Finite Group Databasebeta

← C113×#7428 #43275448

Subgroups — C113×#7428 #43275448

Order 28928.

226 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 46 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×#2025C211yesmaximal, characteristic
2C113×#1393C211yesmaximal, characteristic
3C113×#1318C211yesmaximal, characteristic
4C2×#125×C113C411yescharacteristic, complemented
5C2×#102×C113—21no—
6C2×#99×C113—21no—
7#390×C113C2211yescharacteristic
8#340×C113—21no—
9#336×C113C411yescharacteristic, complemented
10#324×C113—21no—
11C22×D4×C113D411yescharacteristic
12C22×C8×C113—21no—
13#125×C113—42no—
14C2×C4⋊C4×C113—21no—
15C2×C4⋊C4×C113—41no—
16C2×C4⋊C4×C113D411yescharacteristic
17C2×C22⋊C4×C113—41no—
18C2×C22⋊C4×C113—41no—
19C2×C42×C113C2×C411yescharacteristic
20#102×C113—42no—
21#99×C113—22no—
22#99×C113—41no—
23C22⋊C8×C113—41no—
24C24×C113—21no—
25C2×D4×C113—21no—
26C2×D4×C113—41no—
27C2×D4×C113—41no—
28C2×D4×C113SD1611yescharacteristic
29C2×D4×C113Q1611yescharacteristic
30C22×C4×C113—21no—
31C22×C4×C113—21no—
32C22×C4×C113—41no—
33C22×C4×C113—81no—
34C22×C4×C113C22⋊C411yescharacteristic
35C2×C8×C113—41no—
36C2×C8×C113—41no—
37C2×C8×C113—41no—
38C2×C8×C113—81no—
39C4⋊C4×C113—22no—
40C4⋊C4×C113—41no—
41C4⋊C4×C113—41no—
42C4⋊C4×C113—42no—
43C4⋊C4×C113—42no—
44C22⋊C4×C113—42no—
45C22⋊C4×C113—82no—
46C22⋊C4×C113—81no—
47C42×C113—41no—
48C23×C113—21no—
49C23×C113—21no—
50C23×C113—41no—
51C23×C113—41no—
52C23×C113—81no—
53C23×C113—81no—
54C23×C113#9911yescharacteristic
55D4×C113—41no—
56D4×C113—41no—
57D4×C113—81no—
58C2×C4×C113—21no—
59C2×C4×C113—21no—
60C2×C4×C113—41no—
61C2×C4×C113—41no—
62C2×C4×C113—41no—
63C2×C4×C113—42no—
64C2×C4×C113—41no—
65C2×C4×C113—81no—
66C2×C4×C113—81no—
67C2×C4×C113—81no—
68C2×C4×C113—82no—
69C2×C4×C113—161no—
70C2×C4×C113—161no—
71C2×C4×C113#10311yescharacteristic
72C2×C4×C113#10411yescharacteristic
73C8×C113—81no—
74C8×C113—161no—
75C22×C113—21no—
76C22×C113—21no—
77C22×C113—41no—
78C22×C113—41no—
79C22×C113—81no—
80C22×C113—81no—
81C22×C113—81no—
82C22×C113—81no—
83C22×C113—161no—
84C22×C113#32811yescharacteristic
85C22×C113AΣL(1,𝔽16)11yescharacteristic
86C22×C113#35411yescharacteristic
87C4×C113—21no—
88C4×C113—21no—
89C4×C113—81no—
90C4×C113—82no—
91C4×C113—81no—
92C4×C113—162no—
93#7428C11311yesmaximal, characteristic, direct product factor, Sylow
94C2×C113—21no—
95C2×C113—21no—
96C2×C113—81no—
97C2×C113—81no—
98C2×C113#135111yescharacteristic
99C2×C113#141211yescharacteristic
100C2×C113#141411yescharacteristic
101#2025C2×C11311yescharacteristic
102#1393C2×C11311yescharacteristic
103#1318C2×C11311yescharacteristic
104C113#742811yescharacteristic, direct product factor, Sylow
105C2×#125C4×C11311yescharacteristic, complemented
106C2×#102—21no—
107C2×#99—21no—
108#390C22×C11311yescharacteristic
109#340—21no—
110#336C4×C11311yescharacteristic, complemented
111#324—21no—
112C22×D4D4×C11311yescharacteristic
113C22×C8—21no—
114#125—42no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4D4×C11311yescharacteristic
118C2×C22⋊C4—41no—
119C2×C22⋊C4—41no—
120C2×C42C2×C4×C11311yescharacteristic
121#102—42no—
122#99—22no—
123#99—41no—
124C22⋊C8—41no—
125C24—21no—
126C2×D4—21no—
127C2×D4—41no—
128C2×D4—41no—
129C2×D4SD16×C11311yescharacteristic
130C2×D4Q16×C11311yescharacteristic
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—41no—
134C22×C4—81no—
135C22×C4C22⋊C4×C11311yescharacteristic
136C2×C8—41no—
137C2×C8—41no—
138C2×C8—41no—
139C2×C8—81no—
140C4⋊C4—22no—
141C4⋊C4—41no—
142C4⋊C4—41no—
143C4⋊C4—42no—
144C4⋊C4—42no—
145C22⋊C4—42no—
146C22⋊C4—82no—
147C22⋊C4—81no—
148C42—41no—
149C23—21no—
150C23—21no—
151C23—41no—
152C23—41no—
153C23—81no—
154C23—81no—
155C23#99×C11311yescharacteristic
156D4—41no—
157D4—41no—
158D4—81no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—42no—
165C2×C4—41no—
166C2×C4—81no—
167C2×C4—81no—
168C2×C4—81no—
169C2×C4—82no—
170C2×C4—161no—
171C2×C4—161no—
172C2×C4#103×C11311yescharacteristic
173C2×C4#104×C11311yescharacteristic
174C8—81no—
175C8—161no—
176C22—21no—
177C22—21no—
178C22—41no—
179C22—41no—
180C22—81no—
181C22—81no—
182C22—81no—
183C22—81no—
184C22—161no—
185C22#328×C11311yescharacteristic
186C22AΣL(1,𝔽16)×C11311yescharacteristic
187C22#354×C11311yescharacteristic
188C4—21no—
189C4—21no—
190C4—81no—
191C4—82no—
192C4—81no—
193C4—162no—
194C2—21no—
195C2—21no—
196C2—81no—
197C2—81no—
198C2C113×#135111yescharacteristic
199C2C113×#141211yescharacteristic
200C2C113×#141411yescharacteristic
subgroupG/H
center, socleC22×C113#354
commutatorC2×C42C2×C4×C113
Frattini, cosocle#390C22×C113
prime radicalC22×D4×C113D4
LCSG ▷ C2×C42 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C23×C113 ◁ C22×C4×C113 ◁ #390×C113 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×#125×C113C4semidirect
9. #336×C113C4semidirect
93. #7428C113direct (N × H)
104. C113#7428direct (N × H)
105. C2×#125C4×C113semidirect
110. #336C4×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#20252
C113×#13932
C113×#13182
#7428113