Finite Group Databasebeta

← #29582305

Subgroups — #29582305

Order 15616.

466 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 105 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#21456960C212yesmaximal
2#21446639C211yesmaximal, characteristic
3#21444383C212yesmaximal
4#21443664C211yesmaximal, characteristic
5C61×#3162C211yesmaximal, characteristic
6C2×#14519777C2211yescharacteristic
7#16840158—22no—
8#16840112—22no—
9#16840090—24no—
10#16840047—24no—
11#16839815C2212yes—
12C2×#14519702—22no—
13#16839628C2211yescharacteristic
14#16839499—24no—
15C61×#533C2212yes—
16C61×#501—22no—
17C61×#501—22no—
18C61×#427—22no—
19C2×#97×C61C2211yescharacteristic
20C22×Dic122—21no—
21#14519777—22no—
22#14519777—21no—
23#14519777D412yes—
24C2×C4⋊Dic61—22no—
25C2×C4⋊Dic61—21no—
26#14519708—28no—
27C4⋊#92418—22no—
28#14519702—44no—
29#14519701—28no—
30C22⋊#92418D414yes—
31C4×#92418—22no—
32#14519684—22no—
33C22×C8×C61D412yes—
34C4⋊Q8×C61D412yes—
35C4⋊Q8×C61D412yes—
36#125×C61—22no—
37C22⋊Q8×C61—22no—
38C22⋊Q8×C61—22no—
39C4×Q8×C61—22no—
40C4×Q8×C61—22no—
41#117×C61—22no—
42C2×C42×C61C2311yescharacteristic
43#107×C61—24no—
44#106×C61—22no—
45#106×C61—22no—
46#97×C61—22no—
47C2×Q8×C61—22no—
48C2×Q8×C61—22no—
49C22×C4×C61C2×D412yes—
50C22×C4×C61C2×D411yescharacteristic
51C22×Dic61—41no—
52C22×Dic61—41no—
53C2×Dic122—22no—
54C2×Dic122—42no—
55C2×Dic122—42no—
56C2×Dic122—41no—
57C2×C8×C61—22no—
58C2×C8×C61—22no—
59C2×C8×C61SD1614yes—
60C4⋊C4×C61—22no—
61C4⋊C4×C61—22no—
62C4⋊C4×C61—22no—
63C4⋊C4×C61—22no—
64C4⋊C4×C61—42no—
65C4⋊C4×C61—42no—
66C22⋊C4×C61—42no—
67C42×C61—42no—
68C42×C61C2×D411yescharacteristic
69C42×C61C2×D412yes—
70C42×C61#4111yescharacteristic
71C4⋊Dic61—24no—
72C4⋊Dic61—42no—
73C4⋊Dic61—42no—
74C2×#92418—24no—
75C23×C61#12711yescharacteristic
76Q8×C61—44no—
77Q8×C61—82no—
78C2×C4×C61—42no—
79C2×C4×C61—42no—
80C2×C4×C61—42no—
81C2×C4×C61#12012yes—
82C2×C4×C61#12011yescharacteristic
83C2×C4×C61#12112yes—
84C2×C4×C61#12111yescharacteristic
85C2×C4×C61C2×SD1612yes—
86C2×C4×C61#13712yes—
87C2×Dic61—42no—
88C2×Dic61—81no—
89C2×Dic61—81no—
90C2×Dic61—82no—
91C2×Dic61—81no—
92Dic122—44no—
93Dic122—82no—
94C8×C61—24no—
95#92418—44no—
96#10227—611nomaximal, Sylow
97C22×C61—22no—
98C22×C61#39211yescharacteristic
99C22×C61#49211yescharacteristic
100C22×C61#49711yescharacteristic
101C4×C61—22no—
102C4×C61—22no—
103C4×C61—82no—
104C4×C61—82no—
105C4×C61#44812yes—
106C4×C61#46112yes—
107Dic61—82no—
108Dic61—161no—
109#3229—612no—
110#3162D6111yescharacteristic
111#1960—611no—
112#1518—612no—
113#1281—611no—
114C2×C61—21no—
115C2×C61—21no—
116C2×C61#200912yes—
117C2×C61#201311yescharacteristic
118#533C2×D6112yes—
119C2×C4⋊Q8—611no—
120#501—22no—
121#501—22no—
122#498—1222no—
123#487—1222no—
124#483—1224no—
125#475—1224no—
126#431—612no—
127#427—22no—
128C2×#103—1222no—
129C2×#97C2×D6111yescharacteristic
130#382—611no—
131#328—1224no—
132C61#1022711yescharacteristic, complemented, Sylow
133C22×Q8—1221no—
134C22×C8C22⋊D6112yes—
135C4⋊Q8—612no—
136C4⋊Q8—1221no—
137C4⋊Q8—1222no—
138C4⋊Q8C22⋊D6112yes—
139C4⋊Q8C22⋊D6112yes—
140#125—22no—
141C22⋊Q8—22no—
142C22⋊Q8—22no—
143C4×Q8—22no—
144C4×Q8—22no—
145#117—22no—
146C2×C4⋊C4—1222no—
147C2×C4⋊C4—1221no—
148C2×C42C22×D6111yescharacteristic
149#107—24no—
150#106—22no—
151#106—22no—
152#106—1228no—
153C4⋊C8—1222no—
154#103—1228no—
155#103—2444no—
156C22⋊C8—614no—
157#97—22no—
158C4×C8—1222no—
159#95—1222no—
160C2×Q8—22no—
161C2×Q8—22no—
162C2×Q8—1222no—
163C2×Q8—2442no—
164C2×Q8—2442no—
165C2×Q8—2441no—
166C22×C4—2441no—
167C22×C4—2441no—
168C22×C4D4×D6112yes—
169C22×C4C2×C22⋊D6111yescharacteristic
170C2×C8—22no—
171C2×C8—22no—
172C2×C8—1224no—
173C2×C8#1175820114yes—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—22no—
177C4⋊C4—22no—
178C4⋊C4—42no—
179C4⋊C4—42no—
180C4⋊C4—1224no—
181C4⋊C4—2442no—
182C4⋊C4—2442no—
183C22⋊C4—42no—
184C42—42no—
185C42D4×D6111yescharacteristic
186C42#1175822411yescharacteristic
187C42C2×C22⋊D6112yes—
188C23#1451977311yescharacteristic
189Q8—44no—
190Q8—82no—
191Q8—4882no—
192Q8—2444no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—4882no—
197C2×C4—4881no—
198C2×C4—4881no—
199C2×C4—4881no—
200C2×C4—2442no—
201C2×C4#1451974512yes—
202C2×C4#1451974611yescharacteristic
203C2×C4#1451974811yescharacteristic
204C2×C4#1451974912yes—
205C2×C4C2×#1175820112yes—
206C2×C4#1451980812yes—
207C8—24no—
208C8—2444no—
209C22—22no—
210C22#1683967011yescharacteristic
211C22#1684013611yescharacteristic
212C22#1684015411yescharacteristic
213C4—22no—
214C4—22no—
215C4—82no—
216C4—82no—
217C4—9761no—
218C4—4882no—
219C4#1683990112yes—
220C4#1683996412yes—
221C2—21no—
222C2—21no—
223C2#2144687612yes—
224C2#2144690211yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#3162C2
socleC22×C61#392
prime radicalC23×C61#127
hypercenter#3162D61
hypocenterC61#10227
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3162

Complements

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

NH ≅ G/Ntype
132. C61#10227semidirect

Maximal subgroups

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

subgroupindex
#214569602
#214466392
#214443832
#214436642
C61×#31622
#1022761