Finite Group Databasebeta

← C2×#14582914 #19143135

Subgroups — C2×#14582914 #19143135

Order 5504.

772 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D43C211yesmaximal, characteristic
2C2×M16×D43C211yesmaximal, characteristic, complemented
3C2×#13063282C211yesmaximal, characteristic, complemented
4#14582914C218yesmaximal, direct product factor
5C2×#13063253C211yesmaximal, characteristic, complemented
6C2×#13063252C211yesmaximal, characteristic, complemented
7C2×#13063251C211yesmaximal, characteristic, complemented
8C2×#104×C43C211yesmaximal, characteristic, complemented
9C2×#10621902C411yescharacteristic, complemented
10C2×#10621898—21no—
11C2×#10621898C2211yescharacteristic
12C2×#10621900—21no—
13C2×#10621900C411yescharacteristic, complemented
14#41×D43—22no—
15#41×D43—22no—
16#41×D43C414yescomplemented
17#41×D43C2214yes—
18C2×Q8×D43C411yescharacteristic, complemented
19C2×D4×D43—21no—
20C2×D4×D43C411yescharacteristic, complemented
21C22×C4×D43—21no—
22C22×C4×D43C2211yescharacteristic
23C2×#10621877C2211yescharacteristic, complemented
24C2×#10621872—21no—
25M16×D43—22no—
26M16×D43C2214yescomplemented
27C2×C8×D43—21no—
28#13063282—22no—
29#13063282C2214yescomplemented
30C2×Dic43⋊C4—21no—
31C2×(C2×D43)⋊C4—21no—
32C2×C4×Dic43C2211yescharacteristic, complemented
33#13063253C2214yescomplemented
34#13063252C2214yescomplemented
35#13063251C2214yescomplemented
36C2×#41×C43C2211yescharacteristic
37C2×M16×C43C2211yescharacteristic, complemented
38C2×C42×C43C2211yescharacteristic, complemented
39#104×C43C2214yescomplemented
40C23×D43—21no—
41C23×D43D411yescharacteristic
42#41×C43—21no—
43#41×C43—21no—
44#41×C43C2×C412yes—
45#41×C43C2312yes—
46C2×Q8×C43C2×C411yescharacteristic
47C2×D4×C43—21no—
48C2×D4×C43C2×C411yescharacteristic
49C22×C4×C43—21no—
50C22×C4×C43—21no—
51C22×C4×C43C2311yescharacteristic
52C2×C22⋊D43—21no—
53C2×C22⋊D43—21no—
54C2×C22⋊D43—21no—
55C22×Dic43—21no—
56C22×Dic43—21no—
57C22×Dic43D411yescharacteristic
58#10621902—22no—
59#10621902C2×C414yescomplemented
60Q8×D43—22no—
61Q8×D43C2×C414yescomplemented
62#10621900—24no—
63#10621900—24no—
64#10621900—22no—
65#10621900C2×C414yescomplemented
66D4×D43—22no—
67D4×D43—24no—
68D4×D43—24no—
69D4×D43C2×C414yescomplemented
70#10621898—21no—
71#10621898—21no—
72#10621898—24no—
73#10621898—24no—
74#10621898C2×C412yes—
75#10621898C2312yes—
76C2×D172—21no—
77C2×D172C2×C411yescharacteristic
78C2×C4×D43—21no—
79C2×C4×D43—21no—
80C2×C4×D43—24no—
81C2×C4×D43—24no—
82C2×C4×D43—21no—
83C2×C4×D43C2×C411yescharacteristic
84C2×C4×D43C2×C412yes—
85C2×C4×D43C2×C411yescharacteristic
86C2×C4×D43D411yescharacteristic
87C2×C4×D43D412yes—
88C2×C4×D43D411yescharacteristic
89C2×C4×D43D412yes—
90C2×C4×D43C2312yes—
91C2×Dic86—21no—
92C2×Dic86C2×C411yescharacteristic
93M16×C43—21no—
94M16×C43C2312yescomplemented
95C2×C8×C43—21no—
96C42×C43—21no—
97C42×C43C2312yescomplemented
98(C2×D43)⋊C4—24no—
99Dic43⋊C4—24no—
100C4×Dic43—21no—
101C4×Dic43C2312yescomplemented
102#10621877—21no—
103#10621877C2312yescomplemented
104C2×C43⋊C8—21no—
105#10621872—24no—
106C8×D43—24no—
107C23×C43—21no—
108C23×C43C2×D411yescharacteristic
109C22×D43—21no—
110C22×D43—24no—
111C22×D43—42no—
112C22×D43—44no—
113C22×D43C22⋊C411yescharacteristic
114C22×D43C22⋊C411yescharacteristic
115C22×D43C22⋊C412yes—
116C22×D43C2×D412yes—
117Q8×C43—21no—
118Q8×C43C22×C412yes—
119D4×C43—22no—
120D4×C43—22no—
121D4×C43—21no—
122D4×C43C22×C412yes—
123C2×C4×C43—21no—
124C2×C4×C43—22no—
125C2×C4×C43—22no—
126C2×C4×C43—22no—
127C2×C4×C43—42no—
128C2×C4×C43C22×C411yescharacteristic
129C2×C4×C43C22×C411yescharacteristic
130C2×C4×C43C2×D411yescharacteristic
131C2×C4×C43C2×D411yescharacteristic
132C2×C4×C43C2×D411yescharacteristic
133C2×C4×C43C2411yescharacteristic
134C22⋊D43—22no—
135C22⋊D43—22no—
136C22⋊D43—24no—
137C22⋊D43—24no—
138C2×Dic43—21no—
139C2×Dic43—24no—
140C2×Dic43—22no—
141C2×Dic43—42no—
142C2×Dic43C22⋊C411yescharacteristic
143C2×Dic43C22⋊C411yescharacteristic
144C2×Dic43C22⋊C412yes—
145C2×Dic43C2×D412yes—
146D172—24no—
147D172—21no—
148D172C22×C412yes—
149C4×D43—24no—
150C4×D43—22no—
151C4×D43—22no—
152C4×D43—24no—
153C4×D43C22⋊C412yes—
154C4×D43C22⋊C412yes—
155C4×D43C22⋊C412yes—
156C4×D43C22⋊C412yes—
157C4×D43C22×C412yes—
158C4×D43C22×C412yes—
159C4×D43C2×D412yes—
160C4×D43C2×D412yes—
161Dic86—21no—
162Dic86—24no—
163Dic86C22×C412yes—
164C8×C43—22no—
165C43⋊C8—22no—
166C22×C43—22no—
167C22×C43—22no—
168C22×C43—42no—
169C22×C43C2×C22⋊C411yescharacteristic
170C22×C43C2×C22⋊C411yescharacteristic
171C22×C43C22×D411yescharacteristic
172C2×D43—22no—
173C2×D43—22no—
174C2×D43—22no—
175C2×D43—42no—
176C2×D43—42no—
177C2×D43—48no—
178C2×D43—42no—
179C2×D43C2×C22⋊C412yes—
180C2×D43C2×C22⋊C412yes—
181C4×C43—22no—
182C4×C43—42no—
183C4×C43C2×C22⋊C411yescharacteristic
184C4×C43C2×C22⋊C411yescharacteristic
185C4×C43C23×C411yescharacteristic
186C4×C43C22×D411yescharacteristic
187Dic43—22no—
188Dic43—42no—
189Dic43C2×C22⋊C412yes—
190Dic43C2×C22⋊C412yes—
191C2×#421—431nomaximal, Sylow
192C2×C43—21no—
193C2×C43—21no—
194C2×C43—42no—
195C2×C43#42112yescomplemented
196C2×C43C22×C22⋊C411yescharacteristic
197D43—22no—
198D43—22no—
199D43—42no—
200C22×#41—431no—
201C22×M16—431no—
202C2×#117—431no—
203#421—438no—
204C2×#104—431no—
205C2×#104—431no—
206C2×#104—431no—
207C2×#104D4311yescharacteristic, complemented
208C43C2×#42111yescharacteristic, complemented, Sylow
209C2×#41—434no—
210C2×#41—434no—
211C2×#41—431no—
212C2×#41—431no—
213C2×#41—431no—
214C2×#41—861no—
215C2×#41—861no—
216C2×#41—862no—
217C2×#41—862no—
218C2×#41C2×D4311yescharacteristic
219C22×Q8—431no—
220C22×D4—431no—
221C22×D4—861no—
222C23×C4—431no—
223C23×C4—861no—
224C2×M16—431no—
225C2×M16—434no—
226C2×M16—861no—
227C2×M16—862no—
228C2×M16C2×D4311yescharacteristic, complemented
229C22×C8—861no—
230#117—434no—
231#117—862no—
232C2×C4⋊C4—861no—
233C2×C22⋊C4—861no—
234C2×C42—431no—
235C2×C42C2×D4311yescharacteristic, complemented
236#104—434no—
237#104—434no—
238#104—434no—
239#104C2×D4314yescomplemented
240C24—431no—
241C24—861no—
242#41—21no—
243#41—21no—
244#41—434no—
245#41—434no—
246#41—432no—
247#41—432no—
248#41—864no—
249#41—864no—
250#41—864no—
251#41—864no—
252#41—862no—
253#41—862no—
254#41—861no—
255#41—861no—
256#41C4×D4312yes—
257#41C22×D4312yes—
258C2×Q8—434no—
259C2×Q8—431no—
260C2×Q8—861no—
261C2×Q8—862no—
262C2×Q8C4×D4311yescharacteristic
263C2×D4—21no—
264C2×D4—434no—
265C2×D4—431no—
266C2×D4—861no—
267C2×D4—862no—
268C2×D4—861no—
269C2×D4—864no—
270C2×D4—864no—
271C2×D4—861no—
272C2×D4—861no—
273C2×D4C4×D4311yescharacteristic
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—431no—
277C22×C4—431no—
278C22×C4—431no—
279C22×C4—432no—
280C22×C4—432no—
281C22×C4—432no—
282C22×C4—431no—
283C22×C4—431no—
284C22×C4—432no—
285C22×C4—861no—
286C22×C4—864no—
287C22×C4—864no—
288C22×C4—861no—
289C22×C4—861no—
290C22×C4—861no—
291C22×C4—861no—
292C22×C4C22×D4311yescharacteristic
293M16—21no—
294M16—432no—
295M16—864no—
296M16—861no—
297M16C22×D4312yescomplemented
298C2×C8—21no—
299C2×C8—864no—
300C2×C8—861no—
301C4⋊C4—864no—
302C22⋊C4—864no—
303C42—21no—
304C42—432no—
305C42—861no—
306C42C22×D4312yescomplemented
307C23—21no—
308C23—431no—
309C23—431no—
310C23—432no—
311C23—432no—
312C23—864no—
313C23—861no—
314C23—1722no—
315C23—1724no—
316C23D4×D4311yescharacteristic
317Q8—21no—
318Q8—432no—
319Q8—864no—
320Q8—861no—
321Q8C2×C4×D4312yes—
322D4—22no—
323D4—22no—
324D4—21no—
325D4—432no—
326D4—864no—
327D4—864no—
328D4—864no—
329D4—862no—
330D4—862no—
331D4—861no—
332D4C2×C4×D4312yes—
333C2×C4—21no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—42no—
338C2×C4—431no—
339C2×C4—431no—
340C2×C4—432no—
341C2×C4—432no—
342C2×C4—432no—
343C2×C4—432no—
344C2×C4—432no—
345C2×C4—432no—
346C2×C4—432no—
347C2×C4—432no—
348C2×C4—432no—
349C2×C4—432no—
350C2×C4—864no—
351C2×C4—864no—
352C2×C4—864no—
353C2×C4—861no—
354C2×C4—862no—
355C2×C4—862no—
356C2×C4—862no—
357C2×C4—1722no—
358C2×C4C2×C4×D4311yescharacteristic
359C2×C4C2×C4×D4311yescharacteristic
360C2×C4D4×D4311yescharacteristic
361C2×C4D4×D4311yescharacteristic
362C2×C4D4×D4311yescharacteristic
363C2×C4C23×D4311yescharacteristic
364C8—22no—
365C8—862no—
366C22—22no—
367C22—22no—
368C22—42no—
369C22—432no—
370C22—432no—
371C22—862no—
372C22—862no—
373C22—862no—
374C22—1722no—
375C22—1722no—
376C22—1728no—
377C22—1722no—
378C22C22⋊C4×D4311yescharacteristic
379C22C22⋊C4×D4311yescharacteristic
380C22C2×D4×D4311yescharacteristic
381C4—22no—
382C4—42no—
383C4—432no—
384C4—432no—
385C4—862no—
386C4—1722no—
387C4C22⋊C4×D4311yescharacteristic
388C4C22⋊C4×D4311yescharacteristic
389C4C22×C4×D4311yescharacteristic
390C4C2×D4×D4311yescharacteristic
391C2—21no—
392C2—21no—
393C2—42no—
394C2—862no—
395C2—862no—
396C2—1722no—
397C2#1458291412yesdirect product factor
398C2C2×C22⋊C4×D4311yescharacteristic
subgroupG/H
centerC2×C4D4×D43
commutatorC4×C43C23×C4
FrattiniC2×C4C23×D43
FittingC2×#104×C43C2
socleC22×C43C2×C22⋊C4
hypercenterC2×#104D43
hypocenterC43C2×#421
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×M16×D43C2semidirect
3. C2×#13063282C2semidirect
4. #14582914C2direct (N × H)
5. C2×#13063253C2semidirect
6. C2×#13063252C2semidirect
7. C2×#13063251C2semidirect
8. C2×#104×C43C2semidirect
9. C2×#10621902C4semidirect
13. C2×#10621900C4semidirect
16. #41×D43C4semidirect
18. C2×Q8×D43C4semidirect
20. C2×D4×D43C4semidirect
23. C2×#10621877C22semidirect
26. M16×D43C22semidirect
29. #13063282C22semidirect
32. C2×C4×Dic43C22semidirect
33. #13063253C22semidirect
34. #13063252C22semidirect
35. #13063251C22semidirect
37. C2×M16×C43C22semidirect
38. C2×C42×C43C22semidirect
39. #104×C43C22semidirect
59. #10621902C2×C4semidirect
61. Q8×D43C2×C4semidirect
65. #10621900C2×C4semidirect
69. D4×D43C2×C4semidirect
94. M16×C43C23semidirect
97. C42×C43C23semidirect
101. C4×Dic43C23semidirect
103. #10621877C23semidirect
195. C2×C43#421semidirect
207. C2×#104D43semidirect
208. C43C2×#421semidirect
228. C2×M16C2×D43semidirect
235. C2×C42C2×D43semidirect
239. #104C2×D43semidirect
297. M16C22×D43semidirect
306. C42C22×D43semidirect
397. C2#14582914direct (N × H)