Finite Group Databasebeta

← #29593037

Subgroups — #29593037

Order 15616.

342 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 59 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#21453887C211yesmaximal, characteristic
2#21447169C211yesmaximal, characteristic
3#21444829C212yesmaximal
4#21443826C212yesmaximal
5C61×#1324C211yesmaximal, characteristic
6#16840393C2211yescharacteristic
7C2×#14519769—21no—
8#16840093—22no—
9#16839802—21no—
10#16839702—22no—
11#16839694—22no—
12#16839692—21no—
13#16839692C2212yes—
14#16839531C2211yescharacteristic
15#16839522—21no—
16#16839500—22no—
17C61×#382C2211yescharacteristic
18C61×#324C2212yes—
19C2×#11758194—21no—
20#14519776—41no—
21#14519769—42no—
22#14519769—42no—
23#14519768—41no—
24#14519756—22no—
25#14519736—21no—
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61—21no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61D412yes—
30C2×#11758196—22no—
31C2×#11758196—22no—
32#14519710—41no—
33#14519709—42no—
34#14519708—41no—
35#14519702—42no—
36#14519684—22no—
37#14519684—21no—
38#14519684—22no—
39#14519684D412yes—
40C2×C4⋊C4×C61D411yescharacteristic
41C2×C4⋊C4×C61C2311yescharacteristic
42C2×C42×C61D411yescharacteristic
43C22⋊C8×C61—22no—
44#95×C61—22no—
45C22×C4×C61—21no—
46C22×C4×C61—21no—
47C22×C4×C61C2×D411yescharacteristic
48C22×C4×C61C2×D412yes—
49C22×Dic61—22no—
50C22×Dic61—22no—
51C2×Dic122—22no—
52C2×C8×C61—42no—
53C4⋊C4×C61—41no—
54C4⋊C4×C61—41no—
55C42×C61—21no—
56C42×C61SD1612yes—
57C22⋊Dic61—41no—
58C4⋊Dic61—21no—
59C4⋊Dic61—22no—
60C4⋊Dic61—21no—
61C4⋊Dic61—42no—
62C4⋊Dic61—42no—
63C4⋊Dic61—42no—
64C4⋊Dic61—81no—
65#11758196—44no—
66#11758196—42no—
67#11758196—42no—
68#11758196—42no—
69C4×Dic61—41no—
70#11758194—22no—
71#11758194—41no—
72C2×#92418—41no—
73C23×C61#12011yescharacteristic
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—41no—
79C2×C4×C61—41no—
80C2×C4×C61—42no—
81C2×C4×C61—42no—
82C2×C4×C61—41no—
83C2×C4×C61C2×SD1611yescharacteristic
84C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
85C2×Dic61—42no—
86C2×Dic61—42no—
87C2×Dic61—42no—
88C2×Dic61—42no—
89C2×Dic61—42no—
90C2×Dic61—41no—
91C2×Dic61—41no—
92C2×Dic61—42no—
93Dic122—82no—
94C8×C61—82no—
95#92418—42no—
96#12251—611nomaximal, Sylow
97C22×C61—21no—
98C22×C61—21no—
99C22×C61#45011yescharacteristic
100C22×C61#45611yescharacteristic
101C22×C61B(4,𝔽2)11yescharacteristic
102C4×C61—21no—
103C4×C61—21no—
104C4×C61—42no—
105C4×C61—42no—
106C4×C61—81no—
107Dic61—82no—
108Dic61—82no—
109Dic61—81no—
110Dic61—81no—
111#2822—611no—
112#2061—611no—
113#1611—612no—
114#1346—612no—
115#1324D6111yescharacteristic
116C2×C61—21no—
117C2×C61—21no—
118C2×C61#160411yescharacteristic
119C2×C61#220111yescharacteristic
120C2×C61#220311yescharacteristic
121#544—611no—
122C2×#125—1221no—
123#483—1222no—
124#428—1221no—
125#400—1222no—
126#398—612no—
127#398—1222no—
128#398—1221no—
129#382C2×D6111yescharacteristic
130#343—611no—
131#339—1221no—
132#328—1222no—
133#324C2×D6112yes—
134C61#1225111yescharacteristic, complemented, Sylow
135C2×M16—1221no—
136C4⋊Q8—2441no—
137#125—2442no—
138#125—2441no—
139#125—2442no—
140C22⋊Q8—1222no—
141#117—1221no—
142C2×C4⋊C4—612no—
143C2×C4⋊C4—1221no—
144C2×C4⋊C4—1221no—
145C2×C4⋊C4—1222no—
146C2×C4⋊C4—1221no—
147C2×C4⋊C4—1222no—
148C2×C4⋊C4D24411yescharacteristic
149C2×C4⋊C4C22×D6111yescharacteristic
150C2×C42D24411yescharacteristic
151#107—2441no—
152#106—2441no—
153#106—2442no—
154#103—2442no—
155C22⋊C8—22no—
156#95—22no—
157#95—612no—
158#95—1222no—
159#95—1221no—
160#95—1222no—
161C2×Q8—1222no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—1222no—
165C22×C4—1222no—
166C22×C4C2×D24411yescharacteristic
167C22×C4D4×D6112yes—
168M16—1222no—
169M16—2441no—
170C2×C8—42no—
171C2×C8—2441no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—1221no—
175C4⋊C4—1222no—
176C4⋊C4—1221no—
177C4⋊C4—4881no—
178C4⋊C4—2442no—
179C4⋊C4—2444no—
180C4⋊C4—2442no—
181C4⋊C4—2442no—
182C4⋊C4—2442no—
183C4⋊C4—2442no—
184C4⋊C4—2442no—
185C22⋊C4—2441no—
186C42—21no—
187C42—2441no—
188C42#1175819012yes—
189C23#1451974711yescharacteristic
190Q8—4882no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—41no—
200C2×C4—2442no—
201C2×C4—2442no—
202C2×C4—2442no—
203C2×C4—2441no—
204C2×C4—2441no—
205C2×C4—2442no—
206C2×C4—2442no—
207C2×C4—2442no—
208C2×C4C2×#1175819011yescharacteristic
209C2×C4#1451980511yescharacteristic
210C8—82no—
211C8—2442no—
212C22—21no—
213C22—21no—
214C22#1683991511yescharacteristic
215C22#1683994711yescharacteristic
216C22#1683995011yescharacteristic
217C4—21no—
218C4—21no—
219C4—42no—
220C4—42no—
221C4—81no—
222C4—4882no—
223C4—4881no—
224C4—4881no—
225C4—4882no—
226C2—21no—
227C2—21no—
228C2#2144479011yescharacteristic
229C2#2144783411yescharacteristic
230C2#2144784211yescharacteristic
subgroupG/H
centerC22#16839950
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1324C2
socleC22×C61B(4,𝔽2)
prime radicalC23×C61#120
hypercenter#1324D61
hypocenterC61#12251
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
134. C61#12251semidirect

Maximal subgroups

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

subgroupindex
#214538872
#214471692
#214448292
#214438262
C61×#13242
#1225161