Finite Group Databasebeta

← #29584452

Subgroups — #29584452

Order 15616.

494 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 145 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#21446582C212yesmaximal
2#21445975C211yesmaximal, characteristic
3#21443702C211yesmaximal, characteristic
4#21443660C212yesmaximal
5C61×#2551C211yesmaximal, characteristic
6C2×#14519708—22no—
7C2×#14519708—22no—
8C2×C4⋊#92418C2212yes—
9C2×C4×#92418C2211yescharacteristic
10#16839632C2211yescharacteristic
11#16839524—22no—
12C2×C4⋊Q8×C61—22no—
13C61×#395—22no—
14C61×#389—22no—
15C61×#384C2211yescharacteristic
16C4×C4⋊C4×C61C2212yes—
17C22×#92418—21no—
18C22×#92418—22no—
19C2×C4⋊Dic61—22no—
20C2×C4⋊Dic61—21no—
21#14519708—44no—
22#14519708—44no—
23C4⋊#92418—22no—
24C4⋊#92418Q814yescomplemented
25C4×#92418—21no—
26C4×#92418Q812yescomplemented
27C22×Q8×C61—22no—
28C4⋊Q8×C61—44no—
29C4⋊Q8×C61—44no—
30C2×C4⋊C4×C61—24no—
31C2×C4⋊C4×C61—22no—
32C2×C4⋊C4×C61D412yes—
33C2×C4⋊C4×C61D412yes—
34C2×C4⋊C4×C61D412yes—
35C2×C42×C61—22no—
36C2×C42×C61C2311yescharacteristic
37#95×C61—22no—
38#95×C61—22no—
39C2×Q8×C61—48no—
40C2×Q8×C61—82no—
41C22×C4×C61—22no—
42C22×C4×C61—22no—
43C22×C4×C61—22no—
44C22×C4×C61C2×D411yescharacteristic
45C22×C4×C61C2×D412yes—
46C22×Dic61—41no—
47C4⋊C4×C61—22no—
48C4⋊C4×C61—22no—
49C4⋊C4×C61—48no—
50C4⋊C4×C61—42no—
51C4⋊C4×C61—42no—
52C4⋊C4×C61—42no—
53C4⋊C4×C61SD1614yes—
54C4⋊C4×C61SD1614yes—
55C42×C61—42no—
56C42×C61—42no—
57C42×C61C2×Q811yescharacteristic
58C42×C61C2×Q812yes—
59C42×C61#4111yescharacteristic
60C4⋊Dic61—42no—
61C4⋊Dic61—42no—
62C4⋊Dic61—42no—
63C2×#92418—22no—
64C2×#92418—22no—
65C2×#92418—22no—
66C2×#92418—24no—
67C2×#92418—42no—
68C2×#92418—42no—
69C23×C61#12011yescharacteristic
70Q8×C61—88no—
71C2×C4×C61—21no—
72C2×C4×C61—21no—
73C2×C4×C61—24no—
74C2×C4×C61—24no—
75C2×C4×C61—42no—
76C2×C4×C61—42no—
77C2×C4×C61—42no—
78C2×C4×C61—42no—
79C2×C4×C61—44no—
80C2×C4×C61—42no—
81C2×C4×C61C22⋊Q811yescharacteristic
82C2×C4×C61C22⋊Q812yes—
83C2×C4×C61C4⋊Q811yescharacteristic
84C2×C4×C61C4⋊Q812yes—
85C2×C4×C61C2×SD1612yes—
86C2×C4×C61C2×SD1612yes—
87C2×C4×C61AGL(1,ℤ/8)12yes—
88C2×C4×C61#13712yes—
89C2×Dic61—82no—
90C2×Dic61—81no—
91#92418—24no—
92#92418—44no—
93#10574—611nomaximal, Sylow
94C22×C61#39511yescharacteristic
95C22×C61#44812yes—
96C22×C61#45012yes—
97C22×C61#45311yescharacteristic
98C22×C61#45611yescharacteristic
99C4×C61—21no—
100C4×C61—21no—
101C4×C61—44no—
102C4×C61—44no—
103C4×C61—82no—
104C4×C61#47512yes—
105C4×C61#47612yes—
106C4×C61#49812yes—
107C4×C61#50112yes—
108Dic61—161no—
109#2551D6111yescharacteristic
110#1948—612no—
111#1844—611no—
112#1296—611no—
113#1279—612no—
114C2×C61#162311yescharacteristic
115C2×C61#162911yescharacteristic
116C2×C61#165112yes—
117C2×C61#205812yes—
118C2×C61#206011yescharacteristic
119C2×C4⋊Q8—22no—
120C2×#106—1222no—
121C2×#106—1222no—
122C2×C4⋊C8—612no—
123C2×C4×C8—611no—
124#395—22no—
125#389—22no—
126#384—611no—
127#384C2×D6111yescharacteristic
128C4×C4⋊C4C2×D6112yes—
129#340—1222no—
130C61#1057411yescharacteristic, complemented, Sylow
131C22×Q8—22no—
132C22×C8—1221no—
133C22×C8—1222no—
134C4⋊Q8—44no—
135C4⋊Q8—44no—
136C2×C4⋊C4—24no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—1222no—
139C2×C4⋊C4—1221no—
140C2×C4⋊C4C22⋊D6112yes—
141C2×C4⋊C4C22⋊D6112yes—
142C2×C4⋊C4C22⋊D6112yes—
143C2×C42—22no—
144C2×C42C22×D6111yescharacteristic
145#106—2444no—
146#106—2444no—
147C4⋊C8—614no—
148C4⋊C8—1222no—
149C4×C8—612no—
150C4×C8—1221no—
151#95—22no—
152#95—22no—
153C2×Q8—48no—
154C2×Q8—82no—
155C22×C4—22no—
156C22×C4—22no—
157C22×C4—22no—
158C22×C4—2441no—
159C22×C4C2×C22⋊D6111yescharacteristic
160C22×C4C2×C22⋊D6112yes—
161C2×C8—1222no—
162C2×C8—1222no—
163C2×C8—1222no—
164C2×C8—1224no—
165C2×C8—2442no—
166C2×C8—2442no—
167C4⋊C4—22no—
168C4⋊C4—22no—
169C4⋊C4—42no—
170C4⋊C4—48no—
171C4⋊C4—42no—
172C4⋊C4—42no—
173C4⋊C4—2442no—
174C4⋊C4—2442no—
175C4⋊C4—2442no—
176C4⋊C4#1175820014yes—
177C4⋊C4#1175820114yes—
178C42—42no—
179C42—42no—
180C42Q8×D6111yescharacteristic
181C42Q8×D6112yes—
182C42#1175822611yescharacteristic
183C23#1451974611yescharacteristic
184Q8—88no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—24no—
188C2×C4—24no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—44no—
194C2×C4—42no—
195C2×C4—4882no—
196C2×C4—4881no—
197C2×C4#1451975311yescharacteristic
198C2×C4#1451975312yes—
199C2×C4#1451977511yescharacteristic
200C2×C4#1451977512yes—
201C2×C4C2×#1175820112yes—
202C2×C4C2×#1175820012yes—
203C2×C4#1451980312yes—
204C2×C4#1451980812yes—
205C8—1224no—
206C8—2444no—
207C22#1683968111yescharacteristic
208C22#1683990112yes—
209C22#1683991312yes—
210C22#1683993011yescharacteristic
211C22#1683994511yescharacteristic
212C4—21no—
213C4—21no—
214C4—44no—
215C4—44no—
216C4—82no—
217C4—9761no—
218C4#1684004412yes—
219C4#1684004912yes—
220C4#1684015812yes—
221C4#1684016812yes—
222C2#2144489711yescharacteristic
223C2#2144493511yescharacteristic
224C2#2144508212yes—
225C2#2144714912yes—
226C2#2144716111yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2551C2
socle, prime radicalC23×C61#120
hypercenter#2551D61
hypocenterC61#10574
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2551

Complements

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

NH ≅ G/Ntype
24. C4⋊#92418Q8semidirect
26. C4×#92418Q8semidirect
130. C61#10574semidirect

Maximal subgroups

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

subgroupindex
#214465822
#214459752
#214437022
#214436602
C61×#25512
#1057461