Finite Group Databasebeta

← C113×#8224 #43276244

Subgroups — C113×#8224 #43276244

Order 28928.

528 conjugacy classes of subgroups.

The subgroup lattice has 272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#124×C113C211yesmaximal, characteristic
2C113×#1745C212yesmaximal, complemented
3C2×#329×C113C212yesmaximal
4C113×#1295C212yesmaximal, complemented
5C2×#124×C113C2211yescharacteristic
6C2×C4×Q8×C113C411yescharacteristic
7C2×C4×D4×C113C411yescharacteristic
8C2×#97×C113C2214yes—
9#391×C113C411yescharacteristic
10#390×C113C411yescharacteristic
11#388×C113—22no—
12#382×C113C2211yescharacteristic
13C4×C22⋊C4×C113—22no—
14C43×C113C2211yescharacteristic
15#336×C113—22no—
16#336×C113—22no—
17#329×C113C418yescomplemented
18C22×Q8×C113C2×C411yescharacteristic
19C22×D4×C113C2×C411yescharacteristic
20C23×C4×C113—21no—
21C22×C8×C113—24no—
22#124×C113—22no—
23#124×C113C2×C414yes—
24C4×Q8×C113—42no—
25C4×D4×C113—42no—
26C2×C4⋊C4×C113—21no—
27C2×C4⋊C4×C113C2×C411yescharacteristic
28C2×C4⋊C4×C113C2×C411yescharacteristic
29C2×C22⋊C4×C113—22no—
30C2×C22⋊C4×C113—21no—
31C2×C22⋊C4×C113—22no—
32C2×C42×C113—21no—
33C2×C42×C113C2×C411yescharacteristic
34C2×C42×C113C2×C411yescharacteristic
35C2×C42×C113D412yes—
36C2×C42×C113D412yes—
37C2×C42×C113C2311yescharacteristic
38#97×C113—24no—
39#97×C113C2×C418yescomplemented
40#95×C113—22no—
41#95×C113—22no—
42C24×C113—21no—
43C2×Q8×C113—21no—
44C2×Q8×C113—41no—
45C2×Q8×C113—41no—
46C2×Q8×C113C4212yes—
47C2×D4×C113—21no—
48C2×D4×C113—41no—
49C2×D4×C113—41no—
50C2×D4×C113C4212yes—
51C22×C4×C113—21no—
52C22×C4×C113—21no—
53C22×C4×C113—21no—
54C22×C4×C113—44no—
55C22×C4×C113—42no—
56C22×C4×C113C22⋊C412yes—
57C22×C4×C113C22⋊C411yescharacteristic
58C22×C4×C113C22⋊C411yescharacteristic
59C22×C4×C113C22×C411yescharacteristic
60C22×C4×C113C2×D412yes—
61C2×C8×C113—28no—
62C2×C8×C113—44no—
63C2×C8×C113—44no—
64C4⋊C4×C113—41no—
65C4⋊C4×C113—41no—
66C4⋊C4×C113—42no—
67C22⋊C4×C113—28no—
68C22⋊C4×C113—44no—
69C22⋊C4×C113—42no—
70C42×C113—22no—
71C42×C113—41no—
72C42×C113—42no—
73C42×C113—42no—
74C42×C113—42no—
75C42×C113C22×C412yes—
76C42×C113#4112yes—
77C23×C113—22no—
78C23×C113—41no—
79C23×C113—41no—
80C23×C113—42no—
81C23×C113—42no—
82C23×C113C2×C22⋊C411yescharacteristic
83Q8×C113—42no—
84Q8×C113—42no—
85D4×C113—42no—
86D4×C113—42no—
87C2×C4×C113—21no—
88C2×C4×C113—21no—
89C2×C4×C113—22no—
90C2×C4×C113—22no—
91C2×C4×C113—22no—
92C2×C4×C113—22no—
93C2×C4×C113—21no—
94C2×C4×C113—22no—
95C2×C4×C113—22no—
96C2×C4×C113—22no—
97C2×C4×C113—22no—
98C2×C4×C113—41no—
99C2×C4×C113—41no—
100C2×C4×C113—41no—
101C2×C4×C113—41no—
102C2×C4×C113—42no—
103C2×C4×C113—42no—
104C2×C4×C113—84no—
105C2×C4×C113#10012yes—
106C2×C4×C113C2×C4211yescharacteristic
107C2×C4×C113#11711yescharacteristic
108C2×C4×C113C4×D414yes—
109C8×C113—48no—
110C22×C113—42no—
111C22×C113—44no—
112C22×C113—81no—
113C22×C113—81no—
114C22×C113—82no—
115C22×C113C4×C22⋊C411yescharacteristic
116C22×C113C2×#10011yescharacteristic
117C22×C113#41311yescharacteristic
118C22×C113#42112yes—
119C22×C113#42112yes—
120C4×C113—21no—
121C4×C113—21no—
122C4×C113—24no—
123C4×C113—22no—
124C4×C113—41no—
125C4×C113—42no—
126C4×C113—42no—
127C4×C113—81no—
128C4×C113—81no—
129#8224C11311yesmaximal, characteristic, direct product factor, Sylow
130C2×C113—82no—
131C2×C113#153311yescharacteristic
132C2×C113#153512yes—
133C2×C113#153611yescharacteristic
134C2×C113C4×#10011yescharacteristic
135C2×C113#175912yes—
136C4×#124C2×C11311yescharacteristic
137#1745C2×C11312yescomplemented
138C2×#329C2×C11312yes—
139#1295C2×C11312yescomplemented
140C113#822411yescharacteristic, direct product factor, Sylow
141C2×#124C22×C11311yescharacteristic
142C2×C4×Q8C4×C11311yescharacteristic
143C2×C4×D4C4×C11311yescharacteristic
144C2×#97C22×C11314yes—
145#391C4×C11311yescharacteristic
146#390C4×C11311yescharacteristic
147#388—22no—
148#382C22×C11311yescharacteristic
149C4×C22⋊C4—22no—
150C43C22×C11311yescharacteristic
151#336—22no—
152#336—22no—
153#329C4×C11318yescomplemented
154C22×Q8C2×C4×C11311yescharacteristic
155C22×D4C2×C4×C11311yescharacteristic
156C23×C4—21no—
157C22×C8—24no—
158#124—22no—
159#124C2×C4×C11314yes—
160C4×Q8—42no—
161C4×D4—42no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4C2×C4×C11311yescharacteristic
164C2×C4⋊C4C2×C4×C11311yescharacteristic
165C2×C22⋊C4—22no—
166C2×C22⋊C4—21no—
167C2×C22⋊C4—22no—
168C2×C42—21no—
169C2×C42C2×C4×C11311yescharacteristic
170C2×C42C2×C4×C11311yescharacteristic
171C2×C42D4×C11312yes—
172C2×C42D4×C11312yes—
173C2×C42C23×C11311yescharacteristic
174#97—24no—
175#97C2×C4×C11318yescomplemented
176#95—22no—
177#95—22no—
178C24—21no—
179C2×Q8—21no—
180C2×Q8—41no—
181C2×Q8—41no—
182C2×Q8C42×C11312yes—
183C2×D4—21no—
184C2×D4—41no—
185C2×D4—41no—
186C2×D4C42×C11312yes—
187C22×C4—21no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—44no—
191C22×C4—42no—
192C22×C4C22⋊C4×C11312yes—
193C22×C4C22⋊C4×C11311yescharacteristic
194C22×C4C22⋊C4×C11311yescharacteristic
195C22×C4C22×C4×C11311yescharacteristic
196C22×C4C2×D4×C11312yes—
197C2×C8—28no—
198C2×C8—44no—
199C2×C8—44no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—42no—
203C22⋊C4—28no—
204C22⋊C4—42no—
205C22⋊C4—44no—
206C42—22no—
207C42—41no—
208C42—42no—
209C42—42no—
210C42—42no—
211C42C22×C4×C11312yes—
212C42#41×C11312yes—
213C23—22no—
214C23—41no—
215C23—41no—
216C23—42no—
217C23—42no—
218C23C2×C22⋊C4×C11311yescharacteristic
219Q8—42no—
220Q8—42no—
221D4—42no—
222D4—42no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—84no—
241C2×C4#100×C11312yes—
242C2×C4C2×C42×C11311yescharacteristic
243C2×C4#117×C11311yescharacteristic
244C2×C4C4×D4×C11314yes—
245C8—48no—
246C22—42no—
247C22—44no—
248C22—81no—
249C22—82no—
250C22—81no—
251C22C4×C22⋊C4×C11311yescharacteristic
252C22C2×#100×C11311yescharacteristic
253C22#413×C11311yescharacteristic
254C22#421×C11312yes—
255C22#421×C11312yes—
256C4—22no—
257C4—21no—
258C4—21no—
259C4—24no—
260C4—42no—
261C4—41no—
262C4—42no—
263C4—81no—
264C4—81no—
265C2—82no—
266C2C113×#153311yescharacteristic
267C2C113×#153512yes—
268C2C113×#153611yescharacteristic
269C2C4×#100×C11311yescharacteristic
270C2C113×#175912yes—
subgroupG/H
center, socleC23×C113C2×C22⋊C4
commutatorC2×C4C2×C42×C113
Frattini, cosocleC2×C42C23×C113
prime radicalC22×D4×C113C2×C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C113 ◁ C43×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C113×#1745C2semidirect
4. C113×#1295C2semidirect
17. #329×C113C4semidirect
39. #97×C113C2×C4semidirect
129. #8224C113direct (N × H)
137. #1745C2×C113semidirect
139. #1295C2×C113semidirect
140. C113#8224direct (N × H)
153. #329C4×C113semidirect
175. #97C2×C4×C113semidirect

Maximal subgroups

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

subgroupindex
C4×#124×C1132
C113×#17452
C2×#329×C1132
C113×#12952
#8224113