Finite Group Databasebeta

← C2×#519×D43 #26003179

Subgroups — C2×#519×D43 #26003179

Order 11008.

11230 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Q8×D43C211yesmaximal, characteristic
2C2×#14583377C211yesmaximal, characteristic, complemented
3C2×#14583376C216yesmaximal, complemented
4C2×#14583375C218yesmaximal, complemented
5#519×D43C2132yesmaximal, direct product factor
6C2×C4×Q8×D43C218yesmaximal, complemented
7C2×#117×D43C216yesmaximal
8C2×C43×#519C211yesmaximal, characteristic, complemented
9C23×Dic86C2213yes—
10C22×Q8×D43C4132yescomplemented
11C22×Q8×D43C2214yes—
12C22×Q8×D43C22116yes—
13C22×Q8×D43C2214yes—
14C23×C4×D43C2213yes—
15#14583377C22116yescomplemented
16#14583376C22196yescomplemented
17#14583375C221128yescomplemented
18C2×Q8×Dic43C2218yescomplemented
19C2×C4×Dic86C22124yescomplemented
20C2×#13063290C22124yescomplemented
21C4×Q8×D43C221128yescomplemented
22C2×#13063284C2216yes—
23C2×#13063283C22112yes—
24C2×#13063282C22112yes—
25C2×#13063281C22112yes—
26#117×D43C22196yes—
27C2×C4⋊C4×D43C22112yes—
28C2×C22⋊C4×D43C2214yes—
29C2×C42×D43C22112yes—
30C23×Q8×C43C2211yescharacteristic
31C43×#519C22116yescomplemented
32C2×C4×Q8×C43C2218yescomplemented
33C2×#117×C43C2216yes—
34C24×D43C2311yescharacteristic
35C22×Dic86C2×C4148yescomplemented
36C22×Dic86C23112yes—
37C22×Dic86C23124yes—
38C2×Q8×D43C2×C4164yes—
39C2×Q8×D43C2×C4164yescomplemented
40C2×Q8×D43C2×C41256yescomplemented
41C2×Q8×D43C23132yes—
42C2×Q8×D43C23132yes—
43C23×Dic43C2313yes—
44C22×C4×D43C2×C4148yes—
45C22×C4×D43C2318yes—
46C22×C4×D43C2316yes—
47C22×C4×D43C23124yes—
48C22×C4×D43C2316yes—
49Q8×Dic43C23164yescomplemented
50C4×Dic86C231192yescomplemented
51#13063290C231192yescomplemented
52#13063284C23148yes—
53#13063283C23196yes—
54#13063282C23196yes—
55#13063281C23196yes—
56C2×C4⋊Dic43C23112yes—
57C2×Dic43⋊C4C23124yes—
58C4⋊C4×D43C23196yes—
59C2×C22⋊Dic43C2314yes—
60C2×(C2×D43)⋊C4C2318yes—
61C22⋊C4×D43C23132yes—
62C2×C4×Dic43C23124yes—
63C2×C4×Dic43C23112yes—
64C42×D43C23196yes—
65C22×Q8×C43C2×C4116yescomplemented
66C22×Q8×C43C2314yes—
67C22×Q8×C43C2318yes—
68C23×C4×C43C2313yes—
69C4×Q8×C43C23164yescomplemented
70#117×C43C23148yes—
71C2×C4⋊C4×C43C23112yes—
72C2×C22⋊C4×C43C2314yes—
73C2×C42×C43C23112yes—
74C24×C43C2411yescharacteristic
75C23×D43—28no—
76C23×D43C22×C418yes—
77C23×D43C2414yes—
78C23×D43C2411yescharacteristic
79C23×D43C2411yescharacteristic
80C2×Q8×C43C22×C4132yes—
81C2×Q8×C43C22×C4164yescomplemented
82C2×Q8×C43C24116yes—
83C22×C4×C43C22×C4124yes—
84C22×C4×C43C2418yes—
85C22×C4×C43C2416yes—
86C22×C4×C43C24112yes—
87C22×Dic43C22×C4124yes—
88C22×Dic43C2418yes—
89C22×Dic43C2416yes—
90C22×Dic43C24112yes—
91Q8×D43C22×C41256yes—
92Q8×D43C22×C41256yescomplemented
93C2×C4×D43—232no—
94C2×C4×D43C22×C4148yes—
95C2×C4×D43C22×C41192yes—
96C2×C4×D43C22×C4148yes—
97C2×C4×D43C24132yes—
98C2×C4×D43C24124yes—
99C2×C4×D43C24124yes—
100C2×Dic86C22×C4196yes—
101C2×Dic86C22×C41192yescomplemented
102C2×Dic86C24148yes—
103C4⋊C4×C43C24148yes—
104C22⋊C4×C43C24116yes—
105C42×C43C24148yes—
106C22⋊Dic43C24116yes—
107(C2×D43)⋊C4C24132yes—
108C4⋊Dic43C24148yes—
109Dic43⋊C4C24196yes—
110C4×Dic43C24196yes—
111C4×Dic43C24148yes—
112C23×C43—24no—
113C23×C43C23×C414yes—
114C23×C43C2512yes—
115C23×C43C2511yescharacteristic
116C22×D43—24no—
117C22×D43—232no—
118C22×D43—216no—
119C22×D43C23×C414yes—
120C22×D43C23×C4116yes—
121C22×D43C23×C414yes—
122C22×D432−1+418yes—
123C22×D43C2512yes—
124C22×D43C2512yes—
125Q8×C43C23×C4164yes—
126C2×C4×C43—216no—
127C2×C4×C43C23×C4124yes—
128C2×C4×C43C23×C4148yes—
129C2×C4×C43C25116yes—
130C2×C4×C43C25112yes—
131C2×Dic43—216no—
132C2×Dic43C23×C4124yes—
133C2×Dic43C23×C4148yes—
134C2×Dic43C25116yes—
135C2×Dic43C25112yes—
136C4×D43—264no—
137C4×D43C23×C4196yes—
138C4×D43C23×C4196yes—
139Dic86C23×C41192yes—
140C22×#519—431nomaximal, Sylow
141C22×C43—24no—
142C22×C43—28no—
143C22×C43C24×C414yes—
144C22×C43C24×C412yes—
145C22×C43C2×2−1+414yes—
146C22×C43C2611yescharacteristic
147C2×D43—24no—
148C2×D43—28no—
149C2×D43—232no—
150C2×D43#519116yesdirect product factor
151C2×D43C24×C414yes—
152C2×D43C24×C414yes—
153C2×D43C2×2−1+418yes—
154C4×C43—216no—
155C4×C43C24×C4124yes—
156Dic43—216no—
157Dic43C24×C4124yes—
158C24×Q8—431no—
159C2×#519—431no—
160C2×#519—4332no—
161C2×#519—438no—
162C2×#519—436no—
163C2×#519D4311yescharacteristic, direct product factor
164C22×C4×Q8—438no—
165C22×#117—436no—
166C2×C43—24no—
167C2×C43C2×#51914yescomplemented
168C2×C43C25×C411yescharacteristic
169C2×C43C22×2−1+412yes—
170D43—24no—
171D43C2×#51918yesdirect product factor
172C23×Q8—434no—
173C23×Q8—434no—
174C23×Q8—4316no—
175C23×Q8—4332no—
176C23×Q8—433no—
177C23×Q8C2×D4311yescharacteristic
178C24×C4—433no—
179#519—4316no—
180#519—43128no—
181#519—4396no—
182#519C2×D43116yesdirect product factor
183C2×C4×Q8—438no—
184C2×C4×Q8—43128no—
185C2×C4×Q8—4324no—
186C2×C4×Q8—4324no—
187C2×C4×Q8C2×D4318yescomplemented
188C2×#117—436no—
189C2×#117—4396no—
190C2×#117—4312no—
191C2×#117—4312no—
192C2×#117—4312no—
193C2×#117C2×D4316yes—
194C22×C4⋊C4—4312no—
195C22×C22⋊C4—434no—
196C22×C42—4312no—
197C43C22×#51911yescharacteristic, complemented, Sylow
198C25—431no—
199C22×Q8—4364no—
200C22×Q8—4364no—
201C22×Q8—43256no—
202C22×Q8—4332no—
203C22×Q8—4332no—
204C22×Q8—4348no—
205C22×Q8—4312no—
206C22×Q8—4324no—
207C22×Q8C4×D43116yescomplemented
208C22×Q8C22×D4314yes—
209C22×Q8C22×D4318yes—
210C23×C4—433no—
211C23×C4—4348no—
212C23×C4—436no—
213C23×C4—4324no—
214C23×C4—436no—
215C23×C4—438no—
216C23×C4C22×D4313yes—
217C4×Q8—4364no—
218C4×Q8—43192no—
219C4×Q8—43192no—
220C4×Q8C22×D43164yescomplemented
221#117—4348no—
222#117—4396no—
223#117—4396no—
224#117—4396no—
225#117C22×D43148yes—
226C2×C4⋊C4—4324no—
227C2×C4⋊C4—4312no—
228C2×C4⋊C4—4396no—
229C2×C4⋊C4C22×D43112yes—
230C2×C22⋊C4—434no—
231C2×C22⋊C4—438no—
232C2×C22⋊C4—4332no—
233C2×C22⋊C4C22×D4314yes—
234C2×C42—4324no—
235C2×C42—4312no—
236C2×C42—4396no—
237C2×C42C22×D43112yes—
238C24—431no—
239C24—438no—
240C24—434no—
241C24—431no—
242C24—868no—
243C24C23×D4311yescharacteristic
244C2×Q8—43256no—
245C2×Q8—43256no—
246C2×Q8—4396no—
247C2×Q8—43192no—
248C2×Q8—4348no—
249C2×Q8C2×C4×D43132yes—
250C2×Q8C2×C4×D43164yescomplemented
251C2×Q8C23×D43116yes—
252C22×C4—4324no—
253C22×C4—4312no—
254C22×C4—436no—
255C22×C4—4348no—
256C22×C4—4348no—
257C22×C4—43192no—
258C22×C4—4324no—
259C22×C4—4324no—
260C22×C4—438no—
261C22×C4—4332no—
262C22×C4—8632no—
263C22×C4C2×C4×D43124yes—
264C22×C4C23×D4318yes—
265C22×C4C23×D43112yes—
266C22×C4C23×D4316yes—
267C4⋊C4—4396no—
268C4⋊C4—4348no—
269C4⋊C4C23×D43148yes—
270C22⋊C4—4316no—
271C22⋊C4—4332no—
272C22⋊C4C23×D43116yes—
273C42—4396no—
274C42—4348no—
275C42C23×D43148yes—
276C23—24no—
277C23—434no—
278C23—438no—
279C23—432no—
280C23—4316no—
281C23—434no—
282C23—432no—
283C23—8632no—
284C23—8616no—
285C23—864no—
286C23C22×C4×D4314yes—
287C23C24×D4312yes—
288C23C24×D4311yescharacteristic
289Q8—43192no—
290Q8C22×C4×D43164yes—
291C2×C4—216no—
292C2×C4—4348no—
293C2×C4—4324no—
294C2×C4—4312no—
295C2×C4—4396no—
296C2×C4—4396no—
297C2×C4—4316no—
298C2×C4—8664no—
299C2×C4—8616no—
300C2×C4C22×C4×D43124yes—
301C2×C4C22×C4×D43148yes—
302C2×C4C24×D43116yes—
303C2×C4C24×D43112yes—
304C22—28no—
305C22—24no—
306C22—4316no—
307C22—434no—
308C22—438no—
309C22—434no—
310C22—8632no—
311C22—868no—
312C22—864no—
313C22C23×C4×D4314yes—
314C22C23×C4×D4312yes—
315C222−1+4×D4314yes—
316C22C25×D4311yescharacteristic
317C4—216no—
318C4—4324no—
319C4—8616no—
320C4C23×C4×D43124yes—
321C2—24no—
322C2—438no—
323C2—864no—
324C2#519×D4314yesdirect product factor
325C2C24×C4×D4311yescharacteristic
326C2C2×2−1+4×D4312yes—
subgroupG/H
centerC23C24×D43
commutatorC2×C43C25×C4
FrattiniC22C25×D43
FittingC2×C43×#519C2
socleC23×C43C25
prime radicalC24×D43C23
cosocleC22×C43C26
hypercenterC2×#519D43
hypocenterC43C22×#519
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#519

Complements

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

NH ≅ G/Ntype
2. C2×#14583377C2semidirect
3. C2×#14583376C2semidirect
4. C2×#14583375C2semidirect
5. #519×D43C2direct (N × H)
6. C2×C4×Q8×D43C2semidirect
8. C2×C43×#519C2semidirect
10. C22×Q8×D43C4semidirect
15. #14583377C22semidirect
16. #14583376C22semidirect
17. #14583375C22semidirect
18. C2×Q8×Dic43C22semidirect
19. C2×C4×Dic86C22semidirect
20. C2×#13063290C22semidirect
21. C4×Q8×D43C22semidirect
31. C43×#519C22semidirect
32. C2×C4×Q8×C43C22semidirect
35. C22×Dic86C2×C4semidirect
39. C2×Q8×D43C2×C4semidirect
40. C2×Q8×D43C2×C4semidirect
49. Q8×Dic43C23semidirect
50. C4×Dic86C23semidirect
51. #13063290C23semidirect
65. C22×Q8×C43C2×C4semidirect
69. C4×Q8×C43C23semidirect
81. C2×Q8×C43C22×C4semidirect
92. Q8×D43C22×C4semidirect
101. C2×Dic86C22×C4semidirect
150. C2×D43#519direct (N × H)
163. C2×#519D43direct (N × H)
167. C2×C43C2×#519semidirect
171. D43C2×#519direct (N × H)
182. #519C2×D43direct (N × H)
187. C2×C4×Q8C2×D43semidirect
197. C43C22×#519semidirect
207. C22×Q8C4×D43semidirect
220. C4×Q8C22×D43semidirect
250. C2×Q8C2×C4×D43semidirect
324. C2#519×D43direct (N × H)

Maximal subgroups

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

subgroupindex
C23×Q8×D432
C2×#145833772
C2×#145833762
C2×#145833752
#519×D432
C2×C4×Q8×D432
C2×#117×D432
C2×C43×#5192
C22×#51943