Finite Group Databasebeta

← C43×#36600 #24956617

Subgroups — C43×#36600 #24956617

Order 11008.

1574 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2859C212yesmaximal
2C43×#2859C211yesmaximal, characteristic
3C43×#2585C218yesmaximal
4C43×#2570C214yesmaximal
5C43×#2552C212yesmaximal
6C43×#2453C214yesmaximal
7C43×#2370C214yesmaximal
8C43×#2355C212yesmaximal
9C4×#125×C43C212yesmaximal
10C4×#125×C43C211yesmaximal, characteristic
11C42×Q8×C43C211yesmaximal, characteristic
12C2×#125×C43C2211yescharacteristic
13C2×#125×C43C2212yes—
14C2×#125×C43C2214yes—
15C2×C4×Q8×C43C2212yes—
16C2×C4×Q8×C43C2211yescharacteristic
17C43×#400C2218yes—
18C43×#398C2218yes—
19C43×#398C2218yes—
20C43×#391C2214yes—
21C43×#389C2214yes—
22C43×#389C2218yes—
23C43×#389C2218yes—
24C43×#389C2214yes—
25C43×#389C2214yes—
26C43×#389C2214yes—
27C43×#389C2212yes—
28C43×#387C2218yes—
29C43×#387C2214yes—
30C43×#387C2218yes—
31C43×#387C2218yes—
32C43×#387C2218yes—
33C43×#384C2212yes—
34C43×#384C2214yes—
35C43×#382C2214yes—
36C43×#382C2212yes—
37C43×#382C2211yescharacteristic
38C4×C4⋊C4×C43C2214yes—
39C4×C4⋊C4×C43C2218yes—
40C4×C4⋊C4×C43C2214yes—
41C4×C4⋊C4×C43C2212yes—
42C4×C4⋊C4×C43C2214yes—
43C4×C4⋊C4×C43C2212yes—
44C4×C4⋊C4×C43C2214yes—
45C4×C4⋊C4×C43C2211yescharacteristic
46C4×C4⋊C4×C43C2212yes—
47C43×C43C2211yescharacteristic
48C43×C43C2212yes—
49C22×Q8×C43C2311yescharacteristic
50#125×C43—216no—
51#125×C43—28no—
52#125×C43—24no—
53C4×Q8×C43—28no—
54C4×Q8×C43Q818yes—
55C2×C4⋊C4×C43C2314yes—
56C2×C4⋊C4×C43C2312yes—
57C2×C4⋊C4×C43C2314yes—
58C2×C4⋊C4×C43C2314yes—
59C2×C4⋊C4×C43C2318yes—
60C2×C4⋊C4×C43C2318yes—
61C2×C4⋊C4×C43C2314yes—
62C2×C4⋊C4×C43C2318yes—
63C2×C4⋊C4×C43C2312yes—
64C2×C4⋊C4×C43C2314yes—
65C2×C4⋊C4×C43C2314yes—
66C2×C4⋊C4×C43C2318yes—
67C2×C4⋊C4×C43C2311yescharacteristic
68C2×C4⋊C4×C43C2312yes—
69C2×C4⋊C4×C43C2312yes—
70C2×C42×C43C2312yes—
71C2×C42×C43C2314yes—
72C2×C42×C43C2314yes—
73C2×C42×C43C2311yescharacteristic
74C2×C42×C43C2312yes—
75C2×C42×C43C2314yes—
76C2×C42×C43C2312yes—
77C2×C42×C43C2318yes—
78C2×C42×C43C2312yes—
79C2×C42×C43C2311yescharacteristic
80C2×C42×C43C2311yescharacteristic
81#95×C43C2314yes—
82#95×C43C2314yes—
83#95×C43C2312yes—
84#95×C43C2318yes—
85#95×C43C2314yes—
86#95×C43C2314yes—
87#95×C43C2318yes—
88#95×C43C2318yes—
89#95×C43C2318yes—
90#95×C43C2318yes—
91C2×Q8×C43—24no—
92C2×Q8×C43C2×Q814yes—
93C22×C4×C43C2412yes—
94C22×C4×C43C2414yes—
95C22×C4×C43C2414yes—
96C22×C4×C43C2418yes—
97C22×C4×C43C2412yes—
98C22×C4×C43C2412yes—
99C22×C4×C43C2411yescharacteristic
100C22×C4×C43C2414yes—
101C22×C4×C43C2412yes—
102C22×C4×C43C2411yescharacteristic
103C22×C4×C43C2411yescharacteristic
104C4⋊C4×C43—28no—
105C4⋊C4×C43—216no—
106C4⋊C4×C43—216no—
107C4⋊C4×C43—216no—
108C4⋊C4×C43—28no—
109C4⋊C4×C43—28no—
110C4⋊C4×C43—24no—
111C4⋊C4×C43—28no—
112C4⋊C4×C43—24no—
113C4⋊C4×C43—44no—
114C4⋊C4×C43—48no—
115C4⋊C4×C43—44no—
116C4⋊C4×C43C2×Q818yes—
117C4⋊C4×C43C2×Q814yes—
118C4⋊C4×C43#4118yes—
119C42×C43—28no—
120C42×C43—24no—
121C42×C43—28no—
122C42×C43—24no—
123C42×C43—22no—
124C42×C43—44no—
125C42×C43—42no—
126C42×C43—48no—
127C42×C43C2×Q818yes—
128C42×C43C2×Q814yes—
129C42×C43#4114yes—
130C23×C43C2511yescharacteristic
131Q8×C43—28no—
132C2×C4×C43—22no—
133C2×C4×C43—24no—
134C2×C4×C43—24no—
135C2×C4×C43—22no—
136C2×C4×C43—24no—
137C2×C4×C43—22no—
138C2×C4×C43—24no—
139C2×C4×C43—24no—
140C2×C4×C43—22no—
141C2×C4×C43—24no—
142C2×C4×C43—28no—
143C2×C4×C43—24no—
144C2×C4×C43—28no—
145C2×C4×C43—22no—
146C2×C4×C43—24no—
147C2×C4×C43—24no—
148C2×C4×C43—28no—
149C2×C4×C43—22no—
150C2×C4×C43—24no—
151C2×C4×C43C22×Q814yes—
152C2×C4×C43C22×Q812yes—
153C2×C4×C43C22×Q814yes—
154C2×C4×C43C22×Q812yes—
155C2×C4×C43C22×Q812yes—
156C2×C4×C43C2×#4118yes—
157C2×C4×C43C2×#4114yes—
158C2×C4×C43C2×#4114yes—
159C2×C4×C43C2×#4112yes—
160C2×C4×C432−1+412yes—
161#36600C4311yesmaximal, characteristic, direct product factor, Sylow
162C22×C43C23×Q811yescharacteristic
163C22×C43C22×#4112yes—
164C22×C43C22×#4111yescharacteristic
165C22×C43C2×2−1+411yescharacteristic
166C22×C43#58512yes—
167C4×C43—24no—
168C4×C43—24no—
169C4×C43—24no—
170C4×C43—22no—
171C4×C43—28no—
172C4×C43—44no—
173C4×C43—48no—
174C4×C43—42no—
175C4×C43—44no—
176C4×C43#53314yes—
177C4×C43#55714yes—
178#2859C2×C4311yescharacteristic
179#2859C2×C4312yes—
180#2585C2×C4318yes—
181#2570C2×C4314yes—
182#2552C2×C4312yes—
183#2453C2×C4314yes—
184#2370C2×C4314yes—
185#2355C2×C4312yes—
186C4×#125C2×C4312yes—
187C4×#125C2×C4311yescharacteristic
188C42×Q8C2×C4311yescharacteristic
189C2×C43C2×#53311yescharacteristic
190C2×C43C2×#55711yescharacteristic
191C2×C43#348012yes—
192C2×C43#350411yescharacteristic
193C2×C43#351512yes—
194C2×#125C22×C4312yes—
195C2×#125C22×C4311yescharacteristic
196C2×#125C22×C4314yes—
197C2×C4×Q8C22×C4312yes—
198C2×C4×Q8C22×C4311yescharacteristic
199#400C22×C4318yes—
200#398C22×C4318yes—
201#398C22×C4318yes—
202#391C22×C4314yes—
203#389C22×C4312yes—
204#389C22×C4314yes—
205#389C22×C4314yes—
206#389C22×C4318yes—
207#389C22×C4318yes—
208#389C22×C4314yes—
209#389C22×C4314yes—
210#387C22×C4314yes—
211#387C22×C4318yes—
212#387C22×C4318yes—
213#387C22×C4318yes—
214#387C22×C4318yes—
215#384C22×C4314yes—
216#384C22×C4312yes—
217#382C22×C4311yescharacteristic
218#382C22×C4312yes—
219#382C22×C4314yes—
220C4×C4⋊C4C22×C4314yes—
221C4×C4⋊C4C22×C4318yes—
222C4×C4⋊C4C22×C4312yes—
223C4×C4⋊C4C22×C4314yes—
224C4×C4⋊C4C22×C4312yes—
225C4×C4⋊C4C22×C4314yes—
226C4×C4⋊C4C22×C4314yes—
227C4×C4⋊C4C22×C4312yes—
228C4×C4⋊C4C22×C4311yescharacteristic
229C43C22×C4311yescharacteristic
230C43C22×C4312yes—
231C43#3660011yescharacteristic, direct product factor, Sylow
232C22×Q8C23×C4311yescharacteristic
233#125—216no—
234#125—28no—
235#125—24no—
236C4×Q8—28no—
237C4×Q8Q8×C4318yes—
238C2×C4⋊C4C23×C4314yes—
239C2×C4⋊C4C23×C4314yes—
240C2×C4⋊C4C23×C4312yes—
241C2×C4⋊C4C23×C4314yes—
242C2×C4⋊C4C23×C4318yes—
243C2×C4⋊C4C23×C4318yes—
244C2×C4⋊C4C23×C4314yes—
245C2×C4⋊C4C23×C4318yes—
246C2×C4⋊C4C23×C4312yes—
247C2×C4⋊C4C23×C4314yes—
248C2×C4⋊C4C23×C4314yes—
249C2×C4⋊C4C23×C4318yes—
250C2×C4⋊C4C23×C4311yescharacteristic
251C2×C4⋊C4C23×C4312yes—
252C2×C4⋊C4C23×C4312yes—
253C2×C42C23×C4312yes—
254C2×C42C23×C4314yes—
255C2×C42C23×C4314yes—
256C2×C42C23×C4311yescharacteristic
257C2×C42C23×C4312yes—
258C2×C42C23×C4314yes—
259C2×C42C23×C4312yes—
260C2×C42C23×C4318yes—
261C2×C42C23×C4312yes—
262C2×C42C23×C4311yescharacteristic
263C2×C42C23×C4311yescharacteristic
264#95C23×C4314yes—
265#95C23×C4314yes—
266#95C23×C4312yes—
267#95C23×C4318yes—
268#95C23×C4314yes—
269#95C23×C4314yes—
270#95C23×C4318yes—
271#95C23×C4318yes—
272#95C23×C4318yes—
273#95C23×C4318yes—
274C2×Q8—24no—
275C2×Q8C2×Q8×C4314yes—
276C22×C4C24×C4312yes—
277C22×C4C24×C4314yes—
278C22×C4C24×C4314yes—
279C22×C4C24×C4318yes—
280C22×C4C24×C4312yes—
281C22×C4C24×C4312yes—
282C22×C4C24×C4311yescharacteristic
283C22×C4C24×C4314yes—
284C22×C4C24×C4312yes—
285C22×C4C24×C4311yescharacteristic
286C22×C4C24×C4311yescharacteristic
287C4⋊C4—28no—
288C4⋊C4—216no—
289C4⋊C4—216no—
290C4⋊C4—216no—
291C4⋊C4—28no—
292C4⋊C4—28no—
293C4⋊C4—28no—
294C4⋊C4—24no—
295C4⋊C4—24no—
296C4⋊C4—44no—
297C4⋊C4—48no—
298C4⋊C4—44no—
299C4⋊C4C2×Q8×C4318yes—
300C4⋊C4C2×Q8×C4314yes—
301C4⋊C4#41×C4318yes—
302C42—28no—
303C42—24no—
304C42—28no—
305C42—24no—
306C42—22no—
307C42—44no—
308C42—42no—
309C42—48no—
310C42C2×Q8×C4318yes—
311C42C2×Q8×C4314yes—
312C42#41×C4314yes—
313C23C25×C4311yescharacteristic
314Q8—28no—
315C2×C4—22no—
316C2×C4—24no—
317C2×C4—24no—
318C2×C4—22no—
319C2×C4—24no—
320C2×C4—22no—
321C2×C4—24no—
322C2×C4—24no—
323C2×C4—22no—
324C2×C4—24no—
325C2×C4—28no—
326C2×C4—24no—
327C2×C4—28no—
328C2×C4—22no—
329C2×C4—24no—
330C2×C4—24no—
331C2×C4—28no—
332C2×C4—22no—
333C2×C4—24no—
334C2×C4C22×Q8×C4314yes—
335C2×C4C22×Q8×C4312yes—
336C2×C4C22×Q8×C4314yes—
337C2×C4C22×Q8×C4312yes—
338C2×C4C22×Q8×C4312yes—
339C2×C4C2×#41×C4318yes—
340C2×C4C2×#41×C4314yes—
341C2×C4C2×#41×C4314yes—
342C2×C4C2×#41×C4312yes—
343C2×C42−1+4×C4312yes—
344C22C23×Q8×C4311yescharacteristic
345C22C22×#41×C4312yes—
346C22C22×#41×C4311yescharacteristic
347C22C2×2−1+4×C4311yescharacteristic
348C22C43×#58512yes—
349C4—24no—
350C4—24no—
351C4—24no—
352C4—22no—
353C4—28no—
354C4—44no—
355C4—48no—
356C4—42no—
357C4—44no—
358C4C43×#53314yes—
359C4C43×#55714yes—
360C2C2×C43×#53311yescharacteristic
361C2C2×C43×#55711yescharacteristic
362C2C43×#348012yes—
363C2C43×#350411yescharacteristic
364C2C43×#351512yes—
subgroupG/H
center, socle, prime radicalC23×C43C25
commutator, Frattini, cosocleC23C25×C43
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C43 ◁ G

Complements

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

NH ≅ G/Ntype
161. #36600C43direct (N × H)
231. C43#36600direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#28592
C43×#25852
C43×#25702
C43×#25522
C43×#24532
C43×#23702
C43×#23552
C4×#125×C432
C42×Q8×C432
#3660043