Finite Group Databasebeta

← #29584470

Subgroups — #29584470

Order 15616.

406 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 127 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#21451061C211yesmaximal, characteristic
2#21446575C212yesmaximal
3#21443702C211yesmaximal, characteristic
4#21443659C212yesmaximal
5C61×#1844C211yesmaximal, characteristic
6C2×#14519710—22no—
7C2×C4⋊#92418C2212yes—
8#16839701—22no—
9#16839661—22no—
10#16839627—22no—
11C4×C4⋊Dic61C2212yes—
12#16839524—22no—
13C2×#106×C61—22no—
14C2×C4×C8×C61C2211yescharacteristic
15C61×#384C2211yescharacteristic
16C61×#384C2211yescharacteristic
17C22×#92418—22no—
18C2×C4⋊Dic61—22no—
19C2×C4⋊Dic61D412yes—
20C2×C4⋊Dic61D412yes—
21C2×C4×Dic61—22no—
22#14519710—44no—
23C4⋊#92418—22no—
24C4⋊#92418Q814yes—
25#14519684—22no—
26#14519684—24no—
27#14519684—22no—
28C22×C8×C61—21no—
29C2×C4⋊C4×C61—22no—
30C2×C4⋊C4×C61—22no—
31C2×C4⋊C4×C61—21no—
32C2×C4⋊C4×C61D412yes—
33C2×C42×C61C2311yescharacteristic
34#106×C61—44no—
35C4×C8×C61—21no—
36C4×C8×C61Q812yes—
37C22×C4×C61—22no—
38C22×C4×C61—41no—
39C22×C4×C61C2×D411yescharacteristic
40C22×C4×C61C2×D412yes—
41C22×Dic61—22no—
42C22×Dic61—22no—
43C2×C8×C61—22no—
44C2×C8×C61—22no—
45C2×C8×C61—22no—
46C4⋊C4×C61—42no—
47C4⋊C4×C61—42no—
48C4⋊C4×C61—42no—
49C4⋊C4×C61—42no—
50C4⋊C4×C61—42no—
51C4⋊C4×C61—42no—
52C42×C61C2×Q811yescharacteristic
53C42×C61C2×Q812yes—
54C42×C61#4111yescharacteristic
55C4⋊Dic61—22no—
56C4⋊Dic61—22no—
57C4⋊Dic61—22no—
58C4⋊Dic61—22no—
59C4⋊Dic61—82no—
60C4×Dic61—42no—
61C4×Dic61—42no—
62C2×#92418—24no—
63C2×#92418—42no—
64C2×#92418—42no—
65C23×C61#12011yescharacteristic
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61—44no—
69C2×C4×C61—42no—
70C2×C4×C61—82no—
71C2×C4×C61—81no—
72C2×C4×C61C22⋊Q811yescharacteristic
73C2×C4×C61C22⋊Q812yes—
74C2×C4×C61C4⋊Q811yescharacteristic
75C2×C4×C61C4⋊Q812yes—
76C2×C4×C61#13512yes—
77C2×C4×C61#13512yes—
78C2×C4×C61AGL(1,ℤ/8)12yes—
79C2×C4×C61#13712yes—
80C2×Dic61—42no—
81C2×Dic61—42no—
82C2×Dic61—42no—
83C2×Dic61—42no—
84C2×Dic61—42no—
85C2×Dic61—42no—
86C8×C61—24no—
87#92418—44no—
88#10577—611nomaximal, Sylow
89C22×C61#39511yescharacteristic
90C22×C61#44912yes—
91C22×C61#45212yes—
92C22×C61#45311yescharacteristic
93C22×C61#45611yescharacteristic
94C4×C61—21no—
95C4×C61—21no—
96C4×C61—82no—
97C4×C61—161no—
98C4×C61#47812yes—
99C4×C61#47912yes—
100C4×C61#49912yes—
101C4×C61#50112yes—
102Dic61—82no—
103Dic61—82no—
104#2571—611no—
105#1947—612no—
106#1844D6111yescharacteristic
107#1296—611no—
108#1279—612no—
109C2×C61#162411yescharacteristic
110C2×C61#163011yescharacteristic
111C2×C61#165212yes—
112C2×C61#205912yes—
113C2×C61#206011yescharacteristic
114C2×#107—1222no—
115C2×#106—22no—
116C2×C4⋊C8—612no—
117C2×C4×C8C2×D6111yescharacteristic
118#400—1222no—
119#389—1222no—
120#384C2×D6111yescharacteristic
121#384C2×D6111yescharacteristic
122#382—1222no—
123C4×C4⋊C4—612no—
124#340—1222no—
125C61#1057711yescharacteristic, complemented, Sylow
126C22×C8—21no—
127C22×C8—1222no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—612no—
132C2×C4⋊C4—612no—
133C2×C4⋊C4—1222no—
134C2×C4⋊C4C22⋊D6112yes—
135C2×C42—1222no—
136C2×C42C22×D6111yescharacteristic
137#107—2444no—
138#106—44no—
139C4⋊C8—614no—
140C4⋊C8—1222no—
141C4×C8—21no—
142C4×C8Dic12212yes—
143#95—1222no—
144#95—1224no—
145#95—1222no—
146C22×C4—22no—
147C22×C4—41no—
148C22×C4—1222no—
149C22×C4—1222no—
150C22×C4D4×D6112yes—
151C22×C4C2×C22⋊D6111yescharacteristic
152C2×C8—22no—
153C2×C8—22no—
154C2×C8—22no—
155C2×C8—1224no—
156C2×C8—2442no—
157C2×C8—2442no—
158C4⋊C4—42no—
159C4⋊C4—42no—
160C4⋊C4—42no—
161C4⋊C4—42no—
162C4⋊C4—42no—
163C4⋊C4—42no—
164C4⋊C4—1222no—
165C4⋊C4—1222no—
166C4⋊C4—1222no—
167C4⋊C4—1222no—
168C4⋊C4—4882no—
169C42—2442no—
170C42—2442no—
171C42C2×Dic12211yescharacteristic
172C42#1175822211yescharacteristic
173C42Q8×D6112yes—
174C23#1451974511yescharacteristic
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—44no—
178C2×C4—42no—
179C2×C4—82no—
180C2×C4—81no—
181C2×C4—2442no—
182C2×C4—2442no—
183C2×C4—2442no—
184C2×C4—2442no—
185C2×C4—2442no—
186C2×C4—2442no—
187C2×C4#1451975512yes—
188C2×C4#1451975611yescharacteristic
189C2×C4#1451977511yescharacteristic
190C2×C4#1451977612yes—
191C2×C4#1451979812yes—
192C2×C4#1451979812yes—
193C2×C4#1451980412yes—
194C2×C4#1451980612yes—
195C8—24no—
196C8—2444no—
197C22#1683968211yescharacteristic
198C22#1683990612yes—
199C22#1683992112yes—
200C22#1683992911yescharacteristic
201C22#1683994411yescharacteristic
202C4—21no—
203C4—21no—
204C4—82no—
205C4—161no—
206C4—4882no—
207C4—4882no—
208C4#1684006112yes—
209C4#1684007212yes—
210C4#1684016212yes—
211C4#1684016912yes—
212C2#2144490011yescharacteristic
213C2#2144493811yescharacteristic
214C2#2144508612yes—
215C2#2144715912yes—
216C2#2144716411yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1844C2
socle, prime radicalC23×C61#120
hypercenter#1844D61
hypocenterC61#10577
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1844

Complements

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

NH ≅ G/Ntype
125. C61#10577semidirect

Maximal subgroups

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

subgroupindex
#214510612
#214465752
#214437022
#214436592
C61×#18442
#1057761