Finite Group Databasebeta

← C43×#12153 #24932170

Subgroups — C43×#12153 #24932170

Order 11008.

424 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 74 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×#2582C211yesmaximal, characteristic, complemented
2C43×#2039C211yesmaximal, characteristic
3C43×#1610C212yesmaximal
4C43×#1346C212yesmaximal, complemented
5C43×#1325C211yesmaximal, characteristic, complemented
6C43×#537C2211yescharacteristic
7C2×C4×Q8×C43—21no—
8C43×#480—22no—
9C2×#104×C43—21no—
10C43×#417—21no—
11C43×#398—21no—
12C43×#398C2212yes—
13C43×#391—22no—
14C43×#389—22no—
15C43×#384C2211yescharacteristic
16C43×#343C2211yescharacteristic
17C43×#327—22no—
18C43×#324C2212yes—
19C2×#41×C43—21no—
20C22×Q8×C43—21no—
21C2×M16×C43—21no—
22C22⋊Q8×C43—41no—
23#121×C43—22no—
24#121×C43—41no—
25C4×Q8×C43—42no—
26C4×Q8×C43—42no—
27C2×C4⋊C4×C43—21no—
28C2×C4⋊C4×C43—22no—
29C2×C4⋊C4×C43—22no—
30C2×C4⋊C4×C43—21no—
31C2×C4⋊C4×C43D411yescharacteristic
32C2×C4⋊C4×C43D412yes—
33C2×C4⋊C4×C43C2311yescharacteristic
34C2×C42×C43—22no—
35C2×C42×C43D411yescharacteristic
36#107×C43—42no—
37#104×C43—42no—
38#103×C43—41no—
39#102×C43—41no—
40#102×C43—42no—
41C22⋊C8×C43—22no—
42#95×C43—22no—
43#95×C43—21no—
44#95×C43—22no—
45#95×C43D412yes—
46#41×C43—41no—
47#41×C43—41no—
48#41×C43—41no—
49#41×C43—41no—
50C2×Q8×C43—24no—
51C2×Q8×C43—21no—
52C2×Q8×C43—42no—
53C2×Q8×C43—42no—
54C2×D4×C43—21no—
55C2×D4×C43—22no—
56C2×D4×C43—41no—
57C22×C4×C43—21no—
58C22×C4×C43—22no—
59C22×C4×C43—21no—
60C22×C4×C43—22no—
61C22×C4×C43—41no—
62C22×C4×C43C2×D411yescharacteristic
63C22×C4×C43C2×D412yes—
64M16×C43—41no—
65M16×C43—41no—
66C2×C8×C43—42no—
67C2×C8×C43—41no—
68C4⋊C4×C43—22no—
69C4⋊C4×C43—41no—
70C4⋊C4×C43—41no—
71C4⋊C4×C43—42no—
72C4⋊C4×C43—44no—
73C4⋊C4×C43—42no—
74C4⋊C4×C43—42no—
75C4⋊C4×C43—42no—
76C4⋊C4×C43—81no—
77C22⋊C4×C43—42no—
78C42×C43—21no—
79C42×C43—44no—
80C42×C43D812yes—
81C23×C43—41no—
82C23×C43#12011yescharacteristic
83Q8×C43—48no—
84Q8×C43—41no—
85Q8×C43—41no—
86D4×C43—41no—
87D4×C43—41no—
88D4×C43—82no—
89D4×C43—81no—
90D4×C43—81no—
91C2×C4×C43—22no—
92C2×C4×C43—22no—
93C2×C4×C43—22no—
94C2×C4×C43—21no—
95C2×C4×C43—21no—
96C2×C4×C43—24no—
97C2×C4×C43—22no—
98C2×C4×C43—42no—
99C2×C4×C43—42no—
100C2×C4×C43—42no—
101C2×C4×C43—42no—
102C2×C4×C43—42no—
103C2×C4×C43—42no—
104C2×C4×C43—41no—
105C2×C4×C43—42no—
106C2×C4×C43—41no—
107C2×C4×C43—81no—
108C2×C4×C43—81no—
109C2×C4×C43C2×D811yescharacteristic
110C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
111C8×C43—81no—
112C8×C43—82no—
113#12153C4311yesmaximal, characteristic, direct product factor, Sylow
114C22×C43—21no—
115C22×C43—21no—
116C22×C43—81no—
117C22×C43—81no—
118C22×C43—81no—
119C22×C43#44711yescharacteristic
120C22×C43#45411yescharacteristic
121C22×C43B(4,𝔽2)11yescharacteristic
122C4×C43—24no—
123C4×C43—21no—
124C4×C43—21no—
125C4×C43—44no—
126C4×C43—42no—
127C4×C43—82no—
128C4×C43—81no—
129C4×C43—81no—
130#2582C2×C4311yescharacteristic, complemented
131#2039C2×C4311yescharacteristic
132#1610C2×C4312yes—
133#1346C2×C4312yescomplemented
134#1325C2×C4311yescharacteristic, complemented
135C2×C43—21no—
136C2×C43—21no—
137C2×C43—161no—
138C2×C43#159811yescharacteristic
139C2×C43#219811yescharacteristic
140C2×C43#220511yescharacteristic
141#537C22×C4311yescharacteristic
142C2×C4×Q8—21no—
143#480—22no—
144C2×#104—21no—
145#417—21no—
146#398—21no—
147#398C22×C4312yes—
148#391—22no—
149#389—22no—
150#384C22×C4311yescharacteristic
151#343C22×C4311yescharacteristic
152#327—22no—
153#324C22×C4312yes—
154C43#1215311yescharacteristic, direct product factor, Sylow
155C2×#41—21no—
156C22×Q8—21no—
157C2×M16—21no—
158C22⋊Q8—41no—
159#121—22no—
160#121—41no—
161C4×Q8—42no—
162C4×Q8—42no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4D4×C4311yescharacteristic
168C2×C4⋊C4D4×C4312yes—
169C2×C4⋊C4C23×C4311yescharacteristic
170C2×C42—22no—
171C2×C42D4×C4311yescharacteristic
172#107—42no—
173#104—42no—
174#103—41no—
175#102—41no—
176#102—42no—
177C22⋊C8—22no—
178#95—22no—
179#95—21no—
180#95—22no—
181#95D4×C4312yes—
182#41—41no—
183#41—41no—
184#41—41no—
185#41—41no—
186C2×Q8—24no—
187C2×Q8—21no—
188C2×Q8—42no—
189C2×Q8—42no—
190C2×D4—21no—
191C2×D4—22no—
192C2×D4—41no—
193C22×C4—21no—
194C22×C4—22no—
195C22×C4—21no—
196C22×C4—22no—
197C22×C4—41no—
198C22×C4C2×D4×C4311yescharacteristic
199C22×C4C2×D4×C4312yes—
200M16—41no—
201M16—41no—
202C2×C8—42no—
203C2×C8—41no—
204C4⋊C4—22no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C4⋊C4—44no—
210C4⋊C4—42no—
211C4⋊C4—42no—
212C4⋊C4—81no—
213C22⋊C4—42no—
214C42—21no—
215C42—44no—
216C42D8×C4312yes—
217C23—41no—
218C23#120×C4311yescharacteristic
219Q8—48no—
220Q8—41no—
221Q8—41no—
222D4—41no—
223D4—41no—
224D4—82no—
225D4—81no—
226D4—81no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—24no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—41no—
243C2×C4—81no—
244C2×C4—81no—
245C2×C4C2×D8×C4311yescharacteristic
246C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
247C8—81no—
248C8—82no—
249C22—21no—
250C22—21no—
251C22—81no—
252C22—81no—
253C22—81no—
254C22C43×#44711yescharacteristic
255C22C43×#45411yescharacteristic
256C22C43×B(4,𝔽2)11yescharacteristic
257C4—24no—
258C4—21no—
259C4—21no—
260C4—44no—
261C4—42no—
262C4—82no—
263C4—81no—
264C4—81no—
265C2—21no—
266C2—21no—
267C2—161no—
268C2C43×#159811yescharacteristic
269C2C43×#219811yescharacteristic
270C2C43×#220511yescharacteristic
subgroupG/H
center, socleC22×C43B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C43
prime radicalC43×#537C22
LCSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C43 ◁ C2×C4⋊C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#2582C2semidirect
4. C43×#1346C2semidirect
5. C43×#1325C2semidirect
113. #12153C43direct (N × H)
130. #2582C2×C43semidirect
133. #1346C2×C43semidirect
134. #1325C2×C43semidirect
154. C43#12153direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#25822
C43×#20392
C43×#16102
C43×#13462
C43×#13252
#1215343