Finite Group Databasebeta

← C113×#9757 #43277777

Subgroups — C113×#9757 #43277777

Order 28928.

400 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 134 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×#1835C211yesmaximal, characteristic, complemented
3C113×#1518C212yesmaximal, complemented
4C113×#1517C212yesmaximal
5C113×#1450C211yesmaximal, characteristic, complemented
6#533×C113C2211yescharacteristic
7#532×C113C2211yescharacteristic
8#488×C113—21no—
9#488×C113—21no—
10#487×C113C412yescomplemented
11#486×C113C412yescomplemented
12#431×C113C2212yes—
13#416×C113—22no—
14C2×C4×C8×C113C2211yescharacteristic
15#382×C113C2212yes—
16#340×C113—22no—
17#328×C113—24no—
18#327×C113—24no—
19#322×C113—21no—
20C82×C113—21no—
21C2×#41×C113—21no—
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×C4⋊C4×C113—22no—
34C2×C42×C113C2311yescharacteristic
35C4⋊C8×C113—22no—
36#103×C113—22no—
37#103×C113—22no—
38#102×C113—22no—
39#102×C113—22no—
40C22⋊C8×C113D414yes—
41C4×C8×C113—22no—
42C4×C8×C113C2×C412yes—
43C4×C8×C113D411yescharacteristic
44C4×C8×C113D411yescharacteristic
45#95×C113—22no—
46#95×C113—22no—
47#41×C113—44no—
48C2×Q8×C113—21no—
49C2×Q8×C113—22no—
50C2×D4×C113—21no—
51C2×D4×C113—22no—
52C2×D4×C113—41no—
53C22×C4×C113—41no—
54C22×C4×C113—42no—
55C22×C4×C113C2×D412yes—
56C22×C4×C113C2×D411yescharacteristic
57C2×C8×C113—24no—
58C2×C8×C113—24no—
59C2×C8×C113C22⋊C412yes—
60C2×C8×C113C22⋊C412yes—
61C4⋊C4×C113—22no—
62C4⋊C4×C113—22no—
63C4⋊C4×C113—22no—
64C4⋊C4×C113—42no—
65C4⋊C4×C113—44no—
66C22⋊C4×C113—41no—
67C22⋊C4×C113—42no—
68C42×C113—41no—
69C42×C113C22×C411yescharacteristic
70C42×C113C2×D411yescharacteristic
71C42×C113#4112yes—
72C23×C113—41no—
73C23×C113#12711yescharacteristic
74Q8×C113—42no—
75Q8×C113—82no—
76D4×C113—42no—
77D4×C113—82no—
78D4×C113—82no—
79C2×C4×C113—42no—
80C2×C4×C113—42no—
81C2×C4×C113—41no—
82C2×C4×C113—82no—
83C2×C4×C113—84no—
84C2×C4×C113—82no—
85C2×C4×C113C2×C22⋊C411yescharacteristic
86C2×C4×C113C4×D412yes—
87C2×C4×C113#12112yes—
88C2×C4×C113#12411yescharacteristic
89C2×C4×C113#13514yes—
90C8×C113—22no—
91C8×C113—22no—
92C8×C113—44no—
93C22×C113—22no—
94C22×C113—81no—
95C22×C113—82no—
96C22×C113#39011yescharacteristic
97C22×C113#49512yes—
98C4×C113—22no—
99C4×C113—22no—
100C4×C113—81no—
101C4×C113—82no—
102C4×C113—162no—
103C4×C113#41612yes—
104C4×C113#48812yes—
105#9757C11311yesmaximal, characteristic, direct product factor, Sylow
106C2×C113—22no—
107C2×C113—161no—
108C2×C113#195811yescharacteristic
109C2×C113#197612yes—
110#3131C2×C11311yescharacteristic
111#1835C2×C11311yescharacteristic, complemented
112#1518C2×C11312yescomplemented
113#1517C2×C11312yes—
114#1450C2×C11311yescharacteristic, complemented
115C113#975711yescharacteristic, direct product factor, Sylow
116#533C22×C11311yescharacteristic
117#532C22×C11311yescharacteristic
118#488—21no—
119#488—21no—
120#487C4×C11312yescomplemented
121#486C4×C11312yescomplemented
122#431C22×C11312yes—
123#416—22no—
124C2×C4×C8C22×C11311yescharacteristic
125#382C22×C11312yes—
126#340—22no—
127#328—24no—
128#327—24no—
129#322—21no—
130C82—21no—
131C2×#41—21no—
132C22×C8D4×C11312yes—
133C4⋊Q8C2×C4×C11311yescharacteristic
134C4⋊Q8C2×C4×C11312yes—
135#127C2×C4×C11311yescharacteristic
136#125—21no—
137#124—21no—
138C22⋊Q8—22no—
139#121—22no—
140C4×Q8—22no—
141C4×D4—22no—
142#117—21no—
143C2×C4⋊C4—22no—
144C2×C42C23×C11311yescharacteristic
145C4⋊C8—22no—
146#103—22no—
147#103—22no—
148#102—22no—
149#102—22no—
150C22⋊C8D4×C11314yes—
151C4×C8—22no—
152C4×C8C2×C4×C11312yes—
153C4×C8D4×C11311yescharacteristic
154C4×C8D4×C11311yescharacteristic
155#95—22no—
156#95—22no—
157#41—44no—
158C2×Q8—21no—
159C2×Q8—22no—
160C2×D4—21no—
161C2×D4—22no—
162C2×D4—41no—
163C22×C4—41no—
164C22×C4—42no—
165C22×C4C2×D4×C11312yes—
166C22×C4C2×D4×C11311yescharacteristic
167C2×C8—24no—
168C2×C8—24no—
169C2×C8C22⋊C4×C11312yes—
170C2×C8C22⋊C4×C11312yes—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—42no—
175C4⋊C4—44no—
176C22⋊C4—41no—
177C22⋊C4—42no—
178C42—41no—
179C42C22×C4×C11311yescharacteristic
180C42C2×D4×C11311yescharacteristic
181C42#41×C11312yes—
182C23—41no—
183C23#127×C11311yescharacteristic
184Q8—42no—
185Q8—82no—
186D4—42no—
187D4—82no—
188D4—82no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—41no—
192C2×C4—82no—
193C2×C4—84no—
194C2×C4—82no—
195C2×C4C2×C22⋊C4×C11311yescharacteristic
196C2×C4C4×D4×C11312yes—
197C2×C4#121×C11312yes—
198C2×C4#124×C11311yescharacteristic
199C2×C4#135×C11314yes—
200C8—22no—
201C8—22no—
202C8—44no—
203C22—22no—
204C22—81no—
205C22—82no—
206C22#390×C11311yescharacteristic
207C22#495×C11312yes—
208C4—22no—
209C4—22no—
210C4—81no—
211C4—82no—
212C4—162no—
213C4#416×C11312yes—
214C4#488×C11312yes—
215C2—22no—
216C2—161no—
217C2C113×#195811yescharacteristic
218C2C113×#197612yes—
subgroupG/H
center, socleC22×C113#390
commutatorC42C22×C4×C113
Frattini, cosocleC2×C42C23×C113
prime radical#532×C113C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C113 ◁ C2×C42×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C113×#1835C2semidirect
3. C113×#1518C2semidirect
5. C113×#1450C2semidirect
10. #487×C113C4semidirect
11. #486×C113C4semidirect
105. #9757C113direct (N × H)
111. #1835C2×C113semidirect
112. #1518C2×C113semidirect
114. #1450C2×C113semidirect
115. C113#9757direct (N × H)
120. #487C4×C113semidirect
121. #486C4×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#31312
C113×#18352
C113×#15182
C113×#15172
C113×#14502
#9757113