Finite Group Databasebeta

← C43×#19265 #24939282

Subgroups — C43×#19265 #24939282

Order 11008.

606 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3170C211yesmaximal, characteristic
2C43×#3113C212yesmaximal
3C2×C8×Q8×C43C211yesmaximal, characteristic
4C43×#1680C214yesmaximal, complemented
5C43×#1674C212yesmaximal, complemented
6C43×#1670C212yesmaximal, complemented
7C43×#1568C211yesmaximal, characteristic
8C43×#1552C212yesmaximal
9C43×#533C2212yes—
10C2×C4×Q8×C43C2211yescharacteristic
11C43×#500C2211yescharacteristic
12C43×#494C2211yescharacteristic
13C43×#487C2212yes—
14C43×#483—22no—
15C43×#475C2214yes—
16C43×#467—21no—
17C43×#467—21no—
18C43×#462C2214yes—
19C43×#451—22no—
20C8×Q8×C43—21no—
21C8×Q8×C43—21no—
22C8×Q8×C43C2212yes—
23C8×Q8×C43C2212yes—
24C43×#441—24no—
25C4×Q16×C43—21no—
26C4×Q16×C43—21no—
27C43×#432C2212yes—
28C2×C4⋊C8×C43—21no—
29C2×C4⋊C8×C43C2211yescharacteristic
30C2×C4×C8×C43—21no—
31C2×C4×C8×C43C2211yescharacteristic
32C43×#335C2212yes—
33C43×#334C2212yes—
34C43×#332C2214yes—
35C43×#332C2214yes—
36C22×Q8×C43D411yescharacteristic
37C2×Q16×C43—24no—
38C2×Q16×C43—21no—
39C2×Q16×C43—21no—
40C22×C8×C43—21no—
41C22×C8×C43D411yescharacteristic
42C22×C8×C43D411yescharacteristic
43C4⋊Q8×C43C2312yes—
44C4⋊Q8×C43C2312yes—
45#125×C43—22no—
46C22⋊Q8×C43—22no—
47C22⋊Q8×C43—22no—
48C4×Q8×C43—21no—
49C4×Q8×C43—21no—
50C4×Q8×C43—22no—
51C4×Q8×C43—22no—
52C4×Q8×C43D412yes—
53C4×Q8×C43C2312yes—
54#117×C43—22no—
55C2×C4⋊C4×C43—21no—
56C2×C4⋊C4×C43D411yescharacteristic
57C2×C42×C43—21no—
58C2×C42×C43C2311yescharacteristic
59#107×C43—21no—
60#107×C43—21no—
61#106×C43—24no—
62C4⋊C8×C43—22no—
63C4⋊C8×C43—22no—
64C4⋊C8×C43—21no—
65C4⋊C8×C43C2312yes—
66C4⋊C8×C43C2314yes—
67#103×C43—24no—
68#103×C43—22no—
69#103×C43—22no—
70#103×C43—24no—
71C22⋊C8×C43—22no—
72#97×C43—22no—
73C4×C8×C43—22no—
74C4×C8×C43—22no—
75C4×C8×C43D411yescharacteristic
76C4×C8×C43D411yescharacteristic
77C4×C8×C43C2311yescharacteristic
78C4×C8×C43C2311yescharacteristic
79C2×Q8×C43—24no—
80C2×Q8×C43—21no—
81C2×Q8×C43—22no—
82C2×Q8×C43—22no—
83C2×Q8×C43C2×D412yes—
84C22×C4×C43—21no—
85C22×C4×C43—21no—
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43#4111yescharacteristic
89Q16×C43—42no—
90Q16×C43—48no—
91Q16×C43—42no—
92C2×C8×C43—22no—
93C2×C8×C43—22no—
94C2×C8×C43—24no—
95C2×C8×C43—41no—
96C2×C8×C43—42no—
97C2×C8×C43C2×D411yescharacteristic
98C2×C8×C43C2×D411yescharacteristic
99C2×C8×C43C2×D411yescharacteristic
100C2×C8×C43C2×D411yescharacteristic
101C4⋊C4×C43—22no—
102C4⋊C4×C43—21no—
103C4⋊C4×C43—22no—
104C4⋊C4×C43—22no—
105C4⋊C4×C43—22no—
106C4⋊C4×C43—22no—
107C4⋊C4×C43—22no—
108C4⋊C4×C43—42no—
109C4⋊C4×C43—42no—
110C4⋊C4×C43C2×D412yes—
111C22⋊C4×C43—42no—
112C42×C43—22no—
113C42×C43—22no—
114C42×C43—42no—
115C42×C43C2×D411yescharacteristic
116C42×C43C2×D411yescharacteristic
117C42×C43#4111yescharacteristic
118C42×C43C2411yescharacteristic
119C23×C43#12111yescharacteristic
120Q8×C43—24no—
121Q8×C43—22no—
122Q8×C43—44no—
123Q8×C43—42no—
124Q8×C43—42no—
125Q8×C43#13514yes—
126C2×C4×C43—24no—
127C2×C4×C43—22no—
128C2×C4×C43—22no—
129C2×C4×C43—22no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—22no—
133C2×C4×C43—42no—
134C2×C4×C43—42no—
135C2×C4×C43—42no—
136C2×C4×C43#12111yescharacteristic
137C2×C4×C43#12111yescharacteristic
138C2×C4×C43#12111yescharacteristic
139C2×C4×C43C22×D411yescharacteristic
140C2×C4×C43C22×D411yescharacteristic
141C2×C4×C43C2×#4111yescharacteristic
142C8×C43—21no—
143C8×C43—21no—
144C8×C43—21no—
145C8×C43—44no—
146C8×C43—42no—
147C8×C43#13712yes—
148#19265C4311yesmaximal, characteristic, direct product factor, Sylow
149C22×C43—21no—
150C22×C43—21no—
151C22×C43#47312yes—
152C22×C43C2×#12111yescharacteristic
153C4×C43—21no—
154C4×C43—24no—
155C4×C43—21no—
156C4×C43—21no—
157C4×C43—21no—
158C4×C43—42no—
159C4×C43—82no—
160C4×C43—82no—
161C4×C43C2×#13512yes—
162C4×C43C2×#13711yescharacteristic
163C4×C43#57511yescharacteristic
164#3170C2×C4311yescharacteristic
165#3113C2×C4312yes—
166C2×C8×Q8C2×C4311yescharacteristic
167#1680C2×C4314yescomplemented
168#1674C2×C4312yescomplemented
169#1670C2×C4312yescomplemented
170#1568C2×C4311yescharacteristic
171#1552C2×C4312yes—
172C2×C43—22no—
173C2×C43#303711yescharacteristic
174C2×C43#305011yescharacteristic
175C2×C43C2×#47311yescharacteristic
176#533C22×C4312yes—
177C2×C4×Q8C22×C4311yescharacteristic
178#500C22×C4311yescharacteristic
179#494C22×C4311yescharacteristic
180#487C22×C4312yes—
181#483—22no—
182#475C22×C4314yes—
183#467—21no—
184#467—21no—
185#462C22×C4314yes—
186#451—22no—
187C8×Q8—21no—
188C8×Q8—21no—
189C8×Q8C22×C4312yes—
190C8×Q8C22×C4312yes—
191#441—24no—
192C4×Q16—21no—
193C4×Q16—21no—
194#432C22×C4312yes—
195C2×C4⋊C8—21no—
196C2×C4⋊C8C22×C4311yescharacteristic
197C2×C4×C8—21no—
198C2×C4×C8C22×C4311yescharacteristic
199#335C22×C4312yes—
200#334C22×C4312yes—
201#332C22×C4314yes—
202#332C22×C4314yes—
203C43#1926511yescharacteristic, direct product factor, Sylow
204C22×Q8D4×C4311yescharacteristic
205C2×Q16—24no—
206C2×Q16—21no—
207C2×Q16—21no—
208C22×C8—21no—
209C22×C8D4×C4311yescharacteristic
210C22×C8D4×C4311yescharacteristic
211C4⋊Q8C23×C4312yes—
212C4⋊Q8C23×C4312yes—
213#125—22no—
214C22⋊Q8—22no—
215C22⋊Q8—22no—
216C4×Q8—21no—
217C4×Q8—21no—
218C4×Q8—22no—
219C4×Q8—22no—
220C4×Q8D4×C4312yes—
221C4×Q8C23×C4312yes—
222#117—22no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4D4×C4311yescharacteristic
225C2×C42—21no—
226C2×C42C23×C4311yescharacteristic
227#107—21no—
228#107—21no—
229#106—24no—
230C4⋊C8—22no—
231C4⋊C8—22no—
232C4⋊C8—21no—
233C4⋊C8C23×C4312yes—
234C4⋊C8C23×C4314yes—
235#103—24no—
236#103—22no—
237#103—22no—
238#103—24no—
239C22⋊C8—22no—
240#97—22no—
241C4×C8—22no—
242C4×C8—22no—
243C4×C8D4×C4311yescharacteristic
244C4×C8D4×C4311yescharacteristic
245C4×C8C23×C4311yescharacteristic
246C4×C8C23×C4311yescharacteristic
247C2×Q8—24no—
248C2×Q8—21no—
249C2×Q8—22no—
250C2×Q8—22no—
251C2×Q8C2×D4×C4312yes—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4C2×D4×C4311yescharacteristic
255C22×C4C2×D4×C4311yescharacteristic
256C22×C4#41×C4311yescharacteristic
257Q16—42no—
258Q16—48no—
259Q16—42no—
260C2×C8—22no—
261C2×C8—22no—
262C2×C8—24no—
263C2×C8—41no—
264C2×C8—42no—
265C2×C8C2×D4×C4311yescharacteristic
266C2×C8C2×D4×C4311yescharacteristic
267C2×C8C2×D4×C4311yescharacteristic
268C2×C8C2×D4×C4311yescharacteristic
269C4⋊C4—22no—
270C4⋊C4—21no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—42no—
277C4⋊C4—42no—
278C4⋊C4C2×D4×C4312yes—
279C22⋊C4—42no—
280C42—22no—
281C42—22no—
282C42—42no—
283C42C2×D4×C4311yescharacteristic
284C42C2×D4×C4311yescharacteristic
285C42#41×C4311yescharacteristic
286C42C24×C4311yescharacteristic
287C23#121×C4311yescharacteristic
288Q8—24no—
289Q8—22no—
290Q8—44no—
291Q8—42no—
292Q8—42no—
293Q8#135×C4314yes—
294C2×C4—24no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4#121×C4311yescharacteristic
305C2×C4#121×C4311yescharacteristic
306C2×C4#121×C4311yescharacteristic
307C2×C4C22×D4×C4311yescharacteristic
308C2×C4C22×D4×C4311yescharacteristic
309C2×C4C2×#41×C4311yescharacteristic
310C8—21no—
311C8—21no—
312C8—21no—
313C8—44no—
314C8—42no—
315C8#137×C4312yes—
316C22—21no—
317C22—21no—
318C22C43×#47312yes—
319C22C2×#121×C4311yescharacteristic
320C4—21no—
321C4—24no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—42no—
326C4—82no—
327C4—82no—
328C4C2×#135×C4312yes—
329C4C2×#137×C4311yescharacteristic
330C4C43×#57511yescharacteristic
331C2—22no—
332C2C43×#303711yescharacteristic
333C2C43×#305011yescharacteristic
334C2C2×C43×#47311yescharacteristic
subgroupG/H
center, socleC22×C43C2×#121
commutator, Frattini, cosocleC42C24×C43
prime radicalC23×C43#121
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
4. C43×#1680C2semidirect
5. C43×#1674C2semidirect
6. C43×#1670C2semidirect
148. #19265C43direct (N × H)
167. #1680C2×C43semidirect
168. #1674C2×C43semidirect
169. #1670C2×C43semidirect
203. C43#19265direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#31702
C43×#31132
C2×C8×Q8×C432
C43×#16802
C43×#16742
C43×#16702
C43×#15682
C43×#15522
#1926543