Finite Group Databasebeta

← C43×#28451 #24948468

Subgroups — C43×#28451 #24948468

Order 11008.

1130 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#497C212yesmaximal, complemented
2C2×C43×#462C212yesmaximal, complemented
3C2×C43×#460C212yesmaximal
4C43×#2858C211yesmaximal, characteristic
5C4×C4⋊Q8×C43C211yesmaximal, characteristic, complemented
6C43×#2015C214yesmaximal, complemented
7C43×#1959C212yesmaximal, complemented
8C43×#1767C211yesmaximal, characteristic, complemented
9C22×Q16×C43C2214yes—
10C22×SD16×C43C2214yes—
11C2×C4⋊Q8×C43C2211yescharacteristic
12C2×C4⋊Q8×C43C2211yescharacteristic
13C2×#127×C43C2211yescharacteristic
14C2×#124×C43C2212yes—
15C2×#124×C43C2212yes—
16C2×C4×Q8×C43C2212yes—
17C43×#497—28no—
18C43×#462—28no—
19C43×#460—28no—
20C2×C4⋊C8×C43C2212yes—
21C2×#103×C43C2214yes—
22C2×#102×C43C2214yes—
23C2×#97×C43C2212yes—
24C43×#391C2212yes—
25C43×#390—22no—
26C43×#390—22no—
27C43×#389—22no—
28C43×#384C2211yescharacteristic
29C4×C4⋊C4×C43—22no—
30C43×C43C2211yescharacteristic
31C43×#336C2212yes—
32C22×Q8×C43C2312yes—
33C22×Q8×C43C2312yes—
34C22×D4×C43—21no—
35C22×D4×C43—21no—
36C22×D4×C43C2312yes—
37C2×Q16×C43—28no—
38C2×Q16×C43—28no—
39C2×Q16×C43—44no—
40C2×SD16×C43—28no—
41C2×SD16×C43—28no—
42C2×SD16×C43—44no—
43C22×C8×C43C2314yes—
44C4⋊Q8×C43—24no—
45C4⋊Q8×C43—22no—
46C4⋊Q8×C43D414yescomplemented
47#127×C43—24no—
48#124×C43—24no—
49#124×C43—24no—
50#124×C43—44no—
51C4×Q8×C43—24no—
52C4×Q8×C43—24no—
53C2×C4⋊C4×C43—22no—
54C2×C4⋊C4×C43—22no—
55C2×C4⋊C4×C43—21no—
56C2×C4⋊C4×C43—21no—
57C2×C4⋊C4×C43—22no—
58C2×C4⋊C4×C43C2312yes—
59C2×C22⋊C4×C43—24no—
60C2×C22⋊C4×C43—24no—
61C2×C42×C43—22no—
62C2×C42×C43D412yes—
63C2×C42×C43D412yes—
64C2×C42×C43C2311yescharacteristic
65C2×C42×C43C2311yescharacteristic
66C2×C42×C43C2311yescharacteristic
67C4⋊C8×C43D418yes—
68#103×C43—28no—
69#102×C43—28no—
70#97×C43—24no—
71#95×C43—24no—
72C24×C43—22no—
73C2×Q8×C43—22no—
74C2×Q8×C43—22no—
75C2×Q8×C43—22no—
76C2×Q8×C43—24no—
77C2×Q8×C43—22no—
78C2×Q8×C43—22no—
79C2×Q8×C43—22no—
80C2×Q8×C43—22no—
81C2×Q8×C43—24no—
82C2×Q8×C43C2×D414yes—
83C2×D4×C43—24no—
84C2×D4×C43—22no—
85C2×D4×C43—22no—
86C2×D4×C43—24no—
87C2×D4×C43—44no—
88C2×D4×C43—42no—
89C2×D4×C43—42no—
90C2×D4×C43—44no—
91C22×C4×C43—22no—
92C22×C4×C43—22no—
93C22×C4×C43—22no—
94C22×C4×C43C2×D412yes—
95C22×C4×C43C2×D412yes—
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2411yescharacteristic
99Q16×C43—416no—
100SD16×C43—416no—
101C2×C8×C43—24no—
102C2×C8×C43—24no—
103C2×C8×C43C2×D418yes—
104C4⋊C4×C43—28no—
105C4⋊C4×C43—22no—
106C4⋊C4×C43—22no—
107C4⋊C4×C43—44no—
108C4⋊C4×C43—44no—
109C4⋊C4×C43—42no—
110C4⋊C4×C43—42no—
111C22⋊C4×C43—48no—
112C22⋊C4×C43—48no—
113C42×C43—24no—
114C42×C43—22no—
115C42×C43—42no—
116C42×C43—44no—
117C42×C43C2×D412yes—
118C42×C43C2×D414yes—
119C42×C43#4112yes—
120C23×C43—42no—
121C23×C43—42no—
122C23×C43—42no—
123C23×C43—44no—
124C23×C43—44no—
125C23×C43C22×D411yescharacteristic
126Q8×C43—24no—
127Q8×C43—24no—
128Q8×C43—42no—
129Q8×C43—42no—
130Q8×C43—44no—
131Q8×C43—44no—
132D4×C43—44no—
133D4×C43—44no—
134D4×C43—84no—
135D4×C43—84no—
136C2×C4×C43—22no—
137C2×C4×C43—22no—
138C2×C4×C43—22no—
139C2×C4×C43—24no—
140C2×C4×C43—22no—
141C2×C4×C43—22no—
142C2×C4×C43—22no—
143C2×C4×C43—42no—
144C2×C4×C43—42no—
145C2×C4×C43—42no—
146C2×C4×C43—42no—
147C2×C4×C43—42no—
148C2×C4×C43—42no—
149C2×C4×C43—44no—
150C2×C4×C43#12114yes—
151C2×C4×C43#12712yes—
152C2×C4×C43#12712yes—
153C2×C4×C43#13714yes—
154C2×C4×C43C22×D411yescharacteristic
155C2×C4×C43C22×D412yes—
156C2×C4×C43C2×#4111yescharacteristic
157C2×C4×C43H(5,𝔽2)12yes—
158C8×C43—28no—
159#28451C4311yesmaximal, characteristic, direct product factor, Sylow
160C22×C43—82no—
161C22×C43—82no—
162C22×C43—84no—
163C22×C43—84no—
164C22×C43—82no—
165C22×C43C2×#12111yescharacteristic
166C22×C43C2×#12711yescharacteristic
167C22×C43#53511yescharacteristic
168C22×C43C2×#13712yes—
169C22×C43#57512yes—
170C4×C43—22no—
171C4×C43—24no—
172C4×C43—42no—
173C4×C43—44no—
174C4×C43—82no—
175C4×C43—82no—
176C4×C43#49714yescomplemented
177C4×C43D4212yes—
178C4×C43#55012yes—
179C2×#497C2×C4312yescomplemented
180C2×#462C2×C4312yescomplemented
181C2×#460C2×C4312yes—
182#2858C2×C4311yescharacteristic
183C4×C4⋊Q8C2×C4311yescharacteristic, complemented
184#2015C2×C4314yescomplemented
185#1959C2×C4312yescomplemented
186#1767C2×C4311yescharacteristic, complemented
187C2×C43—162no—
188C2×C43#254111yescharacteristic
189C2×C43#303712yes—
190C2×C43C2×#49711yescharacteristic
191C2×C43#315311yescharacteristic
192C2×C43#321612yes—
193C22×Q16C22×C4314yes—
194C22×SD16C22×C4314yes—
195C2×C4⋊Q8C22×C4311yescharacteristic
196C2×C4⋊Q8C22×C4311yescharacteristic
197C2×#127C22×C4311yescharacteristic
198C2×#124C22×C4312yes—
199C2×#124C22×C4312yes—
200C2×C4×Q8C22×C4312yes—
201#497—28no—
202#462—28no—
203#460—28no—
204C2×C4⋊C8C22×C4312yes—
205C2×#103C22×C4314yes—
206C2×#102C22×C4314yes—
207C2×#97C22×C4312yes—
208#391C22×C4312yes—
209#390—22no—
210#390—22no—
211#389—22no—
212#384C22×C4311yescharacteristic
213C4×C4⋊C4—22no—
214C43C22×C4311yescharacteristic
215#336C22×C4312yes—
216C43#2845111yescharacteristic, direct product factor, Sylow
217C22×Q8C23×C4312yes—
218C22×Q8C23×C4312yes—
219C22×D4—21no—
220C22×D4—21no—
221C22×D4C23×C4312yes—
222C2×Q16—28no—
223C2×Q16—28no—
224C2×Q16—44no—
225C2×SD16—28no—
226C2×SD16—28no—
227C2×SD16—44no—
228C22×C8C23×C4314yes—
229C4⋊Q8—24no—
230C4⋊Q8—22no—
231C4⋊Q8D4×C4314yescomplemented
232#127—24no—
233#124—24no—
234#124—24no—
235#124—44no—
236C4×Q8—24no—
237C4×Q8—24no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4C23×C4312yes—
244C2×C22⋊C4—24no—
245C2×C22⋊C4—24no—
246C2×C42—22no—
247C2×C42D4×C4312yes—
248C2×C42D4×C4312yes—
249C2×C42C23×C4311yescharacteristic
250C2×C42C23×C4311yescharacteristic
251C2×C42C23×C4311yescharacteristic
252C4⋊C8D4×C4318yes—
253#103—28no—
254#102—28no—
255#97—24no—
256#95—24no—
257C24—22no—
258C2×Q8—22no—
259C2×Q8—22no—
260C2×Q8—22no—
261C2×Q8—24no—
262C2×Q8—22no—
263C2×Q8—22no—
264C2×Q8—22no—
265C2×Q8—22no—
266C2×Q8—24no—
267C2×Q8C2×D4×C4314yes—
268C2×D4—24no—
269C2×D4—22no—
270C2×D4—22no—
271C2×D4—24no—
272C2×D4—44no—
273C2×D4—42no—
274C2×D4—42no—
275C2×D4—44no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4C2×D4×C4312yes—
280C22×C4C2×D4×C4312yes—
281C22×C4C2×D4×C4311yescharacteristic
282C22×C4C2×D4×C4311yescharacteristic
283C22×C4C24×C4311yescharacteristic
284Q16—416no—
285SD16—416no—
286C2×C8—24no—
287C2×C8—24no—
288C2×C8C2×D4×C4318yes—
289C4⋊C4—28no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—44no—
293C4⋊C4—44no—
294C4⋊C4—42no—
295C4⋊C4—42no—
296C22⋊C4—48no—
297C22⋊C4—48no—
298C42—24no—
299C42—22no—
300C42—42no—
301C42—44no—
302C42C2×D4×C4312yes—
303C42C2×D4×C4314yes—
304C42#41×C4312yes—
305C23—42no—
306C23—42no—
307C23—42no—
308C23—44no—
309C23—44no—
310C23C22×D4×C4311yescharacteristic
311Q8—24no—
312Q8—24no—
313Q8—42no—
314Q8—42no—
315Q8—44no—
316Q8—44no—
317D4—44no—
318D4—44no—
319D4—84no—
320D4—84no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—24no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—44no—
335C2×C4#121×C4314yes—
336C2×C4#127×C4312yes—
337C2×C4#127×C4312yes—
338C2×C4#137×C4314yes—
339C2×C4C22×D4×C4311yescharacteristic
340C2×C4C22×D4×C4312yes—
341C2×C4C2×#41×C4311yescharacteristic
342C2×C4H(5,𝔽2)×C4312yes—
343C8—28no—
344C22—82no—
345C22—82no—
346C22—84no—
347C22—84no—
348C22—82no—
349C22C2×#121×C4311yescharacteristic
350C22C2×#127×C4311yescharacteristic
351C22C43×#53511yescharacteristic
352C22C2×#137×C4312yes—
353C22C43×#57512yes—
354C4—22no—
355C4—24no—
356C4—42no—
357C4—44no—
358C4—82no—
359C4—82no—
360C4C43×#49714yescomplemented
361C4D42×C4312yes—
362C4C43×#55012yes—
363C2—162no—
364C2C43×#254111yescharacteristic
365C2C43×#303712yes—
366C2C2×C43×#49711yescharacteristic
367C2C43×#315311yescharacteristic
368C2C43×#321612yes—
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC2×#127×C43C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C43×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#497C2semidirect
2. C2×C43×#462C2semidirect
5. C4×C4⋊Q8×C43C2semidirect
6. C43×#2015C2semidirect
7. C43×#1959C2semidirect
8. C43×#1767C2semidirect
46. C4⋊Q8×C43D4semidirect
159. #28451C43direct (N × H)
176. C4×C43#497semidirect
179. C2×#497C2×C43semidirect
180. C2×#462C2×C43semidirect
183. C4×C4⋊Q8C2×C43semidirect
184. #2015C2×C43semidirect
185. #1959C2×C43semidirect
186. #1767C2×C43semidirect
216. C43#28451direct (N × H)
231. C4⋊Q8D4×C43semidirect
360. C4C43×#497semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4972
C2×C43×#4622
C2×C43×#4602
C43×#28582
C4×C4⋊Q8×C432
C43×#20152
C43×#19592
C43×#17672
#2845143