Finite Group Databasebeta

← C43×#7751 #24927768

Subgroups — C43×#7751 #24927768

Order 11008.

492 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 98 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
1C43×#2724C211yesmaximal, characteristic
2C43×#2057C212yesmaximal, complemented
3C43×#2013C211yesmaximal, characteristic
4C43×#1271C212yesmaximal, complemented
5C43×#1270C211yesmaximal, characteristic
6C22×SD16×C43—21no—
7C2×C4⋊Q8×C43C2211yescharacteristic
8C2×#123×C43—21no—
9C2×#107×C43—22no—
10C2×#103×C43—21no—
11C43×#398—21no—
12C43×#397—22no—
13C43×#390C2211yescharacteristic
14C43×#389C2212yes—
15C43×#385—22no—
16C43×#340—22no—
17C43×#336C2211yescharacteristic
18C43×#336C2212yes—
19C22×Q8×C43—21no—
20C22×D4×C43D411yescharacteristic
21C23×C4×C43—21no—
22C2×SD16×C43—42no—
23C2×SD16×C43—42no—
24C2×SD16×C43—42no—
25C22×C8×C43—21no—
26C22×C8×C43—22no—
27C4⋊Q8×C43—42no—
28#123×C43—42no—
29#123×C43—42no—
30C2×C4⋊C4×C43—22no—
31C2×C4⋊C4×C43—22no—
32C2×C4⋊C4×C43—21no—
33C2×C4⋊C4×C43D412yes—
34C2×C4⋊C4×C43D412yes—
35C2×C4⋊C4×C43D411yescharacteristic
36C2×C22⋊C4×C43—22no—
37C2×C22⋊C4×C43—21no—
38C2×C22⋊C4×C43—22no—
39C2×C42×C43C2311yescharacteristic
40#107×C43—44no—
41#103×C43—42no—
42#95×C43—22no—
43#95×C43—21no—
44#95×C43—22no—
45C24×C43—21no—
46C2×Q8×C43—22no—
47C2×Q8×C43—41no—
48C2×Q8×C43—41no—
49C2×Q8×C43—41no—
50C2×Q8×C43—41no—
51C2×Q8×C43—41no—
52C2×D4×C43—21no—
53C2×D4×C43—41no—
54C2×D4×C43—41no—
55C2×D4×C43D812yes—
56C22×C4×C43—22no—
57C22×C4×C43—21no—
58C22×C4×C43—22no—
59C22×C4×C43—42no—
60C22×C4×C43—41no—
61C22×C4×C43—81no—
62C22×C4×C43—81no—
63C22×C4×C43C2×D411yescharacteristic
64C22×C4×C43C2×D412yes—
65SD16×C43—48no—
66C2×C8×C43—22no—
67C2×C8×C43—24no—
68C2×C8×C43—42no—
69C2×C8×C43—41no—
70C2×C8×C43—41no—
71C2×C8×C43—42no—
72C4⋊C4×C43—24no—
73C4⋊C4×C43—22no—
74C4⋊C4×C43—22no—
75C4⋊C4×C43—41no—
76C4⋊C4×C43—42no—
77C4⋊C4×C43—42no—
78C4⋊C4×C43—42no—
79C4⋊C4×C43—42no—
80C4⋊C4×C43—81no—
81C22⋊C4×C43—42no—
82C22⋊C4×C43—44no—
83C22⋊C4×C43—42no—
84C22⋊C4×C43—42no—
85C42×C43—41no—
86C23×C43—22no—
87C23×C43—42no—
88C23×C43—41no—
89C23×C43—42no—
90C23×C43—41no—
91C23×C43#12011yescharacteristic
92Q8×C43—42no—
93Q8×C43—42no—
94Q8×C43—81no—
95Q8×C43—81no—
96D4×C43—42no—
97D4×C43—81no—
98C2×C4×C43—21no—
99C2×C4×C43—22no—
100C2×C4×C43—22no—
101C2×C4×C43—21no—
102C2×C4×C43—42no—
103C2×C4×C43—42no—
104C2×C4×C43—42no—
105C2×C4×C43—42no—
106C2×C4×C43—41no—
107C2×C4×C43—42no—
108C2×C4×C43—42no—
109C2×C4×C43—42no—
110C2×C4×C43—42no—
111C2×C4×C43—84no—
112C2×C4×C43—81no—
113C2×C4×C43—81no—
114C2×C4×C43C2×D811yescharacteristic
115C2×C4×C43#13512yes—
116C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
117C2×C4×C43#13712yes—
118C8×C43—44no—
119C8×C43—42no—
120#7751C4311yesmaximal, characteristic, direct product factor, Sylow
121C22×C43—42no—
122C22×C43—44no—
123C22×C43—82no—
124C22×C43—81no—
125C22×C43—81no—
126C22×C43#44711yescharacteristic
127C22×C43#45212yes—
128C22×C43#45311yescharacteristic
129C22×C43#45612yes—
130C22×C43B(4,𝔽2)11yescharacteristic
131C4×C43—21no—
132C4×C43—21no—
133C4×C43—22no—
134C4×C43—22no—
135C4×C43—82no—
136C4×C43—82no—
137C4×C43—81no—
138C4×C43—82no—
139#2724C2×C4311yescharacteristic
140#2057C2×C4312yescomplemented
141#2013C2×C4311yescharacteristic
142#1271C2×C4312yescomplemented
143#1270C2×C4311yescharacteristic
144C2×C43—82no—
145C2×C43#159511yescharacteristic
146C2×C43#160312yes—
147C2×C43#163011yescharacteristic
148C2×C43#164712yes—
149C2×C43#166011yescharacteristic
150C22×SD16—21no—
151C2×C4⋊Q8C22×C4311yescharacteristic
152C2×#123—21no—
153C2×#107—22no—
154C2×#103—21no—
155#398—21no—
156#397—22no—
157#390C22×C4311yescharacteristic
158#389C22×C4312yes—
159#385—22no—
160#340—22no—
161#336C22×C4312yes—
162#336C22×C4311yescharacteristic
163C43#775111yescharacteristic, direct product factor, Sylow
164C22×Q8—21no—
165C22×D4D4×C4311yescharacteristic
166C23×C4—21no—
167C2×SD16—42no—
168C2×SD16—42no—
169C2×SD16—42no—
170C22×C8—21no—
171C22×C8—22no—
172C4⋊Q8—42no—
173#123—42no—
174#123—42no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4D4×C4312yes—
179C2×C4⋊C4D4×C4312yes—
180C2×C4⋊C4D4×C4311yescharacteristic
181C2×C22⋊C4—22no—
182C2×C22⋊C4—21no—
183C2×C22⋊C4—22no—
184C2×C42C23×C4311yescharacteristic
185#107—44no—
186#103—42no—
187#95—22no—
188#95—21no—
189#95—22no—
190C24—21no—
191C2×Q8—22no—
192C2×Q8—41no—
193C2×Q8—41no—
194C2×Q8—41no—
195C2×Q8—41no—
196C2×Q8—41no—
197C2×D4—21no—
198C2×D4—41no—
199C2×D4—41no—
200C2×D4D8×C4312yes—
201C22×C4—22no—
202C22×C4—21no—
203C22×C4—22no—
204C22×C4—42no—
205C22×C4—41no—
206C22×C4—81no—
207C22×C4—81no—
208C22×C4C2×D4×C4311yescharacteristic
209C22×C4C2×D4×C4312yes—
210SD16—48no—
211C2×C8—22no—
212C2×C8—24no—
213C2×C8—42no—
214C2×C8—41no—
215C2×C8—41no—
216C2×C8—42no—
217C4⋊C4—24no—
218C4⋊C4—22no—
219C4⋊C4—22no—
220C4⋊C4—41no—
221C4⋊C4—42no—
222C4⋊C4—42no—
223C4⋊C4—42no—
224C4⋊C4—42no—
225C4⋊C4—81no—
226C22⋊C4—42no—
227C22⋊C4—44no—
228C22⋊C4—42no—
229C22⋊C4—42no—
230C42—41no—
231C23—22no—
232C23—42no—
233C23—41no—
234C23—42no—
235C23—41no—
236C23#120×C4311yescharacteristic
237Q8—42no—
238Q8—42no—
239Q8—81no—
240Q8—81no—
241D4—42no—
242D4—81no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—41no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—84no—
257C2×C4—81no—
258C2×C4—81no—
259C2×C4C2×D8×C4311yescharacteristic
260C2×C4#135×C4312yes—
261C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
262C2×C4#137×C4312yes—
263C8—42no—
264C8—44no—
265C22—42no—
266C22—44no—
267C22—82no—
268C22—81no—
269C22—81no—
270C22C43×#44711yescharacteristic
271C22C43×#45212yes—
272C22C43×#45311yescharacteristic
273C22C43×#45612yes—
274C22C43×B(4,𝔽2)11yescharacteristic
275C4—21no—
276C4—21no—
277C4—22no—
278C4—22no—
279C4—82no—
280C4—82no—
281C4—81no—
282C4—82no—
283C2—82no—
284C2C43×#159511yescharacteristic
285C2C43×#160312yes—
286C2C43×#163011yescharacteristic
287C2C43×#164712yes—
288C2C43×#166011yescharacteristic
subgroupG/H
center, socleC23×C43#120
commutator, Frattini, cosocleC2×C42C23×C43
prime radicalC22×D4×C43D4
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2057C2semidirect
4. C43×#1271C2semidirect
120. #7751C43direct (N × H)
140. #2057C2×C43semidirect
142. #1271C2×C43semidirect
163. C43#7751direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#27242
C43×#20572
C43×#20132
C43×#12712
C43×#12702
#775143