Finite Group Databasebeta

← C113×#8742 #43276762

Subgroups — C113×#8742 #43276762

Order 28928.

450 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 118 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×#2296C211yesmaximal, characteristic
2C113×#1464C212yesmaximal
3C113×#1285C214yesmaximal, complemented
4C2×#117×C113C411yescharacteristic
5C2×#117×C113C2211yescharacteristic
6C22×C42×C113C411yescharacteristic
7#432×C113C2214yes—
8#389×C113—22no—
9#385×C113—22no—
10C4×C4⋊C4×C113C412yes—
11C4×C4⋊C4×C113C2212yes—
12#324×C113—22no—
13#323×C113—22no—
14C23×C4×C113—21no—
15C23×C4×C113C2×C411yescharacteristic
16#117×C113—24no—
17#117×C113—42no—
18C2×C4⋊C4×C113—21no—
19C2×C4⋊C4×C113—22no—
20C2×C4⋊C4×C113—22no—
21C2×C4⋊C4×C113D412yes—
22C2×C22⋊C4×C113—21no—
23C2×C22⋊C4×C113D412yes—
24C2×C42×C113—21no—
25C2×C42×C113—42no—
26C2×C42×C113C2×C411yescharacteristic
27C2×C42×C113C2×C412yes—
28C2×C42×C113C2×C412yes—
29C2×C42×C113C2311yescharacteristic
30C4⋊C8×C113—24no—
31C22⋊C8×C113—24no—
32#97×C113—24no—
33#95×C113—22no—
34#95×C113—22no—
35C24×C113C22⋊C411yescharacteristic
36C22×C4×C113—22no—
37C22×C4×C113—22no—
38C22×C4×C113—22no—
39C22×C4×C113—22no—
40C22×C4×C113—22no—
41C22×C4×C113—44no—
42C22×C4×C113—42no—
43C22×C4×C113C22⋊C411yescharacteristic
44C22×C4×C113C22⋊C412yes—
45C22×C4×C113C22×C411yescharacteristic
46C22×C4×C113C2×D412yes—
47C2×C8×C113—44no—
48C4⋊C4×C113—24no—
49C4⋊C4×C113—44no—
50C4⋊C4×C113—44no—
51C4⋊C4×C113—42no—
52C22⋊C4×C113—24no—
53C22⋊C4×C113—42no—
54C42×C113—22no—
55C42×C113—42no—
56C42×C113—42no—
57C42×C113—42no—
58C42×C113#4114yes—
59C23×C113—21no—
60C23×C113—21no—
61C23×C113—42no—
62C23×C113#10012yes—
63C23×C113C2×C22⋊C411yescharacteristic
64C2×C4×C113—28no—
65C2×C4×C113—21no—
66C2×C4×C113—21no—
67C2×C4×C113—21no—
68C2×C4×C113—21no—
69C2×C4×C113—24no—
70C2×C4×C113—22no—
71C2×C4×C113—42no—
72C2×C4×C113—42no—
73C2×C4×C113—48no—
74C2×C4×C113—42no—
75C2×C4×C113—42no—
76C2×C4×C113—42no—
77C2×C4×C113—42no—
78C2×C4×C113—42no—
79C2×C4×C113#10112yes—
80C2×C4×C113#11712yes—
81C2×C4×C113#12314yes—
82C8×C113—84no—
83C22×C113—22no—
84C22×C113—22no—
85C22×C113—42no—
86C22×C113—42no—
87C22×C113—42no—
88C22×C113#38111yescharacteristic
89C22×C113C2×#10011yescharacteristic
90C22×C113C2×#10111yescharacteristic
91C4×C113—22no—
92C4×C113—22no—
93C4×C113—24no—
94C4×C113—44no—
95C4×C113—42no—
96C4×C113—82no—
97#8742C11311yesmaximal, characteristic, direct product factor, Sylow
98C2×C113—21no—
99C2×C113—21no—
100C2×C113—42no—
101C2×C113#182111yescharacteristic
102C2×C113#182712yes—
103#2296C2×C11311yescharacteristic
104#1464C2×C11312yes—
105#1285C2×C11314yescomplemented
106C113#874211yescharacteristic, direct product factor, Sylow
107C2×#117C4×C11311yescharacteristic
108C2×#117C22×C11311yescharacteristic
109C22×C42C4×C11311yescharacteristic
110#432C22×C11314yes—
111#389—22no—
112#385—22no—
113C4×C4⋊C4C4×C11312yes—
114C4×C4⋊C4C22×C11312yes—
115#324—22no—
116#323—22no—
117C23×C4—21no—
118C23×C4C2×C4×C11311yescharacteristic
119#117—24no—
120#117—42no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4D4×C11312yes—
125C2×C22⋊C4—21no—
126C2×C22⋊C4D4×C11312yes—
127C2×C42—21no—
128C2×C42—42no—
129C2×C42C2×C4×C11311yescharacteristic
130C2×C42C2×C4×C11312yes—
131C2×C42C2×C4×C11312yes—
132C2×C42C23×C11311yescharacteristic
133C4⋊C8—24no—
134C22⋊C8—24no—
135#97—24no—
136#95—22no—
137#95—22no—
138C24C22⋊C4×C11311yescharacteristic
139C22×C4—22no—
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—22no—
144C22×C4—44no—
145C22×C4—42no—
146C22×C4C22⋊C4×C11311yescharacteristic
147C22×C4C22⋊C4×C11312yes—
148C22×C4C22×C4×C11311yescharacteristic
149C22×C4C2×D4×C11312yes—
150C2×C8—44no—
151C4⋊C4—24no—
152C4⋊C4—42no—
153C4⋊C4—44no—
154C4⋊C4—44no—
155C22⋊C4—24no—
156C22⋊C4—42no—
157C42—22no—
158C42—42no—
159C42—42no—
160C42—42no—
161C42#41×C11314yes—
162C23—21no—
163C23—21no—
164C23—42no—
165C23#100×C11312yes—
166C23C2×C22⋊C4×C11311yescharacteristic
167C2×C4—28no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—24no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—48no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4#101×C11312yes—
183C2×C4#117×C11312yes—
184C2×C4#123×C11314yes—
185C8—84no—
186C22—22no—
187C22—22no—
188C22—42no—
189C22—42no—
190C22—42no—
191C22#381×C11311yescharacteristic
192C22C2×#100×C11311yescharacteristic
193C22C2×#101×C11311yescharacteristic
194C4—22no—
195C4—22no—
196C4—24no—
197C4—44no—
198C4—42no—
199C4—82no—
200C2—21no—
201C2—21no—
202C2—42no—
203C2C113×#182111yescharacteristic
204C2C113×#182712yes—
subgroupG/H
center, socleC22×C113#381
commutatorC22×C4C22×C4×C113
Frattini, cosocleC2×C42C23×C113
prime radicalC24×C113C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C113 ◁ C2×C42×C113 ◁ G

Complements

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

NH ≅ G/Ntype
3. C113×#1285C2semidirect
97. #8742C113direct (N × H)
105. #1285C2×C113semidirect
106. C113#8742direct (N × H)

Maximal subgroups

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

subgroupindex
C113×#22962
C113×#14642
C113×#12852
#8742113