Finite Group Databasebeta

← C43×#13248 #24933265

Subgroups — C43×#13248 #24933265

Order 11008.

394 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#510C211yesmaximal, characteristic
2C43×#2155C211yesmaximal, characteristic, complemented
3C43×#2143C211yesmaximal, characteristic
4C43×#2141C211yesmaximal, characteristic, complemented
5C43×#2110C211yesmaximal, characteristic, complemented
6C43×#1979C211yesmaximal, characteristic, complemented
7C43×#1976C211yesmaximal, characteristic
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
17C43×#427C2211yescharacteristic
18C43×#421—21no—
19C43×#419—21no—
20C2×#101×C43—21no—
21C43×#410—21no—
22C43×#405C2211yescharacteristic
23C43×#365—22no—
24C43×#359—22no—
25C43×#358—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—
43C2×M16×C43D411yescharacteristic
44C22×C8×C43C2311yescharacteristic
45#117×C43—21no—
46#117×C43D411yescharacteristic
47Q32×C43—24no—
48SD32×C43—24no—
49M32×C43—21no—
50M32×C43—21no—
51M32×C43D412yes—
52M32×C43D412yes—
53C2×C16×C43C2×C412yes—
54C2×C16×C43D412yes—
55#108×C43—21no—
56#108×C43—21no—
57#107×C43—21no—
58#106×C43—21no—
59#104×C43—42no—
60#103×C43—42no—
61#101×C43—42no—
62#99×C43—42no—
63#97×C43—21no—
64C4×C8×C43—21no—
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—41no—
79C22×C4×C43—41no—
80C22×C4×C43C2×D411yescharacteristic
81Q16×C43—22no—
82Q16×C43—21no—
83Q16×C43—22no—
84Q16×C43—21no—
85Q16×C43—41no—
86Q16×C43—41no—
87SD16×C43—41no—
88SD16×C43—41no—
89D8×C43—21no—
90D8×C43—21no—
91M16×C43—21no—
92M16×C43—21no—
93M16×C43—41no—
94M16×C43—41no—
95C2×C8×C43—21no—
96C2×C8×C43—41no—
97C2×C8×C43C22×C411yescharacteristic
98C2×C8×C43C2×D411yescharacteristic
99C2×C8×C43C2×D411yescharacteristic
100C2×C8×C43C2×D411yescharacteristic
101C2×C8×C43#4111yescharacteristic
102C2×C8×C43#4111yescharacteristic
103C4⋊C4×C43—21no—
104C4⋊C4×C43—41no—
105C22⋊C4×C43—21no—
106C22⋊C4×C43—41no—
107C42×C43—21no—
108C42×C43—41no—
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—41no—
124C2×C4×C43—42no—
125C2×C4×C43—41no—
126C2×C4×C43—81no—
127C2×C4×C43—81no—
128C2×C4×C43—81no—
129C2×C4×C43—81no—
130C2×C4×C43—81no—
131C2×C4×C43C4×D411yescharacteristic
132C2×C4×C43#12111yescharacteristic
133C2×C4×C43#12711yescharacteristic
134C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
137C8×C43—41no—
138C8×C43—81no—
139C8×C43C2×C22⋊C411yescharacteristic
140C8×C43C4×D411yescharacteristic
141C8×C43#12111yescharacteristic
142C8×C43#12411yescharacteristic
143#13248C4311yesmaximal, characteristic, direct product factor, Sylow
144C22×C43—41no—
145C22×C43—81no—
146C22×C43—161no—
147C22×C43#44211yescharacteristic
148C22×C43#46911yescharacteristic
149C22×C43#49611yescharacteristic
150C4×C43—81no—
151C4×C43—81no—
152C4×C43—82no—
153C4×C43—161no—
154C4×C43#39011yescharacteristic
155C4×C43#44211yescharacteristic
156C4×C43#46911yescharacteristic
157C4×C43#49611yescharacteristic
158C2×#510C2×C4311yescharacteristic
159#2155C2×C4311yescharacteristic, complemented
160#2143C2×C4311yescharacteristic
161#2141C2×C4311yescharacteristic, complemented
162#2110C2×C4311yescharacteristic, complemented
163#1979C2×C4311yescharacteristic, complemented
164#1976C2×C4311yescharacteristic
165C2×C43—21no—
166C2×C43—21no—
167C2×C43—21no—
168C2×C43—161no—
169C2×C43#197211yescharacteristic
170C2×#135C22×C4311yescharacteristic
171C22×Q16C22×C4311yescharacteristic
172#510—22no—
173#510—22no—
174C2×Q32C4×C4312yescomplemented
175C2×SD32C4×C4312yescomplemented
176C2×M32C22×C4311yescharacteristic
177C2×M32C22×C4311yescharacteristic
178C2×#108C22×C4311yescharacteristic
179#427C22×C4311yescharacteristic
180#421—21no—
181#419—21no—
182C2×#101—21no—
183#410—21no—
184#405C22×C4311yescharacteristic
185#365—22no—
186#359—22no—
187#358—22no—
188#347—22no—
189C43#1324811yescharacteristic, direct product factor, Sylow
190C2×#41—21no—
191C22×Q8—21no—
192#135—21no—
193#135—21no—
194#135—21no—
195#135—21no—
196C2×Q16—21no—
197C2×Q16—21no—
198C2×Q16—21no—
199C2×Q16—21no—
200C2×Q16—21no—
201C2×Q16C2×C4×C4312yes—
202C2×Q16C2×C4×C4311yescharacteristic
203C2×SD16—21no—
204C2×D8C2×C4×C4311yescharacteristic
205C2×M16—21no—
206C2×M16D4×C4311yescharacteristic
207C22×C8C23×C4311yescharacteristic
208#117—21no—
209#117D4×C4311yescharacteristic
210Q32—24no—
211SD32—24no—
212M32—21no—
213M32—21no—
214M32D4×C4312yes—
215M32D4×C4312yes—
216C2×C16C2×C4×C4312yes—
217C2×C16D4×C4312yes—
218#108—21no—
219#108—21no—
220#107—21no—
221#106—21no—
222#104—42no—
223#103—42no—
224#101—42no—
225#99—42no—
226#97—21no—
227C4×C8—21no—
228#41—41no—
229#41—41no—
230#41—41no—
231#41—41no—
232C2×Q8—21no—
233C2×Q8—22no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8—41no—
238C2×Q8—41no—
239C2×D4—21no—
240C2×D4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4C2×D4×C4311yescharacteristic
244Q16—22no—
245Q16—21no—
246Q16—22no—
247Q16—21no—
248Q16—41no—
249Q16—41no—
250SD16—41no—
251SD16—41no—
252D8—21no—
253D8—21no—
254M16—21no—
255M16—21no—
256M16—41no—
257M16—41no—
258C2×C8—21no—
259C2×C8—41no—
260C2×C8C22×C4×C4311yescharacteristic
261C2×C8C2×D4×C4311yescharacteristic
262C2×C8C2×D4×C4311yescharacteristic
263C2×C8C2×D4×C4311yescharacteristic
264C2×C8#41×C4311yescharacteristic
265C2×C8#41×C4311yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—41no—
268C22⋊C4—21no—
269C22⋊C4—41no—
270C42—21no—
271C42—41no—
272C16—22no—
273C16C22⋊C4×C4314yes—
274C23—41no—
275C23AGL(1,ℤ/8)×C4311yescharacteristic
276Q8—41no—
277Q8—42no—
278Q8—42no—
279Q8—41no—
280Q8—81no—
281Q8—81no—
282D4—41no—
283D4—41no—
284D4—81no—
285D4—81no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—41no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4C4×D4×C4311yescharacteristic
295C2×C4#121×C4311yescharacteristic
296C2×C4#127×C4311yescharacteristic
297C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
298C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
299C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
300C8—41no—
301C8—81no—
302C8C2×C22⋊C4×C4311yescharacteristic
303C8C4×D4×C4311yescharacteristic
304C8#121×C4311yescharacteristic
305C8#124×C4311yescharacteristic
306C22—41no—
307C22—81no—
308C22—161no—
309C22C43×#44211yescharacteristic
310C22C43×#46911yescharacteristic
311C22C43×#49611yescharacteristic
312C4—81no—
313C4—81no—
314C4—82no—
315C4—161no—
316C4C43×#39011yescharacteristic
317C4C43×#44211yescharacteristic
318C4C43×#46911yescharacteristic
319C4C43×#49611yescharacteristic
320C2—21no—
321C2—21no—
322C2—21no—
323C2—161no—
324C2C43×#197211yescharacteristic
subgroupG/H
center, socleC2×C43#1972
commutatorC2×C8C22×C4×C43
Frattini, cosocleC22×C8C23×C43
prime radicalC2×#135×C43C22
LCSG ▷ C2×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
2. C43×#2155C2semidirect
4. C43×#2141C2semidirect
5. C43×#2110C2semidirect
6. C43×#1979C2semidirect
12. C2×Q32×C43C4semidirect
13. C2×SD32×C43C4semidirect
143. #13248C43direct (N × H)
159. #2155C2×C43semidirect
161. #2141C2×C43semidirect
162. #2110C2×C43semidirect
163. #1979C2×C43semidirect
174. C2×Q32C4×C43semidirect
175. C2×SD32C4×C43semidirect
189. C43#13248direct (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
C43×#21552
C43×#21432
C43×#21412
C43×#21102
C43×#19792
C43×#19762
#1324843