Finite Group Databasebeta

← #29579397

Subgroups — #29579397

Order 15616.

400 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 119 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#21445950C211yesmaximal, characteristic, complemented
2#21444383C212yesmaximal, complemented
3#21444379C212yesmaximal
4#21444102C211yesmaximal, characteristic, complemented
5C61×#3131C211yesmaximal, characteristic
6#16839815C2212yes—
7#16839628C2212yes—
8#16839525—22no—
9#16839499—24no—
10#16839496—24no—
11#16839483—21no—
12C8×#92418—21no—
13C61×#533C2211yescharacteristic
14C61×#532C2211yescharacteristic
15C61×#488—21no—
16C61×#488—21no—
17C61×#487C412yescomplemented
18C61×#486C412yescomplemented
19C61×#416—22no—
20C2×C4×C8×C61C2211yescharacteristic
21C2×C4⋊Dic61—22no—
22C4⋊#92418—22no—
23C22⋊#92418D414yes—
24C4×#92418—22no—
25#14519684—22no—
26#14519684—22no—
27C2×#41×C61—21no—
28C22×C8×C61D412yes—
29C4⋊Q8×C61C2×C411yescharacteristic
30C4⋊Q8×C61C2×C412yes—
31#127×C61C2×C411yescharacteristic
32#125×C61—21no—
33#124×C61—21no—
34C22⋊Q8×C61—22no—
35#121×C61—22no—
36C4×Q8×C61—22no—
37C4×D4×C61—22no—
38#117×C61—21no—
39C2×C42×C61C2311yescharacteristic
40#103×C61—22no—
41#103×C61—22no—
42#102×C61—22no—
43#102×C61—22no—
44C4×C8×C61C2×C412yes—
45C4×C8×C61D411yescharacteristic
46C4×C8×C61D411yescharacteristic
47#41×C61—44no—
48C2×Q8×C61—21no—
49C2×Q8×C61—22no—
50C2×D4×C61—21no—
51C2×D4×C61—22no—
52C2×D4×C61—41no—
53C22×C4×C61—41no—
54C22×C4×C61C2×D412yes—
55C22×C4×C61C2×D411yescharacteristic
56C22×Dic61—42no—
57C2×C8×C61—24no—
58C2×C8×C61C22⋊C412yes—
59C2×C8×C61C22⋊C412yes—
60C4⋊C4×C61—22no—
61C4⋊C4×C61—22no—
62C4⋊C4×C61—22no—
63C4⋊C4×C61—42no—
64C22⋊C4×C61—41no—
65C22⋊C4×C61—42no—
66C42×C61—41no—
67C42×C61C22×C411yescharacteristic
68C42×C61C2×D411yescharacteristic
69C42×C61#4112yes—
70C4⋊Dic61—44no—
71C2×#92418—24no—
72C23×C61—41no—
73C23×C61#12711yescharacteristic
74Q8×C61—42no—
75Q8×C61—82no—
76D4×C61—42no—
77D4×C61—82no—
78D4×C61—82no—
79C2×C4×C61—42no—
80C2×C4×C61—42no—
81C2×C4×C61—41no—
82C2×C4×C61—82no—
83C2×C4×C61C2×C22⋊C411yescharacteristic
84C2×C4×C61C4×D412yes—
85C2×C4×C61#12112yes—
86C2×C4×C61#12411yescharacteristic
87C2×C4×C61#13514yes—
88C2×Dic61—84no—
89C2×Dic61—82no—
90C8×C61—22no—
91C8×C61—22no—
92#92418—44no—
93#9757—611nomaximal, Sylow
94C22×C61—22no—
95C22×C61—81no—
96C22×C61—82no—
97C22×C61#39011yescharacteristic
98C22×C61#49512yes—
99C4×C61—22no—
100C4×C61—22no—
101C4×C61—81no—
102C4×C61—82no—
103C4×C61#41612yes—
104C4×C61#48812yes—
105Dic61—162no—
106#3131D6111yescharacteristic
107#1835—611no—
108#1518—612no—
109#1517—612no—
110#1450—611no—
111C2×C61—22no—
112C2×C61—161no—
113C2×C61#195811yescharacteristic
114C2×C61#197612yes—
115#533C2×D6111yescharacteristic
116#532C2×D6111yescharacteristic
117#488—21no—
118#488—21no—
119#487Dic6112yescomplemented
120#486Dic6112yescomplemented
121#431—612no—
122#416—22no—
123C2×C4×C8C2×D6111yescharacteristic
124#382—612no—
125#340—1222no—
126#328—1224no—
127#327—1224no—
128#322—1221no—
129C82—1221no—
130C61#975711yescharacteristic, complemented, Sylow
131C2×#41—21no—
132C22×C8C22⋊D6112yes—
133C4⋊Q8C2×Dic6111yescharacteristic
134C4⋊Q8C2×Dic6112yes—
135#127C2×Dic6111yescharacteristic
136#125—21no—
137#124—21no—
138C22⋊Q8—22no—
139#121—22no—
140C4×Q8—22no—
141C4×D4—22no—
142#117—21no—
143C2×C4⋊C4—1222no—
144C2×C42C22×D6111yescharacteristic
145C4⋊C8—1222no—
146#103—22no—
147#103—22no—
148#102—22no—
149#102—22no—
150C22⋊C8—614no—
151C4×C8—1222no—
152C4×C8C2×Dic6112yes—
153C4×C8C22⋊D6111yescharacteristic
154C4×C8C22⋊D6111yescharacteristic
155#95—1222no—
156#95—1222no—
157#41—44no—
158C2×Q8—21no—
159C2×Q8—22no—
160C2×D4—21no—
161C2×D4—22no—
162C2×D4—41no—
163C22×C4—41no—
164C22×C4—2442no—
165C22×C4D4×D6112yes—
166C22×C4C2×C22⋊D6111yescharacteristic
167C2×C8—24no—
168C2×C8—1224no—
169C2×C8C22⋊Dic6112yes—
170C2×C8C22⋊Dic6112yes—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—42no—
175C4⋊C4—2444no—
176C22⋊C4—41no—
177C22⋊C4—42no—
178C42—41no—
179C42#1175822412yes—
180C42C22×Dic6111yescharacteristic
181C42C2×C22⋊D6111yescharacteristic
182C23—41no—
183C23#1451977311yescharacteristic
184Q8—42no—
185Q8—82no—
186D4—42no—
187D4—82no—
188D4—82no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—41no—
192C2×C4—82no—
193C2×C4—4884no—
194C2×C4—4882no—
195C2×C4C2×C22⋊Dic6111yescharacteristic
196C2×C4D4×Dic6112yes—
197C2×C4#1451974812yes—
198C2×C4#1451976411yescharacteristic
199C2×C4#1451979714yes—
200C8—22no—
201C8—22no—
202C8—2444no—
203C22—22no—
204C22—82no—
205C22—81no—
206C22#1683966511yescharacteristic
207C22#1684014412yes—
208C4—22no—
209C4—22no—
210C4—82no—
211C4—81no—
212C4—9762no—
213C4#1683975812yes—
214C4#1684011612yes—
215C2—22no—
216C2—161no—
217C2#2144663111yescharacteristic
218C2#2144671812yes—
subgroupG/H
centerC22#16839665
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#3131C2
socleC22×C61#390
prime radicalC61×#532C22
cosocleC2×C42×C61C23
hypercenter#3131D61
hypocenterC61#9757
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3131

Complements

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

NH ≅ G/Ntype
1. #21445950C2semidirect
2. #21444383C2semidirect
4. #21444102C2semidirect
17. C61×#487C4semidirect
18. C61×#486C4semidirect
119. #487Dic61semidirect
120. #486Dic61semidirect
130. C61#9757semidirect

Maximal subgroups

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

subgroupindex
#214459502
#214443832
#214443792
#214441022
C61×#31312
#975761