Finite Group Databasebeta

← C43×#13250 #24933267

Subgroups — C43×#13250 #24933267

Order 11008.

408 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#510C211yesmaximal, characteristic
2C2×C43×#365C211yesmaximal, characteristic, complemented
3C2×C43×#362C211yesmaximal, characteristic, complemented
4C2×C43×#360C211yesmaximal, characteristic
5C2×C43×#347C211yesmaximal, characteristic, complemented
6C43×#1975C211yesmaximal, characteristic
7C43×#1971C211yesmaximal, characteristic, complemented
8C2×#135×C43C2211yescharacteristic
9C22×Q16×C43C2211yescharacteristic
10C43×#510—22no—
11C43×#510—22no—
12C2×Q32×C43C412yescomplemented
13C2×SD32×C43C412yescomplemented
14C2×M32×C43C2211yescharacteristic
15C2×M32×C43C2211yescharacteristic
16C2×#108×C43C2211yescharacteristic
17C2×#106×C43C2211yescharacteristic
18C2×#104×C43—21no—
19C2×#103×C43—21no—
20C43×#408—21no—
21C2×#97×C43C2211yescharacteristic
22C43×#391—21no—
23C43×#365—22no—
24C43×#362—22no—
25C43×#360—22no—
26C43×#347—22no—
27C2×#41×C43—21no—
28C22×Q8×C43—21no—
29#135×C43—21no—
30#135×C43—21no—
31#135×C43—21no—
32#135×C43—21no—
33C2×Q16×C43—21no—
34C2×Q16×C43—21no—
35C2×Q16×C43—21no—
36C2×Q16×C43—21no—
37C2×Q16×C43—21no—
38C2×Q16×C43C2×C412yes—
39C2×Q16×C43C2×C411yescharacteristic
40C2×SD16×C43—21no—
41C2×D8×C43C2×C411yescharacteristic
42C2×M16×C43—21no—
43C22×C8×C43D411yescharacteristic
44C22×C8×C43C2311yescharacteristic
45C2×C4⋊C4×C43—21no—
46C2×C42×C43D411yescharacteristic
47Q32×C43—24no—
48SD32×C43—24no—
49M32×C43—21no—
50M32×C43D412yes—
51M32×C43D412yes—
52M32×C43D412yes—
53C2×C16×C43—21no—
54C2×C16×C43C2×C412yes—
55#108×C43—21no—
56#108×C43—21no—
57#106×C43—21no—
58#106×C43—21no—
59#104×C43—42no—
60#103×C43—42no—
61C22⋊C8×C43—42no—
62#97×C43—21no—
63#97×C43—21no—
64#95×C43—42no—
65#41×C43—41no—
66#41×C43—41no—
67#41×C43—41no—
68#41×C43—41no—
69C2×Q8×C43—21no—
70C2×Q8×C43—22no—
71C2×Q8×C43—41no—
72C2×Q8×C43—41no—
73C2×Q8×C43—41no—
74C2×Q8×C43—41no—
75C2×Q8×C43—41no—
76C2×D4×C43—21no—
77C2×D4×C43—41no—
78C22×C4×C43—21no—
79C22×C4×C43—41no—
80C22×C4×C43—41no—
81C22×C4×C43—41no—
82C22×C4×C43C2×D411yescharacteristic
83Q16×C43—22no—
84Q16×C43—21no—
85Q16×C43—22no—
86Q16×C43—21no—
87Q16×C43—41no—
88Q16×C43—41no—
89SD16×C43—41no—
90SD16×C43—41no—
91D8×C43—21no—
92D8×C43—21no—
93M16×C43—41no—
94M16×C43—41no—
95C2×C8×C43—21no—
96C2×C8×C43—21no—
97C2×C8×C43—21no—
98C2×C8×C43—41no—
99C2×C8×C43C22×C411yescharacteristic
100C2×C8×C43C2×D411yescharacteristic
101C2×C8×C43C2×D411yescharacteristic
102C2×C8×C43C2×D411yescharacteristic
103C2×C8×C43#4111yescharacteristic
104C2×C8×C43#4111yescharacteristic
105C4⋊C4×C43—41no—
106C4⋊C4×C43—41no—
107C42×C43—21no—
108C42×C43—21no—
109C16×C43—22no—
110C16×C43C22⋊C414yes—
111C23×C43—41no—
112C23×C43AGL(1,ℤ/8)11yescharacteristic
113Q8×C43—41no—
114Q8×C43—42no—
115Q8×C43—42no—
116Q8×C43—41no—
117Q8×C43—81no—
118Q8×C43—81no—
119D4×C43—41no—
120D4×C43—41no—
121D4×C43—81no—
122D4×C43—81no—
123C2×C4×C43—42no—
124C2×C4×C43—41no—
125C2×C4×C43—42no—
126C2×C4×C43—41no—
127C2×C4×C43—81no—
128C2×C4×C43—81no—
129C2×C4×C43—81no—
130C2×C4×C43—81no—
131C2×C4×C43—82no—
132C2×C4×C43—81no—
133C2×C4×C43C4×D411yescharacteristic
134C2×C4×C43#12111yescharacteristic
135C2×C4×C43#12711yescharacteristic
136C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
139C8×C43—41no—
140C8×C43—81no—
141C8×C43C2×C22⋊C411yescharacteristic
142C8×C43C4×D411yescharacteristic
143C8×C43#12111yescharacteristic
144C8×C43#12411yescharacteristic
145#13250C4311yesmaximal, characteristic, direct product factor, Sylow
146C22×C43—22no—
147C22×C43—82no—
148C22×C43—81no—
149C22×C43#44211yescharacteristic
150C22×C43#46911yescharacteristic
151C22×C43#49611yescharacteristic
152C4×C43—81no—
153C4×C43—81no—
154C4×C43—82no—
155C4×C43—161no—
156C4×C43#39011yescharacteristic
157C4×C43#44211yescharacteristic
158C4×C43#46911yescharacteristic
159C4×C43#49611yescharacteristic
160C2×#510C2×C4311yescharacteristic
161C2×#365C2×C4311yescharacteristic, complemented
162C2×#362C2×C4311yescharacteristic, complemented
163C2×#360C2×C4311yescharacteristic
164C2×#347C2×C4311yescharacteristic, complemented
165#1975C2×C4311yescharacteristic
166#1971C2×C4311yescharacteristic, complemented
167C2×C43—21no—
168C2×C43—21no—
169C2×C43—161no—
170C2×C43#197211yescharacteristic
171C2×C43#218012yes—
172C2×#135C22×C4311yescharacteristic
173C22×Q16C22×C4311yescharacteristic
174#510—22no—
175#510—22no—
176C2×Q32C4×C4312yescomplemented
177C2×SD32C4×C4312yescomplemented
178C2×M32C22×C4311yescharacteristic
179C2×M32C22×C4311yescharacteristic
180C2×#108C22×C4311yescharacteristic
181C2×#106C22×C4311yescharacteristic
182C2×#104—21no—
183C2×#103—21no—
184#408—21no—
185C2×#97C22×C4311yescharacteristic
186#391—21no—
187#365—22no—
188#362—22no—
189#360—22no—
190#347—22no—
191C43#1325011yescharacteristic, direct product factor, Sylow
192C2×#41—21no—
193C22×Q8—21no—
194#135—21no—
195#135—21no—
196#135—21no—
197#135—21no—
198C2×Q16—21no—
199C2×Q16—21no—
200C2×Q16—21no—
201C2×Q16—21no—
202C2×Q16—21no—
203C2×Q16C2×C4×C4312yes—
204C2×Q16C2×C4×C4311yescharacteristic
205C2×SD16—21no—
206C2×D8C2×C4×C4311yescharacteristic
207C2×M16—21no—
208C22×C8D4×C4311yescharacteristic
209C22×C8C23×C4311yescharacteristic
210C2×C4⋊C4—21no—
211C2×C42D4×C4311yescharacteristic
212Q32—24no—
213SD32—24no—
214M32—21no—
215M32D4×C4312yes—
216M32D4×C4312yes—
217M32D4×C4312yes—
218C2×C16—21no—
219C2×C16C2×C4×C4312yes—
220#108—21no—
221#108—21no—
222#106—21no—
223#106—21no—
224#104—42no—
225#103—42no—
226C22⋊C8—42no—
227#97—21no—
228#97—21no—
229#95—42no—
230#41—41no—
231#41—41no—
232#41—41no—
233#41—41no—
234C2×Q8—21no—
235C2×Q8—22no—
236C2×Q8—41no—
237C2×Q8—41no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×D4—21no—
242C2×D4—41no—
243C22×C4—21no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4C2×D4×C4311yescharacteristic
248Q16—22no—
249Q16—21no—
250Q16—22no—
251Q16—21no—
252Q16—41no—
253Q16—41no—
254SD16—41no—
255SD16—41no—
256D8—21no—
257D8—21no—
258M16—41no—
259M16—41no—
260C2×C8—21no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—41no—
264C2×C8C22×C4×C4311yescharacteristic
265C2×C8C2×D4×C4311yescharacteristic
266C2×C8C2×D4×C4311yescharacteristic
267C2×C8C2×D4×C4311yescharacteristic
268C2×C8#41×C4311yescharacteristic
269C2×C8#41×C4311yescharacteristic
270C4⋊C4—41no—
271C4⋊C4—41no—
272C42—21no—
273C42—21no—
274C16—22no—
275C16C22⋊C4×C4314yes—
276C23—41no—
277C23AGL(1,ℤ/8)×C4311yescharacteristic
278Q8—41no—
279Q8—42no—
280Q8—42no—
281Q8—41no—
282Q8—81no—
283Q8—81no—
284D4—41no—
285D4—41no—
286D4—81no—
287D4—81no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—41no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—82no—
297C2×C4—81no—
298C2×C4C4×D4×C4311yescharacteristic
299C2×C4#121×C4311yescharacteristic
300C2×C4#127×C4311yescharacteristic
301C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
302C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
303C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
304C8—41no—
305C8—81no—
306C8C2×C22⋊C4×C4311yescharacteristic
307C8C4×D4×C4311yescharacteristic
308C8#121×C4311yescharacteristic
309C8#124×C4311yescharacteristic
310C22—22no—
311C22—82no—
312C22—81no—
313C22C43×#44211yescharacteristic
314C22C43×#46911yescharacteristic
315C22C43×#49611yescharacteristic
316C4—81no—
317C4—81no—
318C4—82no—
319C4—161no—
320C4C43×#39011yescharacteristic
321C4C43×#44211yescharacteristic
322C4C43×#46911yescharacteristic
323C4C43×#49611yescharacteristic
324C2—21no—
325C2—21no—
326C2—161no—
327C2C43×#197211yescharacteristic
328C2C43×#218012yes—
subgroupG/H
center, socleC22×C43#442
commutatorC2×C8C22×C4×C43
Frattini, cosocleC22×C8C23×C43
prime radicalC2×#135×C43C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C22×C4×C43 ◁ C2×#97×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C43×#365C2semidirect
3. C2×C43×#362C2semidirect
5. C2×C43×#347C2semidirect
7. C43×#1971C2semidirect
12. C2×Q32×C43C4semidirect
13. C2×SD32×C43C4semidirect
145. #13250C43direct (N × H)
161. C2×#365C2×C43semidirect
162. C2×#362C2×C43semidirect
164. C2×#347C2×C43semidirect
166. #1971C2×C43semidirect
176. C2×Q32C4×C43semidirect
177. C2×SD32C4×C43semidirect
191. C43#13250direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#5102
C2×C43×#3652
C2×C43×#3622
C2×C43×#3602
C2×C43×#3472
C43×#19752
C43×#19712
#1325043