Finite Group Databasebeta

← #29593011

Subgroups — #29593011

Order 15616.

394 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 63 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#21447164C211yesmaximal, characteristic
2#21444826C212yesmaximal
3#21443825C212yesmaximal
4#21443765C211yesmaximal, characteristic
5C61×#2582C211yesmaximal, characteristic
6#16840393C2211yescharacteristic
7#16840092—22no—
8#16839802—21no—
9#16839531C2211yescharacteristic
10#16839522—21no—
11#16839498—22no—
12#16839488C2212yes—
13C2×C4×Q8×C61—21no—
14C61×#398—21no—
15C61×#398C2212yes—
16C61×#391—22no—
17C61×#389—22no—
18C61×#384C2211yescharacteristic
19C2×#11758194—21no—
20#14519776—41no—
21#14519768—41no—
22#14519756—22no—
23#14519736—21no—
24#14519710—41no—
25#14519708—41no—
26#14519708—42no—
27#14519700—42no—
28C22⋊#92418—22no—
29C22×Q8×C61—21no—
30C4×Q8×C61—42no—
31C4×Q8×C61—42no—
32C2×C4⋊C4×C61—21no—
33C2×C4⋊C4×C61—22no—
34C2×C4⋊C4×C61—22no—
35C2×C4⋊C4×C61—21no—
36C2×C4⋊C4×C61D411yescharacteristic
37C2×C4⋊C4×C61D412yes—
38C2×C4⋊C4×C61C2311yescharacteristic
39C2×C42×C61—22no—
40C2×C42×C61D411yescharacteristic
41#95×C61—22no—
42#95×C61—21no—
43#95×C61—22no—
44#95×C61D412yes—
45C2×Q8×C61—24no—
46C2×Q8×C61—42no—
47C2×Q8×C61—42no—
48C22×C4×C61—21no—
49C22×C4×C61—22no—
50C22×C4×C61—21no—
51C22×C4×C61—22no—
52C22×C4×C61C2×D411yescharacteristic
53C22×C4×C61C2×D412yes—
54C2×Dic122—22no—
55C4⋊C4×C61—41no—
56C4⋊C4×C61—44no—
57C4⋊C4×C61—42no—
58C4⋊C4×C61—42no—
59C4⋊C4×C61—41no—
60C4⋊C4×C61—42no—
61C4⋊C4×C61—42no—
62C4⋊C4×C61—81no—
63C42×C61—21no—
64C42×C61—44no—
65C42×C61SD1612yes—
66C22⋊Dic61—41no—
67C4⋊Dic61—21no—
68C4⋊Dic61—22no—
69C4⋊Dic61—21no—
70#11758196—42no—
71C4×Dic61—41no—
72#11758194—22no—
73#11758194—41no—
74C2×#92418—41no—
75C2×#92418—42no—
76C23×C61#12011yescharacteristic
77Q8×C61—48no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—24no—
84C2×C4×C61—22no—
85C2×C4×C61—42no—
86C2×C4×C61—42no—
87C2×C4×C61—42no—
88C2×C4×C61—42no—
89C2×C4×C61—42no—
90C2×C4×C61—42no—
91C2×C4×C61—42no—
92C2×C4×C61—41no—
93C2×C4×C61C2×SD1611yescharacteristic
94C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
95C2×Dic61—41no—
96C2×Dic61—41no—
97Dic122—82no—
98#92418—42no—
99#92418—82no—
100#12247—611nomaximal, Sylow
101C22×C61—21no—
102C22×C61—21no—
103C22×C61#45011yescharacteristic
104C22×C61#45611yescharacteristic
105C22×C61B(4,𝔽2)11yescharacteristic
106C4×C61—24no—
107C4×C61—21no—
108C4×C61—21no—
109C4×C61—44no—
110C4×C61—42no—
111C4×C61—82no—
112C4×C61—81no—
113Dic61—81no—
114Dic61—81no—
115#2582D6111yescharacteristic
116#2060—611no—
117#1611—612no—
118#1346—612no—
119#1325—611no—
120C2×C61—21no—
121C2×C61—21no—
122C2×C61#160411yescharacteristic
123C2×C61#219811yescharacteristic
124C2×C61#220511yescharacteristic
125#544—611no—
126C2×C4×Q8—21no—
127#483—1222no—
128#428—1221no—
129#398—21no—
130#398C2×D6112yes—
131#391—22no—
132#389—22no—
133#384C2×D6111yescharacteristic
134#343—611no—
135#339—1221no—
136#328—1222no—
137#324—612no—
138C61#1224711yescharacteristic, complemented, Sylow
139C22×Q8—21no—
140C2×M16—1221no—
141C4⋊Q8—2441no—
142#125—2441no—
143C22⋊Q8—1222no—
144C4×Q8—42no—
145C4×Q8—42no—
146#117—1221no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4C22⋊D6111yescharacteristic
152C2×C4⋊C4C22⋊D6112yes—
153C2×C4⋊C4C22×D6111yescharacteristic
154C2×C42—22no—
155C2×C42C22⋊D6111yescharacteristic
156#107—2441no—
157#106—2441no—
158#106—2442no—
159#103—2442no—
160C22⋊C8—1222no—
161#95—22no—
162#95—21no—
163#95—22no—
164#95C22⋊D6112yes—
165C2×Q8—24no—
166C2×Q8—42no—
167C2×Q8—42no—
168C2×Q8—1222no—
169C22×C4—21no—
170C22×C4—22no—
171C22×C4—21no—
172C22×C4—22no—
173C22×C4C2×C22⋊D6111yescharacteristic
174C22×C4C2×C22⋊D6112yes—
175M16—1222no—
176M16—2441no—
177C2×C8—2442no—
178C2×C8—2441no—
179C4⋊C4—41no—
180C4⋊C4—42no—
181C4⋊C4—41no—
182C4⋊C4—42no—
183C4⋊C4—44no—
184C4⋊C4—42no—
185C4⋊C4—42no—
186C4⋊C4—81no—
187C4⋊C4—1221no—
188C4⋊C4—1222no—
189C4⋊C4—1221no—
190C4⋊C4—2442no—
191C22⋊C4—2441no—
192C42—21no—
193C42—44no—
194C42—2441no—
195C42#1175820012yes—
196C23#1451974611yescharacteristic
197Q8—48no—
198Q8—4882no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—24no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—41no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—2441no—
215C2×C4—2441no—
216C2×C4C2×#1175820011yescharacteristic
217C2×C4#1451980311yescharacteristic
218C8—4882no—
219C8—2442no—
220C22—21no—
221C22—21no—
222C22#1683991311yescharacteristic
223C22#1683994511yescharacteristic
224C22#1683994911yescharacteristic
225C4—24no—
226C4—21no—
227C4—21no—
228C4—44no—
229C4—42no—
230C4—81no—
231C4—82no—
232C4—4881no—
233C4—4881no—
234C2—21no—
235C2—21no—
236C2#2144478811yescharacteristic
237C2#2144781511yescharacteristic
238C2#2144784911yescharacteristic
subgroupG/H
centerC22#16839949
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
FittingC61×#2582C2
socleC22×C61B(4,𝔽2)
prime radicalC23×C61#120
hypercenter#2582D61
hypocenterC61#12247
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2582

Complements

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

NH ≅ G/Ntype
138. C61#12247semidirect

Maximal subgroups

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

subgroupindex
#214471642
#214448262
#214438252
#214437652
C61×#25822
#1224761