Finite Group Databasebeta

← C43×#13374 #24933391

Subgroups — C43×#13374 #24933391

Order 11008.

360 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3163C211yesmaximal, characteristic, complemented
2C43×#2145C211yesmaximal, characteristic
3C2×C43×#360C211yesmaximal, characteristic
4C43×#1976C211yesmaximal, characteristic
5C43×#1386C211yesmaximal, characteristic, complemented
6C43×#1384C211yesmaximal, characteristic, complemented
7C43×#1378C211yesmaximal, characteristic, complemented
8C2×#135×C43C2211yescharacteristic
9C43×#544—21no—
10C2×M32×C43C2211yescharacteristic
11C2×M32×C43C2211yescharacteristic
12C43×#501—22no—
13C43×#499—21no—
14C43×#498—21no—
15C43×#428—21no—
16C43×#427C2211yescharacteristic
17C43×#427C2211yescharacteristic
18C2×#106×C43C2211yescharacteristic
19C43×#421—21no—
20C43×#410—21no—
21C43×#405C2211yescharacteristic
22C43×#360—22no—
23C43×#360—21no—
24C43×#360—21no—
25C2×#41×C43—21no—
26#135×C43—21no—
27#135×C43—21no—
28#135×C43—21no—
29#135×C43—21no—
30C2×Q16×C43Q811yescharacteristic, complemented
31C2×SD16×C43—21no—
32C2×D8×C43Q811yescharacteristic, complemented
33C2×M16×C43D411yescharacteristic
34C22×C8×C43C2311yescharacteristic
35C4⋊Q8×C43—22no—
36C4⋊Q8×C43—41no—
37#125×C43—22no—
38#125×C43—41no—
39C22⋊Q8×C43—42no—
40#117×C43—21no—
41#117×C43—21no—
42#117×C43D411yescharacteristic
43C2×C4⋊C4×C43—21no—
44M32×C43—21no—
45M32×C43—21no—
46M32×C43—21no—
47M32×C43—21no—
48C2×C16×C43—21no—
49C2×C16×C43—21no—
50#107×C43—22no—
51#107×C43—21no—
52#107×C43—21no—
53#106×C43—22no—
54#106×C43—21no—
55#106×C43—21no—
56#106×C43D411yescharacteristic
57#106×C43D411yescharacteristic
58#106×C43D412yes—
59#104×C43—42no—
60#99×C43—42no—
61#97×C43—21no—
62C4×C8×C43—21no—
63#41×C43—41no—
64#41×C43—41no—
65#41×C43—41no—
66#41×C43—41no—
67C2×Q8×C43—21no—
68C2×Q8×C43—42no—
69C2×D4×C43—21no—
70C2×D4×C43—41no—
71C22×C4×C43—41no—
72C22×C4×C43—41no—
73C22×C4×C43C2×D411yescharacteristic
74Q16×C43—21no—
75Q16×C43—21no—
76SD16×C43—41no—
77SD16×C43—41no—
78D8×C43—21no—
79D8×C43—21no—
80M16×C43—21no—
81M16×C43SD1612yes—
82C2×C8×C43—21no—
83C2×C8×C43C2×D411yescharacteristic
84C2×C8×C43C2×D411yescharacteristic
85C2×C8×C43C2×Q811yescharacteristic
86C2×C8×C43#4111yescharacteristic
87C2×C8×C43#4111yescharacteristic
88C2×C8×C43#4111yescharacteristic
89C4⋊C4×C43—21no—
90C4⋊C4×C43—22no—
91C4⋊C4×C43—21no—
92C4⋊C4×C43—21no—
93C4⋊C4×C43—42no—
94C4⋊C4×C43—42no—
95C4⋊C4×C43—42no—
96C4⋊C4×C43—41no—
97C4⋊C4×C43—41no—
98C22⋊C4×C43—41no—
99C22⋊C4×C43—41no—
100C22⋊C4×C43D812yes—
101C42×C43—21no—
102C42×C43—41no—
103C42×C43—41no—
104C16×C43—41no—
105C16×C43—41no—
106C23×C43—41no—
107C23×C43C2×D811yescharacteristic
108Q8×C43—41no—
109Q8×C43—41no—
110Q8×C43—162no—
111D4×C43—41no—
112D4×C43—41no—
113D4×C43—81no—
114D4×C43—81no—
115C2×C4×C43—22no—
116C2×C4×C43—41no—
117C2×C4×C43—41no—
118C2×C4×C43—42no—
119C2×C4×C43—41no—
120C2×C4×C43—81no—
121C2×C4×C43—81no—
122C2×C4×C43—81no—
123C2×C4×C43—161no—
124C2×C4×C43#12011yescharacteristic
125C2×C4×C43C22⋊Q811yescharacteristic
126C2×C4×C43#12411yescharacteristic
127C2×C4×C43C2×SD1611yescharacteristic
128C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C43#13711yescharacteristic
130C8×C43—22no—
131C8×C43C22⋊Q811yescharacteristic
132C8×C43C22⋊Q811yescharacteristic
133C8×C43#12411yescharacteristic
134C8×C43#12411yescharacteristic
135#13374C4311yesmaximal, characteristic, direct product factor, Sylow
136C22×C43—41no—
137C22×C43—81no—
138C22×C43—161no—
139C22×C43#44711yescharacteristic
140C22×C43#47411yescharacteristic
141C22×C43#48611yescharacteristic
142C4×C43—42no—
143C4×C43—81no—
144C4×C43—82no—
145C4×C43—81no—
146C4×C43—81no—
147C4×C43—161no—
148C4×C43#39311yescharacteristic
149C4×C43#44811yescharacteristic
150C4×C43#47611yescharacteristic
151C4×C43#48911yescharacteristic
152#3163C2×C4311yescharacteristic, complemented
153#2145C2×C4311yescharacteristic
154C2×#360C2×C4311yescharacteristic
155#1976C2×C4311yescharacteristic
156#1386C2×C4311yescharacteristic, complemented
157#1384C2×C4311yescharacteristic, complemented
158#1378C2×C4311yescharacteristic, complemented
159C2×C43—21no—
160C2×C43—21no—
161C2×C43—21no—
162C2×C43—161no—
163C2×C43#202311yescharacteristic
164C2×#135C22×C4311yescharacteristic
165#544—21no—
166C2×M32C22×C4311yescharacteristic
167C2×M32C22×C4311yescharacteristic
168#501—22no—
169#499—21no—
170#498—21no—
171#428—21no—
172#427C22×C4311yescharacteristic
173#427C22×C4311yescharacteristic
174C2×#106C22×C4311yescharacteristic
175#421—21no—
176#410—21no—
177#405C22×C4311yescharacteristic
178#360—22no—
179#360—21no—
180#360—21no—
181C43#1337411yescharacteristic, direct product factor, Sylow
182C2×#41—21no—
183#135—21no—
184#135—21no—
185#135—21no—
186#135—21no—
187C2×Q16Q8×C4311yescharacteristic, complemented
188C2×SD16—21no—
189C2×D8Q8×C4311yescharacteristic, complemented
190C2×M16D4×C4311yescharacteristic
191C22×C8C23×C4311yescharacteristic
192C4⋊Q8—22no—
193C4⋊Q8—41no—
194#125—22no—
195#125—41no—
196C22⋊Q8—42no—
197#117—21no—
198#117—21no—
199#117D4×C4311yescharacteristic
200C2×C4⋊C4—21no—
201M32—21no—
202M32—21no—
203M32—21no—
204M32—21no—
205C2×C16—21no—
206C2×C16—21no—
207#107—22no—
208#107—21no—
209#107—21no—
210#106—22no—
211#106—21no—
212#106—21no—
213#106D4×C4312yes—
214#106D4×C4311yescharacteristic
215#106D4×C4311yescharacteristic
216#104—42no—
217#99—42no—
218#97—21no—
219C4×C8—21no—
220#41—41no—
221#41—41no—
222#41—41no—
223#41—41no—
224C2×Q8—21no—
225C2×Q8—42no—
226C2×D4—21no—
227C2×D4—41no—
228C22×C4—41no—
229C22×C4—41no—
230C22×C4C2×D4×C4311yescharacteristic
231Q16—21no—
232Q16—21no—
233SD16—41no—
234SD16—41no—
235D8—21no—
236D8—21no—
237M16—21no—
238M16SD16×C4312yes—
239C2×C8—21no—
240C2×C8C2×D4×C4311yescharacteristic
241C2×C8C2×D4×C4311yescharacteristic
242C2×C8C2×Q8×C4311yescharacteristic
243C2×C8#41×C4311yescharacteristic
244C2×C8#41×C4311yescharacteristic
245C2×C8#41×C4311yescharacteristic
246C4⋊C4—21no—
247C4⋊C4—22no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C22⋊C4—41no—
256C22⋊C4—41no—
257C22⋊C4D8×C4312yes—
258C42—21no—
259C42—41no—
260C42—41no—
261C16—41no—
262C16—41no—
263C23—41no—
264C23C2×D8×C4311yescharacteristic
265Q8—41no—
266Q8—41no—
267Q8—162no—
268D4—41no—
269D4—41no—
270D4—81no—
271D4—81no—
272C2×C4—22no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—161no—
281C2×C4#120×C4311yescharacteristic
282C2×C4C22⋊Q8×C4311yescharacteristic
283C2×C4#124×C4311yescharacteristic
284C2×C4C2×SD16×C4311yescharacteristic
285C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
286C2×C4#137×C4311yescharacteristic
287C8—22no—
288C8C22⋊Q8×C4311yescharacteristic
289C8C22⋊Q8×C4311yescharacteristic
290C8#124×C4311yescharacteristic
291C8#124×C4311yescharacteristic
292C22—41no—
293C22—81no—
294C22—161no—
295C22C43×#44711yescharacteristic
296C22C43×#47411yescharacteristic
297C22C43×#48611yescharacteristic
298C4—42no—
299C4—82no—
300C4—81no—
301C4—81no—
302C4—81no—
303C4—161no—
304C4C43×#39311yescharacteristic
305C4C43×#44811yescharacteristic
306C4C43×#47611yescharacteristic
307C4C43×#48911yescharacteristic
308C2—21no—
309C2—21no—
310C2—21no—
311C2—161no—
312C2C43×#202311yescharacteristic
subgroupG/H
center, socleC2×C43#2023
commutator, Frattini, cosocleC22×C8C23×C43
prime radicalC2×#135×C43C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C43 ◁ C22×C4×C43 ◁ C43×#405 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3163C2semidirect
5. C43×#1386C2semidirect
6. C43×#1384C2semidirect
7. C43×#1378C2semidirect
30. C2×Q16×C43Q8semidirect
32. C2×D8×C43Q8semidirect
135. #13374C43direct (N × H)
152. #3163C2×C43semidirect
156. #1386C2×C43semidirect
157. #1384C2×C43semidirect
158. #1378C2×C43semidirect
181. C43#13374direct (N × H)
187. C2×Q16Q8×C43semidirect
189. C2×D8Q8×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#31632
C43×#21452
C2×C43×#3602
C43×#19762
C43×#13862
C43×#13842
C43×#13782
#1337443