Finite Group Databasebeta

← #29584469

Subgroups — #29584469

Order 15616.

406 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 129 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#21446577C212yesmaximal
2#21445975C211yesmaximal, characteristic
3#21443702C211yesmaximal, characteristic
4#21443660C212yesmaximal
5C61×#2571C211yesmaximal, characteristic
6C2×#14519710—22no—
7C2×#14519708—22no—
8C2×C4⋊#92418C2212yes—
9C2×C4×#92418C2211yescharacteristic
10#16839632C2211yescharacteristic
11#16839524—22no—
12C61×#400—22no—
13C61×#389—22no—
14C61×#384C2211yescharacteristic
15C61×#382—22no—
16C4×C4⋊C4×C61C2212yes—
17C22×#92418—21no—
18C22×#92418—22no—
19C2×C4⋊Dic61—22no—
20C2×C4⋊Dic61—21no—
21#14519710—44no—
22#14519708—44no—
23C4⋊#92418—22no—
24C4⋊#92418Q814yes—
25C4×#92418—21no—
26C4×#92418Q812yes—
27C2×C4⋊C4×C61—22no—
28C2×C4⋊C4×C61—22no—
29C2×C4⋊C4×C61D412yes—
30C2×C4⋊C4×C61D412yes—
31C2×C4⋊C4×C61D412yes—
32C2×C42×C61—22no—
33C2×C42×C61C2311yescharacteristic
34#95×C61—22no—
35#95×C61—24no—
36#95×C61—22no—
37C22×C4×C61—22no—
38C22×C4×C61—22no—
39C22×C4×C61—22no—
40C22×C4×C61C2×D411yescharacteristic
41C22×C4×C61C2×D412yes—
42C22×Dic61—41no—
43C4⋊C4×C61—22no—
44C4⋊C4×C61—22no—
45C4⋊C4×C61—22no—
46C4⋊C4×C61—22no—
47C4⋊C4×C61—42no—
48C4⋊C4×C61—42no—
49C4⋊C4×C61—42no—
50C4⋊C4×C61—82no—
51C42×C61—42no—
52C42×C61—42no—
53C42×C61C2×Q811yescharacteristic
54C42×C61C2×Q812yes—
55C42×C61#4111yescharacteristic
56C4⋊Dic61—42no—
57C4⋊Dic61—42no—
58C4⋊Dic61—42no—
59C2×#92418—22no—
60C2×#92418—22no—
61C2×#92418—22no—
62C2×#92418—24no—
63C2×#92418—42no—
64C2×#92418—42no—
65C23×C61#12011yescharacteristic
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61—42no—
69C2×C4×C61—42no—
70C2×C4×C61—42no—
71C2×C4×C61—42no—
72C2×C4×C61—44no—
73C2×C4×C61—42no—
74C2×C4×C61—42no—
75C2×C4×C61—42no—
76C2×C4×C61C22⋊Q811yescharacteristic
77C2×C4×C61C22⋊Q812yes—
78C2×C4×C61C4⋊Q811yescharacteristic
79C2×C4×C61C4⋊Q812yes—
80C2×C4×C61#13512yes—
81C2×C4×C61#13512yes—
82C2×C4×C61AGL(1,ℤ/8)12yes—
83C2×C4×C61#13712yes—
84C2×Dic61—82no—
85C2×Dic61—81no—
86#92418—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—82no—
98C4×C61—82no—
99C4×C61#47812yes—
100C4×C61#47912yes—
101C4×C61#49912yes—
102C4×C61#50112yes—
103Dic61—161no—
104#2571D6111yescharacteristic
105#1947—612no—
106#1844—611no—
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—1222no—
116C2×C4⋊C8—612no—
117C2×C4×C8—611no—
118#400—22no—
119#389—22no—
120#384—611no—
121#384C2×D6111yescharacteristic
122#382—22no—
123C4×C4⋊C4C2×D6112yes—
124#340—1222no—
125C61#1057711yescharacteristic, complemented, Sylow
126C22×C8—1221no—
127C22×C8—1222no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—1222no—
131C2×C4⋊C4—1221no—
132C2×C4⋊C4C22⋊D6112yes—
133C2×C4⋊C4C22⋊D6112yes—
134C2×C4⋊C4C22⋊D6112yes—
135C2×C42—22no—
136C2×C42C22×D6111yescharacteristic
137#107—2444no—
138#106—2444no—
139C4⋊C8—614no—
140C4⋊C8—1222no—
141C4×C8—612no—
142C4×C8—1221no—
143#95—22no—
144#95—24no—
145#95—22no—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—2441no—
150C22×C4C2×C22⋊D6111yescharacteristic
151C22×C4C2×C22⋊D6112yes—
152C2×C8—1222no—
153C2×C8—1222no—
154C2×C8—1222no—
155C2×C8—1224no—
156C2×C8—2442no—
157C2×C8—2442no—
158C4⋊C4—22no—
159C4⋊C4—22no—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—42no—
163C4⋊C4—42no—
164C4⋊C4—42no—
165C4⋊C4—82no—
166C4⋊C4—2442no—
167C4⋊C4—2442no—
168C4⋊C4—2442no—
169C42—42no—
170C42—42no—
171C42Q8×D6111yescharacteristic
172C42Q8×D6112yes—
173C42#1175822611yescharacteristic
174C23#1451974611yescharacteristic
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—44no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—4882no—
186C2×C4—4881no—
187C2×C4#1451975311yescharacteristic
188C2×C4#1451975312yes—
189C2×C4#1451977511yescharacteristic
190C2×C4#1451977512yes—
191C2×C4#1451979712yes—
192C2×C4#1451979712yes—
193C2×C4#1451980212yes—
194C2×C4#1451980712yes—
195C8—1224no—
196C8—2444no—
197C22#1683968111yescharacteristic
198C22#1683990712yes—
199C22#1683992412yes—
200C22#1683993011yescharacteristic
201C22#1683994511yescharacteristic
202C4—21no—
203C4—21no—
204C4—82no—
205C4—82no—
206C4—82no—
207C4—9761no—
208C4#1684005912yes—
209C4#1684006612yes—
210C4#1684016112yes—
211C4#1684017212yes—
212C2#2144490211yescharacteristic
213C2#2144494011yescharacteristic
214C2#2144508912yes—
215C2#2144715412yes—
216C2#2144716111yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2571C2
socle, prime radicalC23×C61#120
hypercenter#2571D61
hypocenterC61#10577
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2571

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
#214465772
#214459752
#214437022
#214436602
C61×#25712
#1057761