Finite Group Databasebeta

← #29584524

Subgroups — #29584524

Order 15616.

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

normal subgroups only

This group has 350 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#21445953C212yesmaximal
3#21445952C211yesmaximal, characteristic
4#21443701C212yesmaximal
5C61×#1295C211yesmaximal, characteristic
6C2×#14519688C2211yescharacteristic
7#16839696—22no—
8#16839695—22no—
9#16839694—22no—
10#16839632C2211yescharacteristic
11#16839628C2212yes—
12#16839525—22no—
13#16839525—22no—
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#14519688—21no—
26#14519688Q812yes—
27#14519684—22no—
28#14519684—22no—
29#14519684—22no—
30C22×C8×C61—22no—
31C2×C4⋊C4×C61D412yes—
32C2×C42×C61C2311yescharacteristic
33#97×C61—22no—
34#97×C61Q814yes—
35#95×C61—22no—
36C22×C4×C61—22no—
37C22×C4×C61C2×D411yescharacteristic
38C22×C4×C61C2×D412yes—
39C22×Dic61—22no—
40C22×Dic61—22no—
41C22×Dic61—41no—
42C2×C8×C61—24no—
43C2×C8×C61—42no—
44C2×C8×C61—42no—
45C4⋊C4×C61—42no—
46C42×C61C2×Q812yes—
47C42×C61C2×Q811yescharacteristic
48C42×C61#4111yescharacteristic
49C4⋊Dic61—42no—
50C4⋊Dic61—42no—
51C4⋊Dic61—42no—
52C4⋊Dic61—44no—
53C4⋊Dic61—82no—
54#11758196—82no—
55#11758196—82no—
56C2×#92418—22no—
57C2×#92418—41no—
58C2×#92418—41no—
59C23×C61#12011yescharacteristic
60C2×C4×C61—21no—
61C2×C4×C61—22no—
62C2×C4×C61—21no—
63C2×C4×C61—22no—
64C2×C4×C61—42no—
65C2×C4×C61—42no—
66C2×C4×C61—42no—
67C2×C4×C61C22⋊Q812yes—
68C2×C4×C61C22⋊Q811yescharacteristic
69C2×C4×C61C4⋊Q812yes—
70C2×C4×C61C4⋊Q811yescharacteristic
71C2×Dic61—42no—
72C2×Dic61—42no—
73C2×Dic61—42no—
74C2×Dic61—42no—
75C2×Dic61—42no—
76C2×Dic61—42no—
77C2×Dic61—82no—
78C2×Dic61—81no—
79C8×C61—44no—
80#92418—42no—
81#10586—611nomaximal, Sylow
82C22×C61#39511yescharacteristic
83C22×C61#45412yes—
84C22×C61#45411yescharacteristic
85C22×C61#45512yes—
86C22×C61#45511yescharacteristic
87C4×C61—21no—
88C4×C61—22no—
89C4×C61—22no—
90C4×C61—21no—
91C4×C61—82no—
92Dic61—82no—
93Dic61—82no—
94Dic61—161no—
95#2845—611no—
96#1836—612no—
97#1836—611no—
98#1295—612no—
99#1295D6111yescharacteristic
100C2×C61#165811yescharacteristic
101C2×C61#166211yescharacteristic
102C2×C61#166212yes—
103C2×C61#206112yes—
104C2×C61#206111yescharacteristic
105C2×#97—611no—
106C2×#97C2×D6112yes—
107#398—1222no—
108#398—1222no—
109#398—1222no—
110#384—611no—
111#382—612no—
112#382C2×D6111yescharacteristic
113#340—1222no—
114#340—1222no—
115#340—1222no—
116C61#1058611yescharacteristic, complemented, Sylow
117C22×C8—22no—
118C22×C8—1221no—
119C2×C4⋊C4—612no—
120C2×C4⋊C4—612no—
121C2×C4⋊C4—1222no—
122C2×C4⋊C4—1222no—
123C2×C4⋊C4—1222no—
124C2×C4⋊C4—1221no—
125C2×C4⋊C4—1222no—
126C2×C4⋊C4D24412yes—
127C2×C42C22×D6111yescharacteristic
128#97—22no—
129#97—612no—
130#97—1221no—
131#97Dic12214yes—
132#95—22no—
133#95—1222no—
134#95—1222no—
135#95—1222no—
136C22×C4—22no—
137C22×C4—1222no—
138C22×C4—1222no—
139C22×C4—2441no—
140C22×C4C2×D24411yescharacteristic
141C22×C4D4×D6112yes—
142C2×C8—24no—
143C2×C8—42no—
144C2×C8—42no—
145C2×C8—1222no—
146C2×C8—2441no—
147C2×C8—2441no—
148C4⋊C4—42no—
149C4⋊C4—4882no—
150C4⋊C4—4882no—
151C4⋊C4—4882no—
152C4⋊C4—2444no—
153C4⋊C4—2442no—
154C4⋊C4—2442no—
155C4⋊C4—2442no—
156C42C2×Dic12212yes—
157C42#1175822411yescharacteristic
158C42Q8×D6111yescharacteristic
159C23#1451974711yescharacteristic
160C2×C4—22no—
161C2×C4—21no—
162C2×C4—22no—
163C2×C4—21no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—4882no—
168C2×C4—4881no—
169C2×C4—2442no—
170C2×C4—2442no—
171C2×C4—2442no—
172C2×C4—2442no—
173C2×C4—2442no—
174C2×C4—2442no—
175C2×C4#1451975412yes—
176C2×C4#1451975711yescharacteristic
177C2×C4#1451977612yes—
178C2×C4#1451977711yescharacteristic
179C8—44no—
180C8—2442no—
181C22#1683968311yescharacteristic
182C22#1683993612yes—
183C22#1683993711yescharacteristic
184C22#1683994112yes—
185C22#1683994211yescharacteristic
186C4—22no—
187C4—22no—
188C4—21no—
189C4—21no—
190C4—82no—
191C4—9761no—
192C4—4882no—
193C4—4882no—
194C2#2144512211yescharacteristic
195C2#2144514311yescharacteristic
196C2#2144514412yes—
197C2#2144716812yes—
198C2#2144717011yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1295C2
socle, prime radicalC23×C61#120
hypercenter#1295D61
hypocenterC61#10586
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
116. C61#10586semidirect

Maximal subgroups

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

subgroupindex
#214540942
#214459532
#214459522
#214437012
C61×#12952
#1058661