Finite Group Databasebeta

← C113×#8729 #43276749

Subgroups — C113×#8729 #43276749

Order 28928.

514 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 166 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×#2285C211yesmaximal, characteristic
2C113×#1797C212yesmaximal
3C113×#1296C214yesmaximal, complemented
4C2×#117×C113C412yes—
5C22×C42×C113C2211yescharacteristic
6C2×C4⋊C8×C113C2214yes—
7C2×C22⋊C8×C113—22no—
8#384×C113C2212yes—
9#382×C113C412yes—
10#380×C113—22no—
11C4×C4⋊C4×C113—22no—
12#336×C113—22no—
13C23×C4×C113C2×C411yescharacteristic
14C23×C4×C113D412yes—
15C22×C8×C113—24no—
16#117×C113—44no—
17C2×C4⋊C4×C113—22no—
18C2×C4⋊C4×C113—22no—
19C2×C4⋊C4×C113C2×C414yes—
20C2×C22⋊C4×C113—22no—
21C2×C42×C113—24no—
22C2×C42×C113—22no—
23C2×C42×C113C2×C411yescharacteristic
24C2×C42×C113D412yes—
25C2×C42×C113C2311yescharacteristic
26C4⋊C8×C113—28no—
27C22⋊C8×C113—44no—
28#95×C113—24no—
29C24×C113C22⋊C411yescharacteristic
30C22×C4×C113—22no—
31C22×C4×C113—22no—
32C22×C4×C113—22no—
33C22×C4×C113—24no—
34C22×C4×C113—24no—
35C22×C4×C113—22no—
36C22×C4×C113—22no—
37C22×C4×C113—24no—
38C22×C4×C113C22⋊C412yes—
39C22×C4×C113C22⋊C411yescharacteristic
40C22×C4×C113C22×C411yescharacteristic
41C22×C4×C113C2×D412yes—
42C2×C8×C113—44no—
43C2×C8×C113—44no—
44C2×C8×C113—44no—
45C4⋊C4×C113—44no—
46C4⋊C4×C113—44no—
47C4⋊C4×C113—42no—
48C4⋊C4×C113—42no—
49C22⋊C4×C113—44no—
50C42×C113—22no—
51C42×C113—24no—
52C42×C113—44no—
53C42×C113#4114yes—
54C23×C113—21no—
55C23×C113—21no—
56C23×C113—22no—
57C23×C113—22no—
58C23×C113#10012yes—
59C23×C113C2×C22⋊C411yescharacteristic
60C2×C4×C113—28no—
61C2×C4×C113—21no—
62C2×C4×C113—21no—
63C2×C4×C113—21no—
64C2×C4×C113—21no—
65C2×C4×C113—22no—
66C2×C4×C113—22no—
67C2×C4×C113—22no—
68C2×C4×C113—44no—
69C2×C4×C113—44no—
70C2×C4×C113—44no—
71C2×C4×C113—44no—
72C2×C4×C113—44no—
73C2×C4×C113#10112yes—
74C2×C4×C113#11712yes—
75C2×C4×C113#12314yes—
76C2×C4×C113#13514yes—
77C2×C4×C113AGL(1,ℤ/8)12yes—
78C2×C4×C113#13712yes—
79C8×C113—84no—
80C22×C113—24no—
81C22×C113—22no—
82C22×C113—41no—
83C22×C113—41no—
84C22×C113—42no—
85C22×C113#38111yescharacteristic
86C22×C113C2×#10011yescharacteristic
87C22×C113C2×#10111yescharacteristic
88C22×C113#41612yes—
89C22×C113#41712yes—
90C4×C113—22no—
91C4×C113—22no—
92C4×C113—42no—
93C4×C113—84no—
94C4×C113#48214yes—
95C4×C113#48514yes—
96#8729C11311yesmaximal, characteristic, direct product factor, Sylow
97C2×C113—42no—
98C2×C113#154411yescharacteristic
99C2×C113#155112yes—
100C2×C113#156111yescharacteristic
101C2×C113#182111yescharacteristic
102C2×C113#182512yes—
103#2285C2×C11311yescharacteristic
104#1797C2×C11312yes—
105#1296C2×C11314yescomplemented
106C113#872911yescharacteristic, direct product factor, Sylow
107C2×#117C4×C11312yes—
108C22×C42C22×C11311yescharacteristic
109C2×C4⋊C8C22×C11314yes—
110C2×C22⋊C8—22no—
111#384C22×C11312yes—
112#382C4×C11312yes—
113#380—22no—
114C4×C4⋊C4—22no—
115#336—22no—
116C23×C4C2×C4×C11311yescharacteristic
117C23×C4D4×C11312yes—
118C22×C8—24no—
119#117—44no—
120C2×C4⋊C4—22no—
121C2×C4⋊C4—22no—
122C2×C4⋊C4C2×C4×C11314yes—
123C2×C22⋊C4—22no—
124C2×C42—24no—
125C2×C42—22no—
126C2×C42C2×C4×C11311yescharacteristic
127C2×C42D4×C11312yes—
128C2×C42C23×C11311yescharacteristic
129C4⋊C8—28no—
130C22⋊C8—44no—
131#95—24no—
132C24C22⋊C4×C11311yescharacteristic
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—22no—
136C22×C4—24no—
137C22×C4—24no—
138C22×C4—22no—
139C22×C4—22no—
140C22×C4—24no—
141C22×C4C22⋊C4×C11312yes—
142C22×C4C22⋊C4×C11311yescharacteristic
143C22×C4C22×C4×C11311yescharacteristic
144C22×C4C2×D4×C11312yes—
145C2×C8—44no—
146C2×C8—44no—
147C2×C8—44no—
148C4⋊C4—44no—
149C4⋊C4—44no—
150C4⋊C4—42no—
151C4⋊C4—42no—
152C22⋊C4—44no—
153C42—22no—
154C42—24no—
155C42—44no—
156C42#41×C11314yes—
157C23—21no—
158C23—21no—
159C23—22no—
160C23—22no—
161C23#100×C11312yes—
162C23C2×C22⋊C4×C11311yescharacteristic
163C2×C4—28no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—44no—
172C2×C4—44no—
173C2×C4—44no—
174C2×C4—44no—
175C2×C4—44no—
176C2×C4#101×C11312yes—
177C2×C4#117×C11312yes—
178C2×C4#123×C11314yes—
179C2×C4#135×C11314yes—
180C2×C4AGL(1,ℤ/8)×C11312yes—
181C2×C4#137×C11312yes—
182C8—84no—
183C22—24no—
184C22—22no—
185C22—41no—
186C22—41no—
187C22—42no—
188C22#381×C11311yescharacteristic
189C22C2×#100×C11311yescharacteristic
190C22C2×#101×C11311yescharacteristic
191C22#416×C11312yes—
192C22#417×C11312yes—
193C4—22no—
194C4—22no—
195C4—42no—
196C4—84no—
197C4#482×C11314yes—
198C4#485×C11314yes—
199C2—42no—
200C2C113×#154411yescharacteristic
201C2C113×#155112yes—
202C2C113×#156111yescharacteristic
203C2C113×#182111yescharacteristic
204C2C113×#182512yes—
subgroupG/H
center, socleC23×C113C2×C22⋊C4
commutatorC22×C4C22×C4×C113
Frattini, cosocleC2×C42C23×C113
prime radicalC24×C113C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C113 ◁ C22×C42×C113 ◁ G

Complements

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

NH ≅ G/Ntype
3. C113×#1296C2semidirect
96. #8729C113direct (N × H)
105. #1296C2×C113semidirect
106. C113#8729direct (N × H)

Maximal subgroups

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

subgroupindex
C113×#22852
C113×#17972
C113×#12962
#8729113