Finite Group Databasebeta

← #29584453

Subgroups — #29584453

Order 15616.

494 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 135 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#21450848C211yesmaximal, characteristic
2#21446580C212yesmaximal
3#21443702C211yesmaximal, characteristic
4#21443659C212yesmaximal
5C61×#1844C211yesmaximal, characteristic
6C2×#14519776—22no—
7C2×#14519708—22no—
8C2×C4⋊#92418C2212yes—
9#16839682—22no—
10#16839658—22no—
11C4×C4⋊Dic61C2212yes—
12#16839524—22no—
13C2×#106×C61—22no—
14C2×C4×C8×C61C2211yescharacteristic
15C61×#384C2211yescharacteristic
16C61×#384C2211yescharacteristic
17C22×Dic122—22no—
18C22×#92418—22no—
19#14519776—44no—
20#14519776—44no—
21C2×C4⋊Dic61D412yes—
22C2×C4⋊Dic61D412yes—
23C2×#11758196—24no—
24C2×C4×Dic61—22no—
25#14519708—44no—
26C4⋊#92418—22no—
27C4⋊#92418Q814yescomplemented
28#14519684—22no—
29#14519684—22no—
30C22×C8×C61—21no—
31C2×C4⋊C4×C61—22no—
32C2×C4⋊C4×C61—22no—
33C2×C4⋊C4×C61—21no—
34C2×C4⋊C4×C61D412yes—
35C2×C42×C61C2311yescharacteristic
36#106×C61—44no—
37C4×C8×C61—21no—
38C4×C8×C61Q812yescomplemented
39C22×C4×C61—22no—
40C22×C4×C61—41no—
41C22×C4×C61C2×D411yescharacteristic
42C22×C4×C61C2×D412yes—
43C22×Dic61—22no—
44C22×Dic61—22no—
45C2×Dic122—48no—
46C2×Dic122—82no—
47C2×C8×C61—22no—
48C2×C8×C61—22no—
49C2×C8×C61—22no—
50C4⋊C4×C61—42no—
51C4⋊C4×C61—42no—
52C4⋊C4×C61—42no—
53C4⋊C4×C61—42no—
54C4⋊C4×C61—42no—
55C4⋊C4×C61—42no—
56C42×C61C2×Q811yescharacteristic
57C42×C61C2×Q812yes—
58C42×C61#4111yescharacteristic
59C4⋊Dic61—22no—
60C4⋊Dic61—22no—
61C4⋊Dic61SD1614yes—
62C4⋊Dic61SD1614yes—
63#11758196—48no—
64C4×Dic61—42no—
65C4×Dic61—42no—
66C2×#92418—24no—
67C2×#92418—42no—
68C2×#92418—42no—
69C23×C61#12011yescharacteristic
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—44no—
73C2×C4×C61—42no—
74C2×C4×C61—82no—
75C2×C4×C61—81no—
76C2×C4×C61C22⋊Q811yescharacteristic
77C2×C4×C61C22⋊Q812yes—
78C2×C4×C61C4⋊Q811yescharacteristic
79C2×C4×C61C4⋊Q812yes—
80C2×C4×C61C2×SD1612yes—
81C2×C4×C61C2×SD1612yes—
82C2×C4×C61AGL(1,ℤ/8)12yes—
83C2×C4×C61#13712yes—
84C2×Dic61—24no—
85C2×Dic61—24no—
86C2×Dic61—42no—
87C2×Dic61—42no—
88C2×Dic61—42no—
89C2×Dic61—42no—
90Dic122—88no—
91C8×C61—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—82no—
102C4×C61—161no—
103C4×C61#47512yes—
104C4×C61#47612yes—
105C4×C61#49812yes—
106C4×C61#50112yes—
107Dic61—44no—
108Dic61—44no—
109#2551—611no—
110#1948—612no—
111#1844D6111yescharacteristic
112#1296—611no—
113#1279—612no—
114C2×C61#162311yescharacteristic
115C2×C61#162911yescharacteristic
116C2×C61#165112yes—
117C2×C61#205812yes—
118C2×C61#206011yescharacteristic
119C2×C4⋊Q8—1222no—
120C2×#106—22no—
121C2×#106—1222no—
122C2×C4⋊C8—612no—
123C2×C4×C8C2×D6111yescharacteristic
124#395—1222no—
125#389—1222no—
126#384C2×D6111yescharacteristic
127#384C2×D6111yescharacteristic
128C4×C4⋊C4—612no—
129#340—1222no—
130C61#1057411yescharacteristic, complemented, Sylow
131C22×Q8—1222no—
132C22×C8—21no—
133C22×C8—1222no—
134C4⋊Q8—2444no—
135C4⋊Q8—2444no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—612no—
140C2×C4⋊C4—612no—
141C2×C4⋊C4—1224no—
142C2×C4⋊C4C22⋊D6112yes—
143C2×C42—1222no—
144C2×C42C22×D6111yescharacteristic
145#106—44no—
146#106—2444no—
147C4⋊C8—614no—
148C4⋊C8—1222no—
149C4×C8—21no—
150C4×C8Dic12212yescomplemented
151#95—1222no—
152#95—1222no—
153C2×Q8—4882no—
154C2×Q8—2448no—
155C22×C4—22no—
156C22×C4—41no—
157C22×C4—1222no—
158C22×C4—1222no—
159C22×C4D4×D6112yes—
160C22×C4C2×C22⋊D6111yescharacteristic
161C2×C8—22no—
162C2×C8—22no—
163C2×C8—22no—
164C2×C8—1224no—
165C2×C8—2442no—
166C2×C8—2442no—
167C4⋊C4—42no—
168C4⋊C4—42no—
169C4⋊C4—42no—
170C4⋊C4—42no—
171C4⋊C4—42no—
172C4⋊C4—42no—
173C4⋊C4—614no—
174C4⋊C4—614no—
175C4⋊C4—1222no—
176C4⋊C4—1222no—
177C4⋊C4—2448no—
178C42—2442no—
179C42—2442no—
180C42C2×Dic12211yescharacteristic
181C42#1175822211yescharacteristic
182C42Q8×D6112yes—
183C23#1451974511yescharacteristic
184Q8—4888no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—44no—
188C2×C4—42no—
189C2×C4—82no—
190C2×C4—81no—
191C2×C4—1224no—
192C2×C4—1224no—
193C2×C4—2442no—
194C2×C4—2442no—
195C2×C4—2442no—
196C2×C4—2442no—
197C2×C4#1451975512yes—
198C2×C4#1451975611yescharacteristic
199C2×C4#1451977511yescharacteristic
200C2×C4#1451977612yes—
201C2×C4SD16×D6112yes—
202C2×C4SD16×D6112yes—
203C2×C4#1451980412yes—
204C2×C4#1451980612yes—
205C8—24no—
206C8—2444no—
207C22#1683968211yescharacteristic
208C22#1683989912yes—
209C22#1683991112yes—
210C22#1683992911yescharacteristic
211C22#1683994411yescharacteristic
212C4—21no—
213C4—21no—
214C4—82no—
215C4—161no—
216C4—2444no—
217C4—2444no—
218C4#1684004612yes—
219C4#1684005112yes—
220C4#1684015912yes—
221C4#1684016912yes—
222C2#2144489511yescharacteristic
223C2#2144493311yescharacteristic
224C2#2144507912yes—
225C2#2144715012yes—
226C2#2144716411yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1844C2
socle, prime radicalC23×C61#120
hypercenter#1844D61
hypocenterC61#10574
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
27. C4⋊#92418Q8semidirect
38. C4×C8×C61Q8semidirect
130. C61#10574semidirect
150. C4×C8Dic122semidirect

Maximal subgroups

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

subgroupindex
#214508482
#214465802
#214437022
#214436592
C61×#18442
#1057461