Finite Group Databasebeta

← C2×#19144001 #25963336

Subgroups — C2×#19144001 #25963336

Order 11008.

4790 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583470C213yesmaximal, complemented
2#19144001C2116yesmaximal, direct product factor
3C2×#14583089C218yesmaximal, complemented
4C2×#14582873C213yesmaximal, complemented
5C2×C43×#585C211yesmaximal, characteristic
6C23×Dic86C2211yescharacteristic, complemented
7#14583470—212no—
8#14583470C22124yescomplemented
9C2×#13063323—23no—
10C2×#13063312—23no—
11C2×#13063306C22112yescomplemented
12C2×#13063304—26no—
13C2×#13063284C2213yescomplemented
14#14583089C22164yescomplemented
15#14582873C22124yescomplemented
16C2×#13063240C22112yescomplemented
17C43×#585—212no—
18C43×#585C2218yes—
19C2×2−1+4×C43—23no—
20C2×H(5,𝔽2)×C43—23no—
21C2×H(5,𝔽2)×C43C2214yes—
22C22×#41×C43—26no—
23C22×#41×C43C2213yes—
24C22×Dic86—23no—
25C22×Dic86—23no—
26C22×Dic86—26no—
27C22×Dic86C2314yescomplemented
28C23×Dic43C2312yes—
29#13063323—224no—
30#13063312—224no—
31#13063306—224no—
32#13063306C23148yescomplemented
33#13063304—248no—
34#13063284—26no—
35#13063284C23112yescomplemented
36C2×C4⋊Dic43—23no—
37C2×Dic43⋊C4—212no—
38C2×C22⋊Dic43—212no—
39C2×C22⋊Dic43C2316yes—
40C2×C4×Dic43—23no—
41#13063240C23148yescomplemented
422−1+4×C43—224no—
432−1+4×C43—224no—
44H(5,𝔽2)×C43—224no—
45H(5,𝔽2)×C43—224no—
46H(5,𝔽2)×C43—224no—
47H(5,𝔽2)×C43C23116yes—
48C2×#41×C43—24no—
49C2×#41×C43—212no—
50C2×#41×C43—248no—
51C2×#41×C43—26no—
52C2×#41×C43—212no—
53C2×#41×C43—248no—
54C2×#41×C43—26no—
55C2×#41×C43—212no—
56C2×#41×C43D4112yes—
57C2×#41×C43C23112yes—
58C22×Q8×C43—26no—
59C22×Q8×C43D413yes—
60C22×D4×C43—26no—
61C22×D4×C43—212no—
62C22×D4×C43D413yes—
63C22×D4×C43C2316yes—
64C23×C4×C43—24no—
65C23×C4×C43D416yes—
66C23×C4×C43C2311yescharacteristic
67C24×C43—24no—
68C24×C43C2×D416yes—
69C24×C43C2411yescharacteristic
70#41×C43—232no—
71#41×C43—248no—
72#41×C43—296no—
73#41×C43—224no—
74#41×C43—224no—
75#41×C43—224no—
76#41×C43—248no—
77#41×C43—224no—
78C2×Q8×C43—24no—
79C2×Q8×C43—248no—
80C2×Q8×C43—26no—
81C2×Q8×C43—26no—
82C2×Q8×C43C2×D4112yes—
83C2×D4×C43—212no—
84C2×D4×C43—248no—
85C2×D4×C43—248no—
86C2×D4×C43—26no—
87C2×D4×C43—26no—
88C2×D4×C43—212no—
89C2×D4×C43—248no—
90C2×D4×C43—212no—
91C2×D4×C43C2×D4112yes—
92C2×D4×C43C2×D4112yes—
93C2×D4×C43C24112yes—
94C22×C4×C43—212no—
95C22×C4×C43—232no—
96C22×C4×C43—26no—
97C22×C4×C43—26no—
98C22×C4×C43—212no—
99C22×C4×C43C2×D416yes—
100C22×C4×C43C2×D4124yes—
101C22×C4×C43C2×D413yes—
102C22×C4×C43C2×D413yes—
103C22×C4×C43C2×D416yes—
104C22×C4×C43C2412yes—
105C22×Dic43—26no—
106C22×Dic43—26no—
107C22×Dic43—26no—
108C22×Dic43C2414yes—
109C2×Dic86—212no—
110C2×Dic86—212no—
111C2×Dic86—41no—
112C2×Dic86—43no—
113C2×Dic86—46no—
114C2×Dic86—46no—
115C22⋊Dic43—248no—
116C22⋊Dic43—26no—
117C22⋊Dic43C24112yes—
118C4⋊Dic43—212no—
119Dic43⋊C4—248no—
120C4×Dic43—212no—
121C23×C43—216no—
122C23×C43—26no—
123C23×C43—26no—
124C23×C43—42no—
125C23×C43—412no—
126C23×C43—88no—
127C23×C43C22×D413yes—
128C23×C43C22×D4112yes—
129C23×C43C22×D413yes—
130C23×C43C2511yescharacteristic
131Q8×C43—216no—
132Q8×C43—224no—
133D4×C43—248no—
134D4×C43—224no—
135D4×C43—224no—
136D4×C43—224no—
137C2×C4×C43—248no—
138C2×C4×C43—26no—
139C2×C4×C43—26no—
140C2×C4×C43—224no—
141C2×C4×C43—224no—
142C2×C4×C43#12011yescharacteristic
143C2×C4×C43#12013yes—
144C2×C4×C43#12016yes—
145C2×C4×C43#12016yes—
146C2×C4×C43C22×D4112yes—
147C2×C4×C43C22×D416yes—
148C2×C4×C43C22×D416yes—
149C2×Dic43—212no—
150C2×Dic43—212no—
151C2×Dic43—412no—
152C2×Dic43—46no—
153C2×Dic43—42no—
154Dic86—44no—
155Dic86—412no—
156C2×#3028—431nomaximal, Sylow
157C22×C43—26no—
158C22×C43—212no—
159C22×C43—43no—
160C22×C43—41no—
161C22×C43—412no—
162C22×C43—412no—
163C22×C43—86no—
164C22×C43—816no—
165C22×C43C2×#12013yes—
166C22×C43C2×#12011yescharacteristic
167C22×C43C23×D413yes—
168C4×C43—212no—
169C4×C43C2×#12012yes—
170C4×C43C2×#12016yes—
171Dic43—412no—
172Dic43—44no—
173C2×#585D4311yescharacteristic
174C2×#536—433no—
175#3028—4316no—
176C2×#458—438no—
177C2×#410—433no—
178C2×C43—23no—
179C2×C43—23no—
180C2×C43—412no—
181C2×C43#302812yescomplemented
182C2×C43C22×#12011yescharacteristic
183#585—212no—
184#585C2×D4318yes—
185C2×2−1+4—23no—
186C2×H(5,𝔽2)—23no—
187C2×H(5,𝔽2)C2×D4314yes—
188C22×#41—26no—
189C22×#41C2×D4313yes—
190C23×Q8—431no—
191#536—4324no—
192#536—8612no—
193C2×C4⋊Q8—863no—
194C2×#124—863no—
195C2×#123—4312no—
196C2×C22⋊Q8—866no—
197C2×#117—433no—
198#458—4364no—
199#410—4324no—
200C2×#99—4312no—
201C43C2×#302811yescharacteristic, complemented, Sylow
2022−1+4—224no—
2032−1+4—224no—
204H(5,𝔽2)—224no—
205H(5,𝔽2)—224no—
206H(5,𝔽2)—224no—
207H(5,𝔽2)C22×D43116yes—
208C2×#41—24no—
209C2×#41—212no—
210C2×#41—248no—
211C2×#41—26no—
212C2×#41—212no—
213C2×#41—248no—
214C2×#41—26no—
215C2×#41—212no—
216C2×#41C22⋊D43112yes—
217C2×#41C22×D43112yes—
218C22×Q8—26no—
219C22×Q8—434no—
220C22×Q8—863no—
221C22×Q8—863no—
222C22×Q8—866no—
223C22×Q8C22⋊D4313yes—
224C22×D4—26no—
225C22×D4—212no—
226C22×D4C22⋊D4313yes—
227C22×D4C22×D4316yes—
228C23×C4—24no—
229C23×C4—432no—
230C23×C4C22⋊D4316yes—
231C23×C4C22×D4311yescharacteristic
232C4⋊Q8—8624no—
233#124—8624no—
234#123—4348no—
235#123—8624no—
236C22⋊Q8—8648no—
237#117—4312no—
238#117—866no—
239C2×C4⋊C4—863no—
240C2×C4⋊C4—8612no—
241C2×C22⋊C4—436no—
242C2×C22⋊C4—8612no—
243C2×C42—863no—
244#99—4348no—
245C24—24no—
246C24C2×C22⋊D4316yes—
247C24C23×D4311yescharacteristic
248#41—232no—
249#41—248no—
250#41—296no—
251#41—224no—
252#41—224no—
253#41—224no—
254#41—248no—
255#41—224no—
256C2×Q8—24no—
257C2×Q8—248no—
258C2×Q8—26no—
259C2×Q8—26no—
260C2×Q8—8612no—
261C2×Q8—8612no—
262C2×Q8—1726no—
263C2×Q8—1726no—
264C2×Q8—1721no—
265C2×Q8—1723no—
266C2×Q8C2×C22⋊D43112yes—
267C2×D4—212no—
268C2×D4—248no—
269C2×D4—248no—
270C2×D4—212no—
271C2×D4—248no—
272C2×D4—212no—
273C2×D4—26no—
274C2×D4—26no—
275C2×D4C2×C22⋊D43112yes—
276C2×D4C2×C22⋊D43112yes—
277C2×D4C23×D43112yes—
278C22×C4—212no—
279C22×C4—232no—
280C22×C4—26no—
281C22×C4—26no—
282C22×C4—212no—
283C22×C4—434no—
284C22×C4—866no—
285C22×C4—866no—
286C22×C4—866no—
287C22×C4C2×C22⋊D4316yes—
288C22×C4C2×C22⋊D43124yes—
289C22×C4C2×C22⋊D4313yes—
290C22×C4C2×C22⋊D4313yes—
291C22×C4C2×C22⋊D4316yes—
292C22×C4C23×D4312yes—
293C4⋊C4—8612no—
294C4⋊C4—8648no—
295C22⋊C4—4312no—
296C22⋊C4—866no—
297C22⋊C4—8648no—
298C42—8612no—
299C23—216no—
300C23—26no—
301C23—26no—
302C23—42no—
303C23—412no—
304C23—88no—
305C23C22×C22⋊D4313yes—
306C23C22×C22⋊D43112yes—
307C23C22×C22⋊D4313yes—
308C23C24×D4311yescharacteristic
309Q8—216no—
310Q8—224no—
311Q8—1724no—
312Q8—17212no—
313D4—248no—
314D4—224no—
315D4—224no—
316D4—224no—
317C2×C4—248no—
318C2×C4—26no—
319C2×C4—26no—
320C2×C4—224no—
321C2×C4—224no—
322C2×C4—8612no—
323C2×C4—8612no—
324C2×C4—17212no—
325C2×C4—1726no—
326C2×C4—1722no—
327C2×C4#1306329416yes—
328C2×C4#1306329416yes—
329C2×C4#1306329411yescharacteristic
330C2×C4#1306329413yes—
331C2×C4C22×C22⋊D43112yes—
332C2×C4C22×C22⋊D4316yes—
333C2×C4C22×C22⋊D4316yes—
334C22—26no—
335C22—212no—
336C22—43no—
337C22—41no—
338C22—412no—
339C22—412no—
340C22—86no—
341C22—816no—
342C22C2×#1306329413yes—
343C22C2×#1306329411yescharacteristic
344C22C23×C22⋊D4313yes—
345C4—212no—
346C4—17212no—
347C4—1724no—
348C4C2×#1306329412yes—
349C4C2×#1306329416yes—
350C2—23no—
351C2—23no—
352C2—412no—
353C2#1914400112yesdirect product factor
354C2C22×#1306329411yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
Fitting, prime radicalC2×C43×#585C2
socleC22×C43C2×#120
hypercenterC2×#585D43
hypocenterC43C2×#3028
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#585

Complements

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

NH ≅ G/Ntype
1. C2×#14583470C2semidirect
2. #19144001C2direct (N × H)
3. C2×#14583089C2semidirect
4. C2×#14582873C2semidirect
6. C23×Dic86C22semidirect
8. #14583470C22semidirect
11. C2×#13063306C22semidirect
13. C2×#13063284C22semidirect
14. #14583089C22semidirect
15. #14582873C22semidirect
16. C2×#13063240C22semidirect
27. C22×Dic86C23semidirect
32. #13063306C23semidirect
35. #13063284C23semidirect
41. #13063240C23semidirect
181. C2×C43#3028semidirect
201. C43C2×#3028semidirect
353. C2#19144001direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834702
#191440012
C2×#145830892
C2×#145828732
C2×C43×#5852
C2×#302843