Finite Group Databasebeta

← C113×#9863 #43277883

Subgroups — C113×#9863 #43277883

Order 28928.

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

normal subgroups only

This group has 412 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×#3131C211yesmaximal, characteristic
2C113×#1837C211yesmaximal, characteristic, complemented
3C113×#1493C212yesmaximal, complemented
4C113×#1492C212yesmaximal
5C2×#322×C113C211yesmaximal, characteristic, complemented
6#533×C113C2211yescharacteristic
7#532×C113C2211yescharacteristic
8#488×C113—22no—
9#487×C113C412yes—
10#486×C113C412yes—
11#423×C113C2212yes—
12#416×C113—22no—
13C2×C4×C8×C113C2212yes—
14C2×C4×C8×C113C2211yescharacteristic
15#341×C113—22no—
16Q8⋊C8×C113—24no—
17D4⋊C8×C113—24no—
18#322×C113—22no—
19C2×#41×C113—21no—
20C2×M16×C113—22no—
21C22×C8×C113—22no—
22C22×C8×C113D412yes—
23C4⋊Q8×C113C2×C411yescharacteristic
24C4⋊Q8×C113C2×C412yes—
25#127×C113C2×C411yescharacteristic
26#125×C113—21no—
27#124×C113—21no—
28C22⋊Q8×C113—22no—
29#121×C113—22no—
30C4×Q8×C113—22no—
31C4×D4×C113—22no—
32#117×C113—21no—
33C2×C42×C113C2311yescharacteristic
34C4⋊C8×C113—22no—
35C4⋊C8×C113—22no—
36#103×C113—24no—
37#102×C113—24no—
38C4×C8×C113—22no—
39C4×C8×C113C2×C412yes—
40C4×C8×C113D414yes—
41C4×C8×C113D412yes—
42#41×C113—44no—
43C2×Q8×C113—21no—
44C2×Q8×C113—22no—
45C2×D4×C113—21no—
46C2×D4×C113—22no—
47C2×D4×C113—41no—
48C22×C4×C113—41no—
49C22×C4×C113C2×D411yescharacteristic
50C22×C4×C113#4112yes—
51M16×C113—44no—
52C2×C8×C113—24no—
53C2×C8×C113—24no—
54C2×C8×C113—44no—
55C2×C8×C113—42no—
56C2×C8×C113C22⋊C414yes—
57C4⋊C4×C113—22no—
58C4⋊C4×C113—22no—
59C4⋊C4×C113—22no—
60C4⋊C4×C113—42no—
61C22⋊C4×C113—41no—
62C22⋊C4×C113—42no—
63C42×C113—41no—
64C42×C113C22×C411yescharacteristic
65C42×C113C2×D411yescharacteristic
66C42×C113C2×D412yes—
67C23×C113—41no—
68C23×C113#12411yescharacteristic
69Q8×C113—42no—
70Q8×C113—44no—
71D4×C113—42no—
72D4×C113—44no—
73D4×C113—82no—
74C2×C4×C113—24no—
75C2×C4×C113—42no—
76C2×C4×C113—41no—
77C2×C4×C113—82no—
78C2×C4×C113C2×C22⋊C411yescharacteristic
79C2×C4×C113C4×D412yes—
80C2×C4×C113#12112yes—
81C2×C4×C113#12711yescharacteristic
82C2×C4×C113#13514yes—
83C8×C113—24no—
84C8×C113—44no—
85C8×C113—82no—
86C22×C113—22no—
87C22×C113—81no—
88C22×C113—82no—
89C22×C113#39011yescharacteristic
90C22×C113#48812yes—
91C4×C113—22no—
92C4×C113—81no—
93C4×C113—82no—
94C4×C113#41612yes—
95C4×C113#44414yes—
96C4×C113#49512yes—
97#9863C11311yesmaximal, characteristic, direct product factor, Sylow
98C2×C113—22no—
99C2×C113—161no—
100C2×C113#195811yescharacteristic
101C2×C113#197512yes—
102#3131C2×C11311yescharacteristic
103#1837C2×C11311yescharacteristic, complemented
104#1493C2×C11312yescomplemented
105#1492C2×C11312yes—
106C2×#322C2×C11311yescharacteristic, complemented
107C113#986311yescharacteristic, direct product factor, Sylow
108#533C22×C11311yescharacteristic
109#532C22×C11311yescharacteristic
110#488—22no—
111#487C4×C11312yes—
112#486C4×C11312yes—
113#423C22×C11312yes—
114#416—22no—
115C2×C4×C8C22×C11312yes—
116C2×C4×C8C22×C11311yescharacteristic
117#341—22no—
118Q8⋊C8—24no—
119D4⋊C8—24no—
120#322—22no—
121C2×#41—21no—
122C2×M16—22no—
123C22×C8—22no—
124C22×C8D4×C11312yes—
125C4⋊Q8C2×C4×C11311yescharacteristic
126C4⋊Q8C2×C4×C11312yes—
127#127C2×C4×C11311yescharacteristic
128#125—21no—
129#124—21no—
130C22⋊Q8—22no—
131#121—22no—
132C4×Q8—22no—
133C4×D4—22no—
134#117—21no—
135C2×C42C23×C11311yescharacteristic
136C4⋊C8—22no—
137C4⋊C8—22no—
138#103—24no—
139#102—24no—
140C4×C8—22no—
141C4×C8C2×C4×C11312yes—
142C4×C8D4×C11314yes—
143C4×C8D4×C11312yes—
144#41—44no—
145C2×Q8—21no—
146C2×Q8—22no—
147C2×D4—21no—
148C2×D4—22no—
149C2×D4—41no—
150C22×C4—41no—
151C22×C4C2×D4×C11311yescharacteristic
152C22×C4#41×C11312yes—
153M16—44no—
154C2×C8—24no—
155C2×C8—24no—
156C2×C8—44no—
157C2×C8—42no—
158C2×C8C22⋊C4×C11314yes—
159C4⋊C4—22no—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—42no—
163C22⋊C4—41no—
164C22⋊C4—42no—
165C42—41no—
166C42C22×C4×C11311yescharacteristic
167C42C2×D4×C11311yescharacteristic
168C42C2×D4×C11312yes—
169C23—41no—
170C23#124×C11311yescharacteristic
171Q8—42no—
172Q8—44no—
173D4—42no—
174D4—44no—
175D4—82no—
176C2×C4—24no—
177C2×C4—42no—
178C2×C4—41no—
179C2×C4—82no—
180C2×C4C2×C22⋊C4×C11311yescharacteristic
181C2×C4C4×D4×C11312yes—
182C2×C4#121×C11312yes—
183C2×C4#127×C11311yescharacteristic
184C2×C4#135×C11314yes—
185C8—24no—
186C8—44no—
187C8—82no—
188C22—22no—
189C22—81no—
190C22—82no—
191C22#390×C11311yescharacteristic
192C22#488×C11312yes—
193C4—22no—
194C4—81no—
195C4—82no—
196C4#416×C11312yes—
197C4#444×C11314yes—
198C4#495×C11312yes—
199C2—22no—
200C2—161no—
201C2C113×#195811yescharacteristic
202C2C113×#197512yes—
subgroupG/H
centerC2×C4×C113#127
commutatorC42C22×C4×C113
Frattini, cosocleC2×C42C23×C113
socleC22×C113#390
prime radical#532×C113C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C113 ◁ C2×C42×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C113×#1837C2semidirect
3. C113×#1493C2semidirect
5. C2×#322×C113C2semidirect
97. #9863C113direct (N × H)
103. #1837C2×C113semidirect
104. #1493C2×C113semidirect
106. C2×#322C2×C113semidirect
107. C113#9863direct (N × H)

Maximal subgroups

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

subgroupindex
C113×#31312
C113×#18372
C113×#14932
C113×#14922
C2×#322×C1132
#9863113