Finite Group Databasebeta

← C43×#19150 #24939167

Subgroups — C43×#19150 #24939167

Order 11008.

586 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3160C211yesmaximal, characteristic
2C43×#3104C212yesmaximal
3C2×C43×#446C211yesmaximal, characteristic
4C43×#1696C212yesmaximal, complemented
5C43×#1694C212yesmaximal, complemented
6C43×#1692C214yesmaximal, complemented
7C43×#1564C211yesmaximal, characteristic
8C43×#1542C212yesmaximal
9C43×#533C2212yes—
10C2×C4×Q8×C43C2211yescharacteristic
11C43×#500C2211yescharacteristic
12C43×#500C2211yescharacteristic
13C43×#499—21no—
14C43×#499—21no—
15C43×#498C2212yes—
16C43×#484—22no—
17C43×#477C2214yes—
18C43×#462C2214yes—
19C43×#451—22no—
20C43×#446—21no—
21C43×#446—21no—
22C43×#446C2212yes—
23C43×#446C2212yes—
24C4×Q16×C43—24no—
25C43×#431C2212yes—
26C43×#427—21no—
27C43×#427—21no—
28C2×C4⋊C8×C43—21no—
29C2×C4⋊C8×C43C2211yescharacteristic
30C2×#97×C43—21no—
31C2×C4×C8×C43C2211yescharacteristic
32C43×#335C2212yes—
33C43×#334C2212yes—
34C43×#333C2214yes—
35C43×#332C2214yes—
36C22×Q8×C43D411yescharacteristic
37C2×Q16×C43—24no—
38C22×C8×C43—21no—
39C22×C8×C43D411yescharacteristic
40C22×C8×C43D411yescharacteristic
41C4⋊Q8×C43C2312yes—
42C4⋊Q8×C43C2312yes—
43#125×C43—22no—
44C22⋊Q8×C43—22no—
45C22⋊Q8×C43—22no—
46C4×Q8×C43—21no—
47C4×Q8×C43—21no—
48C4×Q8×C43—22no—
49C4×Q8×C43—22no—
50C4×Q8×C43D412yes—
51C4×Q8×C43C2312yes—
52#117×C43—22no—
53C2×C4⋊C4×C43—21no—
54C2×C4⋊C4×C43D411yescharacteristic
55C2×C42×C43—21no—
56C2×C42×C43C2311yescharacteristic
57#107×C43—21no—
58#107×C43—21no—
59#107×C43—21no—
60#107×C43—21no—
61#107×C43—24no—
62#106×C43—22no—
63#106×C43—22no—
64C4⋊C8×C43—22no—
65C4⋊C8×C43—22no—
66C4⋊C8×C43—21no—
67C4⋊C8×C43C2312yes—
68C4⋊C8×C43C2314yes—
69#103×C43—24no—
70#103×C43—24no—
71C22⋊C8×C43—22no—
72#97×C43—22no—
73#97×C43—22no—
74C4×C8×C43—22no—
75C4×C8×C43D411yescharacteristic
76C4×C8×C43D411yescharacteristic
77C4×C8×C43C2311yescharacteristic
78C4×C8×C43C2311yescharacteristic
79C2×Q8×C43—21no—
80C2×Q8×C43—22no—
81C2×Q8×C43—22no—
82C2×Q8×C43—42no—
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—48no—
90C2×C8×C43—22no—
91C2×C8×C43—24no—
92C2×C8×C43—22no—
93C2×C8×C43—42no—
94C2×C8×C43Q1614yescomplemented
95C2×C8×C43C2×D411yescharacteristic
96C2×C8×C43C2×D411yescharacteristic
97C2×C8×C43C2×D411yescharacteristic
98C2×C8×C43C2×D411yescharacteristic
99C4⋊C4×C43—22no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43—22no—
102C4⋊C4×C43—22no—
103C4⋊C4×C43—22no—
104C4⋊C4×C43—22no—
105C4⋊C4×C43—22no—
106C4⋊C4×C43—42no—
107C4⋊C4×C43—42no—
108C4⋊C4×C43C2×D412yes—
109C22⋊C4×C43—42no—
110C42×C43—22no—
111C42×C43—22no—
112C42×C43—42no—
113C42×C43C2×D411yescharacteristic
114C42×C43C2×D411yescharacteristic
115C42×C43#4111yescharacteristic
116C42×C43C2411yescharacteristic
117C23×C43#12111yescharacteristic
118Q8×C43—24no—
119Q8×C43—42no—
120Q8×C43—44no—
121Q8×C43—82no—
122C2×C4×C43—22no—
123C2×C4×C43—22no—
124C2×C4×C43—22no—
125C2×C4×C43—41no—
126C2×C4×C43—42no—
127C2×C4×C43—42no—
128C2×C4×C43—42no—
129C2×C4×C43—42no—
130C2×C4×C43#12111yescharacteristic
131C2×C4×C43#12111yescharacteristic
132C2×C4×C43#12111yescharacteristic
133C2×C4×C43C2×Q1612yes—
134C2×C4×C43#13712yes—
135C2×C4×C43C22×D411yescharacteristic
136C2×C4×C43C22×D411yescharacteristic
137C2×C4×C43C2×#4111yescharacteristic
138C8×C43—21no—
139C8×C43—21no—
140C8×C43—42no—
141C8×C43—44no—
142C8×C43C2×Q1612yes—
143C8×C43C2×Q1612yes—
144#19150C4311yesmaximal, characteristic, direct product factor, Sylow
145C22×C43—21no—
146C22×C43—21no—
147C22×C43#46212yes—
148C22×C43C2×#12111yescharacteristic
149C4×C43—21no—
150C4×C43—21no—
151C4×C43—21no—
152C4×C43—42no—
153C4×C43—42no—
154C4×C43—82no—
155C4×C43—82no—
156C4×C43#46212yes—
157C4×C43C22×Q1611yescharacteristic
158C4×C43C2×#13711yescharacteristic
159C4×C43#57512yes—
160#3160C2×C4311yescharacteristic
161#3104C2×C4312yes—
162C2×#446C2×C4311yescharacteristic
163#1696C2×C4312yescomplemented
164#1694C2×C4312yescomplemented
165#1692C2×C4314yescomplemented
166#1564C2×C4311yescharacteristic
167#1542C2×C4312yes—
168C2×C43—22no—
169C2×C43C2×#46211yescharacteristic
170C2×C43#305411yescharacteristic
171C2×C43#306711yescharacteristic
172#533C22×C4312yes—
173C2×C4×Q8C22×C4311yescharacteristic
174#500C22×C4311yescharacteristic
175#500C22×C4311yescharacteristic
176#499—21no—
177#499—21no—
178#498C22×C4312yes—
179#484—22no—
180#477C22×C4314yes—
181#462C22×C4314yes—
182#451—22no—
183#446—21no—
184#446—21no—
185#446C22×C4312yes—
186#446C22×C4312yes—
187C4×Q16—24no—
188#431C22×C4312yes—
189#427—21no—
190#427—21no—
191C2×C4⋊C8—21no—
192C2×C4⋊C8C22×C4311yescharacteristic
193C2×#97—21no—
194C2×C4×C8C22×C4311yescharacteristic
195#335C22×C4312yes—
196#334C22×C4312yes—
197#333C22×C4314yes—
198#332C22×C4314yes—
199C43#1915011yescharacteristic, direct product factor, Sylow
200C22×Q8D4×C4311yescharacteristic
201C2×Q16—24no—
202C22×C8—21no—
203C22×C8D4×C4311yescharacteristic
204C22×C8D4×C4311yescharacteristic
205C4⋊Q8C23×C4312yes—
206C4⋊Q8C23×C4312yes—
207#125—22no—
208C22⋊Q8—22no—
209C22⋊Q8—22no—
210C4×Q8—21no—
211C4×Q8—21no—
212C4×Q8—22no—
213C4×Q8—22no—
214C4×Q8D4×C4312yes—
215C4×Q8C23×C4312yes—
216#117—22no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4D4×C4311yescharacteristic
219C2×C42—21no—
220C2×C42C23×C4311yescharacteristic
221#107—21no—
222#107—21no—
223#107—21no—
224#107—21no—
225#107—24no—
226#106—22no—
227#106—22no—
228C4⋊C8—22no—
229C4⋊C8—22no—
230C4⋊C8—21no—
231C4⋊C8C23×C4312yes—
232C4⋊C8C23×C4314yes—
233#103—24no—
234#103—24no—
235C22⋊C8—22no—
236#97—22no—
237#97—22no—
238C4×C8—22no—
239C4×C8D4×C4311yescharacteristic
240C4×C8D4×C4311yescharacteristic
241C4×C8C23×C4311yescharacteristic
242C4×C8C23×C4311yescharacteristic
243C2×Q8—21no—
244C2×Q8—22no—
245C2×Q8—22no—
246C2×Q8—42no—
247C2×Q8C2×D4×C4312yes—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4C2×D4×C4311yescharacteristic
251C22×C4C2×D4×C4311yescharacteristic
252C22×C4#41×C4311yescharacteristic
253Q16—48no—
254C2×C8—22no—
255C2×C8—24no—
256C2×C8—22no—
257C2×C8—42no—
258C2×C8Q16×C4314yescomplemented
259C2×C8C2×D4×C4311yescharacteristic
260C2×C8C2×D4×C4311yescharacteristic
261C2×C8C2×D4×C4311yescharacteristic
262C2×C8C2×D4×C4311yescharacteristic
263C4⋊C4—22no—
264C4⋊C4—21no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—42no—
271C4⋊C4—42no—
272C4⋊C4C2×D4×C4312yes—
273C22⋊C4—42no—
274C42—22no—
275C42—22no—
276C42—42no—
277C42C2×D4×C4311yescharacteristic
278C42C2×D4×C4311yescharacteristic
279C42#41×C4311yescharacteristic
280C42C24×C4311yescharacteristic
281C23#121×C4311yescharacteristic
282Q8—24no—
283Q8—42no—
284Q8—44no—
285Q8—82no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4#121×C4311yescharacteristic
295C2×C4#121×C4311yescharacteristic
296C2×C4#121×C4311yescharacteristic
297C2×C4C2×Q16×C4312yes—
298C2×C4#137×C4312yes—
299C2×C4C22×D4×C4311yescharacteristic
300C2×C4C22×D4×C4311yescharacteristic
301C2×C4C2×#41×C4311yescharacteristic
302C8—21no—
303C8—21no—
304C8—42no—
305C8—44no—
306C8C2×Q16×C4312yes—
307C8C2×Q16×C4312yes—
308C22—21no—
309C22—21no—
310C22C43×#46212yes—
311C22C2×#121×C4311yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—42no—
316C4—42no—
317C4—82no—
318C4—82no—
319C4C43×#46212yes—
320C4C22×Q16×C4311yescharacteristic
321C4C2×#137×C4311yescharacteristic
322C4C43×#57512yes—
323C2—22no—
324C2C2×C43×#46211yescharacteristic
325C2C43×#305411yescharacteristic
326C2C43×#306711yescharacteristic
subgroupG/H
centerC2×C4×C43#121
commutator, Frattini, cosocleC42C24×C43
socleC22×C43C2×#121
prime radicalC23×C43#121
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
4. C43×#1696C2semidirect
5. C43×#1694C2semidirect
6. C43×#1692C2semidirect
94. C2×C8×C43Q16semidirect
144. #19150C43direct (N × H)
163. #1696C2×C43semidirect
164. #1694C2×C43semidirect
165. #1692C2×C43semidirect
199. C43#19150direct (N × H)
258. C2×C8Q16×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#31602
C43×#31042
C2×C43×#4462
C43×#16962
C43×#16942
C43×#16922
C43×#15642
C43×#15422
#1915043