Finite Group Databasebeta

← C2×C43×#2985 #24980262

Subgroups — C2×C43×#2985 #24980262

Order 11008.

1750 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#533C211yesmaximal, characteristic
2C43×#2985C2116yesmaximal, direct product factor
3C2×C43×#446C212yesmaximal, complemented
4C2×C43×#446C214yesmaximal, complemented
5C2×C8×Q8×C43C212yesmaximal, complemented
6C2×C43×#433C214yesmaximal
7C2×C43×#432C211yesmaximal, characteristic
8C2×C43×#431C211yesmaximal, characteristic
9C43×#533C418yes—
10C43×#533C2218yes—
11C2×C4⋊Q8×C43C411yescharacteristic
12C2×C4⋊Q8×C43C411yescharacteristic
13C2×#125×C43C412yes—
14C2×C22⋊Q8×C43C412yes—
15C2×C22⋊Q8×C43C412yes—
16C2×C4×Q8×C43C2212yes—
17C2×C4×Q8×C43C2212yes—
18C2×#117×C43C2212yes—
19C22×C42×C43C2211yescharacteristic
20C43×#446C22116yescomplemented
21C43×#446C22132yescomplemented
22C8×Q8×C43C22116yescomplemented
23C43×#433C22132yes—
24C43×#432C2218yes—
25C43×#431C2218yes—
26C2×C4⋊C8×C43C2212yes—
27C2×C4⋊C8×C43C2212yes—
28C2×C4⋊C8×C43C2214yes—
29C2×C4⋊C8×C43C2214yes—
30C2×C22⋊C8×C43C2212yes—
31C2×C22⋊C8×C43C2212yes—
32C2×#97×C43C2212yes—
33C2×#97×C43C2214yes—
34C2×C4×C8×C43C2211yescharacteristic
35C2×C4×C8×C43C2211yescharacteristic
36C2×C4×C8×C43C2214yes—
37C22×Q8×C43C2×C412yes—
38C22×Q8×C43C2×C412yes—
39C23×C4×C43C2×C411yescharacteristic
40C23×C4×C43C2×C411yescharacteristic
41C23×C4×C43C2311yescharacteristic
42C22×C8×C43C2312yes—
43C22×C8×C43C2312yes—
44C22×C8×C43C2314yes—
45C4⋊Q8×C43C2×C418yes—
46C4⋊Q8×C43C2×C418yes—
47#125×C43C2×C4116yes—
48C22⋊Q8×C43C2×C4116yes—
49C22⋊Q8×C43C2×C4116yes—
50C4×Q8×C43C2×C418yes—
51C4×Q8×C43C2×C418yes—
52C4×Q8×C43C2318yes—
53C4×Q8×C43C2318yes—
54#117×C43C2×C418yes—
55#117×C43C2318yes—
56C2×C4⋊C4×C43C2×C412yes—
57C2×C4⋊C4×C43C2×C412yes—
58C2×C4⋊C4×C43C2×C414yes—
59C2×C4⋊C4×C43C2×C414yes—
60C2×C4⋊C4×C43C2×C412yes—
61C2×C4⋊C4×C43C2×C412yes—
62C2×C22⋊C4×C43C2×C414yes—
63C2×C42×C43C2×C411yescharacteristic
64C2×C42×C43C2×C411yescharacteristic
65C2×C42×C43C2×C414yes—
66C2×C42×C43C2314yes—
67C2×C42×C43C2311yescharacteristic
68C2×C42×C43C2311yescharacteristic
69C2×C42×C43C2314yes—
70C4⋊C8×C43C2318yes—
71C4⋊C8×C43C2318yes—
72C4⋊C8×C43C23116yes—
73C4⋊C8×C43C23116yes—
74C22⋊C8×C43C2318yes—
75C22⋊C8×C43C2318yes—
76#97×C43C2318yes—
77#97×C43C23116yes—
78C4×C8×C43C2314yes—
79C4×C8×C43C2314yes—
80C4×C8×C43C23116yes—
81C24×C43C22×C411yescharacteristic
82C2×Q8×C43—28no—
83C2×Q8×C43—44no—
84C2×Q8×C43C22×C418yes—
85C2×Q8×C43C22×C418yes—
86C22×C4×C43—24no—
87C22×C4×C43—24no—
88C22×C4×C43—42no—
89C22×C4×C43C22×C411yescharacteristic
90C22×C4×C43C22×C412yes—
91C22×C4×C43C22×C411yescharacteristic
92C22×C4×C43C22×C411yescharacteristic
93C22×C4×C43C22×C411yescharacteristic
94C22×C4×C43C22×C414yes—
95C22×C4×C43C22×C414yes—
96C22×C4×C43C22×C414yes—
97C22×C4×C43C22×C414yes—
98C22×C4×C43C22×C411yescharacteristic
99C22×C4×C43C2412yes—
100C22×C4×C43C2411yescharacteristic
101C2×C8×C43—24no—
102C2×C8×C43—24no—
103C2×C8×C43—28no—
104C2×C8×C43C2414yes—
105C2×C8×C43C2414yes—
106C2×C8×C43C2418yes—
107C4⋊C4×C43C22×C418yes—
108C4⋊C4×C43C22×C418yes—
109C4⋊C4×C43C22×C4116yes—
110C4⋊C4×C43C22×C4116yes—
111C4⋊C4×C43C22×C418yes—
112C4⋊C4×C43C22×C418yes—
113C22⋊C4×C43C22×C4116yes—
114C42×C43C22×C412yes—
115C42×C43C22×C412yes—
116C42×C43C22×C414yes—
117C42×C43C22×C414yes—
118C42×C43C22×C418yes—
119C42×C43C2412yes—
120C42×C43C2418yes—
121C42×C43C2412yes—
122C23×C43—22no—
123C23×C43—22no—
124C23×C43—22no—
125C23×C43C23×C412yes—
126C23×C43C23×C411yescharacteristic
127Q8×C43—216no—
128Q8×C43—48no—
129C2×C4×C43—22no—
130C2×C4×C43—22no—
131C2×C4×C43—28no—
132C2×C4×C43—22no—
133C2×C4×C43—22no—
134C2×C4×C43—28no—
135C2×C4×C43—24no—
136C2×C4×C43—28no—
137C2×C4×C43—24no—
138C2×C4×C43—44no—
139C2×C4×C43#13114yes—
140C2×C4×C43C23×C412yes—
141C2×C4×C43C23×C412yes—
142C2×C4×C43C23×C412yes—
143C2×C4×C43C23×C412yes—
144C2×C4×C43C23×C418yes—
145C2×C4×C43C23×C418yes—
146C2×C4×C43C23×C411yescharacteristic
147C2×C4×C43C23×C412yes—
148C2×C4×C432−1+414yes—
149C2×C4×C43C2511yescharacteristic
150C8×C43—24no—
151C8×C43—24no—
152C8×C43—28no—
153C2×#2985C4311yesmaximal, characteristic, direct product factor, Sylow
154C22×C43—22no—
155C22×C43—22no—
156C22×C43—22no—
157C22×C43—44no—
158C22×C43#51912yes—
159C22×C43C2×#13112yes—
160C22×C43#56812yes—
161C22×C43C24×C411yescharacteristic
162C4×C43—22no—
163C4×C43—22no—
164C4×C43—28no—
165C4×C43—22no—
166C4×C43—22no—
167C4×C43—28no—
168C4×C43#51912yes—
169C4×C43C2×#13114yes—
170C4×C43C2×2−1+412yes—
171C2×#533C2×C4311yescharacteristic
172#2985C2×C43116yesdirect product factor
173C2×#446C2×C4312yescomplemented
174C2×#446C2×C4314yescomplemented
175C2×C8×Q8C2×C4312yescomplemented
176C2×#433C2×C4314yes—
177C2×#432C2×C4311yescharacteristic
178C2×#431C2×C4311yescharacteristic
179C2×C43—42no—
180C2×C43#298514yesdirect product factor
181C2×C43C2×#51911yescharacteristic
182C2×C43C22×#13111yescharacteristic
183C2×C43C2×#56811yescharacteristic
184#533C4×C4318yes—
185#533C22×C4318yes—
186C2×C4⋊Q8C4×C4311yescharacteristic
187C2×C4⋊Q8C4×C4311yescharacteristic
188C2×#125C4×C4312yes—
189C2×C22⋊Q8C4×C4312yes—
190C2×C22⋊Q8C4×C4312yes—
191C2×C4×Q8C22×C4312yes—
192C2×C4×Q8C22×C4312yes—
193C2×#117C22×C4312yes—
194C22×C42C22×C4311yescharacteristic
195#446C22×C43116yescomplemented
196#446C22×C43132yescomplemented
197C8×Q8C22×C43116yescomplemented
198#433C22×C43132yes—
199#432C22×C4318yes—
200#431C22×C4318yes—
201C2×C4⋊C8C22×C4312yes—
202C2×C4⋊C8C22×C4312yes—
203C2×C4⋊C8C22×C4314yes—
204C2×C4⋊C8C22×C4314yes—
205C2×C22⋊C8C22×C4312yes—
206C2×C22⋊C8C22×C4312yes—
207C2×#97C22×C4312yes—
208C2×#97C22×C4314yes—
209C2×C4×C8C22×C4311yescharacteristic
210C2×C4×C8C22×C4311yescharacteristic
211C2×C4×C8C22×C4314yes—
212C43C2×#298511yescharacteristic, direct product factor, Sylow
213C22×Q8C2×C4×C4312yes—
214C22×Q8C2×C4×C4312yes—
215C23×C4C2×C4×C4311yescharacteristic
216C23×C4C2×C4×C4311yescharacteristic
217C23×C4C23×C4311yescharacteristic
218C22×C8C23×C4312yes—
219C22×C8C23×C4312yes—
220C22×C8C23×C4314yes—
221C4⋊Q8C2×C4×C4318yes—
222C4⋊Q8C2×C4×C4318yes—
223#125C2×C4×C43116yes—
224C22⋊Q8C2×C4×C43116yes—
225C22⋊Q8C2×C4×C43116yes—
226C4×Q8C2×C4×C4318yes—
227C4×Q8C2×C4×C4318yes—
228C4×Q8C23×C4318yes—
229C4×Q8C23×C4318yes—
230#117C2×C4×C4318yes—
231#117C23×C4318yes—
232C2×C4⋊C4C2×C4×C4312yes—
233C2×C4⋊C4C2×C4×C4312yes—
234C2×C4⋊C4C2×C4×C4314yes—
235C2×C4⋊C4C2×C4×C4314yes—
236C2×C4⋊C4C2×C4×C4312yes—
237C2×C4⋊C4C2×C4×C4312yes—
238C2×C22⋊C4C2×C4×C4314yes—
239C2×C42C2×C4×C4311yescharacteristic
240C2×C42C2×C4×C4311yescharacteristic
241C2×C42C2×C4×C4314yes—
242C2×C42C23×C4314yes—
243C2×C42C23×C4311yescharacteristic
244C2×C42C23×C4311yescharacteristic
245C2×C42C23×C4314yes—
246C4⋊C8C23×C4318yes—
247C4⋊C8C23×C4318yes—
248C4⋊C8C23×C43116yes—
249C4⋊C8C23×C43116yes—
250C22⋊C8C23×C4318yes—
251C22⋊C8C23×C4318yes—
252#97C23×C4318yes—
253#97C23×C43116yes—
254C4×C8C23×C4314yes—
255C4×C8C23×C4314yes—
256C4×C8C23×C43116yes—
257C24C22×C4×C4311yescharacteristic
258C2×Q8—28no—
259C2×Q8—44no—
260C2×Q8C22×C4×C4318yes—
261C2×Q8C22×C4×C4318yes—
262C22×C4—24no—
263C22×C4—24no—
264C22×C4—42no—
265C22×C4C22×C4×C4311yescharacteristic
266C22×C4C22×C4×C4311yescharacteristic
267C22×C4C22×C4×C4311yescharacteristic
268C22×C4C22×C4×C4314yes—
269C22×C4C22×C4×C4314yes—
270C22×C4C22×C4×C4314yes—
271C22×C4C22×C4×C4311yescharacteristic
272C22×C4C22×C4×C4312yes—
273C22×C4C22×C4×C4314yes—
274C22×C4C22×C4×C4311yescharacteristic
275C22×C4C24×C4312yes—
276C22×C4C24×C4311yescharacteristic
277C2×C8—24no—
278C2×C8—24no—
279C2×C8—28no—
280C2×C8C24×C4314yes—
281C2×C8C24×C4314yes—
282C2×C8C24×C4318yes—
283C4⋊C4C22×C4×C4318yes—
284C4⋊C4C22×C4×C4318yes—
285C4⋊C4C22×C4×C43116yes—
286C4⋊C4C22×C4×C43116yes—
287C4⋊C4C22×C4×C4318yes—
288C4⋊C4C22×C4×C4318yes—
289C22⋊C4C22×C4×C43116yes—
290C42C22×C4×C4312yes—
291C42C22×C4×C4312yes—
292C42C22×C4×C4314yes—
293C42C22×C4×C4314yes—
294C42C22×C4×C4318yes—
295C42C24×C4312yes—
296C42C24×C4318yes—
297C42C24×C4312yes—
298C23—22no—
299C23—22no—
300C23—22no—
301C23C23×C4×C4312yes—
302C23C23×C4×C4311yescharacteristic
303Q8—216no—
304Q8—48no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—28no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—28no—
311C2×C4—24no—
312C2×C4—28no—
313C2×C4—24no—
314C2×C4—44no—
315C2×C4#131×C4314yes—
316C2×C4C23×C4×C4312yes—
317C2×C4C23×C4×C4312yes—
318C2×C4C23×C4×C4312yes—
319C2×C4C23×C4×C4312yes—
320C2×C4C23×C4×C4318yes—
321C2×C4C23×C4×C4318yes—
322C2×C4C23×C4×C4311yescharacteristic
323C2×C4C23×C4×C4312yes—
324C2×C42−1+4×C4314yes—
325C2×C4C25×C4311yescharacteristic
326C8—24no—
327C8—24no—
328C8—28no—
329C22—22no—
330C22—22no—
331C22—22no—
332C22—44no—
333C22C43×#51912yes—
334C22C2×#131×C4312yes—
335C22C43×#56812yes—
336C22C24×C4×C4311yescharacteristic
337C4—22no—
338C4—22no—
339C4—28no—
340C4—22no—
341C4—22no—
342C4—28no—
343C4C43×#51912yes—
344C4C2×#131×C4314yes—
345C4C2×2−1+4×C4312yes—
346C2—42no—
347C2C43×#298514yesdirect product factor
348C2C2×C43×#51911yescharacteristic
349C2C22×#131×C4311yescharacteristic
350C2C2×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×#2985C2direct (N × H)
3. C2×C43×#446C2semidirect
4. C2×C43×#446C2semidirect
5. C2×C8×Q8×C43C2semidirect
20. C43×#446C22semidirect
21. C43×#446C22semidirect
22. C8×Q8×C43C22semidirect
153. C2×#2985C43direct (N × H)
172. #2985C2×C43direct (N × H)
173. C2×#446C2×C43semidirect
174. C2×#446C2×C43semidirect
175. C2×C8×Q8C2×C43semidirect
180. C2×C43#2985direct (N × H)
195. #446C22×C43semidirect
196. #446C22×C43semidirect
197. C8×Q8C22×C43semidirect
212. C43C2×#2985direct (N × H)
347. C2C43×#2985direct (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×#29852
C2×C43×#4462
C2×C8×Q8×C432
C2×C43×#4332
C2×C43×#4322
C2×C43×#4312
C2×#298543