Finite Group Databasebeta

← #29579394

Subgroups — #29579394

Order 15616.

400 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 111 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#21456142C211yesmaximal, characteristic
2#21444382C212yesmaximal, complemented
3#21444378C212yesmaximal
4#21444102C211yesmaximal, characteristic, complemented
5C61×#1835C211yesmaximal, characteristic, complemented
6#16840319C2211yescharacteristic
7#16840312C2211yescharacteristic
8#16840117—21no—
9#16840117—21no—
10#16840113C412yescomplemented
11#16840109C412yescomplemented
12#16839815C2212yes—
13#16839759—22no—
14#16839498—24no—
15#16839495—24no—
16#16839483—21no—
17C8×#92418—21no—
18C2×C4×C8×C61C2211yescharacteristic
19C61×#382C2212yes—
20C61×#340—22no—
21C2×#11758222—21no—
22#14519777C2×C411yescharacteristic
23#14519777C2×C412yes—
24#14519774C2×C411yescharacteristic
25#14519769—21no—
26#14519765—21no—
27#14519756—22no—
28#14519751—22no—
29C4×Dic122—22no—
30C4×D244—22no—
31#14519736—21no—
32C4⋊#92418—22no—
33#14519702—22no—
34#14519702—22no—
35#14519699—22no—
36#14519699—22no—
37C22⋊#92418D414yes—
38C4×#92418—22no—
39C22×C8×C61D412yes—
40C2×C4⋊C4×C61—22no—
41C2×C42×C61C2311yescharacteristic
42C4×C8×C61C2×C412yes—
43C4×C8×C61D411yescharacteristic
44C4×C8×C61D411yescharacteristic
45#95×C61—22no—
46#95×C61—22no—
47C22×C4×C61—42no—
48C22×C4×C61C2×D412yes—
49C22×C4×C61C2×D411yescharacteristic
50C2×C22⋊D61—41no—
51#11758222—44no—
52C2×D244—21no—
53C2×D244—22no—
54C2×C4×D61—41no—
55C2×Dic122—21no—
56C2×Dic122—22no—
57C2×C8×C61—24no—
58C2×C8×C61C22⋊C412yes—
59C2×C8×C61C22⋊C412yes—
60C4⋊C4×C61—44no—
61C42×C61C22×C411yescharacteristic
62C42×C61C2×D411yescharacteristic
63C42×C61#4112yes—
64C22⋊Dic61—41no—
65#11758198—42no—
66C4⋊Dic61—22no—
67C4⋊Dic61—22no—
68C4⋊Dic61—22no—
69#11758196—42no—
70C4×Dic61—41no—
71C2×#92418—24no—
72C23×C61#12711yescharacteristic
73C22×D61—41no—
74C2×C4×C61—42no—
75C2×C4×C61—84no—
76C2×C4×C61—82no—
77C2×C4×C61C2×C22⋊C411yescharacteristic
78C2×C4×C61C4×D412yes—
79C2×C4×C61#12112yes—
80C2×C4×C61#12411yescharacteristic
81C2×C4×C61#13514yes—
82C22⋊D61—82no—
83C2×Dic61—42no—
84C2×Dic61—41no—
85D244—42no—
86D244—82no—
87C4×D61—82no—
88Dic122—42no—
89Dic122—82no—
90C8×C61—22no—
91C8×C61—22no—
92#92418—44no—
93#9757—611nomaximal, Sylow
94C22×C61—22no—
95C22×C61#39011yescharacteristic
96C22×C61#49512yes—
97C2×D61—81no—
98C2×D61—82no—
99C4×C61—22no—
100C4×C61—22no—
101C4×C61—162no—
102C4×C61#41612yes—
103C4×C61#48812yes—
104Dic61—81no—
105Dic61—82no—
106#3131—611no—
107#1835D6111yescharacteristic, complemented
108#1518—612no—
109#1517—612no—
110#1450—611no—
111C2×C61—22no—
112C2×C61#195811yescharacteristic
113C2×C61#197612yes—
114D61—161no—
115#533—611no—
116#532—611no—
117#488—1221no—
118#488—1221no—
119#487—612no—
120#486—612no—
121#431—612no—
122#416—1222no—
123C2×C4×C8C2×D6111yescharacteristic
124#382C2×D6112yes—
125#340—22no—
126#328—1224no—
127#327—1224no—
128#322—1221no—
129C82—1221no—
130C61#975711yescharacteristic, complemented, Sylow
131C2×#41—1221no—
132C22×C8C22⋊D6112yes—
133C4⋊Q8—611no—
134C4⋊Q8—612no—
135#127—611no—
136#125—1221no—
137#124—1221no—
138C22⋊Q8—1222no—
139#121—1222no—
140C4×Q8—1222no—
141C4×D4—1222no—
142#117—1221no—
143C2×C4⋊C4—22no—
144C2×C42C22×D6111yescharacteristic
145C4⋊C8—1222no—
146#103—1222no—
147#103—1222no—
148#102—1222no—
149#102—1222no—
150C22⋊C8—614no—
151C4×C8—1222no—
152C4×C8C4×D6112yes—
153C4×C8D24411yescharacteristic
154C4×C8D24411yescharacteristic
155#95—22no—
156#95—22no—
157#41—2444no—
158C2×Q8—1221no—
159C2×Q8—1222no—
160C2×D4—1221no—
161C2×D4—1222no—
162C2×D4—2441no—
163C22×C4—42no—
164C22×C4—2441no—
165C22×C4D4×D6112yes—
166C22×C4C2×C22⋊D6111yescharacteristic
167C2×C8—24no—
168C2×C8—1224no—
169C2×C8#1175819812yes—
170C2×C8#1175819812yes—
171C4⋊C4—44no—
172C4⋊C4—1222no—
173C4⋊C4—1222no—
174C4⋊C4—1222no—
175C4⋊C4—2442no—
176C22⋊C4—2441no—
177C22⋊C4—2442no—
178C42—2441no—
179C42C2×C4×D6111yescharacteristic
180C42C2×D24411yescharacteristic
181C42#1175822612yes—
182C23—2441no—
183C23#1451977311yescharacteristic
184Q8—4882no—
185Q8—2442no—
186D4—4882no—
187D4—4882no—
188D4—2442no—
189C2×C4—42no—
190C2×C4—84no—
191C2×C4—82no—
192C2×C4—4882no—
193C2×C4—2442no—
194C2×C4—2441no—
195C2×C4C2×#1175819811yescharacteristic
196C2×C4#1451973912yes—
197C2×C4#1451975212yes—
198C2×C4#1451976611yescharacteristic
199C2×C4#1451979714yes—
200C8—22no—
201C8—22no—
202C8—2444no—
203C22—22no—
204C22—4882no—
205C22—4881no—
206C22#1683966311yescharacteristic
207C22#1684014412yes—
208C4—22no—
209C4—22no—
210C4—162no—
211C4—4882no—
212C4—4881no—
213C4#1683975612yes—
214C4#1684011912yes—
215C2—22no—
216C2—9761no—
217C2#2144662811yescharacteristic
218C2#2144671512yes—
subgroupG/H
centerC22#16839663
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1835C2
socleC22×C61#390
prime radical#16840312C22
cosocleC2×C42×C61C23
hypercenter#1835D61
hypocenterC61#9757
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1835

Complements

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

NH ≅ G/Ntype
2. #21444382C2semidirect
4. #21444102C2semidirect
5. C61×#1835C2semidirect
10. #16840113C4semidirect
11. #16840109C4semidirect
107. #1835D61semidirect
130. C61#9757semidirect

Maximal subgroups

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

subgroupindex
#214561422
#214443822
#214443782
#214441022
C61×#18352
#975761