Finite Group Databasebeta

← C43×#13246 #24933263

Subgroups — C43×#13246 #24933263

Order 11008.

422 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×SD32×C43C211yesmaximal, characteristic
2C2×C43×#368C211yesmaximal, characteristic, complemented
3C2×C43×#362C211yesmaximal, characteristic, complemented
4C2×C43×#361C211yesmaximal, characteristic
5C43×#2108C211yesmaximal, characteristic, complemented
6C43×#1979C211yesmaximal, characteristic, complemented
7C43×#1978C211yesmaximal, characteristic
8C22×Q16×C43C2211yescharacteristic
9C22×D8×C43C2211yescharacteristic
10C2×SD32×C43—21no—
11C2×SD32×C43—21no—
12C2×SD32×C43—22no—
13C2×SD32×C43C414yescomplemented
14C2×M32×C43C2211yescharacteristic
15C22×C16×C43C2211yescharacteristic
16C2×#108×C43C2211yescharacteristic
17C2×#108×C43C2211yescharacteristic
18C43×#419—21no—
19C43×#418—21no—
20C2×#101×C43—21no—
21C2×#100×C43—21no—
22C43×#405C2211yescharacteristic
23C43×#368—22no—
24C43×#362—22no—
25C43×#361—22no—
26C43×#346—21no—
27C4×C16×C43—21no—
28C22×Q8×C43—21no—
29C22×D4×C43—21no—
30C2×Q16×C43—21no—
31C2×Q16×C43—21no—
32C2×Q16×C43—21no—
33C2×Q16×C43—21no—
34C2×Q16×C43—21no—
35C2×Q16×C43C2×C412yes—
36C2×D8×C43—21no—
37C2×D8×C43—21no—
38C2×D8×C43—21no—
39C2×D8×C43—21no—
40C2×D8×C43—21no—
41C2×D8×C43C2×C412yes—
42C2×M16×C43—21no—
43C2×M16×C43—21no—
44C2×M16×C43D411yescharacteristic
45C22×C8×C43C2311yescharacteristic
46#117×C43D411yescharacteristic
47SD32×C43—24no—
48SD32×C43—24no—
49M32×C43—21no—
50M32×C43D412yes—
51C2×C16×C43—21no—
52C2×C16×C43C2×C412yes—
53C2×C16×C43D411yescharacteristic
54C2×C16×C43D411yescharacteristic
55C2×C16×C43D412yes—
56#108×C43—21no—
57#108×C43—21no—
58#108×C43—21no—
59#108×C43—21no—
60#103×C43—42no—
61#102×C43—42no—
62#101×C43—42no—
63#100×C43—42no—
64#97×C43—21no—
65C4×C8×C43—21no—
66C24×C43—41no—
67C2×Q8×C43—22no—
68C2×Q8×C43—41no—
69C2×Q8×C43—41no—
70C2×Q8×C43—41no—
71C2×Q8×C43—41no—
72C2×Q8×C43—41no—
73C2×D4×C43—22no—
74C2×D4×C43—41no—
75C2×D4×C43—41no—
76C2×D4×C43—41no—
77C2×D4×C43—41no—
78C2×D4×C43—41no—
79C22×C4×C43—41no—
80C22×C4×C43C2×D411yescharacteristic
81Q16×C43—22no—
82Q16×C43—22no—
83Q16×C43—41no—
84Q16×C43—41no—
85D8×C43—22no—
86D8×C43—22no—
87D8×C43—41no—
88D8×C43—41no—
89M16×C43—21no—
90M16×C43—41no—
91M16×C43—41no—
92M16×C43—41no—
93M16×C43—41no—
94M16×C43D812yes—
95C2×C8×C43—21no—
96C2×C8×C43—41no—
97C2×C8×C43—41no—
98C2×C8×C43C22×C411yescharacteristic
99C2×C8×C43C2×D411yescharacteristic
100C2×C8×C43C2×D411yescharacteristic
101C2×C8×C43C2×D411yescharacteristic
102C2×C8×C43#4111yescharacteristic
103C2×C8×C43#4111yescharacteristic
104C4⋊C4×C43D812yes—
105C22⋊C4×C43—21no—
106C42×C43—21no—
107C16×C43—22no—
108C16×C43C22⋊C412yes—
109C16×C43C22⋊C412yes—
110C23×C43—42no—
111C23×C43—81no—
112C23×C43—81no—
113C23×C43—162no—
114C23×C43#13511yescharacteristic
115Q8×C43—42no—
116Q8×C43—42no—
117Q8×C43—81no—
118Q8×C43—81no—
119D4×C43—42no—
120D4×C43—42no—
121D4×C43—81no—
122D4×C43—81no—
123C2×C4×C43—22no—
124C2×C4×C43—42no—
125C2×C4×C43—81no—
126C2×C4×C43—81no—
127C2×C4×C43C4×D411yescharacteristic
128C2×C4×C43#12111yescharacteristic
129C2×C4×C43#12711yescharacteristic
130C2×C4×C43C2×D811yescharacteristic
131C2×C4×C43C2×D811yescharacteristic
132C2×C4×C43#13511yescharacteristic
133C8×C43—22no—
134C8×C43—81no—
135C8×C43—81no—
136C8×C43C2×C22⋊C411yescharacteristic
137C8×C43C4×D411yescharacteristic
138C8×C43#12111yescharacteristic
139C8×C43#12411yescharacteristic
140#13246C4311yesmaximal, characteristic, direct product factor, Sylow
141C22×C43—22no—
142C22×C43—82no—
143C22×C43—162no—
144C22×C43—162no—
145C22×C43—162no—
146C22×C43C4×D811yescharacteristic
147C22×C43#46611yescharacteristic
148C22×C43#49511yescharacteristic
149C4×C43—42no—
150C4×C43—82no—
151C4×C43#39011yescharacteristic
152C4×C43C4×D811yescharacteristic
153C4×C43#46611yescharacteristic
154C4×C43#49311yescharacteristic
155C22×SD32C2×C4311yescharacteristic
156C2×#368C2×C4311yescharacteristic, complemented
157C2×#362C2×C4311yescharacteristic, complemented
158C2×#361C2×C4311yescharacteristic
159#2108C2×C4311yescharacteristic, complemented
160#1979C2×C4311yescharacteristic, complemented
161#1978C2×C4311yescharacteristic
162C2×C43—21no—
163C2×C43—21no—
164C2×C43—162no—
165C2×C43#197011yescharacteristic
166C2×C43#222312yes—
167C22×Q16C22×C4311yescharacteristic
168C22×D8C22×C4311yescharacteristic
169C2×SD32—21no—
170C2×SD32—21no—
171C2×SD32—22no—
172C2×SD32C4×C4314yescomplemented
173C2×M32C22×C4311yescharacteristic
174C22×C16C22×C4311yescharacteristic
175C2×#108C22×C4311yescharacteristic
176C2×#108C22×C4311yescharacteristic
177#419—21no—
178#418—21no—
179C2×#101—21no—
180C2×#100—21no—
181#405C22×C4311yescharacteristic
182#368—22no—
183#362—22no—
184#361—22no—
185#346—21no—
186C4×C16—21no—
187C43#1324611yescharacteristic, direct product factor, Sylow
188C22×Q8—21no—
189C22×D4—21no—
190C2×Q16—21no—
191C2×Q16—21no—
192C2×Q16—21no—
193C2×Q16—21no—
194C2×Q16—21no—
195C2×Q16C2×C4×C4312yes—
196C2×D8—21no—
197C2×D8—21no—
198C2×D8—21no—
199C2×D8—21no—
200C2×D8—21no—
201C2×D8C2×C4×C4312yes—
202C2×M16—21no—
203C2×M16—21no—
204C2×M16D4×C4311yescharacteristic
205C22×C8C23×C4311yescharacteristic
206#117D4×C4311yescharacteristic
207SD32—24no—
208SD32—24no—
209M32—21no—
210M32D4×C4312yes—
211C2×C16—21no—
212C2×C16C2×C4×C4312yes—
213C2×C16D4×C4311yescharacteristic
214C2×C16D4×C4311yescharacteristic
215C2×C16D4×C4312yes—
216#108—21no—
217#108—21no—
218#108—21no—
219#108—21no—
220#103—42no—
221#102—42no—
222#101—42no—
223#100—42no—
224#97—21no—
225C4×C8—21no—
226C24—41no—
227C2×Q8—22no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8—41no—
233C2×D4—22no—
234C2×D4—41no—
235C2×D4—41no—
236C2×D4—41no—
237C2×D4—41no—
238C2×D4—41no—
239C22×C4—41no—
240C22×C4C2×D4×C4311yescharacteristic
241Q16—22no—
242Q16—22no—
243Q16—41no—
244Q16—41no—
245D8—22no—
246D8—22no—
247D8—41no—
248D8—41no—
249M16—21no—
250M16—41no—
251M16—41no—
252M16—41no—
253M16—41no—
254M16D8×C4312yes—
255C2×C8—21no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8C22×C4×C4311yescharacteristic
259C2×C8C2×D4×C4311yescharacteristic
260C2×C8C2×D4×C4311yescharacteristic
261C2×C8C2×D4×C4311yescharacteristic
262C2×C8#41×C4311yescharacteristic
263C2×C8#41×C4311yescharacteristic
264C4⋊C4D8×C4312yes—
265C22⋊C4—21no—
266C42—21no—
267C16—22no—
268C16C22⋊C4×C4312yes—
269C16C22⋊C4×C4312yes—
270C23—42no—
271C23—81no—
272C23—81no—
273C23—162no—
274C23#135×C4311yescharacteristic
275Q8—42no—
276Q8—42no—
277Q8—81no—
278Q8—81no—
279D4—42no—
280D4—42no—
281D4—81no—
282D4—81no—
283C2×C4—22no—
284C2×C4—42no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4C4×D4×C4311yescharacteristic
288C2×C4#121×C4311yescharacteristic
289C2×C4#127×C4311yescharacteristic
290C2×C4C2×D8×C4311yescharacteristic
291C2×C4C2×D8×C4311yescharacteristic
292C2×C4#135×C4311yescharacteristic
293C8—22no—
294C8—81no—
295C8—81no—
296C8C2×C22⋊C4×C4311yescharacteristic
297C8C4×D4×C4311yescharacteristic
298C8#121×C4311yescharacteristic
299C8#124×C4311yescharacteristic
300C22—22no—
301C22—82no—
302C22—162no—
303C22—162no—
304C22—162no—
305C22C4×D8×C4311yescharacteristic
306C22C43×#46611yescharacteristic
307C22C43×#49511yescharacteristic
308C4—42no—
309C4—82no—
310C4C43×#39011yescharacteristic
311C4C4×D8×C4311yescharacteristic
312C4C43×#46611yescharacteristic
313C4C43×#49311yescharacteristic
314C2—21no—
315C2—21no—
316C2—162no—
317C2C43×#197011yescharacteristic
318C2C43×#222312yes—
subgroupG/H
center, socleC22×C43#466
commutatorC2×C8C22×C4×C43
Frattini, cosocleC22×C8C23×C43
prime radicalC22×D8×C43C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C22×C4×C43 ◁ C43×#405 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C43×#368C2semidirect
3. C2×C43×#362C2semidirect
5. C43×#2108C2semidirect
6. C43×#1979C2semidirect
13. C2×SD32×C43C4semidirect
140. #13246C43direct (N × H)
156. C2×#368C2×C43semidirect
157. C2×#362C2×C43semidirect
159. #2108C2×C43semidirect
160. #1979C2×C43semidirect
172. C2×SD32C4×C43semidirect
187. C43#13246direct (N × H)

Maximal subgroups

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

subgroupindex
C22×SD32×C432
C2×C43×#3682
C2×C43×#3622
C2×C43×#3612
C43×#21082
C43×#19792
C43×#19782
#1324643