Finite Group Databasebeta

← #29582304

Subgroups — #29582304

Order 15616.

466 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 103 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#21456963C212yesmaximal
2#21456343C211yesmaximal, characteristic
3#21444382C212yesmaximal
4#21443664C211yesmaximal, characteristic
5C61×#1960C211yesmaximal, characteristic
6#16840319C2212yes—
7#16840171—22no—
8#16840171—22no—
9#16840158—22no—
10#16840114—22no—
11#16840092—24no—
12#16840044—24no—
13#16839815C2212yes—
14#16839800—22no—
15#16839498—24no—
16C2×C4⋊Q8×C61C2211yescharacteristic
17C2×#103×C61—22no—
18C2×#97×C61C2211yescharacteristic
19C61×#382C2211yescharacteristic
20#14519777D412yes—
21#14519777D412yes—
22#14519769—22no—
23#14519756—22no—
24#14519756—22no—
25C4×Dic122—22no—
26C4×Dic122—22no—
27#14519736—22no—
28#14519711—24no—
29#14519709—22no—
30#14519709—22no—
31#14519708—28no—
32C4⋊#92418—22no—
33#14519700—28no—
34C22⋊#92418D414yes—
35C4×#92418—22no—
36C22×Q8×C61—21no—
37C22×C8×C61D412yes—
38C4⋊Q8×C61—22no—
39C4⋊Q8×C61—21no—
40C4⋊Q8×C61D412yes—
41C2×C4⋊C4×C61—22no—
42C2×C4⋊C4×C61—21no—
43C2×C42×C61C2311yescharacteristic
44#103×C61—44no—
45#97×C61—22no—
46#95×C61—22no—
47C2×Q8×C61—22no—
48C2×Q8×C61—41no—
49C2×Q8×C61—42no—
50C2×Q8×C61—42no—
51C22×C4×C61—41no—
52C22×C4×C61—41no—
53C22×C4×C61C2×D412yes—
54C22×C4×C61C2×D411yescharacteristic
55C2×Dic122—22no—
56C2×Dic122—22no—
57C2×C8×C61—22no—
58C2×C8×C61—22no—
59C2×C8×C61SD1614yes—
60C4⋊C4×C61—24no—
61C4⋊C4×C61—42no—
62C4⋊C4×C61—42no—
63C42×C61C2×D411yescharacteristic
64C42×C61C2×D412yes—
65C42×C61#4111yescharacteristic
66C22⋊Dic61—42no—
67C4⋊Dic61—22no—
68C4⋊Dic61—22no—
69C4⋊Dic61—22no—
70C4⋊Dic61—22no—
71#11758196—42no—
72#11758196—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—81no—
81C2×C4×C61—81no—
82C2×C4×C61—82no—
83C2×C4×C61—81no—
84C2×C4×C61#12012yes—
85C2×C4×C61#12011yescharacteristic
86C2×C4×C61#12112yes—
87C2×C4×C61#12111yescharacteristic
88C2×C4×C61C2×SD1612yes—
89C2×C4×C61#13712yes—
90C2×Dic61—42no—
91C2×Dic61—42no—
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—161no—
105C4×C61#44812yes—
106C4×C61#46112yes—
107Dic61—82no—
108Dic61—82no—
109#3229—612no—
110#3162—611no—
111#1960D6111yescharacteristic
112#1518—612no—
113#1281—611no—
114C2×C61—21no—
115C2×C61—21no—
116C2×C61#200912yes—
117C2×C61#201311yescharacteristic
118#533—612no—
119C2×C4⋊Q8C2×D6111yescharacteristic
120#501—1222no—
121#501—1222no—
122#498—1222no—
123#487—1222no—
124#483—1224no—
125#475—1224no—
126#431—612no—
127#427—1222no—
128C2×#103—22no—
129C2×#97C2×D6111yescharacteristic
130#382C2×D6111yescharacteristic
131#328—1224no—
132C61#1022711yescharacteristic, complemented, Sylow
133C22×Q8—21no—
134C22×C8C22⋊D6112yes—
135C4⋊Q8—21no—
136C4⋊Q8—22no—
137C4⋊Q8—612no—
138C4⋊Q8—612no—
139C4⋊Q8D24412yes—
140#125—1222no—
141C22⋊Q8—1222no—
142C22⋊Q8—1222no—
143C4×Q8—1222no—
144C4×Q8—1222no—
145#117—1222no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—21no—
148C2×C42C22×D6111yescharacteristic
149#107—1224no—
150#106—1228no—
151#106—1222no—
152#106—1222no—
153C4⋊C8—1222no—
154#103—44no—
155#103—1228no—
156C22⋊C8—614no—
157#97—22no—
158C4×C8—1222no—
159#95—22no—
160C2×Q8—22no—
161C2×Q8—41no—
162C2×Q8—42no—
163C2×Q8—42no—
164C2×Q8—1222no—
165C2×Q8—1222no—
166C22×C4—41no—
167C22×C4—41no—
168C22×C4D4×D6112yes—
169C22×C4C2×C22⋊D6111yescharacteristic
170C2×C8—22no—
171C2×C8—22no—
172C2×C8—1224no—
173C2×C8#1175820014yes—
174C4⋊C4—24no—
175C4⋊C4—42no—
176C4⋊C4—42no—
177C4⋊C4—1222no—
178C4⋊C4—1222no—
179C4⋊C4—1222no—
180C4⋊C4—1222no—
181C4⋊C4—2442no—
182C4⋊C4—2442no—
183C22⋊C4—2442no—
184C42—2442no—
185C42C2×D24411yescharacteristic
186C42#1175822211yescharacteristic
187C42D4×D6112yes—
188C23#1451977311yescharacteristic
189Q8—44no—
190Q8—82no—
191Q8—4882no—
192Q8—2444no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—81no—
196C2×C4—81no—
197C2×C4—82no—
198C2×C4—81no—
199C2×C4—2442no—
200C2×C4—2442no—
201C2×C4#1451974511yescharacteristic
202C2×C4#1451974712yes—
203C2×C4#1451975012yes—
204C2×C4#1451975111yescharacteristic
205C2×C4C2×#1175820012yes—
206C2×C4#1451980712yes—
207C8—24no—
208C8—2444no—
209C22—22no—
210C22#1683967111yescharacteristic
211C22#1684013411yescharacteristic
212C22#1684015711yescharacteristic
213C4—22no—
214C4—22no—
215C4—82no—
216C4—161no—
217C4—4882no—
218C4—4882no—
219C4#1683990012yes—
220C4#1683996712yes—
221C2—21no—
222C2—21no—
223C2#2144688112yes—
224C2#2144690111yescharacteristic
subgroupG/H
centerC22#16839671
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1960C2
socleC22×C61#392
prime radicalC23×C61#127
hypercenter#1960D61
hypocenterC61#10227
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1960

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
#214569632
#214563432
#214443822
#214436642
C61×#19602
#1022761