Finite Group Databasebeta

← C2×C43×#2962 #24980206

Subgroups — C2×C43×#2962 #24980206

Order 11008.

1938 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#533C211yesmaximal, characteristic
2C43×#2962C2116yesmaximal, direct product factor
3C2×C43×#446C212yesmaximal, complemented
4C2×C43×#446C214yesmaximal, complemented
5C2×C8×Q8×C43C212yesmaximal, complemented
6C2×C43×#424C212yesmaximal
7C22×C4⋊C8×C43C211yesmaximal, characteristic
8C2×C43×#405C212yesmaximal
9C2×C4×M16×C43C211yesmaximal, characteristic
10C22×M16×C43C2211yescharacteristic
11C22×M16×C43C2211yescharacteristic
12C23×C8×C43C2212yes—
13C43×#533C418yes—
14C43×#533C2218yes—
15C2×C4⋊Q8×C43C411yescharacteristic
16C2×C4⋊Q8×C43C411yescharacteristic
17C2×#125×C43C412yes—
18C2×C22⋊Q8×C43C412yes—
19C2×C22⋊Q8×C43C412yes—
20C2×C4×Q8×C43C2212yes—
21C2×C4×Q8×C43C2212yes—
22C2×#117×C43C2212yes—
23C22×C42×C43C2211yescharacteristic
24C43×#446C22116yescomplemented
25C43×#446C22132yescomplemented
26C8×Q8×C43C22116yescomplemented
27C43×#424C22116yes—
28C2×C4⋊C8×C43C2211yescharacteristic
29C2×C4⋊C8×C43C2211yescharacteristic
30C2×C4⋊C8×C43C2212yes—
31C2×C4⋊C8×C43C2218yes—
32C2×C4⋊C8×C43C2214yes—
33C2×C4⋊C8×C43C2214yes—
34C43×#405C22116yes—
35C4×M16×C43C2218yes—
36C2×#97×C43C2212yes—
37C2×#97×C43C2214yes—
38C2×C4×C8×C43C2212yes—
39C2×C4×C8×C43C2214yes—
40C22×Q8×C43C2×C412yes—
41C22×Q8×C43C2×C412yes—
42C23×C4×C43C2×C411yescharacteristic
43C23×C4×C43C2×C411yescharacteristic
44C23×C4×C43C2311yescharacteristic
45C2×M16×C43—24no—
46C2×M16×C43Q818yescomplemented
47C2×M16×C43C2314yes—
48C2×M16×C43C2314yes—
49C22×C8×C43—28no—
50C22×C8×C43C2318yes—
51C22×C8×C43C2312yes—
52C22×C8×C43C2312yes—
53C22×C8×C43C2312yes—
54C22×C8×C43C2312yes—
55C4⋊Q8×C43C2×C418yes—
56C4⋊Q8×C43C2×C418yes—
57#125×C43C2×C4116yes—
58C22⋊Q8×C43C2×C4116yes—
59C22⋊Q8×C43C2×C4116yes—
60C4×Q8×C43C2×C418yes—
61C4×Q8×C43C2×C418yes—
62C4×Q8×C43C2318yes—
63C4×Q8×C43C2318yes—
64#117×C43C2×C418yes—
65#117×C43C2318yes—
66C2×C4⋊C4×C43C2×C412yes—
67C2×C4⋊C4×C43C2×C412yes—
68C2×C4⋊C4×C43C2×C414yes—
69C2×C4⋊C4×C43C2×C414yes—
70C2×C4⋊C4×C43C2×C412yes—
71C2×C4⋊C4×C43C2×C412yes—
72C2×C22⋊C4×C43C2×C414yes—
73C2×C42×C43C2×C411yescharacteristic
74C2×C42×C43C2×C411yescharacteristic
75C2×C42×C43C2×C414yes—
76C2×C42×C43C2314yes—
77C2×C42×C43C2311yescharacteristic
78C2×C42×C43C2311yescharacteristic
79C2×C42×C43C2314yes—
80C4⋊C8×C43C2314yes—
81C4⋊C8×C43C2314yes—
82C4⋊C8×C43C2318yes—
83C4⋊C8×C43C23116yes—
84C4⋊C8×C43C23116yes—
85#97×C43C2318yes—
86#97×C43C23116yes—
87C4×C8×C43C2318yes—
88C4×C8×C43C23116yes—
89C24×C43C22×C411yescharacteristic
90C2×Q8×C43—28no—
91C2×Q8×C43—44no—
92C2×Q8×C43C22×C418yes—
93C2×Q8×C43C22×C418yes—
94C22×C4×C43—24no—
95C22×C4×C43—42no—
96C22×C4×C43C22×C411yescharacteristic
97C22×C4×C43C22×C411yescharacteristic
98C22×C4×C43C22×C411yescharacteristic
99C22×C4×C43C22×C414yes—
100C22×C4×C43C22×C414yes—
101C22×C4×C43C22×C414yes—
102C22×C4×C43C22×C414yes—
103C22×C4×C43C22×C411yescharacteristic
104C22×C4×C43C22×C412yes—
105C22×C4×C43C22×C411yescharacteristic
106C22×C4×C43C2×Q814yes—
107C22×C4×C43#4114yes—
108C22×C4×C43C2412yes—
109C22×C4×C43C2411yescharacteristic
110M16×C43—28no—
111M16×C43C2×Q8116yescomplemented
112C2×C8×C43—24no—
113C2×C8×C43—24no—
114C2×C8×C43—216no—
115C2×C8×C43—24no—
116C2×C8×C43C2×Q818yes—
117C2×C8×C43C2414yes—
118C2×C8×C43C2414yes—
119C2×C8×C43C2414yes—
120C2×C8×C43C2414yes—
121C4⋊C4×C43C22×C418yes—
122C4⋊C4×C43C22×C418yes—
123C4⋊C4×C43C22×C4116yes—
124C4⋊C4×C43C22×C4116yes—
125C4⋊C4×C43C22×C418yes—
126C4⋊C4×C43C22×C418yes—
127C22⋊C4×C43C22×C4116yes—
128C42×C43C22×C412yes—
129C42×C43C22×C412yes—
130C42×C43C22×C414yes—
131C42×C43C22×C414yes—
132C42×C43C22×C418yes—
133C42×C43C2412yes—
134C42×C43C2418yes—
135C42×C43C2412yes—
136C23×C43—22no—
137C23×C43—22no—
138C23×C43C4×Q814yes—
139C23×C43C23×C412yes—
140C23×C43C23×C411yescharacteristic
141Q8×C43—216no—
142Q8×C43—48no—
143C2×C4×C43—22no—
144C2×C4×C43—28no—
145C2×C4×C43—22no—
146C2×C4×C43—22no—
147C2×C4×C43—28no—
148C2×C4×C43—28no—
149C2×C4×C43—44no—
150C2×C4×C43C4×Q818yes—
151C2×C4×C43C4×Q814yes—
152C2×C4×C43#13114yes—
153C2×C4×C43C23×C412yes—
154C2×C4×C43C23×C412yes—
155C2×C4×C43C23×C412yes—
156C2×C4×C43C23×C418yes—
157C2×C4×C43C23×C418yes—
158C2×C4×C43C23×C411yescharacteristic
159C2×C4×C43C23×C412yes—
160C2×C4×C43C23×C412yes—
161C2×C4×C43C22×Q812yes—
162C2×C4×C43C22×Q814yes—
163C2×C4×C43C2×#4112yes—
164C2×C4×C43C2×#4114yes—
165C2×C4×C43C2511yescharacteristic
166C8×C43—24no—
167C8×C43—24no—
168C8×C43—24no—
169C8×C43C22×Q818yes—
170C2×#2962C4311yesmaximal, characteristic, direct product factor, Sylow
171C22×C43—28no—
172C22×C43—22no—
173C22×C43—22no—
174C22×C43C2×C4×Q814yes—
175C22×C43C2×C4×Q812yes—
176C22×C43C2×#13112yes—
177C22×C43#56812yes—
178C22×C43C24×C411yescharacteristic
179C4×C43—22no—
180C4×C43—28no—
181C4×C43—22no—
182C4×C43—22no—
183C4×C43—28no—
184C4×C43C2×C4×Q812yes—
185C4×C43C2×C4×Q814yes—
186C4×C43C2×#13114yes—
187C4×C43C23×Q811yescharacteristic
188C4×C43C22×#4111yescharacteristic
189C2×#533C2×C4311yescharacteristic
190#2962C2×C43116yesdirect product factor
191C2×#446C2×C4312yescomplemented
192C2×#446C2×C4314yescomplemented
193C2×C8×Q8C2×C4312yescomplemented
194C2×#424C2×C4312yes—
195C22×C4⋊C8C2×C4311yescharacteristic
196C2×#405C2×C4312yes—
197C2×C4×M16C2×C4311yescharacteristic
198C2×C43—24no—
199C2×C43#296214yesdirect product factor
200C2×C43C22×C4×Q811yescharacteristic
201C2×C43C22×#13111yescharacteristic
202C2×C43C2×#56811yescharacteristic
203C22×M16C22×C4311yescharacteristic
204C22×M16C22×C4311yescharacteristic
205C23×C8C22×C4312yes—
206#533C4×C4318yes—
207#533C22×C4318yes—
208C2×C4⋊Q8C4×C4311yescharacteristic
209C2×C4⋊Q8C4×C4311yescharacteristic
210C2×#125C4×C4312yes—
211C2×C22⋊Q8C4×C4312yes—
212C2×C22⋊Q8C4×C4312yes—
213C2×C4×Q8C22×C4312yes—
214C2×C4×Q8C22×C4312yes—
215C2×#117C22×C4312yes—
216C22×C42C22×C4311yescharacteristic
217#446C22×C43116yescomplemented
218#446C22×C43132yescomplemented
219C8×Q8C22×C43116yescomplemented
220#424C22×C43116yes—
221C2×C4⋊C8C22×C4311yescharacteristic
222C2×C4⋊C8C22×C4311yescharacteristic
223C2×C4⋊C8C22×C4312yes—
224C2×C4⋊C8C22×C4318yes—
225C2×C4⋊C8C22×C4314yes—
226C2×C4⋊C8C22×C4314yes—
227#405C22×C43116yes—
228C4×M16C22×C4318yes—
229C2×#97C22×C4312yes—
230C2×#97C22×C4314yes—
231C2×C4×C8C22×C4312yes—
232C2×C4×C8C22×C4314yes—
233C43C2×#296211yescharacteristic, direct product factor, Sylow
234C22×Q8C2×C4×C4312yes—
235C22×Q8C2×C4×C4312yes—
236C23×C4C2×C4×C4311yescharacteristic
237C23×C4C2×C4×C4311yescharacteristic
238C23×C4C23×C4311yescharacteristic
239C2×M16—24no—
240C2×M16Q8×C4318yescomplemented
241C2×M16C23×C4314yes—
242C2×M16C23×C4314yes—
243C22×C8—28no—
244C22×C8C23×C4312yes—
245C22×C8C23×C4312yes—
246C22×C8C23×C4318yes—
247C22×C8C23×C4312yes—
248C22×C8C23×C4312yes—
249C4⋊Q8C2×C4×C4318yes—
250C4⋊Q8C2×C4×C4318yes—
251#125C2×C4×C43116yes—
252C22⋊Q8C2×C4×C43116yes—
253C22⋊Q8C2×C4×C43116yes—
254C4×Q8C2×C4×C4318yes—
255C4×Q8C2×C4×C4318yes—
256C4×Q8C23×C4318yes—
257C4×Q8C23×C4318yes—
258#117C2×C4×C4318yes—
259#117C23×C4318yes—
260C2×C4⋊C4C2×C4×C4312yes—
261C2×C4⋊C4C2×C4×C4312yes—
262C2×C4⋊C4C2×C4×C4314yes—
263C2×C4⋊C4C2×C4×C4314yes—
264C2×C4⋊C4C2×C4×C4312yes—
265C2×C4⋊C4C2×C4×C4312yes—
266C2×C22⋊C4C2×C4×C4314yes—
267C2×C42C2×C4×C4311yescharacteristic
268C2×C42C2×C4×C4311yescharacteristic
269C2×C42C2×C4×C4314yes—
270C2×C42C23×C4314yes—
271C2×C42C23×C4311yescharacteristic
272C2×C42C23×C4311yescharacteristic
273C2×C42C23×C4314yes—
274C4⋊C8C23×C4314yes—
275C4⋊C8C23×C4314yes—
276C4⋊C8C23×C4318yes—
277C4⋊C8C23×C43116yes—
278C4⋊C8C23×C43116yes—
279#97C23×C4318yes—
280#97C23×C43116yes—
281C4×C8C23×C4318yes—
282C4×C8C23×C43116yes—
283C24C22×C4×C4311yescharacteristic
284C2×Q8—28no—
285C2×Q8—44no—
286C2×Q8C22×C4×C4318yes—
287C2×Q8C22×C4×C4318yes—
288C22×C4—24no—
289C22×C4—42no—
290C22×C4C22×C4×C4311yescharacteristic
291C22×C4C22×C4×C4311yescharacteristic
292C22×C4C22×C4×C4311yescharacteristic
293C22×C4C22×C4×C4314yes—
294C22×C4C22×C4×C4314yes—
295C22×C4C22×C4×C4314yes—
296C22×C4C22×C4×C4314yes—
297C22×C4C22×C4×C4311yescharacteristic
298C22×C4C22×C4×C4312yes—
299C22×C4C22×C4×C4311yescharacteristic
300C22×C4C2×Q8×C4314yes—
301C22×C4#41×C4314yes—
302C22×C4C24×C4311yescharacteristic
303C22×C4C24×C4312yes—
304M16—28no—
305M16C2×Q8×C43116yescomplemented
306C2×C8—24no—
307C2×C8—24no—
308C2×C8—216no—
309C2×C8—24no—
310C2×C8C2×Q8×C4318yes—
311C2×C8C24×C4314yes—
312C2×C8C24×C4314yes—
313C2×C8C24×C4314yes—
314C2×C8C24×C4314yes—
315C4⋊C4C22×C4×C4318yes—
316C4⋊C4C22×C4×C4318yes—
317C4⋊C4C22×C4×C43116yes—
318C4⋊C4C22×C4×C43116yes—
319C4⋊C4C22×C4×C4318yes—
320C4⋊C4C22×C4×C4318yes—
321C22⋊C4C22×C4×C43116yes—
322C42C22×C4×C4312yes—
323C42C22×C4×C4312yes—
324C42C22×C4×C4314yes—
325C42C22×C4×C4314yes—
326C42C22×C4×C4318yes—
327C42C24×C4312yes—
328C42C24×C4318yes—
329C42C24×C4312yes—
330C23—22no—
331C23—22no—
332C23C4×Q8×C4314yes—
333C23C23×C4×C4312yes—
334C23C23×C4×C4311yescharacteristic
335Q8—216no—
336Q8—48no—
337C2×C4—22no—
338C2×C4—28no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—28no—
342C2×C4—28no—
343C2×C4—44no—
344C2×C4C4×Q8×C4318yes—
345C2×C4C4×Q8×C4314yes—
346C2×C4#131×C4314yes—
347C2×C4C23×C4×C4312yes—
348C2×C4C23×C4×C4312yes—
349C2×C4C23×C4×C4312yes—
350C2×C4C23×C4×C4318yes—
351C2×C4C23×C4×C4318yes—
352C2×C4C23×C4×C4311yescharacteristic
353C2×C4C23×C4×C4312yes—
354C2×C4C23×C4×C4312yes—
355C2×C4C22×Q8×C4312yes—
356C2×C4C22×Q8×C4314yes—
357C2×C4C2×#41×C4312yes—
358C2×C4C2×#41×C4314yes—
359C2×C4C25×C4311yescharacteristic
360C8—24no—
361C8—24no—
362C8—24no—
363C8C22×Q8×C4318yes—
364C22—28no—
365C22—22no—
366C22—22no—
367C22C2×C4×Q8×C4314yes—
368C22C2×C4×Q8×C4312yes—
369C22C2×#131×C4312yes—
370C22C43×#56812yes—
371C22C24×C4×C4311yescharacteristic
372C4—22no—
373C4—28no—
374C4—22no—
375C4—22no—
376C4—28no—
377C4C2×C4×Q8×C4312yes—
378C4C2×C4×Q8×C4314yes—
379C4C2×#131×C4314yes—
380C4C23×Q8×C4311yescharacteristic
381C4C22×#41×C4311yescharacteristic
382C2—24no—
383C2C43×#296214yesdirect product factor
384C2C22×C4×Q8×C4311yescharacteristic
385C2C22×#131×C4311yescharacteristic
386C2C2×C43×#56811yescharacteristic
subgroupG/H
centerC22×C4×C43C24
commutatorC22C24×C4×C43
Frattini, cosocleC2×C4C25×C43
socleC23×C43C23×C4
prime radicalC24×C43C22×C4
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2962C2direct (N × H)
3. C2×C43×#446C2semidirect
4. C2×C43×#446C2semidirect
5. C2×C8×Q8×C43C2semidirect
24. C43×#446C22semidirect
25. C43×#446C22semidirect
26. C8×Q8×C43C22semidirect
46. C2×M16×C43Q8semidirect
111. M16×C43C2×Q8semidirect
170. C2×#2962C43direct (N × H)
190. #2962C2×C43direct (N × H)
191. C2×#446C2×C43semidirect
192. C2×#446C2×C43semidirect
193. C2×C8×Q8C2×C43semidirect
199. C2×C43#2962direct (N × H)
217. #446C22×C43semidirect
218. #446C22×C43semidirect
219. C8×Q8C22×C43semidirect
233. C43C2×#2962direct (N × H)
240. C2×M16Q8×C43semidirect
305. M16C2×Q8×C43semidirect
383. C2C43×#2962direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#5332
C43×#29622
C2×C43×#4462
C2×C8×Q8×C432
C2×C43×#4242
C22×C4⋊C8×C432
C2×C43×#4052
C2×C4×M16×C432
C2×#296243