Finite Group Databasebeta

← C43×#7755 #24927772

Subgroups — C43×#7755 #24927772

Order 11008.

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

normal subgroups only

This group has 480 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×#2804C211yesmaximal, characteristic
2C43×#2024C212yesmaximal, complemented
3C43×#2013C211yesmaximal, characteristic
4C43×#1272C212yesmaximal, complemented
5C43×#1270C211yesmaximal, characteristic
6C22×SD16×C43—21no—
7C2×C4⋊Q8×C43C2211yescharacteristic
8C2×#103×C43—22no—
9C2×#103×C43—21no—
10C43×#400—21no—
11C43×#393—22no—
12C43×#391C2212yes—
13C43×#390C2211yescharacteristic
14C43×#386—21no—
15C43×#385—22no—
16C43×#340—22no—
17C43×#336C2211yescharacteristic
18C43×#336C2212yes—
19C22×Q8×C43—21no—
20C22×Q8×C43D412yes—
21C22×D4×C43D411yescharacteristic
22C23×C4×C43—21no—
23C2×SD16×C43—42no—
24C2×SD16×C43—42no—
25C2×SD16×C43—42no—
26C22×C8×C43—21no—
27C22×C8×C43—22no—
28C4⋊Q8×C43—42no—
29C2×C4⋊C4×C43—22no—
30C2×C4⋊C4×C43—21no—
31C2×C4⋊C4×C43D412yes—
32C2×C4⋊C4×C43D411yescharacteristic
33C2×C22⋊C4×C43—22no—
34C2×C22⋊C4×C43—22no—
35C2×C22⋊C4×C43—21no—
36C2×C42×C43C2311yescharacteristic
37#103×C43—44no—
38#103×C43—42no—
39#95×C43—22no—
40#95×C43—21no—
41#95×C43—22no—
42#95×C43—22no—
43C24×C43—21no—
44C2×Q8×C43—22no—
45C2×Q8×C43—22no—
46C2×Q8×C43—22no—
47C2×Q8×C43—41no—
48C2×Q8×C43—42no—
49C2×Q8×C43—42no—
50C2×Q8×C43—41no—
51C2×Q8×C43—41no—
52C2×Q8×C43—41no—
53C2×Q8×C43—41no—
54C2×D4×C43—21no—
55C2×D4×C43—41no—
56C2×D4×C43—41no—
57C2×D4×C43SD1612yes—
58C22×C4×C43—22no—
59C22×C4×C43—21no—
60C22×C4×C43—22no—
61C22×C4×C43—41no—
62C22×C4×C43—81no—
63C22×C4×C43—82no—
64C22×C4×C43C2×D411yescharacteristic
65C22×C4×C43C2×D412yes—
66SD16×C43—48no—
67C2×C8×C43—22no—
68C2×C8×C43—41no—
69C2×C8×C43—41no—
70C2×C8×C43—42no—
71C2×C8×C43—42no—
72C2×C8×C43—42no—
73C4⋊C4×C43—24no—
74C4⋊C4×C43—41no—
75C4⋊C4×C43—42no—
76C4⋊C4×C43—42no—
77C4⋊C4×C43—81no—
78C22⋊C4×C43—42no—
79C22⋊C4×C43—42no—
80C22⋊C4×C43—82no—
81C22⋊C4×C43—81no—
82C42×C43—41no—
83C23×C43—22no—
84C23×C43—42no—
85C23×C43—41no—
86C23×C43—42no—
87C23×C43—41no—
88C23×C43#12011yescharacteristic
89Q8×C43—42no—
90Q8×C43—42no—
91Q8×C43—44no—
92Q8×C43—82no—
93Q8×C43—81no—
94Q8×C43—81no—
95D4×C43—42no—
96D4×C43—81no—
97C2×C4×C43—21no—
98C2×C4×C43—22no—
99C2×C4×C43—22no—
100C2×C4×C43—21no—
101C2×C4×C43—42no—
102C2×C4×C43—42no—
103C2×C4×C43—41no—
104C2×C4×C43—42no—
105C2×C4×C43—42no—
106C2×C4×C43—42no—
107C2×C4×C43—42no—
108C2×C4×C43—42no—
109C2×C4×C43—42no—
110C2×C4×C43—84no—
111C2×C4×C43—81no—
112C2×C4×C43—81no—
113C2×C4×C43C2×SD1611yescharacteristic
114C2×C4×C43#13512yes—
115C2×C4×C43#13711yescharacteristic
116C2×C4×C43#13712yes—
117C8×C43—42no—
118C8×C43—82no—
119#7755C4311yesmaximal, characteristic, direct product factor, Sylow
120C22×C43—42no—
121C22×C43—44no—
122C22×C43—82no—
123C22×C43—81no—
124C22×C43—81no—
125C22×C43#44811yescharacteristic
126C22×C43#45212yes—
127C22×C43#45311yescharacteristic
128C22×C43#45512yes—
129C22×C43B(4,𝔽2)11yescharacteristic
130C4×C43—21no—
131C4×C43—21no—
132C4×C43—22no—
133C4×C43—22no—
134C4×C43—82no—
135C4×C43—82no—
136C4×C43—81no—
137C4×C43—82no—
138#2804C2×C4311yescharacteristic
139#2024C2×C4312yescomplemented
140#2013C2×C4311yescharacteristic
141#1272C2×C4312yescomplemented
142#1270C2×C4311yescharacteristic
143C2×C43—82no—
144C2×C43#159611yescharacteristic
145C2×C43#160612yes—
146C2×C43#163011yescharacteristic
147C2×C43#164312yes—
148C2×C43#165911yescharacteristic
149C22×SD16—21no—
150C2×C4⋊Q8C22×C4311yescharacteristic
151C2×#103—22no—
152C2×#103—21no—
153#400—21no—
154#393—22no—
155#391C22×C4312yes—
156#390C22×C4311yescharacteristic
157#386—21no—
158#385—22no—
159#340—22no—
160#336C22×C4311yescharacteristic
161#336C22×C4312yes—
162C43#775511yescharacteristic, direct product factor, Sylow
163C22×Q8—21no—
164C22×Q8D4×C4312yes—
165C22×D4D4×C4311yescharacteristic
166C23×C4—21no—
167C2×SD16—42no—
168C2×SD16—42no—
169C2×SD16—42no—
170C22×C8—21no—
171C22×C8—22no—
172C4⋊Q8—42no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4D4×C4312yes—
176C2×C4⋊C4D4×C4311yescharacteristic
177C2×C22⋊C4—22no—
178C2×C22⋊C4—22no—
179C2×C22⋊C4—21no—
180C2×C42C23×C4311yescharacteristic
181#103—44no—
182#103—42no—
183#95—22no—
184#95—21no—
185#95—22no—
186#95—22no—
187C24—21no—
188C2×Q8—22no—
189C2×Q8—22no—
190C2×Q8—22no—
191C2×Q8—41no—
192C2×Q8—42no—
193C2×Q8—42no—
194C2×Q8—41no—
195C2×Q8—41no—
196C2×Q8—41no—
197C2×Q8—41no—
198C2×D4—21no—
199C2×D4—41no—
200C2×D4—41no—
201C2×D4SD16×C4312yes—
202C22×C4—22no—
203C22×C4—21no—
204C22×C4—22no—
205C22×C4—41no—
206C22×C4—81no—
207C22×C4—82no—
208C22×C4C2×D4×C4311yescharacteristic
209C22×C4C2×D4×C4312yes—
210SD16—48no—
211C2×C8—22no—
212C2×C8—41no—
213C2×C8—41no—
214C2×C8—42no—
215C2×C8—42no—
216C2×C8—42no—
217C4⋊C4—24no—
218C4⋊C4—41no—
219C4⋊C4—42no—
220C4⋊C4—42no—
221C4⋊C4—81no—
222C22⋊C4—42no—
223C22⋊C4—42no—
224C22⋊C4—82no—
225C22⋊C4—81no—
226C42—41no—
227C23—22no—
228C23—42no—
229C23—41no—
230C23—42no—
231C23—41no—
232C23#120×C4311yescharacteristic
233Q8—42no—
234Q8—42no—
235Q8—44no—
236Q8—82no—
237Q8—81no—
238Q8—81no—
239D4—42no—
240D4—81no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—84no—
255C2×C4—81no—
256C2×C4—81no—
257C2×C4C2×SD16×C4311yescharacteristic
258C2×C4#135×C4312yes—
259C2×C4#137×C4311yescharacteristic
260C2×C4#137×C4312yes—
261C8—42no—
262C8—82no—
263C22—42no—
264C22—44no—
265C22—82no—
266C22—81no—
267C22—81no—
268C22C43×#44811yescharacteristic
269C22C43×#45212yes—
270C22C43×#45311yescharacteristic
271C22C43×#45512yes—
272C22C43×B(4,𝔽2)11yescharacteristic
273C4—21no—
274C4—21no—
275C4—22no—
276C4—22no—
277C4—82no—
278C4—82no—
279C4—81no—
280C4—82no—
281C2—82no—
282C2C43×#159611yescharacteristic
283C2C43×#160612yes—
284C2C43×#163011yescharacteristic
285C2C43×#164312yes—
286C2C43×#165911yescharacteristic
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×#2024C2semidirect
4. C43×#1272C2semidirect
119. #7755C43direct (N × H)
139. #2024C2×C43semidirect
141. #1272C2×C43semidirect
162. C43#7755direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#28042
C43×#20242
C43×#20132
C43×#12722
C43×#12702
#775543