Finite Group Databasebeta

← #29584521

Subgroups — #29584521

Order 15616.

382 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 97 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#21454094C211yesmaximal, characteristic
2#21445987C212yesmaximal
3#21445952C211yesmaximal, characteristic
4#21443701C212yesmaximal
5C61×#1295C211yesmaximal, characteristic
6C2×#14519711—22no—
7C2×#14519709—22no—
8C2×#14519688C2211yescharacteristic
9#16839696—22no—
10#16839695—22no—
11#16839694—22no—
12#16839632C2211yescharacteristic
13#16839628C2212yes—
14#16839524—22no—
15C2×#97×C61C2212yes—
16C61×#382C2211yescharacteristic
17C22×#92418—21no—
18C2×C4⋊Dic61—21no—
19C2×C4⋊Dic61—22no—
20C2×C4⋊Dic61—22no—
21C2×C4⋊Dic61D412yes—
22C2×C4⋊Dic61D412yes—
23C2×#11758196—22no—
24C2×#11758196—22no—
25#14519711—44no—
26#14519709—44no—
27#14519688—21no—
28#14519688Q812yes—
29#14519684—22no—
30#14519684—22no—
31#14519684—22no—
32C22×C8×C61—22no—
33C2×C4⋊C4×C61D412yes—
34C2×C42×C61C2311yescharacteristic
35#97×C61—22no—
36#97×C61Q814yes—
37#95×C61—22no—
38C22×C4×C61—22no—
39C22×C4×C61C2×D411yescharacteristic
40C22×C4×C61C2×D412yes—
41C22×Dic61—22no—
42C22×Dic61—22no—
43C22×Dic61—41no—
44C2×C8×C61—24no—
45C2×C8×C61—24no—
46C2×C8×C61—24no—
47C4⋊C4×C61—42no—
48C42×C61C2×Q812yes—
49C42×C61C2×Q811yescharacteristic
50C42×C61#4111yescharacteristic
51C4⋊Dic61—42no—
52C4⋊Dic61—42no—
53C4⋊Dic61—42no—
54C4⋊Dic61—42no—
55C4⋊Dic61—42no—
56C4⋊Dic61—82no—
57#11758196—82no—
58#11758196—82no—
59C2×#92418—22no—
60C2×#92418—41no—
61C2×#92418—41no—
62C23×C61#12011yescharacteristic
63C2×C4×C61—22no—
64C2×C4×C61—21no—
65C2×C4×C61—21no—
66C2×C4×C61—22no—
67C2×C4×C61—42no—
68C2×C4×C61—42no—
69C2×C4×C61—42no—
70C2×C4×C61C22⋊Q812yes—
71C2×C4×C61C22⋊Q811yescharacteristic
72C2×C4×C61C4⋊Q812yes—
73C2×C4×C61C4⋊Q811yescharacteristic
74C2×Dic61—42no—
75C2×Dic61—42no—
76C2×Dic61—42no—
77C2×Dic61—42no—
78C2×Dic61—42no—
79C2×Dic61—42no—
80C2×Dic61—82no—
81C2×Dic61—81no—
82C8×C61—28no—
83#92418—42no—
84#10585—611nomaximal, Sylow
85C22×C61#39511yescharacteristic
86C22×C61#45312yes—
87C22×C61#45411yescharacteristic
88C22×C61#45511yescharacteristic
89C22×C61#45612yes—
90C4×C61—22no—
91C4×C61—22no—
92C4×C61—21no—
93C4×C61—21no—
94C4×C61—82no—
95Dic61—82no—
96Dic61—82no—
97Dic61—161no—
98#2845—611no—
99#1847—612no—
100#1836—611no—
101#1295—612no—
102#1295D6111yescharacteristic
103C2×C61#165611yescharacteristic
104C2×C61#166112yes—
105C2×C61#166311yescharacteristic
106C2×C61#206012yes—
107C2×C61#206111yescharacteristic
108C2×#107—1222no—
109C2×#106—1222no—
110C2×#97—611no—
111C2×#97C2×D6112yes—
112#398—1222no—
113#398—1222no—
114#398—1222no—
115#384—611no—
116#382—612no—
117#382C2×D6111yescharacteristic
118#340—1222no—
119C61#1058511yescharacteristic, complemented, Sylow
120C22×C8—22no—
121C22×C8—1221no—
122C2×C4⋊C4—612no—
123C2×C4⋊C4—612no—
124C2×C4⋊C4—1222no—
125C2×C4⋊C4—1222no—
126C2×C4⋊C4—1222no—
127C2×C4⋊C4—1221no—
128C2×C4⋊C4—1222no—
129C2×C4⋊C4D24412yes—
130C2×C42C22×D6111yescharacteristic
131#107—2444no—
132#106—2444no—
133#97—22no—
134#97—612no—
135#97—1221no—
136#97Dic12214yes—
137#95—22no—
138#95—1222no—
139#95—1222no—
140#95—1222no—
141C22×C4—22no—
142C22×C4—1222no—
143C22×C4—1222no—
144C22×C4—2441no—
145C22×C4C2×D24411yescharacteristic
146C22×C4D4×D6112yes—
147C2×C8—24no—
148C2×C8—24no—
149C2×C8—24no—
150C2×C8—1222no—
151C2×C8—2441no—
152C2×C8—2441no—
153C4⋊C4—42no—
154C4⋊C4—4882no—
155C4⋊C4—4882no—
156C4⋊C4—4882no—
157C4⋊C4—2442no—
158C4⋊C4—2442no—
159C4⋊C4—2442no—
160C4⋊C4—2442no—
161C4⋊C4—2442no—
162C42C2×Dic12212yes—
163C42#1175822411yescharacteristic
164C42Q8×D6111yescharacteristic
165C23#1451974711yescharacteristic
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—4881no—
174C2×C4—4882no—
175C2×C4—2442no—
176C2×C4—2442no—
177C2×C4—2442no—
178C2×C4—2442no—
179C2×C4—2442no—
180C2×C4—2442no—
181C2×C4#1451975412yes—
182C2×C4#1451975711yescharacteristic
183C2×C4#1451977612yes—
184C2×C4#1451977711yescharacteristic
185C8—28no—
186C8—2442no—
187C22#1683968311yescharacteristic
188C22#1683993112yes—
189C22#1683993711yescharacteristic
190C22#1683994211yescharacteristic
191C22#1683994612yes—
192C4—21no—
193C4—21no—
194C4—22no—
195C4—22no—
196C4—82no—
197C4—9761no—
198C4—4882no—
199C4—4882no—
200C2#2144511411yescharacteristic
201C2#2144513912yes—
202C2#2144514811yescharacteristic
203C2#2144716312yes—
204C2#2144717011yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1295C2
socle, prime radicalC23×C61#120
hypercenter#1295D61
hypocenterC61#10585
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
119. C61#10585semidirect

Maximal subgroups

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

subgroupindex
#214540942
#214459872
#214459522
#214437012
C61×#12952
#1058561