Finite Group Databasebeta

← C113×#8736 #43276756

Subgroups — C113×#8736 #43276756

Order 28928.

498 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 126 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
1C113×#2312C211yesmaximal, characteristic
2C2×#323×C113C212yesmaximal
3C113×#1282C214yesmaximal, complemented
4C22×C22⋊C4×C113C2211yescharacteristic
5C2×C22⋊C8×C113C2214yes—
6#388×C113—24no—
7#380×C113C412yes—
8#379×C113C412yes—
9C4×C22⋊C4×C113C2212yes—
10#323×C113—24no—
11C25×C113C2×C411yescharacteristic
12C23×C4×C113C2×C411yescharacteristic
13C23×C4×C113C2311yescharacteristic
14C22×C8×C113—24no—
15C2×C4⋊C4×C113—22no—
16C2×C22⋊C4×C113—24no—
17C2×C22⋊C4×C113—22no—
18C2×C22⋊C4×C113—22no—
19C2×C22⋊C4×C113C2×C414yes—
20C2×C22⋊C4×C113D414yes—
21C2×C42×C113—22no—
22C22⋊C8×C113—24no—
23C22⋊C8×C113—24no—
24#95×C113—22no—
25#95×C113—22no—
26C24×C113—22no—
27C24×C113—24no—
28C24×C113—81no—
29C24×C113—81no—
30C24×C113C22⋊C412yes—
31C24×C113C22×C411yescharacteristic
32C22×C4×C113—22no—
33C22×C4×C113—24no—
34C22×C4×C113—81no—
35C22×C4×C113—81no—
36C22×C4×C113C22⋊C412yes—
37C22×C4×C113C2×D412yes—
38C22×C4×C113#4114yes—
39C2×C8×C113—44no—
40C2×C8×C113—84no—
41C4⋊C4×C113—82no—
42C22⋊C4×C113—28no—
43C22⋊C4×C113—28no—
44C22⋊C4×C113—82no—
45C22⋊C4×C113—82no—
46C42×C113—82no—
47C23×C113—22no—
48C23×C113—24no—
49C23×C113—41no—
50C23×C113—41no—
51C23×C113—42no—
52C23×C113—42no—
53C23×C113—44no—
54C23×C113—82no—
55C23×C113—82no—
56C23×C113—88no—
57C23×C113C2×C22⋊C411yescharacteristic
58C23×C113#11712yes—
59C23×C113#13114yes—
60C2×C4×C113—22no—
61C2×C4×C113—42no—
62C2×C4×C113—44no—
63C2×C4×C113—42no—
64C2×C4×C113—44no—
65C2×C4×C113—44no—
66C2×C4×C113—44no—
67C2×C4×C113—82no—
68C2×C4×C113#12314yes—
69C8×C113—84no—
70C22×C113—21no—
71C22×C113—22no—
72C22×C113—21no—
73C22×C113—22no—
74C22×C113—44no—
75C22×C113—42no—
76C22×C113—42no—
77C22×C113—42no—
78C22×C113—84no—
79C22×C113—88no—
80C22×C113#38111yescharacteristic
81C22×C113#40812yes—
82C22×C113#43314yes—
83C4×C113—24no—
84C4×C113—42no—
85C4×C113—84no—
86#8736C11311yesmaximal, characteristic, direct product factor, Sylow
87C2×C113—22no—
88C2×C113—24no—
89C2×C113—82no—
90C2×C113#181811yescharacteristic
91C2×C113#182811yescharacteristic
92C2×C113#182911yescharacteristic
93#2312C2×C11311yescharacteristic
94C2×#323C2×C11312yes—
95#1282C2×C11314yescomplemented
96C113#873611yescharacteristic, direct product factor, Sylow
97C22×C22⋊C4C22×C11311yescharacteristic
98C2×C22⋊C8C22×C11314yes—
99#388—24no—
100#380C4×C11312yes—
101#379C4×C11312yes—
102C4×C22⋊C4C22×C11312yes—
103#323—24no—
104C25C2×C4×C11311yescharacteristic
105C23×C4C2×C4×C11311yescharacteristic
106C23×C4C23×C11311yescharacteristic
107C22×C8—24no—
108C2×C4⋊C4—22no—
109C2×C22⋊C4—24no—
110C2×C22⋊C4—22no—
111C2×C22⋊C4—22no—
112C2×C22⋊C4C2×C4×C11314yes—
113C2×C22⋊C4D4×C11314yes—
114C2×C42—22no—
115C22⋊C8—24no—
116C22⋊C8—24no—
117#95—22no—
118#95—22no—
119C24—22no—
120C24—24no—
121C24—81no—
122C24—81no—
123C24C22⋊C4×C11312yes—
124C24C22×C4×C11311yescharacteristic
125C22×C4—22no—
126C22×C4—24no—
127C22×C4—81no—
128C22×C4—81no—
129C22×C4C22⋊C4×C11312yes—
130C22×C4C2×D4×C11312yes—
131C22×C4#41×C11314yes—
132C2×C8—44no—
133C2×C8—84no—
134C4⋊C4—82no—
135C22⋊C4—28no—
136C22⋊C4—28no—
137C22⋊C4—82no—
138C22⋊C4—82no—
139C42—82no—
140C23—22no—
141C23—24no—
142C23—41no—
143C23—41no—
144C23—42no—
145C23—42no—
146C23—44no—
147C23—82no—
148C23—82no—
149C23—88no—
150C23C2×C22⋊C4×C11311yescharacteristic
151C23#117×C11312yes—
152C23#131×C11314yes—
153C2×C4—22no—
154C2×C4—42no—
155C2×C4—44no—
156C2×C4—42no—
157C2×C4—44no—
158C2×C4—44no—
159C2×C4—44no—
160C2×C4—82no—
161C2×C4#123×C11314yes—
162C8—84no—
163C22—21no—
164C22—22no—
165C22—21no—
166C22—22no—
167C22—44no—
168C22—42no—
169C22—42no—
170C22—42no—
171C22—84no—
172C22—88no—
173C22#381×C11311yescharacteristic
174C22#408×C11312yes—
175C22#433×C11314yes—
176C4—24no—
177C4—42no—
178C4—84no—
179C2—22no—
180C2—24no—
181C2—82no—
182C2C113×#181811yescharacteristic
183C2C113×#182811yescharacteristic
184C2C113×#182911yescharacteristic
subgroupG/H
center, socleC22×C113#381
commutatorC24C22×C4×C113
Frattini, cosocleC23×C4C23×C113
prime radicalC25×C113C2×C4
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C23×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
3. C113×#1282C2semidirect
86. #8736C113direct (N × H)
95. #1282C2×C113semidirect
96. C113#8736direct (N × H)

Maximal subgroups

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

subgroupindex
C113×#23122
C2×#323×C1132
C113×#12822
#8736113