Finite Group Databasebeta

← C113×#8721 #43276741

Subgroups — C113×#8721 #43276741

Order 28928.

526 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 142 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×#1749C212yesmaximal
3C113×#1295C214yesmaximal, complemented
4C2×#117×C113C412yes—
5C22×C42×C113C2211yescharacteristic
6C2×C22⋊C8×C113—22no—
7C2×#97×C113C2214yes—
8#384×C113C411yescharacteristic
9#384×C113C411yescharacteristic
10#382×C113C2212yes—
11#380×C113—22no—
12C4×C4⋊C4×C113—22no—
13#336×C113—22no—
14C23×C4×C113C2×C411yescharacteristic
15C23×C4×C113D412yes—
16C22×C8×C113—24no—
17#117×C113—44no—
18C2×C4⋊C4×C113—22no—
19C2×C4⋊C4×C113—22no—
20C2×C4⋊C4×C113C2×C412yes—
21C2×C4⋊C4×C113C2×C412yes—
22C2×C22⋊C4×C113—22no—
23C2×C42×C113—24no—
24C2×C42×C113—22no—
25C2×C42×C113C2×C411yescharacteristic
26C2×C42×C113D412yes—
27C2×C42×C113C2311yescharacteristic
28C22⋊C8×C113—28no—
29#97×C113—28no—
30#95×C113—24no—
31C24×C113C22⋊C411yescharacteristic
32C22×C4×C113—22no—
33C22×C4×C113—22no—
34C22×C4×C113—22no—
35C22×C4×C113—24no—
36C22×C4×C113—24no—
37C22×C4×C113—22no—
38C22×C4×C113—22no—
39C22×C4×C113—42no—
40C22×C4×C113C22⋊C411yescharacteristic
41C22×C4×C113C22⋊C412yes—
42C22×C4×C113C22×C411yescharacteristic
43C22×C4×C113C2×D412yes—
44C2×C8×C113—28no—
45C2×C8×C113—44no—
46C2×C8×C113—44no—
47C4⋊C4×C113—42no—
48C4⋊C4×C113—42no—
49C4⋊C4×C113—44no—
50C4⋊C4×C113—44no—
51C22⋊C4×C113—44no—
52C42×C113—22no—
53C42×C113—24no—
54C42×C113—44no—
55C42×C113#4114yes—
56C23×C113—21no—
57C23×C113—21no—
58C23×C113—22no—
59C23×C113—22no—
60C23×C113#10112yes—
61C23×C113C2×C22⋊C411yescharacteristic
62C2×C4×C113—28no—
63C2×C4×C113—21no—
64C2×C4×C113—22no—
65C2×C4×C113—21no—
66C2×C4×C113—21no—
67C2×C4×C113—21no—
68C2×C4×C113—22no—
69C2×C4×C113—22no—
70C2×C4×C113—22no—
71C2×C4×C113—48no—
72C2×C4×C113—42no—
73C2×C4×C113—42no—
74C2×C4×C113—44no—
75C2×C4×C113—44no—
76C2×C4×C113#10012yes—
77C2×C4×C113#10414yes—
78C2×C4×C113#11712yes—
79C2×C4×C113#12314yes—
80C8×C113—48no—
81C22×C113—22no—
82C22×C113—24no—
83C22×C113—41no—
84C22×C113—42no—
85C22×C113—41no—
86C22×C113#38111yescharacteristic
87C22×C113C2×#10011yescharacteristic
88C22×C113C2×#10111yescharacteristic
89C22×C113C2×#10412yes—
90C22×C113#42112yes—
91C4×C113—22no—
92C4×C113—22no—
93C4×C113—24no—
94C4×C113—24no—
95C4×C113—82no—
96C4×C113—82no—
97#8721C11311yesmaximal, characteristic, direct product factor, Sylow
98C2×C113—42no—
99C2×C113#152511yescharacteristic
100C2×C113#153112yes—
101C2×C113#153611yescharacteristic
102C2×C113#182111yescharacteristic
103C2×C113#182612yes—
104#2285C2×C11311yescharacteristic
105#1749C2×C11312yes—
106#1295C2×C11314yescomplemented
107C113#872111yescharacteristic, direct product factor, Sylow
108C2×#117C4×C11312yes—
109C22×C42C22×C11311yescharacteristic
110C2×C22⋊C8—22no—
111C2×#97C22×C11314yes—
112#384C4×C11311yescharacteristic
113#384C4×C11311yescharacteristic
114#382C22×C11312yes—
115#380—22no—
116C4×C4⋊C4—22no—
117#336—22no—
118C23×C4C2×C4×C11311yescharacteristic
119C23×C4D4×C11312yes—
120C22×C8—24no—
121#117—44no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4C2×C4×C11312yes—
125C2×C4⋊C4C2×C4×C11312yes—
126C2×C22⋊C4—22no—
127C2×C42—24no—
128C2×C42—22no—
129C2×C42C2×C4×C11311yescharacteristic
130C2×C42D4×C11312yes—
131C2×C42C23×C11311yescharacteristic
132C22⋊C8—28no—
133#97—28no—
134#95—24no—
135C24C22⋊C4×C11311yescharacteristic
136C22×C4—22no—
137C22×C4—22no—
138C22×C4—22no—
139C22×C4—24no—
140C22×C4—24no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—42no—
144C22×C4C22⋊C4×C11311yescharacteristic
145C22×C4C22⋊C4×C11312yes—
146C22×C4C22×C4×C11311yescharacteristic
147C22×C4C2×D4×C11312yes—
148C2×C8—28no—
149C2×C8—44no—
150C2×C8—44no—
151C4⋊C4—42no—
152C4⋊C4—42no—
153C4⋊C4—44no—
154C4⋊C4—44no—
155C22⋊C4—44no—
156C42—22no—
157C42—24no—
158C42—44no—
159C42#41×C11314yes—
160C23—21no—
161C23—21no—
162C23—22no—
163C23—22no—
164C23#101×C11312yes—
165C23C2×C22⋊C4×C11311yescharacteristic
166C2×C4—28no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—48no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—44no—
179C2×C4—44no—
180C2×C4#100×C11312yes—
181C2×C4#104×C11314yes—
182C2×C4#117×C11312yes—
183C2×C4#123×C11314yes—
184C8—48no—
185C22—24no—
186C22—22no—
187C22—41no—
188C22—41no—
189C22—42no—
190C22#381×C11311yescharacteristic
191C22C2×#100×C11311yescharacteristic
192C22C2×#101×C11311yescharacteristic
193C22C2×#104×C11312yes—
194C22#421×C11312yes—
195C4—22no—
196C4—22no—
197C4—24no—
198C4—24no—
199C4—82no—
200C4—82no—
201C2—42no—
202C2C113×#152511yescharacteristic
203C2C113×#153112yes—
204C2C113×#153611yescharacteristic
205C2C113×#182111yescharacteristic
206C2C113×#182612yes—
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×#1295C2semidirect
97. #8721C113direct (N × H)
106. #1295C2×C113semidirect
107. C113#8721direct (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×#17492
C113×#12952
#8721113