Finite Group Databasebeta

← #29577546

Subgroups — #29577546

Order 15616.

436 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 103 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#21454925C211yesmaximal, characteristic, complemented
2#21444533C212yesmaximal
3#21444457C211yesmaximal, characteristic, complemented
4#21443691C212yesmaximal, complemented
5C61×#3138C211yesmaximal, characteristic
6#16839893—24no—
7#16839823—22no—
8#16839819C2212yes—
9#16839819C2212yes—
10#16839506—24no—
11#16839504—22no—
12C61×#533C2211yescharacteristic
13C2×#127×C61C2211yescharacteristic
14C61×#490—22no—
15C61×#486C414yes—
16C61×#418—22no—
17C4×M16×C61C2211yescharacteristic
18C4⋊#92418—24no—
19C4⋊#92418—22no—
20C4⋊#92418D414yes—
21C22⋊#92418—22no—
22C22⋊#92418—22no—
23#14519688—22no—
24#14519688—22no—
25#14519688—22no—
26C4×#92418—22no—
27C22×D4×C61—21no—
28C22×D4×C61—22no—
29C2×M16×C61—21no—
30C4⋊Q8×C61C2×C412yes—
31#127×C61—22no—
32#127×C61—21no—
33#127×C61C2×C412yes—
34#125×C61D412yes—
35C22⋊Q8×C61—22no—
36C4×Q8×C61—22no—
37#117×C61D412yes—
38C2×C42×C61C2311yescharacteristic
39#102×C61—28no—
40#97×C61—21no—
41C4×C8×C61C2×C412yes—
42C24×C61—41no—
43C2×Q8×C61—22no—
44C2×D4×C61—22no—
45C2×D4×C61—24no—
46C2×D4×C61—44no—
47C2×D4×C61—41no—
48C2×D4×C61—42no—
49C2×D4×C61—84no—
50C22×C4×C61C2×D411yescharacteristic
51C22×C4×C61#4112yes—
52M16×C61—42no—
53C2×C8×C61—22no—
54C4⋊C4×C61—22no—
55C4⋊C4×C61—24no—
56C4⋊C4×C61C22⋊C414yes—
57C22⋊C4×C61—22no—
58C42×C61—22no—
59C42×C61C22×C411yescharacteristic
60C42×C61C2×D411yescharacteristic
61C42×C61C2×D412yes—
62C2×#92418—24no—
63C2×#92418—42no—
64C23×C61—42no—
65C23×C61—82no—
66C23×C61—84no—
67C23×C61#12311yescharacteristic
68Q8×C61—82no—
69D4×C61—44no—
70D4×C61—84no—
71D4×C61—84no—
72D4×C61—82no—
73C2×C4×C61—22no—
74C2×C4×C61—24no—
75C2×C4×C61—42no—
76C2×C4×C61C2×C22⋊C411yescharacteristic
77C2×C4×C61C4×D412yes—
78C2×C4×C61#12011yescharacteristic
79C2×C4×C61#12112yes—
80C8×C61—42no—
81#92418—44no—
82#92418—82no—
83#9424—611nomaximal, Sylow
84C22×C61—21no—
85C22×C61—22no—
86C22×C61—82no—
87C22×C61—84no—
88C22×C61—164no—
89C22×C61#38611yescharacteristic
90C4×C61—21no—
91C4×C61—22no—
92C4×C61—22no—
93C4×C61—44no—
94C4×C61#45412yes—
95#3138D6111yescharacteristic
96#2987—611no—
97#1555—612no—
98#1537—611no—
99#1291—612no—
100C2×C61—41no—
101C2×C61—162no—
102C2×C61#188811yescharacteristic
103C2×C61#190312yes—
104#533C2×D6111yescharacteristic
105C2×#127C2×D6111yescharacteristic
106#490—22no—
107#486Dic6114yes—
108#446—1224no—
109#433—1222no—
110#432—612no—
111#432—612no—
112#418—22no—
113C4×M16C2×D6111yescharacteristic
114#331—1224no—
115#330—1222no—
116C61#942411yescharacteristic, complemented, Sylow
117C22×D4—22no—
118C22×D4—21no—
119C2×M16—21no—
120C4⋊Q8C2×Dic6112yes—
121#127—22no—
122#127—21no—
123#127C2×Dic6112yes—
124#125C22⋊D6112yes—
125C22⋊Q8—22no—
126C4×Q8—22no—
127#117C22⋊D6112yes—
128C2×C42C22×D6111yescharacteristic
129C4⋊C8—614no—
130C4⋊C8—1224no—
131C4⋊C8—1222no—
132#102—28no—
133C22⋊C8—1222no—
134C22⋊C8—1222no—
135#97—21no—
136#97—1222no—
137#97—1222no—
138#97—1222no—
139C4×C8—1222no—
140C4×C8C2×Dic6112yes—
141C24—41no—
142C2×Q8—22no—
143C2×D4—22no—
144C2×D4—24no—
145C2×D4—44no—
146C2×D4—41no—
147C2×D4—42no—
148C2×D4—84no—
149C22×C4#1175822412yes—
150C22×C4C2×C22⋊D6111yescharacteristic
151M16—42no—
152C2×C8—22no—
153C2×C8—1224no—
154C2×C8—2442no—
155C4⋊C4—22no—
156C4⋊C4—24no—
157C4⋊C4C22⋊Dic6114yes—
158C22⋊C4—22no—
159C42—22no—
160C42D4×D6112yes—
161C42C22×Dic6111yescharacteristic
162C42C2×C22⋊D6111yescharacteristic
163C23—42no—
164C23—82no—
165C23—84no—
166C23#1451975811yescharacteristic
167Q8—82no—
168D4—44no—
169D4—84no—
170D4—84no—
171D4—82no—
172C2×C4—22no—
173C2×C4—24no—
174C2×C4—42no—
175C2×C4C2×C22⋊Dic6111yescharacteristic
176C2×C4D4×Dic6112yes—
177C2×C4#1451974511yescharacteristic
178C2×C4#1451974912yes—
179C8—42no—
180C8—4882no—
181C8—2444no—
182C22—21no—
183C22—22no—
184C22—82no—
185C22—84no—
186C22—164no—
187C22#1683964211yescharacteristic
188C4—21no—
189C4—22no—
190C4—22no—
191C4—44no—
192C4#1683993412yes—
193C2—41no—
194C2—162no—
195C2#2144622311yescharacteristic
196C2#2144630112yes—
subgroupG/H
centerC22#16839642
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#3138C2
socleC22×C61#386
prime radicalC2×#127×C61C22
cosocleC2×C42×C61C23
hypercenter#3138D61
hypocenterC61#9424
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3138

Complements

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

NH ≅ G/Ntype
1. #21454925C2semidirect
3. #21444457C2semidirect
4. #21443691C2semidirect
116. C61#9424semidirect

Maximal subgroups

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

subgroupindex
#214549252
#214445332
#214444572
#214436912
C61×#31382
#942461