44no—
103C8×C61—42no—
104#92418—42no—
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#45511yescharacteristic
114C4×C61#45611yescharacteristic
115Dic61—42no—
116Dic61—82no—
117Dic61—82no—
118Dic61—81no—
119#3249—611no—
120#3113—612no—
121#1985—611no—
122#1531—612no—
123#1290D6111yescharacteristic
124C2×C61—22no—
125C2×C61#200711yescharacteristic
126C2×C61#201011yescharacteristic
127C2×C61#202011yescharacteristic
128#533—612no—
129C2×C4×Q8—611no—
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#432C2×D6112yes—
139C2×C4⋊C8C2×D6111yescharacteristic
140C2×#97—611no—
141#336—1222no—
142#330—1224no—
143C61#1003111yescharacteristic, complemented, Sylow
144C22×Q8—611no—
145C2×Q16—1222no—
146C2×Q16—1224no—
147C22×C8—1221no—
148C22×C8D24412yes—
149C4⋊Q8—612no—
150C4⋊Q8—612no—
151#125—1222no—
152C22⋊Q8—1222no—
153C22⋊Q8—1222no—
154C4×Q8—1222no—
155C4×Q8—1222no—
156C4×Q8—1222no—
157C4×Q8—1222no—
158#117—1222no—
159C2×C4⋊C4—611no—
160C2×C4⋊C4—1221no—
161C2×C42—1221no—
162C2×C42C22×D6111yescharacteristic
163#107—1222no—
164#106—1224no—
165C4⋊C8—22no—
166C4⋊C8—22no—
167#103—1224no—
168#103—1224no—
169#103—1224no—
170C22⋊C8—22no—
171#97—1222no—
172#97D24414yes—
173C2×Q8—1222no—
174C2×Q8—1222no—
175C2×Q8—1222no—
176C2×Q8—2442no—
177C22×C4—1221no—
178C22×C4—1221no—
179C22×C4C2×D24411yescharacteristic
180C22×C4D4×D6111yescharacteristic
181C22×C4#1175822611yescharacteristic
182Q16—4882no—
183Q16—2448no—
184C2×C8—24no—
185C2×C8—22no—
186C2×C8—42no—
187C2×C8—1222no—
188C2×C8—2441no—
189C2×C8—2441no—
190C4⋊C4—1222no—
191C4⋊C4—1222no—
192C4⋊C4—1222no—
193C4⋊C4—1222no—
194C4⋊C4—1222no—
195C4⋊C4—2442no—
196C4⋊C4—2442no—
197C4⋊C4—2442no—
198C22⋊C4—2442no—
199C42—2441no—
200C42—2442no—
201C42—2441no—
202C42C2×D24412yes—
203C42D4×D6112yes—
204C23#1451975211yescharacteristic
205Q8—1224no—
206Q8—2444no—
207Q8—2442no—
208Q8—2442no—
209Q8—2442no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—41no—
214C2×C4—1222no—
215C2×C4—2442no—
216C2×C4—2441no—
217C2×C4—2442no—
218C2×C4—2442no—
219C2×C4—2441no—
220C2×C4—2441no—
221C2×C4#1451974712yes—
222C2×C4#1451974711yescharacteristic
223C2×C4#1451975212yes—
224C2×C4#1451977411yescharacteristic
225C8—44no—
226C8—42no—
227C8—2442no—
228C22—21no—
229C22—21no—
230C22#1683967211yescharacteristic
231C22#1684003812yes—
232C4—22no—
233C4—21no—
234C4—22no—
235C4—4881no—
236C4—4882no—
237C4—4882no—
238C4—2442no—
239C4#1683994211yescharacteristic
240C4#1683994711yescharacteristic
241C2—22no—
242C2#2144686811yescharacteristic
243C2#2144688711yescharacteristic
244C2#2144694111yescharacteristic
subgroupG/H
centerC22#16839672
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1290C2
socleC22×C61#392
prime radicalC23×C61#121
hypercenter#1290D61
hypocenterC61#10031
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1290

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
#214559502
#214467582
#214444352
C61×#12902
#1003161