Finite Group Databasebeta

← C43×#2690 #19131507

Subgroups — C43×#2690 #19131507

Order 5504.

456 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×C43C211yesmaximal, characteristic, complemented
2C2×C22⋊Q8×C43C211yesmaximal, characteristic
3C43×#400C211yesmaximal, characteristic, complemented
4C43×#400C211yesmaximal, characteristic, complemented
5C43×#398C211yesmaximal, characteristic, complemented
6C43×#397C211yesmaximal, characteristic
7C43×#397C211yesmaximal, characteristic
8C43×#395C211yesmaximal, characteristic, complemented
9C43×#391C211yesmaximal, characteristic, complemented
10C43×#388C211yesmaximal, characteristic
11C43×#388C211yesmaximal, characteristic
12C43×#387C211yesmaximal, characteristic, complemented
13C43×#387C211yesmaximal, characteristic, complemented
14C43×#385C211yesmaximal, characteristic
15C43×#380C211yesmaximal, characteristic
16C22×Q8×C43C2211yescharacteristic
17C23×C4×C43C2211yescharacteristic
18#125×C43—24no—
19C22⋊Q8×C43—24no—
20C2×C4⋊C4×C43C2211yescharacteristic
21C2×C4⋊C4×C43C2211yescharacteristic
22C2×C4⋊C4×C43C2211yescharacteristic
23C2×C4⋊C4×C43C2211yescharacteristic
24C2×C4⋊C4×C43C2211yescharacteristic
25C2×C4⋊C4×C43C2211yescharacteristic
26C2×C4⋊C4×C43C2211yescharacteristic
27C2×C4⋊C4×C43C2211yescharacteristic
28C2×C4⋊C4×C43C2211yescharacteristic
29C2×C4⋊C4×C43C2211yescharacteristic
30C2×C4⋊C4×C43C2211yescharacteristic
31C2×C22⋊C4×C43C2211yescharacteristic
32C2×C22⋊C4×C43C2211yescharacteristic
33C2×C22⋊C4×C43C2211yescharacteristic
34C2×C22⋊C4×C43C2211yescharacteristic
35C2×C22⋊C4×C43C2211yescharacteristic
36C2×C22⋊C4×C43C2211yescharacteristic
37C2×C42×C43C2211yescharacteristic
38C2×C42×C43C2211yescharacteristic
39#95×C43C2211yescharacteristic
40#95×C43C2211yescharacteristic
41#95×C43C2211yescharacteristic
42#95×C43C2211yescharacteristic
43#95×C43C2211yescharacteristic
44#95×C43C2211yescharacteristic
45#95×C43C2211yescharacteristic
46#95×C43C2211yescharacteristic
47#95×C43C2211yescharacteristic
48#95×C43C2211yescharacteristic
49#95×C43C2211yescharacteristic
50#95×C43C2211yescharacteristic
51#95×C43C2211yescharacteristic
52#95×C43C2211yescharacteristic
53C24×C43C2311yescharacteristic
54C2×Q8×C43—22no—
55C2×Q8×C43—22no—
56C2×Q8×C43—41no—
57C22×C4×C43—22no—
58C22×C4×C43—22no—
59C22×C4×C43—41no—
60C22×C4×C43C2311yescharacteristic
61C22×C4×C43C2311yescharacteristic
62C22×C4×C43C2311yescharacteristic
63C22×C4×C43C2311yescharacteristic
64C22×C4×C43C2311yescharacteristic
65C22×C4×C43C2311yescharacteristic
66C22×C4×C43C2311yescharacteristic
67C22×C4×C43C2311yescharacteristic
68C22×C4×C43C2311yescharacteristic
69C22×C4×C43C2311yescharacteristic
70C22×C4×C43C2311yescharacteristic
71C22×C4×C43C2311yescharacteristic
72C22×C4×C43C2311yescharacteristic
73C22×C4×C43C2311yescharacteristic
74C4⋊C4×C43—22no—
75C4⋊C4×C43—22no—
76C4⋊C4×C43—22no—
77C4⋊C4×C43—22no—
78C4⋊C4×C43—22no—
79C4⋊C4×C43—22no—
80C4⋊C4×C43—22no—
81C4⋊C4×C43—22no—
82C4⋊C4×C43—41no—
83C4⋊C4×C43—41no—
84C4⋊C4×C43D414yes—
85C22⋊C4×C43—22no—
86C22⋊C4×C43—22no—
87C22⋊C4×C43—22no—
88C22⋊C4×C43—22no—
89C22⋊C4×C43—22no—
90C22⋊C4×C43—41no—
91C42×C43—22no—
92C42×C43—41no—
93C23×C43—21no—
94C23×C43—21no—
95C23×C43—21no—
96C23×C43—21no—
97C23×C43—21no—
98C23×C43—21no—
99C23×C43#4112yes—
100C23×C43C2411yescharacteristic
101Q8×C43—44no—
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—44no—
141C2×C4×C43C2×D412yes—
142C2×C4×C43C2×D412yes—
143C2×C4×C43C2×D412yes—
144C2×C4×C43#4112yes—
145C22×C43—22no—
146C22×C43—22no—
147C22×C43—22no—
148C22×C43—41no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43C22×D411yescharacteristic
153C22×C43C2×#4111yescharacteristic
154C22×C43C2×#4111yescharacteristic
155C22×C43H(5,𝔽2)11yescharacteristic
156C22×C432−1+411yescharacteristic
157C22×C432−1+411yescharacteristic
158C22×C432−1+411yescharacteristic
159C4×C43—22no—
160C4×C43—22no—
161C4×C43—22no—
162C4×C43—22no—
163C4×C43—41no—
164C4×C43—41no—
165C4×C43—41no—
166C4×C43—41no—
167C4×C43—41no—
168C4×C43—41no—
169C4×C43—41no—
170C4×C43—41no—
171C4×C43—41no—
172C4×C43—41no—
173#2690C4311yesmaximal, characteristic, direct product factor, Sylow
174C2×C43—42no—
175C2×C43#53611yescharacteristic
176C2×C43#53911yescharacteristic
177C2×C43#54111yescharacteristic
178C2×C43#54611yescharacteristic
179C2×C43#54811yescharacteristic
180C2×C43#55211yescharacteristic
181C2×C43#56311yescharacteristic
182C2×#125C2×C4311yescharacteristic, complemented
183C2×C22⋊Q8C2×C4311yescharacteristic
184#400C2×C4311yescharacteristic, complemented
185#400C2×C4311yescharacteristic, complemented
186#398C2×C4311yescharacteristic, complemented
187#397C2×C4311yescharacteristic
188#397C2×C4311yescharacteristic
189#395C2×C4311yescharacteristic, complemented
190#391C2×C4311yescharacteristic, complemented
191#388C2×C4311yescharacteristic
192#388C2×C4311yescharacteristic
193#387C2×C4311yescharacteristic, complemented
194#387C2×C4311yescharacteristic, complemented
195#385C2×C4311yescharacteristic
196#380C2×C4311yescharacteristic
197C43#269011yescharacteristic, direct product factor, Sylow
198C22×Q8C22×C4311yescharacteristic
199C23×C4C22×C4311yescharacteristic
200#125—24no—
201C22⋊Q8—24no—
202C2×C4⋊C4C22×C4311yescharacteristic
203C2×C4⋊C4C22×C4311yescharacteristic
204C2×C4⋊C4C22×C4311yescharacteristic
205C2×C4⋊C4C22×C4311yescharacteristic
206C2×C4⋊C4C22×C4311yescharacteristic
207C2×C4⋊C4C22×C4311yescharacteristic
208C2×C4⋊C4C22×C4311yescharacteristic
209C2×C4⋊C4C22×C4311yescharacteristic
210C2×C4⋊C4C22×C4311yescharacteristic
211C2×C4⋊C4C22×C4311yescharacteristic
212C2×C4⋊C4C22×C4311yescharacteristic
213C2×C22⋊C4C22×C4311yescharacteristic
214C2×C22⋊C4C22×C4311yescharacteristic
215C2×C22⋊C4C22×C4311yescharacteristic
216C2×C22⋊C4C22×C4311yescharacteristic
217C2×C22⋊C4C22×C4311yescharacteristic
218C2×C22⋊C4C22×C4311yescharacteristic
219C2×C42C22×C4311yescharacteristic
220C2×C42C22×C4311yescharacteristic
221#95C22×C4311yescharacteristic
222#95C22×C4311yescharacteristic
223#95C22×C4311yescharacteristic
224#95C22×C4311yescharacteristic
225#95C22×C4311yescharacteristic
226#95C22×C4311yescharacteristic
227#95C22×C4311yescharacteristic
228#95C22×C4311yescharacteristic
229#95C22×C4311yescharacteristic
230#95C22×C4311yescharacteristic
231#95C22×C4311yescharacteristic
232#95C22×C4311yescharacteristic
233#95C22×C4311yescharacteristic
234#95C22×C4311yescharacteristic
235C24C23×C4311yescharacteristic
236C2×Q8—22no—
237C2×Q8—22no—
238C2×Q8—41no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—41no—
242C22×C4C23×C4311yescharacteristic
243C22×C4C23×C4311yescharacteristic
244C22×C4C23×C4311yescharacteristic
245C22×C4C23×C4311yescharacteristic
246C22×C4C23×C4311yescharacteristic
247C22×C4C23×C4311yescharacteristic
248C22×C4C23×C4311yescharacteristic
249C22×C4C23×C4311yescharacteristic
250C22×C4C23×C4311yescharacteristic
251C22×C4C23×C4311yescharacteristic
252C22×C4C23×C4311yescharacteristic
253C22×C4C23×C4311yescharacteristic
254C22×C4C23×C4311yescharacteristic
255C22×C4C23×C4311yescharacteristic
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4D4×C4314yes—
267C22⋊C4—22no—
268C22⋊C4—22no—
269C22⋊C4—22no—
270C22⋊C4—22no—
271C22⋊C4—22no—
272C22⋊C4—41no—
273C42—22no—
274C42—41no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23#41×C4312yes—
282C23C24×C4311yescharacteristic
283Q8—44no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—44no—
323C2×C4C2×D4×C4312yes—
324C2×C4C2×D4×C4312yes—
325C2×C4C2×D4×C4312yes—
326C2×C4#41×C4312yes—
327C22—22no—
328C22—22no—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22C22×D4×C4311yescharacteristic
335C22C2×#41×C4311yescharacteristic
336C22C2×#41×C4311yescharacteristic
337C22H(5,𝔽2)×C4311yescharacteristic
338C222−1+4×C4311yescharacteristic
339C222−1+4×C4311yescharacteristic
340C222−1+4×C4311yescharacteristic
341C4—22no—
342C4—22no—
343C4—22no—
344C4—22no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—41no—
355C2—42no—
356C2C43×#53611yescharacteristic
357C2C43×#53911yescharacteristic
358C2C43×#54111yescharacteristic
359C2C43×#54611yescharacteristic
360C2C43×#54811yescharacteristic
361C2C43×#55211yescharacteristic
362C2C43×#56311yescharacteristic
subgroupG/H
center, socleC23×C43C24
commutator, Frattini, cosocleC23C24×C43
prime radicalC24×C43C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#125×C43C2semidirect
3. C43×#400C2semidirect
4. C43×#400C2semidirect
5. C43×#398C2semidirect
8. C43×#395C2semidirect
9. C43×#391C2semidirect
12. C43×#387C2semidirect
13. C43×#387C2semidirect
173. #2690C43direct (N × H)
182. C2×#125C2×C43semidirect
184. #400C2×C43semidirect
185. #400C2×C43semidirect
186. #398C2×C43semidirect
189. #395C2×C43semidirect
190. #391C2×C43semidirect
193. #387C2×C43semidirect
194. #387C2×C43semidirect
197. C43#2690direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#125×C432
C2×C22⋊Q8×C432
C43×#4002
C43×#3982
C43×#3972
C43×#3952
C43×#3912
C43×#3882
C43×#3872
C43×#3852
C43×#3802
#269043